The Coexistence of Phases

In Fig. XI-3, the pressure scale is changed in the other direction, so that we show up to 12,000 atm. Here the gaseous phase, which exists for pressures only up to a few hundred atmospheres, cannot be shown on account of the scale. On the other hand, a great deal of detail has appeared in the region of the solid. It appears that, in addition to the familiar form of ice, there arc at least five other forms (the fifth exists at higher pressures than those shown in the figure). These forms, called polymorphic forms, presumably differ in crystal structure and in all their physical properties, as density, specific heat, etc. The regions whore these phases exist separately are divided by equilibrium lines, on 

The Equation of State.—The three figures that we have drawn give only part of the information about the phase equilibrium for greater 

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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. 

The equilibrium in the solid state between such substances as the allotropic forms of tin or sulphur, or between the participants in any other chemical reaction, is governed by principles precisely similar to those which regulate the coexistence of phases such as solid and liquid. 

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