| A generalized thermodynamic model for crystallization in random copolymers has been developed. The model is applicable to crystallization under quiescent conditions or under the influence of anisotropic stress, which is the dominant mode of crystallization in a number of polymer processing operations. The effect of anisotropic stress, which has been largely ignored in existing formulations for crystallization in random copolymers, has been introduced into the free energy expression through the free energy change of the melt upon deformation, ΔG def. ΔGdef has been obtained by two methods: (i) The Gaussian network model and (ii) A theory of orientation development in flowing melts. The effect of copolymerization with comonomers that differ significantly from the predominant monomer in chain conformational characteristics and melt-flow behavior has also been investigated. Thus, the model incorporates a more detailed description of the primary structure of the polymer and processing conditions such as temperature and stress.; Calculations of equilibrium crystallization temperature and the kinetics of crystallization (primary and secondary nucleation rates) have been done for PET-based random copolymers as an illustrative example. The results of these calculations bring out a range of crystallization phenomena observed in stressed random copolymers and copolymers with both rigid and flexible units in the backbone. For example, (i) experimentally observed increase in crystallization rate upon copolymerization with rigid comonomers, (ii) the temperature dependence of the “copolymer effect” in certain random copolymers, (iii) the vast difference in the nature of the melt → crystal phase boundary and crystallization kinetics between quiescent and stressed conditions, and (iv) sharper crystal orientation distributions in copolymers compared to homopolymers, are all predicted by the model and borne out by experimental observations. Several of these predictions run counter to typical generalizations regarding the influence of random copolymerization on crystallization.; Thus, by incorporating the influence of anisotropic stress and chain rigidity on the free energy of crystallization of a random copolymer, a generalized model that provides a more complete description of crystallization in random copolymers is obtained. Such a formulation can be of much value in designing copolymers to obtain the desired combination of properties. |
