Occupied Volume of Liquids and Polymers

Abstract

Recently, much progress has been made in developing a theory of the liquid state. In their most advanced form these theories start with intermolecular force fields and their relation to intermolecular distances, and, then, by the application and computation of Monte Carlo-type statistics, it is possible to arrive at a convincing picture of the thermodynamics of simple liquids with a minimum of specific assumptions [1,2]. At present, such treatments are most effectively applied in the simplest cases, e.g., to a monatomic fluid [3J. On the other hand, very many scientists have to deal with systems including polymeric systems which are much more complicated. In these cases, it is not always practicable to work with the most sophisticated techniques, even though, if unlimited effort and computer capacity was available, such means could sometimes be effective. Thus, there is still a requirement for intermediate concepts or specific models which can be useful in describing the properties of liquids and of polymers in the liquid state. To meet this requirement a number of theories have grown up which make use of the concept of “free volume” to describe the properties of liquids, and a perusal of current literature will provide many references to this concept. Unfortunately, it is not always clear how free volume is defined: neither is it possible to clarify this point by reference to the standard textbooks of physical chemistry [4]. It is, therefore, the object of this review to describe useful definitions of free volume and to consider in particular how far the free volume, which is defined by the total thermal expansion of initially close-packed molecules at 0°K, can be related to the types of free volume theories currently being developed. We may note, however, that there is only one type of empty space between molecules. Different requirements arise only when theories are developed which are concerned with the way this free space enters into molecular processes. From this point of view the same basic geometry may be treated in different ways.