Swelling is not due to electrostatic repulsion between montmorillonite particles
Few things confuse me more than how the role of electrostatics in clay swelling is described in the scientific literature. Consider e.g. this statement from Bratko et al. (1986)
The interaction between charged aggregates in solution is generally interpreted in terms of electrostatic repulsion between double layers surrounding the aggregates.
But in the same paper we learn that the main contribution to the force between two charged surfaces in solution is the entropy of mixing of counter-ions, and that electrostatic interactions actually may result in an attractive force between the surfaces.
Nevertheless, I think Bratko et al. (1986) are right: swelling is, for some reason, often “interpreted” in terms of electrostatic repulsion between electric double layers. It is easy to find statements that e.g. the expression for the osmotic pressure in the Gouy-Chapman model describes “the electrostatic force per unit area”, or that lamellar phases are “electrostatically swollen”, with an osmotic pressure “mainly of electrostatic origin”. Segad (2013) writes
The interactions between the negatively charged platelets lead to a repulsive long-ranged electrostatic force promoting swelling.
and Tester et al. (2016) write
The DLVO theory describes the interaction between two colloidal particles as a balance between electrostatic repulsion, in this case between two negatively charged clay layers, and vdW attraction.
Laird (2006) claims that electrostatics cause both repulsion and (strong) attraction between clay layers
A balance between strong electrostatic-attraction and hydration-repulsion forces controls crystalline swelling. The extent of crystalline swelling decreases with increasing layer charge. Double-layer swelling occurs between quasicrystals. An electrostatic repulsion force develops when the positively charged diffuse portions of double layers from two quasicrystals overlap in an aqueous suspension. Layer charge has little or no direct effect on double-layer swelling.
Although many authors reasonably understand the actual mechanisms of double layer repulsion, I think it is very unfortunate that this language is established and contributes to unnecessary confusion.
To gain some intuition for that clay swelling is not primarily due to electrostatic repulsion between montmorillonite particles, let us consider the Poisson-Boltzmann equation. This is, after all, the description usually referred to when authors speak of “electrostatic repulsion” between clay layers. The Poisson-Boltzmann equation may be used to describe the electrostatic potential, and the corresponding counter-ion equilibrium distribution, between two equally charged surfaces, and a typical result looks like this1
Here we assume two negatively charged parallel surfaces with uniform charge density, and the counter-ions are represented by a continuous charge density. The system is assumed infinitely extended in the x- (in/out of the page) and y- (up/down) directions, and thus rotationally symmetric around the z-axis.
With a lot of equal charges “facing” each other, the illustration may indeed give the impression that there somehow is an electrostatic repulsion between the surfaces. That this is not the case, however, may be seen from the symmetry of the potential. In fact, replacing one of the negatively charged surfaces by a neutral surface at half the distance does not change the solution to the Poisson-Boltzmann equation! A charged and a neutral surface thus experience the same repulsion as two charged surfaces, if only placed at half the distance.2
With one surface being uncharged, “interpreting” the force as an electrostatic repulsion between the particles makes little sense.
A related way to convince yourself that there is no electrostatic repulsion between the two charged surfaces is to consider the electric field generated by one “half” of the original system. This field vanishes on the outside of the considered “half”-system.
This means that removing a “half”-system would not be “noticed” by the other “half”-system, in the sense that the electric field configuration remains the same (and corresponds to having a neutral particle at half the distance).
It may be helpful to also remember from electrostatics that the electric field outside a plate capacitor vanishes. Thus, configuring two plate capacitors as shown below, there is no electric field between the positively charged surfaces, regardless of how close they are3.
This “plate capacitor” configuration is actually reminiscent of the charge distribution in an interlayer at low water content (where the continuum assumption of the Poisson-Boltzmann equation is not valid).
A squeezed ion cloud
Having established that there is no direct electrostatic repulsion between clay particles, the obvious question is: what is the main cause for the repulsion? What the two configurations above have in common — with either two charged surfaces or one charged and one neutral surface — is that they restrict the counter ions to a certain volume. Hence, there is an entropic driving force for transporting more water into the region between the surfaces, thereby pushing them apart. Nelson (2013) describes this quite well 4
One may be tempted to say, “Obviously two negatively charged surfaces will repel.” But wait: Each surface, together with its counterion cloud, is an electrically neutral object! Indeed, if we could turn off thermal motion the mobile ions would collapse down to the surfaces, rendering them neutral. Thus the repulsion between like-charged surfaces can only arise as an entropic effect. As the surfaces get closer than twice their Gouy–Chapman length, their diffuse counterion clouds get squeezed; they then resist with an osmotic pressure.
Notice that the presence of this osmotic pressure requires contact with an “external” solution. The existence of a repulsive force between clay layers thus requires that water is available to be transported into the interlayer region. This seems to often be “forgotten” about in many descriptions of clay swelling. But let Kjellander et al. (1988) remind us
The PB pressure between two planar surfaces with equal surface charge equals \(P_\mathrm{ionic} = k_BT\sum_i n_i(0)\), where \(n_i(0)\) is the ion density at the midplane between the surfaces. Due to symmetry there is no electrostatic force between the two halves of the system (the electrostatic fluctuation forces due to ion-ion correlations are neglected). To obtain the net pressure when the system is surrounded by a bulk electrolyte solution, it is necessary to subtract the external pressure calculated in the same approximation; this is given by the ideal gas contribution \(P_\mathrm{bulk} = k_BT \sum_i n_i^\mathrm{bulk}\).
There is no repulsive force of this kind in an isolated, internally equilibrated, clay.
Moreover, the force is usually conceived of as repulsive because the water chemical potential of the surrounding (“external”) solution is typically larger than in the clay. But from an osmotic viewpoint there is nothing fundamentally different going on when the external phase is, say, vapor of low pressure (set e.g. by a saturated salt solution), causing the clay to lose water, i.e to shrink. Thus, if swelling is “interpreted” as electrostatic repulsion between montmorillonite particles, then drying should be “interpreted” as electrostatic attraction between the same particles.
The fact that there is repulsion — in the osmotic sense — between a montmorillonite particle and a neutral surface has huge implications for how to handle interfaces between montmorillonite and other phases in compacted bentonite components. Rather than to simply assume these to contain bulk water (“free water”), there is every reason to believe that the physico-chemical conditions at such interfaces are similar to “ordinary” interlayer pores. Since any type of mineral alteration occurs at such interfaces, there is no escape from understanding interlayer chemistry if a satisfying geochemical description of bentonite is desired.
The role of electrostatics in clay swelling
Although swelling is not primarily due to direct electrostatic repulsion between clay particles, electrostatics is of course essential to consider when calculating the osmotic pressure. And rather than contributing to repulsion, electrostatic interactions actually reduce the pressure. This is clearly seen from e.g. the Poisson-Boltzmann solution for two charged surfaces, where the resulting osmotic pressure corresponds to an ideal solution with a concentration corresponding to the value at the midpoint (cf. the quotation from Kjellander et al. (1988) above). But the midpoint concentration — and hence the osmotic pressure — is lowered as compared with the average, because of electrostatic attraction between layers and counter-ions.
Moreover, a treatment of the electrostatic problem beyond the mean-field (i.e. beyond the Poisson-Boltzmann description) shows that ion-ion correlation cause an explicit attraction between equally charged surfaces (similar to a van der Waals force). In systems with divalent counter ions, this attraction is large enough to prevent swelling beyond a certain limit — a prediction in qualitative agreement with observation. Electrostatics could thus be claimed to contribute to prevent clay swelling.
I think comparison with a simple salt solution can be useful. Nobody (?) would come up with the idea that the primary reason for the osmotic pressure of a NaCl solution is due to electrostatic repulsion between, say, chloride ions. In fact, the electrostatic interactions in such a solution reduce the osmotic pressure compared with a corresponding ideal solution.
Below is plotted the swelling pressure of Na-montmorillonite as a function of the average concentration of counter-ions (data from here). For comparison, the osmotic pressures of a NaCl solution and an ideal solution are also plotted (data from here), as a function of the total amount of ions (i.e. two times the NaCl concentration)5
This plot demonstrates the attractive aspect of electrostatic interactions in these systems. While the NaCl pressure is only slightly reduced, Na-montmorillonite shows strong non-ideal behavior. In the “low” concentration regime (\(<2\) mol/kgw) we understand the pressure reduction as an effect of counter-ions electrostatically attracted to the clay surfaces. The dramatic increase of swelling pressure in the high concentration limit is reasonably an effect of hydration of ions and surfaces; it should be kept in mind that an average ion concentration of 3 mol/kgw in Na-montmorillonite roughly corresponds to a water-to-solid-mass ratio of only 0.3, and an average interlayer width below 1 nm.
Even though there seems to be quite some confusion regarding clay swelling pressure in the bentonite literature, the message here is not that everything about it is in reality understood. On the contrary, there are quite a number of behaviors that, as far as I’m aware, lack fully satisfactory explanations. For example, at room temperature the basal spacing in Ca-montmorillonite is never observed to be larger than \(\sim 19\) Å6, corresponding to a (dry) density of approximately \(1300 \;\mathrm{kg/m^3}\); yet, this material systematically exerts swelling pressure at considerably lower density (\(\sim 700 \;\mathrm{kg/m^3}\)). But in order to tackle issues like these, it is essential to be clear about the swelling mechanisms that we actually do understand.
Update (221018): A correction to this blog post is discussed here.
Footnotes
[1] This particular calculation uses the formulas presented in Engström and Wennerström (1978), and assumes mono-valent counter-ions at room temperature, a charge density of \(-0.1 \;\mathrm{C/m^2}\), and a surface-surface distance of 2 nm.
[2] Here is only considered the Poisson-Boltzmann pressure. If e.g. van der Waals attraction between the surfaces is included, the resulting forces are not necessarily equal. The point here, however, concerns the repulsion due to the presence of diffuse layers.
[3] Having strictly zero field is of course an ideal result, corresponding to an infinitely extended capacitor.
[4] The quotation is taken from a draft version of this book.
[5] The graph denoted “Ideal solution” is simply the van’t Hoff relation \(\Pi = RT c\), which strictly is only valid in the low concentration limit. It is nevertheless here extended to the whole concentration range. In the same way, the NaCl-curve is simply \(\Pi = \varphi RT c\), where \(\varphi\) is the osmotic coefficient for NaCl. Sorry about that.
[6] Upon cooling, Svensson and Hansen (2010) actually observed a basal spacing of 21.6 Å in pure Ca-montmorillonite.