The entropy production and variable surface tension barriers to nucleation and growth in steady- and quasi-steady state condensing systems

Abstract

The quasi-static free energy barrier to nucleation which characterizes classical theory with its spontaneous positive change allowed only by fluctuations has a dynamical analogue in the dissipation function which can undergo a spontaneous negative change by fluctuation only. The need for such a generalization in nucleation theory appears within the steady-state spinodal decomposition of exciton gases in semiconductors to electron-hole drops. Onsager^[23] had already suggested in 1931 how one might construct the analogue of the Boltzmann fluctuation probability exp (ΔS/R) as exp [S_iτ/R], whereS _i is the entropy production rate and t is a characteristic time on the transformation path. That is to say,S _i τ corresponds to a path entropy which, in this class of nucleation events, must surmount a negative barrier by fluctuation. Since morphological instabilities near the constitutional supercooling margin in binary, forced-velocity solidification are now known to be of finite amplitude, we briefly examine this behavior in such dynamical terms. The local hydrodynamic theory of gas-liquid spinodal decomposition consists of first-order differential equations, so sinusoidal decompositions are ruled out, and thus, as usually acknowledged, discrete phase separations are to be expected. However, there is noa priori requirement that the droplet should instantaneously achieve the maximum density configuration, since a continuously variable density difference and concomitant gradual increase in the surface tension are allowed by an equation of state in the metastable region. This is a variant of the gradient energy concept. It is suggested that the classical theory of condensation might be usefully modified to the dissipation and variable surface tension format. This construction applied to near critical states is not inconsistent with the theory of Lothe and Pound,^[21] which has particular application to highly supersaturated fine-grained spinodal states.