Eliminating the Pre-exponential Factor in Classical Nucleation Theory
Blander and Katz give a formula in classical nucleation theory, J = A exp K, for homogeneous nucleation (liquid-->gas). Jennings proved that dlnA/dK = 1/6K for all pure liquids by combining two theories, taking the limit as polymer concentration-->0. This gives lnA = (1/12)ln(K2) + C, where C is the integration constant. The conjecture is that C is a constant for fluids of low molecular weight. We used data for 7 sample solvents, and solved for C. The surface tension drops out in C, which makes C more accurate, as the surface tension is difficult to get at 0.89Tc, the limit of superheat. Tc= critical point in Kelvin. All quantities are evaluated at the limit of superheat, which is approximately 0.89Tc for solvents. C = 74.77 ± 0.33 for the 7 solvents (not all alkanes). This eliminates the prefactor A, streamlining J: ln J = (1/12)ln(K2) + 74.77 + K is the exact new equation. A computer can more easily be used to calculate J, the nucleation rate.
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