Detailed Structure of Copolymers from Dielectric Measurements

Abstract

The effective dipole moment of each polar group in polar-polar or polar-nonpolar copolymers is expressed in terms of the moment of an equivalent isolated polar group and the average of the vector sum of the moments of all of the polar groups surrounding it. If effects of short-range forces leading to angular correlations of dipole pairs are neglected except for interactions between nearest neighbors along the chain, an expression for the average of the effective moments of the two types of polar groups present can be written as a function of the composition of the copolymer in the form 〈μ2〉Av=x1(μ12)eff+(1−x1)(μ22)eff=L+Mx1+Nx1P11(x1). Here, x1 is the mole fraction of one of the monomers in the copolymer, (μ12)eff and (μ22)eff are the squares of the effective moments of the two polar groups. L, M, and N are constants involving the dipole-moments of the equivalent isolated groups and the average cosines of the angles between nearest-neighboring dipole pairs of types 1 − 1, 1 − 2, and 2 − 2. The quantity P11(x1) is the probability of a monomer of type 1 adding to a free radical of its own kind at the end of a growing chain in the polymerization mixture. It can be calculated from r1 and r2, the reactivity ratios of the two monomers, and the composition of the monomer feed mixture. Interactions extending farther along the chain than nearest neighbors introduce terms in higher powers of P11(x1). Onsager's equation for the dipole moments of molecules in mixtures of polar liquids has been modified to express the average of the effective moments of the polar groups present in terms of the dipolar contribution to the dielectric constant, εs−ε∞. Using this equation, values of 〈μ2〉Av have been calculated from measurements of εs−ε∞ for several copolymers of poly-(p-chlorostyrenestyrene) representing the whole range of copolymer composition. Measurements were made on bulk copolymers at temperatures above the glass-transition temperature. A curve of the form L+Mx1+Nx1P11(x) has been fit within experimental error to the calculated values of 〈μ2〉Av over the whole range of copolymer composition. This indicates that within the limits of error of this work only nearest-neighbors on the polymer chain contribute to the effective moments of the polar groups. The average cosines have been calculated for the angles between each of the three kinds of dipole pairs in the copolymer.