Relation of glass transition temperature to molecular structure of addition copolymers

An equation is proposed relating the glass transition temperature (TG) of copolymers to their molecular structure in terms of the mole fractions of the various diad sequences of monomer units combined in the copolymer chain, and temperature parameters (Tij) characteristic of each type of sequence, ij. The equation, an extension of the Gibbs and DiMarzio copolymer TG theory, accounts for the effect on TG of the different types of bonds between repeating units in different diad sequences, and is in its general form: {article}{empty}{document}TG = ∑i,j n'ᵢⱼ Tᵢⱼ{document} . In a binary copolymer of structure [(a) × (b)y] n, corresponding to the ij sequences ‐aa‐, ‐ba‐, ‐ab‐, and ‐bb‐. The term n'ij is the mole fraction of ij sequences, nij weighted according to the number of rotatable bonds per sequence, αij, and {article}{empty}{document}nᵢⱼ = nᵢⱼ α ij/∑i,j (nᵢⱼ α ᵢⱼ ){document} . The variation in the distribution of sequences with overall composition is obtained from the copolymerization reactivity ratios. The theory, which quantitatively describes the sometimes observed maximum or minimum in TG ‐ composition plots, gives good agreement with published data for 11 copolymer systems. Application of the theory to give homopolymer TG's by extrapolation is demonstrated. Inter‐relations are found with other published theories of copolymer TG.