Eliminating the Pre-exponential Factor in Classical Nucleation Theory
Chemical Science International Journal,
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.
- Homogeneous nucleation
- Flory-Huggins theory
- limit of superheat
- differential equation
- polymer solutions
How to Cite
Siow KS, Patterson D. Surface thermo-dynamics of polymer solutions. J. Phys. Chem. 1973;77(3):356-365.
Jennings JH. Homogeneous nucleation from polymer solutions. Polymers Research J. 2014;8(4):311-319.
Jennings JH, Middleman S. Homogeneous nucleation of vapor from polymer solutions. Macromol. 1985;18:2274-2276.
Jennings JH. Limit of superheat of polystyrene-cyclohexane solutions: Theory. Int. J. Thermodynamics. 2012;15(3):127-132.
Shiau L. The temperature dependence of the pre-exponential factor and interfacial energy for aqueous glycine solutions based on the Metastable zone width data. J. Crystal Growth. 2018;496-497:18-23.
Bovey FA, Winslow FH. Macromolecules: An introduction to polymer science. Academic Press; 1979.
Abstract View: 1415 times
PDF Download: 530 times