J. Phys. Chem. 1980, 84, 1483-1485
1483
Some Mechanlstlc Questions in Nucleation Ronald Lovett Depwtment
of Chemlstw, Washington University, St. Louis. Mlssouri
63 130 (Received July 9, 1979)
Publication costs assisted by Washington Universw
A hydrodynamic description of nucleation in vapor condensation or liquid-liquid separation associates a depletion region with a growing drop. This characterization differs qualitatively from the classical characterization. The mechanistic difference and the role of microscopic reversibility are described.
I. Introduction Hydrodynamics usefully describes the time evolution of a system in which there is a clear separation between the time-scale for macroscopic, collective motions and microscopic, molecular motions.l Such a separation is present in a system undergoing nucleation. In the usual vapor condensation experiment, for example, collisions occur at a rate N lo9 s-l while nuclei appear at a rate N 1s-l. Thus forming a critical nucleus is a collective motion on a hydrodynamic time scale, and the usual reaction coordinate? the drop radius R, is a hydrodynamic variable. This is a useful observation because equilibrium statistical distributions may be used tQ average out the rapidly evolving variables and only the remaining slow, hydrodynamic variables arc! required to describe the nucleation process. The work of formation V(R) of a critical nucleus, for example, is usually2 evaluated by invoking this time scale separation. The drop radius R is prescribed and equilibrium thermodynamics is applied to the remaining degrees of freedom. R is the only nonequilibrium variable and V(R)is a thermodynamic potential for this coordinate. If the initial distribution over R itself is an equilibrium distribution, one can predict that passage over a barrier 60kBT will occur with probability of height V* e-"*lkBT,which is the result of Volmer and Weber.3 To actually determine a rate of passage over the barrier, however, one must go beyond the hydrodynamic description. One must know how rapidly fluctuations cause the energy in the reaction coordinate to change or, equivalently, the spectrum of the thermal noise in the system. This is a standard ingredient of hydrodynamic fluctuation theory4 and 11 hydrodynamic characterization of the nucleation in liquid-liquid separation5 and in vapor condensation6 has been given, This hydrodynamic characterization of the nucleation process does differ in detail from the classical characterization7 and the present discussion provides an informal assessment of the relative importance of these two mechanisms. The hydrodynamic characterization is briefly described in the next section. Section I11 then contrasts the time scale and statistical likelihood of this mechanism with those of the classical mechanism. An overview is presented in section IV. N
a rate I?
