Topomorphism and phase dualism of flexible chain polymers
Authors: Frenkel S. , Baranov V. G. 
Published: April 2007

The polymer topomorphism concept previously treated in terms of crystalline topomorphism only is reconsidered on the basis of thermodynamic dualism following from T. Hill's thermodynamics of small systems.1This leads to substantial generalisations extending to ‘amorphous’ topomorphism as well. Thus we can treat, in a physically rigorous manner the problems of inherent ‘thermodynamic dissymmetry’ of the melting‐crystallisation on behaviour of flexible chain polymers and of their phase dualism. The latter involves W. Kuhn's statistical elements (segments) as ‘supermolecules’ belonging both to small systems (macromolecules) and to the large one (the whole amorphous polymeric sample) the latter being a superposition of interpenetrating statistical coils which in their turn are accumulated in subsystems, or groups, having equal degrees of coiling β. It is essential that the β distribution and the corresponding conformational entropy distribution is the same as Maxwell's distribution for kinetic energy in the theory of gases. This equivalence of two distributions of essential thermodynamic parameters is not a mere formal coincidence but reflects the dualistic behaviour of segments which must be treated as ‘gas molecules’ within a given coil and as molecules of a liquid when the large system is considered. It follows immediately that many essential properties of amorphous polymers and melts (including their crystallisation behaviour) must be due to the superposition of gas‐like and liquid‐like properties of segments, and that some important properties of the large system are due exclusively to contributions from the small systems.

This general approach is used to investigate the behaviour of polymer melts under high pressure. In accord with the Le Chatelier's principle, increasing pressure changes the gas‐likeness to the liquid‐likeness and the liquid‐likeness to some type of ordering (crystalline or liquid crystalline if the former state is impossible due to the lack of tacticity). The small systems can become liquid‐like due to supercoiling or touncoiling, and it is shown that the latter case is energetically much more favourable. Solely due to this uncoiling the large system undergoes a transition into a nematic state followed (if the chain configuration is appropriate) by an extended chain crystallisation.

In this instant the effects of pressure are the same as effects of melt extension prior to crystallisation. In both cases a critical value β = β* appears when further spontaneous uncoiling occurs. The phase transition of the whole system at crytical values of β is a typical ‘behavioural’ transition in Prigogine's3sense being a bifurcation in a non‐equilibrium state, leading to the change of mode of crystalline growth. However, even in static and close to macroscopic equilibrium conditions a similar bifurcation may occur due to the fact that the above mentioned groups may be far from equilibrium (depending on their particular β values). Again the crystalline topomorphism results, the growth of extended chain crystals proceeding by the mechanism of ‘order through fluctuations’.

Finally, a remark is made on a possibility of developing a theory of crystallisation and melting of polymers leading directly to the above mentioned ‘thermodynamic dissymmetry’ and based on some analogies with para‐ferromagnetic transitions.