An established procedure in clay research is to differ between regions of “crystalline” and “osmotic” swelling. Although this distinction makes sense in many ways, I think it is unfortunate that one of the regions has been named “osmotic”, as it may suggest that bentonite1 swelling is only partly osmotic, or that it is only osmotic in certain density ranges.
In this post I argue for that bentonite swelling pressure should be understood as an osmotic pressure under all conditions, and discuss the distinction between “crystalline” and “osmotic” swelling in some detail.
Bentonite swelling pressure is an osmotic pressure, under all conditions
A macroscopic definition of osmosis and osmotic pressure cannot depend on specific microscopic aspects. Here we take the description from Atkins’ Physical Chemistry2 as a starting point
The phenomenon of osmosis is the spontaneous passage of a pure solvent into a solution separated from it by a semipermeable membrane , a membrane permeable to the solvent but not to the solute. The osmotic pressure , \(\Pi\), is the pressure that must be applied to the solution to stop the influx of solvent.
These definitions are written with simple aqueous solutions in mind,3 but can easily be generalized to include bentonite lab samples. For such a case the role of the “solution” is taken by the bentonite sample, and the “solutes” are the exchangeable cations and other dissolved species, as well as the individual clay particles. The semipermeable membrane in a bentonite set-up is typically filters confining the sample. Note that such filters are impermeable only to the clay particles, while e.g. the exchangeable ions can freely move across them. That the exchangeable ions anyway are located in the sample is because of the electrostatic coupling between them and the clay particles; the filters keep the clay particles in place, and the requirement of charge neutrality forces, in turn, the exchangeable ions to stay in place. Finally, in a bentonite set-up the external water source is in general itself an aqueous solution (often a salt solution). But even if the above description assumes a source of pure solvent it is clear that the mechanism (passage of solvent) is active also if the external source contains several components.
With these remarks it should be clear that water uptake in a laboratory bentonite sample is an osmotic effect and that swelling pressure is an osmotic pressure: swelling pressure is the pressure (difference) that must be applied to prevent further spontaneous inflow of water from the external source.
Note that the definition of osmotic pressure says nothing about the specific microscopic conditions — it would be rather bizarre if it did. That would imply that the poor lab worker must have knowledge, e.g. of whether a certain interlayer distance is realized in the sample, in order to judge whether or not the measured swelling pressure is an osmotic pressure.
What qualifies swelling pressure as an osmotic pressure is summarized in the relation
\begin{equation} P_s = -\frac{\Delta \mu_w}{v}, \tag{1} \end{equation}
which in earlier blog posts was shown to be generally valid in bentonite. Here \(\Delta \mu_w\) is the difference in water chemical potential between the non-pressurized bentonite and the external solution, and \(v\) is the partial molar volume of water. The presence of \(\Delta \mu_w\) in eq. 1 expresses the “spontaneous” character of the phenomenon: “spontaneous” in this context means movement of water from higher to lower chemical potential. \(\Delta \mu_w\) may have contributions both from entropy and energy, which can be expressed (a bit sloppy) as
\begin{equation} \Delta \mu_w = \Delta h_w – T \Delta s_w, \tag{2} \end{equation}
where \(\Delta h_w\) and \(\Delta s_w\) are the differences in (partial) molar enthalpy and entropy, respectively, and \(T\) is the absolute temperature.
Indeed, \(\Delta h_w\) dominates in very dense bentonite. But the chemical potential having both energetic and entropic contributions is in principle no different from more conventional aqueous solutions, as manifested in osmotic coefficients generally being different from unity.
When only mixing entropy contributes to \(\Delta \mu_w\), and in the limit of a dilute solution, eq. 1 reduces to van ‘t Hoff’s formula \(\Pi = RTc\), where \(c\) is the solute concentration. Thus, rather than defining osmotic pressure, van ‘t Hoff’s formula is a limit of the the general relation expressed in eq. 1.
“Crystalline” vs. “osmotic” swelling
Although a division between “crystalline” and “osmotic” swelling regions can be found in the literature as far back as the 1930s, there doesn’t seem to be fully coherent definitions of these terms.
Some authors use an interlayer spacing range to define the crystalline swelling regions, some emphasize “hydration” of ions or surfaces (or both) as the defining feature. Some associate crystalline swelling with the release of an appreciable amount of heat, and others with that it occurs in discrete steps. There are also examples of authors differing between “limited” and “extensive” crystalline swelling.
Note that any of these definitions complies with swelling pressure being an osmotic pressure of the form discussed above; the release of heat, or effects of “hydration”, is accommodated by a non-zero enthalpy contribution (\(\Delta h_w\)) in eq. 2.
Also the “osmotic” swelling region is defined by some authors in terms of an interlayer spacing range. But in defining this region, many authors allude to some emerging “diffusive” property of the exchangeable cations, and here I really think the definitions become problematic. E.g. Madsen and Müller-Vonmoos (1989) discuss two “phases” of swelling, and write
Unlike innercrystalline swelling, which acts over small distances (up to 1 nm), osmotic swelling, which is based on the repulsion between electric double layers, can act over much larger distances. In sodium montmorillonite it can result in the complete separation of the layers. […] The driving force for the osmotic swelling is the large difference in concentration between the ions electrostatically held close to the clay surface and the ions in the pore water of the rock.
Leaving aside what is exactly meant by the term “pore water”, there are several issues here. Firstly, it appears that the authors have in mind a text book version of osmosis — basically van ‘t Hoff’s formula — when writing that the driving force is due to “differences in concentration”. But the actual driving force is differences in water chemical potential, which only under certain circumstances can be translated to differences in solute concentration. Note that also in the case of “crystalline” swelling is water transported from regions of low to regions of (really) high ion concentration. So, with the same logic you can also claim that the driving force for “crystalline” swelling is “large differences in concentration”.
Secondly, the electric double layer is an example of a system where there is no simple relation between ion concentration differences and transport driving forces — the diffuse layer displays an ion concentration gradient in equilibrium, and very weakly overlapping diffuse layers can be conceived of, where the driving force for in-transport of water is minimal, even though the ion concentration closest to the surfaces is large. To arrive at a van ‘t Hoff-like equation for the osmotic pressure of an overlapping diffuse layer, you first have to solve an electrostatic problem (the Poisson-Boltzmann equation, or something worse). With that analysis made, the (approximate4) osmotic pressure can be related to the midpoint concentration in the interlayer space. Madsen and Müller-Vonmoos (1989) present some electrostatic treatment, but, as far as I can see, don’t reflect over the amount of energetics involved in evaluating the osmotic pressure.
Lastly, the way these and many other authors single out the “diffusive” nature of the exchangeable cations when defining “osmotic” swelling implies that they do not consider ions to be diffusive in “crystalline” swelling states. Norrish (1954) states this quite explicitly (writing about the “crystalline” swelling region)
Nor can the interaction of diffuse double layers produce a repulsive force since in this region diffuse double layers are not formed. The repulsive forces of ion hydration and surface adsorption are probably the initial repulsive forces for many other colloids. They can cause surface separations of \(\sim 10\) Å, where the ions could begin to form diffuse double layers.
Even though I cannot find any explicit statements in Norrish (1954), writing like this makes me fear that authors of this era were under the impression that the initial interlayer hydration states consist of actual crystalline (non-liquid) water; I note that e.g. Grim (1953) has a several pages long section entitled “Evidence for the Crystalline State of the Initially Adsorbed Water”. Could it be that the original use of the term “crystalline” swelling was influenced by this belief?
Anyway, nowadays we have vast amount of evidence that interlayer water — at least down to the bihydrate — is liquid-like, and that ions in such states certainly diffuse. It follows that the osmotic pressure in such states has a contribution from mixing entropy.5 It should also be pointed out that the prevailing qualitative explanation for limited swelling in Ca-montmorillonite — which often is described as only displaying “crystalline” swelling — is due to ion-ion correlations in a diffusive system (“overlapping” diffuse layers).
Despite the evidence for interlayer diffusivity, it is very common to find descriptions in the bentonite literature that diffuse layers “develop” or “form” as the interlayers distances (or some other presumed pore) becomes large enough. This is usually claimed without giving a mechanism of how such a “development” or “formation” occurs. I genuinely wonder what authors using such descriptions believe the ions are doing when they have not “formed” a diffuse layer…
My message here is not that a division between “crystalline” and “osmotic” swelling should be discarded — for certain issues it makes a lot of sense to make a distinction, especially as the transition between these regions is not fully understood. But I think authors can do a better job in defining what exactly they mean by terms such as “osmotic”, “crystalline”, “diffusive”, etc. I furthermore wish that another name could be established for the “osmotic” swelling region (Norrish (1954) actually used “Region 1” and “Region 2”), although that seems rather unlikely. Until then we have to live with that bentonite swelling is described as “osmotic” only in a certain density range, while — if reasonable definitions are adopted — bentonite swelling pressure actually is an osmotic pressure under all conditions.
Footnotes
[1] In the following I usually mean bentonite when writing “bentonite”, even though the main points of the blog post also apply to claystone with swelling properties.
[2] The quotation is taken from the 8th edition.
[3] Note how this description does not refer to any microscopic concepts, nor to differences in concentrations. There seems to be a whole academic field devoted to sorting out misconceptions about osmosis. For further reading, I can recommend e.g. (Kramer and Mayer, 2012) and (Bowler, 2017).
[4] There may be additional significant activity corrections. I guess a solution of the Gouy-Chapman model could be compared to using the Debye-Hückel equation for a conventional aqueous salt solution.
[5] I am not arguing for that swelling is driven by entropy in these states — the entropy contribution is actually negative. But the entropy reasonably has both a positive (mixing) and a negative (hydration) part.
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