Conformational study of branched vinylpolymers. Cascade theory applied to chain transfer

Abstract

Highly branched materials, obtained by chain transfer between polymers in free radical polymerization, are treated by means of cascade theory which is based on the use of probability generating functions. The necessary link probability generating functions, composed of various probabilities of reaction, have been calculated from the kinetic scheme of the polymerization process. Application of the cascade theory allows prediction of the critical point of conversion where gelation should occur. Analytical expressions are given for the number and the weight average degree of polymerization, the z-average mean square radius of gyration and the particle scattering factor of the molecules in the pre- and post-gel state of the system. Furthermore, the mass fraction of linear chains and the sol fraction in the gel are calculated, and finally, the density of branching and the number of elastically effective chains in the gel are evaluated. Evidence of branching may not be apparent from the 〈S²〉_z and P_z(Θ) measurements of the unfractionated samples due to the presence of large amount of linear chains, but can be detected when the linear fractions are removed from the sample. No noticeable differences are observed in the properties of molecules in the pre- and post-gelation period. The increase in the number of elastically effective chains after gelation with increasing monomer conversion is compared with the case of a randomly branched trifunctional polycondensate. A much lower elastic modulus is found for the present system than for the trifunctional polycondensate. The theoretical expression for DP_w, derived in this paper, shows good agreement with the experimental data of Stein on poly-vinyl acetate. While Stein did not take into consideration gel formation, the present theory now predicts gelation at a monomer conversion of about 67 %. The close agreement between experiment and theory lends not only strong support to the present calculations, but also vindicates the use of cascade theory for the study of chain transfer reactions.