Free Volume Estimation

Originally, free volume was interpreted (H. Fujita, M.H. Cohen and D. Turnbull, J.S. Vrentas and J.L. Duda) as an abstract parameter that fits the equation of free volume model. The methods for quantitative determination of free volume were proposed by S. Sugden and later by A. Bondi (1968). According to the latter, free volume V_f (cc/g) can be estimated as the difference: V_f = V_sp – V_occ, where the specific volume is defined as V_sp = 1/ρ (ρ is the polymer density), while occupied volume V_occ can be found as 1.3 V_w, where V_w is the van der Waals volume of the repeat unit of the polymer. The V_w value can be estimated from the increments tabulated for various groups (Van Krevelen and te Nijenhuis 2009). The factor 1.3 is taken from the packing density of molecular crystal at 0 K (accounting for inaccessible volume). Bondi’s formula was criticized: the factor 1.3 might not be a universal constant, applicable in all cases; V_wof repeat units cannot be considered as the sum of increments...