Predictions of nucleation theory applied to Ehrenfest thermodynamic transitions

摘要

This paper deals with the applicability of classical nucleation theory to second‐order thermodynamic transitions in the Ehrenfest sense. A mathematical formulation is presented in which physically meaningful expressions for a critical nucleus size as well as a critical activation energy barrier for second‐order transitions are derived as functions of the degree of undercooling θ, interfacial energy γ, heat capacity difference ΔCp, specific volume of the transformed phase υβ, and the equilibrium transition temperature Tt. These expressions are rc=4υβTt/(ΔCp)2θ2 and ΔGc=(64π/3)γ 3υ2β(Tt)2/ (ΔCp)2θ4. These results arise from the expansion of the effective free energy in a Maclaurin series and evaluating the expansion coefficients in terms of thermodynamic relations. As a consequence of this manipulation a break is made from the customary approximations which are normally employed in elementary homogeneous nucleation theory. Secondly, this approach yields nonlinear correction terms which can be applied when calculating the critical nucleus size and critical activation energy barrier for a first‐order transition. Finally, graphical descriptions of systems undergoing first‐ and second‐order Ehrenfest transitions are presented in order to give a semiquantitative meaning to the expressions derived with this approach.