A critical review of free volume and occupied volume calculation methods

• Free volume concepts and assumptions are reviewed.
• The frequently cited “1.3” factor is critically challenged.
• A method for calculating free volume in a mixed system is presented.
• Improvements to our understanding of free volume from first principles are proposed.

Free volume affects many properties of polymers but is relatively difficult to access experimentally. Several methods of calculating free volume are available, but the assumptions implicit in their use are not always examined closely. This paper reviews free volume concepts and examines the methods of calculating free volume from first principles, giving particular attention to the history of the frequently used “1.3” factor quoted from Van Krevelen. Calculating free volume using the “1.3” factor, a method first proposed by Lee, is shown to be incorrect according to first principles. The error becomes particularly significant when calculating the free volume of a mixed system, such as a polymer with sorbed gas. However, the “1.3” factor can still be useful in the absence of certain physical data. A comparison of free volume calculation techniques is also presented, followed by an evaluation of free volume correlations with gas permeability and recommendations for future research.