Pergamon Chemicul Engineering Science, Vol. 49, No. 5, pp. 733-748, 1994 copyright 0 1994 Elswicr saena I.** Printed in Orcal Britain. zyxwvutsrqponm A ll ri&hts re se nwl OCC9-2509/94 $6.00 + 0.W zyxwvu NON-FICKIAN TRANSPORT OF ALKYL ALCOHOLS THROUGH PRESTRETCHED POLY-METHYLMETHACRYLATE zyxwvutsrqponmlkjihgfedcbaZYXWVU GIULIO C. SARTI and FERRUCCIO DOGHIERI Dipartimento zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA di Ingegneria Chimica e di Processo, Universita di Bologna, viale Risorgimento 2, I-40136 Bologna, Italy (Received for publication 18 August 1993) Abstract-The effect of the deformation of the solid matrix on the sorption kinetics of low molecular weight alcohols into PMMA was studied. Sorbed mass and cross-sectional area were measured as a function of time for sorption experiments into polymeric films which had been previously stretched. The effect of different draw ratios and different molecular weights of the solvent on the sorption process is disctised in terms of transport kinetics character, swelling front velocity and relaxation time. An interpretation of the experimental data is also presented based on the relevant dimensionless numbers comparing the character- istic times of the elementary processes involved. 1. lNTRODUClTON The mass transfer process of low molecular weight species in solid polymers is well known to show a rather broad variety of behaviors by changing the polymer-penetrant pairs and the operating condi- tions, particularly temperature and penetrant activity [e.g. Nicolais et zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA al. (1978) and Berens and Hopfenberg (1978)]. The geometry of the polymer samples is also relevant in terms of shape (Berens and Hopfenberg, 1978) as well as mere dimensions (Park, 1953; Jacques et al., 1974). In addition, as in most phenomena in- volving polymers, the response to a mass transfer driving force is also affected by the mechanical and thermal pretreatment of the polymer (Hopfenberg et al., 1975; Nicolais er al., 1979; Sarti and Apicella, 1980; Sarti et al., 1983) as well as by the concentration history experienced by the polymer matrix (Enscore et al., 1980). In view of their importance in various technical applications, several different reviews have appeared [e.g. Comyn (1985), Fan and Singh (1989) and Vieth (1991)] and so we will not enter into the details of the several different aspects of the pheno- menological behaviors. For our present purpose we simply recall that typically one obtains: -for rather low jumps in the penetrant activity a Fickian-like behavior even for swelling pen- etrants; -for sufficiently high penetrant activities a sharp discontinuity in the physical properties and in the refractive index, moving inside the matrix. Such a front marks also a shock discontinuity in the concentration profile and typically separates two regions, one rather swollen and the other almost unpenetrated. The sorption behavior associated with a constant shock velocity is called Case II transport (Alfrey et al., 1966) while the behavior obtained when the front velocity decreases with time is normally referred to as anomalous diffusion [e.g. Nicolais et al. (1978)]. Un- der some conditions [e.g. Jacques et al. (1974)], de- creasing temperatures and/or decreasing the sample thickness, an acceleration of the sorption rate during time may also be obtained, which is commonly re- ferred to as Super Case II. Due to the several aspects associated with the pecu- liar structure and the viscoelastic behavior of poly- mers, both in transport phenomena as well as in thermodynamics, polymer scientists are well used to being faced with unexpected and striking behaviors of the polymer response to different external driving forces. The mathematical description and modelling tools which are available, on the other hand, are either simplified in many respects and suitable to describe only some of the observed features (Astarita and Sarti, 1978; Petropoulos and Roussis, 1978; Koros et al., 1981; Thomas and Windle, 1982; Gostoli and Sarti, 1983; Neogi, 1983; Durning, 1985; Camera-Roda and Sarti, 1986) or else are rather comprehensive but rather complex to be used and require the simultan- eous knowledge of several different transport and mechanical properties, either elastic or viscoelastic (Petropoulos, 1984; Carbonell and Sarti, 1990; Doghieri et al., 1992; Lustig et aI., 1992; Doghieri and Sarti, 1993). In view of this, a proper dimensional analysis may be useful in order to adequately account for the sev- eral different responses and to avoid the heavy diffi- culties as well as the uncertainties of complex and as yet unassessed mathematical models. In the present work we will analyze in particular the effects induced on the sorption behavior of alkyl alco- hols by the elongations which have been previously frozen into the polymer matrix. Methyl, ethyl and n-propyl alcohols have been used as penetrants in glassy polymeric films which experienced uniaxial prestretching up to a draw ratio of about 4. The analysis of the experimental data indicates for the present case a rather significant effect of the an- isotropy frozen into the polymer matrix, much more