Gas chromatographic measurements of infinite dilution diffusion coefficients of volatile liquids in amorphous polymers at elevated temperatures

Measurements were made of infinite dilution diffusion coefficients of volatile liquids in amorphous polymers at elevated temperatures, using inverse gas chromatography. The liquids used were benzene, toluene, ethylbenzene, and n-decane. The polymers used were polystyrene and poly(vinyl acetate), and temperatures ranged from 30°C to 120°C above the glass transition temperatures of the polymers. Packed chromatographic columns were used to obtain data of the variation of the plate height with the average gas velocity, which was then used to determine diffusion coefficients with the aid of the van Deemter equation. In the present investigation, we have used different sizes of glass beads (0.3, 0.5, 0.6, and 1.0 mm in diameter), depending on the system temperature and the polymer/solute pair chosen. An attempt was made to correlate on the diffusion coefficient D measured at various temperatures T, using in Dζ as ordinate and 1/(K₂₂ + T ? T_g2)/T_c] (hereafter referred to as the reciprocal of reduced free volume temperature, 1/T_RF) as abscissa, in which ζ = M^1/2/TV, M being the molecular weight, T_c the critical temperature, and V_c the critical volume of the solute, K₂₂ is a free volume parameter of the polymer, and T_g2 is the glass transition temperature of the polymer. It has been found that such plots give rise to two linear regions having different slopes, separated by a critical value of 1/T_RF. The critical value of 1/T_RF is found to be insensitive to the type of solute and the type of polymer used. We have concluded that the infinite dilution diffusion coefficient of volatile liquids in amorphous polymers is controlled predominatly by the free volume of polymer above a critical value of 1/T_RF, but energy effects are significant below the critical value of this parameter. In order to apply the generalized relationships in conjunction with gas chromatographic measurements, the results of this study indicate that, for values of 1/T_RF larger than a critical value, which is approximately 4.8, the following expression, In Dζ = α + b/T_RF, may be used to predict infinite dilution diffusion coefficients of volatile liquids in amorpous polymers at elevated temperatures, in which α is a constant, independent of the type of solute, and b is approximately a constant for a given polymer in the free volume region, independent of the type of solute. More experimental studies are needed, particularly for temperatures higher than those reported in this study, to corroborate and/or extend the correlations presented here.