Thermal Expansion and Compressibility of Amorphous Polymers

Abstract

Thermodynamic properties of amorphous polymers are hereunder discussed on the basis of some refined cell model. It is assumed that each polymer chain is surrounded by six nearest neighbours which form a hexagonal lattice (Fig. 1). We shall further assume the Lennard-Jones potential between the chain units along the axes of polymer chains.The configurational energy and cell partition function are thus obtained. Then the reduced equation of state can be written in the formpV/T=[1-0.831(V)-1/2]-1+T-1[4.263(V)-11/2-6.635(V)-5/2] (1)where the reduced variables are defined byT=sλkT/3(1-f)e*r*, V=v/v*, p=λv*p/3(1-f)e*r*λ: bond lengths: the parameter as a measure of chain flexibilityr*, e*: the parameters of distance and energy in the Lennard-Jones potentialv*: the characteristic value for the van der Waals volume v per chain unitf: free volume fractionEq. (1) shows the principle of corresponding state. From this equation, we can calculate the thermal expansion coefficient and isothermal compressibility for the van der Waals volume. We can treat them for the rubbery state as well as glassy state, considering the growth of holes' or free volume owing to the micro-Brownian motions of the chain segments.In Table I, we show the predicted values of molecular force constants, lattice energies and cohesion energy densities for a few amorphous polymers. They give fairly good agreement with available experimental data.