Role of Free Volume in Polymer Solution Thermodynamics

The principal effects determining the value of the free energy of mixing of polymer solutions are discussed and compared, namely the combinatorial, energetic and structural effects. The influence of the last on the thermodynamic behaviour of polymer solutions is then dealt with, as revealed in the lower critical solution temperature. and in the effect of pressure on polymer—solvent compatibility, the second virial coefficient and the coil dimensions. Quantitative aspects of polymer solution thermodynamics are then discussed; arguments in favour of the use of the segment fraction (instead of the volume fraction) in expressing the combinatorial term are given, and the noncombinatorial contribution at zero pressure and the effect of pressure on the x parameter are characterized. Finally, a difficulty is noted in assessing the possible effect of a difference in diameter between polymer chains and solvent molecules or chains. The first topic to be dealt with by the Microsymposium is 'interactions arising from the difference in size and shape of the polymer and solvent molecules'. The most important interaction of this type comes from the 'structural effect' of Prigogine, Mathot, Bellemans and Trappeniers'. The 'equation of state effect' which has become familiar through the recent work of Flory and collaborators2 is similar in nature. The importance of the structural effect was recognized twenty years ago by Mathot3. It is the main new concept in the theory of polymer solution thermodynamics of Prigogine and collaborators. THE STRUCTURAL EFFECT Introducing the structural effect, Prigogine points out that a polymer liquid and a solvent or 'monomeric' liquid typically have very different equation of state properties. This is related to the polymer having a very low degree of thermal expansion or 'free volume't compared to the solvent. This difference of free volume is independent of any difference in chemical t The term 'free volume' is chosen here because of its intuitive appeal in an essentially qualitative discussion. It was not used by Prigogine and collaborators, and may be replaced by terms such as 'degree of thermal expansion above close-packed volume'.