Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed “wetting” film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a “bridging” transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein–Zernike equations.
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In order to locate the single particle thin-thick adsorbed film transition line, one approach is to calculate density profiles at a series of state points along a particular path in the phase diagram. If one uses as a starting approximation in the numerical (iterative) procedure for calculating the density profiles those profiles corresponding to the previous point on the path, then one finds at some state point there is a jump from a thin to a thick adsorbed film. However, this jump does not occur at the equilibrium transition, rather it occurs at the “spinodal” for this single particle thin-thick adsorbed film transition. In order to locate correctly the equilibrium transition line, one must calculate the grand potential corresponding to the profiles with a thick and those with a thin adsorbed film. The proper location for the transition is where these two grand potential curves cross. Near the thin-thick adsorbed film critical point there is little hysteresis and therefore very little difference between the location of the line of equilibrium transitions and the spinodal lines. However, for the present system well away from the critical point, there can be very substantial hysteresis. In Ref. 9 a spinodal line was calculated rather than the true transition line, plotted here in Fig. 1. Similar problems of metastability were elucidated in recent DFT studies of layering transitions for a model colloid-polymer mixture adsorbed at a hard wall (Ref. 31).
