The impact of shear strain

As wc pointed out in S tion 4.3.1, the confiiKHl fluid an be cxj)osed to a nonvanisliiug shear strain by misaligning the two chemically striped surfaces. Misaligmnent is specified quantitatively in terms of the parameter a in Eq. (4.48a). On account of the discrete nature of our model, a can only be varied discretely iu increments of Aa = l/n. This section is devoted to a discussion of both structure and phase behavior of a confined lattice fluid exposed to a shear strain. 

We begin with the simplest situation in which the substrates are in registry, that is, a = 0 in Eq. (4.48a). Applying the numerical procedmre detailed in Appendix D.2.1 permits us to calculate the local density p x,z) as a solution of Eq. (4.86). Because of the discrete nature of the our model, 

The bridge phase is unique in the sense that it has no counterpart in the bulk because its structure is sort of imprinted on the fluid by the chemical structure of the confining substrates. The importance of confinement for the existence of bridge phases is illustrated by plots of phase diagrams for various degrees of confinement in Fig. 4.12. The horizontal line in Fig. 4.12(a) represents the bulk pheise diagram, which we include for comparison. Thermodynamic states p Pxb T) = —3 and p pxb = —3 pertain to the one-phase region of bulk liquid and gas, respectively T Tcb = ). 

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. 

The preceding section clearly illustrates the complex phase behavior one can expect if fluids are confined between chemically decorated substrate surfaces. Three different length scales, which are present in our model, are primarily responsible for this complexity. In addition to the one corresponding to the range of interactions between lattice-fluid molecules (i.e., C), another length scale refers to confinement (i.e., rt ) and is already present if the substrates aic chemically homogcnc ous. It causes 

If n decreases, a bifurcation appears at T = Tt,. Only (inhomogeneous) liquid- and gas-like phases coexist along the line /i (T) T Tir). At T = Ti, the latter two are in thermodynamic equilibritmi with a bridge phase. For T Tit, the eoexistenee curve consists of two branches. Tlic upper one, /i (T), can be interpreted as a line of first-order phase transitions involving liquid-like and bridge phases whereas the lower one, pf T), corresponds to bridge and gas-like phases, respectively. Both branches terminate at their respective critical points //., 7 and /if, 7 . The entire coexistence curve fix (T) of the lattice fluid is formed by /if (T), /t (T), /tj( (T), and the point /itriTir. Moreover, we verified numerically that 

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