An energetics approach to the analysis of molecular motions in polymeric solids

Abstract

The feasibility of certain modes of intra-and intermolecular motion in polymeric solids are examined in terms of interaction energetics and geometrical constraints. Energy methods for determining equilibrium chain structures and stable deformation structures are reviewed. A systematic approach to the specification of explicit geometrical constraints in condensed phase polymeric systems is developed by matrix techniques. Combination rules are derived which provide straightforward means of constructing deformation structures for oriented polymers. Applications of these general methods are illustrated for paraffinic systems. Structure-energy maps, based on empirically justified potential functions, are presented for assemblies of paraff inic chains. The potential energy surface in the vicinity of the minima associated with the orthorhombic crystal structure is described by a Taylor's series in the unit cell parameters. Applications of this approximate representation of the energy surface to the prediction of the moduli, thermal expansion coefficients, and bulk compressibility of crystalline paraffins and polyethylene are discussed. Detailed energy maps for coupled rotations of rigid chains and coupled translation-rotation motions are developed. Feasible modes of motion are identified as low-energy structural conversion paths; activation energies are determined from the saddle points in the structure-energy map. The temperature dependence of barriers to motion is estimated by introducing empirical functions which relate average chain spacings to temperature.