It is easy to find models assuming montmorillonite interlayers devoid of “anions” . Here I will present empirical evidence that such an assumption is incorrect. Before doing so, just a quick remark on the term “anions” in this context. If anions reside in interlayers, they certainly do so accompanied by excess cations, in order to maintain overall charge neutrality. Thus, when speaking of “anions” in the interlayer we really mean “salt” (= anion(s) + cation(s)). In the following I will use the term “salt” because it better reflects the overall charge neutral character of the process (we are not interested in pushing a handful of negative charge into an interlayer).

The nature of bentonite swelling

The evidence for salt having access to interlayers follows directly from the observed swelling pressure response to changes in external salinity. It is therefore important to first understand the thermodynamic basis for swelling pressure, which I wrote about in an earlier post (the same nomenclature is adopted here). In essence, swelling is a consequence of balancing the water chemical potential¹ in the clay with that in the external solution², and swelling pressure quantifies the difference in chemical potential between the external solution and the non-pressurized bentonite sample, as illustrated here

Since the chemical potential in the external solution depends on the salt content, we generally expect a response in swelling pressure when altering external salinity.

Labeling the salt concentration \(c^{ext}\), we write the chemical potential of the external solution in terms of an osmotic pressure³

\begin{equation}
\mu_w^{ext} = \mu_0 – P_{osm.}^{ext}(c^{ext})\cdot v_w
\tag{1}
\end{equation}

where \(v_w\) is the partial molar volume of water. \(P_{osm}^{ext}\) is not the pressure in the external solution, but the pressure that would be required to keep the solution in equilibrium with pure water. The actual pressure in this compartment is the same as for the reference state: \(P_0\). It may seem confusing to use a “pressure” to specify the chemical potential, but we will see that it has its benefits. Experimentally we have full control of \(P_{osm}^{ext}\) by choosing an appropriate \(c^{ext}\).

Response in an indifferent clay

With salt in the external solution, the big question is what happens to the chemical potential of the clay. We will start by assuming (incorrectly) that external salt cannot access the interlayers. This means that the chemical potential of the (non-pressurized) bentonite does not change when the external salinity changes. We refer to this hypothetical bentonite as indifferent. In analogy with the external solution, we write the chemical potential of the indifferent non-pressurized bentonite as⁴ \begin{equation} \mu_w^{int}(P_0) = \mu_0 -P_s^0\cdot v_w \;\; \;\; \;\; \text{(indifferent clay)} \end{equation}

were \(P_s^0\) is the swelling pressure in case of pure water as external solution. By assumption, \(\mu_w^{int}(P_0)\) does not depend on the external salinity (it is independent of \(P_{osm}^{ext}\)). The chemical potential in the indifferent clay at an elevated pressure \(P\) is

\begin{equation}
\mu_w^{int}(P) = \mu_0 – P_s^0\cdot v_w +(P-P_0)\cdot v_w \;\;
\;\; \;\; \text{(indifferent clay)}
\tag{2}
\end{equation}

The swelling pressure (defined as the difference in pressure between bentonite and external solution, when the two are in equilibrium: \(P_s \equiv P_{eq} – P_0\)) in an indifferent clay is given by equating eqs. 1 and 2, giving the neat formula

\begin{equation}
P_s(c^{ext}) = P_s^0 – P_{osm}^{ext}(c^{ext}) \;\; \;\; \;\;
\text{(indifferent clay)}
\end{equation}

Note the following:

• Although an indifferent clay is not affected by salt, it certainly has a swelling pressure response, demonstrating that swelling pressure depends as much on the external solution as it does on the clay.
• Since swelling pressure in this case decreases linearly with the osmotic pressure of the external solution, it is predicted to vanish when the osmotic pressure equals \(P_s^0\).
• External osmotic pressures larger than \(P_s^0\) implies “drying” of the clay (water transport from the clay into the external compartment)

If the above derivation feels a bit messy, with all the different types of pressure quantities to keep track of, here is a hopefully helpful animation

Real swelling pressure response

Equipped with the swelling pressure response of an indifferent clay, let’s compare with the real response: The swelling pressure response in real bentonite deviates strongly from the indifferent clay response. This is seen e.g. here for Na-montmorillonite equilibrated in sequence with NaCl solutions of increasing concentration⁵ (data from Karnland et al., 2005 )

Swelling pressure indeed drops with increased concentration, but the drop is not linear in \(P^{ext}_{osm}\), and is weaker as compared with the indifferent clay response (shown by dashed lines). All samples in the diagram above exert swelling pressure when \(P^{ext}_{osm} \gg P_s^0\), i.e. far beyond the point where the swelling pressure in an indifferent clay is lost.

The deviation of the observed response from that of an indifferent clay directly demonstrates that the clay is affected by salt, i.e. that the chemical potential of the non-pressurized clay depends on the external salt concentration. The only reasonable way for salt to influence the chemical potential in the bentonite is of course to reside in the interlayer pores. Consequently, the observed swelling pressure response proves that salt from the external solution enters the interlayer pores.

Here is an illustration of how the chemical potentials relate to the swelling pressure in real bentonite

Although the observed swelling pressure response in itself is sufficient to dismiss the idea that salt does not have access to interlayers, the study by Karnland et al., (2005) provides a much broader verification of the thermodynamic nature of swelling pressure. In particular, the chemical potential was measured (by means of vapor pressure) separately in the same samples as used for swelling pressure tests, after they had been isolated and unloaded. The terms in the relation \(P_s = \left(\mu_w^{ext} – \mu_w^{int}(P_0) \right)/v_w\) were thus checked independently, as indicated here

A striking confirmation of salt residing in interlayers is given by the observation that the chemical potential in the non-pressurized samples is lower than that in the corresponding external solution, as well as that in non-pressurized samples of similar density, but equilibrated with pure water.

Another interesting observation is that the sample with the highest density behaves qualitatively similar to the others: although the external osmotic pressure never exceeded \(P_s^0\) (\(\approx\)56 MPa), the response strongly deviates from that of an indifferent clay

Because the pore space of samples this dense (\(2.02\;\mathrm{g/cm^3}\)) mainly consists of mono- and bihydrated interlayers, this similarity in response shows that salt has access also to such pores.

Implications

The issue of whether “anions” have access to montmorillonite interlayers has — for some reason — been a “hot” topic within the bentonite research community for a long time, and a majority of contemporary models rest on some version of the assumption that “anions” does not have access to the full pore volume. But, as far as I can see, this whole idea is based on misconceptions. I guess that saying so may sound quite grandiose, but note that swelling pressure is not at all considered in most chemical models of bentonite. And if it is, it is usually treated incorrectly. As an example, here is what Bradbury and Baeyens (2003) writes in a very influential publication

One of the main premises in the approach proposed here is that highly compacted bentonite can function as an efficient semi-permeable membrane (Horseman et al., 1996). This implies that the re-saturation of compacted bentonite involves predominantly the movement of water molecules and not solute molecules. Thus, to a first approximation, the composition of the external saturating aqueous phase should be a second-order effect which has little influence on the initial compacted bentonite porewater composition.

If the composition of the re-saturating water were to play an important role in determining the porewater composition, then it should also have a significant influence on swelling (Bolt, 1979). Dixon (2000) recently reviewed the role of salinity on the development of swelling pressure in bentonite buffer and backfill materials. He concluded that provided the initial dry densities were greater than 900 \(\mathrm{kg\;m^{-3}}\), the swelling pressures developed are unaffected for groundwater salinities \(< 75 \;\mathrm{g\;l^{-1}}\). Even brines appear to have little or no influence for initial dry densities \(>1500 \;\mathrm{kg\;m^{-3}}\).

But, as we just have learned, a system with a weak swelling pressure response necessarily has a significant contribution to its water chemical potential due to externally provided salt. In contrast, the approximation discussed in the first paragraph of the quotation — which is basically that of an indifferent clay — maximizes the swelling pressure response. Thus, the discussed “main premise” does not hold, and the provided empirical “support” is actually an argument for the opposite (i.e. that salt has access to the clay).

Footnotes

[1] In the following I will write only “chemical potential” — it is always the chemical potential of water that is referred to.

[2] This is just a complicated way of saying that swelling is (an effect of) osmosis.

[3] Some may say that \(P_{osm}^{ext}\) is simply the “suction” of the solution, but I am not a fan of using that concept in this context. I will comment on “suction” in a later blog post.

[4] The density dependence of the chemical potential in the bentonite is not explicitly stated here, in order to keep the formulas readable, but we assume throughout that the bentonite has some specific water-to-solid mass ratio \(w\).

[5] The NaCl concentrations are 0.0 M, 0.1 M, 0.3 M, 1.0 M, and 3.0 M.