THETA-TEMPERATURE OF LINEAR AND STAR POLYMERS

The 9-temperature dependence on chain length and number of arms f for linear and regular star polymers was determined analytically as the temperature at which balance is reached between the repulsive three-body and the attractive two-body interactions; the latter increase with decreasing temperature, unlike the former, which are essentially constant. From an equivalent bead-and-spring model in the Gaussian approximation, 0 is found to decrease with increasing molecular weight for linear and lightly branched chains (f < 4), whereas it increases if > 5 to a common asymptotic limit 0. In fact, for linear chains the ratio between the number of the three-body and that of the two-body contacts increases with molecular weight because the minimum chain length for a three-body contact is about twice that for a two-body contact. Therefore, short chains need less temperature lowering to compensate the three-body repulsions than long ones. Conversely, the lower 0 temperature for short branched chains with many arms is due to the high density of segments near the star core: this gives rise to a large number of three-body repulsions to be compensated. If the molecular weight is very large, the fraction of segments close to the star core becomes negligible and the same temperature 0 is attained for any polymer architecture, in agreement with experimental results. © 1990, American Chemical Society. All rights reserved.