2ND VIRIAL-COEFFICIENTS, CRITICAL-TEMPERATURES, AND THE MOLECULAR SHAPES OF LONG N-ALKANES

The second virial coefficient for a molecular model of iz-alkanes with up to 200 carbon atoms has been computed for temperatures in the rang e of 1000 K<T<2000 K. The model used in the calculations is based on o ne which reproduces the experimental values of the second virial coeff icient 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 c hains the Boyle temperature and the critical temperature, denoted as t he theta temperature are the same. On this basis using the present mod el we find theta=1620 K as the critical temperature of polymethylene. Scaling laws for the square of the end-to-end distance and for the rad ius of gyration at several temperatures are analyzed. For high tempera tures, the scaling laws correspond to good solvent conditions whereas at the theta 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 t o that of a parallelepiped with a ratio of sizes of 1:1.7:3.6. (C) 199 6 American Institute of Physics.