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Nucleation And Solubility Of Monosodium-Urate In Relation To Gouty Arthritis

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Nucleation And Solubility Of Monosodium-Urate In Relation To Gouty Arthritis

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Content NUCLEATION A N D SOLUBILITY OF M O NO SO DIUM URATE IN RELATION TO G O U TY ARTHRITIS by A li Abdulrahman Khalaf A Dissertation Presented to the FACULTY OF THE G R A D U A TE S C H O O L UNIVERSITY OF SO U TH ERN CALIFORNIA in P a rtial Fulfilm ent of the Requirements fo r the Degree D O C TO R OF PHILOSOPHY (Chemical Engineering) June 1973 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INFORMATION TO USERS This material w a s produced from a microfilm copy of the original documant. While the most advanced technological m e a n s to photograph and raproduca this documant have b ea n usad, the quality is heavily dependant upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The si g n or "target" for p a g e s apparently lacking from the document photographed is "Missing Pege(s)". If it w a s possible to obtain the m issi ng pege(s) or section, they are spliced into the film along with adjacent p a g e s . This may have necessitated cutting thru an imaga and duplicating adjacant p a g a s to insura you complote continuity. 2. Whe n an inwga on the film is oblitereted with a large round black mark, it is an indication that tha photographar susp acte d that the copy may have moved during exposure end thus c au se a blurred imag e. You will find a good imaga of the p ag e in the adjacent frame. 3. Wha n a map, drawing or chert, etc., w a s part of the materiel being photographed the photographer followed a definite method in "sectioning" the materiel. It i s customary to begin photoing at the upper left hand corner of a large sheet end to continue photoing from left to right in equal sections with a small overlap. If nacas sary , sectioning i s continued again — beginning below the first row end continuing on until complete. 4. The majority of u ser s indicate that the textual content i s of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may ba ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific p a g e s you wish reproduced. 5. PLEASE NOTE: Some p a g e s may ha ve indistinct print. Filmed a s received. X«rox University Microfilms 300 North ZMbRoMi Ann Arbor, Michigan 4SI 06 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73-18,823 KHALAF, Ali Abdulrahman, 1942- NUCLEATION AND SOLUBILITY OF MONOSODIUM URATE IN RELATION TO GOUTY ARTHRITIS. University of Southern California, Ph.D., 1973 Engineering, chemical University Microfilms, A XE R O X Company. Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFLIMED EXACTLY AS RECEIVED Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY O F S O UTHERN CA LIFO R NIA THE GRADUATE SCHO O L U N IV E R S IT Y PARK LOS ANGELES. C A L IF O R N IA 8 0 0 0 7 This dissertation, written by A li A bdulrahm an K halaf under the direction of A.i.?.... Dissertation Com mittee, and approved by a ll its members, has been presented to and accepted by The Graduate School, in partial fulfillm ent of requirements of the degree of D O C T O R O F P H IL O S O P H Y ? D un June 1973 D ate. . . . . . . . . . DISSERTATION COMMITTEE Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION To m y beloved fa th e r, A B D U LR A H M A N SALEH AL-KHALAF who, in spite of being s e m i-illite ra te , seeded m e with the educational s p ir it and ambitions. n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AC KN O W LED G EM EN TS In retrospect, the la s t four years which I spent here fo r this accomplishment were m y most fr u itfu l and pleasant years. I am beholden to m y professor. Dr. William Ross Wilcox, who made i t possible. He helped in many ways, academically and s p iritu a lly , and gave so generously of his time during the course of this research. I also wish to express m y gratitude to m y committee members. Dr. J. M. Whelan and Dr. G. J. Friou, fo r th e ir in te re st and sug gestions. A d ditionally, I would lik e to acknowledge Dr. G. J. Friou and the members of the Rheumatology Department a t U S C Medical School fo r th e ir cooperation and help. They supplied us with synovial flu id s and collagen fib e rs . Our periodical meetings and discussions were of great value to m y understanding of gouty a r th r itis . This research was fin a n c ia lly supported by the National Science Foundation under Grant No. GK-17042. I wish to thank the M inistry o f Education in Saudi Arabia fo r supporting m e through m y undergraduate study, and the College of Petroleum and Minerals fo r supporting m e through graduate school. I wish to express m y special thanks to Mrs. Shari Wilcox who prepared the fin a l copy of this dissertation . F in a lly , I am deeply grateful to m y fam ily fo r th e ir encourage ment and patience during m y absence fo r the accomplishment of this work. i i i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS Page DEDICATION.............................................................................................................. i i A C K N O W LED G EM EN TS .............................................................................................. i i i LIST OF TABLES ................................................................................................. v ii LIST O F FIGURES............................................................................................ v i ii N O M EN C LA TU R E ................................................................................................. x ii ABSTRACT............................................................................................................. xvi I. NUCLEATION OF M O NO SO DIUM U R A TE IN RELATION TO G O U TY ARTHRITIS ....................................................... 1 A. Introduction ............................................................................ 1 I I . LITERATURE REVIEW ........................................................................... 5 A. C lin ical Background ............................................................... 5 B. Present Theories of the Mechanism of Acute G o u t............................................................................ 9 C. C ry s ta lliza tio n Background .............................................. 12 D. Physico-Chemical Properties of Uric Acid and Monosodium Urate ...................................... 15 I I I . THEORY OF NUCLEATION IN A Q U EO U S SOLUTIONS ......................... 23 A. S o l u b i l i t y ............................................................................... 23 B. Supersaturation and M etastab ility ................................. 29 C. Homogeneous Nucléation from Solutions ......................... 35 D. Heterogeneous Nucléation .................................................. 58 IV. EXPERIMENTAL WORK........................................................................... 62 A. Preparation of Monosodium Urate ..................................... 62 B. Assay of Prepared Monosodium Urate ............................. 63 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE O F CONTENTS (Continued) Page C. Description of the Experimental Apparatus ................. 69 D. Method of Determining the S o lu b ility and Nucléation of Monosodium Urate in Aqueous S o lu t io n .................................................................................... 75 E. Results fo r Pure W a t e r ...................................................... 82 F. Estimation of the Heat of Solution and Surface Energy o f Monosodium Urate in Pure W a t e r ................................................................................ 85 V. THE INFLUENCE OF ADDITIVES O N SOLUBILITY A N D NUCLEATION OF M O NO SO DIUM URATE .............................................. 88 A. Influence of Ethyl Alcohol .............................................. 88 B. Influence of Synovial Fluid from Gout P a tie n t........................................................................................ 92 C. Influence o f Synovial Fluid from Rheumatoid Patient ............................................................... 94 D. Influence of Sodium I o n .............................................................101 E. Influence o f Potassium I o n .................................................... 102 F. Influence of Calcium I o n ........................................................ 102 G. Influence of Copper I o n .............................................................106 H. Influence o f Collagen ........................................................... 110 I. Comparison of the Influence of Soluble Additives on the Nucléation o f Monosodium U r a te ..................................................................................................118 V I. THE INFLUENCE OF X-IRRADIATION A ND MECHANICAL SH O C K O N NUCLEATION OF M O NO SO DIUM URA TE .............................. 122 A. Influence o f X -Irra d ia tio n ............................................... 122 B. Influence of Mechanical Shock .......................................... 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS (Continued) Page V II. INFLUENCE OF H Y D R O G E N ION CONCENTRATION O N SOLUBILITY A N D NUCLEATION OF M O N O SO D IU M URATE..........................................................................................................124 A. In tr o d u c tio n ................................................................................ 124 B. Influence of pH on Uric Acid and Sodium Urate S o l u b i l i t y ........................................................................ 125 C. Influence of Hydrogen Ion Concentration on the Nucléation of Monosodium Urate ......................... 142 V III. CONCLUSIONS.............................................................................................. 146 IX. DISCUSSION A N D RECOM M ENDATIONS ............................................... 151 REFERENCES............................................................................................. 154 APPENDIX A. SAM PLE CALCULATIONS O F TH E NUCLEATION KINETIC C O NSTANT ......................... 161 APPENDIX B. EXPERIMENTAL D ATA F O R THE SOLUBILITY A N D NUCLEATION O F M O NO SO DIUM URATE .......................................... 166 APPENDIX C. THEORETICAL ANALYSIS O F SOLUBILITY DETERMINATION USING THE H O T STAG E...............................................173 V I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST O F TABLES Paae I I I - l . Experimental Kinetic Constants a fte r Nielsen ( 9 8 ) ....................................................................... 38 I I I - 2 . Values of the Kinetic Constant (A) ...................................... 56 IV-1. X-Ray Powder D iffra c tio n Spacing Data of Monosodium U r a te ........................................................... 70 V-1. Binding of Monosodium Urate by Soluble Collagen at 4 ° C ................................................................ 115 V-2. Apparent Enhanced Nucléation by C o lla g e n ..................................................................................................117 V-3. Influence of Additives on Supersaturation Ratio and Concentration Product Necessary fo r Nucléation a t 3 7 °C .................................................................... 119 V II-1 . The C ritic a l pH fo r Equal S o lu b ility of Uric Acid and Monosodium Urate .............................................. 139 B-1. S o lu b ility and Nucléation of Monosodium Urate in Pure W a t e r .........................................................................167 B-2. S o lu b ility and Nucléation of Monosodium Urate in 25% v A lc o h o l.................................................................... 168 B-3. 5 % V Synovial Fluid from Gout Patient ............................... 169 B-4. 5 % V Synovial Fluid from Rheumatoid Patient ................... 170 B-5. 7.5 X 10"3 M NaCl S o lu tio n ............................................................. 171 B-6. 5 X 10-6 M cucig S o lu t io n ............................................................. 172 C-1. Comparison of the Theoretical and Experimental Error in S o lu b ility Measurements .................................................................................... 179 v n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Page I I - l . Equilibrium Forms of Uric Acid .......................................... 16 II- 2 . O xidization of Uric A c id ............................................................ 17 I 1-3. S o lu b ility o f Monosodium Urate In Buffered Solutions a fte r June (43) ........................................ 19 I 1-4. Photograph o f Amorphous Urate C rystals, 4 2 X ....................................................................... 21 I I - l . S o lu b ility Dependence on Temperature ................................... 24 11-2. The Chemical Potential of Solute In Solid and Liquid Phase............................................................................ 26 I 1-3. S o lu b ility and Supersaturation Curves ............................... 32 11-4. Dependence of S o lu b ility on P a rticle S i z e ...................... 34 11-5. Free Energy Dependence on Embryo R a d iu s ........................... 40 I 1-6. The Transition State Model fo r Nucléation of Ionic Compounds from Aqueous Solutions ..................... 47 11-7. Schematic Potential Energy Curve Hydrated and Dehydrated Reactants ........................................................... 51 I I I - 8 . Surface Energies Components fo r Hetero geneous Nucléation from Liquid on a Substrate ....................................................... 60 IV-1. Photograph of Monosodium Urate Crystals Prepared In our Laboratory, 4 2 X ........................................... 64 IV -2. Photograph of Monosodium Urate Crystals from K & K Laboratories, In c ., Plalnvlew, New York, 42 X ................................................................................ 65 IV -3. Scanning Electron Micrograph of Monosodium Urate Crystals Grown In our Laboratory, 3000X 66 v m Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST O F FIGURES (Continued) Page IV -4. Scanning Electron Micrograph of Monosodium Urate Crystals from Tophus of a Gout P atien t, 10000 X ........................................................................ 67 IV -5. Photograph of Monosodium Urate Single Crystal Grown from Pure Monosodium Urate Solution of 7.7 X 10-3 M N aHU and Refrigerated a t 5“C for a Week......................... 68 IV-6. Photograph of M ettler FP2 Hot Stage and C o n t r o ls ......................................................................................... 71 IV-7. Diagram of M ettler FP2 Hot S t a g e ....................................... 72 IV -8. Photograph of a Microscope Slide with Mono sodium Urate Solution in the Cavity, Sealed with a Cover Glass and E p o x y ............................................... 73 IV-9. Schematic Diagram of a Microscope Slide Sealed with a Cover Glass and Epoxy Cement .................... 74 IV-10. Photograph of the Assembled Experimental A pparatus......................................................................................... 76 IV-11. Dependence of the Observed S o lu b ility Temperature on the Heating R a te .......................................... 80 IV -12. S o lu b ility and Nucléation of Monosodium Urate in Pure W a te r................................................................................ 83 IV -13. S o lu b ility and Nucléation of Monosodium Urate in Pure Water. C is the Monosodium Urate Concentration in the S o lu tio n ............................................... 84 V-1. The Influence of Additives on the S o lu b ility of Monosodium Urate .................................................................... 90 V-2. The Influence of Additives on the Nucléation of Monosodium Urate ................................................................... 91 V-3. The Influence of Various Additives on the S o lu b ility of Monosodium Urate in Aqueous S o lu t io n ........................................................................................ 96 IX Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES (Continued) V-4. V-5. V-6. V-7. V-8. V-9. V-10. V-11. The Influence of Various Additives on the Nucléation of Monosodium Urate in Aqueous Solution ............................................................... Photograph of Monosodium Urate Crystals in 5 % V Synovial Fluid of a Rheumatoid Patient . The Influence of KCl on the Relative S o lu b ility of Monosodium Urate a t 47 to 53°C The Influence of CaCl? on the Relative S o lu b ility of Monosodium Urate a t 47 to 53°C Photograph of Crystals from Monosodium Urate, CaCl2 Solution with Cc@ ++ * 0.1 CNa+, 42X The Supercooling Ratio fo r Nucléation of Monosodium Urate as a Function of Added CaCl2 • The Monosodium Urate Concentration Required fo r Nucléation a t 32°C as a Function of Added CaCl2 .................................................................................... Photograph of Collagen Fibers in Monosodium Urate Solution, Cooled to 16°C ..................... V-12. Diagram of the Dialysis Experimental Apparatus Page 98 100 103 105 107 108 109 112 114 V II-1 . V II-2 . V II-3 . V II-4 . V II-5 . The Proportions of Uric Acid-Urates in Solution a t 37°C which are Present as the D ifferen t Species H^U, HU", and U " ............................................................. 129 Calculated S o lu b ilitie s of Uric Acid, Mono sodium Urate and Disodium Urate, at 3 7 ° C ..........................136 Experimental Data of Sodium Urate S o lu b ility versus p H ..............................................................................................141 The Influence o f pH on the Nucléation of Mono sodium Urate a t 30 to 3 4 ° C .........................................................143 Photograph of P la te le t Crystals Formed Along with Monosodium Urate Needle C rystals, upon Addition of Lactic Acid ........................... . . . . 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES (Continued) Page C-1. Concentration P ro file fo r Two Parallel Crystals as they Dissolve Upon Heating .......................... 175 C-2. Error In the Observed S o lu b ility Temperature versus the Dimenslonless Cooling Rate .............................. 178 X I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. N O M EN CLATU RE O A Nucléation pre-exponential constant in Eq. I I 1-14 (nuclei/ctn sec). a/\a " A c tiv ity of positive and negative ions (moles/cm^). C^.Cg Concentrations of dissociating ions (moles/1 ite r ) = (C^2u ^HU" + Cy) 5 to ta l concentration (moles/l i t e r ) . D Diffusion co e ffic ie n t (cm^/sec). d^.dg Ionie diameters (cm). A E Activation energy in Eq. III-2 9 (erg/m olecule). F Impingement flu x of ions a rriv a i to the nucleus surface in Eq. I I 1-25 (monomer/cmZ sec). f^ Fraction of uric acid-urate present as species ( i ) . ★ A G Free energy o f formation of c r itic a l nucleus (erg ). A G g Activation energy fo r diffusion (erg/molecule) A G Difference of bulk free energy per u n it volume between crystal and solute in solution (erg/cm^). AH^ Heat of c ry s ta lliz a tio n (erg/m olecule). AHdeh Heat of dehydration (erg/molecule). A H g Heat of solution (= -AH^). * i Number o f molecules in the c ritic a l embryo. J Rate of nucléation (nuclei/cm^ sec). K Boltzman constant, 1.38 x 10"^® erg °K"^. K^.Kg Proportionality constants. F irs t dissociation constant for uric acid in Eq. V II-2 . Kjg Second dissociation constant fo r u ric acid in Eq. V II-4 . x ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NO M ENCLATURE (Continued) Kgpi Monosodium urate s o lu b ility product in Eq. V II-1 1 . Kgp2 Disodium urate s o lu b ility product in Eq. V II-1 3 . Water dissociation constant in Eq. V II-6 . I Mean jump distance travelled by an ion (cm). M Molecular weight. m g % Concentration of solute m g per 100 cc o f solution, fo r calcium as Ca++ and fo r monosodium urate as NaHU'HgO. 23 N Avogrado's number, 6.02 x 10 molecules/g mole, n Concentration of the nucleating solute (molecules/cm ). C(n ) Concentration of the c r itic a l embryo. ng,n^ Ionic concentration (molecules/cm^). n Number of water molecules removed from the hydration sheath before ionic clustering. n^ The primary hydration number. l A r o 0(n ) Surface area of the c r itic a l embryo (cm ). P A probability factor in Eq. III-3 8 . r Radius of the embryo (cm), r Radius of the c ritic a l embryo (cm). R The universal gas constant, 8.3 x 10^ erg/g mole °K. AS^ Entropy of c ry s ta lliz a tio n (erg/molecule °K). Sj S o lu b ility of component i (moles/cm ). T Temperature (°K ). AT Absolute supercooling (*C ). u Molecular velocity of the diffusing ion (cm/sec). V Molecular volume of the solute in solid phase (cm ). xi i i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NO M ENCLATURE (Continued) Z Nonequilibrium factor in Eq. I I 1-25. Z* Collision frequency defined in Eq. 111-32. Chemical Symbols H g U Uric acid N aH U Monosodium urate NagU Disodium urate Greek Symbols a Relative supersaturation = C(CACg)^-(C^Cg)g]/(C^Cg)g. 0 Degree of supersaturation = (C/\Cg)^/(C^Cg)g. V A c tivity co e ffic ien t. 2 Y In te rfa c ia l energy (erg/cm ). 2 Ygg In te rfa c ia l energy between crystal and substrate (erg/cm ). 2 Yg^ In te rfa c ia l energy between crystal and liq u id (erg/cm ). Yj^ In te rfa c ia l energy between substrate and liq u id (erg/cm ). n Relative supercooling (Tg-T/Tg). Ç Reduced temperature (temperature at the nucléation divided by the s o lu b ility temperature). 0 Contact angle between the crystal and substrate. \ S o lu b ility o f the undissociated uric acid (moles/cm^). O p Density of the c ry s ta lliz in g compound (gm/cm ). p Chemical potential of the solute. xiv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. N O M ENCLATURE (Continued) Subscripts e Equilibrium conditions, n Nucléation conditions. 0 In it ia l conditions. XV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT I t is well known that gouty a r th r itis is the re s u lt of the c ry s ta lliz a tio n of monosodium urate as needle crystals in the human body jo in ts and nearby tissues. For th is reason the influence of various additives and treatments on the nucléation and s o lu b ility of monosodium urate was investigated. Experimental results showed the follow ing: 1. Addition of 25% v ethyl alcohol reduced the s o lu b ility of monosodium urate to one-third of that in pure water. Nucléation of monosodium urate in alcohol solutions required a lower degree of supersaturation than that required in pure water. The supersaturation ra tio required fo r monosodium urate nucléation in th is alcohol solution was found to be 3 .3 , while th at in pure water was 4 .3 . 2. Addition of small concentrations of calcium ion (as calcium chloride) decreased the monosodium urate s o lu b ility remarkably. The concentration product of monosodium urate required fo r nucléation decreased as the ra tio o f calcium ion to sodium ion increased. Moreover, i t was observed th at calcium ion accelerated the axial growth of urate crystals. 3. Nucléation of monosodium urate in an aqueous solution of 5 % V synovial flu id from two rheumatoid patients required a higher supersaturation ra tio than fo r pure water. The concentration products of monosodium urate fo r nucléation were higher than those obtained X V I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with other additives. This indicated that synovial flu id s from rheumatoid patients tend to in h ib it the nucléation of monosodium urate. Synovial flu id from a gouty patient showed no e ffe c t on the nucléation of monosodium urate. Synovial flu id s , both from a gouty patient and from a rheumatoid p atien t, decreased the s o lu b ility of monosodium urate in aqueous solution because of the presence of extra sodium ion (common ion e ffe c t). 4. The supersaturation ra tio required fo r nucléation of monosodium urate decreased as the pH decreased in aqueous solution. Below pH 6 .3 , uric acid c ry s ta llize d . 5. Exposure of metastable monosodium urate solutions to an X-ray beam did not induce nucléation. The X-ray beam was more intense than normal medical X-rays. 6. W hen metastable solutions o f monosodium urate sealed in microscope slides were snapped with the fin g ern ail or placed in an u ltras o n ically agitated bath, nucléation of monosodium urate crystals was nearly instantaneous. This indicated th at mechanical shock induces the nucléation of monosodium urate. 7. Addition of human and ra t collagen fibers to monosodium urate solution did not a lte r the nucléation temperature. Further more, when nucléation did occur, fewer crystals were formed in the v ic in ity of the collagen than elsewhere. xvii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. During the pursuit of th is work, i t was found th at in the medical lite ra tu re there seemed to be misconceptions and uncertainties about the s o lu b ility of uric acid and sodium u rate, p a rtly because the words were used interchangeably. For th is reason a comprehensive theoretical treatment of factors governing the s o lu b ility of uric acid and sodium urate was accomplished. I t was found th at the s o lu b ility of uric acid increases with increasing pH, while the s o lu b ility of monosodium urate has a minimum near pH 7.7 a t 37°C. The classical nucléation theory developed for nucléation from pure liq u id (melt) and vapor phase was found to predict very high nucléation rates for nucléation of ionic compounds from aqueous solutions. This disagrees with the low nucléation rates observed experim entally. For this reason, a new treatment was developed which predicts lower nucléation rates from aqueous solutions than that predicted by the classical nucléation theory. I t was suggested that the solvation energy hinders nucléation in solution, because the ions have to lose at least some of th e ir solvation sheaths before they are able to unite and form a nucleus. x v iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I NUCLEATION O F M O N O SO D IU M URATE IN RELATION TO G O U TY ARTHRITIS A. Introduction Horace Walpole said in w riting to S ir Horace Mann in 1786: "I think m y dear S ir, th at you w ill be glad to hear that I am getting free from m y parenthesis of gout, which, though I tre a t i t as an interlude, has confined m e above six weeks and fo r a few days was very near being serious. I t began by m y middle fing er of this hand, with which I am now w ritin g , discharding a valley o f chalk, which brought on gout and inflammation, and both together swelled m y arm almost to m y shoulder. In short, I was forced to have a surgeon. But la s t week m y fin g er was delivered of a chalk-stone as big as a large pea, and now I tru st the wound w ill soon heal." Unfortunately, the wound of Earl Horace Walpole from gout never healed. Our s c ie n tific understanding of gout also has a lo t of wounds that have not yet healed. There are many important unanswered questions about gout pathology and formation. In the U.S.A., roughly 0.2% of the population suffer from gout or gouty a r t h r it is .^ Gouty a r th r itis is one of several ailments associated with the c ry s ta lliz a tion of sparingly soluble substances in the human body. I t has been established that gout is the consequence of hyperuricemia (excess uric a c id ), involving the deposition of monosodium urate monohydrate (NaHgCgNgOgHgO) (see Figure II-l) as needle crystals in the synovial (2 3l flu id and nearby connective tis s u e s .' * ' I t has also been found that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 some individuals with hyperuricemia suffer from severe gout while others with equally high supersaturation of uric acid remain free of the d isease.S eegm iller, et al.,^^’®^ observed th at in je ctio n of needle-shaped crystals over 0.5y in length caused inflammation in both gouty and non-gouty ind ivid u als, while in jectio n of smaller "amorphous" crystals rarely caused pain. In recent years, m ultiple etiologies fo r the hyperuricemia of gout have been d e f i n e d , a n d much has been learned about gout by c lin ic a l investigation. Maclochlan and Rodnan^^^ found that moderate consumption of alcohol with normal food intake has no e ffe c t on the serum uric acid content. However, the combination of fasting and consumption of alcohol produced a large increase in the uric acid concentration, which resulted in gout attacks. Gout attacks have also been associated with trauma, local X-ray therapy, prolonged bedrest, and with decreases in barometric pressure. Although the lite ra tu re is abundant with c lin ic a l investigations of gout, many aspects o f its o rig in and development remain unknown. In 1876, Garrod^^O) in his propositions fo r re la tin g c lin ic a l manifestations of gouty a r th r itis to hyperuricemia stated that the deposit of sodium urate may be looked upon as the cause and not the e ffe c t of gouty inflammation. I t thus appears that the study of the nucléation of monosodium urate would be of immense value to the understanding of the o rig in and development of gout. One would expect that substances capable of in h ib itin g nucléation of monosodium urate crystals could be very important in the prevention and treatment of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 gout. I t may be th a t, in the normal body flu id s , there e x is t certain components which in h ib it nucléation of sodium u rate, while in body flu id s of gout patients certain components would accelerate the nucléation of sodium urate. One of the most mysterious things about gout is that only approximately 15% of hyperuricemic individuals have (41 gout.' ' Apparently, the essential difference between the gout patient and non-gouty individuals with equal uric acid supersaturation is merely the nucléation of sodium ura+c crystals. Further deposition of sodium urate crystals probably follows because of seeding by the crystals f i r s t formed. Since nucléation is the f ir s t step in deposition o f sodium urate crystals from hyperuricemic body flu id s , the objective of this work was to study the factors influencing the nucléation o f sodium urate, factors such as supersaturation, pH, im p urities. X-rays, and mechanical shocks. The precise s ite of the in it ia l crystal deposi tion is unknown.Some investigators have suggested th at sodium urate deposits in the collagen and connective tissues, while som e have favored the jo in t cavity. Thus, one hopes that this work will shed some lig h t on many avenues leading to an improved understanding of the development and proper treatment of gouty a rth ritis . In this d issertatio n . Chapter I I I is devoted to the nucléation theory and derivation of a new equation for nucléation o f ionic com pounds from solutions. The preparation of monosodium urate and the experimental methods are discussed in Chapter IV. The influence of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 various additives on the nucléation and s o lu b ility of monosodium urate is discussed in Chapter V, while the influence of X -irra d ia tio n and mechanical shock is discussed in Chapter V I. Chapter V II deals with the influence of pH on nucléation and s o lu b ility of monosodium urate. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I I LITERATURE REVIEW A. C lin ical Background I t is well known that gouty a r th r itis is the re s u lt of the c ry s ta lliz a tio n o f monosodium urate in the jo in ts and nearby connective tissues. Such c ry s ta lliz a tio n is associated with hyperuricemia resulting from purine metabolism disorders, renal malfunctions, f a s t i n g , a n d some d r u g s . T h e gout c lin ic a l e n tity was recognized before the b irth of Christ. Many eminent persons who made and contributed to the history of the world were a fflic te d by gout. Thus gout, by a fflic tin g those noble and h is to ric a l persons, made its ow n infamous history and heritage. Hippocrates (460-370 B.C.) was acquainted with the malady and called i t the unwalkable d i s e a s e .O r ig in a ll y , gout was called podagra, which is derived from the Greek words podus (fo o t) and agra (a tta c k ). The name "gout" now in vogue was derived from the L atin , gutta, which refers to a drop as a resu lt of the discharging flu id . The American poet James Russell Lowell (1819-1891) frequently referred to his gout in his w r i t i n g . H e summarized the gout syndrome in the following passage: " It is generally people who are in what are called easy circumstances who can afford to tre a t themselves to a handsome complaint, and these experience an immediate a lle v ia tio n when once they have found a sonorous Greek name to abuse i t by. The doctor gave m y trouble a nam e --and that by robbing them of mystery, has made them Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. commonplace... He said i t was suppressed g o u t... I t is suppressed a fte r the fashion of the Commune, which has jumped from the Parisian great toe into every nerve and muscle in the body... I t is podagra? I think how much better o ff I am than the poor centipedes must be. The disease derives its name from the patien t's in a b ility to go out. The oridinary derivation from gutta is absurd— fo r not only is the German from Gicht deduced from gehen, but the persons incident to the malady are precisely those who themselves (or th e ir ancestor fo r them) have kept ju s t this side of the g u tte r... I never heard that m y great grandfather died Insolvent, but I am obliged to foot some of his bills fo r p o r t... I c a ll m y gout the unearned increment from m y good grandfather's Madeira and think how excellent i t must have been, and wish he had le f t m e the cause instead of the effect..." The treatment of gout by the ancients was as primative as the diagnosis of the disease it s e lf . Colchicine or colchicum is one of the oldest drugs used in gout treatment along with a great number of herbs, mechanical devices, c o u n te rirrita n ts , acupuncture, blood le ttin g and insertion of setons.^^®^ The modern s c ie n tific era in gout research began in the la te 18th Century when Scheele in 1776 id e n tifie d uric acid in u r i n e . Soon a fte r, in 1797, Wollaston isolated uric acid from a gouty tophus which he had exhumed from his own ear. ^ In 1862, the B ritish physician Alfred Baring Garrod laid the cornerstone in the s c ie n tific diagnosis and m anifestation of gout disease. He conducted several e x p e r im e n ts b y which he independently confirmed the findings of Wollaston. He established that high levels of uric acid in serum (> 5 m g per 100 ml) are prerequisite fo r a diagnosis of gout. Garrod stressed that there could be no doubt that the main component in gouty deposits is sodium urate, c ry s ta llize d in the form of needle Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 crystals. He suggested that the presence of calcium phosphate occasionally in gouty tophi is probably the resu lt of a secondary deposition, the primary deposit o f sodium urate being the causative foreign body. Garrod summarized his findings in a series of propositions which relate c lin ic a l manifestations of gouty a r th r itis to hyperuricemia, as follows: 1) In true gout, uric acid, in the form urate soda, is invariably present in the blood in abnormal q u a n tities , both prior to and at the period of seizure and is essential to its production; but this acid may occasionally exist a t least fo r a tim e, in the circu latin g flu id without the development of inflammatory symptoms, as in cases of lead poisoning. Its mere presence, therefore, does not explain the occurrence of the gouty paroxysm. 2) The investigations detailed in the chapter on the Morbid anatomy of gout prove incontestably that true gouty inflammation is always accompanied with a deposition of urate of soda in the inflammed part. 3) The deposit is c ry s ta llin e and in te r s t it ia l, and when once the c a r tiliages and ligamentous structures become in filtr a te d , remains for a lengthened tim e, often through out life. 4) The deposited urate of soda may be looked upon as the cause, and not the e ffe c t, of the gouty inflammation. 5) The inflammation which occurs in the gouty paroxysm tends to the destruction of the urate of soda in the blood of the inflamed p a rt, and consequently the system generally. 6) The kidneys are implicated in gout, probably in its e a rly , and certa in ly in its chronic stages, and the renal a ffe c tio n , possibly only functional at f i r s t , subse quently becomes s tru c tu ra l; the urinary secretion is also altered in composition. 7) The impure state of the blood, arising p rin c ip a lly from the presence of urate soda, precedes the gout seizure, and many of the anomalous symptoms to which sufferers from gout are lia b le . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 8) The causes which predispose to gout, Independently of those connected with Individual p e c u lia rity , are eith er such as produce an Increased formation of uric acid In the system, or lead to Its retention In the blood. 9) The causes exciting a gouty f i t are those which Induce a less alkalin e condition of the blood; or which greatly augment, fo r the time, the formation of uric acid; or such as temporarily check the elim inating power of the kidneys. 10) In no disease but true gout Is there a deposition of urate soda In the tissues. Despite Roberts' flndlngs^^^^ In 1892 that sodium urate could exist In body flu id only In the form of monosodium u rate, and his experiments on p recipitation of needle crystals upon suspending tarsal bones of swine In saturated solutions of urates, Garrod's proposition on the role of sodium urate In acute gouty a r th r itis was generally denied. The Im p lic it proposition of Garrod that the acute attack of gout and Its tophaceous aspects are consequences of the lim ited s o lu b ility of sodium urate In body flu id s was prim arily discounted, because of the purported fa ilu re of Injected sodium urate suspensions to produce a sig n ific a n t tissue reaction. In addition, colchicine stops the acute attack without lowering serum urate levels. On the other hand, the uricosuric drug probenecid lowers serum urate levels without stopping the acute gouty attack. Furthermore, hyperuricemia was found to be present not only In gouty subjects but also In many apparently normal Individuals. Hyperuricemia was also found In patients with diseases other than gout, such as leukemia. In 1900, the great anatomist His and his student, Freudweller, (25-28) confirmed the theories of Garrod by demonstrating that acute Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 a rth ritis could be provoked in animals by injections of sodium urate microcrystals and that white cells ingested the crystals. Furthermore, they suggested that the phagocytosis which results in inflammation is a possible mechanism to explain gouty inflammation, but they assumed that phagocytosis was required to remove the offending crystals. I t was argued^^^"^^) that the observations of His and Freudweiler fa ile d to implicate uric acid in acute gout, since the soluble urates carried in circulation do not cause inflammatory or toxic effects in the body's tissues. Unfortunately, Minkowski had fa ile d to d iffe re n tia te between the soluble urate and the c ry s ta llin e sodium urate which is the offending agent in gouty disease. I t was not u n til around 1960 that a unitary concept of mono sodium urate being the causative agent of gout was firm ly established. The sophisticated work of McCarty, Hollander, Seegmiller and many other dedicated sci ent i s t s c onf i r me d Garrod's hypothesis th at monosodium urate is always present in gouty tophi and is d ire c tly involved in the pathogenesis of the acute attack of gouty a r th r itis . B. Present Theories o f the Mechanism of Acute Gout A fter i t had been established that gouty tophi and the acute gout attack are associated with the deposition of monosodium urate crystals in the body's flu id and nearby tissues, m ultiple theories have been advanced to explain the mechanism of the inflammation and pain of gout. Several w o r k e r s f o u n d that in jectio n of needle-shaped Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 crystals of sodium urate over 0.5u in length caused inflammation in dogs and in gouty and non-gouty patients. Smaller crystals and aggregates rarely caused pain. Thus i t was concluded that urate crystals trig g e r the inflammatory reaction because of th e ir size and shape rather than chemical nature. Furthermore, the inflammatory reaction was observed in both gouty and normal subjects upon subcutaneous injection of acicu lar sodium orotate crystals. Another characteristic o f the inflammatory reaction of sodium urate in jectio n is the phagocytosis of large crystals by l e u k o c y t e s . T h i s was observed upon microscopical examination of the synovial flu id under polarized lig h t. Recently, this has been documented with time lapse photography, showing leukocytes engulfing (41 ) the acicular urate crystals. The percentage of crystals found w ithin synovial leukocytes was roughly proportional to the severity of the c lin ic a l inflammatory symptoms both in spontaneous acute gout and in the induced pain by in je ctio n of urate crystals. Over 90% of the crystals were observed to be phagocytized in typical acute gout. These results led Seegmiller, Laster and H o w e l l t o propose the following mechanism for an acute gout attack: 1) Deposition of sodium urate crystals from hyperuricemic flu id s into jo in t tissues. 2) An acute inflammatory reaction to the crystals, with local in filtr a tio n by leukocytes that phagocytize the crystals. 3) Self-enhancing propagation of the inflammation, promoted by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. n continuous phagocytosis which increases la c tic acid production and causes further c ry s ta lliz a tio n of urate crystals. The th ird postulate is based on the observation th at during phagocytosis leukocytes produce la c tic acid^*^) which lowers the p H and induces further urate c ry s ta lliz a tio n . Indeed a high la c tic acid concentration has been reported in an acute synovial effusion of Is) g o u t.' Although this hypothesis is a ttra c tiv e , i t leaves several basic questions unanswered. For instance, what causes p recip ita tio n (nucléation)— the low pH or the la c tic acid its e lf? Because o f the confusion in the medical lite ra tu re between uric acid and sodium urate, some authors stated th at monosodium urate c ry s ta lliz a tio n is favored by low pH as a resu lt of lower monosodium urate s o lu b ilitie s . This, however, is not true fo r monosodium urate. I t has been found both th eo retic ally and experimentally (Chanter V II) th at below pH ~ 7 .6 the s o lu b ility of monosodium urate increases with decreasing pH, while uric acid s o lu b ility decreases with decreases in pH.(*^) Furthermore, i f the la c tic acid which results from the phagocytosis of sodium urate crystals does indeed induce c ry s ta lliz a tio n , then one wonders how the f i r s t crystals are formed. n 2) Weissman' ' proposed that hydrogen bonding between the surface of the urate crystals and the lysosomal membranes leads to the rupture o f the membranes, allowing lysosomal enzymes to escape into the c e ll. This would cause fin a l cell death and release of toxic cytoplasmic and lysosomal enzymes, resulting in inflammation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 On the other hand, Kellermeyer^**"*^) suggested that sodium urate crystals in it ia te acute gout by activating Hageman fa c to r, which is an enzymic protein present in plasma in an inactive form. The activated Hageman facto r would in turn in itia te a series of reactions resulting in the development of K a llik re in or K in in -lik e inframmatory mediators. C. C rys ta llizatio n Background A c ry s ta lliz a tio n process is characterized by two steps. The f ir s t is nucléation, the general meaning of which is the conception and the b irth of the f ir s t sub-microscopic c ry s ta l. Second is the growth of nuclei to become v is ib le crystals. In order fo r nucléation to occur, the solution must be supersaturated, i . e . , the concentration of solute must exceed its s o lu b ility . There are three types of nucléation: homogeneous, in which nuclei form in the bulk o f the solution fa r from any foreign p a rtic le or surface; heterogeneous, in which nucléation takes place on a solid surface or some other substance; and secondary nucléation or crystal breeding, in which new crystals form from existing crystals. The surface fo r heterogeneous nucléation can be a sub-microscopic p a rtic le , sometimes called a "mote". Less supersaturation is required fo r heterogeneous and secondary nucléation than fo r homogeneous n u c l é a t i o n . At th is stage i t is not known whether the primary nucléation in in itia tio n of gout is homogeneous or heterogeneous. Although one might speculate that most o f the c ry s ta lliz a tio n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 in the body is heterogeneously nucleated, the nature and the id e n tity of the substrate is usually not k n o w n . G e n e r a l l y , fo r an effe ctive nucléation substrate, the sum of the surface energies between the p a rtic le and crystal plus that between the crystal and the solution must be near that between the p a rtic le and the solution. Absorbing additives (im purities) may enhance or retard the nucléa tio n . Furthermore, there are a host of other factors that influence nucléation of crystals, such as e le c tric f i e l d , X - r a y s , and mechanical s h o c k . S e c o n d a r y nucléation or crystal multiplication^®®"®^^ is the generation of new crystals from parent crystals. This mechanism (crystal breeding) might explain why an acute gouty attack is autocatalytic upon deposition of the f ir s t (parent) sodium urate crystals. Probenecid has been found to lower the serum urate concentration, but the severity of a gout attack increases.One might speculate that this increase in severity of a gout attack is due to breakup of crystal clusters when the surrounding solution becomes undersaturated, thus perm itting increased phagocytosis to occur. Since only needle-shaped crystals have been observed to cause acute gout, the control of the habit (shape) and growth rate of urate crystals would be of great importance in gout treatment. The shape the crystals take upon growing depends on supersaturation and on the presence of im purities in the s o lut io n.A ll en and co-workers (64-66) investigated a host of additives for possible habit modifica tion of monosodium urate crystals. Their objective was to fin d a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 chemical substance which could retard or in h ib it the growth o f mono sodium urate crystals along the needle axis. I t was found that Bismark brown at low concentration remarkably inhib ited the growth of sodium urate. Methylene blue also inhibited the growth, but required four times the concentration fo r the same degree of in h ib itio n as Bismark brown. Benzalkonium chloride 400 times as concentrated as Bismark brown inhibited the growth about h a lf as much. Tris hydroxymethyl amenomethane (THAN) was found to have a remarkable e ffe c t in accelerating the growth of urate along the needle axis. (In te re s tin g ly , TH A M is contraindicated fo r gout patien ts.) Based on q u a lita tiv e experiments, they found that dextran, g e la tin , salicylam ide, v a n illin , b r illia n t green dye, and safranin Y dye appeared to be potential compounds fo r in h ib itio n of sodium urate nucléation. (The molecular formulas of these compounds are found in Reference (6 7 ) .) In addition, the growth habit of sodium urate was investigated by Inagaki and c o - w o r k e r s . T h e y observed that there was a tendency to form a bundle or spherical aggregation of needle crystals at high supersaturation, whereas platy crystals were formed a t low supersaturation. The e ffe c t of pH on crystal habit in 10% gelatin solution with 6.6 £ p H £ 8 was investigated, but no sig n ifican t difference in crystal habit was observed. With s tirrin g , cracks were formed in the crystals and gave the appearance of bundle aggregates of needle crystals. W hen the g elatin solution was d ried, crystal needles grew up to as long as 2 m m in length. Based on Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 th e ir results. Inagaki and Morioka^®®^ suggested that i t might be possible to trace back the surrounding conditions of a gouty tophus from its crystal morphology. D. Physico-Chemical Properties of Uric Acid and Monosodium Urate____________________ Uric acid (Figure I I - l ) is the most highly oxidized member of the purine class of compounds. In alkaline or neutral solution, uric acid is oxidized to allan to in by opening the purine ring and removal of carbon 6 as carbon d i o x i d e . I n acidic solution uric acid is oxidized into alloxan as shown in Figure I I - 2 . Solutions of monosodium urate decompose easily by bacteria attack and mold g rowt h.Also, P a lit and Dhar^^^^ found th at in the presence of sunlight, monosodium urate solution is oxidized by a ir . W hen 36 lite r s of a ir passed through aqueous solution of 0.02 M mono sodium urate, about 20% was oxidized in 5-1/2 hours, and the greater the in tensity of sunlight, the greater the amount oxidized. Uric acid (2,6 ,8-trio x y p u rin e ) is a weak acid which ionizes a t N-9 (pKji = 5.75) and N-3 (pK^g = 10.3).^^®^ Consequently, at the physiological pH, 7 .4 , uric acid dissociates almost completely and exists prim arily as the monovalent urate ion. At the pH of urine, i t is largely undissociated and circulates as free u ric acid. Uric acid was f ir s t isolated by Scheele in 1766 and is known to exist both in enol and keto form. Bergman and Dikstein,^^®^ by deter mination of the optical absorption m axim um versus pH, found = 1.78 X 10'® and K^g = 5 x 10'^^. These values agree with Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H — N 0 I I C 6 I 0 = C 2 HO N 3 N OH I C N 16 H I N ' \ 8 C = 0 , / N A KETO FORM (LACTAM) H N \ I / C— OH ENOL FORM (LACTIM) Figure I I - l . Equilibrium Forms of Uric Acid Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 H — N 0 ’ H g N 0 . H I .N N H ALLANTO IN \ ^ C = 0 + C 0 2 H I N C = 0 NH C 1 1 C ALLO XAN Figure I I- 2 . Oxidization of Uric Acid Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 Kanit's^^^) results from conductivity data, = 2 x 10”® and Kjg = 2.6 X 10”9. The s o lu b ility of uric acid and monosodium urate has attracted the in te re s t of many workers because of th e ir association with gouty deposits. The s o lu b ility of uric acid in pure water (C02-free) was found to be 0.0649 g m per l i t e r at 37°C.^^^^ Jung^^^^ made the most comprehensive studies on the s o lu b ility of uric acid and sodium urate in buffered solutions. Jung found that the s o lu b ility of uric acid increases with pH, and fo r pH < 4 i t approaches the s o lu b ility of the undissociated uric acid (which is a function of temperature). For sodium urate, Jung found th at the s o lu b ility increases with p H un til i t reaches a maximum a t pH 6 and then starts decreasing beyond p H 6, as shown in Figure II- 3 . Jung attrib u ted the increase in monosodium urate s o lu b ility to the increase in pH and the decrease to the com m on ion e ffe c t. Unfortunately, this in terp retatio n caused much confusion regarding the pH dependence of the s o lu b ility of sodium urate. (This w ill be elucidated in Chapter V II.) The p recipitation of urate compounds in modified forms was of considerable in te re st in regard to the physical properties of urates. Ord^^^^ in 1879 was the f i r s t to note th at when hot saturated solutions of urates (o f sodium or ammonium) are rapidly cooled, a metastable gelatineous p recip ita te is formed. A fter a time th is gelatineous p recip itate converts to a mass of crystals. C rystallin e monosodium urate is fa r more soluble in hot than in cold water and i t has been well known that an extremely high degree of supersaturation can be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 LJ ÜJ 08 =! .02 (/) PH Monosodi Figure I 1-3. S o lu b ility of Monosodium Urate and Uric Acid in Buffered of Solutions a fte r Jung(43) 0 : Monosodium urate in KHPO^-NaHPO^ buffer. A : Monosodium urate in NaHPO^-NaHPO^ buffer. X : Monosodium urate in N a acetate + acetic acid buffer. - : Uric acid. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 achieved without c ry s ta lliz a tio n . Gudzent^^*) explained the large variations in s o lu b ility of uric acid salts by invoking two forms of urates; the stable and less soluble lactim form, and the unstable and more soluble lactam form, with a gradual conversion of the lactam to the lactim form in solution. The reported value fo r the s o lu b ility product of sodium urate in aqueous solution a t 37°C is 4.9 x 10"^.^^^ Using this value to calculate the s o lu b ility of urate in serum with 0.13 M sodium chloride, one obtains 6.5 m g of monosodium urate per 100 m l of serum. However, by addition of u ric acid to serum at 37°C, values as high as 60 m g of urate per 100 m l of serum have been obtained. The crystal structure of the lactim form belongs to the monoclinic system. Kesser and Zocher^^®^ showed that certain urate gels are non-crystalline. Also, when monosodium urate solution is cooled rap id ly, amorphous monosodium urate precipitates out. I t is amorphous in the sense that X-ray d iffra c tio n peaks are not obtained. Microscopic observation with crossed polarizers reveals b iréfrin g en t globules and aggregates (as shown in Figure I I- 4 ) . Kellermeyer^**) placed a suspension of monosodium urate crystals and saline solution (0.15 M NaCl) in an electrophoresis apparatus and found that they migrate toward the anode. The migration of the amorphous monosodium urate toward the anode was much slower than the c ry s ta llin e monosodium urate. Therefore, Kellermeyer concluded that monosodium urate crystals are negatively charged and the amorphous monosodium urate crystals possess much less negative charge Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 Figure II- 4 . Photograph o f Amorphous Monosodium Urate 42X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 than the cry s ta llin e monosodium urate. This surface charge is due to the adsorption of negative ions at the crystal surface. Crystals of both sodium urate and uric acid show intense negative birefringence when examined under polarized lig h t. This property permits the detection of urate crystals in synovial flu id and tissues. The most accurate method fo r determining the urate concentration in solutions is the enzymatic spectrophotometrie method which uses the strong characteristic u ltra v io le t spectrum of uric ac id. Th e absorption o f urate ion has a maximum value at 292 m y a t pH 9.4. The optical density is determined before and a fte r the action of the uricase. The difference in absorption of u ltra v io le t lig h t gives a d ire c t measure of the urate concentration o rig in a lly present in the assay solution. For this urate assay, a biological flu id does not have to be deprotenized, but simply diluted with buffer. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I I I TH E O R Y OF NUCLEATION IN A Q U EO U S SOLUTIONS Nucléation may be defined as the in itia tio n of a new phase. A nucleus contains a d e fin ite volume and a boundary separating the old and new phases. The spontaneous appearance of a new phase occurs when a system is in a non-equilibrium state and when the departure from the equilibrium state is s u ffic ie n t fo r the b irth of such a phase. Before discussing the types of nucléation and th e ir theories, we should discuss s o lu b ility and supersaturation, which are the most important and obvious parameters affecting nucléation. A. S o lu b ility B y d e fin itio n , a solution is a single phase system which contains more than one component. Consider the dissolution of a pure crys tallin e substance A in solvent B, and assume that these two substances do not form a solid solution with one another. Figure I I I - l shows a hypothetical s o lu b ility curve fo r solute A. The saturation curve shown in Figure I I I - l represents thermodynamic equilibrium between the solute in the liq u id phase and the same solute in the solid phase. Thus, the chemical potential of the solute is the sam e in both the solution and the solid phase. From thermodynamics the temperature dependence of the chemical potential at constant pressure is , for any phase. 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 < crystals + soturoted solution Supersaturated Solution UJ 3 o <o Ü. O z o < a : H Z W o z 8 Unsoturoted Solution T E M P E R A T U R E Figure I I I - l . S o lu b ility Dependence on Temperature Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 ( = -^A ’ H I-1 ■A*"B where is the chemical potential of solute A and is the molar entropy. The plot of the chemical potential versus the temperature fo r a single component has a negative slope equal to the molar entropy in the existing phase. At any temperature, the molar entropy of a pure substance in liquid phase is larger than th at in the solid phase. Therefore, the chemical potential versus temperature curve has a larger negative slope fo r the pure liq u id than fo r the pure so lid . The chemical potential of a solute in aqueous solution is less than i t would be as a pure liq u id . Thus the p a rtia l molar entropy of a solute in aqueous solution is higher than the molar entropy of the pure liq u id solute. Thus, fo r a solute which s o lid ifie s as a pure s o lid , the p a rtia l molar entropy of the solute in aqueous solution is higher than th at in the pure solid and the solute chemical potential versus temperature curve has a larger negative slope than th at in the s o lid , as shown in Figure I I I - 2 . The intersection of the pure solid and pure liq u id curves represents the melting temperature o f the substance, while the intersection of the pure solid and the solution curves represents the s o lu b ility temperature. Most solutes dissolve with an absorption of heat, so th at the s o lu b ility increases with temperature. The s o lu b ility is also a function o f pressure, but the e ffe c t is negligible in liq u id solvents a t ordinary p r e s s u r e s . most of the te x t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 TEMPER ATURE Figure I I I - 2 . The Chemical Potential of Solute in Solid and Liquid Phase Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 books, the influence of temperature on s o lu b ility is usually derived fo r non-electrolytes substances. Sometimes th is resu lt is misapplied to the case where the solute dissociates into ions, thus leading to great errors in estimating the heat of solution from s o lu b ility data. In the follow ing, the influence of temperature on the s o lu b ility is derived fo r monosodium urate dissolved in aqueous solution and gov erned by the chemical equation NaHU:P±Na* + HU" . I I I - 2 For equilibrium conditions, the chemical potential in the solid and the liq u id phase must be equal. (^NaHu)^ ' (^NaHu)^ I I I - 3 The chemical potential fo r monosodium urate in solution can be expressed as^^®^ “ NaHU * " N a * * “ H U - * Un [(c ^ ,+ ) ( c ^ - ) ( “ H U -)] where and are the concentrations of sodium ion and urate ion respectively, and are the a c tiv ity co efficien ts of sodium * * and urate ions respectively. The and are the standard chemical potentials of sodium and urate ions in solutions where the ionic a c tiv itie s are u n ity, with v's defined as unity at in fin ite d ilu tio n . From Eqs. I I I - 3 and I I I - 4 , i t follows that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 & n I I I - 5 The standard chemical potential y 's and the chemical potential of the pure solid ele c tro ly te are functions only of temperature and pressure and are independent of composition. I t follows from Eq. I I I - 5 that the product (called the s o lu b ility product) "sp = ( S a ^ ) ( W ) ( W ) (^HU’) I I I - 6 is constant a t fixed temperature and pressure. The temperature de pendence of the s o lu b ility product is obtained by d iffe re n tia tin g Eq. I I I - 5 with respect to temperature. I t can be shown (78) that and = -"SaHu/T^ I I I - 7 I I I - 8 where H NaHU is the molar enthalpy of monosodium urate as pure s o lid . and H . 'NaHU p a rtia l molar enthalpy of monosodium urate in solution a t in fin ite d ilu tio n . From Eqs. I I I - 5 , I I I - 7 , and I I I - 8 , the dependence o f the solu b ilit y product on temperature can be expressed as 9 in K I T Ü* u S "NaHU "NaHU — RT‘ I I I - 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 N ow i t should be evident that Eq. I I I - 9 should be w ritten in terms of the s o lu b ility product rather than the s o lu b ility alone, as fo r non-ionized substances. The difference between the p a rtia l molar enthalpy at in fin ite d ilu tio n and molar enthalpy of the pure solid is the heat absorbed or liberated in the process of dissolution, A H ^ = “* s H Over a small range of temperature, AH^ may be taken as a constant which gives a simple integration of Eq. I I I - 9 , as ün Ksp = Y + b III- IO where a = -AH^/R and b is an integration constant. B. Supersaturation and M etastability Depending on the concentration o f the solute and the tempera tu re, a solution may be unsaturated, saturated, or supersaturated. W hen crystals are introduced into an unsaturated solution they dissolve. In a saturated solution the liq u id phase and any crystals present would be in equilibrium and so no net change would occur. A solution whose concentration is higher than that of a saturated solution is said to be supersaturated. The unsaturated and saturated solutions are stable and can be stored in d e fin ite ly with no change. But supersaturated solutions are thermodynamically unstable. The tran sitio n from u n s tab ility to s ta b ility can be accomplished by c ry s ta lliz a tio n . Conversely a supersaturated solution is necessary fo r c ry s ta lliz a tio n . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 The degree of supersaturation of a solution can be defined in two ways.(^^) The absolute supersaturation is defined fo r A8 t A* ♦ B" as AC = ( C ^ ) ( C j ) - ( C * ) , ( C » ) , . where (C^)(Cg) is the concentration product of the dissolved sub stance and (C;^)e(Cg)g is the equilibrium concentration product. Also, the degree of supersaturation can be expressed as the re la tiv e supersaturation. (Ca X C b ) - ( C * ) , ( C g ) , -----------------------------K A 'e t'B 'e ' or as the degree of supersaturation, a = (C^)(Cg)/(C^)g (Cg)^. An alte rn a tiv e measure to supersaturation is supercooling. By analogy with the degree of supersaturation, supercooling can be expressed as the absolute supercooling; AT = T^ - T, the re la tiv e super cooling, n = Tg - T/Tg, or the reduced temperature, ç = T/T^, where T is the temperature of c ry s ta lliz a tio n and T^ is the s o lu b ility temperature. The a b ility of substances to form supersaturated solutions can be represented q u an titatively by the maximum supersaturation or supercooling. The maximum supersaturation represents the lim it beyond which spontaneous c ry s ta lliz a tio n (nucléation) is observable w ithin a reasonable time. The observed value o f maximum super saturation can be influenced by a host o f facto rs, such as mechanical e ffe c ts , the rate of cooling and im purities present in the solution. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 Values fo r the maximum supersaturation or supercooling have been reported in the lite ra tu re fo r d iffe re n t compounds.^ The region between the maximum supersaturation and the s o lu b ility is called the "metastable zone", since c ry s ta lliz a tio n would proceed only i f a seed crystal were introduced. The region above the supersolubility curve is known as the la b ile or unstable zone since nucléation occurs spontaneously. This concept of la b ile and metastable solutions has been accepted and used by many invest igators. A diagram of the various states of a solution is shown schematically in Figure I I I - 3 . The region of the diagram above the curve N-N (called here the supersaturation curve) represents the la b ile zone. The region below the curve S-S is the stable zone o f unsaturated solution and the region between the curves N-N and S-S is the metastable zone. The supersaturation curve, sometimes also called the m etastability lim it , resembles the s o lu b ility curve. Usually these two curves are e ith e r p a ra lle l or almost p a ra lle l. However, when we use the concept of a metast a b ility lim it, we must bear in mind that the supersaturation curve is not rigorously defined. In contrast to the s o lu b ility curve, the supersaturation curve does not depend only on temperature and composition, but also on many other factors such as im p urities, s tirrin g of the solution , mass of the solution, cooling ra te , etc. Some investigators a ttrib u te the existence of the metastable zone to a higher s o lu b ility of small p a r t ic le s .T h e dependence of the s o lu b ility of particles on th e ir size has been a ttrib u te d to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 Z o Labile Zone I - < o: K Z Metastcbie Zone w u supercooling z o u Stable (unsaturated) Zone TEMPERATURE Figure I I I - 3 . S o lu b ility and Supersaturation Curves Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 the dependence of the s o lu b ility on the surface energy y of the boundary separating solid and liq u id phases. Ostwald^®®^ was the f ir s t to re la te the surface energy to the radius of the p a rtic le and the s o lu b ility by the following equation, S, [ k ' k I l l - l l a where M is the molecular weight, p is the density o f the s o lid , y the surface tension, S -j and Sg the s o lu b ilitie s a t ra d ii r^ and rg, T is the absolute temperature, and R is the gas constant. I f the p a rtic le radius r^ is very large, the s o lu b ility o f such a p a rtic le becomes equal to the normal s o lu b ility and Eq. I I I - l l becomes ^ ^ ^ ' I l l - l l b Equation I l l - l l b is shown schematically in Figure I I I - 4 . The Ostwald equation, I I I - l l , involves a number of assumptions. For instance, both the density of the solid and the s o lid -liq u id surface energy are assumed to be independent of the p a rtic le size. In add ition , the p articles are considered to have a spherical shape. The dissociation of the solid in solution was not taken into account. Dundon and Mack^®^^ modified Ostwald's equation fo r the case where dissociation is involved. They assumed th at p a rtic le density and s o lid -liq u id surface energy are independent of size. Their result was presented as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 _J (/) normal solubility PARTICLE SIZE r Figure I I I - 4 . Dependence of S o lu b ility on P a rtic le Size Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 (1 - ^ + n^) ^ 2n ^ 111-12 where t is the degree of dissociation, n is the number of ions formed from the dissociation of one molecule, and the rest of the symbols are the same as those in Eq. I I I - l l . I t should be noted that Eq. III- 1 2 has the same form as Eq. I I I - l l , and fo r zero degree of dissociation they become id e n tic a l. C. Homogeneous Nucléation from Solutions 1. Introduction (88-91) According to classical nucléation theory, ” the rate of formation of nuclei from vapor and melt is given by the equation J = A exp (-AG*/kT) III- 1 3 where J is the nucléation rate (nuclei/sec. c m ) , A is the kinetic constant (sometimes called the pre-exponential fa c to r), AG* is the c ritic a l activation energy necessary fo r nucléation, k is the Boltzmann constant, and T is the absolute temperature. Equation I I I - 13 w ill be derived la te r in this chapter. The theoretical expression fo r the k in e tic constant A depends on the phase in which nucléation occurs. Since the kin etic constant A is merely a frequency fa c to r, Becker and DBring^^Z) considered the kin etic constant A in case of nucléation from vapor as the gas kinetic binary c o llisio n frequency. They derived a theoretical expression fo r the constant A, yielding a numerical value of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 o r _ o _1 approximately 10 cm " sec" . For homogeneous nucléation from (931 m elt, Turnbull and Fisher applied the theory of absolute reaction rates and derived the following expression fo r the kin e tic constant A, A = 4 È I exp (-AGg/kT) III- 1 4 O where n is the solute concentration (molecule/cm ), k is the Boltzmann constant, h is Planck's constant, T is the absolute tempera tu re, and AGp is the activation energy fo r short range diffusion of atoms or molecules moving a fra ctio n of an atomic distance across an interface to jo in the crystal la ttic e . The theoretical value of A calculated from Eq. III- 1 4 was approximately 10^® cm"^ sec"^, which gave good agreement with the experimental data.^^^"®^^ The in it ia l development of nucléation rate theory of ionic salts from aqueous solution followed much the sam e path as in nucléation from the melt. Thus in the literature^^^^ sim ilar values of the kin etic constant A from the m elt were assumed fo r the case of nucléation from aqueous solutions. However, Melia and Moffit^®®’^^^ found th a t, for nucléation o f ammonium chloride, potassium n itra te , and ammonium bromide from supersaturated solutions, the kin etic con stant A had an experimental value in the range of 10^ - 10^ cm"^sec"^. Bransom and Dunning^^®^ also reported this discrepancy between the theoretical and experimental k in e tic constant fo r nucléation of cyclonite from aqueous n itr ic acid and aqueous acetone solutions. They reported the kin etic constant as being on the order of 10^® cm ”^ s e c " \ which is again very fa r from the assumed value of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 25 -3 -1 /qg\ 10 cm' sec' . Dunning and his co-workers attrib u ted the low values of the kin etic constant A fo r nucléation from aqueous solution to the large entropy decrease upon c ry s ta lliz a tio n . This large decrease in entropy would lower the p ro b ab ility of nucléation. Eyring(^^) has shown that this p ro b ab ility facto r depends on the size and complexity o f the reacting molecules. For polyatomic molecules, the value of the p ro b ab ility fa c to r is of the order 10' ^ to 10'^^. This probability facto r p a rtia lly explains the low value of the kin etic constant of nucléation of cyclonite from aqueous n itr ic acid since cyclonite is a complex molecule. There fo r , fo r nucléation of simple ionic compounds from th e ir super saturated solutions, the entropy decrease or the pro b ab ility facto r would not be s u ffic ie n t to account fo r the low value of the kin etic constant obtained from nucléation experiments. Nielsen^^^^) derived the following expression fo r the rate of homogeneous nucléation in aqueous solution: J = exp (-AG*/kT) , III- 1 5 d* where D is the diffusion c o e ffic ie n t and d is the molecular diameter. Thus, the kinetic constant A o f nucléation as derived by Nielsen can be expressed as: III- 1 6 Nielsen estimated a value of A on the order of 10^® cm'^ sec'^ (fo r _ c o n D = 10' c m /sec, and d = 10' cm), which does not d iffe r much from Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 p C _ O that reported for nucléation from melt and vapor (A = 10 cm' sec' ). The experimental values of the kinetic constants fo r sparingly soluble salts as reported by Nielsen ( 100) are given in Table I I I - l TABLE I I I - l Experimental Kinetic Constants a fte r Nielsen (100) S alt A BaSO* 2 X l o f Z PbSO* 1 X lo f ® SrSO* 6.3 X l o J I CaFg 3.2 X 10^3 From Table I I I - l i t can be seen that the experimental values of the kinetic constants are much lower than the theoretical values as pre dicted by Eq. III- 1 6 . Nielsen attrib u ted the low k in e tic constants A fo r SrSOg and CaFg to solvation effe cts . From this b rie f review o f homogeneous nucléation in aqueous solutions i t can be observed th at the application o f the classical nucléation theory (as i t was developed fo r the vapor and m elt) to aqueous solutions always predicts higher nucléation rates than what is observed experim entally. In spite of the reasonable explanations^^®®' ^®^) offered fo r the discrepancy between the experimental and theoretical kin etic constant o f nucléation in aqueous solutions, there was no attempt to put these explanations into an analytical Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 equation which could reasonably predict and show the paramount parameters of the nucléation rate in aqueous solutions. The objectives here are to derive a theoretical expression fo r the rate of nucléa tion of ionic compounds from th e ir aqueous solutions which could account fo r the slow rate of nucléation observed experim entally, and to discuss the parameters and processes which influence nucléation from aqueous solutions. 2. Thermodynamics of Homogeneous Nucléation From Solutions___________________________ The term "homogeneous nucléation" is used to describe the free appearance of a more stable molecular aggregate w ithin the volume of a metastable mother phase which is o rig in a lly devoid of the new phase. As in any phase transformation, fo r the appearance of these stable molecular aggregates (nuclei) there must be a decrease in the to tal free energy associated with the formation of the new and more stable phase. The fre e energy of the formation of a spherical embryo of phase I I in a medium of phase I at constant temperature can be expressed as^®®^ A G = (4 /3 ) wr^AGy + Awr^y , III- 1 7 where r is the radius of the embryo, y is the in te rfa c ia l fre e energy per unit area between embryo and the metastable phase, and AG^ is the difference of the volumetric free energy between phase I I and phase I. The dependence of the change of the fre e energy on embryo size is shown in Figure I I I - 5 . The condition of equilibrium at which embryos Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 criticol free energy Total Free Energy Change For Formation critical y radius Embryo Radius of Embryo R Figure I I I - 5 . Free Energy Dependence on Embryo Radius Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 of a c r itic a l size r are stable and able to grow is obtained by d iffe re n tia tin g Eq. III- 1 7 with respect to r and setting the d erivative equal to zero. ( III- 1 8 From Eq. III- 1 8 , one obtains (AGy) III- 1 9 III- 2 0 For c ry s ta lliz a tio n from solutions. III-2 1 I ... where y is the chemical potential of the solute in the supersaturated solution and y^^ is the chemical potential of the solid solute phase which is equal to that of a saturated solution (since the la tte r would be in equilibrium with formed c ry s ta ls ), p is the density of the s o lid , and M is the molecular weight. For ionic compounds, which dissociate according to the chemical equation A S. aA + 6 8 , a p the difference in the chemical potential can be expressed as III- 2 2 . fiE l - I f a *)“ (a-)6 II III- 2 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 where a 's are the ionic a c tiv itie s , R is the gas constant, and T is the absolute temperature. For the case of a = B = 1 (as in mono sodium u ra te ), and fo r constant a c tiv ity c o e ffic ie n t, Eq. III-2 3 can be w ritten as A G . , III- 2 4 where C is the actual (supersaturation) concentration, and is the saturation (equilibrium ) concentration. I t is emphasized that the degree of supersaturation fo r nucléation of ionic compounds should be expressed as the ra tio of the concentration products as in Eq. III- 2 4 . 3. Kinetics of Homogeneous Nucléation From Aqueous Solutions____________ The f ir s t successful theoretical approach to nucléation was that proposed by Volmer and then modified by Becker and Doering.t*^) The essential assumptions of the theory are th at dense clusters of molecules (embryos) of the more stable phase e x is t in dynamic equilibrium with the metastable mother phase, that these embryos are spherical and that they re s u lt from the stepwise addition of molecules. These molecular aggregates must achieve a c r itic a l size before they s ta rt to form a stable new phase. The proposed expression fo r nucléation rate is given by Eq. III- 1 3 . Since the classical nucléation theory was in it ia lly developed fo r nucléation from vapor phase, one sees that nucléation from vapor and melt Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 involves a straightforward molecular aggregation and cluster forma tion. For nucléation of ionic compounds from aqueous solutions, the clustering of the molecules or the ions is not c le a r, and there is a d is tin c t difference between the aggregation of two neutral molecules and the aggregation of two oppositely charged ions. Thus to understand the nucléation of ionic compounds q u a n tita tiv e ly , we must have some kind of a physical model of the nature of embryos preceding nucléation. To formulate our thinking about the nature o f the embryos in nucléation of ionic compounds, we raise the following questions: 1. D o embryos form by successive addition of the neutral molecules of the nucleating compound or by successive addition of the individual ions? 2. I f embryos form by successive addition of ions, what is the e ffe c t of the solvent sheaths around the ions on the process of aggregation? 3. Must the heat of solvation be overcome before ions can in te ra ct and be able to cluster by successive addition of molecules or ions? 4. Is the nucléation rate influenced by the magnitude of the heat of solvation such th at the larger the heat of solvation, the slower the nucléation rate of the ionic compounds? Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 5. Is there an intermediate (tra n s itio n ) state or configura tion which the ionic compounds must a tta in fo r the aggregation of molecules to have a high probability? 6 . I f there is such an activated state as mentioned above fo r nucleating of hydrated ionic compounds, would we expect that both the individual ions and the acrivated state are solvated? I f yes, how is the nucléation affected? Now, in order to develop an expression fo r the nucléation rate of ionic compounds from th e ir aqueous solutions, le t us s ta rt with the classical nucléation rate expression at the stage where the expression is general fo r nucléation from any phase. According to the classical nucléation theory, embryos arise by successive addition of single monomers to the growing embryo: A + A . ----- » A , + i ^i+l ^ ^ **i+2 The rate of formation of the c r itic a l nuclei is given by J = ZFO(n*)C(n*) , III- 2 5 where Z is a non-equilibrium facto r which expresses the departure of the actual concentration of c r itic a l embryo from its metastable equilibrium value, F is the impingement flu x o f monomer per u n it Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 area of the embryo surface, 0 (n ) is the c ritic a l embryo surface area, and C(n ) is the concentration of c ritic a l embryo. For nucléation from a vapor, the imoingement frequency f in Eq. I I 1-25 was expressed in terms of the kin etic theory of gases as the number of molecules strikin g an embryo of a given size per un it time. Unfortunately, the same values obtained fo r the c o llis io n number in gas phase have often been used fo r reactions taking place in liq u id phase where the co llisio n processes are much slower than in the gas phase. 4. The Activated or Transition State Model In nucléation from vapor or m elt, the formation of embryos involves a straightforward aggregation with a ll molecules present being available fo r aggregation. The structures of molecules in a solution is completely d iffe re n t than that in the la ttic e arrangement in crystals. Thus, for an ionic compound to nucleate, the molecules must be oriented and ordered approximately lik e the crystal la ttic e . Classical nucléation theory assumed that solutions behave lik e pure m elts, in which molecules are close together and only short-range forces have to be overcome before molecules can s trik e the embryo surface. Thus, fo r nucléation of ionic compounds, in addition to diffu sio n of the ions toward each other, the ions must approach each other close enough to form ion pairs in order to be deposited. For a solvated cation to associate or come in con tact with a solvated anion, the ions must lose some of th e ir Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 solvation sheath molecules. For nucléation from aqueous solutions, this association process implies the replacement of at least one water molecule of the hydration sheath of the central ion by the oppositely charged ion (see Figure I I I - 6 ). One should note that this model of ionic association assumes that one of the ions retains its primary hydration sheath. The re s tric tio n o f the ions' movement imposed by the hydration sheath and the requirement of the close approach of the ions before deposition make the nucléation rate slower. Since ions in solutions are fa r from th e ir la ttic e arrangement, the entropy changes which accompany the order and orientation of ions before nucléation would decrease the probability of embryo formation. From the previous discussion, the nucléation o f ionic compounds involves a t least two slow stages: 1. Close approach of the ions as a resu lt of lib e ra tio n of a water molecule from at least one of the ion hydration sheaths, and 2. Diffusion of ions to the embryo surface. One should observe that the requirement o f close approach of the ions fo r nucléation of ionic compounds from solution is not required in case of nucléation from melt or vapor since the la tte r involves a straightforw ard aggregation of neutral molecules. I f we have A and B solvated ions, then the activated state which must be attained before deposition can be represented by the chemical equation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 Water Molecules o o O O ^------------------------ y ------------------------ > Ion Poir. close opprooch before nucleotion — " intermediote stote" 9 Woter molecule dropped from one of the hydrotion sheoths Figure I I I - 6 . The Transition State Model fo r Nucléation of Ionic Compounds from Aqueous Solutions Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 ( A ) (HgO) + (B ) (HgO) s s Reactant Ions Activated Complex III-2 6 (ABitHgOjy Embryo where n^ is the hydration number (number of water molecules comprising the primary hydration sheath of the io n s), n^ is the number of water molecules removed from the hydration sheath fo r close approach of the ions, and y is the number of water molecules in the hydrated crystal. 5. Derivation of Nucléation Rate fo r Ionic Compounds The rate fo r formation of c r itic a l n u clei, Eq. III- 2 5 , can be w ritten as: J = K]C(n*) , III- 2 7 where is constant. From the activated complex model, the concen tra tio n of the c r itic a l nuclei, C (n *), can be expressed as: it i * C(n ) = C(n ) exp(-AG /kT) . III-2 8 The concentration of the activated complex C (n ^ can be expressed as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 C(n^) = kgn^Hg exp(-AE /kT) , III- 2 9 where kg Is a proportionality constant, n^ and n^ are concentrations of the ions (molecules/cm^), and A E is the activation energy required fo r close approach of the ions. From Eqs. I II - 2 9 , III- 2 8 and III- 2 7 , the nucléation rate of ionic compounds can be w ritten as J = A exp ( - -pY” I » III-3 0 a where (■#). (■if). A = k^kgn^ng exp (- p y - | . III-3 0 b 6 . Estimation of the Activation Energy (AE ) The activated complex is based on the ions associating or approaching one another closely, with the ions vibrating in positions close to those of the solid la ttic e . This process is due to the loss of some water molecules from the primary hydration sheath of the ion. Thus the energy involved in activation must be proportional to the heat of dehydration. In nucléation from a m elt, this activa tion energy is taken to be equal to the activatio n energy of d iffu sio n , which is a good approximation since atoms are only a fractio n of an atomic distance away from one another. For ionic com pounds in aqueous solutions, the ions are hydrated. Therefore they have to lose th e ir hydration energy, or in other words, they have to climb a higher potential energy b a rrie r before they become activated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 as shown in Figure I I I - 7 . I t should be pointed out that the activatio n energy of diffusion used in the classical theory of nucléation from melt has a value on the order of 5 Kcal per mole.^^^^ In nucléation from aqueous solution, the activatio n energy should be the sum of the dehydration energy required fo r lib e ra tin g the ion from some of its hydration molecules plus the activation energy required fo r the case where the ions are not hydrated (see Figure I I I - 7 ) . Thus the activation energy fo r nucléation from aqueous solution is much larger than that required fo r nucléation from a melt. From the activated complex model, i f n^ is the number of water molecules which the ion must get rid of to come in contact with another ion, and n^ is the primary hydration n u m b e r , t h dehydration energy required fo r the process can be estimated as A"deh = - A"h ' where AH^ is the heat o f hydration of the ion and AHÿ is the p a rtia l heat of dehydration. The activation energy E in Eq. III- 3 0 is equal to the p a rtia l heat of dehydration. 7. Estimation of the C o llision Frequency Equation III- 3 0 can be w ritten as A = Z'n^ng exp(-AE*/kT) , III-3 0 c where V is merely a co llis io n frequency, which is a measure of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 AE LJ UJ AH REACTION C O O R D IN A TE (i.e . distance along the reaction path) Figure I I I - 7 . Schematic Potential Energy Curve of Hydrated and Dehydrated Reactants Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 rate of ions strikin g an embryo surface. From c o llis io n theory, V = uw(r*)2 , III-3 2 * where u is the velocity of the ion and r is the c r itic a l radius of the embryo. The velocity u of ionic movement is expressed as u = ^ , III-3 3 where I is the mean jump distance travelled by the ion and x is the m ea by( mean jump time. The diffusion c o e ffic ie n t D is related to x and i ,(103) 1 i } D = . III-3 4 From Eq. 111-33 and 111-34 then u = ^ . III-3 5 The mean jump distance I is always approximated by the close approach distance between two ions and is taken to be equal to the ion diameter. This is only ture i f the ions are equal in s ize , otherwise the mean distance A w ill depend on the diameters o f both ions, especially i f there is a great difference between the two diameters, as in sodium and urate ions. Thus the mean distance A should be expressed as A = Y (da+dg) , I I 1-36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 where and dg are the ions' diameters. From Eqs. III- 3 2 , III- 3 5 and I II - 3 6 , Eq. III-3 0 c becomes * “ "a"b F " ) III- 3 7 The frequency facto r expressed in Eq. I I 1-37 implies that a ll collisions lead to nucléation which is not true fo r ions in solutions. W hen solid solute dissolves in solutions the solid la ttic e structure is immensely disturbed (high entropy). Thus the ions before they are able to nucleate must be oriented and in order close to that in the solid la ttic e . Thus there w ill be a large decrease in entropy which would lower the pro b ab ility of what one might c a ll e ffe c tiv e or productive co llisio n s. The probability facto r P can be approximated by AS. P exp — g— , 111-38 where AS^ is the entropy of c ry s ta lliz a tio n . However, near T^, AH. AS^ = , III- 3 9 e where AH^ is the heat of c ry s ta lliz a tio n (defined to be negative when heat is evolved upon c ry s ta lliz a tio n ) and T^ is the equilibrium temperature. From Eqs. III- 3 8 and III- 3 9 , Eq. III- 3 7 becomes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 From Eq. I II- 3 1 , we find that ^ A"deh * where is the heat of dehydration. From Eqs. III- 4 0 and III- 4 1 , the general expression fo r the k in etic constant fo r the nucléation of Ionic compounds can be w ritten as where Z Is the nonequilibrium facto r given In Eq. III- 2 5 . From classical nucléation t h e o r y , Z Is given as ( AG* \ 1/2 \3wkT1*2/ Z = , III-4 2 b where A G Is the c r itic a l free energy of nucléation, 1 Is the number of molecules In the c r itic a l embryo, 1* = 2 n (r*)3 g- N , III- 4 3 r Is the embryo c r itic a l radius, p Is the density of the c ry s ta l, M Is the molecular weight, and N Is Avogadro's number. From Eqs. III- 1 9 and III- 2 0 I t Is seen that AG* = I ïï(r*)^ AGy . I I 1-44 Substituting Eqs. I II- 4 4 , III- 4 3 and III- 2 4 Into Eq. III- 4 2 , the nonequilibrium facto r Z becomes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M 4 ïï(r ) pN 2r*Np (CAifCg) 55 1 1/2 III-45 • 3 The nonequilibrium factor Z has a value of the order 10’ and can be approximated by a constant. From Eq. I I 1-42 we see th at the kin e tic constant A is proportional to the concentrations product as expected fo r ionic compounds. The fin a l expression fo r nucléation rate of ionic compounds from th e ir aqueous solutions is J V b - t r ) ’ ★ where A G is the c r itic a l energy of nucléation and is given by AG* = A , I I 1-47 3[kT in a T where y is the surface energy, v is the molecular volume and a is the supersaturation r a tio , expressed as the ra tio of the actual concentration product to that a t saturation. 8 . Discussion Comparing the values of the nucléation kin e tic constant A c a l culated from Eq. III- 4 2 with the experimental values reported by Melia and M o ffit,^ ^ *) we see that Eq. III- 4 2 predicts higher values than the experimental values, but m uch lower values than those pre dicted by the classical nucléation theory, as shown in Table I I I - 2 . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 TABLE I I 1-2 Values of the Kinetic Constant (A) Solute Experimental A cm"^sec"^ Theoretical Equation^*^) -3 -1 A cm sec Classical The.ry(®")-(®®) -3 -1 A cm sec NH4CI 31 10^ lo^o NH^Br 15 106 10^0 K N O 3 3.4 X 10^ lo'O lo^o NaHU (mono- sodium urate) 10® 10^0 The detailed calculations of the theoretical kin etic constants A fo r nucléation of NH^Cl, NH^Br and NaH U are shown in Appendix A. The number o f water molecules n^ replaced from the ion hydration sheath was assumed to be one fo r estimation of a ll values of the kin etic constant shown in Table I I I - 2 , column 3. In estimating the activa- * tion energy A E in Eq. I I I - 4 1 , the dehydration energy used in Eq. III- 4 2 was the one that gave the minimum activatio n energy aE* required fo r th at p artic u la r ion to loosen its hydration sheath. In other words, i f we had two ions and both of them were hydrated, th e ir activation energies were calculated from Eq. I II - 4 1 , and then the one that gave the lowest activation energy was used to estimate the kin etic constant in Eq. III- 4 2 . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 From the foregoing we see th at fo r nucléation from aqueous solutions the nucléation kinetic constant (pre-exponential facto r) is not a universal constant. Equation III- 4 2 shows th at fo r nucléa tion from aqueous solutions, A depends on the concentration product and on the ions' hydration energies. Thus fo r the nucléation of ionic compounds from th e ir aqueous solutions, the hydration energy represents a hindrance to nucléation. The ions must lose some of this hydration energy before they are able to nucleate. The values of the kinetic constant predicted by Eq. III-4 2 agree with experimental values on the order 10^® chosen by most a u t h o r s . ^ The low experimental values of the kin etic constants shown in Table I I I - 2 as compared to those predicted by Eq. III- 4 2 may be attrib u ted to the uncertainty in estimating the nucléation time which is required fo r nuclei to appear. For ionic compounds the c ritic a l embryos are on the order of 20 A in c r itic a l length^^®^^ so that the waiting time fo r the c r itic a l nuclei to grow to a detectable size is re la tiv e ly long. This long incubation time would lower the nucléation rate when counted as number o f nuclei per unit tim e, and therefore would decrease the experimental value of the nucléation k in e tic constant. I t should be pointed out that Eqs. III- 4 2 and III- 4 6 can be generalized to any solvent. One simply replaces the hydration energy by the solvation energy fo r the p a rtic u la r solvent. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 D. Heterogeneous Nucléation Although homogeneous nucléation does occur and is frequently studied, heterogeneous nucléation is the most com m on form encountered in practice. The underlying postulates which govern heterogeneous nucléation kinetics are sim ilar to those fo r homogeneous nucléation, except that in heterogeneous nucléation, the presence of a catalyzing substrate lowers the surface energy required fo r nucléation ( i . e . , lowers the energy b a rrie r). In addition, soluble and insoluble impurities by th e ir influence on the surface energy may a lte r the supercooling required fo r nucléation, and thus s h ift the m etastab ility lim it. Telkes^^^) found that when sodium su lfate decahydrate was crys tallized in the presence of a small amount of sodium tetraborate decahytrate, the supercooling needed was about 30% of that in a pure solution. I t has been observed that c ry s ta lliz a tio n from a super saturated solution is more lik e ly to be catalyzed by a solid i f the formed crystal and it s substrate are sim ilar in atomic arrangement and la ttic e spacing. 1. Thermodynamics o f Heterogeneous Nucléation Since the presence of a c a ta ly tic surface can lower the m etastability lim it, the activatio n energy required for heterogeneous if nucléation, AG^^, must be less than the corresponding activatio n energy fo r homogeneous nucléation, i . e . , AG = ÿAG^j , I I 1 -4 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 where the facto r ( p is less than unity. In treating such nucléation, consider a spherical cap of radius r of C phase (c ry s ta l) on a f l a t substrate S, and a bulk phase L as shown in Figure I I I - 8 . The three in te rfa c ia l energies shown in Figure I I I - 8 are designated by Yqi_. Ygg and Yj l * Balancing these forces in the horizontal direction^^^^ YSL " Yes + YCL COS G , IH -4 9 where 6 is the equilibrium contact angle between the c ry s ta llin e deposit and the substrate. For the configuration shown in Figure I I I - 8 , the Gibbs fre e energy of the cluster is^^®^ AG jh = y (2 + cos 0)(1 - cos e)^AG^ 2 2 + Tr(r sin 9 ) Ygg - Tr(r sin 0) Y5L + 2n r^ (l - cos 0)Yql • III- 5 0 From Eq. I I I - 4g and setting (3AG/3r) = 0 in Eq. III - 5 0 , we get 2 * ^CL r . 3 5^ . III-5 1 and AGuT = -IV ■ " (2 +.cps 6 ) ^ III- 5 2 Substituting Eq. III- 3 0 into Eq. III- 2 6 we get ( |) = 0 90s 8) ( 2 + cos 0) ^ III- 5 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 Crystal Solid Surface (substrate) Figure I I I - 8 . Surface Energies fo r Heterogeneous Nucléation on a Substrate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 Equations III- 3 0 and III-3 1 show that the activatio n energy fo r nucléation on a substrate should decrease with decreasong contact angle (0 ). For the case of complete w etting, 0=0, and the free energy o f nucléation goes to zero, as in the case of seeding super saturated solutions with tin y crystals. Thus no supersaturation would be required fo r nucléation with such a substrate (4> = 0 ). W hen the c ry s ta lliz a tio n solid and foreign substrate exh ib it complete non wetting (0 = i t ), the free energy of nucléation is the same as that fo r homogeneous nucléation (((, = 1). For heterogeneous nucléation of ionic compounds from aqueous solutions on a solid substrate and fo r Eq, III- 4 7 to hold, the ions must be p a rtia lly desolvated before being absorbed on the substrate in order to come in contact with the substrate. Thus the activated state model discussed previously for homogeneous nucléation is manifested also in case of heterogeneous nucléation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IV EXPERIMENTAL W O R K A. Preparation of Monosodium Urate Monosodiutn urate was prepared according to the method of S e e g m l l l e r . F i r s t , 8.05 g m of commercial u ric acid (J. T. Baker Chemical Co., Phllllpsburg, N ew Jersey) was dissolved In 1600 ml of boiling water containing 48 m l of IN NaOH. The solution was s tirre d u n til a ll of the uric acid was dissolved. The pH of the solution was adjusted to the physiological pH, 7 .4 , by addition of drops of hydrochloric acid. The solution was s tirre d and rapidly filte re d . The filte re d solution was covered and cooled slowly at room tempera ture (24°C), and then allowed to c ry s ta lliz e overnight. Seegmlller f ir s t cooled the solution at room temperature, and then stored I t overnight a t 5°C. In our method of preparation, monosodium urate was precipitated a t room temperature Instead of 5“C because of the following: 1. C ry s ta lliza tio n at 5°C Is very rapid, yielding prim arily amorphous product. 2. P recipitation at 5°C might resu lt In postprecipitation of Im purities. The monosodium urate crystals were separated from the mother liq u id by f iltr a t io n and then washed several times with d is tille d 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 water. The sodium urate crystals were collected and dried a t 60°C to constant weight for about three hours. B. Assay of Prepared Monosodium Urate F irs t the precipitated monosodium urate was examined under the polarizing microscope using a firs t-o rd e r red compensator. This revealed needle-like crystals approximately 100 microns in length and 2 microns wide. W hen the f ir s t red order compensator was inserted into the microscope and the stage was rotated so that the long axis o f the crystal was parallel to the axis of the slow vibration of the compensator, the crystals were yellow. This negative birefringence is a characteristic of monosodium urate cr y s ta l s . ^ Upon comparing our monosodium urate with the commercial sodium urate (K & K Laboratories, In c ., Plainview, New York), i t was found that our sodium urate crystals were larger and much b etter formed than the sodium urate bought from K & K Laboratories (see Figures IV-1 and IV -2 ). Monosodium urate crystals prepared in our laboratory and crystals obtained from a gout tophus were examined with a scanning electronic microscope. At 1000 X some urate crystals were long with p arallel sides and ends which tapered to a fin e point, while other crystals were rod or needle shaped. A th ird type of crystal had p arallel sides and were shaped lik e a bar (see Figures IV -3, IV-4 and IV -4 ). This observation Is in agreement with that of J. M. Riddle and co-workers(23) who examined a gouty tophus using a transmission Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 Figure IV -1 . Photograph of Monosodium Urate Crystals Prepared in our Laboratory, 42X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 Figure IV-2. Photograph o f Monosodium Urate from K & K Laboratories, In c ., Plainview, New York, 42X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 Figure IV-3. Scanning Electron Micrograph o f Monosodium Urate Crystals Grown in our Laboratory, 3000X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 Figure IV-4. Scanning Electron Micrograph of Monosodium Urate Crystals from Tophus of a Gout P atien t, lO O O O X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Figure IV-5. Photograph of Monosodium Urate Single Crystal Grown from Pure Monosodium Urate Solution of 7.7 X 10-3 M NaHU and Refrigerated at 5°C fo r a Week, 42X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 electron microscope. X-ray powder d iffra c tio n provided a d e fin itiv e and more affirm ative means of establishing the id e n tity of monosodium urate. Thus a powder sample of our monosodium urate was prepared and a comparative d iffra c tio n pattern was produced using a N i-filte r e d C u radiation tube. The relationship between the measured angle 0 and the interplanar spacing d characteristic of c ry s ta llin e monosodium urate is given by Bragg's formula: where X is the wave length of the X-radiation used. For N i-filte re d O Cu rad iatio n , X = 1.542 A. The results of X-ray d iffra c tio n compare very well with the standard pattern of monosodium urate established by Howell, Eanes and Seegmiller^^^ as shown in Table IV-1. C. Description of the Experimental Apparatus The M ettler FP2 hot stage (M ettler Analytical and Precision Balances, C M - Greifensee-Zurich, Switzerland) shown in Figures IV-6 and IV-7 was designed fo r a variety of thermomicroscopic analyses over the temperature range -20°C to 300°C. Fresh supersaturated solution was put into the cavity of a slid e and sealed, as shown in Figures IV- 8 and IV -9. The heating plates on both sides elim inated the v e rtic a l temperature gradient, which is in evitab le when the specimen is only heated from below as in conventional hot stages. To prevent adjacent parts of the microscope from damage by over-heating, the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 TABLE IV-1 X-Ray Powder D iffractio n Spacing Data of Monosodium Urate Monosodium Urate Prepared in Our Laboratory d(A) Monosodium Urate Standard^ ^ ) d(A) Tophus of Gouty Patient^ 2) d(A) 7.45 7.61 7.58 5.24 5.3 5.32 4.95 4.92 4.95 4.62 4.7 4.69 4.46 4.54 4.54 4.32 3.54 4.39 3.5 3.50 3.48 3.42 3.4 3.4 3.26 3.28 3.31 3.14 3.16 3.15 3.02 3.04 3.06 2.96 2.89 2 .8 8 2.85 2.82 2.81 2.64 2.66 2.72 2.52 2.53 2 .66 2.45 2.46 2.54 2.4 2.41 2.47 2.36 2.36 2.41 2.27 2.36 2.17 2.29 2.13 2.13 2.19 2.04 2.04 2.14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 Figure IV -6 . Photograph of M ettler FP2 Hot Stage and Controls Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■ o o Q . C g Q . ■ O CD C/) o " 3 8 ■ O v < ë ' 3 CD C p. CD ■ O O Q . C a O 3 ■ O O CD Q . O C ■ O CD C/) o " 3 Window Sample Carrier Microscope Mirrored Housing Heating Plates Air Fan Injection hole for cooling below ambient Figure IV-7. Diagram of M ettler FP2 Hot Stage ' s j ro 73 Figure IV -8 . A Photograph of a Microscope Slide with Mono sodium Urate Solution in the Cavity, Sealed with a Cover Glass and Epoxy Cement Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 EPOXY CEMENT GLASS COVER MICROSCOPE SLIDE SOLUTION Figure IV-9. Schematic Diagram of a Microscope Slide Sealed with a Cover Glass and Epoxy Cement Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 specimen was enclosed by a mirrored housing, giving radiation re fle c tio n , and by a current of a ir delivered by the fan. The upper window was also a heat-shield f i l t e r . The temperature was measured by a platinum resistance thermometer, which is embedded in the lower heating p late. There were available three lin e a r rates of temperature programming: 0 .2 , 2 and 10°C per minute. These pro gramming rates were autom atically controlled, and could be pre selected by operating the push-buttons on the control panel. In addition, other push-buttons could override those controls and enable the temperature to be brought rapidly to w ithin the desired range. The temperature could be programmed up or down and was con tinuously recorded d ig ita lly at the top of the panel. Temperatures of specific events (s o lu b ility , nucléation, e tc .) could be recorded d ig ita lly at three lower positions on the panel by pressing the appropriate button on the hand control unit. A Leitz Ortholux Polarizing Microscope was used with objective lO X/0.18, which had a free working distance suitable fo r use with the hot stage. A Sage C inephotomiorographie Apparatus, Series 500 (Sage Instruments, In c ., White Plains, N ew York), was also used fo r time lapse photography. (See Figure IV -10). D. Method of Determining the S o lu b ility and Nucléation of Monosodium Urate in Aqueous Solution____________ In the beginning of this research, several d iffe re n t cells were designed and trie d fo r the observation of dissolution and nucléation of monosodium urate crystals under the microscope: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 Figure IV-10. Photograph of the Assembled Experimental Apparatus Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 1. A c a p illa ry tube was f ille d with a supersaturated solu tion of monosodium urate, and cement applied to the open end. W hen the cap illary tube was placed in the hot stage and heated, convection currents and the c a p illa ry tube curvature made i t impossible to observe the crystals as they dissolved and so th is cell was discarded. 2. A hole of 4 m m was d rille d in a standard microscope s lid e , and then a cover glass was placed over the hole and sealed with epoxy. Monosodium urate was introduced in the hole of the slid e (turned over), but i t was d iff ic u lt to seal the hole without trapping a ir bubbles. Moreover, sharp edges of glass were observed protruding from the inside of the hole. This discouraged us from using this cell to study nucléation. 3. F in a lly , a commercial microscope s lid e with a polished depression of 18 m m diameter and 0 .8 m m depth was used as a c ry s ta lliza tio n c e ll. Fortunately i t suited our experiments and required much less time fo r preparation than the previous c e lls . By f illin g the slid e cavity with its exact volume of solution, and carefu lly sliding the coverglass and cementing i t with epoxy, a ir bubbles and resulting evaporation problems were avoided. By use o f the microscope hot stage in polarized lig h t, s o lu b ility and nucléation were observed in the same experiment. Solutions of known monosodium urate concentrations were prepared using semiconductor-grade deionized water. A ll weights were determined by M ettler semi-micro balance (Model H20) which had a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 d ig ita l display showing the weight on the pan to yg. Microscope slides with a single depression of 18 m m in diameter and 0 .8 m m in depth were used as c ry s ta lliz a tio n c e lls . Upon preparing a known concentration of monosodium urate solution, the following steps were taken: 1. A desired amount of monosodium urate was weighed into a clean volumetric flas k. 2. Deionized water was added and weighed. 3. The solution in the volumetric flask was heated close to the boiling point in order to dissolve a ll the crystals and protect the solution from bacterial attack. 4. A fter the solution was cooled to room temperature, the cavity of a m icro-slide was f ille d with the solution using clean disposable c a p illa ry pipets. The slid e was sealed by a cover glass and epoxy cement (see Figure IV -8 , 9 ). The slides were boiled and rinsed in deionized water ju s t p rio r to f il li n g . W hen the cement had s e t, the slides were refrig erated overnight to induce c ry s ta lliz a tio n . For every point on the nucléation and s o lu b ility curves, a minimum of three slides were prepared and studied. 5. A fter refrig era tin g a s lid e overnight, i t was taken out and heated in the hot stage under the polarizing microscope. For rapid in it ia l estimation of the s o lu b ility temperature of a given concentration, the slid e was heated a t 2°C per minute. The Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 approximate s o lu b ility temperature was Indicated by dissolution of a ll crystals. Subsequent slides were heated at a slower ra te , 0.2°C per minute. W hen the crystals ju s t began to noticeably dissolve, the heating was Interrupted and the temperature kept con stant u n til the system had reached equilibrium . A minimum In terval o f one hour was allowed for the system to e q u ilib ra te . This Interrup tion of heating and approaching the s o lu b ility temperature very slowly was repeated u n til a ll crystals had dissolved. This temperature was registered on the hot stage panel and was the s o lu b ility temperature. The s lid e was then cooled at 0.2°C per minute. The cooling was Interrupted p erio d ically and the slid e examined fo r the presence o f tin y crystals. W hen crystals f ir s t began to appear, this temperature was registered and i t marked the nucléation temperature. The difference between the s o lu b ility and the nucléation temperatures marked the c r itic a l supercooling necessary fo r nucléation. From the experimental observations. I t was found th at the temperature a t which a ll the crystals dissolved depended on the heating rate. For a fixed concentration of monosodium urate solution, the observed s o lu b ility temperature increased as the heating rate Increased, as shown In Figure IV-11. This departure of the observed temperature from the equilibrium temperature was due to the fa c t that the crystals were not In equilibrium with the solution, and that Is why a very slow heating ra te , accomplished by Interruption of heating, was required to allow s u ffic ie n t time fo r diffusion to take Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 65 o o W (T 3 01 UJ I 60 w h- >■ h- O Q 3 0 W > 0 1 UJ </) 00 o True solubility temperature 50 Figure IV-11. Dependence of the Observed S o lu b ility Temperature on the Heating Rate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 place (see Appendix D fo r theory). From Figure IV-11, the true s o lu b ility temperature is the one at which the crystals would dissolve i f they were held a t th at constant temperature without heating; in other words, a heating rate o f zero. As shown in Figure IV-11, the difference between the observed s o lu b ility tempera ture and the equilibrium one is 1.5°C fo r a heating rate of 0.2°C/min. This would introduce 6% error in the 25°C supercooling required fo r nucléation. Therefore, in determining a ll of the reported s o lu b ility data, the heating of the slides at 0.2°C/min was interrupted p erio d ically and the s o lu b ility temperatures were approached very slowly; in other words, at a rate much slower than 0.2°C/min. Thus the error in the measured supercooling must be much lower than 6%. Likewise, one would expect that the nucléation temperature would have been dependent on the cooling rate and that too low a value would have been obtained i f the solution was cooled too rapidly. Therefore, re p e titiv e interrup tion of cooling to hold the slides a t constant temperature fo r as long as three hours was used throughout a ll of the nucléation experiments, in order to be certain that the true nucléation temperature was not passed. I f there were tin y crystals that did not dissolve upon heating the microscope s lid e , these tiny crystals would s ta rt to grow and appear long before observation of the true nucléation temperature. This tempera ture at which these tin y crystals grow and become observable might be Confused with the nucléation temperature. Thus, to avoid such confusion, slides were held at a temperature s lig h tly above the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 nucléation temperature fo r as long as three hours. No crystals were observed. A fter th a t, the temperature was slowly lowered by 1 to 2°C and kept constant fo r at least two hours. This procedure was repeated u n til nucléation did occur. The average to tal time required from the s ta rt of cooling to the observation of nucléation was about seven hours. E. Results fo r Pure Water The experimental results o f nucléation and s o lu b ility of monosodium urate in pure water are shown in Figure IV -12, and are tabulated in Appendix B. The c r itic a l supercooling necessary for nucléation of monosodium urate in pure water was approximately 25°C, which is substantial. An Arrhenius plot was used to fin d the c r itic a l supersaturation ra tio a (the ra tio of the concentration product fo r nucléation to the concentration product at saturation) fo r nucléation a t body temperature, 37°C. This is shown in Figure IV-13, with the lines determined by a least squares f i t . From the least squares calcu latio n , the concentration product fo r the s o lu b ility of monosodium urate in pure water can be expressed as: [ [ V n ,* ] L0 9 | | C , ,C „ t | X 10® = -2.653 x 1 0 ^ 1 + 9.022 , IV-2 where Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 3.2 3.0 2.8 2.6 C 7» Q2.4 NUCLEATION o SOLUBILITY u 1.4 20 30 40 50 60 70 80 TEMPERATURE (*C) Figure IV-12. S o lu b ility and Nucléation of Monosodium Urate in Pure Water Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 T ( * ( : ) 7 0 m 50 40 30 20 2 0 rj (M 5 - ? 1 0 - NUCLEATION CM SOLUBILITY "^.9 3.0 3.1 3.2 l / T (“K ''x lO ’ ^) 3.3 3.4 Figure IV-13. S o lu b ility and Nucléation of Monosodium Urate in Pure Water. C is the Monosodium Urate Concentration in the Solution Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 is the total urate-uric acid concentration, is the sodium ion concentration, and T is the absolute temperature in degrees Kelvin. For the nucléation curve the concentration product of mono sodium urate in pure water can be correlated as Log [^u‘ V ] n X 10' = -2.273 X lO^ 1 + 8.433 IV-3 From Figure IV-9 or using Eqs. IV-2 and IV -3 , the c r itic a l supersaturation necessary fo r monosodium urate nucléation in pure water at 37° is a = CNa+ C u n _ = 4 .3 , where the subscript n denotes the minimum product at which nucléation was observable, and e denotes the product a t equilibrium (s o lu b ility ). F. Estimation of the Heat of Solution and Surface Energy o f Monosodium Urate in Pure Water______ 1. Heat of Solution From Eqs. I I 1-2 and IV-2 the heat o f solution of monosodium urate in pure water can be calculated as follows: A H 2.303R * = 2.653 X 10^ Therefore, A H g = 2.303 X 1.987 x 2.653 x 10' = 12,000 ca l. per gram mole . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 Allen^®^^ reported that the heat of solution fo r monosodium urate AH^ is 571.7 calories per gram mole. This value is erroneous fo r the following reasons: 1. A l l e n , f r o m his data, obtained an Arrhenius slope of -1.132 X 10^. Instead of m ultiplying by R, he divided by R. 2. Allen plotted the s o lu b ility only and not the s o lu b ility product, but he forgot to carry the necessary facto r of 2 as shown in Eq. III- IO . 3. He omitted the conversion fa c to r, 2.303, of the natural logarithm. 3 Thus, recalculating from his slope, -1.132 x 10 , the heat of solution of monosodium urate based on A llen 's data should be: A H g = 2 X 1.132 X 10^ X 2.303 x 1.987 = 10,400 calories per gram mole This value of 10.4 Kcal obtained from A llen's data is in f a ir agree ment with the value 12 Kcal reported in this work. The heat of solution of uric acid in pure water was estimated from the lite ra tu re s o lu b ility data to be 6 Kcal/mole. 2. Surface Energy From the d e fin itio n of the c r itic a l supercooling and the classical nucléation theory, the surface energy can be calculated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 from nucléation data by (see Chapter I I I ) : Y = 3(Log A )(2 .y 3 RT)^(Log o)^ 161T « 2 «3 1/3 IV-4 The kin etic constant A should be the one derived in Chapter I I I fo r nucléation of ionic compounds. For monosodium urate, the estimated Q value of A is 10 , as was shown in Chapter I I I . The supersaturation ra tio o fo r monosodium urate nucléation in pure water at 37°C is 4.3. Substituting the above values in Eq. IV -4 , the surface energy 2 of monosodium urate was estimated as 19 erg/cm , which is on the order of magnitude of those values obtained fo r sim ilar substances. For example, from nucléation data the in te rfa c ia l energy between liq u id and solid phase of cholesterol was found to be 17 erg/cm^. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V THE INFLUENCE O F ADDITIVES O N SOLUBILITY A N D NUCLEATION O F M O NO SO DIUM U R A TE Som e impurities may catalyze nucléation, i . e . , lower the supersaturation necessary fo r nucléation. These kinds of additives are termed nucleators or nucleating agents. Other additives may in h ib it or retard nucléation, i . e . , increase the supersaturation necessary fo r nucléation and s ta b iliz e the solution. These kinds of additives are termed nucléation in h ib ito rs . Diluted solutions of synovial flu id s from a gout patient and two rheumatoid patients were tested fo r th e ir influence on nucléation and s o lu b ility of monosodium urate. Since the behavior of monosodium urate in synovial flu id may be influenced by the presence of the other ions present in synovial flu id , sodium chloride, potas sium chloride and calcium chloride were also used as additives and tested fo r th e ir separate influence on the nucléation and s o lu b ility of monosodium urate. Because of the h is to ric connection between overindulgence and gout, ethyl alcohol was also tested fo r its influence on monosodium urate s o lu b ility and nucléation. A. Influence o f Ethyl Alcohol In order to test the influence of alcohol on the s o lu b ility and nucléation of monosodium urate, the following experiments were carried out. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 Solutions of known concentrations of monosodium urate were prepared in deionized water. One m l of ethyl alcohol was added to three ml of each monosodium urate solution which yielded 25% v of ethyl alcohol in solution. Ethyl alcohol was added a fte r the preparation of supersaturated monosodium urate solutions in order to prevent the loss of the v o la tile ethyl alcohol upon heating the monosodium urate solutions. Microscope slides were prepared from monosodium urate solutions which contained 25% v ethyl alcohol. These slides were tested in the hot stage as described in Chapter IV. 1. Result and Analysis Although 25% v of ethyl alcohol is not possible physiologically, there was a remarkable e ffe c t of ethyl alcohol on both the s o lu b ility and nucléation of monosodium urate. Addition of 25% ethyl alcohol reduced the s o lu b ility of monosodium urate by about 3X as compared to that in pure water. From the experimental data and least squares calculatio n, the concentration products of monosodium urate in 25% v ethyl alcohol as a function of temperature are expressed as: Log and fo r nucléation Log X 10' -2.59 X 10' + 8.353 , V-1 X 10' -2.11 X 10' + 7.321 V-2 The plots of Eqs. V-1 and V-2 are shown in Figures V-1 and V-2. The c r itic a l supersaturation necessary fo r monosodium urate nucléation in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 T(®C) 60 50 20 I 0 - - C M m 3 u + o 2.925 3.0 3.15 Figure V-1. The Influence of Additives on the S o lu b ility of Monosodium Urate 1. 0 : Pure Water 2. + : 25% V Ethyl Alcohol 3. © : Cga++ = 0.031 C^g+ via CaClg Addition 4. C |^ + = 0.965 0^^+ via KCl Addition Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 40 30 20 2 0 1 0 — X 3.15 3.2 3.3 3.4 Figure V-2. The Influence of Additives on the Nucléation Temperature of Monosodium Urate 1. 0 2. + 3. © 4. © Pure Water 25% V Ethyl Alcohol Cgg++ = 0.031 C^g+ via CaClg Addition C |^+ = 0.965 C^g+ via KCl addition Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 25% V ethyl alcohol a t 37°C was found to be 3 .3 , which is less than that required in pure water. In addition, i t appeared from the experimental observation that monosodium urate crystals grew longer in ethyl alcohol, o r, in other words, ethyl alcohol appeared to accelerate the axial growth of monosodium urate. From Eq. V-1, the heat of solution of monosodium urate in 25% v ethyl alcohol was found to be 11.8 Kcal per gram mole. This value is close to that in pure water. I t should be pointed out th at according to the Los Angeles Police Department, the percentage of alcohol in urine of an intoxicated person is 2.5% v and th at in blood is about 0.3% v. These percentages are much lower than the ones used in our experiments. By lin e a r interp olation between the results of mono sodium urate nucléation in pure water and that in 25% v ethyl alcohol in aqueous solution, the supersaturation ra tio required fo r mono sodium urate nucléation in aqueous solution of 0.3% v ethyl alcohol is 4 .2 , which is the same as that in pure water. B. Influence of Synovial Fluid from a Gout Patient Synovial flu id of a gout patient was obtained from the University of Southern C alifo rn ia Medical School. The synovial flu id was centrifuged and filte r e d in order to separate the c ells and mono sodium urate crystals already present. F irs t an attempt was made to dissolve these monosodium urate crystals in the synovial flu id by heating and without d ilu tio n with deionized water. This process Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 required high temperatures which made the flu id gelatinous, in turn making i t d iff ic u lt to id e n tify monosodium urate crystals. There fo re , solutions of known concentrations of monosodium urate were prepared in deionized water, then 2 ml of each of these solutions were added to 0.1 ml of the synovial flu id , so that the solutions contained 5 % v of synovial flu id . Microscope slides were prepared from the above solutions and experiments were conducted in the hot stage as discussed in Chapter IV. 1. Results and Analysis From the experimental data, the s o lu b ility of monosodium urate in 5 % v synovial flu id o f a gout patient was much lower than th at in pure water. This decrease in s o lu b ility was due prim arily to the presence of sodium ion (common ion e ffe c t) in the synovial flu id . In calculating the concentration product at saturation, the synovial flu id was assumed to contain 0.15 M NaCl and then the to tal concentration of sodium ion was calculated. The concentration products of monosodium urate as a function of temperature in solution of 5% v synovial flu id from a gout patient are expressed from the experimental data and least squares calcula tion as: ,3 ‘■ 09||C„C„ *1 X 10® X 10 + g ^ g g v_ 3 fo r s o lu b ility , and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. '■»9 j [ w ] ^ X 10= 3 = ^ + 9.16 94 V-4 fo r nucléation. The data and plots of Eqs. V-3 and V-4 are shown in Figures V-3 and V-4. The c r itic a l supersaturation, a, necessary fo r nucléation of monosodium urate in solutions of 5 % v of synovial flu id of a gout patient was 4.2 at 37°C. C. Influence of Synovial Fluid from Rheumatoid Patients Synovial flu id from a rheumatoid patient on aspirin therapy was obtained from the University of Southern C alifo rn ia Medical School. The synovial flu id was centrifuged and filte re d and then diluted with known concentrations of monosodium urate solutions in order to make up solutions of S % v synovial flu id . Microscope slides were prepared from these solutions, and hot stage experiments were conducted 1. Results and Analysis The s o lu b ility of monosodium urate in 5 % v of the rheumatoid patient synovial flu id was close to th at in the gout patient synovial flu id . The concentration of sodium ion was assumed to be the same (0.15 M) in both synovial flu id s . The concentration products as a function of the temperature fo r s o lu b ility are cor related by ,3 i W , Logl|c„c„ + 1 X 1 0 = -2 .5 16 X 10~ ^ g 55J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (On following page) Figure V-3. The Influence of Various Additives on the S o lu b ility of Monosodium Urate in Aqueous Solutions 1. 2. 3. 0 * Pure Water 7.5 X 1 0 " 2 M NaCl 5 % V Synovial Fluid from Rheumatoid A rth ritis Patient 5 % V Synovial Fluid from Gout Patient 5. 5 X 10 M CuCl, 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. \ 2.950 5-0 I 1 3 3.1 '/tCK'X 1 0 1 3.175 Figure V-3. The Influence of Various Additives on the S o lu b ility o f Monosodium Urate in Aqueous Solutions Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (On following page) Figure V-4. The Influence of Various Additives on the Nucléation of Monosodium Urate in Aqueous Solutions 1. 0 : Pure Water 2. * : 7.5 X lO'S NaCl 3. Û : 5 % V Synovial Fluid from Rheumatoid A rth ritis Patient 4. o : 5 % V Synovial Fluid from Gout Patient 5. + : 5 X 10"® M CuClg 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 20 I 0 - - C M S in g X 3 H Z O 3.2 Figure V-4. The Influence of Various Additives on the Nucléation of Monosodium Urate in Aqueous Solutions Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 and fo r nucléation are correlated by .3 Log X 10^ 2.3 752 _ x 10 + 13.258 . V-6 The plots of the experimental data are shown in Figures V-3 and V-4. The c ritic a l supersaturation, o, necessary to nucleate monosodium urate in 5 % v of rheumatoid patient synovial flu id at 37°C has a value of 5.3 , which is higher than that in pure water or in the synovial flu id of a gout patient. Synovial flu id from another rheumatoid patient was obtained. This synovial flu id was centrifuged, but i t was not filte r e d . Solutions of known concentrations of monosodium urate and con taining 5 % V of this synovial flu id were prepared. From the experi mental data, i t was observed that monosodium urate had a higher s o lu b ility in this rheumatoid patient synovial flu id than that found previously in the gout patient synovial flu id and the other rheumatoid patient synovial flu id . In add ition , monosodium urate crystals grew as flakes joining a t th e ir tips and they were closer to being amorphous than to c ry s ta llin e (as shown in Figure V-5). These flakey crystals showed a very high s o lu b ility . In some concentrations, i t was close to that in pure water. Though these sem i-spherulitic crystals were very soluble, there were also present tin y crystals on the order of 10 u in s iz e , some of which dissolved at a temperature 5°C higher than the sem i-spherulitic crystals. Som e of these tin y crystals did not dissolve a t a ll upon heating. The apparent increase in monosodium urate s o lu b ility in this 5 % v rheumatoid patient Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 Figure V-5. Photograph of Monosodium Urate Crystals in 5% V Synovial Fluid of a Rheumatoid Patient Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 synovial flu id may be attrib u ted to bacterial growth in the synovial flu id , which would attack the monosodium urate in solution and lower the actual concentration of monosodium urate. A lte rn a tiv e ly , i t could have been due to the existence of a s o lu b ilizin g com ponent in the synovial flu id which would enhance the monosodium urate s o lu b ility . The c r itic a l supersaturation, a , necessary to nucleate monosodium urate at 37°C was found to be 5 .3 , about the same as in the f ir s t rheumatoid patient synovial flu id . D. Influence of Sodium Ion Experiments were conducted to test the influence of sodium ion on the s o lu b ility and nucléation of monosodium urate. A solution of 0.15 M NaCl was prepared fo r comparison with gouty and rheumatoid patient synovial flu id s . Monosodium urate solutions were prepared so that the sodium ion concentration in these solutions was equal to that in gouty and rheumatoid patient synovial solutions. A volume of 9.5 m l of each monosodium urate solution was added to 0.5 ml of 0.15 M NaCl solution. Microscope slides were prepared from these solutions. 1. Results and Analysis The s o lu b ility of monosodium urate in 0.075 M NaCl solution decreased as expected because of the com m on ion e ffe c t. From the experimental data the saturated concentration product as a function of the temperature was correlated by: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. |W , Loglic.c» + 1 X 1 0 ^ 102 2.2.86 X 10^ + 9.675 . V-7 'e The concentration product fo r nucléation was correlated by '■ ° 4 V N a * J „ * 10^ + 12.167 . V-8 The c r itic a l supersaturation, a, required fo r nucléation a t 36*C had a value of about 4 .5 , which is close to that obtained in pure water (4 .3 ). E. Influence of Potassium Ion Solutions of known concentrations o f monosodium urate were prepared with d iffe re n t ratio s of potassium ion to sodium ion. Potassium chloride was used as an add itive. From the hot stage experiments i t was found that addition of KCl up to (K^) = (Na*) increased the s o lu b ility of monosodium urate s lig h tly . The exper imental data are shown in Figure V-6 . I t was observed th at when the concentration of potassium ion exceeded th at of the sodium ion, many crystals precipitated. W hen these crystals were heated to 100°C, they did not dissolve. Presumably they were potassium urate. Addition of KCl did not influence the nucléation of monosodium urate. F. Influence of Calcium Ion The average concentration of calcium in blood plasma is 10 m g per 100 ml (2.5 x 10"^ M), although only about h a lf of this is in the form of free ion.(T04) has been observed that in cases of hyper- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 I.IO 1.05 1.00 0.2 0.4 0.6 0 .8 « y C no* Figure V-6 . The Influence o f KCl on the Relative S o lu b ility of Monosodium Urate a t 47 to 53*0. Here Sk is the S o lu b ility with KCl present and Sq is the S o lu b ility in Pure Water. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 calcemia, the renal excretion of calcium is increased and sometimes calcium stones deposit in the urinary tra c t and soft tissues. More over, the c lin ic a l observation that over 90% of gouty tophi contain calcium^^®®^ was an encouragement to te s t the e ffe c t of calcium ion on the nucléation and s o lu b ility of monosodium urate. Solutions of known concentrations of monosodium urate were prepared from solutions of known concentrations of calcium chloride. 1. Results and Analysis The s o lu b ility of monosodium urate was decreased markedly by addition o f small amounts of CaClg up to C^^++ * 0.04 0^^+. W hen the molar concentration ra tio of calcium to sodium exceeded 0.05, volu minous precipitates formed which did not dissolve upon heating to 100°C. Presumably they consisted of a mixture of sodium and calcium urates. The voluminous p recip itate produced from monosodium urate solutions containing 0^^++ > 0.05 0^^+ was filte r e d and collected fo r X-ray powder d iffra c tio n . Unfortunately, X-ray d iffra c tio n gave no d iffra c tio n peaks fo r id e n tific a tio n . Figure V-7 shows the influence of calcium on the s o lu b ility o f monosodium urate. Addition of CaClg showed that there was a dramatic enhance ment o f the nucléation of monosodium urate. Both the s o lu b ility and supercooling ra tio fo r nucléation were reduced by Ca**. From microscope observation, i t was noted th at calcium ion accelerated the axial growth of crystals. Crystals grown from solutions con taining Ca** were much longer than those grown from pure solutions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 0.9 0.8 0.7 0. 8 0. 01 ^ C o + */ Cwo 0.02 0.03 Figure V-7. The Influence o f CaCl2 on the Relative S o lu b ility of Monosodium Urate at 47 to 53®C. Here $ca is the S o lu b ility with CaCl2 Present and Sq is the S o lu b ility in Pure Water Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 Figure V-8 shows the resultant crys tals. The supercooling ra tio necessary to nucleate monosodium urate continued to decline as more CaClg was added, as shown in Figure V-9. The concentration product of monosodium urate required fo r nucléation at 32°C likewise decreased as the ra tio of calcium to sodium increased, as shown in Figure V-10. G. Influence of Copper Solutions of known concentrations of monosodium urate were prepared in 5 x 10~® M of cupric chloride solutions. The normal copper concentration in blood plasma is 0.1 m g per 100 m l (1.57 x 10"^ M). Microscope slides were prepared from these solutions. 1. Results and Analysis As shown in Figure V-3, the s o lu b ility of monosodium urate was not influenced by the presence of trace amounts of cupric chloride. Even though the molar ra tio o f cupric ion to sodium ion was six times higher in our experimental solutions than encountered in blood plasma, the cupric ion showed neg lig ib le e ffe c t on the nucléation of monosodium urate. The c r itic a l supersaturation required to nucleate monosodium urate in 5 x 10"® M CuClg at 37°C was 4 .2 , which is the same as that in pure water. From the least squares calculations, the concentration products a t s o lu b ility are correlated as ,3 Itu w ], L 0 9 | | C „ C „ * 1 x 10= + 9 .7 5 7 , v -9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 Figure V-8 . Photograph of Crystals from Monosodium Urate — CaCl? Solution with Cp.++ = 0.1 0^3+ , 42X Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 0.08 0.07 1 - ^ , 0.06 0.05 0.04 0 . 0 1 0.02 0.03 No Figure V-9. The Supercooling Ratio fo r Nucléation of Monosodium Urate as a Function of Added CaClo Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 I 0 < 5 > 0 .0 1 0.02 Figure V-10. The monosodium urate concentration required for Nucléation at 32°C as a Function of Added CaCl2 - C is the Concentration of Monosodium Urate. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. no and, at nucléation, LogllC.Cwa+l X ToS|= 2li453_x_lo2 + T2.2 . V-10 \ M „ The plots of the above equations are shown in Figures V-3 and V-4. H. Influence o f Collagen The precise s ite of the in it ia l monosodium urate deposition is unknown.Some investigators suggested th at monosodium urate crystals deposit in connective tissues because of th e ir collagen con te n t, which might act as the in itia tio n s ite fo r gout. I t was sug gested th at sodium urate deposition favors the collagen s ite because of the high amount of bound sodium concentration there, which might lower the sodium urate solubility.^ However, i t has been observed that protein polysaccharides, called PPL, extracted from bovine nasal c a rtilla g e , g reatly enhance the s o lu b ility o f monosodium urate. In order to investigate the p o s s ib ility of collagen acting as a substrate fo r nucléation of monosodium urate, collagen fib ers were placed in the cavities o f the microscope slides and solutions of known concentrations o f monosodium urate were added. The concentrations of the monosodium urate solutions were chosen such th at they would not nucleate at room temperature. W hen these microscope slides con taining monosodium urate solutions with collagen fib e rs were cooled below room temperature a t 0.2°C/min, the nucléation temperatures were the same as that fo r monosodium urate in pure w ater, without the addition of the collagen fib e rs . Furthermore, when nucléation did Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m occur, crystals appeared to nucleate away from the collagen fib e rs . A time-lapse photograph was taken fo r monosodium urate with a collagen fib e r (Figure V-11) during present nucléation and i t showed th at there is no evidence that collagen enhances the nucléation of monosodium urate. In a q u a lita tiv e experiment, a solution containing such a high concentration of monosodium urate that i t would p recip ita te spontaneously at room temperature was prepared and added to a collagen fib e r. Upon examination under the microscope with a 50 X objective, fewer and smaller crystals were formed on the collagen surface than elsewhere. This greater c ry s ta lliz a tio n away from the collagen fib e r suggests that collagen binds urate, so th at i t acts as a sink fo r monosodium urate producing an a c tiv ity gradient with the maximum in the bulk solution and the minimum at the surface of the collagen. For the chemical potential to be equal at the surface of the collagen and in the bulk solution, a s u ffic ie n t time is needed fo r eq u ilib ratio n . Therefore, the above experiments were repeated with collagen fibers which had already been dial 1 zed with monosodium urate solutions. Again the experimental observations showed no evidence fo r collagen enhancing the monosodium urate nucléation. One reason fo r suggesting that collagen might catalyze urate nucléation is that i t has been shown to cause hydroxyapatite nucléa tio n . However, i t was found th at only certain forms of collagen could catalyze the nucléation of hydroxyapatite.^^^^ The collagen structure is very sensitive to pH and various ions. Therefore, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 Figure V-11. Photograph of Collagen Fibers in Monosodium Urate Solution, Cooled to 16°C Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 another experiment was conducted, as follows: A buffered solution was prepared from monobasic and dibasic sodium phosphate with a pH value of 7.2 and a sodium ion concentration of 0.15 M. Monosodium urate was dissolved in 720 m l of this buffer. The concentration of monosodium urate was 5.78 x 10“^ M of the buffer. This solution was heated to 50°C to be sure of the dissolution of a ll monosodium urate. A fter the solution was cooled to room temperature in the d ialysis beaker, two d ialysis bags containing collagen fib e rs were f ille d with monosodium urate solution and placed in the dialyzing solution as shown in Figure V-12. To avoid the bacterial growth which destroys monosodium urate in solution, the dialysis apparatus shown in Figure V-11 was stored in the refrig e ra to r where the temperature was ~5°C. A fter three days of re frig e ra tio n , samples were taken from the monosodium urate solution inside and outside the dialysis bag. The samples from monosodium urate solutions were placed in the cavities of the microscope slides and glass covers were used to prevent evaporation. W hen these samples of monosodium urate were examined under the microscope, no needle crystals were observed in e ith e r solution, outside or inside the dialysis bag. A few very tin y crystals were observed in both solutions. A week la te r, samples were drawn from inside and outside the d ialysis bags and examined under the microscope. The very few tin y crystals were s t i l l present in both solutions. Moreover, some pieces of the collagen fib ers inside the bags were drawn. Upon examination under the microsocpe, there were no monosodium urate crystals to be seen Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 THERMOMETER MOTOR FOR STIRRING BAGS IN SOLUTION BAG HOLDER V » J N N ■ ■ C v \ • \ V « DIALYSIS BAG BEAKER Figure V-12. Diagram of the Dialysis Experimental Apparatus Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 attached to the collagen fib e rs . One should point out that the collagen fibers are also b iré frin g e n t, making id e n tific a tio n of monosodium urate crystals very d iff ic u lt and uncertain. In any case, from the experimental observations there was no noticeable d if ference between the monosodium urate solutions inside the d ialysis bag (with collagen) and the outside solution. The binding of monosodium urate to collagen was also in v e s ti gated by Dr. Rey Florendo at the U S C Medical School. A dialysis bag containing 1 cc of saline solution plus soluble collagen was placed in 100 cc of saline solution containing monosodium urate. The concentration of monosodium urate was determined by enzymatic d if fe re n tia l spectrophotometry over a week long period. The concentra tion of monosodium urate was found to be higher inside the bag than outside. The excess of the monosodium concentration inside the bag over that outside was attrib u ted to urate binding to collagen. The amount of bound urate increased with increasing collagen concentra tion as shown in Table V-1. TABLE V-1 Binding of Monosodium Urate by Soluble Collagen at 4°C Collagen Source Collagen Concentration Mg/100 cc Bound Urate MqNaHU/100 cc Bound Urate Collagen Hum an 43 1.6 0.037 Rat 63 2.33 0.037 Rat 190 5.04 0.027 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 Another experiment was performed by Dr. Florendo to in v e s ti gate the influence of collagen on monosodium urate nucléation. Supersaturated sodium urate solutions with d iffe re n t concentrations were dialyzed with collagen placed in d ialysis bags. The solutions from inside and outside the bags were sampled and observed under the polarizing microscope fo r the presence of crystals. I t was apparently found that for intermediate concentration ranges, crystals formed inside the bag, but not outside, thus indicating a nucléation enhancement e ffe c t fo r the collagen. The results are shown in Table V-2. Unfortunately, our experiments contradicted th is dialysis experiment. This discrepancy may be due to the fa c t that nucléation could occur during sampling. W hen a small drop of monosodium urate solution is placed on a microscope slid e even with a cover, evapora tion produces a high solute concentration causing rapid c ry s ta l liz a tio n . Moreover, nucléation might not have occurred a t a l l , with the experimenter being deceived by an a r tifa c t associated with the collagen fib ers because they too are b iré frin g e n t. Also, the con centration of 21.4 m g % in saline solution is approximately four times the s o lu b ility of N aHU at 4°C. Although our hot stage experi ments indicate that monosodium urate crystals should nucleate spontaneously a t this concentration. Table V-2 showed no crystals were present. A related observation was made by Katz and Schubert^^^^ who found that upon dispersion of a homogenate of bovine nasal c a r t il lage in the buffer of monosodium urate solution, the s o lu b ility of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q . C g Q . ■ D CD C/) o' 3 O CD 8 " O ë ' i 3. 3 " CD CD ■ D O Q . C a O 3 ■ D O CD Q . ■ D CD C/) C/) TABLE V-2 Apparent Enhanced Nucléation by Collagen Collagen Monosodium Urate Concentration of Outside Solution Content of Bag 7.6 m g % 10.0 m g % 15.1 m g % 21.4 m g % 27.7 m g % 0.43 mg/cc human collagen no crystals no crystals crystals in bag only crystals in bag only crystals in side and outside 0.63 mg/cc ra t collagen no crystals no crystals crystals in bag only crystals in bag only crystals in side and outside 0 saline no crystals no crystals no crystals no crystals crystals in side and outside 118 monosodium urate increased to 25.5 m g % compared to 5.7 m g % . A fter the incubation of urate-saturated bovine nasal c a rtilla g e with trypsin, v is ib le precipitation of monosodium urate crystals were observed. This indicates that when homogenate of bovine nasal is added to a metastable solution of monosodium urate, i t would increase the m etastability lim it and s ta b iliz e the solution (prevent precipi ta tio n ). I. Comparison of the Influence of Soluble Additives on Nucléation of Monosodium Urate_______________ The nucléation temperatures and the concentration products are shown in Figure V-2. At body temperature, 37°C, the influence of soluble additives on nucléation of monosodium urate is summarized in Table V-3. Calcium and ethyl alcohol showed the most dramatic e ffe c t on nucléation of monosodium urate a t 3I°C in 25% v ethyl alcohol or with addition of calcium ion of concentration equal to 3% of the sodium ion has a value of four times less than in pure water,as illu s tra te d in Table V-3. The concentration of ethyl alcohol, 25% v, is not possible in a liv in g human body, but the molar concentration of calcium a t which monosodium urate c ry s ta llize d at much lower supersaturation than in pure water is very small and close to that found in body flu id s . The concentration of calcium in the monosodium urate solution of 3 % molar ra tio of calcium to sodium was 1 m g %, which is 1/ 10th o f the concentration of calcium encountered in human plasma.Howeve r, the molar ra tio o f calcium to sodium in plasma is approximately 2% . This might indicate that the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE V-3 The Influence of Additives on Supersaturation Ratio and Concentration Product Necessary fo r Nucléation at 37°C 119 Additives Supersaturation Ratio ^^uSa'*’ * T O ] Pure Water 4.3 12.6 7.5 X lO'Z M NaCl 4.5 12.7 5 % V Fluid from Rheumatoid Patient 5.3 14.3 S % V Fluid from Gout Patient 4.2 9.35 25% V Ethanol 3.3 3.27 5 X 10"® M CuClg 4.2 11.5 CaClg at - - 3.16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 c ry s ta lliz a tio n of monosodium urate in calcium solution depends on the ratio o f calcium to sodium ion. The nucléation of monosodium urate in solutions containing flu id s from rheumatoid patients was found to require a higher supersaturation ra tio than that in pure water. Sodium ion was found to have no appreciable e ffe c t on nucléation o f monosodium urate. Copper ion also showed negligible e ffe c t on nucléation. The increase in monosodium urate s o lu b ility in aqueous solutions containing potassium ion is probably due to the increase in the ionic strength o f the s o l u t i o n , w h i c h decreases the a c tiv ity co e ffic ien t o f monosodium urate. The decrease in monosodium urate s o lu tility in aqueous solutions containing calcium ion is probably caused by incorporation of calcium ion into the monosodium urate crystal la ttic e . I t is interesting to note that the ionic O O radius of calcium (0.99 A) is close to th at of sodium ion (0.95 A), which makes i t easy fo r calcium ion to be incorporated into the mono- sodium urate crystal as a replacement fo r the sodium ion. The decrease in monosodium urate s o lu b ility in aqueous solu tions of ethyl alcohol is due to the fa c t that the solute-solvent interaction energy is less than in pure water. This is because the d ie le c tric constant o f ethyl alcohol has a lower value than pure water. Thus, addition of ethyl alcohol to pure water lowers the d ie le c tric constant o f the combined solvent (water and ethyl alcohol), which weakens the interaction forces between the solvent and the solute. In addition, ethyl alcohol has a larger molecular size than Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 water. This also weakens the solute-solvent in teractio n . I t was previously discussed that calcium ion decreases the s o lu b ility of monosodium urate remarkably. Since calcium ion is present in synovial flu id s , one would expect th at the s o lu b ility of monosodium urate would decrease in synovial flu id s diluted with pure water. Moreover, synovial flu id s contain sodium ion which suppresses the monosodium urate s o lu b ility . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER VI THE INFLUENCE O F X-IRRADIATION AND MECHANICAL S H O C K O N NUCLEATION OF M O NO SO DIUM URATE A. Influence o f X-Irradiat1on on Nucléation Individuals are often subjected to X-rays fo r diagnosis and treatment. I t was thought that X-rays might induce monosodium urate nucléation a t lower supersaturation than normal. Therefore micro scope slides were prepared with monosodium urate solutions of con centrations such that the spontaneous nucléation temperature ranged from 2 to 5°C below room temperature. The concentration of mono- sodium urate ranged from 6.9 x 10" M to 7.9 x 10" M. The slides were exposed to an X-ray beam using CuK irra d ia tio n from a G.E. X-ray d iffra c tio n u n it. The accelerating voltage used was 35 K V and the current was 20 ma. This is much more intense than a normal medical X-ray. The exposure time of these slides ranged from 10 seconds to 10 minutes. A fter the slides were exposed to X-rays, they were examined under the microscope fo r c ry s ta ls , and no crystals were found. One and two days a fte r exposure, the slides were again examined fo r crystals and compared with the control slides that were not exposed to X-rays. No crystals were found in any s lid e . The slides exposed to X-rays and the ones not exposed (co n tro l) looked the same. Thus, i t can be concluded that X-rays do not greatly enhance the nucléation o f monosodium urate. 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 B. Influence of Mechanical Shock on Nucléation I t was observed that nucléation was spontaneous when slides containing supersaturated solution were snapped repeatedly with the fin g ern ail or placed in an u ltras o n ically agitated bath. A mono- sodium urate solution of concentration 5.8 x 10” M, which has a nucléation temperature approximately 10°C below room temperature, was prepared. Three microscope slides were prepared from this solution and allowed to set fo r a day a t room temperature. W hen these slides were examined under the microscope, there were no crystals. A fter the slides were snapped with the fing ernail repeatedly and examined under the microscope, small crystals started to appear and blinked on and o ff in crossed po larizers. Also, i t was observed th at the more the slide was snapped (more shock), the more crystals appeared. The slides were examined two days a fte r, and needle crystals were observed in a ll three slid es. Large aggregates o f needle crystals were observed in one of the slid es. These observa tions may explain the c lin ic a l observation that gout can be in itia te d by a blow to the jo in t. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V II INFLUENCE O F H Y D R O G E N ION CONCENTRATION O N SOLUBILITY A N D NUCLEATION O F M O NO SO DIUM URATE A. Introduction Although the s o lu b ility of uric acid and the urates has been studied fo r over 80 years, an atmosphere of uncertainty and con fusion continues to surround i t . (^^6 ) has been erroneously stated that the s o lu b ility o f monosodium urate increases with Seegmiller^*) proposed a mechanism fo r gouty attack which appeared to assume that the s o lu b ility of monosodium urate decreases with pH. I t was proposed that upon the phagocytosis of urate cry s ta ls , la c tic acid is produced which lowers the pH and leads to a fu rth e r decrease in s o lu b ility of monosodium urate. A l l e n , i n his analytical treatment fo r the urate s o lu b ility versus pH, showed that the solu b ilit y of monosodium urate should decrease as pH decreases. Upon examining A llen's equations fo r the urate s o lu b ility versus pH, one finds that those equations are true only fo r uric acid and not fo r its salts. Moreover, Jung's data^*^) contradict A llen's findings and indicate that in the physiological pH range the s o lu b ility o f mono sodium urate increases with decreasing pH. I t is believed th at this unfortunate uncertainty regarding the s o lu b ility of uric acid and urates was due to the use o f the terms "uric acid" and "urate" interchangeably without regard to the c ry s ta llin e phase actually present. Also, the startin g m aterials fo r s o lu b ility determinations sometimes consisted of sub-micron sized crystals or the so-called 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 "amorphous" solid which should th eo retic ally give larger s o lu b ilitie s than larger well-formed crystals. In this chapter, theoretical expressions are developed fo r the dependence of the s o lu b ility of uric acid and sodium urate on pH, sodium ion concentration, and temperature. F in a lly , the influence of the p H on monosodium urate nucléation is investigated, and the significance of these results to the pathogenesis of gout is discussed. B. Influence of pH on Uric Acid and Sodium Urate S o lu b ility_________ 1. Derivation of Theoretical Uric Acid and Sodium Urate S o lu b ility________________ As mentioned in Chapter I I , uric acid exists in solution as undissociated uric acid HgU, as biurate ion HU", and as urate ion U*. At p H > 13 i t has been suggested that uric acid loses a third hydrogen ion, but this was not v e r i f i e d . U r i c acid , monosodium urate monohydrate and disodium urate can a ll e x is t as c ry s ta llin e m aterials. Thus the chemical e q u ilib ria with which one must be concerned depends on which c ry s ta llin e phases are present. F irs t, consider the chemical e q u ilib ria of u ric acid and its ions. At con stant temperature, the following reactions are always v a lid at equilibrium: V II-1 HgU 5=EH* + H U _ CH+CHU" ^dl ^HgU V II-2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 + V II-3 CH+C"= 'd2 C K.g = " V II-4 H-0 + OH' V II-5 H U \ i = CH+CoH" V II-6 where and are the equilibrium constants fo r the above reactions as they are w ritten . I t should be mentioned that since concentrations are used rather than a c tiv itie s , these constants are not the true thermodynamic equilibrium constants. They therefore depend on the ionic strength of the solution, 1 = ^ 1 0 , 2 . 2 ^ v i I - 7 (where C, is the concentration of species i of charge z, in the so lu tio n ), as well as on the nature of the other substance present. I f (and only i f ) c ry s ta llin e uric acid is present, then at equilibrium the follow ing is true: HgU(c) = H gU (solution) V II-8 A = HgU , V I I - 9 where A is the s o lu b ility of undissociated uric acid, which should be re la tiv e ly insensitive to ionic strength and pH, but is dependent on temperature. For the case where monosodium urate c ry s ta llin e is present, the follow ing are v a lid at equilibrium : Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NaHU ' HgOfc) = Na+ + HU" + H gO ^spl " Sa'^^HU" ' 127 V II-1 0 V II-11 where is the s o lu b ility product o f monosodium urate. For the case where c ry s ta llin e disodium urate is present, the following are true at equilibrium : NagUfc) = 2Na + U* V II-1 2 V II-1 3 where K^pg is the s o lu b ility product of disodium urate. a. Fraction of D ifferen t Species Present as a Function of [%+ From Eqs. V II-2 and V II-4 , the fra c tio n f of total uric acid- urate that is present as each of the three species, HgU, HU" and U", can be expressed as: c.. .. 1 'HgU T "2^ ^%U ^HU" * ^u=) "dl ' V 1 + C H + V II-1 4 ^HU" ^ ^H g U * ^ H U * ^U “^ V II-1 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 + 1 + ¥ 128 V II-1 6 Plotting these fractions as function of pH a t constant temperature, one finds that the fractio n of undissociated uric acid decreases as pH increases, while the fractio n of U" increases and the fra ctio n of HU' exhibits a maximum as shown in Figure V II-1 . b. S o lu b ility Expressions The total measurable s o lu b ility S of uric acid-urates is given by the sum of a ll three species present, when the solution is in equilibrium with one or more of the c rys tallin e phases possible: ^ ^ ^HgU * ^HU' Cu= V II-1 7 The s o lu b ility of uric acid (c ry s ta llin e uric acid in e q u ilib rium with solution) as a function of the pH is found from Eqs. V II-2 , V II-4 , V II-9 and V II-1 7 to be , , *dl , "^d l"^d2 1 + fr - r + -------- J V II-1 8 H g U In pure water the pH is determined by dissociation of the uric acid and using the fa c t that at pH < 7.5, Cjj= «C ^u- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 HU 0.9 0. 8 0.7 0. 6 0.4 0.3 0.2 Figure V II-1 . The Proportions o f Uric Acid-Urates in Solution a t 37*C which are present as D ifferen t Species H2U, HU" and U". from Eqs. V II-1 4 , V II-1 5 and V II-1 6 with X = 3.5 x 10"*, Kdl = 4 .2 X 10-6 and 1(^2 = 10-10 a t 37°C Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 so that “ ^OH" * ^HU" • V II-1 9 Substituting Eqs. V II-2 and V II-6 into Eq. V II-1 9 , the hydrogen ion concentration is found to be V II-2 0 Substituting Eq. V II-2 0 into Eq. V II-1 8 , the s o lu b ility of uric acid in pure water is expressed as: K. ■ * 1 + 'dl V II-21 From Eqs. V II-2 , V II-4 , V II-11 and V II-1 7 , fo r c ry s ta llin e monosodium urate in equilibrium with a solution of known pH and C^g+, the s o lu b ility of monosodium urate is expressed as: ’NaHU V II-2 2 I t should be noted that the product C^^+S does not equal K^pi. but depends on pH as well as the temperature, and i t exhibits a mini m u m a t the maximum of HU". I f there was no Na^ present in it ia lly and a ll Na^ contained in the solution came from dissolution of NaHU, then Eq. V II-2 2 becomes : 'NaHU “ A p i / % - I f NaHU is dissolved in pure water, then i t can be shown (107) V II-2 3 that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 the hydrogen ion concentration is given by . . v n -2 4 spl ' NaHU' dl Noting that ^*^dl^VI I-24 becomes V • " '- 2 5 By substituting Eq. V I1-25 into Eq. V II-2 3 , the s o lu b ility of mono sodium urate in pure water can be solved by t r ia l and error. Since "dl^dZ (5n,Hu) X Eq. V II-2 5 becomes: V \ / i % ■ " '- 2 5 At 37°C the above approximation would give less than 5 % error in the hydrogen concentration. Substituting Eq. V II-2 6 into Eq. V II-2 3 , the fin a l s o lu b ility of monosodium urate in pure water is expressed as: ^spl [' ^NaHU " V %spl I ^ + ^ V lÇ j- V II-2 7 For the case where NaHU is dissolved in buffered solution in it ia lly containing (CNg+)o, then the fin a l Na^ concentration is C M ,+ ' (CN,+). + S w e H U ' "'-28 Substituting Eq. V II-2 8 into Eq. V II-2 2 , the s o lu b ility of NaHU in a buffered solution i n it ia lly containing (C^g+io is given by: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 'NaHU - < W >0 * ( V >0 * «spl ^ * ÿ j V II-2 9 Consider NaHU dissolved in an un-buffered solution in it ia lly containing sodium ion at concentration (C^g+io and an anion of a strong acid, e .g ., NaCl in pure water. To solve for the approximate s o lu b ility of NaHU, Eqs. V II-2 8 and V II-26 are substituted into Eq. V II-2 2 , and one obtains Ç « 1 ^NaHU 2 - < V >0 ' V II-3 0 Next consider the case where NaH U is formed by dissolving uric acid in a buffered solution in it ia lly containing sodium ion at con centration (C|ijg+)Q» Uric acid at pH ^ 7 w ill dissolve to levels fa r exceeding the s o lu b ility o f monosodium urate. I f the concentration of uric acid dissolved in the soluiton is at a level such that ^NaHU - (^^2U^o - ^H U’ then NaHU is nucleated and c ry s ta llize d u n til saturation is reached, then the fin a l sodium ion concentration is CN,+ = < W >0 - ■ ^NaHU I - V II-31 where (C^a+)o is the in it ia l sodium ion concentration in the solution before uric acid is added and (C^^u^o the concentration of uric acid dissolved in the solution before monosodium urate begins to c ry s ta lliz e . Substituting Eq. VII-31 into Eq. V II-2 2 , the fin a l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 s o lu b ility of NaHU is given by 'NaHU (C Na+^o'fCHgU^o + 4K spl V II-3 2 S im ila rly , the s o lu b ility of disodium urate in a solution of known pH and 0^^+ is found from Eqs. V II-2 , V II-4 , V II-1 3 and V II-1 9 to be 'NagU <v>‘ Cu+ (Cu+) 1 * T— + 7— j7 — " ^ d 2 "^drd2 ' Ksp2/(CW,+) fu- V II-3 3 In order to compare the s o lu b ilitie s of uric acid, monosodium urate and disodium urate as a function of pH, we must know the values o f the equilibrium constants appearing in Eqs. V II-1 8 , V II-2 2 , and V II-3 3 . From the conductivity measurement, Gudzent^^*) found that the f i r s t dissociation constant of uric acid ) has a value of about 2.3 X 10”® a t 37°C, and the s o lu b ility of the undissociated uric acid, X, has a value of about 3.582 x 10”* M a t 37°C. Bergman and D ikstein, (70) by determination of optical absorption maximum versus pH, found th a t the f i r s t dissociation constant (Ky^) has a value of about 1.78 x 10”®, and the second dissociation constant (Kjg) has a value o f about 5 x 10”^\ both at 22°C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 Values of X and were also determined from experimental data on uric acid s o l u b i l i t y . B y plotting the uric acid s o lu b ility versus 1/(C ^+), i t can be seen from Eq. V II-1 8 that the intercept at 1/(H+) -+ 0 gives the value of A. Values of were calculated from the slopes. The values of these equilibrium constants obtained by d iffe re n t methods are summarized in our recent paper. <’ <«> At 37°C the value of the monosodium urate s o lu b ility constant, Kspi, was found to be 4.16 x 10”^ (I = 0 . 1 6 ) . There was no data available on the s o lu b ility of disodium urate, so a value of 7 X 10 was assumed fo r the disodium urate s o lu b ility constant, *sp2 ' Upon substituting these equilibrium constants in Eqs. V II-1 8 , V II-2 2 , and V II-3 3 , we see from Figure V II-2 that the s o lu b ility of uric acid increases with the pH, while monosodium urate s o lu b ility decreases with pH, fo r pH > 7.7, and increases with the pH fo r pH < 7.7. Thus, a t high pH, uric acid may dissolve to levels fa r exceed ing the s o lu b ility of monosodium u rate, producing a solution metastable with respect to c ry s ta lliz a tio n of monosodium urate. Like wise, monosodium urate may dissolve a t low pH exceeding the s o lu b ility of u ric acid, producing a solution metastable with respect to the c ry s ta lliz a tio n of u ric acid. As shown in Figure V II-2 , the solu b ilitie s of uric acid and monosodium urate are equal a t a c ritic a l pH, which depends on both the sodium ion concentration and the temperature. Jung(*^) called this point the in fle c tio n point and found that i t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (On the following page) Figure V II-2 . Calculated S o lu b ilitie s of Uric Acid, Monosodium Urate and Disodium Urate at 37°C using: X = 3.5 X 10"*, = 4.2 X 10* Kd2 = 10- 10 Kspi = 5.15 X 10 -5 Ksp2 - 7 X 10 -11 and Curve 1: Uric acid using Eq. V II-1 8 . Curve 2: Monosodium urate in a buffered solution ( I = 0.16) containing 0.142 M (Na+), using Eq. V II-2 2 . Curve 3: Monosodium urate in buffered solution ( I = 0.16) in it ia lly containing no Na+, using Eq. V II-2 3 . Curve 4: Guessed disodium urate curve. 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 1000-1 800 600 400- 200 ^ 1 0 0- - : « °: E 60- 40 20 10 - - (/) Figure V II-2 . Calculated S o lu b ilitie s of Uric Acid, Monosodium Urate and Disodium Urate at 37°C Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 lie s in the range 5 < pH < 6 . His deduction of this range was purely experimental. Since this c r itic a l point of equal s o lu b ili tie s occurs at pH < 7, then f^j= is n eg ligib le and f^j= « f^ y -. With this assumption and from Eqs. V II-1 8 and V II-2 2 , the s o lu b ilitie s of uric acid and monosodium urate are equal at + (Na^) A K., (H )c n ^ . V II-3 4 S p l W hen the hydrogen ion concentration exceeds th is value, uric acid would be the most stable solid phase in contact with the solution because i t has the lowest s o lu b ility . W hen the hydrogen ion con centration is less than this value, monosodium urate would be the most stable phase in contact with the solution. From Eq. V II-3 4 i t is obvious that the c ritic a l pH depends on both the temperature and the sodium ion concentration. For the case where the only source of sodium ion is the c ry s ta llin e monosodium u rate, then (Na^) = Sj^aHU’ by substituting Eq. V II-2 3 into Eq. V II-3 4 , the c ritic a l hydrogen ion concentration fo r equal s o lu b ility of uric acid and sodium urate becomes (Cn+)c “ ? V II-3 5 S im ilarly, from Eqs. V II-2 2 and V II-3 3 , and assuming *dl^d2 ^ fo r pH > disodium urate are equal a t 2 (Cy+) ^ fo r pH > 10, the s o lu b ility of monosodium and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138 (Cu+) = ^&E l*sp2^Na . V II-36 " ^ S p 2 Table V II-1 shows the c r itic a l pH as a function of temperature and sodium ion concentration. There is good agreement between our theoretical values of (pH)^ and Jung's experimental observations. He suggested that the c r itic a l pH lie s in the range 5 < pH < 6 fo r a sodium-containing buffer. For the case where there is no extra sodium ion present in the solution , we see th at the value of the c r itic a l pH can exceed pH = 6 and is a function of temperature only. The higher the temperature, the lower is the c ritic a l pH. This is also in agreement with Jung's data fo r sodium-free buffers. One should observe th at these c ritic a l values o f pH separate the re la tiv e s ta b ility region of the two compounds (u ric acid -u rate). Thus, when pure monosodium urate is prepared, the p H should always exceed the c r itic a l value a t th at temperature and sodium ion concen tra tio n . 2. Experimental Since the existing lite ra tu re data was in s u ffic ie n t to te s t the dependence of monosodium urate s o lu b ility on pH, the following experiments were conducted a t the UCLA Medical School in cooperation with the use workers. Monosodium urate (from K & K Laboratories, In c ., Plainview, New York 11803) was shaken with buffered solutions. The buffer solutions were prepared from monosodium and disodium phosphate in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q. C g Q. ■ D CD C/) W o' 3 0 5 CD 8 " O 3. C Û 3 " 1 3 CD 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. O C ■o CD ( /) o' 3 TABLE V II-1 The C ritic a l pH fo r Equal S o lu b ility of Uric Acid and Monosodium Urate Temp. °C (Na*) mol e s/l it e r X m o le s /lite r Kdl •^spl Theor. (pH)c Jung(*3) (pH)c 18 0.15 1 . 6 8 X 1 0 " * 1.8 X 10"® 1.7 X 10"® 5.57 18 0.083 1 . 6 8 X 1 0 " * 1.8 X 10"® 1.7 X 10"® 5.83 5.8 18 0.03 1.68 X 10"* 1.8 X 10"® 1.7 X 10"® 6.27 6.35 18 ' Sw,HU 1 . 6 8 X 1 0 " * 1.8 X 10"® 1.7 X 10"® 7.12 7.2 37 0.15 3.5 X 10"* 4.2 X 10"® 4.16 X 10"® 5.28 - — 37 (Na ) = 3.5 X 10"* 4.2 X 10"® 4.16 X 10"® 6.63 6.7 W 140 0.15 M NaCl. A fter monosodium urate was shaken at constant tempera tures fo r 16 hours, pH measurements were made and the solutions were centrifuged twice at th e ir bath temperature fo r 15 minutes a t 20 Kg. A sample of the decanted supernatant was analyzed fo r urate by enzymatic d iffe re n tia l spectrophotometry. 3. Results and Analysis From Eq. V II-2 2 , 1 fo r pH < 8 and the s o lu b ility of monosodium urate in buffered solutions can be w ritten as The experimental data fo r monosodium urate at d iffe re n t pH values and at 37°C and 26°C (see appendix) were programmed fo r least squares curve f it tin g according to Eq. V II-3 7 . From the computer least squares calculatio n, the following values of the equilibrium constants were obtained: Temperature K._, K O c spl dl 26 5 . 4 X l O ' S 2 . 4 x 1 0 '® 37 8 . 7 6 X l O ' S 2 . 7 x 1 0 '® As shown in Figure V II-3 , the s o lu b ility of monosodium urate increases with the increase in hydrogen ion concentration as pre dicted by Eq. V II-3 7 . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 <16 0.16 ( V I O ' 2 1 2 V) 26* C Figure V II-3 . Experimental Data of Sodium Urate S o lu b ility Versus p H .(106) Curve a t 37°C from Eq. V II-2 8 : Kspi = 8.76 X 10 -5 « 2.7 X 10 -6 Curve at 26®C from Eq. V II-2 8 : Kjp, = 5.4 X ,0-5. Kj, 2.4 X 10 -6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 C. Influence of Hydrogen Ion Concentration on the Nucléation of Monosodium Urate________________ The e ffe c t of pH on nucléation was studied by addition of 10 ® M HCl and la c tic acid to monosodium urate solutions of known concentrations. The supersaturated solution of monosodium urate was prepared f ir s t . Then the solution was divided into three parts, each in 10 ml volumetric flas ks. Drops of 10”^ M HCl were added to each part o f the solution and pH measurements were made using a Beckman pH meter (Model 55-3). Addition of HCl drops and p H measurements were repeated u n til the desired pH was obtained. Micro scope slides were prepared with these solutions of known pH and mono sodium urate concentrations, and hot stage experiments were conducted as previously mentioned. As we have shown in Figure V II-3 , the e ffe c t of oH on monosodium urate s o lu b ility fo r 6 < pH < 7.4 is n eg lig ib le, and this was confirmed by the hot stage experiments. I t was found that microscope slides with monosodium urate solutions of the same concentration, but a t d iffe re n t pH values, have very close s o lu b ility temperatures, but the nucléation temperature was strongly dependent on pH. As shown in Figure V II-4 , the supersaturation ra tio required to nucleate monosodium urate increased as (pH) increased. Below pH 6 .3 , large numbers of tin y crystals were formed. These crystals did not dissolve upon heating to and above the monosodium urate s o lu b ility temperature. They are believed to have been u ric acid crystals. Although i t appears that the e ffe c t of la c tic acid and HCl on nucléation is nearly the same, small p la te le t crystals (see Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ O O Q . C g Q . ■ D CD e n c / ) CD 8 CD 3. 3 " CD CD ■ D O Q . C a O 3 ■ D O CD Q . ■ D CD 3 H o z o 4.5 LACTIC ACID HCL PURE WATER (O 4.0 N I o > 3.0 2.5 6.0 6.5 7.0 7.5 c / ) c / ) Figure V II-4 . The Influence o f pH on Nucléation of Monosodium Urate a t 30 to 34°C ■Pk W 144 Figure V II-5 ) were formed in addition to the usual needle crystal when solutions of monosodium urate were a c id ifie d with la c tic acid. Most of these p la te le t crystals dissolved under the s lig h t heating caused by the microscope lig h t, leaving behind the urate needle crystals. Thus, one might believe that these p la te le t crystals of rapid formation could act as centers fo r nucléation and, there fo re , accelerate the nucléation of monosodium urate. This re s u lt on the enhancement e ffe c t of acid on nucléation tends to corroborate Seegmiller's^®^ proposed mechanism fo r the genesis of an acute gouty attack. The la c tic acid produced by the phagocytosis of urate crystals would accelerate nucléation of mono sodium urate, even though the s o lu b ility would actu ally be increased s lig h tly . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 Figure V II-5 . Photograph of P la te le t Crystals Formed Along with Monosodium Urate Needle C rystals, Upon Addition of Lactic Acid Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V III CONCLUSION During the pursuance of this work the following were accom plished: 1. The classical nucléation theory as derived fo r vapor and melts was found to predict u n re a lis tic a lly high nucléation rates for nucléation from aqueous solutions. This was manifested in the high theoretical value given to the pre-exponential constant appearing in the classical nucléation theory. Thus a new equation was developed fo r the nucléation of ionic compounds from solutions which predicts lower nucléation rate fo r solutions than that predicted by the classical nucléation theory. This is shown in Eq. III- 4 6 which gives the paramount parameters affecting the nucléation of ionic compound from solutions. I t was suggested that the solvation energy hinders the nucléation in solutions because the ions have to lose at least some of the solvation energy before they are able to unite and form a nucleus. Comparison of the lite ra tu re data fo r nucléation of ionic compounds with our newly derived equation gave a better agreement than the classical nucléation theory. 2. Although the primary objective of this work was to study the nucléation of monosodium urate, misconceptions and uncertainty were discovered in the lite ra tu re on the s o lu b ility of u ric acid and urates and th e ir equilibrium constants. Thus much time was devoted 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 to investigation and recon ciliation of these differences. Theoretical equations showing the dependence of uric acid and sodium urate solu b ilit y on pH were derived and confirmed by experiments. I t was found that w ithin the physiological pH range, the s o lu b ility of mono sodium urate increases as the pH decreases. This was shown in Eq. V II-2 2 and Figure V II-3 . As shown in Eq. V II-1 8 and Figure V II-2 , the s o lu b ility of uric acid increases with pH, and indeed the two s o lu b ility curves of u ric acid and monosodium urate cross each other at a c r itic a l pH. This c ritic a l p H was found to depend on the temperature and sodium ion concentration, as shown in Eqs. V II-3 4 and V II-3 5 . 3. The e ffe c t o f various additives on the nucléation of monosodium urate was investigated. The supersaturation required fo r the nucléation of monosodium urate in pure water was found to be 4 .3 -- a substantial supersaturation. Addition of 25% v ethyl alcohol reduced the s o lu b ility of monosodium urate by about three times as compared to that in pure water, while the supersaturation required fo r nucléation was found to be 3 .3 , which is also much less than that in pure water. In other words, alcohol was found to both reduce the s o lu b ility and to enhance the nucléation o f monosodium urate. Like wise, a dramatic e ffe c t on both the monosodium urate s o lu b ility and nucléation was found upon addition of calcium chloride to a Cca++/C|^a'’’ ra tio close to that found in synovial flu id s . I t was found th at the concentration product of monosodium urate required fo r Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 148 nucléation decreased as the ra tio of calcium to sodium increased. This is shown in Figure V-10. From microscopic observation i t was noted th at calcium ion accelerated the axial growth of urate crystals. Addition of 5% v of synovial flu id s from a rheumatoid a r th r itis patient undergoing aspirin therapy and from a gout patient lowered the s o lu b ility s lig h tly . This is mainly because of the presence of extra sodium ion in the synovial flu id s . However, i t was also found that nucléation in 5% v synovial flu id from one rheumatoid patient required a higher supersaturation ra tio than that in pure water or with synovial flu id from a gout p atien t. Thus, the flu id from the rheumatoid patient tended to in h ib it the nucléation of mono sodium urate, which corroborates the c lin ic a l observation that rheumatoid patients rarely ( i f ever) get gout. Because of great individual variations in properties o f physiological substances, fu rth er experiments are needed to see i f this is £ general phenomenon. Lactic acid was found to enhance the nucléation of monosodium urate, even though the s o lu b ility increases s lig h tly w ithin the physiological pH range. As shown in Figure V II-4 , the supersaturation ra tio fo r nucléation increased as the pH increased. Thus, upon phagocytosis of the urate crystals and production of more la c tic acid (low pH), the supersaturation ra tio required for nucléation would be lower and monosodium urate crystals would nucleate easier. Below pH 6 .3 , uric acid crys tallized and did not dissolve upon heat ing to the monosodium urate s o lu b ility temperature. This explains Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 149 why uric acid often c ry s ta llize s in kidney stones (the pH of the urine is about 6 ) , and why monosodium urate crystals are found in jo in ts and synovial flu id s , in which the pH is about 7.4. 4. Exposure o f metastable monosodium urate solutions to an X-ray beam of an intensity higher than normal medical X-rays fo r short and long times (10 seconds to 10 minutes) did not induce nucléation. Thus, i t appears that X-rays do not enhance nucléation of monosodium urate. 5. I t was observed th at nucléation was instantaneous when solutions of monosodium urate that would not nucleate at room temperature were snapped with the fing ernail or placed in an u ltr a sonic cleaner. Inducement of nucléation by mechanical shocks is a well-known phenomenon in c ry s ta lliz a tio n . 6 . Addition of collagen fib e r to monosodium urate in pure water did not a lte r the nucléation temperature. Furthermore, when nucléation did occur, fewer crystals were formed in the v ic in ity of the collagen than elsewhere. A fter dialyzing collagen fibers with monosodium urate buffered solution of pH 7.2 and examining the solution from inside and outside the dialysis bags, there was no apparent e ffe c t of collagen on monosodium urate nucléation. This contradicts one hypothesis which claims that collagen might act as a substrate fo r monosodium urate c ry s ta lliz a tio n and enhance the nucléation. However, since i t takes certain forms and structures Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 150 of collagen to catalyze the nucléation of hydroxyapatite, i t is possible that the form of collagen used in our experiments was not that required fo r urate nucléation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IX DISCUSSION A N D RECOM M ENDATIONS Calcium ion showed the most dramatic e ffe c t on both the s o lu b ility and nucléation of monosodium urate. Furthermore, crystals tended to grow longer and in more aggregate form in calcium con taining solutions than in any other solution. Since calcium ion m ay be given to a gout patient fo r treatment both in the guise of pharmaceutical preparations and as a constituent of mineral spring water and d ie t, possibly this should be avoided or minimized. Cupric ion showed negligible e ffe c t on the nucléation o f monosodium urate. I t is interesting to note that cupric ion, Cu**, has an ionic radius O + 0 of 0.69 A, which is much less than Na of radius 0.95 A. (Calcium ° + ion has a radius of 0.99 A.) O n the other hand, cuprous ion, Cu , o has an ionic radius of 0.96 A, which is very close to th at of sodium ion. Thus, one raises the query of what is the ionic state of copper in human body flu id s . I f i t is possible that copper can e x is t as monovalent ion, then because of its s im ila r size to sodium i t might act to enhance nucléation and might be incorporated into monosodium urate crystals. From the s o lu b ility study i t was shown th at high supersatura tions o f monosodium urate solution can be prepared by dissolving uric acid in sodium buffer at high pH. This indicates th a t uric acid crystals are not very favorable sites fo r monosodium urate c ry s ta lliz a tio n . Likewise, monosodium urate may dissolve at low 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 p H to levels exceeding the s o lu b ility of u ric acid. However, in this case, the levels o f uric acid that can be reached are moderate and u ric acid starts to c ry s ta lliz e . This indicates that perhaps nucleation-cf u ric acid is easier than nucléation o f monosodium urate, as was observed in the pH nucléation experiments. Based on our study and experimental observations, the follow ing extensions o f this research are recommended. 1. Synovial flu id s from gout patients and nongouty patients (rheumatoid and hyperuricemic) should be fractio n ated and analyzed fo r chemical components. Components that are found solely in one flu id and not the others or are present in larger concentrations in one type of synovial flu id should be tested for th e ir influence on nucléation and s o lu b ility of monosodium urate. Hot stage or d ialysis experiments should be suitable fo r this purpose. 2. Due to the remarkable effect o f calcium ion on the s o lu b ility and nucléation of monosodium u ra te , calcium ion concentra tions should be measured and compared in synovial flu id samples obtained from gout patients, rheumatoid patients and hyperuricemic individuals. Furthermore, the state of existence o f calcium ion in these synovial flu id s is important. In other words, there may be som e substances that bind the calcium p a rtia lly or to ta lly in rheumatoid patients and other nongouty p atien ts, whereas the calcium ion may be more free in the synovial flu id s obtained from the gout patients, and therefore would accelerate the p recip itatio n of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153 monosodium urate. 3. Tophi from gout patients should be analyzed for calcium and calcium urate which could co-precipitate with monosodium urate. Thus, calcium urate crystals should be grown and th e ir s o lu b ility and nucléation parameters should be studied and compared fo r th e ir influence on monosodium urate c ry s ta lliz a tio n . In addition, gouty tophi should be analyzed fo r the presence of other m inerals, especially those of chelating potential such as copper, manganese and iron. 4. D ifferen t collagen tissues (a rtic u la r and nasal c a rtilla g e ) obtained from gout patients and nongouty subjects should be tested fo r th e ir influence on nucléation of monosodium urate. Since protein polysaccharides (PPL) were found to enhance the s o lu b ility of sodium u r a t e ,t h e i r influence on urate nucléation and th e ir concentration in d iffe re n t synovial flu id s should be investigated. 5. Drugs used for therapy of gout as well as rheumatoid patients should be tested fo r th e ir influence on monosodium urate nucléation. This can be investigated in the hot stage experiments. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. REFERENCES 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. REFERENCES 1. T alb o tt, J .H ., Gout, Grune and S tratton , New York (1967). 2. Howell, R.R., Eanes, E .D ., and Seegm iller, J .E ., A rth ritis and Rheumatism 6 , 97 (1963). 3. Sokoloff, L ., A rth ritis and Rheumatism 8 , 707 (1965). 4. Seegmiller, J .R ., Hospital Practice J[, No. 3 (1966). 5. Seegmiller, J .E ., Howell, R .R ., and Malawista, S .E ., J. Am . Med. Assoc. 180, 469 (1962). 6 . Seegmiller, J .E ., A rth ritis and Rheumatism 8 , 714 (1965). 7. Seegm iller, J .E ., G razel, A . I . , Laster, L . , and Liddle, L .J ., C lin. Investigation 40, 1304 (1961). 8 . Seegmiller, J .E ., Laster, L . , Howell, R .R ., New England J. of Medicine 712 (1963). 9. Maclochlan, M .J., and Rodnan, G .P ., A m . J. Med. 4^, 38 (1967). 10. Garrod, A.B., T reatise on Gout and Rheumatic Gout. (Rheumatoid A r th r itis ), 3rd Ed., Longmans, Green & Co., London (1876); through Ref. (1 ). 11. Katz, W.A., and Schubert, J . , J. C lin . Investigation 49, 1783 (1970). ~ 12. Gutman, A .B ., Yu, T .F ., and Weissman, B ., Trans. Ass. A m . Physicians 69, 229 (1956). 13. Lennox, W.G., J. B io l. Chem. 521 (1925). 14 Aronoff, A ., N ew England J. Med. 262, 767 (1960). 15. McCarty, D .J., J r . , A rth ritis and Rheumatism 425 (1961). 16. Hippocrates: The Genuine Works o f Hippocrates, Vol. 1 and Vol. I I . Translated from the Greek with preliminary discourse and annotations by Francis Adams. Wood, New York (1886). 17. Norton, C.E., Letters of James Russell Lowell, Harper, New York (1894); through Ref. (1 ). 155 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156 18. Rodnan, G .P ., and Benedek, T .G ., A rth ritis and Rheumatism 6 , 317 (1963). 19. Sheele, K.W., Opuscula 2» 73 (1766). 20. Wollaston, W.H., P h il. Trans. 87,, 386 (1797). 21. Garrod, A .B ., The Nature and Treatment o f Gout and Rheumatic Gout, 2nd Ed., Walton and Maberly, London (1859); through Ref. (1 ). 22. Roberts, W., B ritish Med. J. 2, 61 (1892). 23. Riddle, J .M ., Gluhm, G .B ., and Barnhart, M .I., Ann. Rheumat. Dis. % , 389 (1967). 24. Ebstein, W., Virchow Arch. Path. Anat. 154, 349 (1898). 25. His, W., J r ., Deutch Arch. K lin. Med. 67, 81 (1900). 26. Freudweller, M ., Deutch Arch. K lin. Med. 266 (1899). 27. B r ill, J .M ., and McCarty, D .J ., J r ., Ann. Intern. Med. 60, 486 (1964). — 28. Freudweller, M ., Deutch Arch. K lin. Med. 69, 155 (1901). 29. B r ill, J.M ., and McCarty, D .J ., J r ., A rth ritis and Rheumatism 8 , 267 (1965). 30. Weissman, G ., Hospital Practice £ , 43 (1971). 31. McCarty, D .J ., J r ., and Hollander, J .L ., Ann. In tern . Med. 54, 452 (1961). ~ 32. McCarty, D .J ., J r ., Kohn, N .N., and Faires, J .S ., Ann. Intern. Med. 56, 738 (1962). 33. Faires, J .S ., and McCarty, D .J ., J r ., Lancet 682 (1962). 34. McCarty, D .J ., J r ., and Hogan, J.M ., A rth ritis and Rheumatism 7, 359 (1964). 35. Malawista, S .E ., and Seegm iller, J .E ., Ann Intern. Med. 62, 648 (1965). 36. Phelps, P ., Steele, A .D ., and McCarty, D .J ., J r ., JAM A 203, 508 (1968). 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Strickland-Constuble, R .F ., Kinetic and Mechanism of Crystal liz a tio n , Academic Press, London (1968). 48. Newman, W .F., and Newman, M.W., The Chemical Dynamics o f Bone M ineralization, University of Chicago Press (1958). 49. Sobel, A .E ., Lawrence, P .A ., and Burger, M ., Trans. N.Y. Acad. Sci. 22. 233 (1960). 50. Glimcher, M .J., Hodge, A .J ., and Schmitt, F .D ., Proc. Nat. Acad. Sci. 43. 860 (1957). 51. States, B .S ., Newman, W .F., and Levinskas, G .J ., J. Phys. Chem . 61, 279 (1957). 52. Solomons, C .C ., and Newman, W.F., J. B iol. Chem. 232, 2502 (1960). 53. Cisse, J . , and B olling , G .F ., J. Crystal Growth 1 , 37 (1970). 54. Roulleou, J ., Ann. Geophys. 20, 319 (1964). 55. Pruppacher, H .R ., J. Geophys. Res. 6 8 , 14 (1963). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 56. Abdullaeva, Ya. S ., and Gumanskii, J .A ., Sov. Phys. Crystal lography 1%, 967 (1968). 57. Frawley, J .J ., and Childs, W .J., Trans. AIME 242, 256 (1968). 58. Hunt, J .D ., and Jackson, K.A., J. Appl. Phys. 37, 254 (1964). 59. G itlin , S .N ., and Lin, S .S ., J. Appl. Phys. 40, 4761 (1969). 60. Cayey, N.W., and E strin , P ., I.&E.C. Fund. 13 (1967). 61. Mason, R .E ., and Strickland-Constable, R .F ., Trans. Faraday Soc. 62, 455 (1966). 62. L ai, O .P ., Mason, R .E .A ., and Strickland-Constable, R .F ., J. Crystal Growth 1 (1969). 63. Buckley, H .E ., Crystal Growth, John Wiley and Sons, In c ., N ew York (1950). 64. A llen, D .J ., The Crystal Growth and Habit M odification of Mono sodium Urate, Ph.D. dissertatio n . University of Michigan (1964). 65. A llen, D .J ., Milosovich, G ., and Mattocks, A.M., J. Pharm. Sci. M , 383 (1965). 6 6 . A llen, D .J ., Milosovich, G ., and Mattocks, A.M., A rth ritis and Rheumatism 8 , 1123 (1965). 67. Weast, R .C ., Ed., Handbook of Chemistry and Physics, The Chemical Rubber Co., Cleveland (1970). 6 8 . Inagaki, K ., and Morioka, S ., Yokohama Med. Bull. !£ , 103 (1968). 69. Inagaki, K ., Morioka, S ., and Yokoyama, H ,, Yokohama Med. B ull. 20, 171 (1969). 70. Bergman, P ., and D ikstein, S., J. Am . Chem. Soc. 77, 691 (1955). 71. Kanitz, A ., Z. Physiol. Chem. 1J[^, 96 (1921). 72. P a lit, C .C ., and Dhar, N .R ., J. Phys. Chem. 32, 1263 (1928). 73. Ord, W.M., O n The Influence of Colloids upon C rystalline Form and Cohesion, London, 1879; through Ref. (64). 74. Gudzent, G ., Z. Physiol. Chem. 60, 25 (1909). 75. Priem, E .L ., and Frondel, C .J ., Urology 949 (1949). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 76. Kesser, E ., and Zacher, J . , Kolloidchem. Belhefte V7» TM (1923). 77. Liddle, L . , Seegm iller, J .E ., and Laster, L ., J. Lab. C lin . Med. 903 (1959). 78. Castellan, G.W., Physical Chemistry, Addison-Wesley, Palo Alto (1964). 79. M ullin, J.W ., C ry s ta lliz a tio n , Butterworth, London (1961). 80. Holven, A .L ., I.&E.C. 34, 1234 (1942). 81. Jones, B.M ., J. Chem. Soc. 93, 1739 (1908). 82. Miers, H .A ., P h il. Trans. 202A, 459 (1904). 83. Miers, H .A ., J. In s t. Metals 37, 331 (1927). 84. Miers, H .A ., and Isaac, F ., J. Chem. Soc. 89, 413 (1906). 85. Miers, H .A ., and Isaac, F ., Proc. Roy. Soc. (London) 79A, 322 (1907). 8 6 . Ostwald, W., Z. Physik. Chem. 34 , 493 (1900). 87. Dundon, M .L ., and Mack, E ., J. A m . Chem. Soc. 45, 2479 (1923). 8 8 . Van Hook, A ., C ry s ta lliza tio n Theory and P ractice, Reinhold Publishing Corporation, New York (1961). 89. Uhlmann, D .R ., and Chalmers, B ., I.&E.C. 18 (1968). 90. N yvlt, J ., J. Crystal Growth 4, 377 (1968). 91. N yvlt, J ., Rychly, R ., G o ttfried , J . , and Wurzelova, J ., J. Crystal Growth 6t 151 (1970). 92. "Symposium on Nucléation Phenomena", I.&E.C. 44, 1292 (1952). 93. Turnbull, D ., and Fisher, J .D ., J. Chem. Phys. ]T_t 71 (1949). 94. Turnbull, D .J ., J. Chem . Phys. 1^, 768 (1950). 95. Turnbull, D ., and Vonnegut, B ., I.&E.C. 44, 1292 (1952). 96. M elia, T .P ., and M o ffit, W .P., Nature, London, 1024 (1957). 97. M elia, T .P ., J. Appl. Chem . l^ , 345 (1965). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 160 98. Bransom, S .H ., Dunning, W .J., and M illa rd , B ., Faraday Society (Discussions) 83 (1949). 99. Glasstone, S ., L aid ler, J ., and Eyrinq, H ., The Theory o f Rate Processes. McGraw-Hill, London (1941). 100. Nielson, A .C ., Kinetic of P re c ip ita tio n , Pergamon Press, Oxford (1964). 101. Zettlem ayer, A .C ., Ed., Nucléation, Marcel Dekker, In c ., New York (1969). 102. Pound, G.M., Energetics in M etallurgical Phenomena, Vol. I I , Edited by W . M euller, Gordon and Breach Science Publisher, New York (1965), pg. 85. 103. Bockris, J. O'M ., and Reddy, A .D ., Modern Electrochemistry, Vol. 1, Plenum Press, New York (1970). 104. Haussay, B .A ., Hum an Physiology, McGraw-Hill, New York (1955). 105. Kramer, L .S ., Private communication, USC Medical School. 106. Wilcox, W.R., Khalaf, A .A ., Weinberger, A ., Kippen, I . , and Klinenberg, J .R ., J. Med. B iol. Eng. 1£, 522 (1972). 107. Pierce, W.C., and Haenisch, E .L ., Q uantitative Analysis, 3rd Ed., W iley, N ew York (1946), pg. 196. 108. Carslaw, H .S ., and Jaeger, J .C ., Conduction o f Heat in Solids, 2nd Ed., Oxford Press, London (1959), pg. 102. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A SA M PLE CALCULATIONS O F THE NUCLEATION KINETIC C O NSTANT S H O W N IN TABLE I I 1-2 161 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162 A. Estimation of the Nucléation Kinetic Constant fo r Ammonium Chloride The nucléation kin etic constant (A) derived in Eq. III- 4 2 is evaluated fo r the case of ammonium chloride (NH^Cl) nucléation as follows: A = Z = Zn(r )^D J p r a ^ M 4ïï(r ) pN "A"B H "r / T e " "s k T / 1/2 III- 4 2 III- 4 5 From References (6 7 ), (9 7 ), (101) and (103) the following data were extracted fo r NH^Cl AH^ = -3533 cal/mole , Tg = 70°C , D = 10"^ cm^/sec , dg^- = 1.8 A, d^g+ = 1.43 A , 21 Oa = ng = 8.52 X 10 molecules/cc , M = 53.44 , r = 20 A , p * 1.5 gm/cc , (C.)(Cg) W ? ’ = 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163 Upon substituting the above data in Eq. III - 4 5 , we obtain 4 X 3.14(20)^ X 10"'” X 1.5 X 6 X 10< .. I 2 X 20 X 10"® X 1.5 X 6 X 10^3 X ------------------------ gr??------------------- = 8.3 X 10"3 X O .jj exp ^ = exp = exp (-5 .1 5 ) = 5.6 x 10“^ For C l", n^ = 1, n^ = 3, = 82.8 Kcal/mole, T = 28°K = exp = Gxp (-4 9 .5 ) = 3.1 x lO"?? Then, upon substituting in Eq. III- 4 2 , the nucléation k in e tic constant A is evaluated as: A = 8.3 X 10"3 X 3.14(20)2 x lOT^G % 10~^ (1.8 + 1.43) X 10"® X (8.52 X 1 0 ^ 1 ) 2 5.6 x 10"^ x 3.1 x 10"^^ = 4 X 10? Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 164 B. Estimation of the Nucléation Kinetic Constant fo r Monosodium Urate_______ For NaHU, the following data are used = -1 2 X 10^ cal/mole , * o r = 20 A , D = 10 ^ cm^/sec , ^ N a * ^HU" ~ 10 A • 21 (n^g+) = (n^y-) = 6 X 10 molecules/cc , Z 10"2, T = 300°K, Tg = 320°K . For Na*, ny = 1, n^ = 6 , AHy^^ = 109.3 Kcal/mole . Upon substituting in Eq. III- 4 2 , the nucléation k in e tic con stant fo r monosodium urate is estimated to be: A = 10~^ X 3.14(20)2 X lO'TG % 10'^ (10) X 10 * X (6 X 10fT)2 X 10'® X 6.3 x 10"^* 4.75 X 10® . it C. Estimation of the C ritic a l Radius r From Eqs. III- 1 9 and I II- 2 4 , the radius of the c r itic a l nuclei can be expressed as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 165 p R T Jin a ' = r l f j l n a • A-1 For monosodium u rate, the following data are used: Y = 19 erg/cm^ = 4.55 x 10'^ cal/cm^ , T = 300°K, p = 1 .9 , 0 * 4 , M = 208 , ^ 2 X 4.55 X 1 0 " 7 X 208 1.9 X 1.987 X 300 x 1.38 = 12 A . Then, the kinetic constant A can be re-evaluated using th is new value o f the c r itic a l radius. W e obtain: A = 1.7 X 10® * 1 X 10® . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B EXPERIMENTAL D A TA FOR SOLUBILITY A N D NUCLEATION O F M O N O SO D IU M URATE 166 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 TABLE B-1 SOLUBILITY AND NUCLEATION OF M O NO SO DIUM URATE IN PU R E W ATER X 10= (1/Tg) X 103 (°K-T) (1/Tg) X 103 4.22 3.163 3.435 4.8 3.143 3.4 6.08 3.113 3.365 8.16 3.057 3.32 9.7 3.029 3.278 11.45 3 3.245 17.9 2.93 3.153 Where T^ is the s o lu b ility temperature and T^ is the nucléation temperature. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE B-2 SOLUBILITY AND NUCLEATION OF MONOSODIUM U R ATE IN 25% V ETHYL ALCOHOL 168 (1/Tg) X 10^ (°K-T) ( 1 / T j X 103 (oK-1 4.52 2.97 3.16 3.33 3.025 3.22 2.7 3.06 3.27 1.96 3.11 3.33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE B-3 5 % SYNOVIAL FLUID F R O M G O U T PATIENT 169 (1/Tg) X 10^ (1 /T J X 103 ( V l ) 4.52 3.12 3.35 5.12 3.1 3.33 6.6 3.06 3.28 8.25 3.03 3.25 The name of the gout patient whose synovial flu id was used was Pio Ruiz. His medical record can be obtained from the Rheumatology Department, U S C Medical School. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 170 TABLE 8-4 5 % SYNOVIAL FLUID F R O M RHEUMATOID PATIENT (I) X 10® (1/Tg) X 10^ (°K-T) ( 1 / T j X 103 4.06 3.16 3.37 6.12 3.09 3.33 7.75 3.04 3.29 10.5 3 3.265 This synovial flu id was obtained from a rheumatoid patient who was on asp irin therapy only. Her name was Mary Washington. (II) (1/Tg) X 103 (1 /T J X 103 ( V l ) 6.7 3.11 3.41 8.8 3.05 3.35 9.7 3.02 3.28 A rheumatoid patient who was taking aspirin only. His name was A vila Candelaria. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE B-5 7.5 X 10*^ M NaCl SOLUTION 171 (1/Tg) X 10^ (1/T_1 X 10^ ” 1 4.25 3.16 3.365 5.45 3.125 3.343 5.82 3.1 3.32 7.07 3.076 3.31 10.8 3.038 3.766 11.35 3 3.234 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 172 TABLE B-6 5 X 10"” M CuClg SOLUTION ( 1 / T g ) X 10^ ( 1 /T j X 10^ n 1 (°K"T) 4.75 3.143 3.35 5.93 3.115 3.332 6 .6 3.095 3.288 6.83 3.085 3.3 9.9 3.035 3.256 R E M A R K S : All of the experimental data shown in the preceding tables are an average of three observations with a maximum deviation o f + 0.5°C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX C THEORETICAL ANALYSIS O F SOLUBILITY DETERMINATION USING THE H O T STAGE 173 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 174 W hen the s o lu b ility o f monosodium urate was determined by heating the crystals u n til they dissolved. I t was found that the observed temperature a t which a ll crystals dissolved depended upon the heating rate (Figure IV -1 1 ). In other words, I f crystals start to dissolve and the heating ra te Is not stopped u ltll all crystals d isso lve, this would give a higher s o lu b ility temperature because there would not be enough time fo r d iffu s io n to take place and equilibrium to be reached. Thus, the observed solubility temperature w ill depart from the true (equilibriu m ) s o lu b ility temperature by an amount depending on the heating ra te . The larg er the heating rate, the g re a te r the departure of the observed s o lu b ility temperature from the equilibrium value. In the follo w in g , a theoretical analysis of the e rro r In the measured s o lu b ility temperature Is given. Consider two p a ra lle l crystals with spacing 2L, a s shown In Figure C-1. The equation which governs the mass transfer Is given by(108) = D ^ , C -1 where C Is the concentration, D Is the d iffu s lv lty , and x Is defined as the distance to the rig h t o f the center lin e between the crystals. I f we l e t A C = C - C^,Q, then Eq. C-1 can be w ritten as: 3(ACl = a^CAC) r _ 2 at 3x • ^ ^ The boundary conditions are: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 175 Figure C-1. Concentration P ro file fo r Two P a ra llel Crystals as they Dissolve Upon Heating Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 176 1. A C * 0 at t = 0 , 2. and 3. (AC)^ ■ m A T a t x . C-3a The second and th ird boundary conditions assume that the s u rfa c e concentration (tru e s o lu b ility ) varies lin e a rly with tem p eratu re, where the proportionably constant is m. I f we le t 6 b e the heating ra te , then the surface concentration is expressed a s (AC)g * met , X = + L . C-3b The solution of these equations is given by Carslaw and (108) J a e g e r as: J U f . tt"' n* 0 ( 2n + l)' ( 2n+l )ttx exp r D(2n«-l)^TT^t C-4 T h i s equation gives the instantaneous concentration as a function of t h e spacing x and time t . The average concentration is 32m6L 2 * exp 4L* D tt n* 0 ( 2n+l) C-5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 177 The temperature a t which this average concentration is the true s o lu b ility is found,by substituting Eq. C-3 into C-5, to be: exp 0(2n+l 4L^ D t t (2n+l) C -6 The observed or apparent s o lu b ility temperature is given by: (6T)g = 6t . C-7 From Eqs. 0-6 and C-7, the erro r in measured s o lu b ility temperature is: E R = (AT)g - (ÂT), (ÂT). 81/ 3D(AT)g 328L< ^ D ir (AT)g n=0 exp (2n+l)VD(AT) 2------------ 41^6 j (2n+l) 1 - BlJ 328L' T , exp (2n+l)^ir^D(AT). C -8 3D(AT)g D r r ‘*(AT)g n=0 (2n+l) 4L^6 “ T " which is plotted as a function of gL /D (aT)^ in Figure C-2. Notice that the error does not depend on the slope of the s o lu b ility curve, m, when the s o lu b ility varies approximately lin e a rly with temperature. I t was shown in Figure IV-11 that the observed s o lu b ility temperature is approximately proportional to the square root o f the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 178 30 20 H 10— I — 0 1 .05 .3 e /3Lyo(ûT)j Figure C-2. Error in the Observed S o lu b ility Temperature Versus the Dimensionless Cooling Rate (From Eq. C-8 ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 179 heating ra te , while Figure C-2 shows that the erro r in the true s o lu b ility temperature should vary approximately lin e a rly with the heating ra te . This discrepancy between the theory and the experimental results is due to the sim plifying assumption that the surface concentrations vary lin e a rly with the temperature, as in Eqs. C-3a,b. Thus, the theoretical resu lt in Eq. C- 8 was expected. To compare the experimental results in Figure IV-11 with the theoretical results in Figure C-2, we must know the spacing between the crystals fo r every measurement of the apparent s o lu b ility . Let us assume an average distance between the crystals to be 70 y and compare the resu lts, as shown in Table C-1. TABLE C-1 Comparison o f the Theoretical and Experimental Error in S o lu b ility Measurements Experimental Theoretical 6 °C/min (AT) (ÂT). [(A T)g-(ûT)g] X 100 6 l2 Error % e ° c 6 °c (ÂT)e DTAT)g Eq. C-2 2 30.2 28.8 4.86 0.0325 1.1 2 33.3 28.8 15.6 0.295 10 10 38.5 28.8 33 1.27 40 In a ll of our s o lu b ility determinations, heating started a t room temperature, assumed to be 24°C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Khalaf, Ali Abdulrahman (author)

Core Title Nucleation And Solubility Of Monosodium-Urate In Relation To Gouty Arthritis

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, chemical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Wilcox, William Ross (committee chair), Friou, George J. (committee member), Whelan, James M. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-808325

Unique identifier UC11363492

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Legacy Identifier 7318823

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Document Type Dissertation

Rights Khalaf, Ali Abdulrahman

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

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