Theory of Structure, Morphology and Conductivity in Polymers

An investigation of the single-chain structure, morphology and DC conductivity of polyacetylene is carried out using various theoretical and computer techniques. Single-chain structure at finite temperature is investigated using the transfer integral formalism. The polymer chain is assumed to have only torsional degrees of freedom, and conformational energies are computed as functions of torsional angles. These energies are used to compute the transfer matrix. The largest eigenvalue of the transfer matrix is calculated using the power method, and the partition function and thermodynamic quantities are obtained. It is found that the lowest-energy conformation at low temperature is cis-transoid, and that there is a significant degree of disorder in the single-chain structure at finite temperature. Formation energies of certain kinds of conformational kinks are calculated in a similar manner. Most of these defects are not energetically favored, but certain short kinks (chainfolds) have negative formation energies. These defects are consistent with the existence of a partially disordered, lamellar morphology. A model for DC conduction in polyacetylene is presented which takes into account the possible presence of disorder in the morphology and dopant distribution. Disorder at three length scales is considered. The observed tangled -fibril network is simulated as a network of temperature -dependent resistances. The temperature dependence of these resistances is computed in a manner that allows for the clustering of dopant into areas of locally high concentration. Conduction within a cluster (and between clusters) is described by a simple hopping model. The temperature dependence of the complete model is found to vary appreciably with doping homogeneity. This is qualitatively consistent with reported preliminary experimental work on the effects of morphological variation on conductivity.