Shear strain lattice fluid

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. 

Because of the similarity between the lattice fluid calculations and the MC simulations for the continuous model, it seems instructive to study the phase behavior in the latter if the confined fluid is exposed to a shear strain. This may be done quantitatively by calculating p as a function of p and as -For sufficiently low p, one expects a gas-like phase to exist along a subcritical isotherm (see Fig. 4.13) defined as the set of points (T = const)... 

However, one-dimensional confined fluids with purely repulsive interactions can be expected to be only of limited usefulness, especially if one is interested in phase transitions that cannot occur in any one-dimensional system. In treating confined fluids in such a broader context, a key theoretical tool is the one usually referred to as mean-field theory. This powerful theory, by which the key problem of statistical thermodynamics, namely the computation of a partition function, becomes tractable, is introduced in Chapter 4 where we focus primarily on lattice models of confined pure fluids and their binary mixtures. In this chapter the emphasis is on features rendering confined fluids unique among other fluidic systems. One example in this context is the solid-like response of a confined fluid to an applied shear strain despite the absence of any solid-like structure of the fluid phase. 

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an... 

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