Capillary Phenomena

We're interested in both general and specific aspects of liquid-vapor equilibria in confined spaces, which is often referred to as capillary condensation . For instance, in a simple model of Xenon adsorbing in a cylindrical silica pore of 4 nm diameter, the two configurations shown below are from systems in thermodynamic equilibrium with each other:

Low density, "vapor-like" state (but really an adsorbed multilayer with gas filling the center of the pore.) The configuration is shown with one quadrant of the simulation cell cut away.

High density, "liquid-like" state (but denser than a bulk liquid, more structured, and is stable at pressures below the bubble point.)

Upon confinement, the position and shape of the liquid-vapor coexistence curve is dramatically changed. The critical temperature is lowered, the critical density is shifted towards the liquid phase, and the coexistence curve is generally narrower than in the bulk phase. In addition, there is considerably more hysteresis in the liquid-vapor transition than is observed in bulk systems.

For liquids in amorphous porous materials, which often contain complex networks of pores, the picture is even more complex. It is very difficult to separate local effects from network ones, especially in real experiments where the network structure is not known. There is some debate about what the critical exponents (universality) class of this transition are as well; they are hypothesized to belong to the Random Field Ising Model class, which itself is not very well understood at this time.

We are presently carrying out simulations of liquid-vapor equilibria in our recently developed models of controlled-pore glasses in order to microscopically examine a number of the present hypotheses about the behavior of these systems. We hope to look at phenomena such as:

critical depletion - can we explain this microscopically? Can we reproduce experimental results on this problem?
closure of the hysteresis loop - can we verify the "tensile strength hypothesis" ?
near-critical behavior - what happens to the density and heat capacity of the near-critical vapor because of confinement?

The first part of this work, currently underway, is an attempt to measure the thermodynamic phase diagrams for a model of xenon adsorbing in a series of porous materials with varying pore size and porosity. Our strategy is to first measure the complete adsorption and desorption isotherms at several temperatures, and then to use thermodynamic intergration methods to obtain the chemical potentials at which the high and low density phases coexist. In order to fill in the rest of the phase diagram, we are using "Gibbs-Duhem" integration, in which the coexistence curve is obtained through numerically integrating the first-order Clausius/Clayperon equation for the slope of the coexistence curve.

The figure gives the appropriate pathway for using thermodynamic integration to find the phase transition in an adsorption system. For the adsorption branch, the grand potential can be obtained by simple integration of the adsorption isotherm itself. For the desorption branch, the pathway is more complicated. First, integration in increasing chemical potential at a supercritical temperature is done, followed by integration along a decreasing-temperature pathway at constant chemical potential, followed by integration in decreasing chemical potential along the desorption isotherm! (Peterson and Gubbins, Mol. Phys. 62 (1987), pp. 215-226.)