Second virial coefficients, critical temperatures, and the molecular shapes of long n-alkanes

Abstract

The second virial coefficient for a molecular model of n-alkanes with up to 200 carbon atoms has been computed for temperatures in the range of 1000 K<T<2000 K. The model used in the calculations is based on one which reproduces the experimental values of the second virial coefficient for short n-alkanes. The Boyle temperature of n-alkanes is not much affected by the length of the chain for n-alkanes with more than 100 carbon atoms. According to the Flory theory, for infinitely long chains the Boyle temperature and the critical temperature, denoted as the θ temperature are the same. On this basis using the present model we find θ=1620 K as the critical temperature of polymethylene. Scaling laws for the square of the end-to-end distance and for the radius of gyration at several temperatures are analyzed. For high temperatures, the scaling laws correspond to good solvent conditions whereas at the θ temperature the scaling laws are those of an ideal chain. The shape of long n-alkanes at several temperatures is also analyzed. We find that the polymethylene chains present an anisotropy similar to that of a parallelepiped with a ratio of sizes of 1:1.7:3.6.