On the glass transition temperature of comblike polymers: Effects of side chain length and backbone chain structure

Abstract

AbstractPolymers composed of monomer units that contain n‐alkyl side chains are characterized by a monotonical decrease in the glass transition temperatures toward a critical value (Tg)c as the number of C atoms in the side chain increases toward a corresponding critical value nc. Thus the glass transition temperatures of these comblike polymers are for a given backbone chain structure directly related to the molecular weight (M) of the monomer unit. This relationship can be represented by the differential equation dTg/dM = −k′M[Tg − (Tg)c], which on integration yields Tg = (ΔTg)0 exp−[k(M2 − M)] + (Tg)c, where (ΔTg) = (Tg)1 − (Tg)c, and the subscript 1 refers to n = 1. Values for Tg calculated according to this relationship are in good agreement with published data on polybutadienes, polystyrenes, poly(vinyl ether)s, polyacrylates, polymethacrylates, polyitaconates, poly(phenylene ether)s, and poly(N‐maleimide)s. For these polymers the critical quantities nc and (Tg)c can be estimated rather well by the simple relationships nc = 1 + 2.8 × 10−2 (Tg)1 and (Tg)c = (Tg)1 − nc(nc − 1). The Tg(M) relationship derived appears to be applicable also to copolymers that contain monomer units with alkyl side chains.