[Advances in Agronomy] Volume 13 || Physical Chemistry of Clay-Water Interaction

PHYSICAL CHEMISTRY OF CLAY-WATER INTERACTION

Philip F. low Department of Agronomy, Purdue University, Lafayette, Indiana

Page I. Introduction ................................................ 269

11. Nature of Ice and Water ...................................... 269 111. Nature of Ionic Solutions ..................................... 277 IV. Mechanisms of Clay-Water Interaction .......................... 284 V. Specific Volume of Clay-Adsorbed Water ........................ 287

VI. Viscosity of Clay-Adsorbed Water .............................. 295 VII. Dielectric Properties of Clay-Adsorbed Water .................... 303

VIII. Supercooling and Freezing of Clay-Adsorbed Water . . . . . . . . . . . . . . 306 IX. Thermodynamic Properties of Clay-Adsorbed Water . . . . . . . . . . . . . . 314 X. A Working Hypothesis ....................................... 322

References .................................................. 323

1. Introduction

Clay and water are two of the most common substances in the earth's crust. Separately and together they influence our daily lives. Frequently the mutual interaction between clay and water controls the formation of clouds and the infiltration of rain water into the soil. It is often responsible for the failure of buildings and highways and the decreased pro- duction of oil wells. It affects the quality of paper coatings and ceramics. And yet our knowledge of clay-water interaction is limited. Despite many investigations a satisfactory concept of this important phenomenon is only just beginning to develop.

This paper is intended to be a critical review of the recent literature on clay-water interaction. From this review certain facts will emerge. Usually these facts can be interpreted in more than one way. The author will give his interpretation of the facts. He will also give alternative interpretations and his reasons for not accepting them. It is hoped that this procedure will stimulate research on the part of the reader so that, in time, speculation will yield to knowledge.

II. Nature of Ice and Water

The nature of clay-water interaction cannot be discussed intelligently unless we understand the nature and properties of the two components. Most of the readers of this article have an understanding of clay. How-

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ever, there may be some who are not so familiar with the nature and properties of water. Therefore, the following discussion is included.

According to Bernal and Fowler (1933), the water molecule consists of a V-shaped arrangement of the atomic nuclei, the internuclear 0-H distances being 0.96 A. and the internuclear angle being 103 to 106 degrees, which is very close to the tetrahedral angle of 109 degrees. In the molecule there are four regions where the density of the outer electrons is maximal (Bernal and Fowler, 1933; Lennard-Jones and Pople, 1951). Two of these regions are associated with the 0-H bonds and coincide with the positions of the protons; the other two are associated with lone pairs of electrons and are located above and below the plane of the atomic nuclei on the opposite side of the oxygen nucleus from the protons. Therefore, the net charge distribution in the water molecule resembles a tetrahedron with two positive and two negative corners. The resultant center of positive electricity, midway between the protons, is separated from the resultant center of negative electricity near the oxygen nucleus on the side next to the protons. Hence the water molecule has a dipole moment. It is equal to 1.83 x

When two water molecules approach each other there is electrostatic attraction between a positive tetrahedral corner of one molecule and a negative tetrahedral comer of the other; i.e., there is electrical interaction between the proton of the former and the lone electron pair of the latter. According to Lennard-Jones and Pople ( 1951) this interaction has little effect on the electron distribution of the lone pair so that the attraction remains essentially electrostatic. However, Frank ( 1958 ) believes that the electron distribution of the lone pair is so distorted by the field of the proton that these electrons may be regarded as shared by the proton. Thus, a covalent character is imparted to the bond between the two molecules. In either event, it is obvious that the proton of the hydrogen is involved. For this reason the bond is called the hydrogen bond. Each water molecule can form four hydrogen bonds, one at each tetrahedral corner. Therefore, in an assembly of water molecules there is a tendency for every molecule to be hydrogen bonded to four neighboring water molecules which surround it tetrahedrally.

At temperatures below 0" C., the water molecules exist in fixed positions in the ice lattice. For this reason it is possible to determine their molecular arrangement by means of X-ray analysis. The results show that each molecule is tetrahedrally coordinated to four others and that the oxygen nuclei are 2.76 A. apart (Pauling, 1945; Owston, 1951, 1958). Infrared and Raman spectra (Ockman, 1958) show that the vibrational stretching frequency of the O-H bond in ice is only slightly different from that in water vapor, indicating that the O-H distances are nearly

electrostatic units.

PHYSICAL CHEMISTRY OF CLAY-WATER INTERACTION 271

the same. The calculated distance for ice is about 1.00 A. Consequently, the hydrogen atom is not midway between the oxygen atoms of the bonded molecules but is 1.00 A. from one oxygen atom and 1.76 A. from the other. It appears, therefore, that the individual water molecules retain their identity and are held together by hydrogen bonds. The strength of these bonds has been estimated (Pauling, 1945) to be 4.5 kcal. per mole. However, it is probable that not all the bonds in ice are intact. As a consequence, ice has residual entropy (Pauling, 1945). Fur- ther, the water molecules can undergo restricted rotation in an alternating electric field (Smyth and Hitchcock, 1932). And the protons in ice are capable of movement because ice conducts a direct electric cur- rent (R . S. Bradley, 1957). Both the dipole rotation and the electrical conductance of ice increase with increasing temperature, suggesting that hydrogen bonds are broken as the thermal energy of the molecules increases. Possibly, this is why ice flows more readily at higher temperatures (Glen, 1958).

When ice melts there is an increase in density from 0.917 for ice to nearly 1.00 for water. The magnitude of this density increase is very revealing. If all the hydrogen bonds were broken in the process of melting, water would have a close-packed arrangement, i.e., each water molecule would be in close contact with twelve others. Then, provided the molecular radius remained at 1.4 A., it would have a density of 1.84. Conversely, for a density of 1.00 the molecular radius would have to be 1.72 A. In the words of Bernal and Fowler (1933), ‘We have therefore the choice of assuming either that water is a simple close-packed liquid in which the effective molecular radius has changed from 1.4 A. in the solid to 1.72 A. in the liquid, or that the radius is still approximately 1.4 A. but that the mutual arrangements of the molecules are far from that of a simple liquid.” The X-ray evidence of Katzoff (1934) and Morgan and Warren (1938) indicate the correct choice. These investigators determined the radial distribution function for water at several temperatures. The radial distribution function gives the probability of finding the center of a water molecule in a spherical shell a distance T

from a given central molecule, Analysis of this function showed that near 0” C. each water molecule has slightly more than four nearest neighbors at a distance of 2.90 A. and a marked concentration of next-nearest neighbors at a distance of 4.5 A. Recall that ice has four nearest neighbors at a distance of 2.76 A. Its next-nearest neighbors are at 4.5 A. Hence, not only is the radius of the water molecule nearly the same as in ice, precluding the above alternative that water is a simple liquid, but the structure of water must be similar to that of ice, at least for short distances. On the other hand, if the structure of water were identical

272 PHILIP F. LOW

with that of ice, the slight increase in internuclear distances would lead to a density for water of 0.78 (Pople, 1951). Obviously, water does not retain the ice structure in detail. As the temperature of the water increases, there is a decrease in the sharpness and intensity of the peaks in the radial distribution function. These changes correspond to a closer packing of water molecules and a breakdown in the degree of order in the water structure.

Because every hydrogen bond is shared by two water molecules, the bond energy associated with each of these molecules is half of the total. Therefore, if all the water molecules in ice form hydrogen bonds with their four neighbors, the bond energy per molecule is twice the energy of the hydrogen bond. On a molar basis this is 9.0 kcal. But the heat of fusion of ice is only 1.44 kcal. per mole. Consequently, no more than 16 per cent of the maximum number of hydrogen bonds are broken on melting. And it may be that these bonds are bent instead of broken. Pople (1951) claims that the bending of a bond (the movement of either the hydrogen atom or the lone pair of electrons out of the 0-0 line as a result of molecular rotation) requires a much smaller supply of energy than its complete rupture, so that bond bending should be of considerable importance near the freezing point. As the temperature is raised, additional bonds are bent or broken. Between 25" and 90°C. the average number of hydrogen bonds is estimated to be somewhat greater than half the number possible (Cross et al., 1937). Using the assumption that water is a mixture of ice and a normal close-packed liquid, each pos- sessing its normal volume at the given temperature, Grjotheim and Krogh-Moe (1954) calculated that the per cent of broken hydrogen bonds in water increases from 55 to 77 as the temperature is raised from 0" to 100" C. However, from heat of vaporization data, Haggis and associates (1952) calculated that the per cent of broken bonds increases from 9 to 20 in the same temperature range. Regardless of which values are correct, it is apparent that liquid water retains a high degree of hydrogen bonding and that this bonding decreases with increasing temperature.

Water has unusual properties relative to those of similar compounds such as H2S, H2Se, H2Ti, CH4. For instance, water has an abnormally high melting point, boiling point, heat of fusion, heat of vaporization, and specific heat. The high values of these quantities are attributed to the extra energy required to break hydrogen bonds (Bernal and Fowler, 1933; Pauling, 1945). The unusually high viscosity of water has the same basis (Ewe11 and Eyring, 1937), as does the elevated dielectric constant ( Pauling, 1945).

Evidence of the kind cited here has led to four different concepts of the structure of water. The first is that proposed by Bernal and Fowler


(1933) and modified by Morgan and Warren (1938). It is probably the most commonly accepted concept. Water is regarded as having a tendency to bond itself tetrahedrally to four neighbors because of the afore- mentioned electron distribution in the molecule. The bonds are con- tinually breaking and re-forming so that, on the average, each molecule has slightly more than four neighbors but is bonded to fewer than four of them. As the hydrogen bonds are broken the resulting fragments tend to pack together as closely as possible. This tendency toward close packing as bonds are broken explains the volume decrease of about 9 per cent on melting even though the intermolecular distance increases. As the temperature increases, the increased thermal agitation results in the rupture of additional hydrogen bonds. But the increased agitation also results in an increase in intermolecular distances. The former effect of thermal agitation predominates below 4" C.; whereas, the latter effect predominates above 4" C. The result is that water has a maximum density at 4" C.

The second concept was proposed by Lennard-Jones and Pople (1951) and expanded by Pople (1951). According to them, the molar heat of fusion (1.44 kcal.) is small compared to the hydrogen bond energy per mole of water in ice (9.0 kcal.). Therefore, few bonds could be ruptured on melting, especially in view of the fact that much of the available energy would be used for distortion or bending of bonds. Further, the value of RT at 0" C. (0.5 kcal. per mole), which is a measure of the kinetic energy of the molecules, is small relative to the bond (potential) energy. Therefore, Pople (1951) states "as the temperature of ice rises, the hydrogen bonds will become increasingly bent, until at a certain stage this leads to a breakdown of the long-range order, corresponding to fusion. After fusion the four hydrogen bonds from one molecule may be regarded to a good approximation as being able to bend independently, whereas before they could only bend in such a way that the lattice order was maintained. This is the essential difference between ice and water in this theory. In water, individual bonds will have increased freedom, as a result of which some of the molecules will move into the formerly unoccupied regions of the tridymite-like ice lattice, leading to the observed volume diminution. This process will lead to a gradual smoothing out of the radial distribution function with rising temperature." Thus, water is regarded as being a giant polymer of hydrogen- bonded water molecules.

A third concept is that advanced by Forslind (1952). He proposed a type of hydrogen bonding between water molecules similar to that of Lennard-Jones and Pople ( 1951 ) but involving bond hybridization. Not all of these bonds are supposed to have equal strength in ice. As the tem-

274 PHILIP F. LOW

perature is increased, the thermal vibrations of the molecules result in the breaking of some of the weaker bonds. If the vibrations are of sufficient amplitude, the vibrating molecule will pass through the face of the surrounding tetrahedron to occupy an interstitial position. The lattice defects thus produced are of the so-called Frenkel type. Just below the melting point, a number of Frenkel defects will appear in the ice lattice. The vacant lattice sites or “holes” and the interstitial molecules associated with them can diffuse independently. When the “holes” reach the boundaries of the system they are annihilated. The annihilation of the “holes” will produce a volume decrease and a corresponding increase in density due to the lone interstitial molecules. Melting, according to this concept, corresponds to the annihilation of “holes” and the latent heat of fusion is determined by the energy of formation of the Frenkel defect. Pre- sumably, the fluidity of water results from the existence of numerous defects in the lattice, the number of defects increasing with the temperature.

Frank and Wen (1957) and Frank (1958) have another concept of water structure. It is based on a different idea of the hydrogen bond. They believe that the hydrogen bond is covalent in character. The covalency arises from the displacement of the lone-pair electrons of one bonded molecule toward the proton of the other as a result of their mutual attraction. This displacement of electrons increases the polarity of the molecule and enhances the possibility of bond formation with a second molecule, and so forth. Thus hydrogen bond formation is considered to be a cooperative phenomenon. According to these authors, liquid water consists of flickering clusters of hydrogen-bonded molecules enclosed in a fluid of nonbonded molecules. The clusters have rigidity because the covalent hydrogen bonds are capable of relatively little “bending.” When the bonds are ruptured there remains the electrostatic interaction of the Bernal and Fowler (1933) and Lennard-Jones and Pople (1951) models so that the nonbonded molecules of the fluid are by no means random in their orientation. Therefore, the energy change involved when a cluster forms or “melts” is not large. These clusters appear or disappear as a result of energy fluctuations in the medium. When an energy fluctuation creates a suitably cold region, a cluster will form. A moment later another energy fluctuation in the same region pro- vides the energy for the cluster to “melt.” The bonded cluster is limited in size by the competition at its boundaries between two kinds of orienting influences, one exerted by the ordered array of molecules in the cluster and the other by the relatively disordered molecules in the surrounding fluid. The torques and displacements of the latter are trans- mitted to the former and provide the necessary energy for “melting.”


Combining this picture of water with the “premelting” of ice indicated by the work of R. S. Bradley (1957) and Glen (1958), cited earlier, Frank (1958) states: “It may be suggested that if water contains flickering clusters of ice-like material and ice contains flickering droplets of water- like nature, then the essential difference between the two may be one of connectivity, so that when solid surrounds liquid we have ice, and when liquid surrounds solid we have water.”

At the present time an unequivocal preference cannot be made for any one of the above concepts. Each of them is capable of explaining the available data. In fact, the concepts are quite similar. Included in each is the basic idea that there is a high degree of hydrogen bonding in water that orders the molecules in a loose icelike arrangement. Consequently, we shall adopt the terminology of Morgan and Warren (1938) and say that water has a “broken down ice structure.”

In view of the preceding discussion it might be expected that the kinetic unit in such processes as dipole rotation in an alternating electric field, self-diffusion, and viscous flow should be a cluster or domain of bonded water molecules. In fact, according to classic theory, the latter process involves the relative movement of whole layers of water molecules. However, the evidence is to the contrary. From the theory of absolute reaction rates (Glasstone et al., 1941), we obtain the equations

h

0 - - e A S t / R e - A H S / R T 1 rl h - - ( 3 )

where: t = the relaxation time, i.e., the time required for the dipolar

molecules to revert to a random distribution after the removal of an impressed electric field. It is also considered as the time required for the molecule to rotate through 180”.

k = Boltzmann constant T = absolute temperature h = Planck‘s constant AS$ = entropy of activation AHt = heat of activation R = molar gas constant D h = distance between successive equilibrium positions

7 = coefficient of viscosity o

= diffusion coefficient of the molecule

along the diffusion path

= volume of the molecule

276 PHILIP F. LOW

For these processes AHt probably equals E, the activation energy, because volume changes should be negligible. Now if the entropy and heat of activation are the same for each process it follows that

D = h 2 / t = kTh2/qv ( 4 )

Another relationship between z and q was obtained by Debye (1945) by quite a different method. His relationship is

Here T is the radius of the rotating molecule. A familiar relationship between D and q is the Stokes-Einstein equation, viz.,

kT 6xry

D = -

The similarity between the latter two equations and those of Eq. ( 4 ) is apparent.

Wang et al. (1953) determined the activation energy for the self- diffusion of water in water and compared the value obtained with the activation energies for the dielectric relaxation (dipole rotation) and viscous flow of water. The activation energies had the same value. Saxton (1952) also found the activation energies for dielectric relaxation and viscous flow to be the same. One would expect the activation mechanism for dielectric relaxation to be the breaking of hydrogen bonds so that the molecule can rotate. The activation mechanism for both self-diffusion and viscous flow should be the breaking of hydrogen bonds and the pushing aside of surrounding water molecules so that the molecule can move forward. However, the identity of the activation energies for these processes suggests that the major activation mechanism is the breaking of hydrogen bonds and that the pushing aside of the surrounding water molecules requires little energy. Possibly this is because vacant spaces in the open water structure are already available for the molecule to move into. From the magnitude of the activation energy Ewe11 and Eyring (1937) and Wang (1951a) calculated that about two bonds had to be broken per molecule for movement to occur. This number agrees with the estimated number of hydrogen bonds remaining in water at room temperature (Cross et al., 1937; Grjotheim and Krogh-Moe, 1954; Haggis et al., 1952). Of course, there is a decrease in the activation energy with an increase in temperature in keeping with the fact that raising the temperature breaks hydrogen bonds.

According to Eqs. (4) and (5) the value of q / t T should be essentially constant at all temperatures. And, further, one should be able to cal-

PHYSICAL (3HEMISTRY OF CLAY-WATER INTERACTION 277

culate the volume of the kinetic unit from the magnitude of this constant. Collie and co-workers (1948) showed that r/tT was constant and, using Eq. (5), showed that the calculated value of z agreed with the experimental value if the radius of the water molecule was used for T. Robinson and Stokes (1955) have summarized the results of Collie, Hasted, and Ritson and have shown that the calculated molecular radius varies only from 1.44 A. to 1.48 A. between temperatures of 0" C. and 75" C., respectively. Saxton (1952) also showed the constancy of y/zT. If Eq. (4) is used with the value of his constant then 0, the molecular volume, can be shown to be 0.5 x 10-22 cc. which is of the same order of magnitude as 0.3 X the known molecular volume. Recently, Grant (1957) presented additional evidence for this relationship and reported that the kinetic unit is of the order of one molecule instead of a cluster or domain of water molecules.

Wang (1951a, b) and Wang et al. (1953) obtained a constant value of Dq/T in the temperature range 10" to 55" C. Hence, their evidence supports the validity of Eqs. (4) and (6). Wang (1951a) also reported that the value of the molecular volume, calculated from Eq. (6), suggests that the diffusing unit is a single molecule. Robinson and Stokes (1955) have summarized these results as well.

It is apparent from the preceding discussion that the processes of dielectric relaxation, self-diffusion, and viscous flow in water all involve the individual molecule rather than a cluster or domain of molecules. Evidently, less energy is expended in dissociating the molecule from the cluster or domain, so that it can move independently, than in moving the intact cluster or domain. Or perhaps the active molecules are between these clusters or at their edges.

111. Nature of Ionic Solutions

In view of the charge distribution in the water molecule, one would expect charged ions to attract water molecules electrostatically. In other words, one would expect the ion to hydrate by the formation of ion-dipole bonds. Hydration will occur if the potential energy of the water molecule is less in the hydration shell of the ion than it is in the hydrogen-bonded water structure. Bernal and Fowler (1933) made calculations to show that this is the case, especially for small or multiply charged ions. How- ever, the water molecules around the ion can exchange with other water molecules in the medium, the frequency of exchange depending on the intensity of the ion-dipole bonds ( Samoilov, 1957). Now, in normal water each molecule is surrounded by four others in tetrahedral fashion. Two of the neighboring water molecules are oriented with their protonic

278 PHILIP F. LOW

corners toward the central molecule; the other two are oriented with their lone-pair electron corners toward it and their protonic corners away from it. When an ion is introduced into the water structure, the situation is different. All the water molecules around a cation have their resultant electronic centers directed inward. Around an anion, all the water molecules have their protonic corners directed inward. Therefore, even if the ion is of the right size to fit into the space normally occupied by a water molecule, the water of hydration cannot "match" or coordinate with the surrounding water. The result is a disruption of the quasi-crystalline water structure. The disruption will be enhanced if the ion differs in size from the water molecule. In general, the larger the ion, the greater the disruptive effect.

In the work of Morgan and Warren (1938) it was established that the second or minor peak in the X-ray diffraction curve of pure water diminishes in height with increasing temperature until, at 83" C., the peak is gone. This diminution in peak height has been regarded as being due to a breakdown of the water structure and an increase in the coordination number of the molecules. Ions are supposed to break down water structure. Therefore, Stewart (1939, 1943, 1944) determined the change in height of the minor diffraction peak with increasing salt concentration and found that it decreased linearly with the mole fraction of the salt. His conclusion was that ions, like an increase in temperature, break down the water structure. This conclusion was substantiated by the fact that the decrease in peak height with salt concentration was related to the change in apparent molal volume of the salt for a number of electrolytes. Evidently, the change in the apparent molal volume of the salt is to be construed as a change in the molal volume of the water. Stewart also observed that the apparent molal volume of a salt changed most rapidly with salt concentration in dilute solution. Had the disruptive effect of the ions been local so that the ionic spheres of influence did not overlap, the apparent molal volume should have remained constant until relatively high concentrations were attained. Consequently, he interpreted this observation to mean that the structural disruption produced in the water by the ions is rather extensive.

The work of Corey (1943) lent support to Stewart's conclusions. He determined the adiabatic compressibility of aqueous electrolyte solutions and showed that the rate of decrease of this quantity with the mole fraction of salt was correlated with the rate of change of peak height for twenty-six different electrolytes. The application of pressure to open- structured water breaks hydrogen bonds and leads to a closer packing of molecules with a resulting decrease in compressibility. Apparently ions produce the same effect as added pressure.


In their classic paper Bernal and Fowler (1933) compared the apparent volumes of salts in solutions and observed that the volumes of the component ions were additive. Therefore, to obtain ionic volumes in solution, they divided the volume contribution of CsCl to a solution in proportion to the volumes of the component ions in the solid. Then, using the latter volumes as a basis, they were able to obtain the apparent volumes in solution for several ionic species. As an example, they could obtain the volume of K+ in a solution of KC1 by subtracting the assumed volume of the C1- ion from the apparent volume of the salt, and so on. They compared the ionic volumes so obtained with the volumes of the same ions in solids. The comparisons revealed that the apparent volumes of cations in solution were the same as those in solids only for Rb+ and Cs+. The apparent volumes of anions in solution were the same as those in solids except for OH- and F-. All other cases showed apparent volumes either much smaller than in solids or actually negative. Their conclusion was that the presence of ions in solution either contracts the water structure or breaks it down to cause a closer packing of water molecules. An analogous approach was used by Gurney (1953) with similar results.

The dielectric constant data on ionic solutions are interesting but dacul t to interpret. However, their interpretation will be facilitated by referring to equations (16) to (19) and the discussion at the beginning of Section VII. Hasted and associates (1948) reported that ions make a negative contribution to the dielectric constant. The magnitude of the negative contribution was linearly related to the salt concentration. In general, at a given concentration, the smaller or more highly charged the ion, either cation or anion, the greater the dielectric decrement. This decrement was assumed to be due to the inability of the water molecules around the ion to rotate in the alternating field. In essence, the hydrated ions were regarded as spherical inclusions of very low dielectric constant in a continuous water medium of uniform dielectric constant. A more significant feature of their study was the depression of the relaxation time produced by the addition of salt. The depression of the relaxation time was also linearly related to the salt concentration. Recall that the relaxation time is the time required for a dipolar molecule to make a single rotation through 180 degrees in an alternating electric field. The authors proposed that molecular reorientation takes place at the boundaries of broken pieces of water lattice; hence, they considered the depression of the relaxation time to be a reasonable index of the structure-breaking effect of the ions. Larger ions, both cations and anions, produced a larger depression of the relaxation time than small ones. There was also a tendency for this depression to increase with the charge on the ion. In a

280 PHILIP F. LOW

subsequent paper, Haggis et al. (1952) showed that the depression of the relaxation time was related to the difference (negative) between the apparent and calculated volumes of the added salt. Thus credence was given to the interpretations of Hasted et al. (1948). But, in concentrated solutions the relaxation time increases again (Harris and O’Konski, 1957). Apparently, this increase in relaxation time is due to the increased orientation of water molecules in the strong electric field produced by cations and anions in proximity.

A valuable index of the effect of ions on the structure of water is provided by viscosity measurements. Viscosity is a structure-sensitive property of a fluid. The relationship between the viscosity of an aqueous salt solution and the salt concentration is reported in Gurney’s (1953) book. It is

q = yo ( 1 + A dF+ Bc) (7 ) where Q is the viscosity of the pure solvent, c is the salt concentration and A and B are constants characteristic of the solute. The Ads term is supposedly related to interionic attractive forces that retard motion when oppositely charged ions move relative to each other. The B coefficients are related to the structure of the water in solution. In dilute solutions these coefficients are additive for ions. As a result, it is possible to obtain values for single ions by a method analogous to that for determining apparent ionic volumes. The B coefficients reported by Gurney (1953) and Kaminsky (1957) become more negative as the ions get larger. In fact, the coefficients for K+ and larger alkali metal cations are negative, as are those for most anions. However, as the temperature increases these coefficients become more positive. Kaminsky ( 1957) ascribes this increase to the temperature-induced breakdown of the water structure with a concomitant decrease in the contribution of the ions to this breakdown. In a revealing graph Gurney showed that the B coefficients decrease linearly with an increase in the partial molal entropy of the ions. Theo- retically, the partial mold entropy of an ionic species is the increase in entropy (disorder) of an infinitely large solution when a mole of ions is added to it at constant pressure and temperature. Apparently then, the ions which have negative B coefficients produce disorder in the solution.

The fluidity of a solution is the reciprocal of its viscosity. The changes in fluidity induced by ions in aqueous solutions are additive, as might be expected. Bingham (1941) has tabulated the ionic elevations of fluidity. His tables reveal that, in the alkali metal cation and halide anion series, the fluidity elevation decreases with decreasing ionic size. In these series only Li+ and F- have negative fluidity elevations. An interesting point is that multiply charged ions have negative fluidity elevations, the neg-


ative character of the elevation increasing with charge. The indication is that a small multiply charged ion reduces the fluidity of the water molecules for a considerable distance from it. Recent X-ray evidence (Brady, 1980) suggests that the water may even have the structure of ice for some distance from a small highly charged ion.

Another structure sensitive quantity is the digusion coefficient of a diffusing species. Wang ( 1954 ) has measured the self-diffusion coefficient of H2018 in solutions of NaCl, KC1, and KI. In the former solution the self-diffusion coefficient decreased with concentration, but in the latter two solutions it increased. Now the presence of the ions should increase the tortuosity of the diffusion path of the water molecules and thereby decrease the observed diffusion coefficient. But in the KCl and KI solutions the presence of the ions increased this coefficient. Therefore, it seems evident that the ions of these salts disrupted the quasi-crystalline structure of water to make the water more fluid. In the case of the NaCl solutions it is possible that the smaller Na+ actually tightened the structure. Or the decrease in diffusion coefficient with salt concentration may have been due to the tortuosity factor mentioned above.

The entropy of a system is a quantitative measure of its disorder: the greater the entropy, the greater the disorder. The partial molal entropy of a component of the system is the change in entropy of the system per mole of added component at constant composition, pressure, and temperature; hence, it is the added disorder per mole of component. With this in mind, Frank and Robinson (1940) determined the partial molal entropies of water in different salt solutions relative to the entropy per mole for pure water at the same pressure and temperature. Their work showed that the relative partial molal entropies of the water in dilute solutions were negative and became more negative as the salt concentration increased until a minimum value was reached. Then the relative partial molal entropies of the water increased with salt concentration to rather large positive values. They explained the initial decrease in the disorder of the water molecules in solution as being due to the polarizing effect of the increasing field strength between oppositely charged ions in accordance with Debye-Huckel theory. The later increase in disorder was attributed to the disruptive effect of the ions, which became predominant at the higher salt concentrations. As would be expected, the minimum in the partial molal entropy versus salt concentration curve occurred at higher concentrations for the smaller ions than for the larger. And the final partial molal entropy values were less positive for the smaller ions than for the larger ones.

Later, Frank and Evans (1945) studied the entropies of vaporization of ions in solution. The entropy of vaporization is the increase in disorder

282 PHILIP F. LOW

of the ions in going from the liquid phase to the gas phase. The entropies of vaporization were obtained by subtracting the partial molal entropies in solution from the statistically calculated molal entropies of the ions as perfect gases. These values were compared with the theoretical entropy losses arising from ( 1 ) restriction of the ions in “free volume” cells in the liquid phase, ( 2 ) immobilization of the water in the hydration shells of the ions, and (3 ) dielectric polarization of more distant water. The results showed that for all the alkali and halide ions except Li+ and F-, too little entropy was lost when the ions were dissolved from the gaseous state. In other words, there was more disorder in the liquid state than the theory would predict. Their conclusion was that this disorder arose from the breakdown of the water structure by the ions. Again, the structural breakdown increased with increasing ionic size. The values for that part of the ionic entropy of vaporization attributed to breakdown of water structure were compared with the ionic fluidity elevations of Bing- ham (1941). In general, the ionic disruption of structure was correlated with the ionic fluidity elevation. Further, the total entropy of vaporization of the ions was correlated with the ionic fluidity elevation. For the small highly charged ions the entropies of vaporization were high and the fluidity elevations had large negative values. The authors proposed that these ions owed both their low entropy and high viscosity in solution to the existence around each ion of a large patch of “frozen” water. Frank and Evans (1945) also listed the partial molal heat capacities of the alkali halides. The partial molal heat capacity is the change in heat capacity of a system per mole of added component at constant pressure, temperature, and composition. The partial molal heat capacities were all negative. This was expected because the water molecules in the hydration shell of an ion are not free to rotate. As a result, they do not absorb heat to increase their rotational energy and thereby contribute to the heat capacity. However, on this basis alone, one would expect the partial molal heat capacity to become more negative as the ionic size decreased. The reverse was true. Therefore, the authors concluded that, in addition to the reduction in heat used for molecular rotation, there was a reduction in the heat used to “melt” hydrogen-bonded clusters because these were already partially destroyed by the structure-breaking effect of the ions. As usual, the structure-breaking effect of the ions increased with ionic size.

Recently, Frank and Wen (1957) discussed the structure of water in ionic solutions. On the basis of evidence of the kind presented in this section, they proposed a reasonable model for ion-water interaction, Ac- cording to them each ion is surrounded by three regions. The innermost region ( A ) is one of immobilization. In this region the water molecules

PHYSICAL (3HEMISTRY OF CLAY-WATER INTERACTION 283

have little kinetic energy. They are strongly oriented in the intense electric field of the ion. In the second region ( B ) the water structure is broken down and is more random or less ice-like than normal. The outer- most region (C) contains normal water which is polarized in the ordinary way by the ionic field which, at this distance, is relatively weak. The cause of the structural breakdown in region B is presumably the competition between the normal structural orienting influence of the neighboring water molecules and the orienting influence of the spherically symmetrical ionic field. The latter influence predominates in region A and the former in region C. The outward orientation of like poles of the water dipoles around the ion should always produce some disorder in region B, the large univalent ions producing the most. Small ions, especially the multivalent ones, should have region B, but region A should be great enough for the entropy of vaporization to be greater than the pre- dicted value. In other words, region A should be more extensive than region B so that the net effect of these ions is to produce order even though the arrangement of the molecules is different from that in normal water.

Before concluding this section something should be said about the effect of nonpolar solutes on the water structure. Frank and Evans (1945) noted that the entropies of vaporization of these solutes from water were much greater than their entropies of vaporization from organic solvents when compared at common heats of vaporization. The entropies of vaporization of nonpolar solutes from water also far exceeded the entropies of vaporization of ions from water. Further, the entropies of vaporization decreased much more rapidly with temperature when the nonpolar solutes were dissolved in water than when they were dissolved in an organic solvent. And the partial molal heat capacities of these solutes in water were abnormally high. These observations led the authors to conclude that, when a nonpolar molecule dissolves in water, it modifies the water structure in the direction of greater “crystallinity.” In their descriptive language, the water builds a tiny “iceberg” around the solute particle. However, it is not implied by them that the quasi-crystalline structure about the nonpolar solute molecule is exactly like ice. The rapid decrease in entropy of vaporization of the nonpolar solutes with temperature was ascribed to the “melting” of the icebergs. The energy consumed in the “melting process was supposed to account for the abnormally high partial molal heat capacities. Additional support was given to this picture of nonpolar solutes in water by the observation of Frank and Wen (1957) that the apparent molal heat capacity of tetra-n-butyl ammonium chloride was about 120 cal. per degree per mole more than the theoretical value calculated from the additivity rules for hydrocar-

284 PHILIP F. LOW

bons. And Frank (1958) has pointed to the fact, reported by Haggis et al. (1952), that nonpolar solutes or solutes with nonpolar groups increase the dielectric relaxation time of the solution. The formation of the “icebergs” is considered to arise from the lack of attraction between the nonpolar molecules and the surrounding water. This water would not be subjected to the normal torques and displacements; hence, it would have a greater opportunity to develop the tetrahedral structure.

Contrary to the postulate of Frank and his co-workers, Claussen (1951) postulated that nonpolar solutes form definite hydrates in water and proposed probable structures for them. Later Stackelberg and Muller (1951) confirmed one of these structures by X-ray analysis. The structure is extensive, having 136 water molecules per unit cell. However, it is by no means certain that definite hydrates form with all nonpolar solutes. Rather, it may be that the larger nonpolar solutes induce the formation of the “icebergs” described earlier. Frank and Wen (1957) point out that the hydrates or cages of Claussen (1951) and Claussen and Polglase (1952) should have specificity in the size and shape of solutes they accommodate; whereas, there seems to be a smooth proportionality between the degree of “ice-like-ness” and the size of the nonpolar region of the molecule.

IV. Mechanisms of Clay-Water Interaction

There are several possible mechanisms by which water may interact with clay surfaces. These mechanisms of interaction may operate separately or unitedly. All we can observe is their net effect on the water. At this time we shall give a brief discussion of each of them. Then, when the experimental data are presented, we shall try to evaluate their relative importance.

We have seen that hydrogen bonds normally form between 0-H groups and oxygen atoms and that there is a tendency for water molecules to be hydrogen bonded in a tetrahedral arrangement. We know that the surface of clay minerals is made up of either oxygen atoms or hydroxyl groups arranged in a hexagonal pattern which, according to Hendricks and Jefferson (1938), Macey ( 1942), and Forslind ( 1952), can coincide at points with a similar pattern in a hydrogen-bonded water structure. Further, we know that the crystal lattice of most clay minerals contains excess electrons which arise from the isomorphous substitution of cations in the lattice. And, from the work of Lennard-Jones and Pople (1951) and Frank (1958), we have reason to believe that covalency may occur in hydrogen bond formation if one of the systems involved is capable of having its lone-pair electrons distorted by the proton or positive element of the other. Such distortion is conducive to the formation of additional

PHYSICAL CHEMISTRY OF CLAY-WATER INTERACI'ION 285

hydrogen bonds in a cooperative manner (Frank, 1958). Now, the lone- pair electrons of the oxygen atoms in the surface of a clay mineral should be easily distorted because of the excess electrons in the lattice. There- fore it is reasonable to believe that water molecules adjacent to a clay- mineral surface are bonded to the oxygen atoms of the surface by covalent hydrogen bonds. The existence of the covalent bonds should alter the electron distribution in these molecules and make it easier for them to form additional covalent bonds with other molecules in the same and next layer. Those in the next layer, in turn, may be expected to form hydrogen bonds of partially covalent character with their neighbors, and so on. The bonded water molecules should be arranged in a tetrahedral fashion because of the directional properties of the bonds. However, the degree of covalency in the bonds should decrease with distance from the surface and, for this reason, the tetrahedral arrangement should become less rigid in the same direction. Thus, it is possible for a tetrahedral structure of water molecules to be attached to and propagated, with decreasing rigidity, away from the oxygen surface of a clay mineral.

It is not unlikely that a hydrogen-bonded water structure builds up also on the hydroxylic surface of a clay mineral. Here the excess of electrons in the mineral lattice should help to screen the protons of the hydroxyl groups and render them less electropositive. Consequently, the lone-pair electrons of the oxygen atoms in the bonded water molecules should experience little distortion and the degree of covalency in the hydrogen bonds should be slight. For this reason the water structure on an hydroxylic surface may be expected to be less stable than that on an oxygen surface. But, as we have seen, the balance between order and disorder in water is delicate. Therefore, even the hydroxylic surface, by fixing the positions of a layer of bonded molecules, should tip the balance in favor of order for considerable distances.

Probably, the water structure that develops on either mineral surface is not that of ice. One reason is that the exchangeable cations would disrupt the water structure (Mackenzie, 1950). Another is that the surface atoms of the mineral may not coincide exactly with protons or oxygens of the ice lattice so that the latter would be distorted (Mathieson and Walker, 1954). Or surface irregularities, which must exist, may produce distortions in the ice lattice. Further, there may be other hydrogen-bonded structures with tetrahedral coordination which are more stable in such an environment (Hendricks and Jefferson, 1938; Claussen, 1951).

A second mechanism by which water may be attracted to a clay surface is hydration of the exchangeable cations. There is little doubt that cations hydrate, especially if they are small or multiply charged. Since the cations cannot escape from the negatively charged surface, neither

286 PHJLIP F. LOW

can the water of hydration. This mechanism of attracting water should be most important at low water contents.

At higher water contents the exchangeable cations should still play a role in clay-water interaction. Those exchangeable ions that are disso- ciated from the surface may be regarded as being in solution. Undoubt- edly, they lower the activity of the water in the vicinity of the clay surface in the same manner as ions lower the activity of water in solution. Consequently, water should tend to move into the surface region. In short, clays may be expected to attract water by osmosis.

As mentioned earlier, the crystal lattice of a clay has an excess of electrons. For this reason, the flat clay particle may be regarded as a negatively charged condenser plate. Double-layer theory predicts that the electric field of this plate decreases with distance from the surface. Water molecules, having a dipolar nature, should tend to orient with their axes parallel to the field and their positive poles directed toward the surface. Their degree of orientation should decrease as the electric field intensity decreases. And midway between the clay plates, where the field intensity is zero, there should be a region of structural disorder in the water because the negative poles of the water molecules on either side are all directed inward. The situation should be analogous to that in the vicinity of an ion. Only the clay, being much larger than the ion, should disrupt the water more extensively. This arrangement of water molecules would occur only if their orientation energy in the electric field of the clay is less than their energy in a tetrahedral arrangement involving hydrogen bonds. The two arrangements are incompatible. How- ever, it should be noted that the presence of the electric field does not preclude the latter arrangement. In fact, the field may aid in distorting the lone-pair electrons of the water molecules and thereby enhance the covalent character of the hydrogen bonds.

Finally, it is possible that London disperson forces are responsible for clay-water interaction. These forces are the ones that exist between neutral molecules and are nondirectional in nature. They arise from the instantaneous in-phase fluctuations of the electronic atmospheres around the oxygen nuclei. As the electronic atmosphere of a given oxygen atom is displaced relative to its positive nucleus, a temporary dipole is formed. This dipole induces corresponding displacements in the electronic atmospheres of neighboring molecules so that dipole-dipole attraction occurs. An instant later the atmospheres are displaced in phase in another direction, but always so that a net electrostatic attraction between molecules exists. According to this picture, the electronic atmospheres of the oxygen atoms in the water would fluctuate in phase with the electronic atmospheres of the surface oxygens. The resulting water structure, being


held together by nondirectional bonds, should be close packed. In addition, it should be more fluid and less extensive than the hydrogen-bonded one.

In the preceding discussion of the possible mechanisms of clay-water interaction it was assumed that the clay surface was clean and uncon- taminated. Frequently this may not be the case. In most natural clay systems there will be hydrous oxide impurities, especially those of alu- minum. And free silica will usually be present. These impurities also contain surfaces composed of oxygen atoms and hydroxyl groups. Fur- ther, their surfaces have electric double layers. Therefore, the mechanisms of water interaction with them will be similar to those for water interaction with the clays. Unfortunately, the experiments which we will now discuss were conducted on clays which may or may not have had hydrous oxides and silica present. We will assume that the results apply to the clays. But we will recognize the possibility that they apply instead to the afore-mentioned impurities. Although it would be desirable to know which substance is the one affecting the water, these substances are so intimately related in the clay fraction of the soil that, for most purposes, the distinction is relatively unimportant. Our major concern is the nature and properties of the water in such a system.

V. Specific Volume of Clay-Adsorbed Water

One property which is very useful in determining whether or not water has a simple close-packed structure is the specific volume or its reciprocal-the density. Attempts have been made to determine the specific volume of clay-adsorbed water by a pycnometer technique. The volume, V, of a pycnometer can be determined accurately at a given temperature. In addition the weight of clay, m, and of the water, w, in the pycnometer are measurable. Hence, using the equation

V = wv, + mv,

and assigning a value to the specific volume of the clay, vm, it is possible to calculate the apparent specific volume of the water, 0,. However, the difficulty lies in assigning a correct specific volume to the clay. This fact is illustrated in Table I, which was prepared from unpublished data of Anderson ( 1958). The clay was Na-saturated Wyoming bentonite. The specific volumes of 0.3703,0.3571, and 0.3448 correspond to clay densities of 2.70, 2.80, and 2.90, respectively. Evidently the apparent specific volume of the water appears to be less than, equal to, or greater than that of pure water (sp. vol. = 1.0029) depending on the value of the specific volume assigned to the clay. And the apparent spec& volume of the

( 8 )

TABLE I The Specific Volumes of Water at 25" C. in Suspensions of Different Na-Clay Concentration, Assuming Different

Specific Volumes for the Clap

Apparent specific Apparent specific Apparent specific Pycnometer Weight of Weight of volume of water volume of water volume of water

Pycnometer volume clay water ( U, = 0.3703) ( U, = 0.3571) (urn = 0.3448) number (e.) (g.) (g.) (cc./g. 1 ( cc./g. (cc./g. 1

49.4477 1.0025 1.0028 1.0031 r 1 49.986 1.1101 4 49.966 2.1392 49.0755 1.0020 1.0026 1.0031 5 49.978 2.6696 48.8910 1.0020 1.0027 1.0034 6 49.980 3.5883 48.5656 1.0018 1.0027 1.0036 7 49.873 4.4417 48.1549 1.0015 1.0027 1.0039 8 49.995 6.3986 47.5741 1.0011 1.0029 1.0045

10 49.896 6.7895 47.3380 Lo009 1.0028 1.0046

5 Data from D. M. Anderson (unpublished).


water appears to decrease, remain constant, or increase with increasing clay concentration depending on this value. It is obvious that the correct interpretation of pycnometer data is contingent upon obtaining a correct value for the specific volume of the clay.

To obtain the correct specific volume of the clay, it has been customary to use pycnometer liquids other than water in the hope that these will not interact with the clay and thereby have their speci6c volumes altered. The normal specific volume is assigned to the liquid being used. However, many years ago Russell (1934) showed conclusively that clay interacted differently with every liquid that he investigated. The liquids were: tetralin (tetrahydronaphthalene), decalin (decahydronaphthalene) xylene ( dimethylbenzene), benzene, carbon tetrachloride, nitrobenzene, aniline, amyl alcohol, benzyl alcohol, and water. The first five liquids are nonpolar, and the remaining liquids are polar. Using the tetralin as the reference liquid he plotted T-Lr against corresponding values of T-L, for several clays. Here T represents the apparent specific volume of a clay in tetralin and L represents the apparent specific volume of the same clay in another liquid, the subscripts i and j denoting different liquids. In this manner the real volumes and weights of the clays and ions were eliminated and only the relative effects of the clays on the pycnometer liquids were observed. The plots were straight lines with different slopes, which depended on Li and LI. These results are consistent with the well-documented fact (Henniker, 1949; Adamson, 1960) that all surfaces influence the structure and properties of a vicinal liquid to a depth of many molecular diameters.

DeWit and h e n s (1950) used a petrol fraction as pycnometer liquid and determined the density of oven-dried Wyoming bentonite to be 2.348 (0 , = 0.426). Then they suspended the bentonite at different moisture contents in this liquid to obtain the densities after hydration. The data permitted them to calculate the apparent specific volumes of the adsorbed water which, for percentage moisture contents (dry weight basis) of 28.4, 16.6, and 11.6 were 0.76, 0.73, and 0.71 cc. per gram, respectively. Two faults in this work make the results unacceptable. One is that the true density of Wyoming bentonite is closer to 2.80, as will be shown later. The second is that water confined in a thin layer between a clay surface and a nonpolar liquid may not have the specific volume it would have in the absence of the nonpolar liquid. In the previous discussion of ionic solutions it was pointed out that nonpolar solutes markedly affect the water structure. Since DeWit and Arens used too large a value for the specific volume of the clay, their calculated apparent specific volumes for the adsorbed water would appear to decrease with decreasing hydration, i.e., increasing clay concentration (see Table I).

290 PHILIP F. LOW

Oakes (1958) used benzene as pycnometer fluid to determine the density of oven-dried Wyoming bentonite and obtained a value of 2.5196 (v , = 0.397). If this value is used with his density-concentration data for bentonite-water systems, it is found that the apparent specific volume of the adsorbed water appears to decrease with increasing clay concentration. However, the objection to the use of such a high value for v, applies here also.

In order to avoid the difficulties inherent in the conventional pycnometer technique, Low and Anderson (1958a) derived an expression for ow, the partial specific volume of water in a clay-water suspension in terms of e, the density of the suspension and c, the clay concentration. The expression is not based on any assumptions. It is

-

in which the subscript m indicates that the weight of clay is constant. A similar expression can be used to determine the partial specific volume of the clay. The partial specific volume of a component is the change in volume of the system per gram of added component at constant pressure, temperature, and composition. It is a differential quantity, whereas the apparent specific volume, if properly measured, is an average quantity. In the clay-water system the volume of the water may not be the same at all points of the system; hence, the partial specific volume of the water will be regarded as the volume per gram of water midway between the particles. Now when Low and Anderson plotted the suspension density against the clay concentration for three homoionic Wyoming bentonites, straight lines were obtained with intercepts on the ordinates at density values corresponding to that of pure water. Therefore, the necessary conclusion was that the partial specific volume of the water was the same at all concentrations of clay (up to 13 per cent by weight) as that of pure water. At the greatest clay concentration the average maximum distance of water from the particles was 84 A.

In an earlier paper Hauser and LeBeau (1938) reported that the apparent density of Wyoming bentonite clay in aqueous suspensions increased with clay concentration. They used the pycnometer technique and assigned the normal density to water. Their maximum clay concentration was 2 per cent by weight. Their conclusion was that the water must be compressed on the surface of the bentonite. But Martin (1960) re-examined their data in terms of Eq. (9) and found that their results agreed with those of Low and Anderson (1958a).

From their pycnometer evidence Low and Anderson (1958a) could conclude only that water in clay suspensions had the same partial specific


volume as normal water beyond about 84 A. from the clay surface. To study the partial specific volume of the water closer to the clay surface, they compressed a homoionic Wyoming bentonite gaste between a mercury piston and a stainless steel filter and observed the corresponding changes in volume of the paste and expressed water. The volumes of expressed water were converted to grams of expressed water. From the latter quantities and the initial water content of the paste, the grams of water in the paste at the different paste volumes were calculated. Then a plot was made of paste volume against grams of water in the paste. The slope of the resulting line at any water content equals the partial specific volume of the water at that water content. Again no assumptions are involved. For the Li, Na, and K bentonites that they worked with, the following conclusions could be drawn: (1) the partial specific volume of water is different from normal water out to distances in excess of 60 A.; (2) the partial specific volume increases continuously as the clay surface is approached; (3) within 10 A. from the clay surface the partial specific volume is as much as 3 per cent greater than that of normal water (ice has a specific volume only about 8 per cent greater); ( 4 ) as the temperature is lowered the partial specific volume of the water increases; (5) the exchangeable ions affect the partial specific volume of the water.

Confirmation for the partial specific volume results of Anderson and Low (1958) has been provided by the calculations of W. F. Bradley ( 1959). He used the unit cell dimensions, based on X-ray measurements, and the structural formula of montmorillonite in analyzed Wyoming bentonite to obtain a density for the clay laminas alone. The calculated density was 2.83. This value is slightly higher than the density of 2.78 which was calculated for another sample of Wyoming bentonite by Mackenzie (1959). It is also slightly higher than the value obtained by Low and Anderson (1958a) using Eq. (9) . Their value was 2.80 for Wyoming bentonite saturated with Na+, the predominant ion on the natural clay. Using his density value, and the data of DeWit and Arens (1950) and of Oakes (1958), Bradley calculated apparent specific volumes of the water by subtracting the volumes of the montmorillonite laminas present from the total volume. He found the apparent specific volumes of the water in the clay-water systems to be larger than the specific volume of pure water. At a clay concentration of 68.5 per cent the calculated apparent specific volume of water was 1.023, in good agreement with the partial speciiic volumes of 1.02 to 1.03 reported by Anderson and Low (1958) for comparable clay concentrations. At higher clay concentrations his calculated values rose as high as 1.33 cc. per gram.

292 PHILIP F. LOW

Using an air pycnometer, Nitzsch (1940) also found high apparent specific volumes for water adsorbed on a montmorillonite-rich clay. Ini- tially the apparent specific volume of the water was as high as 5.00 cc. per gram. As the water content increased to 8 per cent the apparent specific volume decreased to 1. However, as Martin (1960) points out, water can penetrate many spaces in a clay that exclude air; hence, it is probable that his values are too high.

Another method for determining the apparent specific volume of adsorbed water is to measure the C-axis spacing of an expanding mineral by X-ray analysis and multiply the value obtained by one-half the ex- perimentally determined surface area. The product is presumed to be the interlayer volume. This volume is divided by the weight of water present to determine its apparent specific volume. The author considers this method to be unreliable because all the water in the system, whether it is between the clay layers or in the interstices between the particles, is considered to be interlayer water. If any interstitial water is present, the calculated apparent specific volume will be too low. An additional complication is the difficulty in accurately measuring the surface area of the clay. And at water contents corresponding to a few monolayers, water “islands” may exist between clay layers. In this case the calculated apparent specific volume would be too high. Nevertheless, Martin (1960) used the X-ray and water content data of Mooney et al. (195213) and of Norrish (1954) to calculate the apparent densities of adsorbed water on montmorillonite. The values calculated from the data of Mooney et al., for water contents below 0.28 g. per gram of clay, were higher than that of pure water and increased with increasing clay concentration; whereas, the values calculated from the data of Norrish, for water contents above 0.37 g. per gram of clay, were lower than that of pure water and decreased slightly with increasing clay concentration. In terms of the apparent specific volume the converse would be true. Since the results obtained from the data of Mooney et al., agreed with those of DeWit and Arens (1950), and since the results obtained from the data of Norrish agreed with those of Anderson and Low (1958), Martin concluded that all the results were acceptable. Consequently he proposed, in effect, that the specific volume of water is less than that of normal water at water contents below about 0.3 g. per gram of clay and is greater than that of normal water at water contents above this value. Now it is not unreasonable to believe that, at low moisture contents, the exchangeable ions, being concentrated near the clay surface, would disrupt the water structure and lead to a closer packing of molecules. Indeed, this would be expected. But in view of the previous criticism of the work of DeWit and h e n s (1950) and the possible complicsstions in the X-ray method for


determining apparent specific volumes, Martin's conclusion cannot be accepted without serious reservations. In fact, the only evidence not based on questionable assumptions, namely, that provided by Anderson and Low (1958) and by W. F. Bradley (1959), argues against it. There- fore, in the following discussion we will regard the afore-stated conclusions of Anderson and Low as acceptable. However, we will not discount the possibility that for certain relatively dry systems the specific volume of the adsorbed water may be less than that of normal water, especially if the exchangeable ions are small and multivalent.

At this point let us consider the possible mechanisms of clay-water interaction in the light of the specific volume evidence cited thus far. Undoubtedly, water in the vicinity of clay surfaces is not a simple close- packed liquid. It must have a relatively open structure, a fact that suggests the presence of bonds with directional properties. In consequence, the London dispersion forces can be discounted as being of primary importance. Even though the ions infiuence the existing water structure, they are not responsible for it because the evidence is overwhelming that they decrease the specific volume of water, either by contracting the water structure or by breaking it down. Therefore, the only mechanisms that must still be considered as possibilities are the orientation of water molecules in the electric field of the clay plate and hydrogen bond formation between surface atoms and water with the consequent development of a coordinated water structure. The former mechanism will be considered first.

The molar potential energy, 8, of dipoles of polarizability, a, and dipole moment, p, in an electric field of intensity, E, was given by Low and Deming (1953). It is

in which N is Avogadro's number, E is the dielectric constant, k is the Boltzmann constant and T is the temperature. This equation is strictly applicable to nonassociated dipoles, but we will use it as an approximation. For water, the coefficient of E2 has the magnitude at 25" C. of 0.219 cc. per mole, assuming the normal dielectric constant. Therefore, for the molar energy in the electric field to equal the energy required to break a mole of hydrogen bonds (4.5 kcal.) the field intensity would have to be close to 2.8 volts per angstrom. Recall that the zeta potential, i.e., the change in voltage between the plane of shear and a point an infinite distance away, is usually only about 0.05 volt for the clay minerals. Despite the approximate nature of our calculations, it appears that the field strength in the diffuse part of the double layer would not be suf-

294 PHILIP F. LOW

ficient to break enough hydrogen bonds to orient the water molecules. This conclusion becomes more reasonable if one realizes that water is not oriented about an ion for more than a few molecular layers; the field intensity near an ion is much larger than near a clay particle. As a result, it is highly unlikely that the observed elevations of the partial specific volume can be attributed to molecular orientation in the electric field.

Additional evidence which dictates against the electric field being the causative factor is the observed trend (Anderson and Low, 1958) in the partial specific volume. Even at average interlayer distances as small as 20 A., this property was being augmented at a constantly increasing rate. There was no indication of disordered water midway between the layers, which is a necessary consequence of the electric field mechanism. It will be shown later that other evidence also argues against this mechanism.

Now let us evaluate the hydrogen bond mechanism in the light of the specific volume data. If this mechanism obtains, one would expect the adsorbed water to have a very open structure with the degree of openness increasing toward the surface where the degree of covalency of the bonds would be greatest. Such is the case. Moreover, one would expect the degree of openness to increase with a decrease in temperature, since fewer bonds would be disrupted at lower temperatures. Here also the expectation is realized. Further, as might be expected, the exchangeable ions influence the water differently. It appears, therefore, that a hydrogen-bonded water structure is attached to and propagated away from a clay mineral surface. Since there is no indication of a disordered region in the interlayer water, there must be no incompatibility between the molecular configurations induced by adjacent surfaces.

Recently Fripiat and associates ( 1960 ) presented evidence, obtained by infrared spectroscopy, that the 0-H stretching frequency of free water adsorbed on montmorillonite and vermiculite was decreased below that in normal water. The formation of hydrogen bonds is reported to decrease the O-H stretching frequency. Frohnsdorff and Kington (1958), also using infrared spectroscopy, showed that water is hydrogen bonded to zeolitic surfaces. And Mathieson and Walker (1954) determined from X-ray data that the water molecules are attracted toward the surface oxygens. These investigations lend credence to the hydrogen bond mechanism of clay-water interaction.

The point has been made by Bolt (1960) that the partial specific volume data of Anderson and Low (1958) can be explained by the compression of a relatively thin (0 to 10 A.) water layer near the clay surface. An expanded water layer of the proposed magnitude is unacceptable to him. Let us examine his explanation by considering AVe, the excess


volume change of the clay paste over that which would have occurred had the water possessed its normal specific volume. The appropriate equation is

I i

where & is the partial specific volume of the adsorbed water, u is the specific volume of pure water, w is the weight of water per gram of paste and the limits i and f refer to the initial and final water content, respectively. From the data of Anderson and Low (1958) for Na-bentonite, the first term on the right was obtained by graphical integration between the limits of 4 g. of water and 1 g. of water per gram of clay. Then the value of the second term on the right was subtracted from the value of the first. The result was 0.045 cc. At a water content of 1 g. of water per gram of clay, the observed partial specifk volume of the water was 1.029 cc. per gram. If the excess volume change had been confined to the gram of water closest to the surface, then the initial specific volume of this water must have been at least 1.029 + 0.045 = 1.074 cc. per gram, notwithstanding the high ionic concentration. The specific volume of ice is only 1.092. Therefore, if Bolt's explanation is correct, there is an adsorbed water layer about 13.5 A. thick (assuming surface area of 800 m.2 per gram) with a specific volume approximating that of ice; beyond this there is a sudden transition to normal water. It is more reasonable to believe that the change of specific volume is gradual and that near the surface the water is not so icelike.

Finally, let us estimate the degree of hydrogen bonding in the adsorbed water for a specific volume of 1.029 cc. per gram at 25" C. We shall assume that the adsorbed water has a structural arrangement similar to that in ice and ignore the effect of the ions. Using the equations of Grjotheim and Krogh-Moe (1954), the degree of hydrogen bonding turns out to be 55 per cent of the maximum possible. Their calculated value for pure water at 25" C. was about 36 per cent, and at 0" C. about 44 per cent. Thus, according to this calculation, there are more intact hydrogen bonds in the first gram of clay-adsorbed water at 25" C. than in pure water at 0" C.

VI. Viscosity of Clay-Adsorbed Water

Viscosity is a structure-sensitive property of a fluid. It depends on the bond type and coordination of the molecules. This fact is well illustrated by the work of Andrade (1934), Ward (1937), and Ewe11 and Eyring (1937), among others. Therefore, accepting the specific volume

296 PHILIP F. LOW

data of Anderson and Low (1958) and of W. F. Bradley (1959), it can be stated unequivocally that the water on the surface of Wyoming bentonite clay has a viscosity different from normal water out to distances in excess of 60 A. The same should be true for other clay minerals with comparable atomic arrangements. Further, if the proposed quasi-crystalline structure exists, the adsorbed water should have a greater viscosity than normal water. How great the viscosity elevation should be is still uncertain, but the experimental evidence suggests that it is significant.

Before discussing the experimental evidence, attention is directed to the electroviscous effect. The electroviscous effect is a retarding force on water moving through a narrow capillary. I t arises because the counterions in the electric double layer are swept downstream relative to the fixed charges on the surface. The resulting electric potential gradient acts on the ions in a direction opposite to the direction of water flow, retarding their movement and creating an electroviscous drag on the water (Elton, 1948a, b; Elton and Hirschler, 1949; Kemper, 1960). Al- ternatively, the electric potential gradient may cause electroosmotic flow in a direction opposite to the forward flow (Michaels and Lin, 1955). As will be seen, the electroviscous effect is very difficult to separate from the true viscous effect due to structural rearrangements in the water.

It is possible also that the electric field of the particle may have an effect on the viscosity, either by partially orienting the water molecules or by polarizing them so that the intermolecular bonds are strengthened. Following the work of Andrade and his colleagues ( Andrade and Dodd, 1946; Andrade, 1952; Andrade and Hart, 1954) we write

AT/T = f E 2

where Aq is the increase in viscosity due to an electric field of intensity, E, and f is the viscoelectric constant. The viscoelectric constant is of the order of 10-7 when E is expressed in electrostatic units. Therefore, for Aq/y to equal 10 per cent, E would have to be about 0.003 volts per angstrom. This voltage gradient may occur near the clay surface. How- ever, Andrade and his colleagues have shown that the viscoelectric effect in pure liquids is very small compared to the effect when dissolved ions are present. Therefore, it may be assumed that the viscoelectric effect is much smaller than the electroviscous effect.

Different investigators ( Macey, 1942; Winterkorn, 1955; Schmid, 1957) have observed that a plot of the water permeability of clay versus clay porosity yields a straight line until very low permeability values are reached. Then the plot curves toward the origin. If the straight portion of the plot is extrapolated, it intercepts the abscissa at relatively large porosity values. This behavior, and the inapplicability of conventional


flow equations to clays, was taken by these investigators as an indication of an immobile or highly viscous water layer on the particle surfaces which makes the effective porosity much less than the measured porosity. It should be noted that, if an immobile water layer of a given thickness is present, the permeability versus porosity plot should remain linear until it intersects the abscissa; whereas, if the viscosity of the water increases toward the surface, this plot should curve, as it does. This viscous layer, if present, could be due to a combination of structural, electroviscous, and viscoelectric effects.

In a paper by Olsen (1960), the concept is presented that the clay matrix is made up of clusters of clay particles with relatively large intercluster voids through which most of the water flow occurs. As the porosity is decreased by compression, the larger intercluster voids are supposed to collapse first. Then, as the dimensions of the intercluster voids approach those of the intracluster voids, the void space decreases more uniformly. Using this concept, Olsen predicts qualitatively the observed deviations from the Kozeny-Carman equation. The idea of clay clusters is similar to the domain idea of Aylmore and Quirk (1959, 1960). Now, an initially rapid decrease followed by a more gradual decrease in permeability with porosity is qualitatively consistent with Olsen’s concept. Consequently, the observed permeability versus porosity relationship cannot, by itself, be regarded as a reliable criterion for the presence of a surface water layer of high viscosity.

There is another aspect of water flow through clays which points more directly to the existence of the proposed layer of abnormal viscosity. At low hydraulic gradients the flow does not obey Darcy’s law, viz.,

K

r q r - i

where q is the flow rate per unit cross-sectional area, K is the permeability of the medium, q is the viscosity of the fluid, and i is the hydraulic gradient. Instead, there is a disproportionate increase in flow rate with increasing hydraulic gradient, i.e., the flow rate increases more rapidly with increasing gradient than the expected linear relationship predicts. This phenomenon was observed for water flow in sandstones contami- nated with clay by von Engelhardt and Tunn (1955). It was observed for water flow in pure and natural clays by Lutz and Kemper (1959). And it was observed by Hansbo (1960) for water flow in natural clays. Each of the above authors referred to other investigators who had made similar observations. The reports of the latter investigators were not available to the author. Apparently then, it is not uncommon for Darcy’s law to be violated in fine-grained material. Whether or not the law is

298 PHILIP F. LOW

obeyed depends upon the porous medium, its packing, and the hydraulic gradient. Neither von Engelhardt and Tunn (1955) nor Lutz and Kemper (1959) found obedience to Darcy's law at hydraulic gradients up to about 168 and 900, respectively, for sodium-saturated systems. However, Hansbo (1960) found that the law was obeyed above hydraulic gradients of about 5; Low (1959) found the same to be true above hydraulic gradients of 5000.

Kemper (1960) explained the disproportionate increase in flow rate with hydraulic gradient as being due to the electroviscous effect. As the hydraulic gradient increases, the counterions are supposedly swept out of the smaller constrictions in the medium with the result that their retarding effect is diminished. Martin (1960) explained the nonlinearity of flow with hydraulic gradient in terms of the unplugging of voids. But the work of von Engelhardt and Tunn (1955) dictates against both these explanations because their investigations showed that the nonlinearity obtained even for the flow of a 3.5 molal sodium chloride solution through sandstone. In such a concentrated solution the electroviscous effect would be absent. Also, the clay particles would be flocculated and, therefore, unable to move in the small pores. In addition, these investigators found the flow rate-hydraulic gradient relationship to be reversible. Reversibility would not be expected in the unplugging of voids. Note that, had the increase in hydraulic gradient caused a compression of the clay, the flow rate would have decreased with increasing gradient. It appears, therefore, that the most tenable explanation is the one offered by von Engel- hardt and Tunn (1955). They regard the water near the mineral surfaces as a non-Newtonian liquid whose viscosity is dependent on the shearing force. As the shearing force is increased, the water structure breaks down; as a result, the viscosity of the water decreases. Hansbo (1960) also sub- scribes to this explanation.

There is a crucial test of the elevated viscosity concept. If a threshold hydraulic gradient exists which must be exceeded before flow is initiated, then the water must have a yield point and structural resistance to flow. Before flow begins there is no movement of ions relative to the clay surface and, hence, no electroviscous effect; secondly, there is no particle movement with subsequent plugging or unplugging of the voids. For- tunately, this test has already been performed. Hansbo (1960) reported that Derjaguin and Krylov (1944), working with rigid ceramic filters, observed a threshold value of the hydraulic gradient below which flow did not occur. And Derjaguin and Melnikova (1958) referred to the same work in stating their case for the elevated viscosity concept. Dr. G. A. Leonards (private communication, December 20, 1960) has informed the author that the concept of an initial or threshold gradient for water


flow in clays is quite commonly accepted in Russia. Recently, Oakes (1959) discussed an experiment wherein a 6 per cent suspension of Wyoming bentonite about 30 cm. long was subjected to a head of 50 cm. of water for 6 weeks without any detectable flow. Other experiments that he performed gave similar results.

On the basis of studies such as those in the preceding paragraphs the author recommends, following Hansbo (1960), that for water flow in close-packed clays at hydraulic gradients above a certain limit the flow equation be written in the form

( i - io) q = - K

r where i, is the intercept of the extrapolated linear portion of the q versus i plot with the abscissa. At gradients below the afore-mentioned limit, q would be a more complex function of i. Hansbo suggested a simple exponential function, but, in the opinion of the author, the exact form of this function must await further investigation. It is probable that flow in films in dry soils would also obey these equations.

Michaels and Lin (1954) conducted experiments on the permeability of kaolinite. Kaolinite, initially packed in water, was desolvated with as little particle rearrangement as possible by displacing the water with dioxane, acetone, and dry nitrogen in sequence. Then the permeability of the clay to nitrogen was measured and compared with its original permeability to water. The permeability to nitrogen always exceeded the water permeability by at least 40 to 60 per cent. When the kaolinite was initially packed in an organic liquid and was subsequently desolvated with dry nitrogen, its permeability to the gas was essentially the same as its original permeability to the organic liquid. I t is interesting to observe that von Engelhardt and Tunn (1955) reported the water permeability of their sandstone to be much less than the air permeability, but the air permeability and the permeability to organic solvents were nearly the same. Michaels and Lin attributed the relatively small permeability in water to the electroviscous effect. However, in a subsequent paper (Michaels and Lin, 1955) they calculated the permeability reduction due to this effect and found it to be only about 5 per cent. Further, they eliminated the electric double layers of the particles, and thereby the electroviscous effect, by successively increasing the salt concentration of the permeant water. The maximum permeability increase was only about 10 per cent. Consequently the relatively low water permeability of the clay cannot be attributed entirely to the electroviscous effect. Increased structural viscosity must also have been a contributing factor. Yet, neither the electroviscous effect nor the “struc-

300 PHILIP F. LOW

tural" effect seemed to account for the wide differences in kaolinite permeability observed when the clay was packed in different liquids and then permeated by them. The authors attributed these differences to differences in particle arrangement.

Low and his co-workers have utilized the activation energy concept to elucidate the viscous nature of water in clays. Low (1959) replaced q in Eq. (13) by its equivalent from Eq. (3) to obtain

q = - .i e - E / R T

B in which B is a constant and E, the activation energy, has replaced AH' because there should be no volume change involved in the process of flow. Then, to obtain the activation energy for the viscous flow of water through a paste of Wyoming bentonite (containing 55 per cent solids), he plotted the logarithms of observed values of q at constant i against the corresponding values of 1/T. As is evident from Eq. (15), the slope of the resulting line equals -EJR. The activation energy value so obtained was equal to 4350 cal. per mole after 3 weeks of clay-water contact. The activation energy for the viscous flow of normal water in the same temperature range is 3850. These values are approximations. They could be off by as much as 100 cal. per mole. Nevertheless, it is evident that the activation energy for flow in the clay is about 500 cal. per mole greater than that in pure water. And since, in the experiment, the clay was confined in a stainless steel cylinder between stainless steel filters, it is unlikely that any streaming potential developed. According to the equations of electroviscosity (e.g., Elton, 1948a; Michaels and Lin, 1955), the electroviscous effect is absent when the streaming potential is zero. Therefore, the increase in activation energy for water flow in the clay can be ascribed to enhanced structural viscosity.

The conclusion just stated is consistent with the following observations: ( 1) the activation energies for exchangeable ion movement (Low, 1958a) are directly correlated with the partial specific volumes of the adsorbed water (Anderson and Low, 1958) on the same clays; (2) the activation energies for exchangeable ion movement are directly correlated with the unfrozen water at -5" C. (Kolaian, 1960) on the same clays; and (3) the activation energies for exchangeable ion movement have essentially the same values as the activation energies for deuterium oxide diffusion (Dutt, 1960) in the same clays. The interrelationships of these observations have been discussed in two recent articles (Low, 1960a, b). All the ionic activation energies for movement in the clay were greater than those for movement in pure water. Evidently, the adsorbed water properties, as manifested by measurements of partial specific


volume, resistance to freezing, and self-diffusion, govern the movement of the adsorbed cations. This is in keeping with the concept that a coherent, hydrogen-bonded water structure exists in the neighborhood of clay surfaces. The ease of ionic movement through this structure should depend on the viscous resistance it offers.

Martin (1960) has criticized the foregoing activation energy data on the basis that K , the permeability of the clay, and A S , the entropy of activation, may change with temperature. He maintains that these changes would be included in E, the activation energy term. But if these quantities change with temperature and are included in E, K must be an exponential function of 1/T and A S must be a linear function of 1/T (see Eqs. 3 and 15); otherwise a straight line would not be obtained on plotting log 4 against 1/T. Similar considerations would hold for the ionic activation energy data. There is no evidence for the necessary functional relationships. Further, if such functional relationships did exist, the correlation between the experimental values of E and the other water properties would remain to be explained. Therefore, the author contends that, although both K and A S may change slightly with temperature, they do not change suffciently to invalidate the results.

Accepting Low’s (1959) data on the activation energy for viscous flow of water in Na-bentonite as being reliable, we can estimate the degree of hydrogen bonding in this water. The assumption is made, in keeping with the previously mentioned ideas of Ewe11 and Eyring (1937) and of Wang (1951a), that the activation energy equals the energy required to break hydrogen bonds. The number of hydrogen bonds per molecule is, therefore, 4.35/4.5 = 0.97. Recall that each hydrogen bond is shared by two molecules so that, energywise, the number of hydrogen bonds formed by a 4-coordinated molecule is 2. As a result, we may say that 100 x 0.97/2 = 48 per cent of the bonds are unbroken. Using the same method of calculation, we arrive at a figure of 43 per cent for the fraction of unbroken bonds in pure water. Earlier, on the basis of specific volume calculations, we estimated that 55 per cent of the hydrogen bonds were unbroken in the adsorbed water. This figure represented an increase of 19 per cent over that for pure water. The activation energy value is for a water content of 45 per cent; whereas the specific volume value is for a water content of 50 per cent. Both water contents are expressed on a wet weight basis. Although these values are to be regarded as approximations at best, they do suggest an increased degree of hydrogen bonding in the water adjacent to the mineral surfaces.

Rosenqvist (1955) studied the diffusion of deuterium oxide through clay pastes. To correct the observed diffusion coefficients for the path tortuosity, he assumed that all particles were at an angle of 45 degrees

302 PHILIP F. LOW

with the direction of diffusion; the correction factor for a water content of 40 per cent by volume was, therefore, d3/0.40. This correction factor should be valid for randomly arranged particles. It would be in error if particle orientation exists. When the observed diffusion coefficients were multiplied by the correction factor they were of the order of 0.1 to 0.2 cm.2 per day. But the diffusion coefficient for deuterium oxide in pure water is about 3 cm.2 per day. Hence, the diffusion coefficient of the water in the clay voids was only about 5 per cent of that of normal water. The relationship between diffusion and viscosity is apparent from Eqs. (4 ) and (6) . Rosenqvist made the reasonable conclusion that the water in the clay was more viscous than ordinary water.

In a later paper Rosenqvist (1959) presented a graph of the average viscosity of water in a clay paste against the water content of the clay on a dry weight basis. The viscosities were calculated from self-digusion measurements such as the one described in the preceding paragraph. The graph shows a gradual decrease of viscosity from above 153 centipoises at water contents less than 10 per cent to 24 centipoises at a water content of about 30 per cent. The viscosity is represented as approaching that of pure water (near one centipoise) at water contents of 50+ per cent. The latter water content corresponds to an average film thickness of about 40 A. This thickness was calculated from the water content and the clay surface area, which was reported in the earlier (1955) paper to be 130 m.2 per gram.

Rosenqvist (1955) also measured the activation energy for deuterium oxide diffusion through a clay paste using an equation of the form of Eq. (2 ) . His measured activation energy was 11,500 cal. per mole. How- ever, the author is inclined not to accept this value because the diffusion experiment involved the evaporation of the deuterium oxide from the moist clay surface. The activation energy for evaporation from the clay, which may have been the rate limiting step, should have approximated the heat of vaporization. In the range of his experimental temperatures, namely, 14" to 43" C., the heat of vaporization of pure water is 10,500 cal. per mole. Recall that the activation energy for the viscous flow of pure water, which should be nearly the same as the activation energy for self- diffusion, is only about 3850 cal. per mole. If Rosenqvist's experimental value is accepted as valid, the activation energy for water diffusion in the clay is greater than the activation energy for the diffusion of water molecules in ice.

Recently, Pickett and Lemcoe (1959) presented the results of a radio- frequency spectroscopy study of water adsorbed on kaolinite and homoionic Wyoming bentonites. They reported that the width of the absorption curve at half amplitude is a measure of the intensity of intermolec-


ular bonding and, hence, of viscosity. This width was called the line width. The line width was plotted against moisture content on a dry weight basis. For kaolinite the line width decreased uniformly with increasing moisture content to a nearly constant value at 10 per cent moisture; whereas, for the bentonites the line width decreased uniformly with increasing moisture content to a nearly constant value at about 50 per cent moisture but continued to decrease slightly thereafter. Pickett and Lemcoe concluded that the viscosity of water near clay surfaces is greater than that of free water and that it decreases uniformly with distance from the clay surface. If we take the surface areas of the kaolinite and bentonite to be 15 and 800 m.2 per gram, then the films of elevated viscosity were at least 66 A. and 8 A. thick, respectively. The sensitivity of the method precludes reliable interpretation of the data at higher moisture contents.

Now, if water in the vicinity of clay surfaces has a quasi-crystalline structure as postulated, its flow properties should be as follows: (1) it should have a yield value leading to a threshold hydraulic gradient below which flow will not occur; (2 ) after flow commences there should be a range of hydraulic gradients over which non-Newtonian flow occurs, i.e., the viscosity should be dependent on the shearing force; ( 3 ) the viscosity should increase with proximity to the clay surface; and (4) near the clay surface the viscosity of the water should be greater than the viscosity of free water. The experimental observations described in this section are in complete harmony with these requirements.

VI 1. Dielectric Properties of Clay-Adsorbed Water

Before considering the experimental data, a very brief summary of the pertinent equations will be presented. These equations are due largely to Debye (1945), but they have been taken from various sources. The dielectric constant, E ~ , in a static electric field is given by

4x E

E s = l + - P

where E is the field strength and P is the polarization induced by the field per unit volume of dielectric. The polarization is made up of: (1) the distortion of electronic distributions within atoms and of atoms within molecules, which is called distortion polarization and ( 2 ) the partial orientation of permanent electric dipoles, which is called orientation polarization. The distortion polarization occurs instantaneously whereas the orientation polarization requires time. If measurements are made in an alternating electric field of low frequency the dipoles will

304 PHILIP F. LOW

have time to rotate in each half cycle; but as the frequency increases the molecules will have less and less time to rotate. Eventually, depending on the viscosity and temperature, a frequency will be reached at which the molecules have insdcient time to rotate. Then the polarization will decrease and the dielectric constant will fall. The fall of dielectric constant with increasing frequency is called anomalous dispersion. The dielectric constant, E, in the region of anomalous dispersion is given by

where w equals 2xv in which Y is the frequency of the alternating field, t is the relaxation time as before and i is the operator qx. From the equation it is evident that E~ is the dielectric constant at very high frequencies. For water has a value near 80 and E~ has a value near 5.0. Alternatively, the dielectric constant in the region of anomalous dispersion is

where E‘ is the real and E” is the imaginary part, respectively. The values of E’ and E” can be obtained from measured dielectric constants. In the region of normal dispersion e”, which is a measure of the “dielectric loss,” is very small; whereas, in the region of anomalous dispersion E” increases rapidly to a maximum and then falls off. The relaxation time is related to the frequency, vm, at which the masimum occurs by the equation

E = E’ - iE” (18)

- _ - - Ea + 2xvm (19) t & + 2

Cownie and Palmer (1952) showed that the dielectric constant of a natural clay, at a frequency of 430 Mc./sec., increased with increasing water content. Later Palmer (1952), using a formula for calculating the dielectric constant of a mixture from the dielectric constants of its con- stituents, calculated the average dielectric constant of the water in this clay at different moisture contents. The average dielectric constant increased from a value of about 5 at near zero moisture to a value of about 80 at 80 to 100 per cent moisture (dry weight basis). If Palmer’s calculations are correct, the average relaxation time of the molecules must have decreased as successive layers of water were added. Either the ions associated with the clay or the clay surfaces or both reduced the rotational freedom of the adsorbed water.

In another paper Palmer et al. (1952) separated mica plates by thin films of water. They observed that the dielectric constant, at 2 Mc./sec., decreased with the thinness of the film from more than 20 for films about

PHYSICAL CHEMISTRY OF CLAY-WATER INTI%RACTION 305

5 p thick to less than 10 for films about 2 11 thick. They also used a frequency of 2.5 kc./sec. The dielectric constant at the lower frequency was approximately double that at the higher frequency. A check showed that the dielectric constant of the mica alone remained constant at these frequencies. They concluded that the water was acting like “liquid ice” because ice is frequency-sensitive in this range. This conclusion is plausible. The anomalous dispersion of free water occurs at much higher frequencies-of the order of 3 x lo4 Mc./sec. From the work of Hasted and associates (1948) and the expected ionic concentrations between the plates, it is safe to conclude that the mineral surfaces and not the ions were responsible for these results.

The dielectric properties of water on talc, kaolinite, metahalloysite and halloysite at different relative humidities were studied by Muir (1954) in the frequency range 2.5 kc./sec. to 25 Mc./sec. This frequency range is far below that for the anomalous dispersion of free water. He plotted measured values of E” against the frequency of the alternating field. It was pointed out by Muir that the maximum in E” i.e., the maximum dielectric loss, is proportional to the number of absorbing molecules and that Y,, in keeping with Eq. ( 5 ) and (19), depends on the strength of the binding forces preventing the orientation of the dipoles in the alternating field. The following are Muir’s observations.

Talc: A single maximum in dielectric loss at 10 kc./sec. which increased in height through the humidity range of 0 to 80 per cent.

Kaolinite: Two maxima, one which remained at 10 kc./sec. and increased in height through the humidity range of 0 to 30 per cent and another of constant height which moved to higher frequencies with increasing relative humidity.

Metahalloysite: A single maximum which came into the frequency range of the experiment at 20 per cent relative humidity and moved, with increasing height, to higher frequencies as the relative humidity was increased until, at saturation, a v, of 10 Mc./sec. was reached.

The results for halloysite were similar to those for metahalloysite. Since talc has only oxygen surfaces and kaolinite has both oxygen and hydroxyl surfaces, Muir concluded that the stationary loss maximum, which occurred at the same vnl for both minerals, was due to the water on the oxygen surfaces, And we may add that the lower value for this maximum indicates, in keeping with the prediction of Section IV, that water is adsorbed with greater intensity on the oxygen surfaces. Muir attributed the moving maxima for kaolinite and the halloysites to the water on the hydroxyl surfaces. The constancy in height of the moving maximum for kaolinite was attributed to the fact that dielectric loss was occurring only in the initially adsorbed water layer; the moving of this

306 PHILIP F. LOW

maximum to higher frequencies with increasing water content was attributed to interaction of the outer layers with the first. Such interaction is indicative of cooperative bonding between layers. Following Muir’s reasoning, one would conclude that the increase in dielectric loss at constant v, for water on the oxygen surfaces of talc and kaolinite was due to successive increments of water being bonded with the same intensity; further, one would conclude that the increase in dielectric loss and in v, for water on the halloysites was due to successive increments of water being bonded with less intensity. But the water adsorbed on all the clay surfaces had a much lower value for Y,, and hence a much longer relaxation time, than does free water, In fact, the v,,, for water on the oxygen surfaces and for initially adsorbed water on the hydroxyl surfaces was about the same as that for ice at -5’ C., namely, 7 kc./sec. According to Muir, the number of water layers adsorbed on the minerals at the maximum relative humidities varied from 3 for kaolinite to 10 for metahalloysite. Thus, Muir showed that water in the vicinity of these mineral surfaces has less freedom than normal water.

Recently, Goldsmith and Muir (1960) extended the range of frequencies in the dielectric loss experiment to 0.09 kc./sec. They showed that the extended E” versus frequency curves were compatible with those obtained earlier for the same minerals. In addition, they also measured the dielectric properties of the adsorbed water before and after a pre- heating of the clays. And clays saturated with different cations were used. On the basis of the evidence obtained, they concluded that the adsorbed water is more ordered in the presence of the smaller exchangeable cations. Also, it is more ordered when the exchangeable cations are buried in the hexagonal cavities of the lattice by heat treatment than when they are implicated in the water layer. These conclusions are consistent with the ones derived from solution studies.

VIII. Supercooling and Freezing of Clay-Adsorbed Water

The effect of clay particles on the supercooling of water is difficult to ascertain. The reason for this is the uncertainty regarding the extent of supercooling in pure water. It is extremely difficult to rid water com- pletely of all foreign particles which might act as crystallization nuclei. And if water is in contact with any solid surface, particles adhering to the surface or the surface itself may influence the degree of supercooling. In order to eliminate the possible effect of solid surfaces, many investigators have studied the freezing of small water droplets suspended in air or in immiscible liquids. In the opinion of the author, the latter technique may not entirely eliminate the surface effect. The droplets are


usually of the order of 1 p in diameter, and there is ample evidence (Hen- niker, 1949; Adamson, 1960) that surfaces can influence liquid properties over such distances. The difficulties encountered in determining the degree of supercooling of water have been reviewed recently by Mossop (1955), Mason (1957), and Langham and Mason (1958). It is conceded by these investigators that pure water will supercool to 4 0 ' C. Con- trary to the popular belief, supercooled water is rather stable. Its freezing is not initiated readily by mechanical disturbance ( Dorsey, 1948).

Accepting, for the present, d o o C. as the temperature of spontaneous freezing for pure water, we will now consider the effect of clay on its supercooling. I t is known (Kumai, 1951; Isono, 1955) that clay particles occur frequently at the center of snow crystals. But this does not neces- sarily mean that the particles act as crystallization nuclei. Instead, by reason of their adsorptive properties, they may collect the water vapor into droplets which freeze subsequently when conditions are right. Never- theless it does appear that certain clay particles do nucleate supercooled water and cause it to freeze. In an interesting study Mason and May- bank (1958) introduced mineral particles as fine dust into a cloud cham- ber containing a supercooled cloud and noted the number of ice crystals formed as a result. The mineral particles were tested for their ice-nucleating ability at successively higher temperatures to determine a threshold temperature above which they were not effective. At least six tests were made for each kind of mineral particle. Part of their results are shown in Table 11. Although the threshold temperatures for montmorillonite and quartz were not given, the authors noted that these minerals were ineffective as freezing nuclei even at -25' C. Apparently,

TABLE I1 Substances Initially Active as Ice Nuclei at Temperatures Above -18" C.@A

Substance structure Lattice parameters temp. ( '(2.) Crystal Threshold

~

P-Tridymite Hexagonal a = 5.03, c = 8.22 -7 Kaolinite Triclinic a = 5.16, b = 8.94, c = 7.38 -9 Microline -9.5 Gibbsite -11.0 Halloysite Monoclinic a = 5.16, b = 8.94, c = 10.1 -13.0 Biotite -14.0 Vermiculite Monoclinic a = 5.34, b = 9.20, c = 28.9 -15.0 Phlogopite -15.0 Anorthoclase -17.0 Ice Hexagonal a = 4.52, c = 7.37 -

0 Data from Mason and Maybank (1958). b Samples inactive above -18" C. include: monimorillonite, sepiolite, albite,

muscovite, orthoclase, talc, quartz, and P-tridymite.

308 PHILIP F. LOW

particle size has little effect on the threshold temperature. Two ranges of particle sizes were used for kaolinite, namely, 0.2-0.5 p and 5-10 p. No difference in threshold temperature was detected.

The reason for the difference in ice-nucleating ability of the various mineral particles is unknown. It was noted by Mason (1958) in another article that the most effective particles, including non-clay materials, are hexagonal crystals in which the lattice spacing in the a dimension, which is important for epitaxy on basal faces, differs from that of ice by less than 16 per cent. However, as he pointed out, kaolinite and montmorillonite have nearly identical lattice spacings. Yet one nucleates water at -9" C. and the other at less than -25" C. The fit between the mineral and ice lattices must not be the only important factor. In this regard it should be noted, however, that other results (Mason, 1957) showed both a Georgia kaolin and a Montana bentonite to have a threshold temperature within a degree of -22" C. If there is a difference in ice-nucleating ability between kaolinite and montmorillonite, the difference may be due to the exposed hydroxyl surface of the gibbsite layer in the former. Note that the threshold temperatures of kaolinite and gibbsite are comparable. Recall also that the dielectric properties of the adsorbed water were not the same on hydroxyl surfaces as on oxygen surfaces.

An interesting feature reported by Mason and Maybank (1958) was the preactivation of clays by a preliminary freezing of their adsorbed water. If, thereafter, the temperature of the clay particles was not raised above 1 " C., the threshold temperature for subsequent freezings was much higher than the original one. For instance, preactivation raised the threshold temperature from less than -25" C. to -10" C. for montmorillonite. It raised the threshold temperature from -9" C. to 4" C. for kaolinite. The reason for the preactivation is not known, but it may be the result of the retention of ice embryos in surface cracks (Turnbull, 1950).

In the author's laboratory J. H. Kolaian (1960) determined the temperature of spontaneous freezing, i.e., the threshold temperature, for water in Wyoming bentonite pastes containing 65 per cent water. A thermocouple, connected to a potentiometric recorder, was inserted in the clay paste which was cooled uniformly in a refrigeration bath. A sudden rise in the thermocouple temperature indicated the initiation of freezing. The temperature immediately preceding the sudden rise was regarded as the temperature of spontaneous freezing. Regardless of the ion on the clay, this temperature was always in the range -5°C. to -7" C. More than forty determinations were made. The temperature of spontaneous freezing for deionized water was in the same range. His logical conclusion was that an active foreign freezing nucleus contained


in the water was responsible. These determinations illustrate the difficulty in obtaining reliable information on the nucleating ability of clays.

Earlier J. M. Deming (1951) studied the effect of Wyoming bentonite clay on the supercooling of water. Except for one graph in a review article by Low (1958b) his results have not been published. The reason for not publishing is that his data do not allow a clear-cut separation between the effects of zeta potential and solution concentration on the degree of supercooling. To make the zeta potential of the particles in each suspension diflerent from that in every other suspension, the suspensions were made up in solutions of different salt concentration. Never- theless, the data are pertinent to this discussion and will, therefore, be reviewed. Deming placed homoionic clay suspensions, containing about 2 per cent clay by weight, in centrifuge tubes which were immersed in a refrigeration bath at -5" C. If a suspension did not freeze in 12 hours it was diluted with the salt solution originally used in preparing it. Then it was returned to the bath for an additional 12 hours. Dilution of the clay (but not the salt) in the suspension was continued at 12-hour in- tervals until the suspension froze. The concentration of clay in suspension at the time of freezing was measured. The zeta potential of the particles in a duplicate suspension was also measured. In general, the higher the zeta potential of the particles, the more the clay had to be diluted before freezing occurred. This fact suggests that an increase in ion dissociation from the clay surface altered the vicinal water structure so that it became less susceptible to nucleation by foreign freezing nuclei; therefore, the particles had to be moved farther apart in order to reduce their influence on the intervening water.

Very little information is available on the rate of freezing of clay- water systems. Kolaian (1960), in his studies on the freezing of suspensions of Wyoming bentonite, observed that the suspensions took longer to freeze after setting for a while (gel state) than immediately after stirring (sol state). He followed the freezing process by means of a thermocouple inserted in the suspension and connected to a potentiometric recorder. The length of the plateau in the temperature versus time curve was taken as an indication of the time required for freezing. Table I11 is taken from his thesis. Evidently, the water takes longer to freeze when thixotropy obtains. Possibly the transition from water to ice is hindered by a water configuration which either develops with or is responsible for thixotropy. More will be said of this later.

Not all the water in a clay-water system freezes after freezing is initiated. Buehrer and Rose (1943) determined the amount of water remaining unfrozen in Pima clay at 3" C. by the dilatometer technique. They showed that more water remained unfrozen when the clay was

310 PHILIP F. LOW

puddled than when it was unpuddled. In the former state the water would be more intimately associated with the surfaces. More water remained unfrozen after the removal of free salts from the clay than before; hence, the free salts were not responsible for the lack of freezing. Buehrer and Rose calculated that the free salt could lower the freezing point of less than half the water to the temperature of the experiment. However, the exchangeable ions did influence the amount of unfrozen water. In one experiment the Pima clay was saturated with different ions and then the unfrozen water was measured on the homoionic clays. When the moles of unfrozen water per gram-ion of cation was plotted against the surface potential of the ion, a straight line was obtained. However, reasonable estimates of the extent of ion hydration precluded the belief that the ions alone prevented freezing. Buehrer and Rose concluded that the clay surface also plays an important role in the process.

TABLE I11 The Effect of Thixotropic Development on the Rate of Freezing of

Bentonite Suspensions@

Freezing time in minutes Per cent clay Clay tVpe in suspension Sol state Gel state

Li-clay Naelay K-clay

5.9 11.3 12.3

3 3 2

12 8 6

0 Data from Kolaian (1960).

In another paper Buehrer and Aldrich (1946) studied the unfrozen water in pastes of kaolinite and bentonite, the latter being from Otay, California. Very little water remained unfrozen in the kaolinite. For instance, at about 75 per cent moisture (dry weight basis) approximately 3 per cent of the water remained unfrozen. Assuming a surface area of 15 m.2 per gram, this weight of water corresponds to a film 15 A. thick. Approximately 97 per cent of the water remained unfrozen in the bentonite up to a water content of about 75 per cent (wet weight basis). Above this water content there was a sudden drop in the percentage remaining unfrozen, e.g., at a water content of 90 per cent only about 10 per cent of the water remained unfrozen. It is of interest to note that the sudden drop in the percentage of unfrozen water corresponded to the water content at which the gel to sol transformation occurred. As- suming a surface area of 800 m.2 per gram of clay, the thickness of the unfrozen film at a water content of 75 per cent was 36 A. Now the base exchange capacities were 3.3 and 88.5 me. per 100 g. for the kaolinite and montmorillonite, respectively. A simple calculation shows that the exchangeable cations, dissolved in the unfrozen water, were sufficiently


concentrated to prevent freezing at -3" C. in the case of the kaolinite but not in the case of the montmorillonite. In the latter case the freezing point depression due to salt would be only about 0.5" C. Here again we have a difference in the effect of the two minerals on the freezing properties of water.

Hemwall and Low (1956) used the dilatometer technique of Buehrer and Rose (1943) to determine the unfrozen water at -5" C. in four different samples of Wyoming bentonite, namely: a Na-bentonite, a silaned Na-bentonite, a Na-Th-bentonite and a Th-bentonite. An X-ray analysis of these bentonites disclosed that the silane had coated only the external surfaces of the treated clay, rendering them hydrophobic and leaving the internal surfaces unaffected; the Th4+ had bonded the crystal layers together so that only external surfaces were accessible to water; the remaining two clays exhibited normal behavior. Thus, the characteristics of the silaned Na-bentonite and of the Th-bentonite permitted water interaction with internal surfaces to be distinguished from water interaction with external surfaces. The zeta potentials of the different bentonite particles in the suspending solutions were also determined. They were: -35 mv. for the Na-bentonite, -17.6 mv. for the Na-Th-bentonite, and $53.8 mv. for the Th-bentonite. The silaned clay had zero electro- phoretic mobility. From the zeta potential values one can deduce that cation dissociation from the clay surfaces was in order Na+ > Na+- Th4+ > Th4+. At a water content of 85 per cent (wet weight basis) as much as 22 per cent of the total water remained unfrozen in the Na- bentonite. This weight of water corresponds to a film 15 A. thick. Since the exchange capacity of the clay was 1.05 me. per gram, the cation concentration in the unfrozen water was not sufficient to prevent freezing at -5" C. The unfrozen water on the Na-bentonite was from two to three times that on the silaned Na-bentonite, depending on the moisture content. Further, the unfrozen water on the Th-bentonite was about the same as that on the silaned Na-bentonite. These results indicate that external surfaces are much more efficient in preventing the freezing of water than are internal surfaces. The unfrozen water on the three non- silaned clays decreased in the same order as the cation dissociation, suggesting that when the cations are close to the surface the water is less resistant to freezing. Possibly the reason that external surfaces prevent freezing better than internal surfaces is that, owing to the relative proximity of the latter, the ions dissociate less from them. This idea receives additional support from the observation that, as the interlayer and inter- particle distances increased in reponse to the addition of water, the total amount of unfrozen water also increased. On the basis of these results and those from the supercooling study of Deming (1951) it is proposed

312 PHILIP F. LOW

that, as the ions dissociate from the mineral surface, competition between their disordering influence and the ordering influence of the surface atoms is lessened with the result that a more ordered water structure develops. The reasons why such a structure should prevent freezing are discussed in the following paragraph.

I t is possible that the lack of freezing could be due to curved ice- water interfaces in wedges between adjacent, nonparallel surfaces. Sill and Skapsi (1956) have shown that curved solid-liquid interfaces do exist under such conditions. The freezing point depression, AT of the water in these wedges is given by the Kelvin equation, i.e.,

where To is the freezing temperature of the water under a flat surface, 6 is the interfacial tension between water and ice, e is the density of ice, T is the radius of curvature of the ice-water interface, and L is the heat of fusion. According to this equation, the ice front should penetrate farther toward the apex of the wedge as the temperature drops. How- ever, the Kelvin equation, with the customary values for o and L, does not explain the direct corrsepondence between activation energies for ion movement in bentonite-water systems and the amounts of unfrozen water at -5" C. in the same systems. Kolaian (1960) measured the unfrozen water in homoionic pastes of Wyoming bentonite by a calorimetric technique. The amount of unfrozen water depended on the exchangeable cation and ranged from 41 to 55 per cent of the total water present. The pastes contained 65 per cent water (wet weight basis). As before, the exchangeable ions could not account for the water remaining unfrozen. When the activation energies for exchangeable ion movement were determined in the pastes, the afore-mentioned relationship between activation energies and unfrozen water was observed. Undoubtedly, the adsorbed water structure affected both ion movement and freezing. If the Kelvin equation is still to be invoked, it would be logical to ascribe the differences in the amounts of unfrozen water on the different homoionic clays to differences in (r or L. As the water became more or less ordered in response to a change in the cationic suite on the surface, 0 and L would have changed, probably in opposite directions. At this point it is important to note that the clay-adsorbed water does not have the structure of ice, If it did, this water would act as a perfect crystallization nucleus and the water in the system would not supercool; nor would it remain unfrozen at subzero temperatures. For the montmorillonite, at least, it may be supposed that an increase of order in the adsorbed water produces an increase in o. An increase in order would also lower the heat


content of the water, bringing it closer to that of ice; hence, L would decrease. But the Kelvin equation may not be applicable here at all. Babcock and Overstreet (1957) have shown that the electric field of the particle can lower the freezing point of the nearby water. In fact, it can be shown thermodynamically that the freezing point of water is lowered by any force field, long range or intermolecular, which lowers the potential energy of the water relative to that of ice. The potential energy of the water molecules in an ordered structure should be less than in a disordered structure.

Elevated hydrostatic pressures existing close to the mineral surfaces, by reason of adsorptive forces, cannot account for the unfrozen water. Some of the water which remains unfrozen at -5" C. can be squeezed from the clay at pressures of 10 to 15 atmospheres. Added pressure on both phases, ice and water, lowers the equilibrium freezing temperature by only 0.0075" C. per atmosphere. Regardless of the causative factor, the freezing point of the water must become lower as the surface is approached. Love11 (1957) showed that the unfrozen water in a soil clay decreased continuously with decreasing temperature. At a temperature of -24°C. the unfrozen moisture amounted to 13 per cent on a dry weight basis.

It should not be inferred that the structure of the unfrozen water is rigid. Leonards and Andersland (1960) have shown that the electrical resistance of a clay soil mixed with a 0.25 N solution of LiI increases continuously with the percentage of total moisture frozen. The frozen moisture was determined calorimetrically. When 18 per cent of the total moisture was frozen (4" C.) the electrical resistance was 1500 ohms; when 45 per cent of the total moisture was frozen (-16" C.) the electrical resistance was 14,000 ohms. An interesting feature of their data was that the electrical resistance at any temperature was different on the cooling and warming curves. The relatively low resistances observed by them indicate that the ions were quite mobile and, therefore, that the unfrozen water retained considerable fluidity.

In concluding this section of the paper, attention is called to the work of Rosenqvist (1959), who studied the cooling curves of an illitic clay down to extremely low temperatures. When the moist clay was immersed in a dry ice-toluene mixture at -78" C. there were several small irregularities in the temperature versus time curve showing that exothermic reactions (probably freezing) were taking place. But when the same moist clay was immersed in liquid air at -185" C. the cooling curve was smooth. In the latter case the intense cold must have transformed the water to a glassy state which is known to occur on quick-freezing. Ap- parently, Kato (1959) also observed water-ice transitions in clay at

314 PHILLP F. LOW

subzero temperatures. He made a differential thermal analysis of montmorillonite and other clay minerals down to -195" C. by using dry ice and liquid nitrogen. Montmorillonite gave three peaks, one at each of the following temperatures: A", -7", and -20" to 3 0 " C. Attapul- gite, nontronite, vermiculite, and endellite gave three peaks similar to those for montmorillonite; whereas, kaolinite, illite, and alumina gave only one peak at -2" to -5". Here again we observe a difference between montmorillonite and kaolinite in their effect on the freezing of water, The former is conducive to more supercooling and less eventual freezing than the latter.

IX. Thermodynamic Properties of Clay-Adsorbed Water

Thermodynamics is concerned with changes in certain properties of a system such as the free energy, heat content, entropy, etc. It has nothing to do with the mechanism by which these changes are brought about. We are concerned here largely with the mechanism of clay-water interaction. Although thermodynamics cannot be expected to provide this mechanism, it can assist us in selecting between alternative mechanisms. In fact, we have already used thermodynamics for this purpose. In this section we shall consider some of the thermodynamic properties of the adsorbed water. Then we shall attempt to interpret these properties in terms of a suitable mechanism.

The work of adhesion between a solid and a liquid is defined as the work necessary to separate the liquid from the solid by pulling them perpendicularly from each other against the adhesive forces between them. The work of adhesion can be determined from the surface tension of the liquid and the contact angle between liquid and solid (Adam, 1941). If the liquid attracts the solid as much as it attracts itself, the contact angle is zero. As the adhesion between liquid and solid decreases, the contact angle increases. Enright and Weyl (1950) determined the initial contact angles between water and thin dried films of homoionic Wyoming bentonites. They also determined the times required for drops placed on these films to spread uniformly over them. They observed that the contact angle increased with increasing polarizability of the adsorbed cations, being zero for the alkali metal cations and as great as 70 degrees for ions such as Pb++ and Hg++. The average time for spreading of the drop increased with the increase in contact angle. On the clays saturated with the alkali metal cations the spreading was immediate; whereas, 15 to 30 minutes were required for the water drops to spread over the clays saturated with Pb+ + and Hg+ +. The spreading times were intermediate on clays containing cations of intermediate polarizability. Enright and


Weyl ascribed these differences to the hydratability of the cations on the clays. Next to the negative clay surface the ions were assumed to be polarized, their electrons being repelled toward space and their positive nuclei being attracted toward the surface. This polarization reduced the effect of the positive charge on the ion as viewed from the space side; consequently, the attraction of the ion for water was also reduced, the reduction depending on the polarizability of the ion. Although the authors did not mention it, the probability exists that the ions affect the electron distribution in the surface and thereby alter its afEinity for water. In any event, it is apparent that the adsorbed cations have a marked effect on the work of adhesion between clay and water.

Many investigators including Hendricks et al. (1940), Rios and Vi- valdi (1950), Walker and Milne (1950), Keenan et al. (1951), Mooney et al. (1952b), White (1955), and Orchiston ( 1955, 1959), among others, have shown that the nature of the exchangeable cation affects the amount of water adsorbed by a clay. Since the clay will adsorb water until the partial molar free energy of the adsorbed water equals that of the water in the equilibrium solution or vapor, we can conclude that the exchangeable ion also affects the partial molar free energy of the adsorbed water, The pertinent equations are:

and

Here f? is the partial molar free energy of the adsorbed water and F o is the partial molar free energy of pure water. In the first equation, which applies to adsorption from the vapor, p is the pressure of water vapor in equilibrium with the clay and p, is the vapor pressure of pure water. In the second equation, which applies to adsorption from solution, JC is the equilibrium swelling pressure of the clay. The other symbols were defined previously. Evidently, the partial molar free energy of clay-adsorbed water is less than that of pure water until the adsorbed films become very thick because even dilute clay suspensions exert a measureable swelling pressure (Day, 1956; Kolaian and Low, 1960). It is a commonly accepted fact that the osmotic activity of the exchangeable ions makes a significant contribution to clay swelling ( Schofield, 1946; Eriksson, 1950; Norrish, 1954; Bolt and Miller, 1955). But, if the potential energy of the adsorbed water is decreased by reason of its implication in a quasi-crystalline structure induced by either external or intermolecular force fields, this energy decrement should also contribute to swelling (Low and Deming, 1953). In other words, both the osmotic activity of the exchangeable cations and the intensified bonding in the circumambient water are capable of lower-

- F -Fo = RTlnp/p, (21)

P - F o = - t JD ,Jc (22) -

316 PHILIP F. LOW

ing the partial molar free energy of this water. The relative importance of the two factors is still unknown.

Hendricks and co-workers (1940) studied the dehydration of Missis- sippi bentonite by differential thermal analysis. They observed two endothermic peaks when the clay was saturated with Li+ or the alkaline earth cations but only one endothermic peak when the clay was saturated with hydrogen or the alkali metal cations. The lower temperature peak in the former case occurred at the same position as the single peak in the latter case. The lower temperature peaks were ascribed to dehydration of the surface; the higher temperature peaks were ascribed to dehydration of the cations. Hence, it was concluded that the alkali metal cations, excepting Li+, were not hydrated on the clay surface. The clay hydration that did occur when these cations were present was supposed to be due to the surface only. The bulk of the evidence from studies of electrolyte solutions indicates that Cs+, Rb+, and possibly K+ are not hydrated. Therefore, their conclusion is not unreasonable. It is interesting to note from their data that the water ascribed to hydration of the surface decreased with increasing crystallographic radius of the adsorbed ion. This is consistent with the fact that the larger ions would be detrimental to the formation of a water structure.

Other interpretations have been given to the data of Hendricks et al. (1940). Forslind (1950) states that Li+ and the alkaline earth cations, because of their electronegativity, are able to form bonds of partially covalent character with water molecules. Resonance between the covalent and ionic states increases the net ion-water bond energy but produces a disturbance in the surrounding water lattice as the bonded water molecules are pulled toward the ion. Thus the water exists in two energy states, corresponding to the bonded water and the disturbed water, respectively. The other alkali metal cations, on the other hand, are supposedly unable to attain covalent states with the water molecules and so they produce a purely disturbing effect which depends on ionic size. However, Forslind does not argue with the basic conclusions of Hen- dricks and co-workers.

Mackenzie (1950), in criticizing the concept of an ordered water configuration adjacent to a clay surface, pointed out that a linear relationship exists between the peak temperatures obtained by Hendricks et al. (1940) and the hydration energies of the ions. This relationship was regarded as evidence in favor of ion hydration as the primary factor in water adsorption by clays at low water contents. However, the fact should not be overlooked that the Cs+ ion, and possibly the K+ ion, are not hydrated in solution. The data points for these ions fell on Mackenzie’s peak temperature-ionic hydration energy line. In addition, the line intercepted


the peak-temperature axis at a value that was 70 per cent of the maximum value attained. It would appear, therefore, that the mineral surface made a substantial contribution to the average adsorption energy of the water.

Rios and Vivaldi (1950) observed that the amount of water adsorbed by a clay at a given relative humidity was a linear function of the polarization capacity, z/T2, of the exchangeable cation. Here z is the ionic valence and T is the ionic radius. The linear relationship was obtained for both monovalent and divalent cations on kaolinite, a Morroco bentonite and the Mississippi bentonite of Hendricks et d. (1940). For zero ionic polarization capacity the water adsorption amounted to a large fraction of that for the maximum ionic polarization capacity. The authors concluded that both the exchangeable ions and the clay surface affect water adsorption. Apparently, as the size of the exchangeable ion increases, the wettability of the surface (Enright and Weyl, 1950), the energy of water retention (Mackenzie, 1950), and the amount of water adsorbed all decrease.

Working with kaolinite Keenan et al. (1951) found that the number of Li+ ions on the surface had no effect on the amount of water adsorbed from the vapor phase. This was not true for the other ions they used. They believed that the Li+ ion was buried in the hexagonal cavities in the lattice and did not affect water adsorption for this reason. Conse- quently they subtracted the amount of water adsorbed by the Li-clay from the amounts adsorbed by the other homoionic clays to obtain estimates of ionic hydration. The hydration of the ions decreased with increasing ionic size, as expected. The water attributed to surface adsorption alone constituted more than half of the water adsorbed in all cases.

When the water vapor adsorption of Wyoming bentonite was studied by Mooney and associates (1952b), they detected little difference in the amounts of water adsorbed by the K+, Rb+, and Cs+ clays. As a result, they assumed that these ions were not hydrated and assigned all the adsorbed water to the mineral surface. By subtracting the surface-adsorbed water from the total water adsorbed by the other clays, the relative ionic hydrations were obtained. Again the expected order was realized. And again the water held by the surface amounted to more than half the total. On the basis of the evidence cited in the preceding paragraphs, one may conclude that both ions and surface hydrate, the degree of hydration being influenced, for a given ionic charge, by the ionic size.

The heat of adsorption of water on clays can be determined by means of the Clausius-Clapeyron equation, namely,

318 PHILIP F. LOW

In this equation pl and p 2 are the equilibrium water vapor pressures above a clay at the temperatures T 1 and T2, the water content being held constant, and AP is the heat of adsorption. Stated differently, it is the change in the partial qolar heat content of the water on adsorption from the vapor state. All that is needed to obtain values for the variables in the equation are adsorption isotherms at two different temperatures. Since equilibrium conditions are maintained, the partial molar free energy of the water in the clay is the same as that in the vapor; hence, from

we have A 3 = AH/T

where A?? is the partial molar entropy change in the water on adsorption. Thus, it is also possible to obtain the change in disorder of the water molecules in going from the vapor to the condensed phase at the surface.

The heat of adsorption is greater than the heat of condensation of pure water for both kaolinitic clays (Goates and Bennett, 1957) and montmorillonitic clays ( Mooney et al., 1952a; Barshad, 1955). Further, the change in partial molar entropy is greater for water adsorption on these clay types than for condensation to pure water, the initial state being the vapor in each case. Evidence for this was given by the same authors. In fact, Goates and Bennett (1957) point out that the partial molar entropy of the water in a surface monolayer on kaolinite is less than that in ice at the same temperature. Although Mooney et al. (1952a) did not calculate entropy changes in their work, their data permit this calculation. The calculated partial molar entropy of the water on their montmorillonite is less than the partial molar entropy of pure water.

Martin (1959) also used the Clausius-Clapeyron equation and, from his data, calculated negative values for the partial molar entropy of adsorbed water relative to pure water. However, he maintains that an integral entropy, which is not the customary quantity obtained from the partial molar entropy by integration, is the most significant thermodynamic quantity. Because his calculated values of the integral and partial molar entropies are of opposite sign for water adsorption on kaolinite, he is obliged to conclude that the adsorbed water is less ordered than pure water from one approach and more ordered from the other. Martin has provided no explanation for this discrepancy. Therefore, the burden of proof for accepting the integral entropy in preference to the


partial molar entropy is on him. Until such proof is forthcoming, the author will regard the conventional partial molar entropy as a reliable criterion for the degree of disorder in the adsorbed water. Accordingly, there must be greater order in the adsorbed water than in free water. Whether the increased order is due to hydration of the cations or to hydration of the surface is not known. In view of the evidence discussed thus far, it would be reasonable to assume that ions and surface are mutually responsible.

The differential heat of wetting of clays has been determined calorimetrically by Robins ( 1952), Rosenqvist ( 1955), and Zettlemoyer et al. (1955). Integral heats of wetting have been determined calorimetrically by Slabaugh (1955). Additional values for the latter quantity are reported in the book by Grim (1953). Actually, we would be more correct to refer to the differential heat of swelling, but, for the present purpose, we will ignore the distinction. Edlefsen and Anderson (1943) discuss this subject. We will regard the differential heat of wetting as the heat liber- ated per gram of liquid water added to a clay at constant temperature, pressure, and moisture content. It differs from the heat of adsorption by the heat of condensation of pure water.

All the heat of wetting studies referred to have two features in common, namely, the heat of wetting becomes very close to zero when only a few layers of water have been formed and the first layer or two are adsorbed with the release of large amounts of energy, more than that released on the freezing of water. Robins (1952) found that the differential heats of wetting for a Yo10 clay varied continuously from a value of -191 cal. per gram of water at 1 per cent moisture (dry weight basis) to near zero at about 12 per cent moisture. The relative partial specific entropy varied from -1 cal. per gram per degree to near zero in the same moisture range (the relative partial specific entropy for water in ice is about -0.3). The relative partial specific free energy varied cor- respondingly. The partial specific quantities are per gram instead of per mole. Zettlemoyer et al. (1955) found differential heats of wetting for a bentonite clay which ranged from about -380 cal. per gram near zero moisture to practically zero calories per gram at 20 per cent moisture. Rosenqvist’s (1955) data were comparable for an Oslo clay.

The exchangeable cations affect the heats of wetting and adsorption. The data presented by Grim (1953) are illustrative of this fact. Slabaugh (1959) has also presented evidence in this regard, as has Rosenqvist ( 1955). Generally speaking, the heats of wetting increase with decreasing ionic size in keeping with expectation. Rosenqvist (1955) has provided data on 14 different Norwegian and Danish clays which show that the heat of wetting increases linearly with increasing base exchange capacity.

320 PHILIP F. LOW

Grim (1953) has cited similar data. However, Mortland (1954) has shown that base exchange capacity and specific surface are also linearly related; so one cannot be sure that the heat of wetting depends on the exchange capacity instead of the surface.

Throughout this paper we have observed the effect of ionic size on the various properties of free and adsorbed water. For the most part, the property in question changed regularly with the ions in normal order. Although attention has not previously been called to the fact, it should be noted here that the Li+ ion frequently is out of sequence in its effect. The results of Hendricks et al. (1940), Keenan et al. (1951), White (1955), Rosenqvist (1955), Rowland et al. (1956), Anderson and Low (1958), Low (1958a), and Kolaian (1960) are cited in this regard. Pos- sibly the occasional peculiar behavior of the Li+ ion is explicable on the basis of covalent states which it may form with water (Forslind, 1950). Or perhaps this peculiar behavior arises from the relationship of the ion to the crystal lattice (Keenan et al., 1951).

Attention has already been directed to the rapid change in the thermodynamic properties of adsorbed water with distance from the clay surface. On the basis of the vapor adsorption and heat of wetting experiments, one would be justified in assuming that the thermodynamic status of the water was entirely normal at a distance of three or four molecular diameters. Granted, most of the change in these properties occurs in a narrow region adjacent to the surface. But the point is made here that the methods used in these experiments are relatively insensitive. And very small changes in the thermodynamic properties can have significant consequences. The latter point will now be considered briefly.

By existing vapor adsorption methods it is very difFicult to measure relative partial molar free energies to less than 10 to 20 cal. per mole. But at the wilting point the partial molar free energy of the water in a soil is reduced relative to that of pure water by only 6.5 cal. per mole, and most soil processes occur at higher moisture contents than the wilting point. For instance, 1 atmosphere is an appreciable swelling pressure. Yet this is the swelling pressure when the partial molar free energy of the soil water is different from that of pure water by less than 0.5 cal. per mole (see Eq. 22), and water often flows under a hydraulic gradient of < 2. A gradient of this magnitude corresponds to a partial molar free energy difference per centimeter of less than 0.001 cal. per mole. Further, if the heat of adsorption results from the formation of additional hydrogen bonds in the water, and if the heat of activation for viscous 00w is the energy required to rupture hydrogen bonds, then it is evident from Eq. (3) that significant changes in viscosity would result from relatively small changes in the heat of adsorption-changes too small to measure


by the vapor pressure or calorimetric methods. Continuing this line of thought, small entropy changes, representing minor adjustments in the adsorbed water structure, may have appreciable effects on the supercooling of the water involved. Still, such changes may not be detected by these methods. It may be said, therefore, that it is incorrect to assume that thermodynamic changes are insignificant because they are small or not readily measured.

The only work known to the author in which the thermodynamic properties of water in wet clays have been studied is that of Kolaian and Low (1960). These investigators measured the change of water tension with temperature in Wyoming bentonite suspensions containing 5 to 10 per cent clay. Then they used the equation of Low and Anderson ( 1958b), i.e.,

( S - s o ) P o = ~ - ( - ;;) + P,. N

to determine the relative partial molar entropies. In this equation is the partial molar entropy of water in suspension, So is the partial molar entropy of pure water, Po is the pressure on the pure water, N is the composition of the suspension, g is the temperature coefficient of water ex- pansion, and the other symbols have the meanings assigned earlier. From equations (22), (24), and (26) the value of AH was also determined. Their results showed that all of the relevant thermodynamic quantities were less in the dilute clay suspensions than in pure water; hence it appears that the influence of the clay surface extends over rather large distances.

An interesting feature of the work of Kolaian and Low (1960) is that the measured water tension in each suspension increased with time after stirring, i.e., as the suspension became thixotropic. Immediately after stirring the tension was close to zero but as time elapsed it increased to a maximum value which was achieved after about 50 to 100 hours, depending on the adsorbed cation. The tension-time relationship suggested that water molecules were falling into positions of minimum energy in a gradually developing water structure. The development of the water structure and of thixotropy were concomitant. Now remember that Buehrer and Aldrich (1946) found essentially all the water in a bentonite- water system remaining unfrozen as long as the water content of the system was insufficient to convert it from a thixotropic gel to a sol. As soon as enough water was added to prevent thixotropy, the percentage of unfrozen water fell suddenly to a low value. Remember also, that Kolaian (1960) found the rate of freezing of a bentonite suspension to increase remarkably with the development of thixotropy. Evidently, the

322 PHILIP F. LOW

condition of the water is quite different in a clay-water system in the gel state than it is in the same system in the sol state. This idea was commonly accepted by colloid chemists many years ago. To the water was ascribed the role of gelling agent. But with the advent of double-layer theory and the monolayer concept of adsorption, this idea was discarded in favor of particle-particle interaction as the cause of thixotropy. Prob- ably a reconsideration of the problem is warranted.

X. A Working Hypothesis

In a recent presentation Richards (1960), referring to the water films on soil particles, stated: “When the thickness of adsorbed water films is reduced to 6 or 8 monomolecular layers of water, the soil water is so tightly bound that crop growth ceases. All agriculture is conducted in a soil-water film thickness range from this value up to two or three times this thickness.” This being the case, it is essential that we understand the properties of water in these films. As an aid to understanding, and as an aid in designing future research, the author presents the following hypothesis. The reader will recognize that it is new only in its details. Several investigators have entertained similar hypotheses, notably: T. F. Buehrer, E. Forslind, R. E. Grim, S. B. Hendricks, H. H. Macey, I. Th. Rosenqvist, and H. F. Winterkorn. The author hereby acknowledges their contributions to his thinking.

When a clay is exposed to water vapor, the exchangeable cations hydrate first if they are small enough to be capable of hydrating. Then the remainder of the surface hydrates by the formation of hydrogen bonds between the surface hydroxyls, or oxygens, and the water molecules. In the case of the oxygen atoms the bonding tends to be of a covalent character because the excess electrons in the lattice make it easier for the lone-pair electrons of these atoms to be distorted by the protons of the nearby water molecules. The water molecules in the initial layer are not arrayed in perfect order. The competition between adsorbed ions and surface atoms for these molecules is too great. Nevertheless, the initially adsorbed molecules have very low free energy, heat content, and entropy owing to the intensity with which they are held. As other molecules come within the force fields of those in the first layer, they are captured by them. The first-layer molecules, having their electron distributions affected somewhat by covalent bonding with the surface oxygens, form partially covalent bonds with the captured molecules. These, in turn, are induced to form partially covalent bonds with their neighbors, including third-layer molecules. As additional layers accrue by this type of cooperative action, the degree of bond covalency, and hence of rigidity,


decreases. However, the normal electron distribution within the molecules is still conducive to tetrahedral coordination and the neighboring molecules on the side toward the surface do not have the usual freedom to exert torques and promote displacements. Therefore, the degree of order decreases gradually with distance from the surface.

In addition to being responsible for electroviscous and osmotic effects, as modified by the properties of the water, the adsorbed ions promote disorder. If they are small and monovalent their contribution in this direction is relatively small. But if they are large or multivalent their disordering effect is large. Further, the more they dissociate from the critical surface region where the structure is “anchored,” the less they disturb the structure. Those ions that create the least disturbance in the quasi-crystalline water “dissolve” in it most readily. When these ions are present, the water structure may extend with considerable regularity for distances of the order of 75 to 100 A. An attenuated structure may persist as far out as 200 to 300 A. At lower temperatures the structure extends farther and is more coherent than at higher temperatures. Under these conditions the water structure is connected from mineral surface to mineral surface without any intervening region of disorder. However, in the presence of large or multivalent cations there may be little or no order in the adsorbed water.

The specific volume, viscosity, and freezing resistance of the water are directly related to its structural development. Consequently, the magnitudes of these properties decrease continuously with distance from the mineral surface. The same applies to the relative thermodynamic properties. It should be noted, however, that nowhere is the water structure so rigid that ions cannot diffuse through it; nor is it so rigid that it will not shear under stress. Nevertheless, it has a yield point, which depends upon the proximity of adjacent mineral surfaces, and it exhibits non-Newtonian behavior at low hydraulic gradients. Although the precise molecular arrangement of the water cannot be specified, it is not that in ice.

All that has been said regarding water interaction with oxygen surfaces pertains also to hydroxyl surfaces. However, the coherence and extent of the structure which forms on the latter are not so great.

REFERENCES

Adam, N. K. 1941. “The Physics and Chemistry of Surfaces,” 3rd ed. Oxford Univ.

Adamson, A. W. 1960. “Physical Chemistry of Surfaces.” Interscience, New York. Anderson, D. M., and Low, P. F. 1958. Soil Sci. SOC. Am. Proc. 22, 99-103. Andrade, E. N. da C. 1934. Phil. Mag. “71 17, 698-732. Andrade, E. N. da C. 1952. Proc. Roy. SOC. A215, 36-43.

Press, London and New York.

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