Phase transitions phenomenological theory

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

In this connection, we admit that we know little of the real nature and the process of the discontinuous phase transition of gels. Although the phenomenological theory predicts that the whole sample transforms from one phase to the other at a specified temperature (the transition temperature), there has been some experimental evidence that the transition in real gels never occurs in such a manner. For example, a serious deformation erf the sample [7] as well as the coexistence of phases [8] have been observed over a rather wide temperature range around the first-order transition point A curious, and at the same time important point is that these states seem not to be transient but stable states of the gels [8]. 

The present article attempts to clarify the nature of the discontinuous transition of gels. First, in Sect. 2 we give an outline of the fundamental aspect of the volume phase transition on the basis of the Flory-Rehner theory of gels, with special attention to how the discontinuous transition comes about within the phenomenological treatment Then, in Sect 3 previous experimental results... 

The Flory-Rehner phenomenological theory [9,10] has beei most widely used to analyze the volume phase transition of gels. This theory, extended [11] to take into account the concentration dependence of the polymer-solvent interaction parameter x, can predict basic features of the phase transition. 

In the phenomenological theory of phase transitions, it is customary to attribute order parameters to the relevant thermodynamic quantities associated with the macroscopic transition of the state of the material. In our case,... 

In equation (82), the phenomenological coefficients a, and which according to the preceding development may depend on temperature but are independent of the pressure and of the compositions of the gas and adsorbed phases, can be predicted only by more detailed theories such as transition-state theory. 

This conclusion was reached, tentatively, by Frenkel, Shaltyko and Elyashevich A phenomenological analysis presented by Pincus and de Gennes predicted a first-order phase transition even in the absence of cooperativity in the conformational transition. These authors relied on the Maier-Saupe theory for representation of the interactions between rodlike particles. Orientation-dependent interactions of this type are attenuated by dilution in lyotropic systems generally. In the case of a-helical polypeptides they should be negligible owing to the small anisotropy of the polarizability of the peptide unit (cf. seq.). Moreover, the universally important steric interactions between the helices, regarded as hard rods, are not included in the Maier-... 

In a series of works by Salejda and Dzhavadov [148] and Stasyuk et al. [38-42], a microscopic description of the phase transitions in (NH4)3H(Se04)2 has been proposed. The results obtained have been compared with those obtained from the Landau phenomenological theory. The original Hamiltonian has been presented in a bilinear form... 

One sfrategy is phenomenological and rooted in the Landau theory of phase transitions. The basic idea is to assert that the homogeneous free energy density... 

Phenomenological theory of phase transitions a brief review. 136... 

Attempts are being made to develop phenomenological theories " of the monolayer phases, but the problem of dealing realistically with the many interactions has not been solved. Phase transitions in condensed monolayer phases have also been investigated with two-dimensional lattice models. In such theories, the ordering processes are described in terms of order parameters whose precise physical significance need not be defined. They therefore do not lead to detailed physical descriptions of the monolayer phases. 

The hard-sphere phase transition was only the first of many important discoveries that have emerged from these techniques. As has been described frequently in the past, these simulations can serve us in three ways. First, they provide essentially exact results for a given molecular model, which can be used to test the accuracy of approximate theories. Second, through comparison with experiment they can be used to assess the quantitative accuracy of a given molecular model. Third, they can be used for exploring the phenomenological behavior of molecular models in a parallel manner to that in which an experimentalist studies the behavior of a real system. We do not review the techniques themselves because there are now excellent textbooks on the subject [32-34]. We focus instead on the specific aspects of these methods associated with the calculation of SFE. 

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