Lattice fluid bulk critical point

Fig. 27. Phase diagram of an adsorbed film in- the simple cubic lattice from mean-fleld calculations (full curves - flrst-order transitions, broken curves -second-order transitions) and from a Monte Carlo calculation (dash-dotted curve - only the transition of the first layer is shown). Phases shown are the lattice gas (G), the ordered (2x1) phase in the first layer, lattice fluid in the first layer F(l) and in the bulk F(a>). For the sake of clarity, layering transitions in layers higher than the second layer (which nearly coincide with the layering of the second layer and merge at 7 (2), are not shown. The chemical potential at gas-liquid coexistence is denoted as ttg, and 7 / is the mean-field bulk critical temperature. While the layering transition of the second layer ends in a critical point Tj(2), mean-field theory predicts two tricritical points 7 (1), 7 (1) in the first layer. Parameters of this calculation are R = —0.75, e = 2.5p, 112 = Mi/ = d/2, D = 20, and L varied from 6 to 24. (From Wagner and Binder .)...

More subtle effects are observed if the lattice fluid is confin by solid substrates as plots in Fig. 4.12(a) show. For sufficiently large ri, chemical decoration of the substrate does not matter but eonfiuement effects prevail. For example, for Ux = 15, the critical point is shifted to lower 7 and pf compared with bulk Tcb = and peb = —3. Moreover, pf (T) is no longer parallel with the temperature axis as in the bulk. 

In the limit ab = 10, the symmetric binary mixture degenerates to a pure fluid. In this case Tcep —> 0 and the A-linc becomes formally indistinguishable from the /r-axis (and therefore physically meaningless). The remaining coexistence line /Xxb = -3 = /icb (i e-, the phase diagram) involving gas (G) and liquid phases (L) becomes parallel with the T-axis and ends at the critical point where Tcb = as expected for the bulk lattice gas [16] [see, for example, Fig. 4.12(a)]. 

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