University of Southern California Dissertations and Theses

Dental Enamel Electrochemistry

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Dental Enamel Electrochemistry

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Content 70-26,518 DICKERSON, Robert Allen, 1940- DENTAL ENAMEL ELECTROCHEMISTRY. University of Southern California, Ph.D., 1970 Engineering, biomedical University Microfilms, A X E R O X Company, Ann Arbor, Michigan DENTAL ENAMEL ELECTROCHEMISTRY by Robert Allen Dickerson A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OE PHILOSOPHY (Chemical Engineering) June 1970 UNIVERSITY OF SO UTH ERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 0 0 0 0 7 This dissertation, written by . ® £ ® . 9 ? . under the direction of h . l S k . . 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 for the degree of D O C T O R OF P H I L O S O P H Y i ' Dean Date « T m s . . . . l . 9 . 7 Q_ DISSERTATION COMMITTEE AaJHLu . Chairman ....... This worfc is dedicated to my wife, Susan, and daughters, Laurie and Karen. ii ACKNOWLEDGMENTS The author would like to express his appreciation to the following people and .organizations: Dr. J. M. Lenoir, Dr. C. J. Rebart, Dr. L. A. Bavetta, Dr. S. E. Allerton, and Dr. C. S. Copeland for their guidance and encouragement. The North American Rockwell Corporation, for providing a work-study fellowship which allowed the time for this work to be accomplished. iii TABLE OP CONTENTS Page ACKNOWLEDGMENTS....................................iii LIST OF FIGURES................................... vi INTRODUCTION ............................... .... 1 ELECTROCHEMICAL MECHANISM FOR DEGRADATION OF DENTAL ENAMEL ........................................ 8 The M o d e l ........................... 8 Physical and Chemical Structure of Enamel . . . 9 Pertinent Literature ........................... 14 Ionic Membranes............................ 18 Hypothetical Mechanism.................... 33 EXPERIMENTAL RESULTS............................ 39 Oxygen Concentration Cells ..................... 39 Salt Concentration Cells ....................... 43 Effects of Concentration Level on Enamel Membrane Potentials ........................... 51 Effects of pH on Enamel Membrane Potentials . . 64 Effects of Electrical Current Through Dental Enamel ...... ............................. 70 Effects of Fluoride Treatment on Enamel Membrane Potentials ........................... 80 t iv TABLE OP CONTENTS (con't.) Page Effects of Fluoride on Electrical Current Through Enamel ................................. 87 CONCLUSIONS............ 98 REFERENCES ................................... 101 V LIST OP FIGURES Figure Page 1 Cross-Sectional View of the Physical Structure of Enamel (Enlarged Approximately 6,000 X) . . 10 2 Arrangement of Atoms in Dental Enamel Crystals...................................... 12 3 Distribution of Ions in Three Pores of Different Diameter, All at the Same Concen tration of Outside Electrolyte ........ 20 4 Scheme of Variation of Ion Specie Activity for the Fixed Charge Theory of Ionic Membranes 30 5 Hypothesized Concentration of Electrical Current at a Defect Location................. 36 6 Apparatus for Determination of Potentials Due to Oxygen Concentration Differences........ 41 7 Apparatus for Determination of Ionic Membrane Characteristics of Human Dental Enamel .... 44 8 Preparation of Enamel Wafers................. 46 9 Potentials Obtained with a Human Dental Enamel Wafer in KC1 Salt Concentration Cells .... 48 10 Salt Concentration Cell Potentials Using Several Different Salts with an Enamel Wafer . 50 11 Effects of Concentration Level on the Thick ness of the Ionic Double Layer Which Neutral izes the Pore Wall Charge....................; 53 12 Effects of Concentration on the Ionic Double Layer Thickness............................. 55 vi LIST OF FIGURES (con’t.) Figure Page 13 Effects of Concentration Level on Membrane Potential, for Most Common Ionic Membranes . . 56 14 Effects of Concentration Level on Enamel Ionic Membrane Potentials ................... 57 15 Effects of pH on Enamel Membrane Potentials . 66 16 Representation of an Enamel Pore, Showing the Anions Comprising the Pore Wall Negative Charges...................................... 68 17 Apparatus Used to Determine the Effects of Electrical Current on Dental Enamel ........ 71 18 Time Dependence of Electrical Current Through an Enamel Wafer for 42 Hours' Exposure .... 73 19 Time Dependence of Electrical Current Through an Enamel Wafer for 100 Hours' Exposure . . . 74 20 Photomicrographs of Enamel Wafers Exposed to Direct Electrical Current, Magnification: 50X. 79 21 Effects of Concentrated Fluoride and Concen trated Chloride Treatments on Enamel Membrane Potentials................................... 83 22 Effects of Fluoride Addition on Electrical Current Through an Enamel Wafer ....... 90 vii INTRODUCTION This is a study of the mechanism of dental caries formation from a non-biological point of view, it consid ers the behavior of tooth enamel stability and decomposi tion with an electrochemical model. This contrasts with fhe classical theory which states that caries formation is the direct result of the action of acidogenic bacteria on dental enamel, at the location of the caries. The classi cal theory was ostensibly ignored for the purpose of this study, in order to explore alternative mechanisms related to electrochemical phenomena. The electrochemical view point was taken for two basic reasons: 1. It seems un likely with frequent brushing or cleansing of the teeth, that a cluster of acidogenic bacteria would be capable of remaining at a localized point on the tooth for the entire time period required to create a pit in dental enamel; and 2. Electrochemical phenomena are intrinsically capable of concentrated action in a localized manner, for the long time periods which are required for carious penetration of dental enamel. It should be noted that this study was concerned 1 2 with possible mechanisms by which the outer layer of dental enamel might be penetrated. It was not concerned with the decay or biological consumption of the tooth dentin which occurs after the enamel has been penetrated. It is recog nized that dental caries do not always have the same charac teristics, and this study was directed towards the preva lent type of caries wherein one or two small, localized pits are observed in the dental enamel. This study was undertaken because of similarities between dental caries and engineering corrosion problems. There are several features of dental caries which are similar to the features of metallic pitting corrosion. The most striking similarity is the occurrence of pits. Ordinary dental caries consist of small pit-like formations in the layer of dental enamel on the outside of the tooth. These pits, or caries, have a high frequency of occurrence near the gum line, and in creivce like areas between neigh boring teeth. The caries are generally a localized pheno menon, consisting of severe attack at the site of the pit, with no noticeable change in the tooth as a whole. The corresponding case of pitting corrosion in metals consists of the formation of localized pits on a metallic surface which does not simultaneously suffer from general corrosion over its entire surface. Pitting corrosion is one of several specific types of metal corrosion. Pitting corrosion especially occurs among the electrochemically passive metals such as stain less steels, aluminum, titanium, and chromium. The elec trochemical passivity of these metals is due to the forma- i tion of a layer of oxidized metal at the surface, and it is I I this passivity which causes the pitting characteristic of the corrosion. Pits begin by the breakdown of passivity at favored locations on the metal surface. The breakdown results in formation of an electrochemical cell, wherein i the area of breakdown of passivity becomes the anode, and j the remaining large majority of the metallic surface be- j comes the cathode. The two areas of the electrochemical | i cell are connected electrically by the bulk of the metal, | and by the solution in which the metal is immersed. The i I large potential differences of the "passive-active'1 cells result in electrical currents which are concentrated at the relatively small area of breakdown of passivity. The cur- j rent results in dissolution of the metal, and simultaneous-; ly transfers anions from the solution to the area of the 4 pit, helping to assure that the pit area remains non-pas sive. Analogously, dental enamel is a material which might be considered normally protected against attach from its environment by surface films which frequently appear as discoloration and/or mottling. In spite of this layer, enamel suffers from pitting (carious) attack. Pits form on uniformly exposed surfaces of the passive metals; how ever, they more prevalently form at crevices underneath bolts or rivets, or at joints between metal plates. This appears to be analogous to the higher frequency of forma tion of dental caries in crevice-like areas between neigh boring teeth and at the gum line. The surfaces of passive metals can remain completely uncorroded for long periods of j time; but, if corrosion does eventually start, pits form and penetrate the material very rapidly. This behavior is similar to the sudden onset of caries. In metals, pitting characteristics are strongly affected by the nature of the aqueous environment to which the metals are exposed. The presence of chlorides, the degree of aeration, alkalinity, and temperature all affect pitting frequency of met ads. Analogously, the aqueous environment of the tooth is also affected by diet and s&liva, which have some correlation with the frequency of caries. In crevices and at areas of contact with foreign materials, metals frequently suffer from a more general type of corrosion, termed crevice or contact corrosion, j which results from the formation of concentration cells. Concentrations of oxygen or other substances for various reasons become different in the crevice areas, as compared j to the bulk of the solution to which the metal is exposed. These differences in concentration set up an electrochemi- ! cal cell which can corrode the metal. In this case, the corrosion is generally more uniform (within the crevice) than a pit. A similar situation exists at the waterline in j tanks and other devices where oxygen can be locally more concentrated due to intimate contact with air at the water-! line. The mechanism of gingival caries formation may be similar to crevice corrosion and waterline corrosion. Admitting that there are possible similarities be- i tween dental enamel and metals as discussed above, it should be realized that there are also some very profound differences. These differences might result in dental and j I metallic pit formation mechanisms which are not identical, 6 but rather only analogous. Some of the differences are discussed below. The basic hydroxylapatite material of the tooth is an electrical non-conductor. Only when the enamel material! ■ / contains moisture is it capable of being electrically con ductive (1) , and even in this case, the enamel apparently conducts ions through the aqueous phase within the enamel, ! rather than electrons as is the case with metals. Since enamel does not conduct electrons, it is not capable of supporting electrochemical half cell reactions such as: | M* + e“ >• M which typicaly occur, during pitting corrosion, at the in- | terfaces between metals and electrolyte solutions. This j fundamental difference between metal and dental enamel ! rules out the possibility that pit formation in dental j i i enamel caii occur by identically the same mechanism as ob- j served with metals. j Also, dental enamel is a heterogeneous, semiperme- able membrane (2); whereas, metals are essentially non-per- i ' • meable. Work by Tarbet (3) has shown that diffusion of dye molecules and ions through dental enamel occurs in the ; sheath and inter-rod substance which surrounds the myriads j of hydroxylapatite rods which.make up the enamel material. ! An additional .unique feature of dental enamel is ' that it is slightly soluble in aqueous solutions (4). As a; result, dental enamel exchanges ions with the saliva media j in which the enamel is immersed (5). It is partly by this j mechanism that enamel characteristics can be affected by fluoride content of drinking water, saliva characteristics,; and diet. I In spite of the differences between metals and den- j i tal enamel, the physical similarities between corroded i pits in metals and dental caries suggests that analogous i (that is, electrochemical) mechanisms might be involved. | Study of enamel characteristics from this point of view is ; justified by the hope that an electrochemical mechanism of ; tooth decay might be amenable to corrective action which is! j equally as effective as electrochemically oriented methods of protection are for metals. ELECTROCHEMICAL MECHANISM FOR DEGRADATION OF DENTAL ENAMEL The Model For an electrochemical mechanism to be the means of carious dental enamel degradation, there must be an elec trical potential to cause flow of current, and there must be a reason for this current to be directed and concen trated in local areas to form the localized pits character istic of dental caries. The required electrical potential in the oral en vironment is considered to result directly from the ionic membrane characteristics of enamel. Electrical current is assumed to be directed to a specific area of the enamel as a result of some outside influence such as lodged food particles, or bacteria. After a short period of time, the current is assumed to have sufficiently damaged the enamel that it is able to remain concentrated at the same location even after the removal of the food or bacteria, until a carious lesion is eventually formed. Before considering this hypothetical mechanism in more detail, it is desirable to review the structure of enamel, pertinent literature, and ionic membrane theory. 8 9 Physical and Chemical Structure of Enamel In reference to ionic membrane characteristics, it is of interest to discuss the structure of dental enamel. Studies of dental enamel (6) using light microscope and electron microscope techniques have revealed dental enamel to consist of an assembly of rod-like structures radiating from the dentin on the inside of the tooth to the outside of the tooth. These rod structures are partially surround ed by rod sheaths, and the volume between rods is filled by what is termed inter-rod material. Figure 1 is a sche matic representation of this physical structure. Note that the rods and the inter-rod material blend together in the areas where rod sheath is absent, in more matured, fully calcified enamel, the rod sheath becomes thinner than shown in Figure 1, so that the rod-like structure is less obvious. It is thought that the rod sheath and the inter-rod materials are the most permeable portion of the enamel (7), and this is the area through which ions and other substances pass when permeating enamel. When the electron microscope is used to take a much closer look at the enamel material (6), it is found that single rods of enamel do not exist as a single crystal of I I ROD ROD SHEATH INTER-ROD MATERIAL FIGURE 1 CROSS-SECTIONAL VIEW OF THE PHYSICAL STRUCTURE OF ENAMEL (ENLARGED APPROXIMATELY 6,000 X) 11 hydroxylapatite (Ca-^PO^gfOH^) # the basic material of enamel. The same is apparently true of the rod sheaths and the inter-rod material. Instead, these materials exist as myriads of small, broad, plate-like crystallites having lengths from 250 to 10,000 angstroms, widths from 400 to 1200 angstroms, and thicknesses from 100 to 250 angstroms (6). Groups of these crystallites are sometimes found in parallel arrangements, but they are more often found in much less organized arrangements of longitudinal, oblique, and cross-sectional orientations. These myriads of crys tallites present a large relative area of hydroxylapatite crystal surface to any aqueous media permeating the enamel, giving impurities such as fluoride, which can become a part of the crystal lattice at the surface of these crystals, good opportunity to do so. The molecular structure of a hydroxylapatite unit ceil is shown schematically in Figure 2. This structure (8) accounts for the plate-like shape of the enamel crys tallites discussed above. The hydroxide ions are located in favorable positions for ion exchange with the media surrounding the crystallites, and it is generally under stood that fluoride ion can permanently substitute for the FIGURE 2 ARRANGEMENT OF ATOMS IN DENTAL ENAMEL CRYSTALS P04 Ca^ OH H to 13 hydroxyl ion (1,8), giving a compound called fluorapatite when the substitution is complete. Since the size of the fluoride ion is only slightly smaller than the size of the hydroxyl ion, the dimensions of the unit crystal cell of fluorapatite are almost identical to those of the unit cell: of hydroxylapatite (8). The exchange of fluoride for hy droxide in the enamel crystal structure occurs even when fluoride is present in very low concentration, such as found in drinking water. The exchange of fluoride for hy- ■ droxide occurs to the extent that normal teeth have fluo ride contents up to about 0.09 percent (1). Teeth fossil- j ized for extremely long periods of time are frequently found to have fluoride contents much higher than 0.09 per- j cent (1) , indicating that the fluoride reaction with dental 1 enamel is an ordinary chemical process not requiring life processes. Direct substitution of inorganic anions other j than fluoride into previously formed enamel crystal struc ture has not been reported, but traces of other anions have been found to be present, apparently incorporated as im purities when the enamel was originally formed. It may i also be important to note that not all enamel crystals are | perfect Ca10(P04)g(0H)2. Many are imperfect or defective, which led to the Greek name, apatite, meaning "to deceive," Pertineht Literature The earliest recorded investigations of the electro chemical characteristics of dental enamel were carried out by Klein and Amberson (9) in 1929, These investigators discovered that the enamel of dog canine teeth formed an ionic membrane. That is, when a dog canine tooth was used as a membrane separating two solutions of the same salt, but of different concentrations, an electrical potential difference was developed. This potential difference was a result of selective passage of ions of one sign, by the enamel membrane. With uni-univalent salts, the enamel was found to preferentially pass positive ions, so that the more dilute salt solution acquired a positive potential with respect to the concentrated solution. Klein and Am- berson (9) concluded that the enamel pore walls must bear a net negative charge in the presence of uni-univalent salts. Klein and Amberson (9) also studied the electroos- motic transport of water through canine enamel. Electroos mosis is the phenomenon whereby electrically induced mo tion of charged ions through a pore tends to carry the 15 solvent phase along with the Ions, thus causing the flow of solvent. The results of these experiments verified the presence of the previously inferred charges on the enamel pore walls. In a later study, Klein (10) measured membrane po tentials established using enamel membranes from pigs, which were on a low calcium, high phosphorus diet, and from pigs on a normal diet. He found that enamel from pigs on the deficient diet gave membrane potentials which were significantly lower than the potentials obtained using enamel from pigs on the normal diet. He concluded that the calcium deficient diet results in the formation of more permeable enamel (that is, enamel which is more permeable and which, therefore, is less selective to passage of ions of different charge). In still later work, Klein (11) made cataphoretic determinations of the electrical charge resident on enamel materials, including determination of the elffects of pH. Cataphoresis is the motion of electrically charged macro scopic particles in the presence of an electrical field. Positively charged particles move in one direction, and negatively charged particles move in the opposite direction. Prom cataphoresis experiments using small par- I tides of enamel, Klein found that the particles migrated in an electrical field as if they were negatively charged when immersed in KC1 solutions which were sodium acetate buffered to pH greater than about 3.6. When the pH of the solution was less than 3.6, it was found that the particles: migrated in a direction which indicated they were positive ly charged. Klein concluded that enamel possesses ampho teric properties similar to those commonly observed with certain proteins. That is, the sign of the net electrical ; charge resident on enamel changes from negative to positive when the pH is lowered below about 3.6. Observation of i i the direction of solvent flow during electroosmosis experi-j ments with controlled pH, as well as determinations of the i polarity of membrane potentials of dog cuspid enamel led to similar conclusions. i Chicle and Waters (12) extended the results of Klein j and Amber son by determining the effects of exposure of j i i human teeth to various inorganic anions. They used several! human teeth as membranes in a 10:1 ratio KC1 salt concen- j tration cell. After first determining the equilibrium po- ! i ! tential established with these cells, they briefly exposed ! 17 the enamel to solutions of other salts. They then re-de- termined the equilibrium potentials which the teeth were capable of establishing when used as membranes in a 10:1 KC1 salt concentration cell. They found, in several cases, that brief exposure of enamel to solutions of potassium fluoride caused an increase in the observed membrane poten tial. No significant change in the observed potential was found when the enamel was exposed to solutions of K2S04, KH2P04, KCNS, or KN03. In a later work, Chick and Waters (13) determined the effects of exposure of enamel membranes to various or ganic anions. They used the same technique as reported previously (12). In this study, they found that organic I anions had effects similar to fluoride, and in some cases more pronounced than fluoride. That is, brief treatment of enamel by solutions containing organic anions tended to increase the equilibrium potential which was observed when j the enamel was used as an ionic membrane in a 10:1 KC1 salt concentration cell. They observed that citrate, tartrate, j fluoride, oxalate, sulfate, lactate, and acetate had the largest to smallest effects, respectively. In still later work, Waters (14,15) used membranes j ■ I 18 made of synthetic calcium hydroxylapatite, Ca1Q(P04)g(OH)2» ; which is the mineral material making up dental enamel. He j found that the membrane characteristics of synthetic mate rial were similar to those of natural enamel, and there fore concluded that it is the mineral fraction of dental enamel which is responsible for the observed membrane characteristics of dental enamel. Ionic Membranes An excellent qualitative description of the charac teristics of ionic membranes is presented by Sollner (16). Parts of that description are reviewed in the discussion below. The most interesting feature of ionic membranes is their selective permeability to ions in solution. For purposes of this discussion, the only membranes of inter est are “membranes of porous character,” as opposed to “homogeneous phase membranes" (oil membranes). Membranes j of porous character act as sieves which screen out the passage of various dissolved species according to their difference sizes, according to their different adsorbabi- 1 lities, and, for ions, according to the sign and magnitude j of their charge. The most important feature of ionic mem branes is their ability to screen out ions according to the sign and magnitude of their charge. If an ionic membrane is used to separate two solu tions of the same electrolyte, but of different concentra tions, an electrical potential arises which is, in general, ; different from the liquid junction potential which would arise between the same two solutions in free diffusion (that is, in the absence of the membrane). The Tsign and magnitude of the potential depend on the identity of the electrolyte, the absolute concentrations, and the ratio of the concentrations of the adjacent solutions, as well as the nature of the membrane. The most fundamental fact of the electrochemistry of ionic membranes is that electronegative membranes (mem- ; branes possessing a negative charge) are preferentially j cation permeable, while electropositive membranes are pre- j ferentially anion permeable. That is to say, the ion sieve! 1 characteristics of ionic membranes are the direct result ofj i the surface charges attached to the membranes. The charges! i (ions) attached to the membrane are shown in Figure 3 as ! being attached to the inside walls of the membrane pores. ; ^T“'=V A* SMALL PORE B. INTERMEDIATE PORE C. LARGE PORE FIGURE 3 DISTRIBUTION OF IONS IN THREE PORES OF DIFFERENT DIAMETER, ALL AT THE SAME CONCENTRATION OF OUTSIDE ELECTROLYTE These charges are firmly attached, and since they are un able to move, they do not participate in the ionic process es across the membrane, such as diffusion or the transport of electricity. The counterions of the pore wall charges are dissociated into the liquid in the pores, and they are movable and can participate in the ionic processes across the membrane. Dissolved ions of the same sign charge as the pore walls (similions) are prevented, by electric re pulsion, from approaching the spots having permanently fixed pore wall charges. For pores of sufficiently narrow j geometry, such as in Figure 3-A, this electric repulsion completely excludes the similions from the pores, and any diffusion or electrical transport across the membrane must i occur by means of the oppositely charged counterions. This; very narrow pore which completely excludes similions while ; allowing free passage of counterions is a case of a mem- j I brane of ideal ionic selectivity, and when separating two ! j solutions of the same electrolyte, differing in concentra- \ tion, a potential difference is developed which is equal t i in magnitude to the potential difference which would occur I i if the two solutions were connected to each other through j a pair of reversible electrodes (see Equation 2 and the j 22 related discussion). This thermodynamically maximum poten tial represents the largest possible potential which can be developed across the ionic membrane. Shown in Figure 3-C is a very large pore of an ionic membrane. The relatively large geometry of this pore pre vents the pore wall charges from having any significant ef fect on the passage of ions through the pore. In this case, the pores are so large that the potential which is developed across the membrane separating two solutions is identical to the liquid junction potential which would a- rise between the same two solutions in the absence of the membrane. The liquid junction potential therefore, repre sents a kind of a minimum potential difference which can be developed by the membrane. A third case is shown in Figure 3-B, representing a pore of intermediate geometry which allows preferential passage of counterions, but does not completely exclude similions. An ionic membrane having this intermediate geometry would develop a potential intermediate between that of an ideally selective membrane and the normal liquid junction potential. Another factor influencing the ionic sieve 23 characteristics of a membrane is the density of surface charge on the pore walls. A membrane having higher surface charge density is naturally more capable of excluding si milions from the pores than a membrane having a lower sur face charge density, if the pore geometries are the same. It should be noted that most ionic membranes en countered in the laboratory do not have all pores of the same geometry. Instead, membranes are made up of multi tudes of pores all having a range of geometries. It is the dffects of the combined activities of all of these pores which are observed in laboratory experiments. Also, each of the pores do not necessarily have uniform geometry over their entire length. They may have wide and narrow por tions throughout their length. The likelihood that some or most pores will have at least one restricted area portion along their lengths, causing the pore to act as a narrow pore, is increased if the pore is longer (thicker mem& brane); and, therefore, thicker membranes tend to be more ideally selective rthan thinner membranes constructed of the same material. Differences in the sizes of the pores of the same membrane, and throughout the lengths of the individual pores are referred to as heteroporosity. The 24 existence of heteroporosity is frequently relevant in the explanation of the behavior of particular membranes. Qualitative explanation of the reason for existence of membrane potentials is most easily made in terms of an ideally selective ionic membrane. At the instant when an ideal ionic membrane first separates two solutions of dif fering electrolyte concentrations, there is no membrane potential; however, the difference in concentration immedi ately starts diffusion of the permeable ion through the membrane. Diffusion of the permeable ion through the mem brane causes an accumulation of charge and a depletion of charge on the opposite sides of the membrane. This accu mulation and depletion of charge continues until a poten tial difference is developed which is just sufficient to offset the tendency of the permeable ion to diffuse through the membrane as a result of the concentration difference. This final potential is the equilibrium membrane potential. Quantitative description of the membrane potentials is more involved. The quantitative characteristics of ion ic membranes are generally treated from either a strictly thermodynamic viewpoint, or from a more mechanistic view point known as the Fixed Charge Theory. The simple, 25 strictly thermodynamic description of ionic membrane be havior is presented, for example, by So.llner (16). The thermodynamic description merely recognizes the fact that membranes do exist, and that they preferentially permit passage of ions having a particular sign charge. The most direct result of this thermodynamic analysis is the follow ing equation relating the electrical potential created by the membrane to the characteristics of the membrane and the characteristics of the two solutions which the mem brane separates: AE = t+. -A ■ ■ ££ in (1) t+ + t~ P a±2 where, AE = the observed equilibrium potential t+ = positive ion transference number, the fraction of ions passing through the membrane which are positive t“ = negative ion transference number R = ideal gas constant T = absolute temperature P = Faraday's number ■ f * a * -}./ a~2 = mean ionic activity of the uni univalent salt on opposite sides of the membrane, respectively Equation (1) is strictly valid only for salt con centration cells consisting of an ionic membrane separating! two solutions of a single uni-univalent salt. For concen- ; tration cells having more than one salt, or salts of other i valencies, the equation is slightly different. For Equa tion 1, the sum of t+ and t” is unity, and it is obviously : the difference between t+ and t” which determines the sign I and magnitude of AE. For the case in which t+ is equal to; i unity, and t" is zero, at 25°C, Equation 1 becomes: j +. £E = .059 log10 I (2) a-2 The development of Equation 1 is based upon calcu lation of the change in Gibb's free energy, &G, due to j i migration of ions through the membrane when current is re- j I versibly flowed through the electrical potential developed j by the membrane. By definition of the transference num- j bers, t+ and t“, for a uni-univalent electrolyte, t+ and j | t“ net mols of positive and negative ions, respectively, | i I pass in opposite directions through any infinitesimally i thin section of the membrane as a result of each Faraday J I of current flow. The total change in Gibb's free energy j i for this process is: ! ..t 27 -dG = t+ d^ + - t“ d y “ (3) where, G = Gibb's free energy t+, t"” = positive and negative ion trans ference numbers, respectively ^ + , - chemical potentials of the posi tive and negative ions, res pectively. The definition of activity is in terms of the chem ical potential: d U * = RT d (In a+) (4) d = RT d(In a") where, a+, a" = the positive and negative ion activities at temperature T, res pectively. The above equation is applicable only to isothermal conditions. Substituting Equations 4 into Equation 3, -dG = t+ RT d(ln a+) - t" RT d(ln a") (5) Integration of Equation 5 from one side of the mem brane to the other, assuming the transference numbers to 28 remain constant, yields: - AG = t+ RT In - t" RT In (6) a 2 a 2 where, a+1# a“i = positive and negative ion acti vities on one side of the mem brane, respectively a+2 , a”2 = positive and negative ion acti vities on the opposite side of the membrane, respectively. Since it is not possible to experimentally deter mine individual ion activities such as a’ j j . / or a~2' convenient approximation of a term called the mean salt activity, a“ , representing both a+ and a” is used. Equa tion 6 is then written: + 3 i - AG = (t+ - t“) RT In — — (7) * ~ 2 Now, since the change in Gibb's free energy, AG# is equal to the reversible, non-mechanical work done by the system, and since this work is all electrical, we have for the uni-univalent salts: -AG = (t+ + f) FAE r (8) 29 where, F = Faraday's constant A e = the difference in electrical potential from one side of the membrane to the other side. Combination of Equations 7 and 8 results in the de sired relationship, Equation 1. The other theory of ionic membranes, the Fixed Charge Theory, is also known as the Teorell, Meyer, Sievers theory, after those who originated it (17,18,19). For this theory, the membrane is regarded as having surface charges resident on both the interior pore wall surfaces of the membrane, and on the exterior, exposed surface of the mem- | brane. The objective of this theory is to describe the i i membrane potential in terms of the identity of the solu tions to which the membrane is exposed, and in terms of the! t density of surface charge on the membrane. This theory con-* i I siders a scheme for variation of concentration of ion spe- ! i cies through the membrane such as shown in Figure 4. The | I jump in concentration of the ion species very near to the surface of the membrane in Figure 4 is treated as a case wherein the main bulk of solution is in equilibrium with i ! ! 30 IONIC MEMBRANE H < w M o w C O S3 O ' M i t t M4jJ c J i^! s i 5 i5(ff V s « ! ! ! h S " i DISTANCE FIGURE 4 SCHEME OF VARIATION OF ION SPECIE ACTIVITY FOR THE FIXED CHARGE THEORY OF IONIC MEMBRANES the solution at the adjacent surface of the membrane. The solution at the surface of the membrane has different con centration than the bulk solution because of effects due to.close proximity of the membrane surface charge. The jump in concentration between the bulk solution and the solution at the membrane surface could be either an in crease in concentration as shown in Figure 4, or a decrease, depending on the identity of the ion specie and the sign of the pore surface charge. The equilibrium between bulk concentrations and the concentrations at the membrane sur face is assumed to follow the Gibbs-Donnan rule, and it is referred to as a Donnan equilibrium. For a single uni-uni- valent salt, the Gibbs-Donnan rule states that the product of the ion activities in the bulk of the solution is equal to the product of the ion activities at the membrane sur face: (a+b)(a_b> = (a_m><a+m> = ( A 2 (9) j I where, a+j j , a-^ = positive and negative ion activi- ties in the bulk solution, res pectively 32 a+m* a*"m = positive and negative ion activi- i ties at the membrane surface, res pect ively + a~ =s the mean salt activity. + In other words, the mean salt activity, a~, is equal at the surface and in the bulk. If the membrane were, for example, negatively charged, one would expect the concen tration of positive ions to be higher ..nearer the surface than in the bulk solution due to electrical attraction, and correspondingly, the concentration of negative ions would be lower at the surface than in the bulk solution. The Gibbs-Donnan rule, represented by Equation 9, is used to quantitatively describe this situation which is termed a Donnan equilibrium. The Donnan equilibria at the opposite : surfaces of the membrane, together with the concentration gradients within the membrane such as shown on Figure 4 form the basis for the Fixed Charge Theory of ionic mem branes, when considered in terms of the electrochemical potential differences developed. The intermediate steps in deriving the expressions for the total potential dif ference are relatively complicated, especially when com pared to the simple thermodynamic analysis presented above (Equation 1). For this reason, it is not attempted to present the mathematical model details of the Fixed Charge Theory here. It suffices to say that though the two ionic membrane theories are differently based, they lead to similar results when circumstances are identical (17). For the purposes of this dissertation, the model represented by Equation 1 is adequate to describe the mem brane phenomena of interest. Hypothetical Mechanism As described previously, dental enamel forms an ionic membrane which preferentially permits passage of positive ions under most circumstances. This characteris tic of dental enamel must cause the existence of an elec trical potential difference because of the differing ionic j strengths of the saliva which bathes the exterior of the tooth, and the blood fluids which are contained in the in- j terior of the tooth. If the fluid contained in the interior of the tooth i is taken to have the same ionic strength as blood, then it j has a total cation concentration of about 154 milliequiva- | t lents per liter (20), compared to saliva having a total cation concentration of about 33 milliequivalents per liter (21). Both saliva and blood are complex solutions; however, since the cations are mostly K+ and Na+, a reason-! able estimate of the order of magnitude of the potential across dental enamel, in vivo, can be otained by using the total cation concentrations in Equation 1: AE = .059 log. n °.rA54 = 40 millivolts (10) 10 0.033 where the positive ion transference number, t+, and the activity coefficients have been assumed to be unity. The i polarity of the potential is such that the saliva is posi- i tive with respect to the blood. The calculated 40 millivolt potential difference across the enamel of the tooth would not cause harm to the j tooth unless there were some local area on the tooth ena- . i mel incapable of generating the potential difference. This! I i area having zero potential difference due to some natural, ! ! or unnatural local defect in the enamel membrane would act I ■ I i as a short circuit for the potential developed by the rest ! i i of the tooth enamel membrane. The short circuit would ‘ j cause the flow of current (ionic current, not electron j i current) which would be concentrated at the location of i the defect, as shown in Figure 5. Note that there is a relatively small current per unit area over the majority of the tooth, except at the local defect which is unable to generate the 40 millivolt potential difference. If passage of current through the enamel is capable of degrading the enamel, such degradation will first occur at the area of high current density, the area of the local defect. For dental enamel to be permanently degraded as the result of the passage of a high density of electrical cur rent , the current must be capable of removing enamel mater ial. It has been pointed out (4), that dental enamel is slightly soluble, and it is obvious, therefore, that high current density at a local defect could sweep solvated enamel ions out of the pores, thus requiring more enamel to go into solution to maintain solubility equilibrium, and thereby ultimately degrading the enamel at the local de fect. The existence of a high density current at local defects in the enamel which are incapable of generating the 40 millivolt potential generated by normal enamel, to gether with the assertion that very high density current degrades the enamel, constitute the essence of the 36 SALIVA ILOOD \ \ I FIGURE 5 HYPOTHESIZED CONCENTRATION OF ELECTRICAL CURRENT AT A DEFECT LOCATION 37 | hypothetical electrochemical mechanism of caries formation presented in this section. It should be stressed that this mechanism is hypo thesized to be the mechanism of growth, or format ion, and not the cause, or initiation, of dental caries. The cause of dental caries would, in this respect, be whatever pheno menon results in the loss of ability of the locally defec- live area to generate the 40 millivolt potential generated by the rest of the tooth enamel. A local area on the enamel of a tooth could be par tially defective when the tooth is originally formed, generating a low potential, and thereby, resulting in a slight flow of current at the local area over a period of several years. Degradation resulting from the current would eventually cause the area to become totally defec tive; whereupon, the current would become relatively large,! ultimately degrading the area to the extent that it be- i comes a carious lesion. Such areas of enamel which are partially defective when originally formed would likely consist of clusters of relatively large diameter pores located at thin sections of enamel, such as at the dento- enamel junction, or at pits or fissures in the structure of the tooth. In this case, the heteroporosity (that is, the existence of both large diameter and small diameter pores) of the enamel would play an important role in the formation of caries. Frequent lodging of food particles at the same loca tion on the tooth enamel would create a localized chemical environment resulting in a temporary loss of the 40 milli volt potential. Continuous flow of current could then de grade the enamel when the food particles are in place, eventually creating a local defect which would continue to be degraded even after the food particles are removed. Brief habitation of acidogenic or other bacteria on a local area of enamel could be sufficient to create a local defect. The flow of electtical current throi&h the defect could then continue, even after the bacteria were gone, ultimately resulting in the formation of caries. This would allow the bacteria to be the cause of the caries and yet eliminate the unrealistic necessity for the bac teria to remain in the same localized area for the extend ed length of time required to form caries. EXPERIMENTAL RESULTS Oxygen Concentration Cells Oxygen frequently plays an important role in the aqueous corrosion of metals. Oxygen concentration differ ences give rise to electrical potentials Which initiate pitting corrosion in metals. In these cases, electronic conduction in the metals is a necessary requirement for oxygen concentration cells to develop electrical potential. The crystalline material of dental enamel is an electrical insulator (1), even though it can pass ions through its porous structure. Since the enamel is an in sulator, it is doubtful if oxygen concentration differences; over the surface of enamel could cause an electrical po tential. However, the oral environment is such that oxygen; concentration can easily vary over the enamel surfaces of teeth. In crevices and between teeth, oxygen concentration! could become depleted due to bacterial action and digestive; i ! processes; whereas, on the outersurfaces of the teeth, the I oxygen concentration should be nearly in equilibrium with the air being breathed. 39 40 Because of the existence of large oxygen concentra tion differences in the oral environment, a series of ex periments was conducted to determine whether or not oxygen concentration cell potentials could exist. The apparatus used for these :experiments is shown in Figure 6. The apparatus consisted of a whole human tooth, embedded in paraffin wax between compartments of a doubly compartmented paraffin wax vessel. The tooth was embedded in the paraffin wax in such a manner that small areas of about 2 to 4 mm2 were exposed to the aqueous solu tions contained in the respective compartments. Pure gas eous oxygen was bubbled into one compartment, and pure gas eous nitrogen was bubbled into the other compartment, es tablishing an aqueous oxygen concentration difference on the two sides of the tooth. To measure potential differ ences which might be developed, Leeds and Northrup Model 1199-31 standard calomel cells were dipped directly into each of the respective compartments. The standard calomel cells were wired to a Leeds and Northrup Model 7553, Type K-3 Universal potentiometer through a null detector speci ally constructed for these and later experiments. The 12 null detector had 10 ohms input impedance to effectively OXYGEN GAS NULL DETECTOR POTENTIOMETER EXPOSED ENAMEL TWO COMPARTMENT PARAFFIN WAX VESSEL NITROGEN GAS FIGURE 6 APPARATUS FOR DETEBMINATION OF POTENTIALS DUE TO OXYGEN CONCENTRATION DIFFERENCES H* 42 eliminate any significant flow of electrical current through the standard calomel cells and/or through the tooth sample. Using 0.1 N KC1 solutions as the aqueous environ ment in both compartments of the cell shown in Figure 6, no detectable potential differences were observed as a re sult of oxygen concentration differences. These observa tions were made by first bubbling oxygen into the left hand compartment and nitrogen into the right hand compartment for several hours, and noting the observed potential. The oxygen and nitrogen were then switched from the left to right and right to left compartments, respectively, and the potential again observed after allowing several hours for equilibration. Differences of less than 0.1 millivolt were obtained between the two observations. Using laboratory distilled water as the aqueous media in both compartments of the cell shown in Figure 6, the experiment was repeated. In this case, small potential differences of only 0.1 to 3.0 millivolts were observed. It was concluded that oxygen concentration differ ences are not capable of producing significant electrical potentials on dental enamel, and that the small potentials 43 which are developed are negligible in the presence of electrolyte concentrations (0.1 N) characteristic of the saliva media in which the teeth are normally immersed. Salt Concentration Cells To determine the ionic membrane characteristics of human dental enamel, a series of membrane experiments was conducted using wafers of human dental enamel as the mem brane. The apparatus used for these experiments is shown in Figure 7. It consisted of a doubly compartmented paraf-j i fin wax vessel containing the same salt solution in both compartments, but at differing concentrations, and C2 . The respective solutions contacted opposite sides of a human dental enamel wafer which was cast into the center I partition of the paraffin wax vessel, as illustrated in Figure 7. Electrical contact was made with the two solu tions by means of saturated KCl/Agar salt bridges leading i | to saturated aqueous solutions of KC1, into which standard j 1 calomel cells were immersed. The electrical potential was j measured by means of the potentiometer and the high input ! I impedance null detector used in the previous experiments, To help the system reach equilibrium quickly, re- j i | latively thin enamel wafer samples were used, thicknesses NULL DETECTOR POTENTIOMETER AGAR/KC1 SALT BRIDGES ENAMEL WAFER ' SAT'D. KC1 SALT CONC SALT CONC. TWO COMPARTMENT PARAFFIN WAX VESSEL FIGURE 7 APPARATUS FOR DETERMINATION OF IONIC MEMBRANE CHARACTERISTICS OF HUMAN DENTAL ENAMEL 45 j 1 being in the range, 100 to 200 microns (0.004 to 0.008 ' inches). The enamel wafers were prepared from non-carious j human teeth which were previously extracted and stored in formaldehyde and distilled water for an undetermined length of time. The procedure by which the enamel wafers were ob tained from whold teeth is illustrated in Figure 8. A i Bodine Electric Company wire saw with a copper-beryllium i alloy wire and an aqueous suspension of abrasive material i was first used to cut one face off the whole tooth. This wire saw is a relatively slow cutting, water cooled de vice, which assures that no excessive temperatures are generated during the cutting process. The wire saw cut j was made approximately parallel to the enamel layer on the j face of the tooth, but most of the actual cut was in the dentin of the tooth. Next, the tooth fragment was cement- j I ed by means of paraffin wax to a glass microscope slide, j and the fragment was wet sanded with silicon carbide paper i until all of the dentin material was removed, and a flat | surface of enamel was exposed. The sanding was accom- j I j plished progressively fusing 240, 400, and 600 grades i i silicon carbide paper to obtain a reasonably smooth j 46 . ' * * — \ WIRE SAW WHOLE TOOTH WET SANDING, SILICON CARBIDE PAPER ADDITIONAL SANDING FINISHED WAFER FIGURE 8 PREPARATION OF ENAMEL WAFERS 47 finish on the flat :enamel surface. Next,_ the tooth frag ment was uncemented from the microscope slide, turned over and re-cemented with the flat side previously sanded next to the slide. The curved enamel surface was then sanded flat in a similar manner, leaving the 100 to 200 microns thick enamel wafer to be used in the experiments. Pre paration of the enamel wafers in this manner requires several hours per sample, and it assures that the wafer is made up of virgin enamel which has never been exposed directly to the oral saliva environment of the individual from whom the tooth was originally extracted. Using these enamel wafers, membrane concentration cells were set up, as shown in Figure 7. The first salt used was KC1, with the concentration in the left hand com partment, C1# being kept constant at 0.1 N, and the con centration, C2 , in the right hand compartment being pro gressively diluted by one-half for each observation. The observed potential, as a function of the concentration ratio, C-j/C2# is shown Figure 9. The potential ob served was such that the dilute solution was positive with respect to the concentrated solution, indicating that the enamel wafer membrane preferentially allows the passage 48 ioo_ 059 LOG 8 80- I S 60- • V $ B I S 40-- P* DILUTE CELL COMPARTMENT IS ELECTRICALLY POSITIVE 20-- Cl/C2, KC1 CONCENTRATION RATIO FIGURE 9 POTENTIALS OBTAINED WITH A HUMAN DENTAL ENAMEL WAFER IN KC1 CONCENTRATION CELLS 49 of positive ions, as compared to negative ions. Also shown on Figure 9 is a curve of the ideal potential, as obtained from Equation 2. It is seen that the deviations of the experimental data from the ideal curve are not ex cessive, indicating that the enamel membrane is strongly preferential in passing positive ions, under the circum stances of the experiment. As shown in Figure 9, the concentration in the di lute compartment of the cell, C2 / was varied by ratios of 2.0. The enamel wafer was first allowed to soak for sever al hours with 0.1 N KC1 in both compartments of the cell before starting the progressive dilutions in the dilute compartment. In general, it was found that on the order of one to two hours was required to obtain a stable poten tial after each dilution. After completion of the experiments using KC1 in f the concentration cell, a similar series of experiments i i was conducted using CaCl2 as the salt. Still later series j of experiments were conducted using other salts, the re sults of which are shown together on Figure 10. The gen- i eral conclusions to be drawn from Figure 10 are that in i 1 the presence of monovalent cations such as K*, Na+, and j MEMBRANE POTENTIAL, MILLIVOLTS 059 LOG +80 +60 KC1 KF +40 NaCl LiCl CaCl, +20 128 CONCENTRATION RATIO, Cl/C, — o-------- o — -10 FIGURE 10 SALT CONCENTRATION CELL POTENTIALS USING SEVERAL DIFFERENT SALTS WITH AN ENAMEL WAFER Li+, human enamel preferentially allows the passage of the ; positive ions, with only secondary effects being observed due to the presence of the various anions used. In the presence of the divalent cation, Ca++, the enamel wafer no ! t ; longer preferentially passes the cation, but it preferen tially passes the monovalent anion, Cl”. Similar results i with divalent cations were obtained by Klein (9), in mem- I brane experiments and electroosmotic experiments conducted I with dog tooth enamel. i i Effects of Concentration Level on Enamel Membrane Potentials The membrane potential produced when an ionic mem- j brane is exposed to two solutions having differing concen- j trations is dependent not only upon the ratio of the con- j j j centrations in the two solutions, but it is also dependent j i on the absolute level of the concentrations. It is gen- j I erally observed that the membrane potential is decreased J i i when the absolute level of salt concentration is raised, i with the concentration ratio remaining constant. In the i words of Sollner (16), this effect is due to a "salting out" of the ionic double layer which must be present to neutralize the net charges existing on the membrane pore 52 wall. The physical situation which results from large differences In concentration level Is shown schematically on Figure 11. Figure 11-a is a representation of a pore having negatively charged walls exposed to a dilute aque ous electrolyte solution. The positive ions, which must be present in the pore to macroscopically neutralize the pore wall charge are far spread and occupy the entire volume of the pore, and hence, negative ions find it very difficult to pass through the pore. Under these condi tions, the membrane preferentially allows only positive ions to pass through the pore7 and hence, the ionic mem brane potentials are nearly equal to the maximum theoret ically possible. On the other hand, in concentrated solu tions as shown in Figure 11-b, the ions are compactly lo cated, and the neutralizing double layer of positive ions is close to the negatively charged pore wall. As shown in Figure ll£b, the double layer is so compact that most of the pore volume can be occupied by ions of any charge, and hence, the pore is not very preferential with respect to the sign of the ions it allows to pass through. This re sults in membrane potentials which are considerably below 4 4 _ -4- + 4 4 + + 4* 4 + 4 + 4 4 4 + 4- 4 - 4 4 £ -_4 4 4 - + a. DILUTE SOLUTIONS b. CONCENTRATED SOLUTIONS FIGURE 11 EFFECTS OF CONCENTRATION LEVEL ON THE THICKNESS OF THE IONIC DOUBLE LAYER WHICH NEUTRALIZES THE PORE WALL CHARGE U! W the theoretical maximum. A more quantitative representa tion of these effects is shown in Figure 12, which indi cates the effects of concentration level and distance from the charges surface on the potential in the double layer. The net result of these effects is that the membrane potential typically varies qualitatively in the manner shown in Figure 13. As the absolute concentration level is reduced to low values, while maintaining the same concen tration ratio, the membrane potential approaches the theoretical maximum. On the other hand, at high concen tration levels, the membrane double layer becomes "salted out" and the observed potential begins to approach zero. To determine whether or not the same characteristics could be obtained with dental enamel membrane, a series of experiments was conducted. The apparatus used was iden tical to that shown in Figure 7. The Agar/KCl bridges were inserted into the concentration cell only during ac tual measurement of potentials, to avoid leaching KC1 out of the bridges and thereby altering the concentrations in the dilute solutions. The results obtained are shown on Figure 14. Note that at high concentration levels, the observed potential varies as expected, but, at lower 55 H I H d £ 13 0 p* 1 i o w ta 150 100 50 001 N 01 N 0 100 ANGSTRO: DISTANCE FROM PORE WALL FIGURE 12 EFFECTS OF CONCENTRATION ON THE IONIC DOUBLE LAYER THICKNESS POTENTIAL, MILLIVOLTS 56 60 50 AO 30 20 10 0 -2 ,+2 .+6 10° 10 10 10 C2, MOLS/LITER (Cl/C2 - 10,0 - CONSTANT) FIGURE 13 EFFECTS OF CONCENTRATION LEVEL ON MEMBRANE POTENTIAL, FOR MOST COMMON IONIC MEMBRANES POTENTIAL, MILLIVOLTS Cx + 0.00067 Co + 0.00067 059 LOG 1/C, 11.0 - CONST 0.0001 0.001 0.01 Cn, MOLS/LITER FIGURE 14 1 EFFECTS OF CONCENTRATION LEVEL ON OBSERVED ENAMEL MEMBRANE POTENTIALS 0.1 1.0 concentration levels the observed potential decreases rather than increasing. She behavior shown on Figure 14 can be explained in terms of the solubility of the dental enamel membrane. It has been shown by Francis (4) that the equilibrium solubi lity of dental enamel in aqueous solution can be represent ed by. the following ion product: [ca As a result of this solubility product, the geometric mean concentration of calcium and biphosphate ions in the enam- -4 el pores must be 5 x 10 moles per liter. This concentra tion is not insignificant compared to the concentration levels considered on Figure 14. In fact, the presence of solvated enamel ions causes the system to become a two salt system rather than a one salt system when low concentration level membrane concentration cells sure set up, using enamel membrsunes. For such a two salt System, where one salt consisting of solvated ensunel permeates equally to both sides of the membrane, the maximum theoretically obtainable concentration cell potential can be obtained from the Henderson integration for liquid junction potentials. The 1 x ("HPO4 J = 2.5 x 10~7 = const (11) 59 Henderson integration (22) for a two salt system in a soluble ionic membrane pore is developed from the follow ing equation: aE = F l l l r a(in ai> (12) n where, £ = electrical potential R = ideal gas constant F = Faraday's constant T = absolute temperature t^ = transference number of the itl1 ion specie z ± *= valence of the ith ion specie i n = the total number of ion species a^ =» the activity of the i**1 ion specie. Equation 12 is obtained by combination of Equations | 5 and 8 presented earlier, except Equation 12, as written ! above, includes the possibility of ions having a valence other than unity. For present purposes, the Henderson integration is simpler than the general case, because the activities of the solvated enamel ions are assumed to be i constant through the pore, equal to the activities which would be In solubility equilibrium with the enamel pore walls. Furthermore, since it is desired to calculate the maximum possible membrane potential, it is assumed that the negative chloride ions do not enter the pores. (This would be the case for an electronegative ideal ionic membrane which would develop the maximum membrane potential of interest in the present analysis.) The problem, therefore, reduces to consideration of potassium ions which are the only ions having a variation in activity through the mem brane. Equation 12 becomes: dE = v d(ln V 1 (13) where, t. ola = transference number and activity of potassium ion, respectively. i The influence of the solvated enamel ions on the integration of Equation 13 lies in their effect on the transference number of the potassium ion, tj^.. The trans- ; ference number of the potassium ion varies as the amount of potassium ion present in relation to the amount of solvated enamel ions present. The relative mobilities of the ions also affect the potassium ion transference 61 number. The relationship between these variables Is: t-i. “ a„+ + A + H S_ c (14) ■ UK* UK+ where, t--+ = transference number of potassium K ion a^ = activity of the potassium ion, equ ivalent s/lit er A, C = activities of dissolved enamel anions and cations, equivalents/ liter = ratio of ion mobilities in the UK+ pores, enamel anions to potas sium, and enamel cations to potassium, respectively. Equation 14 is essentially a combination of the fundamental definitions of transference number and ion mo bility. Substitution of Equation 14 into Equation 13 gives dE = iF(aK* + rr~ A + «<Hln ar+j (is) It is assumed that the quantity H*_a + Hc_ c UK+ UK+ remains constant throughout the length of the pore because equilibrium with crystalline enamel throughout the pore, and because there is no reason to expect significant vari ation in the ion mobilities through the pore. With this assumption, Equation 15 can be integrated from one end of the pore to the other end to obtain the maximum possible membrane potential. TMe result is: Using potassium ion concentrations instead of activities, the quantity of enamel ions in solution is in solubility (16) and assuming a temperature of 25°C, the above equation be comes : (17) where = maximum possible membrane poten tial, volts c 1 = KC1 concentration in the concen trated cell compartment, equi valents/liter 63 C2 = KC1 concentration in the dilute cell compartment, equivalents/ liter A, C = concentration of dissolved enamel anions and cations in the pores, respectively, equivalents/ liter ratio of ion mobilities in the pores, enamel anions to potas sium, and enamel cations to potassium, respectively. The dotted line shown on Figure 14 gives AEmax, as ob tained from Equation 17, with HiL. a + c = .00067 (18) v- v- The dotted line on Figure 14 is a reasonable representa tion of the behavior of the experimental data at low con centration levels. The concentration expressed by Equa tion 18 is reasonable in view of the solubility product of j enamel, Equation 11. Therefore, it is concluded that the low concentration level behavior of the experimental data shown on Figure 14 is a result of the enamel solubility. i i The results of these experiments indirectly show that enamel ions cure in solution in the enamel pores. This: is a necessary factor for the electrochemical mechanism U, U c - V - UK+ hypothesized for the formation of dental caries, since the enamel ions must be in solution if they are to be carried out of the enamel pores by electrical current. Effects of pH on Enamel Membrane Potentials The exposure of dental enamel to acidic media is frequently taken to be an important factor in the formation of caries (23). If the electrochemical mechanism described previously is a process by which caries are formed, it should be possible to implicate exposure to low pH media in that mechanism. Experiments were conducted to determine the effects of pH on potentials observed when an enamel membrane is used to separate a solution having 0.1 N potassium ion con centration from a solution having 0.03 N potassium ion con centration. The experiments were conducted using several different anions to control the solution pH. The apparatus used to determine the potentials was the same as that pre viously shown in Figure 7. For each experiment, the pH was determined by use of a Beckman Model 72 pH meter. Starting with a solution of KOH, acid corresponding to the desired anion was added until the desired pH level was 65 Obtained? this solution was then diluted to obtain a solu tion 0.1 N in potassium ion concentration. The 0.1 N solu tion was, in turn, diluted to obtain the 0.03 N solution. After these dilutions, the pH of both solutions was re measured, and in all cases, there was no more than 0.1 pH units difference between the 0.1 N and the 0.03 N solu tions. The results of these experiments are shown in Fig ure 15. In general, decreasing the pH below about 6 re sulted in significant decrease of the observed potential. Explanation of these results is possible in terms of the basic concept of the ionic membrane as presented earlier, in Figure 3. The enamel wafer is an electrone gative ionic membrane, as evidenced by the polarity of the membrane potentials produced. That is, the enamel wafer membrane has ionic membrane properties because of net nega tive charges on the walls of its pores. Since the enamel itself is a crystalline material, Ca1Q(P04 )6 (OH),2# the negative charges on the pore walls must consist of anions of that material which are in excess at the crystal-solu- tion interface (or, in alternate words, a deficiency of calcium ions at the pore walls). A schematic 66 30 25 20 15 O KOR + HAc □ KOH + HC1 O KOH + PYRUVIC ACID O KOH + PROPIONIC ACID V kOH + LACTIC ACID 10 5 Cl/C2 - 3.5 - CONSTANT C, » 0.1 N K+ 0 4 2 6 8 12 10 pH FIGURE 15 EFFECTS OF pH ON ENAMEL MEMBRANE POTENTIALS 67 representation of the enamel pores, showing the ions makingi up the fixed charges on the pore wall is shown in Figure 16. Note that the negative charges consist of orthophos phate and hydroxyl ions which do not have counteracting calcium ions in the enamel crystalline matrix. In rela tion to the experimental results shown in Figure 15, it should also be noted that the negative ions forming the pore wall charge are sensitive to the presence or absence of hydrogen ions. That is, the negative charges of these pore wall ions can be eliminated by reaction with hydrogen ions according to: 0H~ HOH PO4 HPO=— ^ h 2po ”— ^ h 3po4 The above reactions have the most likelihood of occurring when a high concentration of hydrogen ions is present (low pH), and it must be concluded that low pH will! eliminate the negative charges on the enamel pore walls. Since the negative pore wall charges are responsible for ionic membrane characteristics of enamel, according to the concepts discudsed >in relation to Figure 3, their elimina tion as a result of low pH should also eliminate the mani festation of the ionic membrane characteristics, which is 68 ENAMEL MATRIX \po£j \ q h ~ n p ° 4 "/ \ p ° 4 ° r PORE m I oh~ \ I ron I o n ~ \ [7^\ ENAMEL MATRIX FIGURE 16 REPRESENTATION OF AN ENAMEL PORE, SHOWING THE ANIONS COMPRISING THE PORE WALL NEGATIVE CHARGES 69 the observed membrane potential. This is exactly what is observed in Figure 15, where decreasing the pH eventually completely eliminates the observed membrane potential. The data of Figure 15 are therefore consistent with the basic concepts of ionic membranes. As related to the hypothetical electrochemical mechanism for the formation of caries, the.-degradation of membrane potential as a result of low pH could play an im portant role. If the membrane potential existing across teeth in the oral environment as a result of the differ ence in ionic strength between blood and saliva were to become degraded at one localized area due to low pH, that localized area would act as a "short circuit" for the rest ; of the tooth, and a current would be concentrated at the localized area. If a concentrated electrical current is capable of permanently harming the dental enamel, as is shown to be true in later experiments, then even after the j pH at the localized area is back to normal, the enamel it- i self may be sufficiently degraded that it will never again be capable of re-establishing the normal membrane poten tial at the localized area. The localized area would, therefore, continue to act as a short circuit, with the 70 continued degradation of enamel eventually resulting in the formation of caries. Effects of Electrical Current Through Dental Enamel If an electrochemical mechanism is the mechanism of formation of dental caries, then the flow of electrical current through dental enamel must result in degradation of the enamel. Experiments were performed to determine if this is true. The apparatus used for these: :experiments is shown in Figure 17. A regulated DC power supply was used to supply a constant electrical potential of 1 0 . 0 volts to the system. The electrical current was passed into the aqueous phase by means of two platinum electrodes immersed in saturated solutions of KC1. The two solutions of saturated KC1 were connected to the solutions on opposite sides of the enamel specimen by means of saturated KC1/ Agar salt bridges as shown in Figure 17. The current through the system was monitored by means of a small re sistor in the electrical circuit, attached to a recorder, as shown. By means of this apparatus, continuous currents were flowed through enamel specimens for periods up to — M W " STANDARD RESISTOR 10.0 V DC RECORDER AGAR/SAT'D. KC1 BRIDGES DENTAL ENAMEL WAFER SAT'D. KC1 SAT'D. KC1 0.1 N KC1 0.1 N KC1 TWO COMPARTMENT PARAFFIN WAX VESSEL FIGURE 17 APPARATUS USED TO DETERMINE THE EFFECTS OF EEEGTRICAL CURRENT ON DENTAL ENAMEL 72 I several days. Results from these experiments consisted of observa tion of changes in the physical condition of the enamel specimens and the time dependence of current through the enamel sample. Typical time dependence of electrical current through two enamel specimens is shown on Figures 18 and 19. In both cases, the current increases in an apparently ex ponential manner with time. The continuously increasing current, at constant voltage, indicates a continuous change; in the enamel material while the test was being conducted. It has been shown by Francis (4), that dental enamel is a slightly soluble substance. Because of the j fineness of the pores in dental enamel, it is reasonable ! to assume that a solubility equilibrium exists within the pores, between the aqueous phase and the enamel. Since ions in solution in the pores are moved when current flows ; through the pores, ions which were originally part of the enamel matrix will be swept away with the current. If enamel solubility equilibrium is maintained within the pores, these ions which were swept away will be immediate ly replaced in solution by ions from the enamel matrix. >0.6 73 0.5 APPLIED POTENTIAL - 10.0 VOLTS - CONSTANT 0.4 H 0.3 0.2 0.1 500 2000 2500 1000 1500 TIME, MINUTES FIGURE 18 TIME DEPENDENCE OF ELECTRICAL CURRENT THROUGH AN ENAMEL WAFER FOR 42 HOURS- EXPOSURE 74 0.20 APPLIED POTENTIAL - 10.0 VOLTS - CONSTANT a s • 0.10 § a 0.05 0 1000 2000 4000 3000 5000 6000 TIME, MINUTES FIGURE 19 TIME DEPENDENCE OF ELECTRICAL CURRENT THROUGH AN ENAMEL WAFER FOR 100 HOURS’ EXPOSURE As this process continues, the fenamel matrix will gradually: be eroded and the pores will grow in size. Pores increas- I ing in;dize with time will naturally lead to an increase in current with time, as was observed in the experiments. A simple mathematical model of this process is developed below. Because of mass removal from the enamel due to electrical transport of calcium out of the enam&l pores, the rate of change of pore area with time is finite and is ; given by Equation 19. Equation 19 is based on the defini- i tion of the calcium ion transference number. dt L fca L Vca where, A = sum of the areas of all of the pores ! in the enamel sample, cm^ t = time, seconds ! Nca = calcium ion removal rate, gram ions/sec i (ca ~ 9rarn ions of calcium per cm3 of ena mel | L = pore length, cm | i I = current, amperes j t+ = calcium ion transference number 76 F = Faradays • ; const ant, 96,500 amp-sec/ gram equivalent and the total electrical resistance across the enamel sample is: r = (20) where, R = sample resistance, ohms (j— = effective mean electrical conductivity of the solution in the enamel pores, and, from ohms law: v - E EAl) , « ■ » • i \ I =3 — SJ - (21) R L where, E = applied potential, volts. Differentiation of Equation 21, with E, L, and <T” constant yields: diE _ Eu dA t dt ’ L dt ' ' combining Equations 20 and 22, and integrating results in: 77 I = I0 EXP |CS- (23) 2FL2 Pca That is, this simple model indicates that the elec trical current through dental enamel should continuously erode, or etch the material such that current will expo nentially increase with time. The timewise exponential increase in current is consistent with the experimental re sults presented in Figures 16 and 17. This model also in fers that if caries are formed by the electrochemical mechanism postulated, their growth should be exponential with time. Electroosmosis was probably also occurring during these experiments, in addition to electrically induced movement of ions through the pores. Electroosmosis is the phenomenon whereby the electrically induced motion of ions through a pore causes the flow of solvent (in this case, water) through the pore, also. Flow of solvent occurs when the motion of ions near the wall of the pore is pre dominantly in one direction, causing the flow of solvent in the same direction. Since enamel preferentially passes positive ions through its pores, the direction of most ion motion is obviously from positive to negative, electrical- j 78 ly, and this must cause the electroosmotic flow of solvent in the same direction. The phenomenon of electroosmosis has been experimentally observed with enamel by Klein (11). The electroosmotic flow of solvent through the pores is essentially a flushing process, and could be at least part ly responsible for the erosion of the enamel pores and the j resultant increase in current with time. Further results from these experiments consist of observation of the physical condition of the samples after they have been exposed to electrical current for a period of time. In general, the areas of the enamel samples which were subjected to current were found to have taken on the white, opaque appearance characteristic of true dental caries, as opposed-to the translucent nature of the j unaffected areas of the enamel which were physically shielded from current. The extent to which the appearance i i of the enamel was altered was qualitatively proportional j i i to the degree of exposure to current. Photomicrographs j of some of the enamel which was exposed to current are shown in Figure 20, illustrating the opaqueness, and in one case actual etching of the enamel caused by current. i It should be noted that other enamel samples exposed to 61 HOURS @ 10.0 VDC 168 HOURS @ 10.0 VDC 45 HOURS @ 10.0 VDC FIGURE 20 PHOTOMICROGRAPHS OF ENAMEL WAFERS EXPOSED TO DIRECT ELECTRICAL CURRENT MAGNIFICATION: 50X 80 ! the same aqueous media for similar lengths of time, hut without current, were found not to have suffered from the same physical changes, therefore proving that the change in condition of the enamel from translucent to opaque was a direct result of the electrical current through the speci mens . Effects of Fluoride Treatment on Enamel Membrane Potentials; It is well known that fluoride ion treatments have a significant effect on the frequency of occurrence of dental caries. If the membrane properties of dental enamel are related to the mechanism of formation of dental caries,j some effect on the membrane properties should be noted as the result of fluoride ion treatments. With this in mind, j a series of experiments was conducted to determine if a significant change in the observed membrane potential couldj be obtained by soaking the enamel wafer in a concentrated solution of fluoride ion for a brief time period between j experimental observations of the membrane potential devel- : oped when the enamel wafer was used as the membrane in an 11:1 KC1 concentration cell. For these: experiments, each data point was obtained j !using a freshly prepared enamel wafer which held no previous I direct exposure to fluoride ion. The process by which the i wafers were prepared was identical to the procedure pre viously outlined. Since the wafer preparation procedure resulted in sanding away the original outer surface of the tooth specimen to obtain the wafer, it is reasonable to assume that exposure of the enamel making up the wafer to fluoride was minimal during the time the tooth was in the oral environment of its original owner. For these experiments, the enamel wafers were cast into double compartmented paraffin wax concentration cells j such as shown in Figure 7. After allowing the wafer to soak in 0.1 N KC1 solution for a period of at least 24 hours, the membrane potential was determined using 0.10 N i KC1 in the left hand cell compartment, and 0.0091 N KC1 in ; the right hand compartment. After a stable potential read- | ing was obtained, both compartments of the cell were emp- j i tied, and filled with 2.8 N KF. The fluoride solution was j l allowed to remain in the cell for a period of 1 0 minutes, j ; after which the entire cell was thoroughly flushed with j j tap water and distilled water to remove all traces of the j ! fluoride solution. The KC1 concentration cell was then re-established by replacing fresh solutions of 0.10 N KC1 | in the left hand compartment, and 0.0091 N KC1 in the right! hand compartment. After a new, stable membrane potential was obtained, it was recorded. The result of experiments in general, was that the membrane potential was signifi cantly increased by the 1 0 minute fluoride ion treatment. As a control, an identical series of experiments was con ducted, except the 1 0 minute fluoride treatment was re placed by a 10 minute treatment with 3.0 N KC1 solution. The KC1 treatment, in general, resulted in no significant change in the observed potential. i The results of these experiments are shown graphi cally in Figure 21. It can be noted from Figure 21 that j ! there is a significant variation in the membrane potentials! observed before treatment with fluoride. These variations ; i are a result of differences in the original wafer samples used, since a different wafer sample was used for each j j data point shown on Figure 21. It can also be noted that j fluoride treatment increases the observed membrane poten- | tial to almost the same value regardless of the originally j i observed potential. The observed membrane potentials, j j | ! after treatment with fluoride, more closely approach the j 83 m 3 50<> TEN MINUTE TREATMENT WITH 2.8 N KF TEN MINUTE TREATMENT WITH 3.0 N KC1 m 40 0.10 N KC1 vs 0.0092 N KCl CONCENTRATION CELL 30 POTENTIAL BEFORE TREATMENT, MILLIVOLTS FIGURE 21 EFFECTS OF CONCENTRATED FLUORIDE AND CONCENTRATED CHLORIDE TREATMENTS ON ENAMEL MEMBRANE POTENTIALS 84 i lvalue obtained from Equation 2, with slightly higher poten tials being observed with samples which were higher before the fluoride treatment. The effect of the chloride treat ment is shown to be nil on Figure 21. Shortly after these experiments were completed, it was found that analogous results using whole, hollowed out human teeth had previously been obtained by Chicle and Waters (12). In this work, Chick and Waters also found that other inorganic anions including NC>3“, CNS“, H2PO4", and SO4 "", as well as Cl”, also had no significant effect on the observed membrane potential. In later work (10), they found that treatment with citrate and tartrate anions increased the membrane potential even more significantly than fluoride treatments. To explain these results, it is recalled that the ionic membrane properties of enamel are due to the exist ence of a net negative charge on the walls of the pores which penetrate the enamel. Anything done to increase the amount of negative charge on the pore walls will lead to a more efficient ionic membrane, and hence, a largerebb- served potential. This is particularly true when it is considered that enamel is heteroporous (that is, enamel ihas pores of widely varying cross-sectional area), since large pores may be very Inefficient at stopping the pas sage of negatively charged ions when the pore wall charge density is only moderate, and yet be very efficient when the pore wall charge density is increased slightly. The effect of fluoride treatment is considered to increase the negative charge density on the enamel pore walls. It is generally agreed (1) that fluoride permanent ly enters into the structure of enamel as a replacement of the hydroxyl group in Ca^Q(P04 )6 (0H)2» This replacement is regarded as being permanent. Once fluoride replaces the hydroxyl group, it is certain that the position of the hydroxyl group will always be occupied by a negative ion. If the fluoride is not present at the molecular interface between the enamel structure and the aqueous environment inside the pore, there is a relatively high probability that the hydroxyl site is unfilled (especially at low pH), and the net negative charge on the pore wall may be lower ithan when the OH~ sites are filled with fluoride ions. These factors provide explanation for the characteristic membrane potential increases observed with fluoride treat ments, and as discussed in the section on conclusions, they also provide explanation for the lowered Incidence of carles with fluoride treatment, In the light of an electro- chemical mechanism for the formation of caries. The ability of citrate and tartrate to improve the observed membrane potentials is also obviously a result of increased negative charge on the enamel pore walls. Cit- tate and tartrate are known to complex strongly with cal cium ions (24) in solution, and this same bonding mechanism undoubtedly helps those negative ions to adhere to the pore walls. Treatment with chloride ion, which was used as the control experiment for the data shown on Figure 21 very obviously had no consistently observable effect on the enamel wafer membrane potentials. The chloride ion is ap proximately one third larger than the fluoride ion, and this fact keeps the chloride ion from substituting for hydroxide in the hydroxylapatite (enamel) crystal struc ture in the same manner as fluoride does. This fact ap parently accounts for the nil effects of chloride ion treatments. This also shows, by inference, that the ob served effects of fluoride treatment are possibly only because fluoride can substitute into the enamel crystal 87 structure. Effects of Fluoride on Electrical Current Through Enamel Because of the well Known beneficial effects of fluoride treatment for reduction of dental caries, it is of interest to determine the effects of fluoride on flow of electrical current through enamel. The electrochemical mechanism proposed for the formation of caries requires electrical current through the enamel to produce carious lesions, as shown experimentally to be possible in the previous section. Fluoride helps to establish more nearly ideal mem brane potentials even with low quality enamel, as shown on Figure 21. As a result of this effect, fluoride makes enamel a more uniform ionic membrane, by minimizing locally defective areas. These locally defective areas are in capable of establishing the normal membrane potential which results from the difference in salt concentration between blood and saliva. By eliminating, or repairing these locally defective areas, fluoride treatment lowers the possibility of the locally defective areas short circuiting the potential developed by the rest of the tooth, causing 88 | high current at the defect and resultant formation of a carious lesion. However, as shown on Figure 21, the im- j ! provement in membrane potential by fluoride treatment is I i i such that small differences in membrane potential will still result between enamel sections which were initially of low quality and those which were initially of high quality and, therefore, the possibility for slight short circuiting by initially defective areas would still exist even after fluoride treatment. To further minimize the possible de gradation of enamel by these short circuit currents, it would be convenient if fluoride treatment were to also in crease the electrical resistance of enamel and thereby minimize any currents. The objective of the experiment re- j ported in this section was to determine whether or not the | presence of fluoride thusly affects the electrical resist ance of enamel. Using apparatus as shown bn Figure 17, electrical | current was flowed through an enamel wafer for a period of approximately 24 hours to establish a quasi-steady state condition. At the end of 24 hours, the 0.1 N KC1 solution I i in the right hand compartment was replaced by a solution of | : • • 1 I • - ! two salts, 0.05 N KF and 0.05 N KC1. That is, half of the KC1 in the right hand solution was essentially replaced by KF. As shown in Figure 17# the right hand solution was connected to the negative electrode of the power supply# thereby causing the fluoride added to the right hand solu- j tion to be electrically driven into the enamel sample. Shown in Figure 22 are the results of this experi- ; i ment. It is seen from Figure 22 that upon addition of fluoride# the electrical conductivity of the enamel sample j temporarily rises to approximately 50 percent greater than ! the value just before addition, and then drops rapidly to j less than approximately 25 percent of the value just before j fluoride addition. It was found that this decrease in current was semi-permanent in nature; that is# the current remained at approximately 25 percent of what it; would have | been if the fluoride had not been added# but# the normal trend toward exponential increase in current with time# j as described theoretically by equation (8) / was not elimi nated. From the viewpoint of the hypothesized electrochemi cal mechanism for caries formation# it must be concluded that fluoride treatment provides the combined benefits of making the enamel membrane potential more uniform over the | 0.3 cn CHANGE RIGHT HAND SOLUTION FROM 0.1 N KC1 TO .05 N KC1 + .05 N KF 0.1 APPLIED POTENTIAL =10.0 VOLTS = CONSTANT 0.0 1,200 1,300 1,400 1,500 TIME FROM EXPERIMENT START, MINUTES 1,600 FIGURE 22 EFFECTS OF FLUORIDE ADDITION ON ELECTRICAL CURRENT THROUGH AN ENAMEL WAFER 91 j surface of the tooth, and making the electrical resistivi ty significantly higher. The effects of fluoride as shown on Figure 22 can be explained in terms of the expected phenomena. It has been shown, by Francis ((4) and others, that fluorapatite is much less soluble than the hydroxylapatite of which !enamel is normally constituted. The addition of fluoride |to the right hand solution undoubtedly results in the con- Iversion of some hydroxylapatite in the enamel pores to i i • fluorapatite. If it is assumed that the entire inner sur- face layer in the enamel pores is converted to fluorapa- i tite, then the concentration of solvated enamel ions in side the pore should be reduced because of the reduced ; solubility. This would reduce the capability of the pores 'to carry current, because of the absence of some of the current carrying ions. Furthermore, the fluoride induced increase in pore ;w&ll charge density (negative charges) makes the pore a i more effective ionic membrane. The pores cure thereby less apt to allow negative ions to pass through the membrane, and minimizing the participation of negative ions in the passage of current in this manner should increase the 92 resistivity of the membrane, as observed experimentally. Additionally, since the fluorapatite is much less soluble than the normal hydroxylapatite enamel material, and since calcium ions are being driven electrically to- j wards the ends of the pores which are exposed to fluoride, i |it is likely that fluorapatite and other relatively in- !soluble calcium fluorides form at the ends of the pores nearest the fluoride solution, partially plugging the pores, and thereby, resulting in the higher electrical re sistance observed on Figure 22. It is likely that a combination of the above pheno mena is responsible for the ultimate increase in the re sistivity of the enamel wafers. It remains to explain the peak, or temporary in- i drease in current which is shown as a cross-hatched area j just after addition of fluoride on Figure 22. The attach- I meat of fluoride to the enamel crystalline structure at | sites in the pore walls which were previously void, is one obvious result of fluoride addition, since the negative | pore wall charge density is increased as evidenced by data i ; previously presented (Figure 21). This increased charge | I density undoubtedly also results in the attachment of some 93 counterions which partly counteract the pore wall charge density increase. This attachment of fluoride ions to the pore walls, and the necessary attachment of neutralizing counterions is a sink for ions passing through the pores. An additional sink for ions passing through the pores is the combination of fluoride ions migrating under the in- : fluence of the electrical field with calcium ions migrat ing in the opposite direction to form the insoluble cal cium fluorides. These ion sinks are in effect an electro- ;lytic capacitance which temporarily short circuits (con nects in parallel with) the normal DC resistance of the pores. This capacitor effect causes a temporary increase in DC current, as measured by the apparatus shown in Fig ure 17 and indicated by the peak on Figure 22. The capa citor effect lasts until attachment of fluoride ion is completed inside the pore. That is, it lasts until the vacant negative ion sites are filled with fluoride ions, ; and until coating of calcium fluorides inside the pore is ! sufficient to minimize solvation of calcium ions and their i ;subsequent precipitation with fluoride as insoluble calcium fluorides. Assuming that half of the current represented by the cross-hatched peak on Figure 22 represents fluoride 94 ion, which becomes attached to the enamel (and the other half the corresponding counterions), then the cross-hatched area is equivalent to a one percent fluoride content by weight for the 3.0 millimeter diameter, 150 micron thick enamel membrane used for the experiment. That is, it is inferred that one percent of the weight of the enamel sample was fluoride after the experiment, as compared to zero percent before the esqperiment. This one percent fluoride content is mugh higher than the 0 . 1 1 percent fluoride content normally found in living human teeth; however, it is known from examination of fossilated teeth that the fluoride content can become much higher than 0 . 1 1 percent under proper conditions (1). Driving fluoride into the enamel sample by application of 1 0 volts applied potential at high fluoride concentration (0.05 N) is certainly a more severe application of fluoride than nor mally encountered by living human beings, so a nine-fold increase in fluoride content is not surprising. An alternate reason for the peak on Figure 22 might be difference in the permeability of the enamel wafer to fluoride ions and chloride ions. If the wafer were much more permeable to fluoride ions, the addition 95 of fluoride to the right hand compartment of the cell would result in a temporary increase in the wafer conduct ance, until the more permanent chemical action of the fluoride eventually makes the permanent decrease in the wafer conductivity. This effect may be operating in ad dition to the capacitor effect discussed above, to cause the overall phenomenon observed. Electroosmosis, the electrically induced motion of solvent through the enamel pores, was likely also occur ring during these experiments. Since positive ions are preferentially passed by the .enamel pores, the direction of electroosmotic flow must be in the direction of posi tive current flow. Any electroosmotic flow must, there fore, be directed into the cell compartment containing fluoride ion. The mere fact that the addition of fluoride to the right hand cell compartment had some observable effect shows that the opposing electroosmotic flow of sol vent was not great enough to prevent fluoride ions from entering the pore. Electroosmotic flow, therefore, may have caused the fluoride to have required a longer time to take effect by opposing its entry into the pores, but it was not able to prevent the end result of increased 96 electrical resistance* It is of interest to quantitatively consider rela tive magnitudes of the velocities of electroosmotic flow and the electrically induced motion of fluoride ions ; through the enamel pores. As discussed above, these velo cities are opposite in direction, and the fluoride ion I moves at greater speed than the electroosmotic flow. The I velocity of electroosmotic motion of water at 25?C is given: (25) by: L (24) | where, Vos « velocity of electroosmotic motion, cm/sec i Z as zeta potential of the membrane/volts : AE/L =s gradient in electrical potential across the membrane, volts/cm. I and the velocity of the fluoride ion is given in terms of ; the fluoride ion mobility according to: VF- " UF~ AE/L (25) ! where VF- =s velocity of the fluoride ion in the pore, cm/sec 97 Up- = mobility of the fluoride ion in the pore, cm2/volt-sec. The ratio of fluoride ion and electroosmotic velo cities is found by dividing Equation 25 into Equation 24: UF“ VF”/Vos = ------ V - (26) * 0 3 7.8 x 10“ 3 Z The range of zeta potentials, which are usually en countered, is from 13 to 70 millivolts (25), and in free -5 solution, the mobility of halide ions is about 80 x 1 0 cm2/volt -sec. If the zeta potential is taken to be 50 millivolts, and the mobility of fluoride ion in the pore —5 2 is taken to be 80 x 1 0 cm /volt-sec, then the ratio of fluoride ion velocity to electroosmotic flow velocity, given by Equation 26, is vF“/vos = 2.05 (27) This is consistent with the experimental observa tion that fluoride ion was able to enter the pores of the enamel, and it also indicates that electroosmosis is probably not an insignificant factor affecting the phenom ena related to flow of electrical current through dental enamel. CONCLUSIONS This study was undertaken to determine whether or not electrochemical phenomena play an important role in the formation of dental caries, analogous to the role which these phenomena have in metallic corrosion problems. The question was approached from the viewpoint of whether or not the electrochemical characteristics of dental enamel are consistent with a hypothesized electrochemical mecha nism for caries formation. The experimentally observed capability of enamel to produce electrical ionic membrane potentials when exposed to salt concentration gradients provides (as a result of differing salt concentrations in blood and in saliva) a means of developing an electrical potential to drive an electrochemical mechanism of caries formation. The observed degradation of these ionic membrane potentials by exposure of enamel to low pH is a means whereby acid producing bacteria or lodged food particles could initiate the formation of caries. Exposure of small portions of the enamel of a tooth to low pH is considered to locally eliminate the normal membrane potential across 98 99 the dental enamel and to thereby, Initiate self perpetuat ing flow of electrical current. This eventually degrades the local area of enamel to such an extent that it cannot re-establish the normal membrane potential even after the source of low pH is eliminated. In this case, the cause of the caries is the source of localized low pH, whatever it may be, but the mechanism of formation of the caries is the electrochemical mechanism which has been hypothesized. ; The effect of electrical current on the physical appearance of enamel material provides experimental proof that electrical phenomena can result in carious lesions. This factor is perhaps the most important of the experi- j mental observations implicating electrochemical phenomena in caries formation. The experimentally observed effects of fluoride treatment on the electrochemical characteristics of dental i j enamel are consistent with the hypothesis that electro- j chemical phenomena play a direct role in the formation of caries. The increase in enamel electrical resistivity and the improvement of enamel membrane potentials as a result of fluoride treatments help to explain clinically observed beneficial effects of fluoride. 100 Taken together, this collection of experimental evidence gives support to the electrochemical mechanism for caries formation. REFERENCES 1. Leicester, H. M., "BIOCHEMISTRY OF THE TEETH," C. V. Mosby Company, St. Louis, 1949. 2. Fosdick, L. A. , and Hutchinson, A. C. S. , "THE MECHA NISM OF CARIES OF DENTAL ENAMEL," Annals of the New York Academy of Sciences, 131, Art. 2, Mechanisms of Dental Caries, 758-770, 1965. 3. Tarbet, W. J., "A STUDY OF THE PERMEABILITY AND POST- ERUPTIVE MATURATION OF HUMAN ENAMEL," Ph.D. Thesis, Northwestern University, 1964. 4. Francis, M. D. , "SOLUBILITY BEHAVIOR OF DENTAL ENAMEL AND OTHER CALCIUM PHOSPHATES," Annals of the New York Academy of Sciences, 131. Art. 2, Mechanisms of Dental Caries, 694-712, 1965. 5. Koulourides, T., Feagin, F., and Pigman, W., "REMIN ERALIZATION OF DENTAL ENAMEL BY SALIVA IN VITRO," Annals of the New York Academy of Sciences, 131. Art. 2, Mechanisms of Dental Caries, 751-757, 1965. 6. Johansen, E. , "MICROSTRUCTURE OF ENAMEL AND DENTIN," Journal of Dental Research, 43, 1007-1020. 1964. 7. Fosdick, L. S., and Hutchinson, A. C. W. , "THE MECHA NISM OF CARIES OF DENTAL ENAMEL," Annals of the New York Academy of Sciences, 131, Art. 2, Mechanisms of Dental Caries, 758-770, 1965. 8. Hagen, A. R. , "ON THE BEHAVIOR OF DENTAL ENAMEL IN INORGANIC SALT SOLUTIONS," Universitetsforlaget, Oslo, 1965. 9. Klein, H., and Amberson, W. R., "A PHYSICO-CHEMICAt. STUDY OF THE STRUCTURE OF DENTAL ENAMEL," Journal of Dental Research, .9, 667-688, 1921. 101 102 10. Klein, H., "PHYSICO-CHEMICAL STUDIES ON THE STRUCTURE OP DENTAL ENAMEL, II. A QUANTITATIVE METHOD FOR DETERMINING RELATIVE DIFFERENCES IN THE PERMEABILITY OF THE TEETH," Journal of Dental Research, IV, 447- 450, 1930. 11. Klein, H., "PHYSICO-CHEMICAL STUDIES ON THE STRUCTURE OF DENTAL ENAMEL," Journal of Dental Research, 12. 79-98, 1932. 12. Chick, A. O., and Waters, N. E., "MEMBRANE POTENTIAL IN TEETH; APPLICATION OF SOME COMMON ANIONS TO ENAMEL," Journal of Dental Research, 42, 934-942, 1963. 13. Chick, A. O., and Waters, N. E. , "MEMBRANE POTENTIAL IN HUMAN TEETH, THE EFFECT OF SOME COMMON ORGANIC ANIONS," Archives of Oral Biology, 10, 1-7, 1965. 14. waters, N. E., "ELECTROCHEMICAL PROPERTIES OF HUMAN DENTAL ENAMEL," Nature, 219. 62-63, 1968. 15. waters, N. E., "MEMBRANE POTENTIALS IN TEETH; SELEC- r TIVITY OF ENAMEL TO IONIC TRANSPORT," Journal of Dental Research, .27, 997, 1968. 16. Sollner, K. , "THE ELECTROCHEMISTRY OF POROUS MEM BRANES," Electrochemistry in Biology and Medicine, Edited by T. Shedlovsky, John Wiley and Sons, New York, 33-64, 1955. 17. Teorell, T., "TRANSPORT PROCESSES AND ELECTRICAL PHENOMENA IN IONIC MEMBRANES," Progress in Biophysics, 3., Edited by J. A. V. Butler and J. J. Randall, Academic Press, Inc., 305-370, 1953. 18. Meyer, K. H., and Sievers, J. F., "THE PERMEABILITY OF MEMBRANES," Helvetica Chimica Acta, 19, 649-677, 987-995, 1936. 19. Meyer, K. H., and Sievers, J. F., "THE PERMEABILITY OF MEMBRANES," Helvetica Chimca Acta, j20, 634-644, 1937. 103 20. Davson, H. , "A TEXTBOOK OF GENERAL PHYSIOLOGY,” 2nd Edition, Little, Brown, and Company, Boston, Mass., 1959. 21. Afonsky, D. , "SALIVA AND ITS RELATION TO ORAL. HEALTH," University of Alabama Press, 1961. 22. Maclnnes, D. A., "PRINCIPLES OF ELECTROCHEMISTRY," Dover, 1938. 23. King, W. J., Weiss, S., Volpe, A. R., and Eigen, "IN VIVO TOOTH SURFACE SOLUBILITY STUDIES," Annals of the New York Academy of Sciences, 131, Art. 2, Mecha nisms of Dental Caries, 713-726, 1965. 24. Neumann, W. F., and Neumann, M. W., "THE CHEMICAL DYNAMICS OF BONE MINERAL," University of Chicago Press, 1958. 25. Mysels, K. A., "INTRODUCTION TO COLLOID CHEMISTRY," Interscience Publishers, New York, N. Y., 1959.

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Creator Dickerson, Robert Allen (author)

Core Title Dental Enamel Electrochemistry

Degree Doctor of Philosophy

Degree Program Chemical Engineering

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

Tag engineering, biomedical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Lenoir, John M. (committee chair), Allerton, Samuel E. (committee member), Bavetta, Lucien A. (committee member), Copeland, Charles S. (committee member), Rebert, Charles J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-434753

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