Vermiculite systems

The water isotherm on natural montmorillonite in Figure 11.6 (Barrer and Reay, 1957), has an ill-defined double step. Similar results were reported by van Olphen (1965) for the water/vermiculite system. After further work, van Olphen (1976) came to the conclusion that the sorption of water molecules produces a stepwise expansion of the layer lattice of smectites and vermiculites, with the interlayer formation of one to four monolayers of water. 

It is clear from this chapter that the coulombic attraction theory potential is much better adapted to explain the experimental phenomena described in Chapter 1 than the DLVO theory potential (Equation 1.2). Of course, if you predict an interaction potential, you predict force-distance curves along the swelling axis. There have been a lot of arguments about how direct measurements of forces between spherical colloidal particles refute the coulombic attraction theory. Let us get the facts first. We now examine the experimental curves for the n-butylammonium vermiculite system. 

Until we discovered the constancy of the surface potential from the uniaxial stress results, like most other people, I had been more interested in constant surface charge models. If you do not know how the valency of a macroion varies with the external conditions, it is reasonable to assume it to be constant unless given evidence to the contrary. Given the evidence that y/0 70 mV is roughly constant for the n-butylammonium vermiculite system, what other consequences follow from this In particular, what happens if we apply the coulombic attraction theory with the constant surface potential boundary condition ... 

We may have made some rough approximations, but we now have the leading features of the behavior that we sought, in terms of elementary analytic functions. The predictions for 5 can, of course, be tested. If 0S is constant with respect to electrolyte concentration, we predict that s will also be constant with respect to c, which appears to be a novel result. For 0S = const = 70 mV, as in the n-butylammonium vermiculite system, we predict. t = 2.8. This second prediction is markedly different from the value s = 4.0 predicted from the Donnan equilibrium. In the next chapter we will describe our experimental tests of these two predictions. 

The n-butylammonium vermiculite system is an example of a three-component system of a monodisperse colloid, electrolyte and solvent. There are four constituents in the macroionic solution — the negatively charged clay plates, n-butylammonium ions (counterions), chloride ions (co-ions), and water — but these may not vary independently because they are subject to the restriction that... 

Let us recall the schematic illustration of the raw phenomenon of the clay swelling in Figure 1.4. In the cases studied in Chapters 1 to 3, V was always much greater than V, the volume occupied by the macroions. We now define Vm to be the volume occupied by the macroions in the coagulated (crystalline) state, as in Figure 1.4a in the vermiculite system. This is an experimentally controlled variable. We define the sol concentration r by... 

Before setting out on the exact mean field theory solution to the one-dimensional colloid problem, I wish to emphasize that the existence of the reversible phase transition in the n-butylammonium vermiculite system provides decisive evidence in favor of our model. The calculations presented in this chapter are deeply rooted in their agreement with the experimental facts on the best-studied system of plate macroions, the n-butylammonium vermiculite system [3], We now proceed to construct the exact mean field theory solution to the problem in terms of adiabatic pah-potentials of both the Helmholtz and Gibbs free energies. It is the one-dimensional nature of the problem that renders the exact solution possible. 

The Nemst equation applies (if we neglect the activity coefficients of the ions, in keeping with PB theory) to the emf (electromotive force) of an electrochemical cell. The emf of such a cell and the surface potential of a colloidal particle are quantities of quite different kinds. It is not possible to measure colloidal particle with a potentiometer (where would we place the electrodes ), and even if we could, we have no reason to expect that it would obey the Nemst equation. We have been at pains to point out that all the experimental evidence on the n-butylam-monium vermiculite system is consistent with the surface potential being roughly constant over two decades of salt concentration. This is clearly incompatible with the Nemst equation, and so are results on the smectite clays [28], Furthermore, if the zeta potential can be related to the electrical potential difference deviations from Nemst behavior, as discussed by Hunter... 

The phase diagram was mapped out on the LOQ instrument at ISIS, Didcot, U.K. [16], just as for the butylammonium vermiculite system [6]. Typical scattering patterns from an r = 0.01, c = 0.25 M propylammonium vermiculite gel are shown at T = 36, 38, 40 and 42°C in Figure 9.6. The story is by now a familiar one a gel with a well-defined d-value at low temperatures (in this case d = 60 A) collapses as the temperature increases at a well-defined phase transition temperature (in this case Tc = 39°C). Note that the butylammonium system will not swell at c > 0.2 M, whereas here we have colloidal swelling at c = 0.25 M. The complete c, T phase diagrams at low r for both the propylammonium and butylammonium systems, taken in contiguous experiments, are shown in Figure 9.7. It is clear that the propylammonium vermiculites will swell in salt concentrations up to about 0.5 M in cold water. In these circumstances, their -values decrease below 50 A, and so could be measured on LAD. 

Before moving on to our attempt to measure the complete double layer in a swollen propylammonium vermiculite with d = 43.6 A [18], we pause to note that (a) at ionic strengths relevant to cell fluids, namely c 0.12 M [19], the phase-transition temperature in the propylammonium vermiculite system is not so far away from our body temperature and (b) similar temperature-induced gel-crystal transitions are observed in many biochemical systems. An example is the deoxyhemoglobin molecule that causes sickle cell anemia [33], We also note that with both counterions, Tc decreases linearly with the logarithm of the salt concentration. 

We do have to be careful in the way we apply the definition of a phase to the n-butylammonium vermiculite system. According to Gibbs [13], a phase is any homogeneous and physically distinct part of a system that is separated from other parts of the system by definite boundary surfaces. Because the gel can be lifted out of the supernatant fluid on a spatula, it clearly justifies description as a phase in the latter sense, but it is inhomogeneous on the nanometer-to-micron (colloidal) length scale. It can only be defined as homogeneous on the macroscopic length scale. The same considerations apply to the tactoid phase. 

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