Experimental anomalies and the conformational theory of polymers

The influence of the size and shape of the torsional potential upon the theoretical temperature coefficient (T? ln 〈r₀²〉/?T) of a polymeric chain was studied. The uncorrelated end-to-end distance equations for isotactic, syndiotactic, and completely atactic chains were differentiated with respect to temperature and the integrals in the resulting equations were evaluated by the method of Gaussian quadrature. The calculated coefficients were found to be nonlinear functions of the energy ratio U_max/KT, where U_max is the maximum potential barrier and possess real roots which critically depend upon the size and shape of the potential. Qualitative anomalies between experiment and theory disappeared when the entire torsional potential was used in the conformational theory. It appears that quantitative agreement between theory and experiment can be established for polymeric materials if the entire potential is used, rotations within bulky side groups are included, and the potential is determined by the method of minimum conformational energy.