Decomposition of symmetric binary mixtures

If we now confine the binary mixture to a slit-pore of nanoscopic dimension, we may, in fact, change the topolgy of the phase diagram. For example, by varying the degree of confinement (i.e., z in our current notation), it turns out to be possible to switch between various types of phase diagrams with profound consequences for liquid liquid and gas liquid phase equilibria. This phenomenon may have practical implications for the decomposition of mixtures of immiscible liquids in nanoporous matrices. 

If one then fixes the thermodynamic state such that the bulk mixture is a gas [represented by in the inset in Fig, 4.15.(a)], confinement to a relatively wide pore (i.e., z — 12) may first cause capillary condensation to a mixed liquid mixture analogous to ordinary capillary condensation in pure fluids. If the fluid is confined to a narrower pore (z = 6), however, decomposition into A-rich and B-rieh liquid phases is triggered by confinement upon condensar tioii. Thus, by choosing an appropriate pore width, one can either promote condensation of a gas to a mixed liquid phase or, alternatively, initiate liquid liquid phase separation in the porous matrix where both processes are solely confinement-driven because the pore walls are nonselective for molecules of either species in our present model. 

This process is further illustrated by the plots in Fig. 4.15(b) where the moan dorusity J of thermodynamically stable confined pha.ses is plotted as a function of z (i.c., the pore width). Three different branches arc discernible. For small z 8, p is relatively high indicating that the pore is filled with liquid. A corresponding plot of the local densities of a representative phase for z = 5 shows that this liquid consists locally of A- (or B-)rich, high-density fluid (because the two cannot be distinguished in a symmetric mixture). Hence, for 2 8, we observe (local) decomposition of liquid mixtures. 

Along an intermediate branch of pore widths, that is, for 8 16, p is somewhat smaller than for the tightest pores (z 8). An inspection of a prototypical plot of the local densities for z = 12 reveals that the confined phase now consists of a locally equimolar mixture. Hence, for intermediate pore sizes, the confined phase is a mixed hquid. 

Finally, for z 16, p is still smaller than along the two previously discussed branches. The local density of a representative state for z = 20 now 

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