doi:10.1016/j.eurpolymj.2004.11.016 
Copyright © 2004 Elsevier Ltd All rights reserved.
Diffusivity of solvent in a polymer solution—expansive free volume effect
Jyh-Ping Hsu and Sung-Hwa Lin
, 
Department of Chemical Engineering and Materials Engineering, National Ilan University, Ilan 26041, Taiwan, ROC
Received 30 August 2004;
revised 11 November 2004;
accepted 17 November 2004.
Available online 6 January 2005.
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Abstract
The concentration dependency of the diffusivity of a solvent in a polymer solution is derived on the basis of a free volume theory. Applying a molecular kinetics approach, the Fujita–Doolittle equation is modified. The result of numerical simulation reveals that the diffusivity of solvent in a polymer solution depends largely on both the polymer chain structure and its concentration. The applicability of the analytical expression derived is justified by fitting the experimental data for n-alkyl acetate-(poly-methyl acrylate) polymer solutions in the literature.
Keywords: Expansive free volume; Fujita–Doolittle equation; Diffusivity of solvent; Thermal expansive coefficient; Retardation effect
Fig. 1. Schematic representation for the diffusion process of solvent molecule in a polymer solution. The rearrangement of the polymer chain caused by collisions is accomplished by the co-operative movement of several monomers (segments).
Fig. 2. Variation of logD0,1 ([D0,1] = cm2/s) as a function of temperature for various alkyl acetates for the case of dilute solvent solution. Discrete symbols, experimental data of Fujita et al. [6], curves, present model, Eq. (16). 
, methyl acetate; ○, ethyl acetate; 
, n-propyl acetate; □, n-butyl acetate.
Fig. 3. Variations of the log(DT,1/D0,1) of ethyl acetate as a function of 
1 at various temperatures. Discrete symbols, experimental data of Fujita et al. [6]; solid curves, present model, Eq. (18).
Fig. 4. Variation of the [log(DT,1/D0,1)]−1 of ethyl acetate as a function of 1/1 at various temperatures. Discrete symbols, experimental data of Fujita et al. [6]; dashed curves, results predicted by linear regression; solid curves, present model, Eq. (22).
Fig. 5. Variations of S as a function of 
for the case of Fig. 4. Discrete symbols, values by linear regression in Fig. 4; dashed curve, values by Fujita–Doolittle equation, Eq. (2); solid curve, values by present model, Eq. (23).
Fig. 6. Variations of the scaled terms on the right-hand side of Eq. (11) as a function of 1 for a typical linear-chained amorphous polymer solution. Dashed curve, Y = exp{−U*[(1 − f)4 − 2(1 − f)2]/kT}/{exp{−U*[(1 − f)4 − 2(1 − f)2]/kT}}min; solid curve, Y = exp(−fc/f)/[exp(−fc/f)]min. Physical properties used are f1 = 0.25, f2 = 0.025, 
, 
, T = 80 °C, and fc = 0.55.
Table 1.
The interactive parameters for n-alkyl acetate-PMA polymer solutions
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