Solid–liquid interfacial free energies of benzene

Abstract

In this work we determine for the range of melting temperatures 284.6 ⩽ T ⩽ 306.7 K , corresponding to equilibrium pressures 20.6 ⩽ P ⩽ 102.9 MPa , the benzene solid–liquid interfacial free energy by a cognitive approach including theoretical and experimental physics, mathematics, computer algebra (MATLAB), and some results from molecular dynamics computer simulations. From a theoretical and mathematical points of view, we deal with the elaboration of an analytical expression for the internal energy derived from a unified solid–liquid–vapor equation of state and with the elaboration of an existing statistical model for the entropy drop of the melt near the solid–liquid interface. From an experimental point of view, we will use our results obtained in collaboration with colleagues concerning the supercooled liquid benzene. Of particular interest for this work is the existing center-of-mass radial distribution function of benzene at 298 K obtained by computer simulation. Crystal-orientation-independent and minimum interfacial free energies are calculated and shown to increase slightly with the above temperatures. Both crystal-orientation-independent and minimum free energies agree with existing calculations and with rare existing experimental data. Taking into account the fact that the extent of supercooling is generally admitted as a constant, we determine the limits of supercooling by which we explore the behavior of the critical nucleus radius which is shown to decrease in terms of the above temperatures. The radius of the, and the number of molecules per, critical nucleus are shown to assume the average values of 20.2 A ˚ and 175 with standard deviations of 0.16 Å and 4.5, respectively.