LIMITATIONS OF THE GOUY–CHAPMAN DIFFUSE DOUBLE LAYER MODEL

The theory of the diffuse double layer provides useful insights into ionic distributions adjacent to clay parti-cles, which, in turn, allow for reasonable predictions of some things, such as flocculation–deflocculation, swelling, and the effects of pore fluid compositional changes under idealized conditions. However, there are serious discrepancies in many cases, owing both to fac-tors that are not accounted for by the theory, for ex-ample, pH, ion size, particle interference, and forces that are neglected, and to deviations from the idealiz-ing assumptions. The DLVO theory, based on the Gouy–Chapman model, gives reasonable prediction for freely swelling clay systems of very fine clay par-ticles with monovalent ions, such as Na and Li mont-morillonite. The DLVO models have had limited quantitative success for other clays.

Gu¨ven (1992) lists the following assumptions as un-realistic:

1. Ions are assumed to be point charges, and their sizes are ignored.

2. Water structure and the electrical properties of water molecules are not taken into account. The dielectric constant of the water is assumed the same as that of free water.

3. The clay particle charge is assumed distributed uniformly on the surface. In reality, there is charge localization, and whether the charge re-sults from isomorphic substitution in the octa-hedral or tetraocta-hedral layer influences the potential fields differently.

4. Both the ions and clay surfaces are hydrated, and this is neglected.

5. The ionic distributions based on the Boltzmann equation lead to unrealistically high concentra-tions at the particle surface. For example, Gu¨ven (1992) shows that for a moderate surface poten-tial of _⫺103 mV, the concentration of sodium at the particle surface would be 0.6 M, whereas that of calcium would have to be 20.8 M for a bulk solution concentration of 0.01 M.

The theory also assumes that the counterion distri-butions remain the same, even when two clay particles come together. In addition, there may be Coulombic attractive forces, as proposed by Sogami and Ise (1984), which are not accounted for, as noted in Sec-tion 6.7 and discussed further below.

Ion Size and Type

The hydrated radii of cations determine their maximum possible concentrations. Values of hydrated radius for some cations are as follows:

160 6 SOIL–WATER–CHEMICAL INTERACTIONS

Figure 6.14 Three mechanisms of cation adsorption on a silicate surface, for example, montmorillonite (from Sposito, 1989).

Ion Hydrated Radius (nm)

Li^⫹ 0.73–1.00

Finite ion size was taken into account by Stern (1924) and Carnie and Torrie (1984), among others.

The Stern layer consists of counterions in a closely packed layer close to the surface, with an adjacent dif-fuse layer extending outward into the solution. Equa-tions based on Stern’s theory are given by van Olphen (1977) for both single and interacting flat double lay-ers. These equations can be used to compute the charge in each layer and the potential at their interface.

Stern layer potentials were deduced from the results of coagulation rate measurements on four clays having about 0.5 _m mean particle size, at pH 10 (Novich and Ring, 1984). The values obtained were_⫺42.7 mV for kaolinite,_⫺40.7 mV for illite,_⫺21.2 mV for mont-morillonite, and_⫺66.9 mV for palygorskite. These val-ues are significantly less than the surface potentials calculated when the computations are made without consideration of a Stern layer. However, these results are consistent with those from other studies that indi-cate that about 75 percent of the diffuse layer ions reside within about 1.0 nm of the particle surface (Sposito, 1989). In another series of experiments using four techniques and three smectites, Low (1987) found that almost all the counterions are in the Stern layer.

This, and data and analyses reviewed in Low (1992), lead to conclusions that there is little dissociation of exchangeable cations from the particle surface, the dif-fuse layer is small and poorly developed, and the swelling of clay is due primarily to water hydration of particle surfaces. This explanation for swelling is dis-cussed further in Chapter 10.

The diffuse double-layer model does not account for adsorption selectivity differences among cations of the same valence. Sposito (1989) identified three mecha-nisms of cation adsorption on a silicate surface, as shown in Fig. 6.14. Inner-sphere cations are ions that are held within the hexagonal ‘‘hole’’ in the silicate surface, with no water molecule between the surface and the cation. Inner-sphere cations involve ionic and / or covalent bonding and are tightly held (ion

fix-ation). The outer-sphere cations are solvated and ad-sorbed on the surface electrostatically. The readily exchangeable ions are those in the diffuse ion swarm and the outer-sphere complex.

Based on considerations such as these, Gu¨ven (1992) proposed the hypothetical model shown in Fig.

6.15 for the distribution of water and ions adjacent to a clay surface. In this figure the _plane is water mol-ecule dipoles on the clay surface. Inner-sphere cations may be in this region as well. The_plane is the closest plane of hydrated counterions to the surface. The D plane is the beginning of the diffuse layer. The 1 /_ plane is in the diffuse region where the potential has decreased to _0/ e (center of gravity of the diffuse layer charge). The _ plane is the shear plane that sep-arates the portion of the bound water and cations that move with the particle from the remainder of the pore water in electrokinetic flow (see Chapter 9).

Reformulations and modifications of the simple Gouy–Chapman theory have been made and evaluated (Carnie and Torrie, 1984). Modified Gouy–Chapman (MGC) theory, in which ion size is taken into account, is summarized by Sposito (1992). He concluded that the MGC provided a reasonable model for the dif-fuse ion swarm adjacent to basal planes of Na-montmorillonite particles in low concentration (_⬍100 moles / m³) solutions of 1_⬊1 electrolytes. On the other hand MGC was inaccurate for electrolyte solutions containing bivalent ions, even at concentrations as low as 5 mol / m³.

Computer simulations offer possibilities for better definition of the actual conditions. The consequences of the following 10 interactions must be considered (Gu¨ven, 1992): (1) water molecule–water molecule, (2) counterion–counterion, (3) coion–coion, (4) clay particle–clay particle, (5) water molecule–counterion,

Figure 6.15 (a) Multilayer configuration of water and ions adjacent to a clay particle surface as proposed by Gu¨ven (1992). (b) Decay of surface potential _0 with distance from the surface.

162 6 SOIL–WATER–CHEMICAL INTERACTIONS

Figure 6.16 Ion distributions according to DLVO and alter-native (electrostatic attraction) theories: (a) DLVO repulsive and (b) alternative attractive.

(6) water molecule–coion, (7) water molecule–clay particle, (8) counterion–coion, (9) counterion–clay, and (10) coion–clay. The net interaction potential of the system is the sum of the interaction energies of the components. Gu¨ven (1992) outlines both Monte Carlo (MC) and molecular dynamics (MD) computer simu-lation procedures for finding this sum as follows. First, several hundred particles are put in a box with finite dimensions. The coordinates of the particles are de-fined, and interactions between them are defined in terms of potentials. MC simulations involve sampling all particle configurations in the box and finding changes in potential energy caused by particle move-ments. The most stable configuration is that where the energy is least. In MD simulations, the equations of motion are solved numerically for the particle in the box. Both the configuration and the dynamics of par-ticle in a liquid are determined. According to Gu¨ven (1992), both MC and MD methods can be used to bet-ter describe clay–wabet-ter inbet-terface details and help in the understanding of clay particle interactions with each other. Recent applications of Monte Carlo simulations for study of net interaction forces between clay parti-cles are described by Delville (2002). Skipper (2002) describes the application of both MC and MD com-puter simulations for modeling of clay–fluid interac-tions in Wyoming bentonite.

Ion Redistributions

As noted earlier, the capabilities of diffuse double-layer models, in which the electrical force is assumed to be repulsive at all interparticle separations, have been challenged by McBride (1997), McBride and Baveye (2002a, 2002b), and others. An alternative de-scription of the fundamental forces is proposed based on the work by Langmuir (1938) and backed up by the electrostatic attraction theory (Sogami and Ise, 1984, Smalley, 1990) and simulation studies using the Monte Carlo technique. When two clay particles merge, an attractive electrostatic force results due to redistribu-tion of counterions (Fig. 6.16b), which is not consid-ered in the DLVO theory (Fig. 6.16a). The attractive force model is supported by the observation that par-ticles in stable dispersions do not necessarily occupy all the volume of the solution as would be expected from the long-range repulsive forces of the DLVO model. Rather they tend to cluster at separations that are not space filling (McBride, 1997). In such a sys-tem, the long-range Coulombic attractive force is re-sisted by hydration and osmotic forces, and the overall force changes from attractive to repulsive due to os-motic forces once the clay plates separate by more than some distance (10 to 30 A˚ ) based on the work by

MacEwan (1948) and Norrish (1954). McBride (1997) and McBride and Baveye (2002a) review numerous ex-perimental observations, including dispersion, osmotic swelling, and transitions among ordered and disordered phases of colloidal particles in dilute salt solutions, to support the existence of an electrostatic attractive term.

Clay Platelet Associations and Particle Interference Diffuse double-layer theory assumes individual and in-dependent colloidal particles. When applied to smectite clay particles, it is usually assumed that the total spe-cific surface, about 800 m²/ g, is covered with a uni-formly thick layer of water and adsorbed cations. In reality, however, this is usually not the case, and the platelets stack into tactoids or quasi-crystals (Quirk and Aylmore, 1971).

When calcium is the adsorbed cation, a typical quasi-crystal consists of four to seven montmorillonite platelets interspersed by two or three molecular layers of water. Each calcium ion is solvated by six water molecules and acts as a cross-link holding the platelets together. This type of cross-linking is probable with any divalent cation and smectite type (Sposito, 1989).

There is clear evidence from light-scattering, neutron-scattering, and other experiments that quasi-crystals also form in the presence of monovalent cati-ons (Sposito, 1989, 1992). The number of platelets per quasi-crystal in monovalent cation systems ranges from 1 to 2 and increases on the order Li _⬍ Na_⬍K.

For nonexpansive clay minerals such as kaolinite and illite, the situation is somewhat different. Individ-ual particles of these minerals are much thicker than smectite unit layer platelets and may consist of up to several hundred unit cell layers. The particle thickness

is large relative to the diffuse layer thickness. As a result, gravity forces are important in suspensions of these minerals, and physical interferences between par-ticles are important in sediments in addition to the in-fluences of double-layer interaction effects.

Effect of pH

Hydroxyls (OH)^⫺ are exposed on the surfaces and edges of clay particles. The tendency for hydroxyls to dissociate in water,

⫺ ⫹

SiOH_→ SiO _⫹H

is influenced strongly by the pH. By definition, pH_⫽

⫺log₁₀ H^⫹ concentration: pH _⬍ 7 is acid (high H^⫹ concentration), and pH _⬎ 7 is basic (low H^⫹ concen-tration). The higher the pH, the greater is the tendency for H^⫹ from the hydroxyls to go into solution, and the greater the effective negative charge of the particle.

Hence, the octahedral face of 1_⬊1 minerals such as kaolinite and the OH termination sites on the edges of both 1_⬊1 and 2_⬊1 clay minerals are affected by the pH.

In addition, alumina, which is exposed at the edges of clay particles, is amphoteric, and it ionizes posi-tively at low pH and negaposi-tively at high pH. As a result, positive diffuse layers can develop at the edges of some clay particles in an acid environment. Such layers are of the constant surface potential type, as opposed to the constant surface charge type, with H^⫹ serving as the potential determining ion.

The surface potential is related to the pH of the so-lution, and therefore pH plays a very important role in the behavior of clay suspensions, especially kaolinite.

A low pH promotes positive edge to negative surface interaction, often leading to flocculation from suspen-sion. Stable suspensions or dispersions of clay particles often require high pH conditions. For clay minerals with a small thickness-to-length ratio such as smectite, the contribution of OH termination sites at the edges is small relative to the total charge of the particles.

Anion Adsorption

Some anion types may be attracted to, and become essentially a part of, particle surfaces or edges, thereby increasing the particle’s electronegativity. Some neg-atively charged radicals, for example, phosphate, ar-senate, and borate, have about the same size and geometry as the silica tetrahedron and are in this cat-egory. Phosphates, in particular, are strongly attracted, and certain of the phosphate compounds are among the most effective deflocculating agents for soil suspen-sions. Tannates can improve the stability of drilling muds (van Olphen, 1977). The tannate ions are

ad-sorbed at particle edges by complexing with the ex-posed octahedral aluminum ions. This produces a negative edge charge that prevents edge-to-face floc-culation. The surface chemistry of anion adsorption is discussed in some detail by Sposito (1989).

Little is known about whether clays have anion exchange spots on basal surfaces, although replace-ment of (OH)^⫺ is a possible mechanism for their ex-istence. Anions, particularly bicarbonate, appear to be important in spontaneous dispersion followed by ero-sion of some low-to-medium sodium content Austra-lian soils (Ingles, 1972).

6.11 ENERGY AND FORCE OF REPULSION