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13b). (c) A spherical interface Possible examples of this geometry include: a spherical meniscus or bubble, a droplet on a solid substrate, or a fluid adsorbed in a spherical cavity. The coordinates are now (r, e, cp) with r normal to the interface. -~ - p(al(r)F = 0 r SIn e acp rp ! 15c) becomes iJPN + 2(PN - PT) _ p(a)(r)Fr = O. a:a: dr. 16) This is the work done on the system against the intermolecular forces in the fluid but does not include any body forces such as the external forces due to a solid adsorbent.

Goshen etal. (1974) have shown how the treatment of such helicoidal structures by a separate procedure can be justified. 91) where I enumerates the irreducible representations and i the members of a representation, Cli being the associated order parameter component. For T > Tc all the factors AI( T, p) must be positive, and at T = Tc just one of these factors (that with index 10 ) must be on the point of changing sign. 46 2. Thermodynamics of interfaces Goshen et al. distinguished two types of model: those for which 10 varies as Tc(P) varies, and those for which 10 does not change, being fixed by symmetry.

87)). In these circumstances the structures which are favoured are those known as "helicoidal", which includes the helix and the conal spiral, in which VrJ is non-zero but V2rJ is zero. A hypothetical phase diagram which includes a Lifshitz point for a magnetic system is shown in Fig. 8. " I ~A T C Parameter p Fig. 8. Suggested phase diagram showing a Lifshitz point (L). The parameter p could be the pressure or alloy composition, according to the nature of the system; k is the wave vector of the helicoidal structure (C*).

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