Coexistence of phases

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

Hirotsu, 5. Coexistence of Phases and the Nature of First-Order Transition in Poly-N-iso-propylacrylamide Gels. Vol. 110,pp. 1-26. 

Coexistence of phases on opposite sides of the reaction equation implies that they are in equilibrium and that the AG of reaction is zero—i.e.,... 

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 phase coexistence observed around the first-order transition in NIPA gels cannot be interpreted by the Flory-Rehner theory because this theory tacitly assumes that the equilibrium state of a gel is always a homogeneous one. Heterogeneous structures such as two-phase coexistence are ruled out from the outset in this theory. Of course, if the observed phase coexistence is a transient phenomenon, it is beyond the thermodynamical theory. However, as will be described below, the result of the detailed experiment strongly indicates that the coexistence of phases is not a transient but rather a stable or metastable equilibrium phenomenon. At any rate, we will focus our attention in this article only on static equilibrium phenomena. 

In some of the examples discussed so far (e.g., Examples 7.12-7.15), we asked the question Which solid phase controls the solubility In addition, we may address the problem of coexistence of phases and ask How many phases can coexist under the conditions given ... 

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