Binary Nucleation Kinetics. III. Transient Behavior and Time Lags

Transient binary nucleation is more complex than unary because of the bidimensionality of the cluster formation kinetics. To investigate this problem qualitatively and quantitatively, we numerically solved the birth-death equations for vapor-to-liquid phase transitions. Our previous work [J. Chem. Phys 103, 1137 (1995)] showed that the customary saddle point and growth path approximations are almost always valid in steady state gas phase nucleation and only fail if the nucleated solution phase is significantly nonideal. The current work demonstrates that in its early transient stages, binary nucleation rarely, if ever, occurs via the saddle point. This affects not only the number of particles forming but their composition and may be important for nucleation in glasses and other condensed mixtures for which time scales are very long. Before reaching the state of saddle point nucleation, most binary systems pass through a temporary stage in which the region of maximum flux extends over a ridge on the free energy surface. When ridge crossing nucleation is the steady state solution, it thus arises quite naturally as an arrested intermediate state that normally occurs in the development of saddle point nucleation. While the time dependent and steady state distributions of the fluxes and concentrations for each binary system are strongly influenced by the gas composition and species impingement rates, the ratio of nonequilibrium to equilibrium concentrations has a quasiuniversal behavior that is determined primarily by the thermodynamic properties of the liquid mixture. To test our quantitive understanding of the transient behavior, we directly calculated the time lag for the saddle point flux and compared it with the available analytical predictions. Although the analytical results overestimate the time lag by factors of 1.2-5, they should be adequate for purposes of planning experiments. We also found that the behavior of the saddle point time lag can indicate when steady state ridge crossing nucleation will occur