Phase coexistence region

As discussed above, lipid membranes are dynamic structures with heterogeneous structure involving different lipid domains. The coexistence of different kinds of domains implies that boundaries must exist. The appearance of leaky interfacial regions, or defects, has been suggested to play a role in abrupt changes in solute permeabilities in the two-phase coexistence regions [91,92]. 

The determination of the character and location of phase transitions has been an active area of research from the early days of computer simulation, all the way back to the 1953 Metropolis et al. [59] MC paper. Within a two-phase coexistence region, small systems simulated under periodic boundary conditions show regions of apparent thermodynamic instability [60] simulations in the presence of an explicit interface eliminate this at some cost in system size and equilibration time. The determination of precise coexistence boundaries was usually done indirectly, through the... 

For bilayers in which each monolayer is transferred in a phase coexistence region of the pressure isotherm, the phase structure in each leaflet of the bilayer is preserved. For example, each leaflet of the bilayer shown in Fig. 8 was transferred in the LE-LC phase coexistence region of the pressure isotherm. 

A partially fluorinated lipid (LL-8-8) was found to form stripe-like microdomains at the gas-liquid phase coexistence region, when spread on water as a Langmuir monolayer [28]. 

In addition to the Uquid liquid coexistence curve, the confined fluid exhibits two further, smaller phase coexistence regions at larger wa and lower T. The coexisting phases represent water-rich films of a thickness corresponding to one or two layers, which are distinguishable only at lower temperatures. The existence of such first-order layering transitions may be overestimated by our lattice model on a homogeneous surface and enforced unrealistically... 

That is, there is a portion of the isotherm where the specific volume varies continuously at fixed temperature and pressure this is the two-phase coexistence region, here the vapor-liquid coexistence region. 

Using the bubble point pressure option in the Visual Basic program of Appendix B.1-3, the DOS-based program VLMU, or the MATHCAD worksheet PRBUBP, and the computed composition for the liquid richer in n-decane, we obtain the following results for the three-phase coexistence region ... 

For a real fluid at sufficiently high temperatures the slope [0 /0(l/p)]y is positive for all values of p, in accordance with Eq. (29). At lower temperatures, there can be one or more regions in which [dpld llp)]j, = 0. These flat portions of the curve in the ip,p ) phase diagram possess mathematical singularities at both ends as a consequence of the limiting process V,N -> oo with p,T constant under which we are studying the fluid. The flat portion corresponds to a two-phase coexistence region. 

It is seen that the phase transition (condensation) in the monolayer is accompanied by a significant decrease of the slope of the surface pressure isotherm. In contrast to the model based on Frumkin s equation and Maxwell s construction (see Fig. 2.19), the dependence of n on 0 in the phase coexistence region does not generally have a horizontal line, except for very small 6 values. 

If one does not introduce any corrections to the 0 in the phase coexistence region, results similar to those reported in [1, 104, 105, 119-128] are obtained. In the phase coexistence region (0>0J we then have const and the critical monomer adsorption is less than F, for... 

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