Conformational properties of a diblock copolymer molecule

Abstract

The conformational properties of an A–B diblock copolymer molecule are studied in terms of the excluded volume parameters u_A, u_B and u_AB, representing the interactions between two A, two B and an A and a B unit, respectively. By means of simple second-order perturbation theory at the dimensionality d= 4 –ε(ε small), the fixed points of the system are determined in agreement with the results of a renormalization group theory. These points represent macroscopic states of the molecule and are characterized by specific values (u^*_A, u^*_B, u^*_AB) of the interaction parameters. A relation between u^*_AB and u^*_A and u^*_B is found by means of which the experimental behaviour of the chain is explained. The simplicity of the method permits the study of a large variety of macroscopic properties such as the probabilities of various configurations of the chain. The evaluation of the mean end-to-end square distance expressing the square of the size of the molecule, up to second-order in the interaction parameters yields an explanation of the dependence of the limiting viscosity numbers and the second virial coefficients on the temperature and the quality of the solvent.