Copolymeric System Research Articles

Matrix Formulation of Copolymerization Statistics. II. Extensions to Multimonomeric Systems

A matrix formulation of copolymerization statistics for binary systems presented earlier is modified and generalized to include multicomponent monomeric systems. The results are applied to condensation copolymerizations for which a kinetic description is also developed. This approach serves to systematize rather diverse results for linear condensation polymerizations. A particularly simple form for the distribution statistics of copolymeric systems in thermodynamic equilibrium is obtained. The steady-state approximation, which affords a matrix representation for the distribution of radical chains, is employed to provide a description of the distribution of stable copolymeric species formed by two types of termination processes. A generalization is presented for a binary copolymeric system with a chain memory which includes the penultimate unit. A modification of the present analysis is suggested which may be applicable to the treatment of the configurational sequences in stereoregular homopolymerizations where the statistics of the analogous copolymerizations are not Markoffian.

Molecular Size Distribution and Gelation of Irradiated Copolymers

A theory is developed about the molecular size distribution in a system of copolymers which are composed of two different kinds of monomer units and undergo random crosslinking when exposed to high-energy radiations. The radiation-induced change in the molecular size distribution is described by an integro-differential equation, which we solve exactly by means of Laplace transform for an arbitrary initial distribution to obtain the number-average as well as the weight-average degree of polymerization as a function of radiation dose. Further, the gel point, or the dose required for incipient gelation, is given as a function of concentrations of the monomer units constituting the copolymeric system. The present theory, which also involves the problem of crosslinking in a mixture of two kinds of polymers as a special case, leads to a condition for gelation of such a mixture due to irradiation when crosslinking competes with main-chain scission. This condition proves to be completely independent of the initial distribution.