Statistical thermodynamics of semi-flexible chain molecules

Abstract

Long-chain polymer molecules are approximated by a model consisting of isodimensional segments which tend to arrange themselves in co-linear succession. A fraction f of the bonds is assumed to be ‘bent’ out of the co-linear direction of preceding segments. The fact that the free energy of solution derived using the lattice model separates into (a) a mixing term dependent only on the concentration, and (b) a disorientation term depending on f but not on the concentration, leads to the concept of an equilibrium ‘flexibility’ f which is characteristic of the polymer chain at a given temperature. This f must exceed a specified critical value, which decreases with dilution, if the disordered phase usually considered to occur is to be more stable than an ordered one in which the chains assume their preferred rod-like form and lie parallel to one another. Transition between the two states should be co-operative, and should involve a latent heat (owing to the change in intramolecular configurational energy) even in the absence of a change in the intermolecular energy. The concept of a phase transition due solely to intramolecular forces thus arises. Configurational dimensions of various polymers are such as to suggest that inflexibility may be a dominant factor in causing them to crystallize. This is certainly true for cellulose derivatives, probably also for polytetrafluoroethylene, and possible for polymethylene as well. Intramolecular forces favouring the rod-like form are, doubtless of major importance also in bringing about crystallization of proteins in the α-form.