Some Thermodynamic Properties of High Polymers, and Their Molecular Interpretation

The past decade has witnessed a rapid growth in the understanding of the thermodynamic properties of polymers and their solutions. This has been achieved largely by the development of statistical theories of rubberlike elasticity and of the free energy of mixing of polymers with liquids. A number of reviews are available dealing with portions of this field of work, but for the most part they are addressed to specialist workers. The object of this review is to survey in broad outline a number of related topics, without entering into detailed discussion of statistical theories. The emphasis is, therefore, laid on the experimental thermodynamic data which form the basis for these theories, and on their physical significance. An attempt is made to develop the argument as far as possible in physical terms, although it must be realized that this is essentially a field in which we are concerned with quantitative measurements and their mathematical interrelations. One fundamental experimental difficulty which is common to nearly all the problems to be discussed below is that of ensuring that the system under investigation has reached a state of equilibrium. The significance of the concept of equilibrium in measurements on polymers has recently been very clearly discussed by Ubbelohde. The difficulty arises from the fact that many processes in a polymer take place so slowly that they may to a good approximation be said not to occur at all during the time involved in an experiment. When this is the case, it is clear that the system cannot be assumed to reach a state of equilibrium with respect to this particular process. It is, indeed, common to find that certain properties of a polymer depend greatly on the previous history of the specimen; examples will be given later. Even when this is the case, the system may still be in equilibrium with respect to other possible changes, and it is, therefore, permissible to apply the thermodynamic criteria of equilibrium. Care is needed in relating the experimental results to theories to make sure that the theory is not based on the assumption of equilibrium with respect to changes which are so slow as to be virtually negligible. The usefulness of considering partial equilibria in this way depends on the possibility of choosing a time scale for the experimental work long enough for the rapid processes to be complete, and at the same time short enough to exclude other slower processes.