Phase transition in interfaces

We shall first review very briefly the thermodynamics of first-order phase transitions between ordinary bulk phases at equilibrium. We shall then be able to deseribe in similar terms the closely analogous phase transitions in interfaces. Among these is the Cahn transition, our present subject. 

First-order phase transitions in interfaces and the critical points assodated with them may be described pictorially in the framework of die generalized van der Waals theory. We imagine the free-energy-deisity... 

The second type is simple phase transitions in which one phase transforms into another of identical composition, e.g., diamond graphite, quartz coe-site, and water ice. This type sounds simple, but it involves most steps of heterogeneous reactions, including nucleation, interface reaction, and coarsening. 

V. M. Sadtler, M. Guely, P. Marchal, and L. Choplin, Shear-induced phase transitions in sucrose ester surfactant,./ Colloid Interface Sci., 270 (2004) 270-275. 

Dietrich, S., (1991), Fluid interfaces - wetting, critical adsorption, van der Waals tails, and the concept of the effective interface potential , in Taub, H., Torzo, G., Lauter, HJ. and Fain, S.C., (eds), Phase. Transitions in Surface Films 2, NATO Advanced Science Series, Physics, Vol. 267, 391-423. 

It is well known that water dispersions of amphiphile molecules may undergo different phase transitions when the temperature or composition are varied [e.g. 430,431]. These phase transitions have been studied systematically for some of the systems [e.g. 432,433]. Occurrence of phase transitions in monolayers of amphiphile molecules at the air/water interface [434] and in bilayer lipid membranes [435] has also been reported. The chainmelting phase transition [430,431,434,436] found both for water dispersions and insoluble monolayers of amphiphile molecules is of special interest for biology and medicine. It was shown that foam bilayers (NBF) consist of two mutually adsorbed densely packed monolayers of amphiphile molecules which are in contact with a gas phase. Balmbra et. al. [437J and Sidorova et. al. [438] were among the first to notice the structural correspondence between foam bilayers and lamellar mesomorphic phases. In this respect it is of interest to establsih the thermal transition in amphiphile bilayers. Exerowa et. al. [384] have been the first to report such transitions in foam bilayers from phospholipids and studied them in various aspects [386,387,439-442]. This was made possible by combining the microscopic foam film with the hole-nucleation theory of stability of bilayer of Kashchiev-Exerowa [300,402,403]. Thus, the most suitable dependence for phase transitions in bilayers were established. 

The density functional(DF) method is one of the most promising tools for the calculation of structure and orientation in heterogeneous fluids near phase boundaries. Among many proposals for the application of DF method, that by Tarazona has been frequently used in the studies of interfaces and phase transitions in hard sphere systems. 

Salje EKH (1995) Chemical mixing and stmctural phase transitions The plateau effect and oscillatoiy zoning near surfaces and interfaces. Eur J Mineral 7 791-806 Salje EKH (1999) Ferroelastic phase transitions and mesoscopic stractures. Ferroelectrics 221 1-7 Salje E, Bismayer U, Wrack B, Hensler J (1991) Influence of lattice imperfections on the transition temperatures of structural phase transitions The plateau effect. Phase Trans 35 61-74 Salje E, Devarajan V (1981) Potts model and phase transition in lead phosphate Pb3(P04)2. J Phys C 14 L1029-L1035... 

Vollhardt D (1999) Phase transition in adsorption layers at the air-water interface. Adv Colloid Interface Sci 79 19-57... 

We return here to the simple mean field description of second-order phase transitions in terms of Landau s theory, assuming a scalar order parameter cj)(x) and consider the situation T < Tc for H = 0. Then domains with = + / r/u can coexist in thermal equilibrium with domains with —domain with exists in the halfspace with z < 0 and a domain with 4>(x) = +

0 (fig. 35a), the plane z = 0 hence being the interface between the coexisting phases. While this interface is sharp on an atomic scale at T = 0 for an (sing model, with = -1 for sites with z < 0, cpi = +1 for sites with z > 0 (assuming the plane z = 0 in between two lattice planes), we expect near Tc a smooth variation of the (coarse-grained) order parameter field (z), as sketched in fig. 35a. Within Landau s theory (remember 10(jc) 1, v 00 01 < 1) the interfacial profile is described by... 

In sect. 2, we have summarized the general theory of phase transitions with an emphasis on low-dimensional phenomena, which are relevant in surface physics, where a surface acts as a substrate on which a two-dimensional adsorbed layer may undergo phase transitions. In the present section, we consider a different class of surface phase transitions wc assume e.g. a semi-infinite system which may undergo a phase transition in the bulk and ask how the phenomena near the transition are locally modified near the surface, sect. 3.1 considers a bulk transition of second order, while sections 3.2 and 3.4-3.6 consider bulk transitions of first order. In this context, a closer look at the roughening transitions of interfaces is necessary (sect. 3.3). Since all these phenomena have been extensively reviewed recently, we shall be very brief and only try to put the phenomena in perspective. 

Unless measurements are made on a substance that is itself fluorescent, fluorescence studies require the addition of an impurity, the probe, to the monolayer. It can be expected that phase transitions in doped monolayers will not be as sharp as in pure systems. The effect of impurity can be investigated by varying the probe concentration. It is possible that a probe can be line active, tending to concentrate at the interface between two surface phases. In such a case even very small concentrations of probe might have marked effects on the structure of the monolayer or on the dynamics of growth of a new phase. As discussed below, however, there is good evidence that these problems do not limit the utility of the fluorescence method. 

One of the most active areas of research in the statistical mechanics of interfacial systems in recent years has been the problem of freezing. The principal source of progress in this field has been the application of the classical density-functional theories (for a review of the fundamentals in these methods, see, for example, Evans ). For atomic fluids, such apphcations were pioneered by Ramakrishnan and Yussouff and subsequently by Haymet and Oxtoby and others (see, for example, Baret et al. ). Of course, such theories can also be applied to the vapor-liquid interface as well as to problems such as phase transitions in liquid crystals. Density-functional theories for these latter systems have not so far involved use of interaction site models for the intermolecular forces. 

Widom, B. (1987) Phase-transitions in surfactant solutions and in their interfaces. Langmuir, 3, 12-17. 

Most of the ensuing part of this book deals with dispersed systems. These generally have one or more kinds of interface, often making up a considerable surface area. This means that surface phenomena are of paramount importance, and they are discussed in Chapter 10. Colloidal interaction forces between structural elements are also essential, as they determine rheological properties and physical stability these forces are the subject of Chapter 12. The various kinds of physical instability are treated in Chapter 13, and the nucleation phenomena involved in phase transitions in Chapter 14. Specific dispersed systems are discussed in Chapters 11 and 17. The present chapter explains important concepts and discusses geometrical aspects. 

---