University of Southern California Dissertations and Theses

Adsorption And Flocculation Studies Of Carbon Black Dispersions In Aqueous Solutions Of Sodium Beta-Naphthalene Sulfonate

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Adsorption And Flocculation Studies Of Carbon Black Dispersions In Aqueous Solutions Of Sodium Beta-Naphthalene Sulfonate

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Content 70-13,674- VAN DOLSEN, Karma Marie Gropp, 1940- ADS0RPTI0N AND FLOCCULATION STUDIES OF CARBON BLACK DISPERSIONS IN AQUEOUS SOLUTIONS OF SODIUM/f-NAPHTHALENE SULFONATE. University of Southern California, Ph.D., 1970 Chemistry, physical University Microfilms, Inc., Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED ADSORPTION AND FLOCCULATION STUDIES OF CARBON BLACK DISPERSIONS IN AQUEOUS SOLUTIONS OF SODIUM s-naphthalene SULFONATE by Karina Marie Gropp Van Dolsen A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Chemistry) January 1970 UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 9 0 0 0 7 This dissertation, written by JCarjoa..Marl.e...G:ropp...Yan..B.Qls.en......... under the direction of her.... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Gradu ate School, in partial fulfillment of require ments of the degree of D O C T O R OF P H I L O S O P H Y 'T/I a t Dean Date. DISSERTATION COMMITTEE ..... O u . CJiairman ACKNOWLEDGMENTS I owe my thanks to Dr. Avrom I. Medalia of the Cabot Corporation, who provided the research sample of Sterling FTg; to Leon Dormant, who measured the nitrogen adsorption isotherm; and to the U.S.C. Computer Sciences Laboratory for use of the Honeywell 800 and IBM 360-65 computers. I will always owe a very special debt to Marjorie J. Void, who has been the "prime instigator" and a marvelous example to all her "children." And most of all I am grateful to my husband and parents, who have given just the right support and understanding through out this endeavor. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS ................................ ii LIST OF TABLES................................... v LIST OF FIGURES................................. vii SYMBOL TABLE ..................................... xi ABSTRACT ....................................... xvi Chapter I. INTRODUCTION ............................. 1 II. CHARACTERIZATION OF MATERIALS ......... 12 Choice of System for Study ......... 12 Characteristics of the Carbon Black . 13 Cleaning Sterling FTg ............... 17 Surface Area Determination ......... 17 Preparation and Characterization of Sodium (3-Naphthalene Sulfonate . . . 22 Surface Tension of SNS Solutions . . . 23 Conductivity of SNS Solutions .... 25 Refractive Increment of SNS Solutions. 29 UV-Visible Absorption Spectra of SNS Solutions.......................... 30 Other Materials...................... 33 III. ADSORPTION OF SNS ON STERLING FTg . . . 34 Determination of the Adsorption Isotherm............................ 34 Theory of Adsorption of 1:1 Electro lytes at an Uncharged Solid-Liquid Interface.......................... 39 Interpretation of the Adsorption Isotherm............................ 60 iii Chapter Page IV. MICROELECTROPHORESIS ........................ 67 V. OPTICAL PROPERTIES OF CARBON DISPERSIONS . 82 Dispersion and Aggregation Studies . . . 100 VI. DISCUSSION OF RESULTS...................... 120 Interpretation of Zeta Potentials . . . 124 Interpretation of Stability Ratio . . 129 Suggestions for Further Work............. 142 REFERENCES............................................145 iv LIST OF TABLES Table Page II-l. Adsorption of SNS at the Air-Water Interface from Surface Tension Measurements ........................ 26 III-l. Adsorption of SNS on Sterling FTg . . 37 III-2. Electrostatic Parameters Calculated from the Experimental Adsorption Isotherm............................ 58 III-3. Calculated Area Available to an Ad sorbed Naphthalene Sulfonate Ion for Various Orientations ........... 64 IV-1. Averaged Data from Microelectrophoresis Experiments........................ 74-75 IV-2. Results of Microelectrophoresis Ex periments: Electrophoretic Velocity and Mobility ............. 77 IV-3. Values of the Zeta Potential and Para meters Related to Its Calculation from Electrophoretic Mobility . . . 81 V-l. Descriptive Details of the Dispersions Studied in Figures V-3 and V-4 . . . 92 V-2a. Absorbance as a Function of Time for Dispersions of Sterling FTg in Aqueous SNS Chosen from Stability Series 3 ............................ 109 V-2b. Absorbance as a Function of Time for Dispersions of Sterling FTg in Aqueous SNS Chosen from Stability Series 4 ............................ 110 v Table Page V-3. Optical Data from Which the Stability Ratio Is Calculated: (1/A )(dA/dt) for Each SNS Concentration.......................... 114 VI-1. Physical Constants of Graphite and Water and Calculated Values of the Hamaker Constant...................................133 vi LIST OF FIGURES Figure Page 1-1. Schematic Diagram of the Interaction Energy between Two Spherical Par ticles as a Function of the Distance of Separation of Their Surfaces ........ 10 II-l. Adsorption Isotherm of N„ on Sterling FTg at 78° K ...........7 ................... 19 II-2. B. E. T. Plot of the N2 Adsorption Iso therm on Sterling FTg ................... 20 II-3. Surface Tension of Aqueous SNS Solutions. . 27 • 1 H H Specific and Equivalent Conductance of Aqueous SNS Solutions ............... . . 28 II-5. Difference Reading, Ad, of the Brice- Phoenix Differential Refractometer as a Function of the Difference in Concentration' of SNS between the Two Halves of the Cell ..................... 31 II-6. UV-Visible Absorption Spectrum of Aqueous SNS Solutions ............................ 32 III-l. Adsorption Isotherm of Aqueous SNS on Sterling FTg at 25° C ................... 38 III-2. Schematic Plot of the Distance Dependence of the Concentration of Ions in the Diffuse Double Layer Showing the Effect of the Negative Adsorption of Similions on the Concentration of Bulk Liquid . . . 41 III-3. Calculated Dependence of the Surface Excess on Distance from an Infinite Flat Interface .......................... 47 III-4. Calculated Dependence of Surface Charge Density on Surface Excess ............... vii 52 Figure Page III-5. Calculated Potential Dependence of the Ratio of Surface Charge Density to Surface Excess ........................ 53 III-6. Constant Potential Isotherms for the Ad sorption of a 1:1 Electrolyte on an Infinite Flat Plate................ 55 III-7. Comparison of Constant Potential Iso therms for the Spherical and Infinite Flat Plate C a s e s .................. 56 III-8. Available Area per Adsorbed Naphthalene Sulfonate Ion Calculated from the Adsorption Isotherm ................... 59 III-9. Langmuir Plot of the Adsorption Isotherm ■ — of Aqueous SNS on Sterling FTg Modified to Include the Variation of „ . . 62 ro IV-1. Schematic Diagram of the Electrophoresis Apparatus................. ............. 68 IV-2. Electrophoretic Velocities Plotted Accord ing to the Linear Form of the Equation of a Parabola.......................... 76 V-l. Variation of Extinction Area Coefficient for Aqueous Carbon Dispersions, Cal culated by Various Authors........... 85 V-2. Beer's Law Plot of Ultrasonically Dispersed Sterling FTg in Aqueous S N S ............................ 90 V-3. Wavelength Dependence of the Absorbance of a Series of Aqueous Sterling FTg Dispersions............................ 93 V-4. Reciprocal Wavelength Dependence of the Absorbance of a Series of Aqueous Sterling FTg Dispersions ............. 94 V-5. Time Dependence of Absorbance of Two Dispersions of Sterling MTg during Agitation in the Waring Blendor . . . 102 viii Figure V-6. V-7. V-8. V-9. V-10. V-ll. V-12. VI-1. VI-2. VI-3. Absorbance of a Series of Aqueous Dis persions of Sterling FTg as a Function of Time of Irradiation in the Delta Sonics Cleaning Tank . . . . Decrease in Absorbance with Time Follow ing Dispersion in the Waring Blendor for Suspensions of Sterling FTg and MTg in Aqueous Solutions of Various Dispersing Agents ...................... Decrease in Absorbance with Time Follow ing Ultrasonic Irradiation of Dis persions of Sterling FTg in Aqueous Solutions of SNS of Differing Concen trations. Smoothed Curves from Stability Series 3 ................... Decrease in Absorbance with Time Follow ing Ultrasonic Irradiation of Dis persions of Sterling FTg in Aqueous Solutions of SNS of Differing Concen trations. Data from Stability Series 5 Plotted on Two Time Scales . . Absorbance as a Function of Time According to the Integrated Optical Rate Equation (5.9b) ......... (1/Aq )(dA/dt)t=Q as a Function of the Concentration of SNS ................. (AA1)/(A - A1) as a Function of Time: An Optical Test for Deflocculation . . Surface Potential Calculated from the Adsorption Isotherm as a Function of the SNS Concentration ............. Zeta Potential of Sterling FTg in Aqueous SNS as a Function of SNS Concentration ...................... Log W vs. Log [SNS]: Experimental Points and Curves Calculated Using Values of the Zeta Potential ................... ix Page 104 106 108 113 115 117 119 122 123 131 Figure Page VI-4. Log W vs. Log [SNS]: Curves Based on ip Calculated from the Adsorption ° Isotherm, 154 mv and 77 m v .............. 135 VI-5. Calculated Curves of the Interaction Energy of Two spherical Particles . . . 136 x SYMBOL TABLE A ’ Absorbance A Haxnaker constant A Area a Particle radius a Area of an adsorbed N2 on graphite at 78.2° K b Slope of the A vs. A plot C Concentration D Diffusion coefficient d Distance of separation of the nearest surfaces of two spheres d Position of the refracted line (micrometer reading) in the differential refractometer E Reduced mobility parameter, 67rrieU/EkT e Charge on an electron e Number system base f Activity coefficient f Distance dependent repulsion function for the interaction of parallel flat diffuse double layers fi Exp (u^) + exp (-u^) G Mass of the wet Wilhelmy slide g Grams g Acceleration of gravity H Distance of separation of the near surface of a o , sphere XI fl Planck's constant divided by 2tt I Flux due to diffusion I Current I Intensity of light J Flux due to a shear field K Extinction area coefficient k Second order rate constant k Boltzmann constant k Constant of proportionality of refractive index to Brice-Phoenix differential refractometer reading L Optical path length L Distance-dependent repulsion function for the interaction of spherical diffuse double layers L Distance from a flat interface used in the calculation of surface excess I Distance from an interface %/ A Conductivity cell constant M Mass of dry Wilhelmy slide m Grams of solid used in adsorption determination m Refractive index m. 1 Slope of the log A vs. log X plot of dispersion i N Number of particles per unit volume a Avogadro1s number n Refractive index s n. 1 Number of moles of component i on one square meter of surface xii p Pressure Po Equilibrium vapor pressure of a liquid So Reduced particle size, <a R Gas constant R Resistance R Distance between particle centers or floe radius (p. 99 only) r Radial distance from particle center rll Radius of the polarizable unit s Reduced distance, R/2a T Absolute temperature T Coagulation time T Constant interval of time in deflocculation studies t Time t Temperature, 0 C t Thickness of Wilhelmy slide U Reduced distance, <d U Electrophoretic mobility u •Reduced Volta potential, ze^/kT V Net potential energy of two interacting double layers VA Potential energy of attraction VR Potential energy of repulsion Vs Volume of the surface-containing region V Molar volume of ^ at STP xiii V Volume of solution used in adsorption deter mination V Microelectrophoretic velocity V a Volume of ^ adsorbed, cc STP V . 1 Partial molecular volume of component i W Stability ratio W Non-electrostatic work of adsorption w Width of the Wilhelmy slide w Lifshitz's integral involving the complex dielectric constant X Electric field strength x . 1 Mole fraction of component i y Depth in microelectrophoresis cell z Reduced surface potential, ze^Q/kT z Valence a Polarizability a Reduced size parameter, ziTRm/X 3 First order rate constant r Surface excess Y Surface tension e Absorption coefficient e Dielectric constant S Zeta potential n Viscosity K Reciprocal Debye length xiv k Specific conductivity k Absorption coefficient Aq Limiting equivalent conductance of a salt XQ Limiting equivalent conductance of an ion X Wavelength Number of ions per unit volume p Density Z Specific surface area cQ Surface charge density a , a Conductance of electrolyte and surface (p. 127 only) < j > s Volume fraction of solid in an aggregate particle X Diamagnetic susceptibility ip Volta potential xv ABSTRACT An investigation was carried out into the applica bility of the theory of the stability of lyophobic colloids, DLVO theory, to the type of colloidal dis persion in which the Volta potential results solely from the physical adsorption of ions of one sign onto the solid surface. The system chosen to act as a model for this type of colloid is Sterling FTg, a graphitized carbon black, dispersed in aqueous solutions of sodium 3-naphthalene sulfonate, SNS. The charge density at the liquid-solid interface was calculated from the experimental adsorption isotherm at 25° C by a method which takes into account the negative adsorption of similions in the diffuse double layer. It was assumed that the adsorption results in the formation of an electric double layer in which the ion concentrations follow a Boltzmann distribution near the interface and the electric field decays accord ing to the solution of the Poisson-Boltzmann equation which is applicable to the geometry of the interface. The Guggenheim "N convention" surface excess was used to relate the composite and individual isotherms. Equiv alent relationships were developed for the double layers xvi at an infinite flat surface and a spherical particle. The Volta potential was calculated from the surface charge density and the concentration of ions in solution. -3 This potential has a broad maximum near 5 x 10 M SNS. Microelectrophoretic mobilities were converted into zeta potential values by the method of Wiersema, Loeb, and Overbeek. £ decreases rapidly with increasing -2 concentration to a minimum at 1 x 10 M SNS and then rises slowly. Measurements were made of the time dependence of the optical density of these carbon black dispersions. A new, improved, semi-empirical equation relating ab sorbance and carbon concentration was developed from the observation that absorbance is a linear function of wavelength. This allows calculation of the bimolecular rate constant for Fuchs-Smoluchowski flocculation from the initial rate of change of optical density with time. The corresponding stability ratio, W, decreases slowly 3 with increasing concentration from approximately 6 x 10 at 10-3M SNS to 10 at 5 x 10-2M electrolyte. Using DLVO theory, several values of W were cal culated from and £ for comparison with experiment. For those values of the electrostatic potential based on the adsorption isotherm, an infinitely stable suspension was predicted over the concentration range studied. When xvii zeta was used as the surface potential, a coagulation _3 concentration of approximately 7 x 10 M was calculated. The experimental stability ratios are lower than those predicted by either approach at low concentrations. The experimental curve crosses the "theoretical" one based _3 on zeta at about 7 x 10 M and does not exhibit the ex pected flocculation value. The difference in the behavior of the zeta potential and stability ratio found for SNS-stabilized dispersions of Sterling FTg from those of classical colloids is interpreted in terms of a mobile layer of charges when the surface coverage is less than one. xviii CHAPTER I INTRODUCTION This dissertation reports the results of an in vestigation into the applicability of the theory of the stability of lyophobic colloids developed by Derjaguin and Landau (20, 21) and Vervey and Overbeek (110), DLVO theory, to the type of colloidal dispersion in which the potential in the solution just outside the solid, the Volta potential, results solely from the physical ad sorption of ions of one sign onto the solid surface. The system chosen to act as a model for this type of colloid is Sterling FTg, a graphitized carbon black, and aqueous solutions of sodium (3-naphthalene sulfonate. This work is also of practical interest since a wide variety of real systems, i.e. inks, coated clays, and emulsion paints, are stabilized by the addition of surface active electrolytes. Two classes of charged solid-liquid interface have been extensively studied: the completely reversible (64, 81, 107) and the completely polarized interfaces (22, 32, 65, 86). With the reversible interface, such as that between a sparingly soluble salt and an aqueous 1 2 solution/ the electrostatic potential in the liquid just outside the solid surface is calculated from the Nernst equation. It depends only upon the concentration of potential-determining ions and the zero point of charge, which is generally not the stoichiometric equivalence point. With the Hg-solution interface, the most exten sively studied polarizable interface, the Volta potential is applied externally and results in a measurable change in surface tension and an experimental double layer capacity. The latter two quantities also depend upon the valence and concentration of the ions in solution and their tendency to specifically adsorb at the charged interface. The characteristics of the diffuse electric double layer at a completely polarized interface are essentially identical with those at a reversible inter face. The two types of interface differ principally in their manner of establishing the potential difference. A third classification of interface derives its electrostatic potential solely from the preferential adsorption of an ion which is chemically unrelated to the solid. It is this type of system which is studied in this dissertation. The adsorption of ionized amphi- pathic molecules at the air-water interface results in an electric double layer with a \jjQ determined by the 3 adsorption, and so falls within this classification. Sur face pressure studies of soluble and insoluble ionized monolayers at the liquid-vapor surface have shown that the interactions between the adsorbed ions are generally in accordance with the predictions of Guoy-Chapman theory (10, 35, 40). Aside from the specific adsorption of counterions in the Stern layer, which depends upon the particular nature of the counterion and the potential- determining ion, the double layer adjacent to this type of interface should be identical to that occurring at the polarizable and reversible interfaces. With all three types of colloidal "electrode" a charge concentrates at the solid-liquid interface. Electroneutrality is maintained by two effects: oppositely charged counterions are attracted to the interface and similarly charged similions are repelled from it. The electrostatic forces acting on these ions are opposed by thermal diffusion. The resultant is a diffuse electric double layer. The general characteristic of lyophobic colloids, that they are not thermodynamically stable, is due to the fact that the surface free energy of the dispersed particles is less than the total van der Waals energy of attraction of the dispersed material when in the bulk state. However, sparingly soluble particles of large 4 surface areas can be maintained for long times in contact with solutions of low ionic strength. This is due to the establishment of a high energy barrier to approach. In the absence of an applied shear field, col loidal particles can approach each other by diffusion or as a result of velocity gradients (caused by convection currents or a large difference in settling rate for particles of different sizes). The relative importance of these two approach mechanisms can be expressed in terms of the ratio of the fluxes, J/I, due to a velocity gradient, du/dz, and diffusion respectively (81). R is the sum of the particle radii. t /t = (du/dz) /3- 2kT This ratio is highly sensitive to particle size. For particles of 1000 A radius, normal perikinetic floccu lation is the primary mechanism for shear gradients of 3 -1 less than 10 sec . Brownian motion of dispersed particles has been observed microscopically for latex particles of as large as 3y (101). The rate of rapid coagulation, where every collision leads to a permanent contact, has been shown by Schmoluchowski (81) to be “ fTE = “ 47rDRN2 5 In this equation, N is the concentration of particles of all sizes; R is the distance between particle centers at contact; and D is the diffusion constant for a single particle. The derivation of this equation involves an assumption which is only valid for particles which are of the same size. The coagulation time, T, in which the total number of particles is halved is given by 4ttDRN o For water and dilute aqueous solutions at 25° C, this is about 2 x 10^^/N sec. o Fuchs (29) has shown that when two particles diffuse in a field of force, dv/dr, the probability of a collision is changed by a factor, W. W ' o exp (V/kT) — s2 s is the reduced distance, R/2a. The DLVO theory of colloid stability hypothesizes that the forces between particles are van der Waals attractive forces and repulsive forces due to an increase in free energy of the system when two particles are close enough together that their double layers overlap. Two approaches to the calculation of van der Waals forces exist. Lifschitz (59) and more recently Kihara and 6 Honda (54) have developed expressions for the attractions between two macroscopic bodies immersed in a medium. Un fortunately the dielectric constant, or equivalent op tical data, is required over all frequencies. The data is not always available, so this approach is, as yet, rarely used. The second approach is based upon the observed inverse sixth power dependence of attractive forces between atoms and gaseous molecules, and assumes that the net attractive force between two macroscopic bodies is the sum of the interactions between all major polariz- able groups in both objects. Hamaker (36) derived the following expressions for the energy of attraction between two equal spheres of radius, a, and between two infinite flat plates whose near surfaces are separated by a distance, d. Here s is equal to (2a + d)/a. A r 2 ^ 2 , . s2 - 4, . VA = “ 6 [~2---7 + ~ + ln — 1 ' spheres s - 4 s s Va/cm2 = - — ' flat plates A 12TTd The Hamaker constant, A, is most commonly cal culated with equations developed by Slater and Kirkwood, and Neugebauer (110). 1 3 -24 2 2 ^ 7 A = 11.25 x 10 it q n a , Slater-Kirkwood _6 2 2 A = -16.2 x 10 i q ax, Neugebauer 7 The physical properties needed for the calculation, a and X, are the polarizability and diamagnetic susceptibility, n is the number of polarizable electrons (assumed to be only valence electrons) and q is the density of atoms. Fowkes (28) has derived an equation A - 6« J lYd which depends upon the separation of surface forces into dispersion and non-dispersion terms which are assumed to be additive. The dispersion contribution to the surface tension, y^, can be calculated from a variety of macro scopic surface properties. In the Lifschitz formulation, or macroscopic approach, the Hamaker constant is A = ^ 4tt w is an integral involving the frequency dependence of the dielectric constant. Krupp has simplified the cal culation of w to integration over the major absorption peaks, and gives data for many substances (56). The attraction of two particles immersed in a medium is modified by the attraction of the molecules of the medium for each other and for the particle. Hamaker (36) showed that the effective constant, A^(2)' • ‘ ■s e(3ua^ 8 i l T T o to (Aj - A2) . This results from the fact that the effec tive Hamaker constant for the interaction of two different materials is the geometric mean of the individual Hamaker constants. Krupp (56) has shown that this also follows as an approximation from the macroscopic approach. The repulsion between charged colloidal particles is due to the increase in free energy when the diffuse parts of the double layers overlap. The repulsive po tential energy, V R, can be calculated, using DLVO theory, for integral values of the reduced surface potential from the repulsion functions, f and L, which are found in Vervey and Overbeek's book (110). V_,/cm^ = ( k/ z ^) f (U,Z ) parallel flat plates K 2 VR = (a/z )L(Z,kHq) identical spheres In the above equations, Z is the reduced surface potential, ze^Q/kT, and U is a reduced distance function, Kd. The reciprocal Debye length, k , is proportional to the square root of the ionic strength. 2 2 1 4ire En. zf 4 K = (______ io_i)2 ' £kT ’ 1 / k is approximately the distance in which the electro static potential is reduced to 1/e of its value at the interface. If the surface potential is very small, the equation of Derjaguin 9 2 VR = (ea^0/2)In [1 + exp(-KHQ)] can be used to calculate the energy of repulsion. The total free energy of interaction, including the Born repulsion, always possesses a deep minimum at close approach and commonly has a high maximum at greater distances. There will also be a second minimum. If the particles are large and have a high value of the Hamaker constant, this secondary minimum may be of sufficient depth (i.e., greater than about 5kT) to cause appreciable flocculation. Figure 1-1 shows schematic curves of VA , V and V predicted by DLVO theory. I\ J L Parfitt and Picton (85) have measured the ad sorption of sodium dodecyl sulfate on Graphon and Sterling MTg and have studied the zeta potentials and stability ratios with both carbon blacks. They observed no instability over the whole concentration range avail able when there was no swamping electrolyte. Under the same conditions they observed a minimum in £. The similarities and differences between their results and those presented here are of the greatest interest. They are discussed in Chapter VI. There have been a number of studies of colloidal Agl and latex dispersions (21, 52, 78, 101, 115) which have tested various aspects of DLVO theory. Some ENERGY 1C DISTANCE FIGURE 1-1: SCHEMATIC DIAGRAM OF THE INTERACTION ENERGY BETWEEN TWO SPHERICAL PARTICLES AS A FUNCTION OF THE DISTANCE OF SEPARATION OF THEIR SURFACES. ------ ELECTROSTATIC REPULSION ------ VAN DER WAALS ATTRACTION ------ TOTAL INTERACTION 11 significant deviations from the theory (42, 101) have been attributed to coagulation in a secondary energy minimum which can be significantly deeper than kT for large particles. With Agl sols, both specific adsorption of univalent cations and evidence of structuring of water near the surface have been found. NMR studies have been combined with stability studies of latices to investigate the role of the structure of water in colloid stability. As with ions and molecules in solution, the structure of water at interfaces is highly sensitive to the chemical nature of the charged surface. A comparison of surface potentials calculated from surface charge densities with experimental zeta potentials and colloid stabilities calculated from them is generally lacking. CHAPTER II CHARACTERIZATION OF MATERIALS Choice of System for Study The solid-dispersing agent pair used in this study was chosen to conform as much as possible to the following two requirements. The solid should have a homogeneous, uncharged, and non-polar surface. The dispersing agent should dissolve in water and should adsorb on the surface to provide the solid particle with a charged layer and a concomitant diffuse double layer. Since the primary purpose of this work was to study the aggregation of the colloidal solid and those physical properties of the system upon which the forces between particles might depend, it was desired to use simple, well-characterized materials whose properties fit within the limitations of DLVO theory. Specifically, the theory is limited to interactions between spheres or flat plates, so a spherical particle shape was preferred. A narrow particle size distribution is desirable because different sized particles settle at varying rates; the equations of DLVO theory are simpler if the interacting particles have the same radius than if a^ ^ ; and there is, as yet, no 12 13 quantitative theory for the rate of aggregation of a system with a broad distribution of particle sizes. Three factors limit the range of acceptable radii: Smoluchowski theory assumes that the mechanism of particle approach is diffusion. In the Introduction it was shown that the ratio of the rate of collision due to convection 3 and that due to diffusion varies with R . Since it is virtually impossible to eliminate convection due to differential heating, or vibration, R should be as small as possible, certainly less than 0.5y. Large particles settle faster than small ones, giving a variation in con centration of particulate matter with time, and necessi tating some form of stirring to redistribute the solid through the solution. A sphere with a density of 2.0 gms/ml and a ly radius will settle in water (at 20° C) at a rate of 19 cm/day. Since the rate is proportional to R , a particle with a 1000 A radius will only settle 1.3 cm in a week. It was necessary that the colloidal solid be visible through a light microscope since the electrophoretic mobility of the carbon was to be measured in a microelectrophoresis cell. It was also hoped to use photomicrography to follow the aggregation process. Characteristics of the Carbon Black The solid used in all but a few preliminary ex periments was a research sample of Sterling FTg manufactured 14 and given us by Dr. Avrom I. Medalia of the Cabot Corpora tion. Electron micrographs show that Sterling FTg has a narrow particle size distribution for a carbon black, O 500 to 3000 A, although it is far from monodisperse. O Sterling FTg has a number average radius of 9 70 A, a O surface average radius of 1210 A, an electron micrograph 2 specific surface area of 13.3 m /gm, according to the 2 manufacturer, and a nitrogen surface area of 13.3 m /gm (see page 22). Initial considerations for the stabilizing agent were that the molecules should adsorb at the graphite- water interface; have a simple, rigid geometrical shape; and exist in solution as completely ionized separate units. Sodium dodecyl sulfate and similar long- hydrocarbon-chain electrolytes were eliminated on the basis of the uncertainty of the configuration of the ad sorbed ion, and their micelle forming tendency. Carboxylic acids were eliminated because the effect of a high electro static surface potential on the ionization constant is not completely clear, and it was desired that the surface charge be calculable from the adsorption isotherm. A series of aromatic-ring-containing electrolytes were tested for their ability to stabilize Sterling FTg suspensions. Judged on the basis of maximum optical density after dispersion in a Waring blendor, it appeared 15 that sodium 8-naphthalene sulfonate was better than either potassium phenanthrene sulfonate or sodium toluene sulfonate. Condensates of sodium naphthalene sulfonate with formaldehyde are commonly available and are highly successful as commercial anionic surface active agents. Ultracentrifugal studies of solutions of SNS (39) showed no evidences of association of SNS in solution, even in 0.1 M NaCl. Neither the surface tensions of SNS solutions (p. 27)nor the specific conductance (p. 28) nor the refractive increment (p. 31)show behavior typical of micelle-forming electrolytes (74). Colloidal carbon blacks are available commercially in a wide variety of particle sizes and "structures." Most carbon blacks have particle diameters of less than O 300 A. These particles fuse together forming aggregates of highly irregular shape and with aggregate sizes of O 1000 to 10,000 A. Thermal blacks have particle diameters O of about 1400 to 5000 A and are single spheres or fused doublets (9). Carbon blacks are graphitized by heating to 2800 to 3200° C in an inert atmosphere. Electron micro graphs (102) show that as a result of graphitization the spherical shape of thermal blacks changes to a polyhedral shape. In cross-section there are six to ten faces with an average of eight faces (for Sterling FTg). A regular 16 polyhedron with eight faces in cross-section is an eicosa- hedron, but these are clearly not regular. Graphitization reduces drastically the amount of UV-absorbing substance extractable with organic solvents. Oxidation of graph- itized blacks proceeds from the outside, gradually reducing the size of the particles. This is in contrast to the oxidation of ungraphitized blacks which proceeds from the inside leaving a hollow outer shell (44). This contrast in behavior toward oxidation could be due either to the removal of porosity or elimination of active sites during graphitization. X-ray diffraction studies of carbon blacks show that only for graphitized thermal blacks are the graphite O crystallite dimensions larger than 100 A (43). Hess's high resolution, phase contrast electron micrographs (45) show that the graphite layers are concentric and bend around the corners. The surface is, effectively, a con tinuous bent graphite sheet. Graphitized surfaces have been extensively studied by gas adsorption and liquid immersion techniques (12, 14, 119, 118) using a variety of molecules, and have been shown to be highly homogeneous with no ionizable or polar groups. They are hydrophobic and have a high 2 surface energy, 110 ergs/cm . 17 Cleaning Sterling FTg Thirty gram samples of Sterling FTg were extracted with toluene in a 250 ml soxhlet extractor at a rate of 5 to 10 cycles per hour for periods of 24 hours. The first extract was yellow and absorbed light at ca. 340mjJ Extraction was considered complete when the last batch of toluene, concentrated from 500 to 50 ml, did not absorb in the near-UV« The carbon was then heated in a drying oven to 90° C to drive off excess toluene and allowed to stand in 3N HCl for 48 hours. The chloride was removed by extracting with water over dilute NaOH in a soxhlet extractor. The carbon was considered chloride- free if the last thimble-full of water gave no cloudiness when mixed with an equal volume of 0.01M AgNO^ and allowed to stand overnight. The carbon was then dried at 110° C and stored in a desiccator over P„Oc. z D Surface Area Determination The BET area of the Sterling FTg was calculated from the ^ adsorption isotherm at 78° K. The apparatus was standard except that the pressure was measured electronically. The sample bulb was immersed in a liquid N2 bath. A constant level for the temperature discontinuity was maintained by placing a copper cylinder over the tubing above the sample bulb and keeping 18 sufficient liquid nitrogen in the bath to contact some part of the copper tubing. The volume of the sample bulb was calibrated with the He at 78.2° K. Two adsorption- desorption runs were made. Figure II-l, the adsorption isotherm, shows the volume of adsorbed nitrogen, v , c L plotted against the relative pressure, P/PQ» of the nitrogen. The corresponding BET plot of the isotherm, Figure II-2, is obtained by plotting (1/v )[P/P /(1-P/P )] S O o against P/PQ« The slope of this plot is equal to (C-1)/Cvm and the intercept is 1/Cvm. C is a parameter related to the heats of adsorption and liquefaction of nitrogen. vm is the volume adsorbed at monolayer coverage. The slopes of both runs were the same, 9.11 x 10 ^cc ■ * " , but the intercepts differed (1 x 10 ^ and -4 -1 5 x 10 cc ). Since vm depends mainly on the value of the slope when the ratio of the slope to intercept is large, C >_ 100, the monolayer volume is accurately known. The specific surface of the carbon is proportional to the monolayer volume. Vg 2 - E is the specific surface area in m /gm; ft and V are Avogadro's number and the molar volume of ^ at STP; a is the area that a ^ molecule occupies on the graphite surface; and g is the mass of the solid. 19 Q W o s <! § § ■ 15 10 5 c 0.3 0.2 0.1 0 p/pr FIGURE II-l: ADSORPTION ISOTHERM OF I ' l g ON STERLING FTG AT ?8 K . ( 1 - p/p, 2.0 1.0 0 0.3 0.2 0.1 P/F0 FIGURE II-2: B. E. T. PLOT OF THE Np ADSORPTION ISOTHERM ON STERLING FTG. 21 °2 A value of 16.2 A has been accepted for many years for the area of ^ on a wide variety of materials. Recently Ewing and Pierce (88, 89, 90, 91) and Isirikyan and Kiselev (50) have shown that ^ and a number of other molecules including benzene exhibit localized adsorption on graphitized surfaces at low surface coverage and up to °2 the monolayer point. A value of 19.3 A should be used, if the data is below P/P of 0.1. Above a P/P o o of 0.4 the in the monolayer rearranges to a close- 0 2 packed configuration, and a value of 15.2 A should be used. The bulk of the research on graphitized surfaces was done with Sterling MTg. However, de Boer (17) has shown that the ^ isotherms on MTg and FTg are identical when corrected for the difference in their areas. Pierce (89) has published a universal ^ adsorption isotherm on graphitized surfaces. Ratios of the specific volumes of a given sample to that of the universal ^ isotherm will give an alternate determination of the specific surface area of the sample. The specific surface area of this sample of Sterling FTg was determined from the slope and intercept of the BET plot, Figure II-2 (over the P/pG range 0.1 0 2 to 0.3, 16.2 A /N2) and also by ratios of the volume adsorbed per gram to those given in Pierce's universal 22 2 isotherm. Both methods give a value of 13.3 ± 0.2 m /gm. This is identical to the E.M. surface average area (9). It is the value which was used in deriving all electrical quantities from the adsorption isotherm of SNS on Sterling FTg. Preparation and Characterization of Sodium 3-Naphthalene Sulfonate Eastman Kodak technical grade SNS was recrystal lized from water after decolorization while hot with decolorizing charcoal, vacuum dried over P2°5 anc^ stored in a desiccator (27). The possible impurities are un reacted napthalene, salts of the disulfonic acid, and inorganic salts. Any naphthalene would be removed by the decolorizing charcoal and the filter. Inorganic salts would not precipitate out of a solution whose total concentration was only about 0.5 M. The disulfonic acid is much more soluble than SNS and should remain in the filtrate. The evidence for purity of the SNS is indirect. No melting point could be determined since it was only possible to reach 350° C in the available apparatus. The surface tension behaves normally for a non-micelle- forming surfactant. The refractive index is a linear function of concentration. The best evidence of purity 23 is that the limiting equivalent conductance, Aq, agrees with the literature value (39). Surface Tension of SNS Solutions The surface tensions of solutions of SNS were measured to look for evidence of solute association (i.e., a c.m.c.), and to compare the adsorption of SNS at the graphite-solution interface with that at the air- solution interface. A Du Nuoy tensiometer with a hydrophilic platinum Wilhelmy slide (83) was used to measure the surface tension. Padday (84) has shown that all detachment methods give consistently higher results than do equi librium methods when measuring surface tensions of solutions. With pure liquids he observed no difference. The difference can be attributed to expansion of the surface during detachment without time to re-establish adsorption equilibrium. The equilibrium, non-detachment method was followed here. All glassware was cleaned by standing overnight in acid dichromate cleaning solution, followed by repeated rinsing with distilled water. The platinum slide was depolished with coarse and fine emery paper. It was cleaned before use by immersion in dilute detergent solution, followed by dipping in 6N HNO^/ and finally 24 by repeated rinsings with distilled water. It was allowed to dry, then flamed before use. The tensiometer was calibrated with known weights. The tensiometer was balanced against the dry Wilhelmy slide so that the reading was due only to the weight of the meniscus. Solution was poured into an open crystal lizing dish, which was carefully raised by a screw jack until the level solution just touched the level lower edge of the pre-balanced slide. Leveling was checked visually. The slide was raised and lowered slightly from the balance point and equilibrium re-established. The surface tension is directly proportional to the tensiometer reading as there is no buoyancy cor rection (38) . y = g(G - M)/2(t + w) G is the apparent mass of the wet slide; M is the dry mass of the slide; g is the acceleration of gravity; t and w are the width and thickness of the platinum slide; and y is the surface tension. The surface excess was calculated using Gibb's equation for 1:1 electrolyte T(1 + 6 In f/(S In c) = - (1/2RT) (fiy/Gln c) and the approximation (15) a. 6In f/dln c = -0.5 8 c • 25 The surface tensions, surface excesses, and areas avail able to an adsorbed molecule are presented in Table II-l and Figure II-3. Conductivity of SNS Solutions The conductivities of aqueous solutions of SNS were measured with a student dip cell and a Fisher Scientific conductivity bridge, model RC 16 B2. The cell constant, Z/A, was found by measuring the conductivity of a 1.976 x 10 KC1 solution (k= 0.002734 mho cm ^). The temperature of the solution was not held constant (a max imum variation was ±2° C) but was measured immediately following the experiment and the resistance corrected (69). R25° C = Rt(1 + °-025At) A cell constant of 0.224 was found. The specific conductivities of a series of solutions of SNS were obtained by measuring the resistance of the solution and correcting for the conductivity of the water — 6 — 1 used (3.3 x 10 ohm ) and the difference in temperature from 25° C. The specific conductances and the calculated equivalent conductances are shown as a function of con centration of SNS in Figure II-4. The limiting equivalent conductance of SNS, 84, agrees with the value found by Hattori (39). Since that of Na+ ion is 50.11, the value 26 TABLE II-l ADSORPTION AT THE AIR-WATER INTERFACE FROM SURFACE TENSION MEASUREMENTS [SNS] M Y dynes/cm x 106 moles/m2 Area per Molecule A2 O.OOl 71. 4 0.05 5600 0.002 71.5 0.06 5000 0.00 5 71.1 0.15 1500 0.010 70.6 0.19 890 0.020 70.0 0.44 580 0.050 69.4 1.6 100 0.040 68.6 5.8 44 0.050 65.5 5.4 48 SURFACE TENSION 27 80 70 60 50 0.10 0.05 o (SNS) FIGURE II-3: SURFACE TENSION OF SNS SQL'.TIOKS. 100 2.0 1.5 K 1.0 0.5 o 0.02 0.01 0 ( S I ' i i S ) FIGURE II-k: SPECIFIC AND EQUIVALENT ' ONn ICTANCES OF AQVEUS SNS SOLUTIONS. O K O---- J\ 29 of XNg needed for calculation of the zeta potential from mobility is found to be 34. Refractive Increment of SNS Solutions Small differences in refractive index (as between two solutions of the same salt with slightly differing concentrations) can be measured more accurately in a differential refractometer than by measuring the refrac tive indices directly. This is a rapid and sensitive method of determining concentrations. The Brice-Phoenix differential refractometer, BPDR, was calibrated with solutions of SNS. The differ ence in refractive index between the contents of the two cell compartments is directly proportional to the differ ences in position, Ad, of An = kAd the refracted fine line of light when the cell is rotated 180°. The constant of proportionality, k, was previously found to be 0.862 x 10-5. A Hg-arc light source with a blue, 436my, filter was used. The cells are filled and emptied with a long eye dropper. They were cleaned by repeated filling and emptying with hexane followed by acetone, "Joy" solution, and water. The instrument zero correction was deter mined with both cells filled with water. For each data 30 point, ten pairs of readings were averaged. The refracto- meter can be used for changes in concentration of SNS solution of 0.002 M with less than 5 per cent error. The results of the BPDR calibration are presented in Figure II-5. It follows directly from the linearity of the calibration plot that there is a linear relation between refractive index and concentration in the region of concentration covered. UV-Visible Absorption Spectra of SNS Solutions The UV-Visible absorption spectra of a series of SNS solutions were determined with the Cary Recording Spectrophotometer for use as a second physical method of concentration determination. There are three peaks in the near UV at 320, 312, and 305my with extinction co efficients of 806, 584, and 690 M '*'cm ^ respectively, which are useful for the concentration range 0.0005 to 0.001 M. The Beer's law plots are linear. The extinction coefficients were determined from four points each. They are sufficiently close together that the concentration, of a solution can be determined three times per UV run. -4 -3 The spectra of 1 x 10 and 1 x 10 M solutions are shown in Figure II-6. 6ooo 2000 0 0.10 0 (SNS) FIGURE II-5: DIFFERENCE READING OF THE DRICE-P1I0ENIX DIFFERENTIAL REFRACTOMETER AS A FUNCTION 01' TJjE DIFFERENCE IN CONCENTRATION OF SNS BETWEEN THE TWO HALVES OF THE CELL. ABSORBANCE 1.0 vo co 0.001 M 0.0001 M 250 300 350 WAVELENGTH, mu FIGURE II-6: UV-VISIBLE ABSORPTION SPECTRA OF AQUEOUS SNS SOLUTIONS. Other Materials Triple A Water Company distilled water (1 ppm total impurity) was used directly except for the surface tension and differential refractometer measurements. For those experiments the distilled water was redistilled from alkaline permanganate in an all-glass still and stored in glass flasks. Eastman Kodak commercial grade p-toluene sulfonic acid was vacuum dried over P2°5* Solutions of sodium p-toluene sulfonate, STS, were made by titration of the acid with NaOH to pH 7. Matheson, Coleman and Bell USP grade sodium benzoate, SB, was used as received. Potassium 3-phenanthrene sulfonate, PPS, was synthesized in this laboratory using the procedure of Fieser (7). CHAPTER III ADSORPTION OF SNS ON STERLING FTg The adsorption isotherm of SNS on Sterling FTg is essential for understanding the mechanism of "stabili zation" of the carbon dispersion by the surface-active ion. From the adsorption isotherm it is possible to calculate the maximum amount of SNS which can be ad sorbed, the extent of surface coverage at any concentra tion, and a number of electrostatic quantities. Of particular interest is the Volta potential, ipQ, which is to be compared with the potential at the plane of shear, £. The zeta-potentials are calculated from experimental electrophoretic mobilities (p. 81). The electrostatic potential, x , or ijj^, is necessary for calculation of the stability ratio, W. Also desired is the heat of ad sorption which determines the shape of the adsorption isotherm and is also considered a significant factor in interpreting the unusual behavior of the zeta-potential. Determination of the Adsorption Isotherm The adsorption isotherm of SNS on Sterling FTg at 25.0° C was carried out over the concentration range from 34 35 -4 -1 10 to 10 M SNS. In all, eight adsorption series were made with a total of 31 separate determinations. The general procedure used on all runs was to weigh a predetermined amount of carbon (between 1 and 5 grams) into a 20 ml test tube, add 10.0 ml of a solution of SNS, stopper firmly with an aluminum foil-covered cork, and irradiate for one hour in a Delta-Sonics cleaning tank (1 gallon, 100 watts, 45 kc). The tubes were then im mersed in a constant temperature bath at 25.0° C for 12 hours, re-dispersed ultrasonically for 30 minutes, and put back in the constant temperature bath for another 12 hours. The dispersion, better described as a thick paste, was transferred to a 10 ml nitrocellulose centrifuge tube and centrifuged in a Servall angle centrifuge for 40 minutes at about 10,000 rpm. The clear liquid was transferred to a second tube and re-centrifuged. The supernatant liquid was then withdrawn with a pipet and either used directly or diluted for the measurement of concentration. In a preliminary series of runs the SNS concen tration after adsorption was measured with the Brice- Phoenix differential refractometer, in which the reading is proportional to the difference in refractive index of the two liquids in the two compartments. Water was used as the reference liquid. The calibration of the BPDR is 36 described in Chapter II (p. 29). For the 31 runs whose results are listed in Table III-l and Figure III-l the final SNS concentrations were determined with the Cary recording spectrophotometer. The absorbance of the three peaks at 305, 312, and 320ny were measured and con verted to concentrations. The extinction coefficients label the SNS absorption spectra, Figure II-6 (p. 32). Initial concentrations were calculated from the weight of SNS used and the size of the volumetric flask in which the solutions were made. There were marked differences in the concentrations of the supernatant determined by the BPDR and by the Cary. A higher final concentration leads to lower values of the surface excess. If an impurity entered the solution during ultrasonic irradiation (admittedly a violent process) or equilibration, it would increase the refrac tive index of the solution. There was no change in the nature of the UV-visi.ble absorption spectrum during adsorption. The hypothesis that a non-absorbing impurity went into solution increasing the refractive index is consistent with the observation that the greatest differ ence between Cary and BPDR values was for a sample with 2.5 times as much carbon (5 g) and a higher SNS con centration (0.5 M) than the rest of the runs. 37 TABLE III-l ADSORPTION OF SNS ON STERLING FTG [SNS] Initial M x 1 0 2 [SNS] Final M x 1 0 2 [SNS] M x 1 0 2 Carbon grams rfj x 106 2 moles/m 1.21 0.941 0.269 2.098 1.37 1.21 0.930 0.280 2.199 1 .3 7 1.56 0.864 0.701 5.018 1.24 1.56 0.974 0.571 4.798 1.27 1.56 1.21 0.355 2.129 1.26 1.56 1.22 0.345 1.915 1.35 9.80 9-37 0.432 1.953 1.66 0.98 0.385 0.595 4.636 0.96 0.196 0.060 0.140 2.943 0.355 0.294 0.080 0.210 3.343 0.47 0.500 0.250 0.250 2.905 O.65 0.980 0.600 0.380 2.959 0.975 4.00 3.45 0.550 3.349 1.24 6.90 6.15 0.750 3.048 1.87 5.01 2.21 0.800 4.067 1.51 5.01 2.41 0.600 2.822 1.60 5.02 4.13 0.890 3.826 1.77 5.02 4.25 0.770 3.082 1.87 D 2.25 a 1 .8 3 0.390 2.096 1.60 D 5.62 b 3.22 0.400 1.689 1.87 D 0.558c 0.345 0.193 1.803 0.89 D = desorption a) V = 11.25 ml b) V° = 10.53 ml c) V° = 11.09 ml A ll fin a l SNS concentrations determined with the Cary recording spectrophotometer. aoo HIGHLY COAGULATED 1 . 0 0 0 0.02 0.04 0.06 j - s n s j 0.08 FIGURE III-l: ADSORPTION ISOTHERM OF AQUEOUS SNS ON STERLING FTG AT 25-0°C. 0.10 39 The Guggenheim "N" convention surface excess is directly calculable from the change in concentration of solution resulting from equilibration with the carbon surface (34). rN = VAC 2 mZ Concentrations before and after adsorption (determined spectrophotometrically), the mass of carbon used for each run, and the experimental surface excesses are listed in Table III-l (p. 37) and presented graphically in Figure III-l (p. 38). Most reports of the adsorption of surface-active electrolytes found in the literature stop at this point and show the grams or moles of adsorbed species per unit mass or area of the solid. As will be shown, this is both an insufficient and misleading treatment. Theory of Adsorption of 1:1 Electrolytes at an Uncharged Solid-Liquid Interface The presence of an adsorbed layer at the solid- solution interface is inferred from an observed con centration change when colloidal solid is placed in contact with solution. If one of the ions adsorbs preferentially, the interface becomes charged, and a diffuse double layer is formed spontaneously extending outward from the charged surface. Since counterions 40 are attracted to the charged interface, their concen tration in the diffuse double layer is greater than in the bulk solution and they are said to be positively adsorbed. Similions are repelled from the surface and are said to be negatively adsorbed. The neutralization of the surface charge is accomplished by the combination of the positive adsorption of counterions and the nega tive adsorption of similions. Since positive adsorption is inferred from a decrease in concentration of the bulk solution, and negative adsorption is inferred from an increase in concentration, the net change will be smaller in magnitude than the larger of the two effects. The situation is shown schematically in Figure III-2. This measured concentration change is usually converted into a surface excess quantity, analogous to that calculable from surface tension data for adsorption at the liquid-vapor interface. In the case of the solid- liquid interface in which the solid is impenetrable to solvent and solute alike, the surface of contact between the solid and solution is a logical choice for the dividing surface. An arbitrary surface must be chosen to separate the bulk solution from the surface-containing region. All extensive quantities of the interfacial region will be dependent on the position of this second surface. Any convention chosen should satisfy the CONCENTRATION — c o o DISTANCE FIGURE III-2: SCHEMATIC PLOT OF THE DISTANCE DEPENDENCE OF THE CONCENTRATION OF IONS IN THE DIFFUSE DOUBLE LAYER SHOWING THE EFFECT OF THE NEGATIVE ADSORPTION OF SIMILIONS ON THE CONCENTRATION OF BULK LIQUID. A. INITIAL ELECTROLYTE CONCENTRATION. B. FINAL ELECTROLYTE CONCENTRATION. C. FINAL CONCENTRATION IF THERE WERE NO NEGATIVE ADSORPTION OF SIMILIONS. 42 following criteria: (i) give a value of the surface excess which is independent of the choice of position of the second dividing surface; (ii) clearly show the relative presence of both solvent and solute in the interfacial region; and (iii) allow a concept of this region which facilitates application of diffuse double layer theory. The Gibbs surface excess, ^ ^ . is conceptually difficult, and has the further disadvantage that the extent of the surface region must change as the com position of the surface region changes (34). The N Guggenheim-Adam "N convention" surface excess, r is a logical choice inasmuch as it satisfies the above criteria and also allows resolution of the composite isotherm into individual isotherms (55). The Guggenheim- Adam surface excess is defined as the number of moles of electrolyte in a volume of solution containing one square meter of surface and N total moles of all species, in excess of the corresponding quantity in a volume of bulk solution, containing the same total number of moles. This surface excess quantity is symmetrical with respect to solvent and solute. It is directly related to the Gibbs surface excess. 43 rN = x r(1) l2 XV2 It is calculable from a measured concentration change = -NoAx2/mZ (3.1a) if the specific area is known and the solid has a well characterized surface. Its definition gives the relation ship between the composite, and individual isotherms, n® and n® (78). . r2 = (1/mE)[n2 - x2(n^ + n2)] (3.1b) The extent of the surface-containing region is not specified by the definition of the surface excess. This region must contain all of the solution whose concentration differs from that of the bulk liquid and may contain any amount of bulk solution. The bulk solution makes no con tribution to the value of the surface excess. No assump tion is involved in the definition of surface excess as to whether either component forms a monolayer on the surface. The above definition of the symmetric surface excess and the classical Guoy-Chapman model of the diffuse double layer are combined below to show that the surface excess cannot be considered a surface concen tration in the presence of an ionized monolayer on an impenetrable solid-liquid interface. 44 It is postulated that one of the ions of the ad sorbed 1:1 electrolyte is surface active and that it forms an ionized monolayer at the solid-liquid interface. All counterions are assumed located in the diffuse double layer (no specific adsorption). Similions are negatively adsorbed in the diffuse double layer. Since the surface-containing region must be electrically g neutral, the total moles of electrolyte adsorbed, ^ , equals the total moles of counterions in the diffuse double layer, which must be equal to the sum of the moles of similions in the diffuse double layer and on the charged surface. These conditions are expressed in Equations 3.2ab, in which N is Avogadro's number and vc and v are the concentrations of the counterion and s similion, respectively. Vs is the volume of the surface- containing region. Vs f v dv (3.2a) c o Vs v dv + Acr (3.2b) o s ° n® = (1/fJ) n® = (1/fl) It is a basic assumption that the preferential adsorption of ions of one sign is the sole source of the electric potential difference between the surface and the bulk solution. The counterions and similions 45 not actually on the surface are assumed to be distributed according to the Boltzmann law, Equation.3.3, which with Equations 3.2a and 3.2b yields Equation 3.4. The in finite flat plate case is treated first. The volume element, dv, has been replaced by Ad£ and the exponentials have been combined to give the cosh u term. u is the reduced surface potential of Overbeek (110) , zeij;/kT. The 4 factor 10 permits the area, A, to be in square meters, consistent with the units of surface excess. Vi = vb exp(zie^/kT) (3.3) u (L) ' cosh u(d£/du)du (3.4) •u o The decay of the electric field with distance from the charged surface is obtained from the first integration of the Poisson-Boltzmann equation (110). (du/di) = - (32ire2vb/ekT) 2 sinh (u/2) (3.5) Substitution of 3.5 into 3.4 and integration results in an exact expression for n®, Equation 3.6, which lacks the explicit introduction of the limits of integration. l n®/A = (104P)/e) (vbkT/8u)T [2 sinh (uq/2) - u (L) (3.6) u o In tanh (u/4 - cosh (u/2)] 46 One of the advantages of using the symmetrical surface excess is that the thickness of the surface region, L, is not at all critical so long as it is allowed to be large enough that the ion concentrations at the limit of the surface region agree with the bulk ion concentrations to the precision desired of the calculation. The value — 6 of L was chosen such that u(L) =10 uq. Solution .con- -4 centrations are within 10 per cent of their bulk value with this choice. For the infinite flat plate case L ° b -3 0 varies from about 1400 A at C =10 M to about 200 A at Cb = 5 x 10-2 M. Figure III-3 shows that, for an infinite flat plate for which uQ is 4.0 and C is 0.01 M, the surface excess (calculated) is independent of the choice of depth of the surface region provided that the latter is equal to O or greater than the Debye "double layer thickness" (33 A for this concentration). Note that the corresponding surface charge density is larger than the surface excess by a factor of 1.44. That expulsion of similions from the immediate vicinity of the surface is the basic source of the difference is supported by the observation that this effect is greatest for the Debye-Hvickel approximation, in which the decay of the potential with distance appears slow, and becomes negligible as the surface potential approaches lOkT/e. If there were no negative adsorption o 0- 1 -! s cvj u 2.0 " 50 25 0 DISTANCE, A FIGURE III-3: CALCULATED DEPENDENCE OF THE SURFACE EXCESS ON DISTANCE FROM AN INFINITE FIAT SOLID- LIQUID INTERFACE „ u = 1*.0, C = 0.01, aQ = b Al x ] 0~' MOLES/METER . -p- 48 of similions near the surface, the surface charge den sity would equal the surface excess, analogous to a monolayer of charges. This is the same as the prediction that the ratio of the negative adsorption to the surface charge density depends on \pQ but is independent of ionic strength (109). In order to calculate the surface excess (which is a composite isotherm) from the derived individual iso therm for component two, Equation 3.6, a further assumption is necessary. That chosen is that the partial molecular volumes of the two components in the surface-containing region are the same as in the bulk solution, even though some of the ions are attached to the surface. The error introduced by this assumption leads to a volume of the surface region which might be somewhat too large, but the primary effect is in the second term in Equation 3.8b, -3 which in these calculations is always less than 10 times the value of the first term. The error in the calculated surface coverage at saturation is probably less than 1 per cent. The remaining pertinent equations are Equation 3.7a for the volume of the surface region and Equation 3.7b for the equilibrium bulk concentration. Introducing the bulk mole fraction, x2, and rearrangement yield the relations, Equations 3.8a and 3.8b, used with Equations 3.7a and 3.7b for numerical calculations. 49 vS = (nl^l + n2^2) (f}/106^ (3.7a) Cb = (103/ft)[nb/(nbv1 + nbvb)] (3.7b) x2 = [103/Nv1Cb - (v2 - v1)/v1]“1 (3.8a) n3 = (106VS/5Iv1) - (v2/v^) n2 (3.8b) For use in these equations, n® is obtained from Equation 3.6. The volume of a sodium 8-naphthalene sulfonate molecule, calculated from bond lengths and appropriate van ° 3 der Waals radii, is taken to be 330 A . The values of the bond lengths and atomic radii used in this calculation are listed in Table III-3 (p. 64). An average molecular ° 3 volume of water of 30 A was calculated from the density of water at 25.0° C. Most of the numerical work was done on a Honeywell 800 digital computer. The symmetric surface excess and the surface charge densities were calculated over a wide range of surface potentials and concentrations. Similar calculations, based on the same principles, were carried out for spherical particles. Since the Poisson-Boltzmann equation can not be integrated ana lytically in spherical symmetry, a numerical integration was performed. The computer-generated numerical tables of reduced potential as a function of reduced distance 50 of Loeb, Wiersema, and Overbeek (60) were used. The integral over the spherical surface region, corresponding to that for an infinite flat plate given in Equation 3.4, was done numerically using Simpson's rule and results in Equation 3.9a. n2/A = ao/2+(l°6vbAr/6Ra2) (f r2+4(nz1>/2f r 2+2(nE1)/2f +f r2) (3*9a) '^**11 O-J On 2 2 j • 1 y s y \ X I • i 2i 21 •—n 21-1 n n 1=1 1-2 fj = exp(uj)+exp(-uj) It is convenient to redefine the pertinent variables in the terms used by Loeb, Wiersema, and Overbeek so that the available tabular quantities can be used directly as input to the computer. These terms are qQ = Ka, x = 1/Kr, and aQ = (ekT/4ire) I (q.Q PQ) • These substitutions give rise to Equation 3.9b. n®/A = (102ekT/8iTe2aR) [qQI (qQ ,uQ) - (Ax/6qQ) . _4 (n-l)/2 _4 (n-l)/2 (flxl +4 .S f2ix2i+2 f2i-lx2i-l+fnxn )] 1=1 1=2 (3.9b) O The calculated surface excesses for spheres of 100 0 A radius are higher than those for a flat plate of the same potential and surfactant concentration by an amount which increases with increasing potential. 51 The integration of the spherical analog of Equation 3.4 can be done analytically only in the Debye- Hiickel approximation, uq << 1, and leads to Equations 3.10a and 3.10b. n2 = Aao/2 + A(106vb/3a2fJ) (r3-a3) (3.10a) oq - 2r2 (3.10b) The latter equation shows that in the extreme case of low potential, low adsorption, and low ionic strength the negative adsorption of similions in the diffuse double layer region is just half of the positive ad sorption due to the charged surface. At the opposite extreme is the high ionic strength region, in which, for spherical particles, = crQ. In the absence of added salt (the only case considered here) as the ionic strength varies so does the relationship between the surface excess and the charge density of the ionized monolayer. Figure III-4 shows that the relation between surface charge density and surface excess (both cal culated) is linear but that the slope decreases from a high of 2.0 in the Debye Huckel approximation to a value of 1.35 for a flat plate with a u of 7.0 and 1.04 for a o O sphere of radius 1000 A and uq equal to 7.0. Figure III-5 shows that the effect of negative adsorption depends on the curvature of the particle as well as on the surface 2.0 'A rH X 1.0 0 0.5 1.0 ,6 N FIGURE III-4: CALCULATED DEPENDENCE OF THE SURFACE CHARGE DENSITY ON THE SURFACE EXCESS. (A) SPHERE, u << 1, (B) SPHERE, u = 1.0, (c) INFINITE FLAT PI ATE, u = 7-0, (D) SPHERE, u = 7.0. 0 2.0 5.0 10.0 0 Uo FIGURE III-5: CALCULATED DEPENDENCE OF THE RATIO OF THE SURFACE CHARGE DENSITY TO THE SURFACE EXCESS ON THE ELECTROSTATIC SURFACE POTENTIAL. CURVE A IS FOR THE INFINITE FLAT PLATE CASE. CURVE B IS FOR SPHERES WITH 1000 R RADIUS. u> 54 potential; the ratio of c r /r^ falls from the Debye-Httckel limiting value of 2.0 to 1.35 for an infinite flat plate at high potential and to close to 1.0 for spherical colloid particles at high potential. The ratio decreases more rapidly with increasing potential for small spheres than for large spheres. Figures III-6 and III-7 show how the calculated values of the surface excess vary with electrolyte con centration for various constant values of the reduced surface potential. These constant potential isotherms are the principal means for interpretation of the experi mental adsorption isotherms. Each pair of values of N b and C corresponds to a specific u q which can be ob tained from these graphs by interpolation. A comparison of the general shape of the constant potential isotherms with the shapes of observed adsorption isotherms of 1:1 surfactants (generally rectangular hyperbolic in the absence of cooperativity) at the graphite-water interface shows that uQ must rise rapidly with increasing sur factant concentration, pass through a maximum and then decrease as the surface region becomes saturated and the ionic strength continues to increase. Zeta potential measurements on sodium dodecyl sulfate and trimethyl ammonium bromide stabilized Graphon and n-decane dis persions in the absence of added salt (2, 41) as well as 2.0 * 1.0 5 OJ u 0 o.oS ,b 0.12 FIGURE III-6: CONSTANT POTENTIAL ISOTHERMS FOR THE ADSORPTION OF A 1:1 ELECTROLYTE ON AN INFINITE FLAT PLATE, (a) u = 5.0 (b) u = 6.0 (c) u = 7.0 (d) u = 8.0 (E) u = 9.0 (F) u = 10.0. 0 0 0 0 0 v ' o \S l \n 2.0 1.5 < —I X 1.0 S C V J L 0 0.005 ,b 0.010 FIGURE III-7: COMPARISON BETWEEN THE CONSTANT POTENTIAL ISOTHERMS FOR THE INFINITE FLAT PLATE CASE AND THOSE FOR SPHERICAL PARTICLES WITH A 1000 R RADIUS. SOLID LINE IS FOR THE FLAT PLATE CASE. DOTTED LINE IS FOR SPHERES. (A) u = 1.0 (b) u =2.0 (C) uo = 3-0. C T \ 57 those observed in the course of this work fail to confirm this general prediction. A given adsorption gives rise to a lower potential on a spherical particle than on a flat plate. The differ ence is significant, but the limited range of concen trations for which data for spherical particles are avail able limit their use for quantitative analysis of the experimental adsorption isotherm. Values of the surface potential calculated from the experimental adsorption isotherm, Figure III-l (p. 38), and the equations for a flat surface are listed in Table III-2 together with the values of the surface excess and surface charge density from which they were calculated. The surface potential rises with increasing SNS concentration to a maximum of 178 millivolts and then slowly drops to about 150 millivolts at higher concentrations. The experi mental adsorption isotherm is not sufficiently precise to determine values of u as the concentration of SNS o approaches zero, but the existence of a maximum and its location at 0.005 M electrolyte is clearly defined. The surface charge densities for these concentrations and N surface potentials are about 1.35 Since the surface charge is assumed to consist of a monolayer of naphtha lene sulfonate ions, the area available to an adsorbed ion is directly calculable from aQ. Figure III-8 is a 58 TABLE III-2 ELECTROSTATIC PARAMETERS DERIVED PROM THE ADSORPTION ISOTHERM OP SNS ON STERLING FTG [SNS] M JN -1^6 r2 x io moles/m^ c r X 106 O 2 moles/m uo ' I ' Yo mv O.OOl 0.5 0 0.5 6 6.5 0 167 0.002 0 .60 o !8i 6.8 0 175 0.005 0.76 1 .0 5 6.8 7 176 0.005 1.0 2 1.57 6 .9 5 178 0.007 1 . 18 1 .5 9 6 .8 8 176 0.010 1 .5 5 1 . 80 6 .7 9 174 0.020 1 .5 9 2.14 6 .4 7 166 0.050 1.76 2 .57 6.24 160 0.040 1.86 2.50 6.0 7 155 0 .0 50 1 .8 9 2.5 5 5 .90 152 . . . ........ .... .............................................................. . lt-00 200 o — 0.02 FIGURE III-8: AVAILABLE AREA PER ADSORBED NAPHTHALENE SULFONATE ION CALCULATED FROM THE ADSORPTION ISOTHERM. v « n VO plot of the concentration dependence of the area per ad sorbed NS . Interpretation of the Adsorption Isotherm The experimental adsorption isotherm is of the Langmuir type. There is no apparent s-curvature charac teristic of isotherms involving cooperative phenomena. It will be shown that over the entire concentration range the adsorption can be characterized by a constant, non electrostatic heat of adsorption and an electrostatic work term which depends upon the extent of surface coverage. The equations used for the Langmuir plot were modifications of the Langmuir equation developed by Groot, Overbeek, and Void (33). The fraction of surface covered was replaced by the ratio of the surface charge density, aQ, to the limiting surface charge density, oQm, °o = ae(e^Q + W)/kT a - a om o a is the activity of the surfactant and the work of ad sorption is expressed as the sum of electrostatic, eijjQ, and non-electrostatic, W, work terms. Since the electro static work is high, eiJ;o/kT >> 1, sinh (e^Q/kT) is well approximated by iexp (eip /2kT) . 6 o 0o = exp(ei|>o/2kT) 61 This expression can be substituted into the modified Langmuir equation and arranged in a linear form. culated from the slope and intercept. The linear plot is shown in Figure III-9. A least squares fit of the The non-electrostatic heat of adsorption was calculated to be -15.8 kT or -9.4 kcal/mole. Since the electro static work of adsorption is 6.7 ± 0.2 kT over most of the concentration range, this corresponds to a net heat of adsorption of -5.3 kcal/mole of SNS. Giles (30), studying the adsorption of benzene sulfonic acid on natural graphite crystals, found a net heat of adsorption of BSA of -5 kcal/mole. There is strong evidence for preferential ad sorption of aromatic ring systems on graphite with the plane of the ring parallel to the graphite surface. Pierce (89, 90) has shown that benzene from the vapor phase adsorbs flat on specific sites on the graphite surface. The interaction energy of benzene with graphite a a o om + llOfrfle^ exp(-W/kT) lO^ekTa om 2 3 2 2 C /a is plotted against C / o Q. a and VJ are cal- om o data gave a slope of 4.92 x 10^, which corresponds to a — 6 2 maximum surface charge density of 2.04 x 10 moles/m . 62 300 200 100 150 200 100 0 FIGURE III-9: LANGMUIR PLOT OF THE ADSORPTION ISOTHERM OF AQUEOUS SNS ON STERLING FTG, MODIFIED TO INCLUDE THE VARIATION OF THE SURFACE POTENTIAL. 63 has been calculated (93) to be -9.84 kcal/mole when flat. But rotations of the benzene ring out of the surface plane result in an additional (repulsive) heat of adsorption of 4.9 kcal/mole times the angle of rotation. Similar conclusions are found in a theoretical treatment (16) of intermolecular forces in crystalline benzene and naphthalene. Craig (16) has shown that the dispersion forces provide most of the lattice energy but that the repulsions of the hydrogen atoms is minimized in the equilibrium molecular arrangement. A comparison of the area per NS ion at monolayer coverage with areas calculated from bond lengths (87) and van der Waals radii (11) leads to the conclusion that the ions are most probably adsorbed flat. The minimum area available to an adsorbed NS ion was found from the °2 Langmuir plot to be 87 A . Geometrical areas for the three possible configurations and areas for the ions packed in a rectangular array are tabulated in Table III-3. The bond lengths and van der Waals radii used, together with a sketch of the molecule, are also shown in °2 Table III-3. The calculated 88 A for a rectangularly packed NS ion is within experimental error (less than °2 5 per cent) of the 87 A found from the adsorption iso therm. 64 TABLE III-3 CALCULATED AREAS O P TH E 0-NAPHTHALENE SULFONATE ION Packing Orientation Non-hydrated Two Waters H-bonded Geometric F lat (no packing) Edge End Rectangular F lat Packing Edge End 64.0 45.6 38.0 88 64 54 76.3 57.9 50.3 136 136 78 van der Waals Radii Covalent Bond Lengths H 1.20 A C-H 1.07 A 0 1.40 C-C 1. 4o C-C 1.54 C =C 1.34 S-0 1.49 H alf-thickness 1.85 i 1 O 65 Strongly hydrated ions are generally very small or polyvalent. Since the NS ion is quite large and only carries a single charge, it seems likely that it adsorbs in an unhydrated state. The rectangular packing model actually allows room for one water per 2NS so some water could be present in the adsorbed layer. A comparison of the adsorption of NS at the air- water and Sterling FTg-water interfaces is interesting. 1 Adsorption at the air-water interface is due solely to interactions between the ions and water. Adsorption onto the solid has those forces driving the adsorption at the air-liquid interface and also has specific attractions between the aromatic rings and the ir-electron system of the graphite. Thus, it would be expected that there would be a more negative heat of adsorption for the latter case. ° 2 That the area found, 87 A for NS on graphite, is not limited by repulsions between the charged heads is evi denced by the smaller limiting area at the air-water surface. Also, paraffin chain sulfonates, whose van der Waals interaction between chains is unlikely to be larger than between the pi electron systems of the naphthalene rings, can occupy considerably smaller areas (114). From the experimental adsorption isotherm at 25° C, it has been possible to calculate the surface 66 charge density and electrostatic potential as well as the heat of adsorption and probable configuration of the ions on the solid surface. CHAPTER IV MICROELECTROPHORESIS The electrophoretic mobilities of particles of Sterling FTg in aqueous solutions of SNS were measured in order to calculate the corresponding zeta potentials. An Abramson microelectrophoresis cell (1) was modified as follows: Two 120 ml reservoirs were joined to existing cell outside of the 4-way stopcock as shown in Figure IV-1. Platinized Pt electrodes were immersed in an 0.01 M SNS solution in the 120 ml reservoirs. The electrodes were connected in series with a DC microammeter and a Keithly regulated voltage supply, model 2004A. A double-pole-double-throw switch completed the circuit and allowed reversal of the direction of the electric field applied to the cell. Field strengths of 1 volt/cm for higher concentrations to 10 volts/cm could be ob tained. A Bausch and Lomb student microscope (#250773) with micrometer fine adjustment was used for viewing the particles. Leitz lOx Periplan and Zeiss 20x KPL (focus ing) eyepieces and Bausch and Lomb lOx (16 mm, 0.25 N.A.), 43x (4 mm, 0.65 N.A.), and 97x (oil immersion) objectives were .available.. 67 68 VOLTAGE SOURCE DC MICROAMMETER DOUBLE POLE DOUBLE THROW SWITCH ABRAMSON CELL FIGURE IV-1: SCHEMATIC DIAGRAM OF THE ELECTROPHORESIS APPARATUS. 69 The microscope micrometer was calibrated with the use of a microscope slide. The thickness of the slide was determined by multiple measurements with calipers. A fine film of carbon was deposited on both sides of the slide. The microscope was focused on the top and bottom carbon deposits and the reading of the micrometer screw recorded. The difference between the readings (in revo lutions of the micrometer screw) was found. This procedure was repeated ten times and the results were averaged. This was done with both lOOx and 430x magnifi cations. The thickness of the slide corresponded to 6.27 ± 0.05 micrometer revolutions and 0.955 mm or 0.153 mm/revolution of the micrometer screw. The length and width of the microelectrophoresis cell were determined with a traveling microscope to be 3.4 cm and 1.15 cm. The total depth of the cell, 1.90 mm, was determined first with calipers and checked with the microscope. Carbon was deposited on the two outer sur faces of the cell and a carbon dispersion placed in the cell. By noting the number of revolutions of the micrometer when the microscope was focused on the outer top, the topmost visible particle, the layer of settled particles, and the outer bottom, it was possible to measure the thicknesses of the two layers of glass and the inner space. This procedure was repeated ten times and 70 the results were averaged. The procedure was also followed at the beginning and end of each electrophoresis run as a check on the reliability of the microscope micrometer. The top and bottom glass sheets are 4.0 revolutions or 0.61 mm thick. The inner space, or actual cell, is 4.5 revolutions or 0.69 mm thick. The total depth of 12.5 revolutions is 1.91 mm which compares well with the 1.90 mm thickness obtained with the calipers. The eyepiece net for the 20x Zeiss KPL focusing eyepiece was calibrated with the use of a Bausch and Lomb 0.1/0.01 mm comparator scale. It was seen that with _2 the lOx objective the calibration was 4.92 x 10 mm/grid unit, and with the 43x objective the calibration is — 2 1.15 x 10 mm/grid unit. These values of the calibra tion correspond to magnifications of 203x and 870x. The working distances of the three objectives determined their use. The 9 7x oil immersion objective has a working distance of less than 0.6 mm and could not be used. The 43x objective has a working distance of about 1.4 mm and could be used to observe particles only in the upper half of the cell. Thus the lOx ob jective with a working distance of greater than 2.0 mm was used for most runs. This was done because, as the particles settled, f rticles were available for 71 observation over a longer time period in the lower half of the cell which could not be seen with the 43x objec tive. A 5 cm path length cell filled with dilute CuSO^ solution was placed between the light source and the microscope mirror. The purpose of this cell was to reduce heating in the Abramson cell and improve the resolution of the images of the particles (1). With this IR trap, Brownian motion of the particles was just barely visible. Without it there was so much Brownian motion or convection that no carbon particles could be seen. Only the larger, rapidly settling, aggregates could be clearly seen. Most particles appeared as fuzzy grey spots. The level of focus was determined by adjusting the micrometer back and forth to get the small grey dot instead of the diffraction ring visible when the particle is just out of focus. The Abramson cell was supported by a rigid net work of bars to which it was clamped. This protected it from damage and prevented accidentally jarring a particle out of focus. The cell could be cleaned, rinsed, filled and emptied in place by use of the 4-way stopcock and a suction bulb. If the cell has a rectangular cross-section, the electric field strength will be the same throughout the cell, and the mobility of a particle should be independent 72 of its position in the cell. However, the cell walls also carry a charge with an equal and oppositely charged double layer in the adjacent solution. This double layer flows under the forces of the electric field and pulls its liquid along with it. Since the cell is closed there must be a return flow of liquid down the center of the cell. It can be shown that there will be a parabolic distribution of liquid velocity with distance from the wall in the cell. The observed velocity of a particle will be the sum of its electrophoretic velocity and that due to electro-osmotic flow. The parabolic distribution of particle velocity with depth was checked using a Dow polyvinyl toluene latex with a 1.90y diameter in 0.01 M KCl. Having done this, it was only necessary to measure the velocities of the particles in the lower half of the cell to get a complete description of the behavior in the whole cell. There are two levels in the cell at which the electro-osmotic flow is zero. The distance of these levels from the top (or bottom) wall depends upon the dimensions of the cell (1). Yv _0 = i ^ (depth) Vl/3 [1 + (384/irb)] (depth/width) 73 For the cell used in these experiments, with a width and depth of 1.15 and 0.069 cm, respectively, this level is 0.206 times the depth. Ideally, the electrophoretic mobility can be found directly by measurements at this depth if it is certain that all particles being observed are in the stationary layer. The velocities of the par ticles are very sensitive to depth in the vicinity of the stationary layer. A more accurate approach is to measure particle velocity as a function of depth, plot the parabola and pick off the averaged velocity at the level of zero electro-osmotic flow. The data from these microelectrophoresis runs are summarized in Table IV-1. For increased accuracy the data were fitted in the linear form 2 v = s (y - y ) +i J ■'max' where v is the electrophoretic velocity; y is the depth of focus; and s and i are the slope and intercept. The plots of the data in the linear form are shown in Figure IV-2. Table IV-2 summarizes the results by listing the concentration of SNS in the cell, the velocity at the level of zero electro-osmotic flow from the drawn parabola and from the linear plot, and the mobility of the carbon particle calculated from the measured velocity. The electrophoretic mobility is the velocity per unit field strength. Neither the field strength nor the 74 TABLE IV-1 AVERAGED DATA FRO M M ICROELECTROPHORESIS EXPERIM ENTS [SNS] Depth Current Distance of ■ 3 v x 10 Observation M micrometer (xamps eyepiece grid units revolutions grid units (xamp-sec ; 0.00278 9.40: Bottom of c e l l; 11.60: Middle of c e ll 9.45 140 1 +1.5 10.00 155 ± 5 4-5 -5.5 ± 0.2 10.20 185 ± 5 4 -4.2 10.50 150 ± 10 4 -4.9 ± 0.5 10.40 150 ± 10 4 -5.8 ± 0.5 11.00 150 ± 10 4 -7.4 ± 0.7 11.40 150 ± 10 4 -8.6 ± 0.4 0.00594 9.40: Bottom of c e ll; 11.65: Middle of c e ll 9.50 210 ± 10 2-5 +1.9 ± 0.5 9.80 200 0 0 10.50 205 ± 5 2 -2.0 ± 0.1 10.40 210 ± 5 2-4 -2.2 ± 0.2 11.00 205 ± 5 4 -2.5 ± 0.2 11.50 210 ± 5 4 -5.4 ± 0.2 .0.00475 9.55: Bottom of c e ll; 11.60: Middle of c e ll 9.40 200 5 +1.5 ± 0.5 10.00 200 2 -1.2 ± 0.5 10.50 190 ± 10 2 -1.5 ± 0.5 10.40 190 2 -1.5 ± 0.5 11.00 190 ± 5 2-5 -2.1 ± 0.5 10.50 190 ± 5 2 -1.4 ± 0.5 11.50 200 2 -2.0 ± 0.5 TABLE IV-1 (Continued) 75 [SNS] M Depth Current micrometer v ^amps revolutions Distance of Observation eyepiece grid units 4 v x 10 grid units j o , amp-sec 0.00974 9.30: Bottom of c e ll; 11.60: Middle of c e ll 9.65 400 ± 5 1 0.8 ± 0.1 9.75 410 J 2 1.4 ± 0.2 10.00 400 ± 5 2 2.5 ± 0.5 10.50 405 ± 5 2 3.7 ± 0.2 11.50 400 * 5 2 5.0 ± 0.5 0.0177 9.50 : Bottom of c e ll; 11.75: Middle of c e ll 9.85 480 1 1.8 10.10 490 i 10 2-5 2.5 ± 0.5 10.45 490 £ 10 2 2.8 ± 0.5 10.75 500 ± 10 2 2.5 ± 0.4 10.90 480 ± 10 2 5.0 ± 0 . 5 11.60 500 ± 10 2 3.7 ± 0.3 12.20 520 ± 10 2 4.3 0.0217 9.25: Bottom of c e ll; 11.50: Middle of c e ll 10.00 600 ± 20 2 2.5 ± 0.5 10.20 600 ± 20 2 2.6 10.50 600 ± 10 2 3.0 ± 0.4 11.00 600 ± 20 2 3.3 ± 0.3 11.40 600 ± 10 2 3.0 ± 0.3 12.00 600 ± 20 2 3.7 ± 0.5 VELOCITY 3 0.0177 M 0 9 6 3 0.0217 M 0 0.00278 M 3 6 k 0 2 inux FIGURE IV-2: ELECTROPHORETIC VELOCITIES PLOTTED ACCORDING TO THE LINEAR FORM OF THE EQUATION OF A PARABOLA. 77 TABLE IV-2 RESULTS O P M ICROELECTROPHORESIS EXPERIM ENTS [SNS] v from Parabolic Plot of Data v from Linear Plot of Data Mobility m M /grid units % ' ^amp-sec ' /grid unitss ' namp-sec ' /ix/sec \ 'volt/cm' 2.78 5.1 x 10 _3 5.2 x 10“3 4.4 3.94 2.0 x 10“3 1.9 x 10"3 2.4 4.73 1.4 x 10“3 1.3 x 10“3 1.9 9.94 -4 3.0 x 10 -4 3.2 x 10 H 1.0 17.7 _4 2.7 x 10 _4 2.7 x 10 1.4 21.7 _4 2.7 x 10 _4 2.7 x 10 1.5 78 voltage drop across the cell is measured but the current, I, through the circuit is known. The field strengths can then be calculated if the specific conductance of the suspension, k , and the cross-sectional area of the cell, A, are known. U = v/X = v k A/I g Since the suspension is very dilute, about 10 particles/ cc, it is assumed that the specific conductance of the suspension is the same as that of a solution of the same SNS concentration. Values of the zeta potential were calculated from measured electrophoretic mobilities by the method of Wiersema, Loeb and Overbeek (116). This method takes into account both relaxation and retardation effects and includes the valence and mobility of all the ions in the diffuse double layer. Essential assumptions of the theory are that the particle is spherical and non-conducting and that only ions in the double layer (not those produc ing the potential) are free to move. None of these assumptions are completely met by the SNS-Sterling FTg system. The parameters of this method are E, qQ, and' yQ, . defined by the equations below. % = Ka 79 yo = e?/kT E = 67rneU/ekT In these equations, k is the reciprocal Debye length; r ) is the viscosity of the solution; k is the Boltzmann constant; T is the absolute temperature, and e is the dielectric constant. The procedure is to plot a series of curves of E from Wiersema's Table I (116) as a function of q for each of a series of values of v . E's cor- ^o J o responding to experimental values of qQ are picked off the curves and corrected for the valence and mobilities of the ions. AE for this system was calculated to be 0.15. Then a series of plots of E + AE as a function of yQ for each experimental qQ are made. E0ks calcula,ted from the electrophoretic mobility and yQ is found from the appropriate E + AE vs. yQ curve. If the double layer is very compact, Ka >> 1, the Helmholtz-Smoluchowski relation applies. In terms of the parameters of Wiersema, this is yQ = (2/3) E Since the particles being observed are polyhedra, not spheres, it would be expected that the compact double layer treatment is more realistic. The "true" value of the zeta potential must be between the values found by these two methods. The values of U, Ka, E and £ are 80 listed in Table IV-3. It is to be noted that £ from both spherical and flat plate treatments is significantly less than calculated from the adsorption isotherm. It has been noted that graphite is a conductor along the plane of the ring system and an insulator in the perpendicular direction. Since the theory of Wiersema is limited to non-conducting particles, it might be assumed that it cannot apply here. This is, however, not the case. It has been shown experimentally with colloidal metals (81) that surface polarization prevents further conduction and that metals behave, in fields of as little as a few microvolts, as insulators. 8l TABLE IV-3 VALUES O F THE ZETA POTENTIAL A N D PARAM ETERS RELATED TO ITS CALCULATION FR O M ELECTROPHORETIC MOBILITY ,[-SNS] ' m M U/X 1 1 /sec v/cm E >ta C W L O mv C H S mv *oGC mv 2.98 4.3 3.2 17.7 77 55 176 3-9^ 2.4 1.8 20.7 39 31 177 4.73 1.9 1. 4 22.7 30 24 178 9.84 1.0 0.7 32.6 17 12 174 17.7 1.4 1.0 43.8 22 17 167 21.7 1.5 1.1 48.4 23 19 166 CHAPTER V OPTICAL PROPERTIES OF CARBON DISPERSIONS In order to study the aggregation process of rapidly aggregating colloidal suspensions, a rapid phys ical method is needed. Many workers (4, 24, 77, 80, 105) have used optical density to study flocculation in dilute suspensions. The attenuation of a beam of light by a colloidal dispersion is due to both scattering and ab sorption of the light. If the distances between the par ticles are large compared with the wavelength of light and the particle diameter, and if secondary scattering is negligible, then the change in the intensity of the light can be expressed as In IQ/I = L ? KiAiNi. (5.1) In the above expression I and I are the intensities of the light before and after passing through the dispersion; L is the path length; N^ is the number concentration of particles of size i; A^ is the cross-sectional area of particles of size i; and is the extinction area co efficient, or the ratio of the optical to the geometrical cross-sections of the particle. As expressed by the 82 83 summation, the attenuation of light by a large number of particles is the sum of that contributed by each indi vidual particle. Mie theory (71) gives the rigorous expression for K for all sizes and refractive indices (of the particle relative to the medium) m ~ mparticle//mmedium for spherical, isotropic particles. If the particles are absorbing or conducting the complex refraction index, in(l - i<) , must be used. Here m is the refractive index and < is the absorption coefficient. Values of K are expressed as a function of the reduced size parameter, a. a = 2irRm/X For small, non-absorbing spheres, the Mie theory reduces to the Rayleigh scattering expression. For very large spheres K becomes constant at 2.0 (8). For inter mediate values of a, 1 < a < 30, K possesses a series of maxima and minima. The effect of a non-zero absorption coefficient is the displacement and damping of these maxima and minima (106). A mixture of particle sizes has the same effect. Values of K as a function of a have been calculated for many values of the refractive index (106). Mie theory 84 has been carefully tested with sulfur sols (4) and with aqueous dispersions of fine natural powders (70, 98). Values of K for absorbing systems are not plentiful since the calculations are difficult and time consuming. Lowan (61) and Chromey (13) have published data from which K can be calculated. Their values agree within 0.3 per cent. Chromey's data cover the widest R/A range. It is limited, however, to a between 0 and 2. A set of extinction area coefficients were derived from graphical representations of Chromey's data. Over the wavelength range from 436 to 632mjj the refractive index of graphite (76) varies from 1.90 to 2.00 and the absorption coefficient varies from 0.36 to 0.33. Over the same wavelength range the refractive index of water (7o) is constant with a value of 1.33. Calculations were made for values of m of 1.40, 1.45, and 1.50, and a value of K of 0.33. Figure V-l shows curves of K for three pairs of values of m and k . In the insert are three curves which show the damping and displacement of the maxima and minima with variation in absorb ion coefficient. Since the maximum value of a, for which values of K applicable to carbon suspensions are available, is 2, the expected maxima and minima cannot be calculated. The limited extent of this calculation restricts prediction of optical density to dispersions of monodisperse 3 2 K 1 2 .25 20 40 0 0 1.0 c* 2.0 FIGURE V-l: VARIATION OF EXTINCTION AREA COEFFICIENT WITH RELATIVE PARTICLE SIZE FOR AQUEOUS CARBON DISPERSIONS. O m = 1.45(1 - 0.331), FROM CHROMEY • m = 1.50(1 - 0.30i), FROM LOWAIi A m = 1.50(1 - 0.331), FROM CHROMEY INSERT: EXTINCTION AREA COEFFICIENT FOR m = 1.59 AND ABSORPTION COEFFICIENTS OF ZERO, 0.25 AND 0.50. 86 O spheres with a maximum radius of 2400 A and a minimum O wavelength of 1200 A. There are a number of reasons why direct applica tion of the Mie curve to aqueous graphitized carbon black suspensions is questionable. The primary particles of graphitized carbon blacks are polyhedra, not spheresThe deviation from spheric ity is small since a large number of faces (an average of 20 per particle) are generally present, but the flat faces will reflect a little light and will cause attenu ation of the transmitted beam beyond that due to ab sorption and scattering. Electron micrographs (9) of acetylene, channel and furnace blacks, and theoretical treatments of the flocculation of spheres (68, 104, 113) show loose, non- spherical aggregate structures. These structures contain large volumes of solution, and the solution-containing regions are of the order of magnitude of the wavelength of light. Either small inter-particle spaces will scatter light which will be secondarily scattered by the carbon black giving a different scattering pattern from that of an homogeneous individual particle, or the aggregate as a whole may scatter light. In the latter case the appropriate index of refraction must be some average of that of the carbon and that of the solution. 87 Individual Sterling FTg particles are known to contain large graphite crystallites. Recent optical studies of single graphite crystals and thin graphite sheets (25, 67) show that graphite is highly anisotropic. The index of refraction when the electric vector of the incident light is parallel to the basal planes is 2.2 and the corresponding absorption index is 0.66. When the electric vector of the incident light is perpendicular to the basal planes an observed reflectance minimum cor responds to an index of refraction of 1.8 and an ab sorption coefficient of 0.01 (67). This result corre sponds to graphite behaving as a conductor along the basal planes and like an insulator perpendicular to the planes. The optical properties of a Sterling FTg par ticle, then, depend on the orientation of the graphite crystallites within it and on the orientation of the particle with respect to the light. McCartney and Ergun have found that graphite absorbs strongly in two regions: in the UV at 250my and in the near IR at 1400 my (26). Since Mie theory for absorbing spheres assumes a constant absorption index, regions with varying k must be avoided if use of a is to retain its significance as a measure of relative particle size. 88 Because of the five areas of difficulty just dis cussed: the limited range of a for which values of K predicted by Mie theory are available, the non-spherical primary particle shape, the question of how to treat aggregate structure, the anisotropy in the refractive index and absorption coefficient of graphite crystal lites, and the variation of the absorption coefficient in the UV and near IR; it does not seem reasonable to try to use the predictions of Mie theory directly in following colloidal flocculation processes optically. One experimental complication arises for a greater than about 20. The true value of K is 2, but if the aperture is too large or if the receiver of the spectro photometer is too close to the sample, there may be significant reception of forward scattered light. As a result K may appear to drop to a value of unity. The experimental optical density will be less than the true optical density. Donoian and Medalia (23) observed this effect with both Sterling NS and Sterling MT. Rose (99) showed that for silica hydrosols the limiting solid angle subtended by the aperture should be kept to less -4 than 2.5 x 10 solid radians to prevent reception of forward scattered light. It is not definitely known whether primary par ticles exist after ultrasonic dispersion; nevertheless, 89 a comparison was made between an experimental and a calculated optical density. The calculation was based O on the average value of the radius, 1000 A, found from examination of electron micrographs of dry Sterling FTg (9). Using a value of 670my for the wavelength (a = 1.41) and the derived Mie plot, Figure V-l (p. 85), a specific optical density, (1/C)(log IQ/I), of 0.30 x 10^ is cal culated. The highest specific optical density for an 5 ultrasonically dispersed suspension of 0.29 x 10 was found using a Klett-Summerson photoelectric colorimeter with a red, 670my filter. This close agreement between the calculated and experimental optical densities can mean that most of the carbon has been dispersed into ultimate particles. The proportionality of absorbance with concen tration was tested. A series of suspensions were made by diluting aliquots of a suspension of Sterling FTg in -2 -2 10 M SNS to known volume with 10 M SNS. The absorb ances were measured with the Klett-Summerson photo electric colorimeter (KSV = 500 A). The resulting Beer's law plot shows no deviation from linearity. See Figure V-2. Hiemenz and Void (46, 47, 48) circumvented the lack of theoretical optical data by developing a semi- empirical equation relating changes in particle size to 90 ~ Uoo o o l/'i § 300 s o a 3 CO & 200 EH 100 - k 5 3 2 1 0 GRAMS STERLING FTG/ML x 105 FIGURE V-2: BEER'S LAW PLOT OF ULTRASONIC:ALLY DISPERSED STERLING FTG IN AQUEOUS SNS. 91 changes in optical density. Their equation is based on an observed proportionality between log absorbance and log wavelength. The general region on the Mie curve applicable to a given dispersion can be found by plotting absorbance as a function of reciprocal wavelength. This latter test tells whether increases or decreases in optical density should occur during flocculation. The optical densities of six separately prepared dispersions were measured on a Cary double beam recording spectrophotometer. In each case a solution of the same SNS concentration as that of the dispersion was used in the reference cell so that the observed wavelength dependence of the optical density is due to the colloidal carbon only. Both aged unstable and freshly-made stable dispersions were studied. The specific charac teristics of these six dispersions are listed in Table V-l. Figures V-3 and V-4 show the variation of absorbance with wavelength and reciprocal wavelength. The reciprocal wavelength or experimental Mie plot shows that the particles in these dispersions are of such an effective size that K is still increasing with increasing a. The observed decrease in optical density with time during coagulation (see p. 108) is due to the decrease in particle concentration and total projected area which is concurrent with coagulation. The slopes 92 TABLE V-l CHARACTERISTICS OF DISPERSIONS USED IN FIGURES V-3 AND V-4 [SNS] A /C x 104 o A/C x 10'4 Age M At Time of Measurement O.OOl 3.3 3.0 11 days 0.003 3.3 3.0 5 days 0.006 2.8 2.4 1 day 0.010 2.5 2.5 1 hour 0.020 2.8 2.3 4 hours 0.030 2.8 1.5 1 day ABSORBANCE l.Oi— ' O.OIO K SNS 0.001 M SNS O.OCh M SNS srs 600 500 WAVELENGTH, mv FIGURE V-3: WAVELENGTH DEPENDENCE OF THE ABSORBANCE OF A SERIES OF AQUEOUS STERLING FTG DISPERSIONS. ABSORBANCE 1.0 0.010 M 0.030 M 0 1.0 2.0 3.0 l/WAVELENGTH, ( } J )-1 FIGURE V-lf-: RECIPROCAL WAVELENGTH DEPENDENCE OF THE ABSORBANCE OF A SERIES OF AQUEOUS STERLING FTG DISPERSIONS. CONCENTRATIONS OF SNS LABEL THE CURVES. 95 of the absorbance vs. wavelength lines are so small that the log A vs. log X linesare also linear. The observed slopes of the A vs. X plots vary from one dispersion -5 -5 -1 to the next, -0.8 x 10 to -1.6 x 10 my , consistent with the hypothesis that different particle size distri butions are present in each. The linear variation of absorbance with wavelength seen in Figure V-3 (p. 93) for all of the dispersions studied gives a simple relationship to use as the basis for a semi-empirical equation relating changes in optical density to the changes in the number of particles and the average particle size that result from flocculation. A = A* + bX (5.2) This equation can be compared with the general optical equation. A = L £ K. i R? N. ii 11 The only factor affecting A which depends upon wavelength is the extinction area coefficient, K, which depends upon the ratio of R to X. If the absorbance is a linear function of wavelength in the visible region, the effec tive extinction area coefficient must be a linear func tion of X/R in this region. 96 K = K* + b*(A/R) (5.3) If the particle size distribution is described by an op tical average radius, R, Equation 5.1 becomes A = (K* + b*(X/R) R2NL (5.4) The conservation of mass during coagulation can be used to relate N and R. C = (4/3) TrR^<j>sNp (5.5) C is the carbon concentration in grams/ml. 4>s and p are the volume fraction of solid in the particle and the density of the solid. By combining Equations 5.4 and 5.5 and differentiating the resulting equation with respect to time Equation 5.6 is found. dA 3CL,K* , 2b*A,,dRv /c dt = " (i2 + ~~^3~ dT (5‘6) K i\ But since flocculation is a kinetic process, it is the variation of particle concentration with time, dN/dt, which is wanted. This is found by differentiating Equation 5.5 with respect to time and combining the result with Equations 5.4 and 5.6. Jc "k 1 ,dAv _ 1 ,dNw K + 2b (X/R) , ,c ~A dT “ 3N'dt *----*----„ _ J Ko.t) K + b (^/R) For particles between 0.1 and 1.0H in radius and visible light, X/R is of the order of 1. K* is about 97 2.5 (certainly between 2 and 3). The experimental slopes -5 -1 of the A vs. X plots are about -10 my . Thus, a rough * calculation of b can be made, based on a particle con- 9 * centration of about 10 . For these systems b is about -5 10 . Equation 5.7 then reduces to 1 /dAi 1 ,clN^ / j - A (dt> - 3N dt (5‘8) This approximation is only valid for very short changes in time and for dispersions whose wavelength dependence of absorbance is linear. For diffusion controlled flocculation, the change of particle concentration with time is a second order process. | | . Combining the bimolecular flocculation expression above with the simplified optical expression, Equation 5.8, a differential and an integrated equation are found. l kN (5.9a) 3A - A 3A - 2A = Nokt (5.9b) A plot of (3A - Aq)/(3A - 2Aq) v s . time will have a slope of N k. N k can also be found from the initial slope of o o the time dependent absorbance curve. 98 The only information which is available from op tical density studies, then, is the product of the par ticle concentration and the bimolecular flocculation constant. An estimate of N for a highly dispersed system can be found from the optical density by assuming that ultimate particles are initially present with a radius equal to that found from electron micrographs. The g maximum particle concentration thus found was 1.2 x 10 particles/ml for a Sterling FTg concentration of 1 x 10 grams/ml. Changes in rate constant can be ob served by studying suspensions with the same concentra tion (made by diluting a stable "stock" suspension). What was done experimentally (p. 114) was to measure the change in absorbance with time, and convert the initial slope to the bimolecular flocculation constant by multi plying l/AQ(dA/dt) by 3/Nq, using as a rough estimate for 9 -5 Nq 10 particles/ml per 10 grams carbon/ml. The wavelength dependence of these aqueous dis persions of Sterling FTg differs from that of dispersions of Sterling NS, Graphon, and other furnace and channel blacks in hydrocarbon media (46, 111) . With the latter systems an exponential decay of absorbance with wave length was observed. ■ » —ni A = bX ‘ (A/C)1' * ^ M (A/C)2 X X 99 On a log A vs. log X plot their data gave a straight line. This enabled Hiemenz to derive an empirical equation which he used as the basis of his calculations of de flocculation rates. 1 iru-m. ( T^ET) ( -T=iI7> r,, - ■ R1 Here it^ and m2 are the slopes of the log-log plots. It has just been shown that a linear relation between absorbance and wavelength leads to a very dif ferent relation (Equation 5.9ab). Hiemenz and Void used carbon blacks which have smaller ultimate particles fused into highly irregularly shaped (tentacular) aggre gates. The scattering unit contains solution as well as carbon black. These blacks are also more heterodisperse than Sterling FTg. The wavelength dependence of Hiemenz’s results corresponds to the right of the first Mie maximum. Thus, the difference in wavelength depend ence of absorbance between these systems appears to be due to the different portion of the Mie curve, correspond ing to a different average particle size, which deter mines the visible absorbance spectrum of the two types of carbon black dispersions. 100 Dispersion and Aggregation Studies It was shown by Reich and Hiemenz that when Graphon and Sterling NS are agitated in a Waring blendor, the optical density rises to a constant value which depends upon the carbon concentration, the speed of rotation of the blendor blades, and the past history of the dis persion. This was interpreted as due to a flocculation- deflocculation equilibrium, the degree of mechanical agitation determining the degree of dispersion of carbon. Similar experiments were performed, first with Sterling MTg and later with Sterling FTg arid a series of dispersing agents. Optical density, measured with the Klett-Summerson photoelectric colorimeter, was used as the measure of dispersion. Higher optical densities in dicate higher degrees of dispersion. For dispersions prepared in the Waring blendor the following technique was used: 80 ml of solution were placed in the clean blendor. Pre-weighed carbon was layered on top of the solution. A 250 ml beaker, fitted with a silicone rubber gasket, was placed on top of the solution so that the liquid-air interface was only a ring meniscus. This prevented the formation of large quantities of foam. The optical density was followed as a function of time. 101 Figure V-5 shows the resulting optical density as a function of time and blendor speed for two dispersions of _2 Sterling FTg in 10 M SNS. The optical density rises rapidly at the beginning and then levels off. Increasing the speed of the blendor increases the apparent maximum optical density. Hiemenz, working with unstable non- aqueous suspensions of Sterling NS found a decrease in optical density with time if the blendor speed were decreased. This type of behavior was not observed here. To the contrary, on decreasing the speed from 14,000 to 12,000 and then 9000 RPM, the optical density was seen to continue rising, although slowly. This system is much more stable than Hiemenz1s. The observed behavior of Sterling FTg in aqueous SNS is consistent with the hypothesis that after dispersion by the blendor and achievement of adsorption equilibrium, there is a high energy barrier preventing observable flocculation during the time that the dispersion is in the blendor. Decreas ing the speed of the blendor decreases the rate at which pre-existing carbon aggregates are pulled apart. Very few studies were made with dispersions pre pared with the Waring blendor because it took hours to reach the optical density plateau at low speeds and the blendor leaked at speeds above 10,000 RPM. Ofice leakage began, foam formed removing carbon and surfactant from KLETT-SUMMERSON VALUE 102 9000 RTM 1.2000 RTM 15000 RBI 300 8000 RBI 200 100 100 0 MINUTES FIGURE V-5: TIME DEPENDENCE OF ABSORBANCE OF WO DISPERSIONS OF STERLING FTG DURING AG CITATION IN THE WARING BLENDOR. DISPERSING AGENT IS 0.01 M TECHNICAL SNS. CARBON CONCENTRATIONS ARE (A) )+.5 x lO-" 3 GMS/ML AND (B) 5-0 X 10""’ GMS/ML. BLENDOR SPEEDS LABEL THE APPROPRIATE SECTIONS OF THE CURVES. 103 the dispersion. In some instances there was visible dis coloration of the dispersion from rust and oil in the blendor-blade assembly. All of the dispersions whose stability was studied optically were prepared in a 100 volt, 1 gallon, 45+2 kilocycle Delta Sonics cleaning tank. It is possible to achieve higher specific optical densities with ultrasonic dispersion than with the Waring blendor. There is no foam formation. There is no contamination since the test tube containing the solution and carbon is placed, stoppered, in the soap solution in the clean ing tank. However, the effect of ultrasonic irradiation appears to be irregular with time and gives irreproducible optical densities for the apparent optical density plateau. Figure V-6 shows the changes in optical density with time during ultrasonic irradiation for five dis persions of Sterling FTg in aqueous SNS. The change of optical density with time was ob served for a preliminary series of dispersions. Both Sterling MTg and FTg were used. The dispersing agents -2 were 10 M solutions of STS, SNS (technical grade) and PPS. The purpose of this experiment was to choose the surfactant for study. Both initial optical density and rate of change of optical density were criteria of choice. Higher optical densities were obtained for the SNS- KLETT-SUMMERSON VALUE 800 132 600 107 112 123 200 100 0 50 MINUTES FIGURE V-6: ABSORBANCE AS A FUNCTION OF TIME OF IRRADIATION OF A SERIES OF AQUEOUS DISPERSIONS OF STERLING FTG IN 0.01 M SNS. SPECIFIC KLETT-SUMMERSON VALUES ( x 1C ML/GM) LABEL THE CURVES. 105 stabilized dispersions than for either PPS or STS- stabilized dispersions. See Figure V-7. This seems -2 surprising since 10 M PPS is closer to the limit of solubility and a higher adsorption would be expected for PPS than SNS. The optical density of PPS and STS- stabilized dispersions decreased rapidly with time. The optical density of SNS-stabilized carbon black changed much less with time on both absolute and relative scales. These experiments were not repeated with dis persions made in the Delta Sonics cleaning tank, although it would be a good idea to do so since the blendor results cannot be relied on (because of the possibility of con tamination) and a comparison of the effects of different sized aromatic ring systems would be interesting. A series of experiments were undertaken to see how the stability of dispersions of Sterling FTg in SNS solution varied with changing concentration of surfactant. Optical density was followed as a function of time for four series, a total of 30, suspensions (series 2 to 5). In series 2 each suspension was made up separately by weighing the carbon, adding 20 ml of SNS solution and dispersing ultrasonically for two hours. With series 3 _ 3 and 4 a stock suspension of about 10 grams carbon/ml -3 in 10 M SNS was made. No changes in optical densxty could be observed for this stock suspension over a KLETT-SUMMERSON VALUE 106 300 O SNS 200 PPS 100 0 STS PPS 0 300 200 0 100 HOURS FIGURE V-7: DECREASE IN ABSORBANCE WITH TIME FOLLOWING DISPERSION IN THE WARING BLENDOR FOR ST'SPENSIONS OF STERLING FTG AND STERLING MTG IN AQUEOUS SOLUTIONS OF VARIOUS DISPERSING AGENTS. • STERLING FTG O STERLING MTG 107 two-week period. 1.0 ml aliquots were diluted with 5.0 ml of SNS solution in a matched Bausch-Lomb Spectronic 20 cell. The advantage of this method is that the same initial particle concentration and particle size dis tribution are present in all runs of the same series so that only the effect of changing the concentration of SNS is being observed, even though an exact value of the bimolecular rate constant cannot be calculated due to the uncertainty in Nq. The Spectronic 20 was used for all absorbance measurements relating to dispersion stability. The measurements were taken at 650mn where it was observed that there was no contribution of the SNS to the ab sorbance even at high concentrations. The Spectronic 20 was zeroed against water. The carbon concentration was chosen so that the initial absorbance would be about 0.5, the region of greatest accuracy with the Spectronic 20. Sample results from this experiment are presented in Figure V-8 and Table V-2ab. In Table V-2ab are listed values of absorbance and the corresponding times for four dispersions from each of series 3 and 4. These data cover the whole concentration range studied. For the most stable suspension (3:0.00183 M) the absorbance only changed 0.02 units in twenty hours while the most rapidly flocculating dispersion (4:0.0417M) had a 0.07 unit change in absorbance in twenty minutes. ABSORBANCE 108 0.35 0.25 HOURS ' FIGURE V-8: DECREASE IN ABSORBANCE WIT1I TIME FOLLOWING ULTRASONIC IRRADIATION OF DISPERSIONS OF STERLING FTC IN AQUEOUS SOLUTIONS OF SNS OF DIFFERING CONCENTRATIONS. SMOOTHED CURVES FROM STABILITY SERIES 3 (AND 5)- 109 TABLE V-2a DATA FRO M SELECTED RUNS IN STABILITY SERIES 3 3: 0.00183M SNS 3: O.OOI67M SNS Hours A Hours A 0 0.475 0 0.485 1.0 0.470 1 0.478 2.0 0.466 5 0.478 4.5 0.464 10 0.477 13.5 0.463 20 0.472 19.0 0.457 60 0.466 90 0. 465 600 0.452 950 0.442 3 :00.00350M SNS 3: 0.0283M SNS Hours A Hours A 0 0.485 0 0.485 0.2 0. 48o 1 0. 48o 0.5 0.474 3 0.476 1.0 0. 469 5 0.468 2.5 0.465 10 0.458 12.5 0.453 20 0. 44l 18.0 0.444 30 0.424 40 0.412 110 TABLE V-2b DATA PR O M SELECTED RUNS IN STABILITY SERIES 4 4: 0.00257M SNS 4; 0.00433M SNS Minutes A Minutes A 0 0.354 0 0.352 5 0.354 5 0.349 20 0.354 30 0.348 40 0.349 60 0.343 6o 0.348 120 0.343 120 0.345 180 0.335 l 8o 0.345 300 0.335 360 0.340 460 0.327 510 0.338 4: 0.0335M SNS 4: 0.0417M SNS Minutes A Minutes A 1 0.359 1 0.360 2 0.354 2 0.355 3 0.350 3 0.351 6 0.342 5 0.340 8 0.330 7 0.334 10 0.324 10 0.323 15 0.310 15 0.308 20 0.299 20 0.293 25 0.292 Ill This behavior is shown in Figure V-8 (p. 10 8) , in which smoothed curves from series 3 and 5 are plotted showing the effect of the concentration of SNS on the time dependence of absorbance. Since all the curves from series 3 have the same initial optical density, the curve 5:0.01M was reduced in scale to have the same Aq value as the rest. That all the data from series 3 (and also within series 4) have the same value of Aq results from the method of preparation in which equal aliquots from the stable stock suspension are diluted to equal volumes. Its significance is that all these runs have the same Nq and same particle size distribution. The fifth series was made from a stock suspension of Sterling FTg in 0.020M SNS. This was an unstable stock suspension. It was initially irradiated for two hours before the first aliquot was taken. It was re-irradiated for 15 to 30 minutes before each succeeding aliquot was taken. The initial optical density increased over the series. Thus, neither Nq nor the particle size distribu tion can be constant. This series was designed to see if there were a competition between adsorption of SNS and flocculation for the suspensions with high concentrations _3 of SNS. The surface coverage of the carbon in 10 M SNS is 20 per cent compared to the surface coverage in 0.020M SNS, which is virtually complete. Plots of four 112 runs covering the whole concentration range are shown in Figure V-9. No significant difference between the behavior of series 5 and series 2, 3, and 4 could be seen. This implies that adsorption equilibrium is reached within a very short time, probably less than five minutes. There was more scatter in the kN values as a function of o concentration for series 5 than either 3 or 4 but this is to be expected from the different methods of prepara tion and reflects the variation of N . o The slope of the curve at zero time, (dA/dt)t _ Q, was measured for each run. The slopes are listed, together with the kNQ values calculated with Equation 5.9a in Table V-3. This method of calculation of kN was checked o for one run (series 2:0.030M SNS) against the integrated equation. (3A - Aq)/(3A - 2Aq) is plotted as a function of time in Figure V-10. The line is straight for about 25 minutes and then curves upward. The slope of this line gives a kNQ value of 1.45 hour This compares with 1.47 hour ^ from the initial slope of the A vs. time plot. It is very difficult to assign slopes to the curves of absorbance vs. time for those suspensions con taining 1 to 5mM SNS as the fluctuations in absorbance between any two readings, 0.001 A, were almost as large as the total change in absorbance. Since the carbon does 113 0.35 0.30 0.25 0.20; 120 MINUTES 0.39 0.37 0.35 0.005CM 0.0058m 0.33 0.31 60 0 30 90 120 HOURS FIGURE V-9: DECREASE IN ABSORBANCE WITH TIME FOLLOWING ULTRASONIC IRRADIATION OF DISPERSIONS OF STERLING FTG IN AQUEOUS SOLUTIONS OF SNS OF DIFFERING CONCENTRATIONS. DATA FROM STABILITY SERIES 5 PLOTTED ON TWO TIME SCALES. 114 TABLE V-3 OPTICAL DATA FR O M W H ICH THE STABILITY RATIO IS CALCULATED Series [SNS] M C x 105 gms/ml Ao - < ^ L o 4 -1 x 10 hr n 0 t =0 hr-1 2 0.006 1.73 0.475 21 0.0043 2 0.008 1.61 0.497 68 0.014 2 0.010 2.03 O.585 71 0.012 2 0.030 1.58 0.438 2140 0.49 3 0.00100 1.54 0. 485 10 0.0025 3 0.00183 1.54 0.485 27 0.0054 3 0.00267 1.54 0.485 37 0.0076 3 0.00350 1.54 0. 485 230 0.047 3 0.00502 1.54 0.485 45 0.0094 3 0.00666 1.54 0.485 90 0.019 3 0.00850 1.54 0.485 160 0.033 3 0.0167 1.54 0.485 330 0.068 3 0.0283 1.54 0.485 1680 0.38 4 0.00357 1.67 0.360 32 0.0093 4 0.00950 1.67 0.360 40 0.011 4 0.00433 1.67 0.360 70 0.020 4 0.00502 1.67 0.360 50 0.014 4 0.0283 1.67 0.360 1120 0.31 4. 0.0335 1.67 0.360 2340 0.64 4 0.0417 1.67 0.360 3000 0.83 5 0.00417 1.25 0.385 14 0.0004 5 0.00500 1.25 0.378 10 0.0008 5 0.00583 1.25 0.380 18 0.014 5 0.0100 1.25 0.384 70 0.026 5 0.0100 1.25 0.400 120 0.090 5 0.0200 1.25 0.385 190 0.049 5 0.0200 1.25 0.385 260 0.068 5 0.0284 1.25 0.396 1450 0.37 5 0.0367 1.25 0.382 3500 0.91 5 0.0450 1.25 0.376 4400 1.20 115 .0 .0 1.0 0 HOURS FIGURE V-10: ABSORBANCE AS A FUNCTION OF TIME ACCORDING TO THE INTEGRATED FORM OF THE OPTICAL RATE EQUATION (5-9^). 116 settle, although slowly, it was necessary to invert the test tubes at least once every 48 hours to suspend settled carbon. The results of these experiments are summarized in Figure V-ll. The linearity of the flocculation rate over the concentration range 0.020M <C < 0.050M, and the sharp break at 0.020M are not predicted by DLVO theory. The detailed comparison of these results with the stability predicted with DLVO theory from the adsorption isotherm and the zeta potential is found in the discussion. The optical equations developed to study the flocculation process assume that the only kinetic process occurring is bimolecular flocculation. In some polymer- stabilized non-aqueous carbon black dispersions (47, 96) deflocculation also occurs as a first order rate process. This leads to a steady state concentration, Ng, equal to 6/k. Over very short times such that the optical density is proportional to the particle concentration, Hiemenz has shown that AA' _ nj. i _ A° ~ AS r-i _~3T, In ^ _ a i pt — In A f t [1 — e ]. o s 117 1.0 r-M< 0.C4 (SNS) °*°3 0.01 0.02 FIGURE V-ll: RESULTS OF OPTICAL FLOCCULATION STUDIES. (l/A )(d£./dt) AS A FUNCTION OF THE CONCENTRATION OF SNS. 118 In the above equation t is the time, A and A1 are the ab sorbances at times separated by a constant interval T, and A and A are the initial and steady state optical den- o s sities. The Sterling FTg-SNS system was tested for de flocculation by applying the above equation to the optical data for four sysiems of varying stabilities. The scatter in the data is due to the fact that for most of the points, and all those at long times, the difference in optical density between two successive times is only in the third significant figure of the optical density. Thus, the data are only good to one significant figure. For systems with a non-zero deflocculation constant Hiemenz found good straight lines with non-zero slope. The value of 8 of zero found from the slopes of the lines in Figure V-12 is in agreement with the same conclusion drawn from the absence of an observable steady state. The finding here, that there is no observable deflocculation occurring in these systems, strengthens the use of optical density to follow the flocculation process. LOG AA'/(A - 3-0 2.0 0 1.0 ▲ XI o o o .ocSm 0.01CM 0.0^CM 0.03CM J HOURS ' FIGURE V-12: (AA' )/(A - A ’) AS A FUNCTION OF TIME. AN OPTICAL TEST FOR DEFLOCCULATION. DISPERSIONS PREPARED BY ULTRASONIC IRRADIATION OF STERLING FTG IN AQUEOUS SOLUTIONS OF SNS. TIE H CONCENTRATION OF SNS IABELS EACH LINE. £ CHAPTER VI DISCUSSION OF RESULTS The three areas of this investigation which bear most directly upon the interpretation of the stability of the carbon black suspension are (1) the adsorption iso therm, which was analyzed to give the electrostatic and non-electrostatic interactions of the adsorbed molecules with the surface; (2) the zeta potential, which was cal culated from electrophoretic mobility; and (3) the stability ratio, W, which was found from the decay of optical density with time. The adsorption isotherm of SNS at the solution- sterling FTg interface, Figure III-l (p. 38) is of the Langmuir (right hyperbolic) type. In Chapter III a derivation was given which made possible the determination of the density of charges "on" the graphite surface, oQ> N and the Volta potential, from and the concentration of SNS. The ratio of the surface charge density to the surface excess is potential-dependent but for the range of i b of interest to this work, 140 to 178 millivolts for To 0.001 < _ (SNS) £ 0.05, the charge density is 1.35 + 0.03 times the adsorption (both expressed in the same units). 120 121 The derived concentration dependence of the Volta po tential, shown in Figure VI-1, is one of rapid increase to a broad maximum followed by slow decrease with in creasing concentration of SNS. The interaction of the NS ion with graphite was found from a Langmuir plot of the experimental adsorption isotherm, using variable electrostatic and constant non electrostatic work terms and a maximum number of ad sorption sites equal to the limiting surface charge density. The value of the heat of adsorption, -5.3 kcal/ mole, and the non-electrostatic interaction with the surface, -9.4 kcal/mole, were shown to agree well with other experimental and theoretical values of similar ions. Values of the zeta potential were calculated from experimental electrophoretic mobilities. Theories relat ing £ and U exist for spheres and flat plates, but since the particles of Sterling FTg are polyhedra with an effective radius of about 1000 & treatments based on both geometries were used. The calculated values of £ are listed in Table IV-3 (p. 81). Those values corre sponding to a spherical particle are shown graphically in Figure VI-2. The curve resulting from the flat plate approximation is of the same shape but the values are slightly lower. 200 150 100, o.cS 0.02 (,SNS) FIGURE VI-1: SURFACE POTENTIAL (IN MILLIVOLTS) CALCULATED FROM THE ADSORPTION ISOTHERM AS A FUNCTION OF THE SNS CONCENTRATION. 122 80 60 40 20 00,0 [SNS] 0 0 2 0 0 FIGURE VI-2: ZETA POTENTIAL OF STERLING FTG IN AQUEOUS SNS AS A FUNCTION OF THE SNS CONCENTRATION. 124 The zeta potentials found are unexpected and differ from the bulk of those in the literature in two regards. The values are unusually low and also exhibit a minimum as a function of concentration. For classical and latex sols (constant surface potential or charge) zeta generally decreases with increasing electrolyte concentration, con sistent with the concept of an increasingly compact double layer and a shear plane removed slightly from the charged interface. Parfitt and Picton (85), working with dispersions of graphitized carbon blacks in sodium dodecyl sulfate solutions, observed a minimum in zeta with increasing concentration of surface-active electrolyte. When they worked at constant ionic strength (0.1 M NaCl), zeta rose to a constant value. The magnitudes of their zeta potentials are also quite low although not so low as those found for Sterling FTg in SNS systems. This is to be expected, however, since SDS adsorbs more strongly than SNS and with approximately two times the limiting adsorption. Interpretation of Zeta Potentials A series of phenomena may exist and have frequently been employed in the literature of colloid chemistry to account for differences between ipQ and £. These are discussed with especial consideration of their ability 125 to account for the observed minimum in the concentration dependence of t,. The zeta potential is the potential at the surface of shear, which is generally not coincident with the charged interface. Thus it is not expected that and t, should be equal. The presence of a high surface charge results in a strong local electric field which can produce dielectric saturation and can increase the vis cosity of the water. These effects have been treated theoretically by Hunter (49) and by Overbeek (82). Al though both phenomena exist, the effects are very short range (a few molecular diameters at most) and have only a small effect on the value of the potential (40). Since such high fields exist in many aqueous colloids without producing a minimum or very low values of t,, it seems unlikely that they are responsible for the effects ob served here. A Stern layer has the effect of reducing the sur face charge as does ion pair formation, and consequently reduces the zeta potential. The counterion in all these experiments is Na+. No divalent ion was present in the electrode compartments which could enter the electro phoresis cell through the wetted stopcocks. The +2 distilled water did have 0.01 ppm Ca and a total of 0.5 ppm divalent cations. The dramatic effect of calcium 126 ion on sodium dodecyl sulfate-stabilized Graphon dis- +2 persions (119) involved Ca concentrations more than a hundredfold larger than could have been present in this work. Matejevic (66) observed no effect on the surface tension of solutions of sodium octyl sulfate with the +2 + addition of Ca . It has been shown that Na is not specifically adsorbed on Hg even at the highest accessible negative potentials (32) and that its specific adsorption potential at the aqueous octadecyl sulfate-air interface is less than kT/e (58). Although there may be very small amounts of specifically adsorbed ions, the effect should be greatest when the electrolyte concentration is low and cannot account for the observed zeta potential minimum or the very large difference between {pQ and £. The discreteness-of-charge effect or finite size of the potential-determining ions has been shown theo retically (40, 57, 95) to be of significance only within the first few molecular layers from the surface. The finite size of the counterion is important only for high electrolyte concentrations (_> 0. 5M) , and in the inner Helmholtz layer. Finite counterions cause the potential to drop less rapidly than predicted and would lead to values of zeta closer to than expected of a shear plane five or ten angstroms removed from the surface. 127 The equations used to calculate zeta from electro phoretic mobility were based upon the assumption of a non-conducting particle. Graphite is, however, conducting in the direction parallel to the basal planes and non conducting normal to that plane. Both electron micro graphs (45) and x-ray diffraction studies (43) lead to the conclusion that the basal planes are parallel to the particle surface for graphitized thermal blacks. Thus the applied electric field will be parallel to the par ticle surface. However, it has been shown (81) that colloidal metals behave as if they were non-conducting. This is thought to be due to rapid polarization of the metal surface which prevents any conduction within the particle. The same is expected of graphitized carbon blacks, i.e. that they will undergo surface polarization and will behave as non-conductors in an applied electric field. The effect of surface conductance is to reduce the mobility by a factor, aa/(a„ + aa) , which depends upon the particle radius, a, and the conductances of the electrolyte and surface, a and a_, respectively (81). The conductivity of the double layer is included in the calculation of zeta in the relaxation anc. retardation effects. The pi electrons in the carbon become immobile 128 as a result of surface polarization. The NS ions are free to move along the surface and are a possible source of surface conductivity. Adsorption-stabilized graphite dispersions differ from classical and latex sols in two significant respects. The surface charge-producing-ions are in an adsorption equilibrium with ions in bulk solution. This equilibrium is characterized by a relatively low energy of transfer so that the amount on the surface is highly dependent upon temperature and electrostatic effects (such as an applied electric field). Secondly, since adsorption is due primarily to dispersion interactions, the ions are not bound to specific sites so they should be mobile. The applied field is roughly parallel to the surface (since xa = 50) exerting a force on the adsorbed ions which will cause them to move along the surface. This is, in effect, a surface conductivity and lowers zeta by a factor proportional to the number of ions on the surface. It has a second result. The force of the electric field on the colloidal particle is the product of the charge and the field. If an ion moves along the surface, then the particle will behave as if its charge were reduced. As the surface coverage approaches one, collisions between adsorbed ions become more probable (a mean-free-path effect), which will reduce their 129 surface mobility. Reduction of surface mobility due to collisions will cause the zeta potential to rise at higher concentrations, producing a minimum in zeta. The mobility of the adsorbed ions and the suggested field dependence of adsorption are two factors present with graphite dispersions coated with a layer of adsorbed ions which do not apply to Au, Agl and latex sols. They can account for an apparent low value of zeta and a zeta potential minimum with increasing concentration of the potential-determining ion. Interpretation of the Stability Ratio It was shown in Chapter V that the observed linear dependence of the absorbance of these dispersions on wavelength in the visible region of the spectrum leads to a proportionality between (d In A/dt)t=0 and the product of the particle concentration, Nq, and the Fuchs- Smoluchowski rate constant, k. The stability ratio, W, is equal to the ratio of the rate constants for fast and slow flocculation, ^fast/^siow* since ^-fast ' * ' s 9i-ven -12 by Smoluchowski theory to be approximately 6 x 10 for spherical particles in water at 25° C, an estimate of W can be made by using an approximate value of the particle concentration calculated with Equation 5.1. 130 The dispersions in stability series 3 and 4 had initial optical densities of 0.49 and 0.36 with carbon — 5 ~5 concentrations of 1.5 x 10 and 1.6 x 10 gms/ml. A 4 specific optical density of 3.0 x 10 corresponds to a O concentration of particles with a 1000 A radius of Q 1.2 x 10 /cc. For the purpose of calculation, a value g of Nq of 1.2 x 10 /cc was used. Although this is only an estimate and the specific optical density varies some what from one series to the next, the error in log W is less than 0.5 and is independent of the concentration of SNS, so will not affect the qualitative interpretation of the results. The values of log W thus calculated from experiment are plotted in Figure VI-3. The scatter of the points is of the order of 1 in log W. This is due to the fact that four series with differing concentration and size distribution are plotted together. That the scatter is greater for the more stable systems reflects the dif ficulty in estimating small changes in absorbance over long periods (weeks) of time. In order to make calculations of W based on DLVO theory for comparison with experiment, it is necessary to assign values to the Hamaker constant, the Volta potential, and the particle radius. o H O s o °o -2 0.10 0.01 0.001 (SNS) FIGURE VI-3: LOG STABILITY RATIO, W, AS A FUNCTION OF LOG SNS CONCENTRATION. EXPERIMENTAL POINTS AND CURVES CALCULATED USING VALUES OF THE ZETA POTENTIAL. A) 76.8 mv. B) ZETA FROM EXPERIMENT BASED ON SPHERE WITH 1000 £ RADIUS. C) ZETA FROM EXPERIMENT BASED ON THE FLAT PLATE APPROXIMATION. O J 132 O 1000 A was used as the particle radius. The prin cipal species in the dispersion are probably primary particles but some fused multiplets and non-dispersed aggregates are certain to exist. It has been shown that for particles which are aggregates the best agreement with theory comes from using the value of the radius of the primary particle (85). The Hamaker constant, as was described in Chapter I, can be calculated from the polarizability and diamagnetic susceptibility of the materials using the equations of Slater-Kirkwood and Neugebauer (110). It can also be calculated from the dispersion contribution of the surface tension using Fowkes method (2 8) or from the frequency dependence of absorbance over the major absorption peaks and Lifshitz equation (56) . Graphite and water are such well characterized materials that sufficient data are available to compare Hamaker constants calculated with all four equations. The physical constants used in these calculations and the Hamaker constants found are listed in Table VI-1. Values of the net constant, A.^/ for -13 -13 graphite m water vary from 2 x 10 to 9 x 10 ergs. -13 The median value of 5 x 10 seems most reasonable since it was found from experimental macroscopic properties (28) using Fowkes equation and also gave a best fit of the experimental stability of aqueous Graphon suspensions (85).__________________________________________________________ 135 TA BLE VI-•1 PHYSICAL C O N STA N TS O F GRAPHITE A N D W A T E R Property Graphite Water O ' O il 0.94 x 10 1 .4 x IQ"24 X -1 .0 5 x 10-29 -2 .2 x 10-29 h tu 7 .2 eV 1. 4 eV Y d 2 110 ergs/cm O 2 1 .8 ergs/cm \ 436 770 m )i K 2 x 10-2m ij,- ^ 2 .4 x lO-9!^"1 & 1000 A 80 cm C A L C U L A T E D V ALU ES O F T H E H A M A K E R C O N ST A N T Method 12 A x x 10- 1 - A2 x 1012 A12 x 1015 Slater-Kirkwood 2.0 0.6 4.1 Neugebauer 1 .4 0.6 1.7 Krupp 2.8 0.54 8.7 Fowkes 1 .6 0.32 4.9 134 Stability ratios were calculated on an IBM 360-65 computer for integral values of the reduced surface po tential, zei|>o/kT, using Overbeek's functions L and f (110) for spheres and flat plates and the complete appropriate Hamaker expression (p. 6). W was also calculated using experimental values of t, and calculated from the ad sorption isotherm. Since these values are non-integral, Overbeek's exact expression cannot be used, so the repulsive contribution to the interaction energy was calculated with Derjaguin's equation (p. 9) adjusted at integral values of the reduced surface potential to the values found using the L function. This is necessary since the Derjaguin expression is only valid for low i j > and leads to a repulsion which is 25 per cent high for a surface potential of 55 millivolts. For those 160 cases in which VT/kT exceeded 10 , the value of the integral was approximated by a graphical integration at the maximum (110). The results of these calculations are shown in Figures VI-3 (p. 131) and VI-4. Two curves of the interaction energy between two spherical particles as a function of the distance of separation of their near surfaces, calculated with Overbeek's function, L, are shown in Figure VI-5. LOG W 135 300 200 100 0 _ 0.100 0.010 0.001 (SNS) FIGURE V I : LOG-LOG PLOT OF THE DEPENDENCE OF THE STABILITY RATIO ON THE SNS CONCENTRATION. CURVES BASED ON YQ CALCULATED FROM THE ADSORPTION ISOTHERM, (A), l$h MILLIVOLTS, (B), AND l 6.8 MILLIBOLTS, (c). TOTAL INTERACTION ENERGY 300 200 100 -100 -200 150 100 0 50 DISTANCE, S . FIGURE VI-5: CALCULATED CURVES OF THE INTERACTION ENERGY OF TWO SPHERICAL PARTICLES WITH 1000 5 RADIUS. A = 5 x 10" UPPER CURVE: C = 0.003M, Y =55.0 MILLIVOLTS; LOWER CURVE: C = O.OO5M, y° = 23-9 MILLIVOLTS. 1 0 137 The surface potential, calculated from the ad sorption isotherm, shows a weak maximum. This leads directly to a predicted maximum in the stability ratio shown in Figure VI-4 (p. 135). The calculated values of W, 10"^^ to 10^^ over the concentration range studied, correspond to infinitely stable suspensions. If W were only 10 1 5, there would be no observable flocculation over a period of years. Thus, if the dispersions behaved as theory predicts, no coagulation could be ob served and the rate of Fuchs-Smoluchowski coagulation could not be used as an experimental test of DLVO theory. The zeta potential is frequently used in place of This was done here for comparison and the results are plotted in Figure VI-3 (p. 131). The calculated log W's decrease rapidly with increasing concentration of SNS to a limiting value of -2. The value of -2 reflects the difference in interaction range between the square well potential which Smoluchowski kinetics assumes and the long range of van der Waals forces for O particles with 1000 A radius. The striking difference between the experimental stability ratios and those calculated from either or x , is both in the order of magnitude of W and the very low value of d log W/d log [SNS]. Although the behavior of these suspensions changes noticeably over 138 the concentration range from 0.001 M to 0.050 M SNS, it corresponds only to a difference of 3 in log W. Rapid flocculation is not observed. At low concentrations the dispersions are far less stable than expected. It is a basic hypothesis of DLVO theory that the electrostatic repulsion is due to an increase in free energy when the diffuse double layers of two approaching particles overlap. Differences between fact and theory must be sought in the nature of the surface charge- potential relationship or of the properties of the diffuse double layer. In the discussion of the zeta po tential results, factors affecting the surface potential and its decay in the inner-Helmholtz layer were con sidered. Evidence is strong that the concentration of ions and the variation of \p in the diffuse part of the double layer generally obey Guoy-Chapman theory. The property which is most sensitive to the struc ture of the double layer is its capacity, o/ipf which can be expressed as the sum of contributions from the diffuse part and the Stern region. The capacity of the latter is assumed not to be a function of concentration. Normal behavior of the capacity of the diffuse part of the double layer has been observed for a wide variety of solid-solution surfaces: by Berube and de Bruyn (6) with TiC>2 sols, Lyklema (64) with Agl, and on Hg (32, 81, 86). 139 The negative adsorption of similions, primarily a property of the diffuse part of the double layer, was found by van den Hul to have a dependence on surface po tential predicted by Guoy-Chapman double layer theory (107). Mysels and Jones (78) found that the thicknesses of equilibrium films of aqueous SDS solutions which depend upon the balance of van der Waals, electrostatic, and gravitational forces were in excellent agreement with those calculated using DLVO theory assuming interacting plane parallel diffuse double layers. A change in dielectric constant and a small change in the value of W (but not dW/dC) can be due to a structuring of water at the interface. Lyklema (64) has attributed an inflection in double layer capacitance with temperature at 50 to 55° C and the change of floccu lation rate of Agl sols over the same temperature range to the melting of an ice-like layer of water. The existence of structured water with polyvinyl acetate sols has been found with NMR studies (52). The corre sponding flocculation rates were slightly lower than predicted by DLVO theory. A linear plot of log W against log C with a short concentration range for transition from stable to rapidly flocculating as predicted by DLVO theory for a 140 constant surface potential has been observed for Se, Au, Agl, sulfonated latex and carboxylated latex dispersions (52, 78, 95, 101, 110, 115). The effects of the discrete ness of the charges, the possibility of penetration of counterions into the layer of surface charges and the layer of structured water are present with sulfonated and carboxylated latex sols and also with soap films, which have been observed to follow DLVO theory quite closely (52, 75, 78, 101, 115). The charges at the latex-water surface are chemically bound and are not free to move. The adsorbed ions at the air-water interface with soap films are free to desorb into solution. However, even when the film is stretched or the pressure increased suddenly, the equi librium adsorption is regained with time. The closest approach of the surfaces reported by Mysels (75) was O 200 A, a distance at which double-layer penetration is still small. There is some indication in the adsorption iso therm that desorption of SNS may occur when the particles coagulate. The adsorption point at 0.10 M SNS (Fig ure III-l, p. 3 8) is considerably lower than expected from the adsorption runs at lower concentrations. The carbon content was 5 grams in 10 ml of solution and the dispersion was highly coagulated. 141 No comparison can be made between the stabilities of Sterling FTg in aqueous SNS solutions and Graphon and Sterling MTg in aqueous SDS studied by Parfitt, since no instability was observed for either of the latter systems in the absence of swamping electrolyte. Since the ad sorption of SDS is higher than that of SNS at the same molarity and also reaches a higher limiting adsorption, the surface potential would be expected to be higher and the adsorbed ions less mobile (the surface coverage being higher) with SDS than with SNS. The argument made concerning the effect of the mobility of the potential-determining ions on the zeta potential can also be made with respect to sol stability. In the low concentration region the surface is only sparsely covered with NS ions and the double layer is very diffuse. As two particles approach, thermodynamic equilibrium demands that the chemical potential of the adsorbed ion remain constant. The repulsion of the two- particle system can be reduced if surface charges are diluted at the surfaces closest together. If the par ticles approach to the distance corresponding to the maximum in the interaction energy, there will be greatly reduced electrostatic repulsion if there are no ions on that portion of the surfaces which are most strongly interacting. It is not necessary to greatly increase 142 the surface charge density on the rest of the particle surface since the interacting regions will be much less than 5 per cent of the total. As the SNS concentration increases and the surface becomes more completely covered with NS ions, formation of vacancies will become more difficult. This model predicts a W which will be much lower than predicted at low C, approaching that predicted by ipQ at hither C. This type of behavior is just what was observed. Though the argument is only qualitative, it does utilize reason able differences in behavior of the potential-determining ion between classical sols and latex sols and the present case to account for the tremendous difference in zeta potential and dispersion stability. Suggestions for Further Work It has been proposed that the difference in the behavior of SNS-stabilized Sterling FTg from that of inorganic and latex sols is primarily due to the mobility and low heat of adsorption of the potential-determining ion. A number of experiments can be performed to directly test this hypothesis. A measurement of the dependence of electrophoretic mobility on field strength can easily be made for SNS concentrations of less than 0.00 8 M. A strongly bound, 143 constant surface charge results in a mobility which is independent of the applied field. If the charges are mobile and/or adsorption is field dependent, the mobility and zeta potential should decrease with increasing field strength. The zeta potential can also be calculated from any other electrokinetic property. Neither sedimentation potential nor streaming potential involves an applied electric field, and either would serve as a useful alternate method for determining £. The suggested dependence of adsorption on the strength of an applied electric field can be tested directly. The experiment would be easier to perform if a graphitized carbon black with a higher specific surface area (e.g. Graphon) were used. This would reduce the centrifugation time from 30 to one or two minutes and would result in a slurry with a reasonable viscosity. The heat of adsorption can be determined from adsorption values at two or more temperatures and would provide a double check on the value found from the Langmuir equa tion, modified to include the variable electrostatic work term. 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Creator Van Dolsen, Karma Marie Gropp (author)

Core Title Adsorption And Flocculation Studies Of Carbon Black Dispersions In Aqueous Solutions Of Sodium Beta-Naphthalene Sulfonate

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Chemistry

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

Tag chemistry (physical chemistry),OAI-PMH Harvest

Language English

Advisor Vold, Marjorie Jean (committee chair), Hyers, Donald Holmes (committee member), Vold, Robert D. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-400229

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Legacy Identifier 7013674.pdf

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Rights Van Dolsen, Karma Marie Gropp

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