Eliminating the Pre-exponential Factor in Classical Nucleation Theory

Main Article Content

John H. Jennings

Abstract

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.

Keywords:
Homogeneous nucleation, Flory-Huggins theory, limit of superheat, differential equation, polymer solutions, derivation.

Article Details

How to Cite
Jennings, J. H. (2019). Eliminating the Pre-exponential Factor in Classical Nucleation Theory. Chemical Science International Journal, 28(3), 1-6. https://doi.org/10.9734/CSJI/2019/v28i330140
Section
Original Research Article

References

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