Gibbs adiabatic potentials

FIGURE 6.20 Trajectories of the stable interplate distance dmlll of the Gibbs adiabatic potential V[G plotted against the concentration c of the external soaking solution for three values of the surface potential s in the Dirichlet model. The width of the container is set to be... 

Finally, consider a two-phase, two-component system in which the two phases are separated by an adiabatic membrane that is permeable only to the first component. In this case we know that the temperatures of the two phases are not necessarily the same, and that the chemical potential of the second component is not the same in the two phases. The two Gibbs-Duhem equations for this system are... 

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 formula for the adiabatic Gibbs potential (Equation 6.51) is exact within the framework of the mean held description. As with the adiabatic Helmholtz potential, we examine it numerically following the Carlson theory of elliptic integrals [15-21], In order to make clear comparisons between the two types of free energy, the width D of the container is set to be 200 nm throughout (except for Figure 6.21). 

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