Some alternatives to the Flory-Huggins-Guggenheim treatment of sorption of liquids by polymers are examined, using data on three systems, water-collagen, benzene-rubber and toluene-polystyrene. It is found that a simple rigid site type of sorption theory is illuminating for the hydrocarbon systems but breaks down badly when applied to water-collagen mixtures. However, an exact "clustering" theory may be applied to all three of these systems. This theory, which is based on the statistical mechanics of fluctuations, does not compete with the Flory-Huggins-Guggenheim treatment in that it does not predict isotherms, but it does serve to interpret them in molecular terms.
Diffusion coefficients of methane in linear polyethylene melts measured by simple sorption experiments are from 1.5 × 10−5 to 3.6 × 10−5 cm.2/sec. between 140.0 and 188.3°C. These diffusion coefficients are one‐third to one‐half those of methane in branched polyethylene melts at these temperatures. Solubilities of methane in branched and linear polyethylene melts are similar, approximately three molecules of methane per one hundred methylene units at 250 atm. partial pressure methane between 140.0 and 188.3°C. Temperature coefficients of solubilities of methane in branched and linear polyethylenes differ in that the solubility of methane in linear polyethylene melt appears to go through a minimum with temperature between 140.0 and 162.8°C. These differences in diffusion coefficients and temperature coefficients of solubilities are consistent with the presence of greater order in linear polyethylene melt than in branched polyethylene melt.
SynopsisDiffusion coefficients and solubilities of methane in polyisobutylene have been measured a t four temperatures between 102 and 188°C. in the pressure range 23-341 atm. Diffusion coefficients extrapolated to atmospheric pressure range from 1.72 X 1 0 P cm.z/ sec. a t 102°C. to 1.5 X cm.2/sec. a t 188°C. corresponding to an activation energy for diffusion of 8.7 f 0.4 kcal./mole. Solubilities are small, about one molecule of methane for every forty carbon atoms in the polyisobutylene a t 300 atm. partial pressure of methane. Solubilities vary little with temperature, but show an apparent minimum between 127 and 188°C. With improved methods of data analysis, diffusion coefficients and solubilities have been recalculated from previously reported studies on nitrogen in branched polyethylene and methane in branched polyethylene, linear polyethylene, and polystyrene. Recalculated diffusion coefficients are essentially the same as those reported previously, but the recalculated solubilities are decreased from 2 to 30%. The solubilities of all five systems show strong deviations from Henry's law, i.e., increases in partial pressure of methane and nitrogen with respect to solubility exceed linearity. Thc partial pressure (or fugacity)-solubility data may be interpreted in terms of a sorption model in which sorbed molecules are accommodated in widely dispersed, unoccupied volumes or sites in the polymer. An almost equivalent, solution model in which the first sorbed molecules to enter the polymer are accommodated to a large cxtent in existing volumes in the polymer, with successively sorbed molecules swelling the polymer to a greater extent (i.e., partial molal volume of sorbed molecules, TI, increasing with concentration) can also account for these data.
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