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The Vrentas–Duda free‐volume theory for diffusion characterizes the diffusivity of a solvent in a polymer in terms of the concentration and size of the solvent, the temperature, and the glass transition temperature (Tg) of the individual components. The effective Tg of the polymer, however, is a function of the concentration of the solvent. This article introduces a modification that corrects for this change in the glass‐transition temperature, thus providing more accurate diffusivities. The model has been verified by comparison with experimental diffusivities of water, acetone, methanol, and tetrahydrofuran in hypromellose acetate succinate (HPMCAS). HPMCAS is widely used in the production of pharmaceutical formulations. One common application is the formation of amorphous solid dispersions with poorly soluble active pharmaceutical ingredients (APIs) for dissolution and solubility enhancement. Frequently, the APIs and HPMCAS are put into solution and spray dried at an outlet temperature below the normal glass‐transition temperature. The modified free‐volume theory is able to directly predict or correlate with only one adjustable parameter the diffusivities as a function of the concentration and temperature. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47351.

Abstract Diffusion of penetrants in polyethylene below the melt temperature is heavily dependent on the crystallinity of the polyethylene, the temperature of the experiment, and the concentration of solvent in the polymer. As the crystallinity of the polyethylene increases, there is an increase in the path that the solvent must travel as the solvent cannot penetrate the tightly packed chains in the crystalline domain. This effect is typically accounted for by a tortuosity factor. In this work, a simple and effective characterization of the tortuosity factor based simply on the crystal weight fraction has been developed. Data have been collected for six polyethylenes having densities ranging from 0.912 to 0.961 g/cm3 and for three solvents – isopentane, cyclohexane, and 1-hexene. Diffusivity predictions have been obtained using the free-volume theory of Vrentas and Duda in conjunction with the new tortuosity factor. The polyethylenes had crystallinities varying from 40% to 82% effecting an approximately 60% change in the diffusivity. The decrease resulting from ignoring the crystallinity altogether was in some cases essentially a factor of 5. The error in the predicted diffusivities over all the systems was 25%. For cyclohexane, it is shown that the same model parameters characterize data below the melt temperature (in the semi-crystalline region) as well as above the melt temperature (in the amorphous region).

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