Configurational properties of model lattice chains under varying solvent conditions

Abstract

Configurational properties, viz mean squares of the end-to-end distance (〈R2〉) and the radius of gyration (〈S2〉), probability distribution of R and the ratio between mean squares of the principal axes of equivalent ellipsoid (〈XX2〉: 〈YY2〉:〈ZZ2〉), have been calculated for model polymer molecules under differing solvent conditions. The present study follows a computational statistical approach which is based on the Metropolis sampling technique. The molecules are represented by tetrahedral chains with trans/gauche bond conformational energy difference equal to 1.0 kT. The solvent condition is characterised by the intersegmental interactions which are assumed to be given by a square-well potential. The depth of the potential well, Δes, serves to define the solvent parameter. It is shown that in the region Δes ∼−0.4 kT the configurational criteria for the existence of the theta condition are fulfilled (the chains assumed 〈R2〉 and 〈S2〉 values that correspond to the random-walk state and the limiting probability function governing the end-to-end distance distribution is gaussian). The calculated values of 〈R2〉,〈S2〉 and 〈XX2〉 〈YY2〉:〈ZZ2〉 indicate that the chains in “good” solvents (Δes < −0.4 kT) exist in highly extended configurations. As the system assumes the below-theta conditions (Δes <−0.4 kT) the extended configurations collapse into compact ones. Such compact configurations are not spherical but retain an appreciable degree of elongation. The probability distribution of R in the limit of infinite chain length deviates significantly from the gaussian behaviour in both the above and below-theta conditions. The present calculations suggest that the introduction of the trans/gauche conformational energy difference leads to the reduction of the long-range excluded volume in the chains.