Kinetics of Crystallization in Multicomponent Systems: I. Binary Mixtures of n-Paraffins

The kinetics of crystallization of a binary mixture of n-paraffins is treated using a theory for the rate of growth of chains in multicomponent systems. The kinetic chain is considered to be a strip of crystalline material composed of molecules of both components that is growing on a substrate of uniform thickness. This substrate is considered to be a close-packed surface step. Using the binary mixture of C₂₄H₅₀ and C₂₆H₅₄ as an example, the calculations are carried out by an iterative procedure so that the mean thickness of the strip equals that of the substrate. This procedure necessitates modification of the rate constants that would be used without this requirement. The rate of growth of the strips (total flux) is calculated as well as their composition over an appropriate range of temperature and a complete range of liquid compositions. The pair distribution in the strips is also determined. The substrate is assumed to be unkinked in the calculations, whereas the substrate is probably highly kinked in the actual system. For this reason the calculated total flux is probably not representative of the actual crystal growth rate in a binary mixture of C₂₄H₅₀ and C₂₆H₅₄. It is believed that the calculated compositions are reasonably accurate. For a binary mixture of longer n-paraffins (e.g., C₅₀H₁₀₂ C₅₂H₁₀₆) the substrate should have many fewer kinks, and the total flux calculated by this theory will be more closely related to actual crystal growth rate studies. However, no data exist for such systems.