First-order phase transitions, features

The formalism sketched above has been used in the literature in more or less the same detail by many authors [87-92]. The predicted membrane structure that follows from this strategy has one essential problem the main gel-to-liquid phase transition known to occur in lipid membranes is not recovered. It is interesting to note that one of the first computer models of the bilayer membrane by Marcelja [93] did feature a first-order phase transition. This author included nematic-like interactions between the acyl tail, similar to that used in liquid crystals. This approach was abandoned for modelling membranes in later studies, because this transition was (unfortunately) lost when the molecules were described in more detail [87]. 

The square tiling model has some attractive features reminiscent of real glasses, such as cooperativity, a relaxation spectrum that can be fit by the KWW equation, and a non-Arrhenius temperature-dependence of the longest relaxation time (Fredrickson 1988). However, the existence of an underlying first-order phase transition in real glasses is doubtful, and the characteristic relaxation time of the tiling model fails to satisfy the Adam-Gibbs equation. 

The classical Clapeyron equation adequately predicts the features of first-order phase transitions, and this has been established for a number of examples of first-order transitions effected by the deliberate variation of temperature or pressure. Second- or higher-order transitions are not readily explained by classical thermodynamics. Unlike the case of first-order transitions, where the free-energy surfaces of the two phases... 

An unusual feature of the heneicosanol measurements was a second scattering peak, which appeared to arise at high pressure at temperatures below 16°C. It was attributed to a weakly first-order phase transition analogous to the rotator Il-to-rotator I transition in lamellar crystalline n-alkanes with n = 23,25. In the rotator II phase, rapid reorientation of the chain around its axis leads to a pseudohexagonal structure. When the chains can no longer reorient, the symmetry of the structure is reduced to a uniaxially distorted hexagonal strueture. 

A much more complex behaviour is observed for the process of penetration of various proteins into phospholipid monolayers. This behaviour depends strongly on the protein and the solution properties although some common features are observed. Fainerman et al. [116] studied the P-lactoglobulin penetration dynamics into DPPC monolayers. For a (i-lactoglobulin bulk concentration of 510 mol/l and molar areas of the lipid larger than the critical value, A > A, first order phase transitions are observed. Thus, two-dimensional condensed phase are formed although at these molar area values the pure DPPC monolayer exists only in the fluid-like state and does not form any domains. The first-order phase transition in the DPPC monolayer becomes visible by the characteristic break point in the dynamic surface pressure curve Fl(t) (see Fig. 4.50). 

An alternative treatment of the first-order phase transitions has been snggested by Retter who has introduced the lattice-gas approach. The most striking feature of this approach is that it disregards completely the role of the solvent molecnles in the properties of the adsorbed layer. Thus, the adsorbed layer behaves as a two-dimensional lattice gas where the solute molecules are distributed over the sites of a regular lattice. 

In summary, the multicanonical method provides unique features that are important for investigating first-order phase transitions and phenomena that occur over a large range of energies, such as protein folding. Upon further optimization, the method is expected to become an important tool for conformational search and for studying phase transitions in macromolecular systems. 

One can see that, as illustrated in Fig. 10.1a, the practical Tc is always lower than The volume-temperature curves for crystallization/melting are roughly the same results. Such a hysteresis loop is an important feature of first-order phase transitions. If we make a reference to the melting point of infinitely large crystals, we can define the... 

I he presence of two minima of G (or F) 2is functions of the order parameter is the main distinguishing feature of first-order phase transitions. 

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