ON THE RELATION BETWEEN THE STANDARD PHASE-FIELD MODEL AND A THERMODYNAMICALLY CONSISTENT PHASE-FIELD MODEL

A further comparison is made between the standard phase-field equation s alpha phi(t)=del(2) phi+(1/xi(2))[g(phi)-u],u(t)=del(2)u+1/2l phi(t) , and the relevant ''thermodynamically consistent model of phase trans itions'' proposed by the authors [Physica D 43 (1990) 44-62]. Here we concentrate on the usual case where g(phi)=phi-phi(3), and for compari son purposes retain this expression for the analogous nonlinear functi ons in the latter model. It is brought out, among other things, that t he standard model is thermodynamically consistent in the sense of bein g derivable from a free-energy functional. However, this free-energy f unctional is of a somewhat unusual kind: it implies that, at constant temperature, the energy density varies linearly with the order paramet er phi and the entropy density is a non-concave function of phi. The e xample of a hard sphere system indicates that such behaviour is not im possible, but in most other models the energy density and the entropy are both strictly concave in phi.