Unit layer interaction in hydrous montmorillonite systems

JOURNAL

OF COLLOID SCIENCE

17, 660-667 (1962)

UNIT LAYER INTERACTION IN HYDROUS MONTMORILLONITE SYSTEMS 1 H. Van Olphen Shell Development Company (A Division of Shell Oil Company), Exploration and Production Research Division, Houston, Texas Received November 6, 1961 ABSTRACT K. Norrish (1) has observed more or less diffuse equilibrium spacings of the unit layers in swollen flakes of montmorillonite clays in contact with electrolyte solutions. These spacings decrease with increasing electrolyte concentrations in a range between about 130 to 19 A. An evaluation of the unit layer interaction forces and energies shows that the double-layer repulsion forces cannot be canceled by van der Waals' attractive forces at each equilibrium distance without making unrealistic assumptions. Alternative attractive forces are considered, with special emphasis on the cross linking of stacks of parallel layers by a relatively small number of nonparallel plates.

In a previous paper (2) the author presented a quantitative discussion of the potential energy of interaction of unit layers in a hydrous system of expanding lattice type clay minerals (montmorillonites). The short-range interaction energy, up to layer separations of about 10 A., was computed directly from water vapor adsorption isotherms. The longer range interaction energy was evaluated by combining the computed van der Waals' attraction energy and the computed electric double-layer repulsion energy. The latter was derived from the known surface charge density based on either the Gouy or the Stern-Gouy model. Since the calculated net potential curve of interaction shows an appreciable net repulsion at any layer distance, spontaneous dissociation of the unit layers in water would be expected. However, in suspensions of most montmorillonite clays, packets of unit layers remain associated. Hence, it was concluded that the doublelayer repulsion in most clays is substantially reduced by specific adsorption of counter-ions at the unit layer surface. The required magnitude of the specific adsorption potential of the cations was estimated to be of the order of 0.2 electron volt. This conclusion contradicts the results of swelling pressure measurements, which seem to agree with the pressures predicted by applying the Gouy model without specific counter-ion adsorption (3). However, in the swelling 1 Presented at the 138th National Meeting of the American Chemical Society, September 11-16, 1960, New York, New York. 66O

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pressure measurements, grain pressures m a y have developed, and hence the swelling pressures m a y have been overestimated (4). Norrish (1), by applying X - r a y diffraction techniques, has observed more or less diffuse long-range equilibrium spacings of up to approximately 130 A. between unit layers in swollen flakes of expanding montmorillonite clays in water and in salt solutions. The equilibrium spacings decrease with increasing electrolyte concentration. Norrish evaluated the double-layer repulsion force and the v a n der Waals' attraction force at the equilibrium distances at each electrolyte concentration studied. These forces should be equal at each equilibrium spacing; however the double-layer repulsion force computed on the basis of the G o u y model and Langmuir's formula appeared to be m u c h larger t h a n the v a n der Waals' attraction force in each case. An appreciable discrepancy between repulsion and attraction at the equilibrium spacings still persists when the Stern-Gouy model, which does lead to a somewhat smaller repulsion, is applied, since the large potential drop in the double layer close to the surface is taken into account. Table I shows the computed Stern-Gouy double-layer repulsion energy and the computed v a n der Waals' attraction energy at the obsel-ved equilibrium spacing for each electrolyte concentration of a sodium W y o m i n g bentonite system studied b y Norrish. (Norrish's data for the G o u y double-layer repulsive force and for the v a n der Waals' attractive force are included in the table.) When the computed repulsive energy and attractive potential energy are combined, a strong net repulsive energy is found in each case. However, the existence of an equilibrium spacing requires t h a t an attraction m i n i m u m occur in the net potential curve of interaction at t h a t layer TABLE I Repulsion and Attraction at Various Equilibrium Spacings

(Sodium bentonite) NaCI conc.

~ (cm-1

0.25 0.063 0.028 0.0156 0.0100 0.0069

0.164 0.0822 0.0549 0.0410 0.0328 0.0272

(equiv.~liter) X l0 -s)

Vn

s (A.)

dGouy (A.)

2~d

43.8 66.5 89.2 112.3 135.0 158.0

11.9 23.3 34.6 46.2 58.5 69.0

3.76 3.70 3.67 3.69 3.64 3.63

VA

(erg/cm'~)

0.235 0.125 0.087 0.065 0.056 0.048

0.0196 0.0036 0.0011 0.00044 0.00021 0.00011

Fn Fa (dynes~era 2 X 10-~) (Norrish)

28.7 11.6 6.]2 3.86 2.59 2.04

9.1 1.0 0.23 0.074 0.029 0.013

s is the observed (001) spacing. d is the half distance between the planes separating the Stern and Gouy layers for opposite plates. With the thickness of the Stern layer taken as 5 A. (equivalent to the thickness of two adsorbed water layers), d = (~) (s - 20)A.

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VAN OLPHEN

distance. The diffuse character of the equilibrium spacings indicates that this minimum is shallow. Therefore, these results would indicate again that the double-layer repulsion is substantially reduced by specific counter-ion adsorption. At the lowest electrolyte concentration studied, a specific adsorption potential of the cations amounting to 0.18 electron volt would reduce the double-layer repulsion sufficiently to create a shallow net attraction minimum in the potential curve. So far,'Norrish's direct measurements of the long-range layer interaction lead to the same conclusions as derived previously from the observations on layer association in dilute suspensions. However, an interesting anomaly is found when the equilibrium spacings at higher electrolyte concentrations are analyzed. As Norrish has pointed out, the product of K and d is practieally the same for the equilibrium spacings at all electrolyte eoncentrations. (1/K is Debye's characteristic length, which is a rough measure for the "thickness" of the double layer, and d is the half distance between the unit layers.) According to Verwey and Overbeek (5) and Maekor (6), the double-layer repulsion energy is proportional to the square root of the electrolyte concentration at equal values of Kd. Hence, the repulsive energy varies by a factor of 5 in the range of electrolyte concentrations studied for the different equilibrium spacings. In the same range, however, the van der Waals' attraction energy varies by a factor of 180 (see Table I). In other words, as shown by Table I, the discrepancy between the doublelayer repulsion which is not corrected for specific adsorption and the van der Waals' attraction which exists at each equilibrium spacing decreases with increasing electrolyte concentration. Therefore, progressively smaller specific ion adsorption potentials would have to be introduced for the reduction of the repulsive energy when the electrolyte concentration is increased. At the highest electrolyte concentration, a specific adsorption potential of only 0.025 electron volt would suffice. The assumption that the chemisorption of the counter-ions would be affected so strongly by the bulk electrolyte concentration seems rather unrealistic. Another argument against this interpretation is the following: As mentioned, Norrish observed that the diffraction patterns belonging to the larger spacings are rather diffuse; moreover, at the highest electrolyte concentrations, two different equilibrium spacings, one at 19 A. and one at 43.8 A., coexist. Therefore, the minima in the potential curves will be rather shallow, of the order of a few times kT at most. Such a depth of the minima corresponds to an interaction energy of a few times 10-4 erg/cm. 2 for plates of 2000 by 2000 A. ~, which is a probable size for the particles of the fine fraction material used by Norrish. In order to create such a shallow minimum, for example, at the highest electrolyte concentration, the doublelayer repulsion energy would have to be reduced precisely to a value a few times 10-4 erg/cm3 lower than the van der Waals' attraction energy, which

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is of the order of 10-2 erg/cm2. Such a situation seems rather accidental. Therefore, it may be justified to consider the alternative interpretation of the data in which a different attractive energy is introduced which is less distance-dependent than the van der Waals' attraction between the unit layers. We shall discuss some possible alternative attractive forces and evaluate whether or not they might explain the observed anomaly. 1. The attractive force is a van der Waals' type force; however, either the force operating between two atoms or the integral force between the interacting plates is modified. A less pronounced distance-dependence of the van der Waals' force between the unit layers in the considered range would be obtained if the van der Waals' attraction energy of two atoms were inversely proportional to the fourth, instead of the sixth, power of the distance. Athough an inverse proportionality to a power somewhat lower than 6 (i.e., 5.6) had to be assumed by Mackor (6) to explain the stability behavior of AgI sols in water-acetone mixtures, there does not. seem to be a good reason to assume a much more drastic change of the power law for the unit layer attraction in clays. In the addition of the forces between all the atoms of the two plates, the contribution to the total force of those atoms which are farther apart than about 10-6 era., while the perpendicular plate distance is smaller, may have to be corrected for the relativistic effect which makes the van der Waals' attraction energy between atoms inversely proportional to the seventh power of the distance beyond 10.6 cm. However, in the summation of the forces, this correction appears to be negligible. 2. The force which counteracts the double-layer repulsion is the gravity force. Gravity forces which are involved in the creation of the phenomenon of Schiller layers in sedimenting suspensions are negligible for the thin flakes, even in their most favorable position with respect to the gravitational field. 8. Confining forces are exerted on the layers by the walls of the container. Confining forces can be ruled out, since the flakes did not touch the walls of the capillaries in which they were studied. Norrish demonstrated that shorter equilibrium spacings are obtained when thicker flakes are used which do touch the wails of the capillaries. 4- The unit layer lattices carry permanent dipoles which are oriented perpendicular to the layers and which are polarized in the same direction in adjoining layers so that an attractive force is created. The unit layer lattice would obtain a permanent dipole character if there were an asymmetrical distribution of charge sites due to isomorphous sub-

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stitution in the interior of the lattice. The attraction between finite layers of dipoles is little dependent on the distance between the layers in the considered range (2) and would therefore meet the requirements if, also, the magnitude of the attraction was right. At present, this type of attraction cannot be ruled out, but neither qualitative nor quantitative information on the dipole character of unit layers is available. 5. The swelling of the clay flakes is limited by "gel forces" due to crosslinking particles. In the interpretation of Norrish's experiments, as well as of swelling pressure measurements, the unit layers are assumed to be in a perfectly parallel position. This assumption may not be justified. If no special efforts are made to obtain parallel orientation, moderately concentrated clay systems become coherent gels. Since it is likely that the edges of the platelike particles carry a positive double-layer charge (7), the gelation is probably a result of the attraction between the positive edges and the negative flat layer surfaces by which a cubic cardhouse of linked plates is created (8). In the oriented flakes prepared by Norrish, some of the plates may be in a nonparallel position because of edge-to-face attraction and thus may supply a cross-linkage between parallel plates. In that case, an analogy would exist between the occurrence of equilibrium spacings and the limited swelling of three-dimensional gel structures. The question is now whether the crosslinking force is of the right order of magnitude to compete with the repulsion and whether this force varies in the required way with electrolyte concentration. The possible magnitude of the cross-linking force can be evaluated as follows. From rheologieal data on gels of sodium Wyoming bentonite in water, the edge-to-face linking force has been estimated to be of the order of 10-~ dyne per link (9, 10). At the lowest electrolyte concentration studied by Norrish, this linking force will be about a factor of 10 lower, since the yield stress of the gel decreases by that factor upon the addition of the corresponding amount of salt to the gel. If one pair of such links acted between two parallel plates in a flake consisting of particles of roughly 2000 by 2000 A.~--a probable size for the fine fraction material used by Norrish-the links would supply a restraining force of the order of 105 dynes/era}. Since the large plates can bridge two parallel plates which are widely separated, a comparatively small number of nonparallel cross-linking plates could limit the swelling of a relatively large number of parallel plates located between the cross-linked plates, as schematically illustrated in Fig. 1. One can easily visualize a number of more complicated arrangements in which cross-linking by a few plates restrains the swelling of many parallel plates. Since the double-layer repulsion force based on the Gouy model is of the order of 105 dynes/em.2 at the equilibrium spacing for the lowest electrolyte

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concentration, the restraining cross-linking force would be large enough to cancel the double-layer repulsion, even in the absence of specific ion adsorption. The repulsive double-layer force computed according to the Gouy model increases by a factor of 14 with decreasing equilibrium spacings at increasing electrolyte concentrations (see Table I). In the same region of electrolyte concentrations, the yield stress of gels was observed to increase in about the same proportion (10) ; hence, the restraining force in the flakes due to crosslinkage can be assumed to increase by the same factor and thus cancel the double-layer repulsion at each equilibrium spacing. Obviously, therefore, the proposed mechanism of cross-linking could explain the observations on swelling flakes. Since the local number of crosslinks, and therefore the restraining force, can be expected to vary throughout the flakes, the observed diffuse character of the diffraction patterns indicating variation of the equilibrium spacings around an average layer distance can also be explained. Since the cross-linking force was estimated to be high enough to counteract Gouy double-layer repulsion, the case for a reduced repulsion due to specific ion adsorption would become less strong, although the cross-linking force may have been overestimated. The argument for specific ion adsorption based on the incomplete dissociation of the unit layers in diinte suspensions of most clays still holds unless cross-linking forces are also responsible for holding thin packets of a few unit layers together. However, in these packets the layers are separated by only a few monomolecular layers of water, and it does not seem likely that ~ cross-linking force would be important in such packets. An interesting test of the reality of the cross-linking mechanism will be to repeat the swelling experiments and the study of layer association in dilute suspensions with clays in which the positive edge charge is converted into negative charge by specific anion adsorption, thus eliminating the edge-to-

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face linking force. This conversion can be achieved by addition of metaphosphate anions and many other polyvalent anions. Small amounts of these additives cause the breakdown of the clay gels in a relative wide range of electrolyte concentrations. NOTE ADDED IN PROOF

Independently, K. Norrish 2 has come to the conclusion that cross-linking particles are responsible for the limited swelling. He actually carried out experiments in the presence of sodium polymetaphosphate, and he observed that indeed greater swelling occurred. He also found that swelling and deswelling with decreasing and increasing salt concentrations, respectively, became more reversible after the addition of phosphates, as one would expect on the basis of the cross-linking mechanism. APPENDIX

The repulsive energy of the Stern-Gouy double layers (VR) is computed on the basis of the following approximate statistical treatment. The ratio of the Stern layer charge (el) and the Gouy layer charge (~2) is taken equal to the ratio of the available positions of the ions given by the respective volumes of the two regions multiplied by the factor eve~1k~, in which Cs is the electric potential in the plane between the Stern and Gouy layers. Hence, with a Stern layer thickness of 5 A. __

~1 _ ~2

5 d

z

e ;

Ye~8

z

[1]

kT

The sum of the Stern and Gouy layer charge is equal to the surface charge, which is 3 N 10~e.s.u./cm?, corresponding to a cation exchange capacity of the clay of 80 meq./100 g. Therefore, ~1-4- ~2 = 3 X 104•

[2]

For interacting Gouy layers, the charge of the Gouy layer is ~2 ( = ) A~ 'V

27r

~v/2 cosh z -- 2,

[31

in which ~ is the dielectric constant of water i n t h e range of the Gouy layer and n is the number of cations in the salt solution per cm.s. When Eqs. [1], [2], and [3] are combined, the value of z is found. Then the repulsive energy can be computed from 64 n . / c T V R

-~

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~

-2~d .e

,

2 "Low angle diffraction studies of the swelling of montmorillonite and vermiculite," by K. Norrish and J. A. Rausell-Colom, presented at the 10th National Conference on Clay Minerals, 16-18 October, 1961, Austin, Texas.

•.flNIT LAYER INTERACTION IN MONTMORILLONITE SYSTEMS

667

in which 2 K

8~nePv2 --

kT

and 7

e 1/2~ - - 1 e1/2~ + 1 "

A c c o r d i n g t o M a c k o r (6), t h i s e q u a t i o n is v a l i d for w e a k i n t e r a c t i o n of S t e r n - G o u y l a y e r s (,~ d > 0.5). T h e v a n d e r W a a l s ' a t t r a c t i o n e n e r g y b e t w e e n t h e u n i t layers is c o m p u t e d f r o m t h e following e q u a t i o n :

vA

A

[I

1

2

1

in w h i c h A ~ 10 -1~, dl is t h e haft d i s t a n c e b e t w e e n t h e centers of t h e o x y g e n l a y e r s of t h e t e t r a h e d r a l sheet of t w o plates, a n d 6 is t h e t h i c k n e s s of t h e u n i t l a y e r s (6.6 A.). H e n c e , dl = ( ~ ) ( s - 6.6). I~EFERENCES 1. NORmS~, K., "The swelling of montmorillonite, Discussions Faraday Soc. No. 18, 120-134 (1954). 2. VAN OLPKEN, H., "Interlayer forces in bentonite," pp. 418-428. Clays and Clay Min., Natl. Research Council Natl. Acad. Sci. (U.S.) Publ. no. 327, Washington, D.C., 1954. 3. BOLT, G. H., AND MILLER, R. D., "Compression studies of illite suspensions," Soil Sci. Soc. Amer. Proc. 19, 285-288 (1955). 4. WAR:K~NTIN, B. P., ANn SCHOFIELD, R. K. "Swelling pressures of dilute Namontmorillonite pastes," pp. 343-349. Proc. 7th Natl. Conf. Clays and Clay Min., Pergamon Press, New York, 1960. 5. VERWEY, E. J. W., ANn OVEI~,BEE]]:, J. TIt. G., Theory of the Stability of Lyophobic

Colloids." Elsevier, Amsterdam, 1948. 6. MACKOR, E. L., "The stability of the AgI sols in water-acetone mixtures," Rec. tray. chim. 70, 841-866 (1951). 7. VAN OLPItEN, I-I., "Rheological phenomena of clay sols in connection with the charge distribution of the micelles," Discussions Faraday Soc. No. 11, 82-84 (1951). 8. VAN OLP~ZEN, H.,"Stabilisation of montmorillonite sols by chemical treatment," Rec. tray. chim. 69, 1308-1322 (1950). 9. VAN OLP~EN, H., "Forces between suspended bentonite particles," pp. 204-224. Clays and Clay Min., Natl. Research Council Natl. Aead. Sei. (U.S.) Publ. No. 456, Washington, D.C., 1950. 10. V~N OLPHEN, H., "Forces between suspended bentonite particles, Part II, Calcium bentonite," pp. 196-206. Proc. 6th Natl. Conf. Clays and Clay Min., Pergamon Press, New York, 1959.