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Volumn 29, Issue 6, 1996, Pages 2275-2288

Methanol absorption in ethylene-vinyl alcohol copolymers: Relation between solvent diffusion and changes in glass transition temperature in glassy polymeric materials

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EID: 0001275007     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma950767p     Document Type: Article
Times cited : (70)

References (111)
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    • It is in this respect different from many common physical phenomena: For example, a one-dimensional description gives a good approximation of the electric field near the surface of a large uniformly charged slab, and the one-dimensional diffusion equation describes well the diffusion of a liquid into a porous (nonswelling) film. In both instances the only corrections to the one-dimensional description come from edge effects.
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    • There is a simple topological reason for this result. In two or three dimensions it is impossible to affinely (uniformly swell (by a ratio other than 1) the outer rubber tube or shell in Treloar's problem without violating the adjacency constraint at the interface between the rigid core and the inner surface of the tube or shell. To satisfy this constraint (which is forced upon the problem by the requirement of adhesive bonding) elastic stresses and concentration gradients must arise. On the other hand, in one dimension the adjacency constraint can be satisfied for any affine deformation.
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    • Over the years several authors have attempted to account for the effect of swelling within a one-dimensional description, e.g., using only the component of the stress perpendicular to the film surface (which for a film is essentially zero as noted in the text). A recent example is found in: Wu, J. C.; Peppas, N. A. J. Polym. Sci., Part B 1993, 31, 1503.
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    • Firestone, B. A.; Siegel, R. A. Polym. Commun. 1988, 29, 204. See also: Siegel, R. A. Adv. Polym. Sci. 1993, 109, 233. These authors provide experimental evidence on how the thickness of their gels affects the onset of the regime of accelerated uptake.
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    • Other treatments which attempt to deal with macroscopic elastic forces arising in the sample in the course of the diffusion process have been proposed. In addition to refs 9 and 19, see: Rosen, B. J. Polym. Sci. 1961, 19, 177. Petropoulos, J. H.; Roussis, P. P. J. Membr. Sci. 1978, 3, 343. Petropoulos, J. H. J. Polym. Sci. 1984, 22, 183. Gostoli, C.; Sarti, G. C. Polym. Eng. Sci. 1982, 22, 1018.
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    • Other treatments which attempt to deal with macroscopic elastic forces arising in the sample in the course of the diffusion process have been proposed. In addition to refs 9 and 19, see: Rosen, B. J. Polym. Sci. 1961, 19, 177. Petropoulos, J. H.; Roussis, P. P. J. Membr. Sci. 1978, 3, 343. Petropoulos, J. H. J. Polym. Sci. 1984, 22, 183. Gostoli, C.; Sarti, G. C. Polym. Eng. Sci. 1982, 22, 1018.
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    • The treatments leading to these results are flawed in a number of other respects. In particular, the inherently three-dimensional geometrical effects discussed in the present paper are systematically neglected. Furthermore, different physical quantities pertaining to either a macroscopic or a microscopic description are incorrectly blended together. Specifically, there seems to be considerable confusion concerning the nature of osmotic pressure. For a discussion in this regard, see: Denbigh, K. The Principles of Chemical Equilibrium; Cambridge University Press: Cambridge, 1901.
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    • We are aware of only one set of experimental results where the initial uptake has been reported to change from linear to √t depending on the size of the sample. Polystyrene spheres exposed to hexane have been reported to exhibit case II behavior if the diameter is d = 184 μm and Fickian behavior if d = 0.534 μm; see: Enscore, D. J.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 793. Hopfenberg, H. B. J. Membr. Sci. 1978, 3, 215. Berens, A. R.; Hopfenberg, H. B. Polymer 1978, 19, 489. With regard to these results we note the following. The two sets of spheres were prepared via different polymerization processes: suspension polymerization for the large spheres and emulsion polymerization for the small ones. The final uptake for the small spheres is nearly 2 times as large as the final uptake for the large spheres under identical exposure conditions. This points to morphological differences between the two materials. In particular, we note that the presence of micropores in the smaller spheres would account for both the initial Fickian behavior (solvent would simply move into the pores following Darcy's law) and the higher equilibrium uptake. Such a difference in morphology would also account for the reported deviation from Fickian behavior observed at finite times, since diffusion of solvent from the pores into the glassy polystyrene would still be controlled by case II diffusion. No attempt to characterize the spheres from a morphological standpoint is reported in the papers quoted above.
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    • We are aware of only one set of experimental results where the initial uptake has been reported to change from linear to √t depending on the size of the sample. Polystyrene spheres exposed to hexane have been reported to exhibit case II behavior if the diameter is d = 184 μm and Fickian behavior if d = 0.534 μm; see: Enscore, D. J.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 793. Hopfenberg, H. B. J. Membr. Sci. 1978, 3, 215. Berens, A. R.; Hopfenberg, H. B. Polymer 1978, 19, 489. With regard to these results we note the following. The two sets of spheres were prepared via different polymerization processes: suspension polymerization for the large spheres and emulsion polymerization for the small ones. The final uptake for the small spheres is nearly 2 times as large as the final uptake for the large spheres under identical exposure conditions. This points to morphological differences between the two materials. In particular, we note that the presence of micropores in the smaller spheres would account for both the initial Fickian behavior (solvent would simply move into the pores following Darcy's law) and the higher equilibrium uptake. Such a difference in morphology would also account for the reported deviation from Fickian behavior observed at finite times, since diffusion of solvent from the pores into the glassy polystyrene would still be controlled by case II diffusion. No attempt to characterize the spheres from a morphological standpoint is reported in the papers quoted above.
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    • We are aware of only one set of experimental results where the initial uptake has been reported to change from linear to √t depending on the size of the sample. Polystyrene spheres exposed to hexane have been reported to exhibit case II behavior if the diameter is d = 184 μm and Fickian behavior if d = 0.534 μm; see: Enscore, D. J.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 793. Hopfenberg, H. B. J. Membr. Sci. 1978, 3, 215. Berens, A. R.; Hopfenberg, H. B. Polymer 1978, 19, 489. With regard to these results we note the following. The two sets of spheres were prepared via different polymerization processes: suspension polymerization for the large spheres and emulsion polymerization for the small ones. The final uptake for the small spheres is nearly 2 times as large as the final uptake for the large spheres under identical exposure conditions. This points to morphological differences between the two materials. In particular, we note that the presence of micropores in the smaller spheres would account for both the initial Fickian behavior (solvent would simply move into the pores following Darcy's law) and the higher equilibrium uptake. Such a difference in morphology would also account for the reported deviation from Fickian behavior observed at finite times, since diffusion of solvent from the pores into the glassy polystyrene would still be controlled by case II diffusion. No attempt to characterize the spheres from a morphological standpoint is reported in the papers quoted above.
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    • This is true of a number of other models where the Deborah number concept is not explicitly invoked; see: Carbonell, R. G.; Sarti, G. C. Ind. Eng. Chem. Res. 1990, 29, 1194. Kalospiros, N. S.; Ocone, R.; Astarita, G.; Meldon, J. H. Ind. Eng. Chem. Res. 1991, 30, 851. Jou, D.; Camacho, J.; Grmela, M. Macromolecules 1991, 24, 3597.
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    • This is true of a number of other models where the Deborah number concept is not explicitly invoked; see: Carbonell, R. G.; Sarti, G. C. Ind. Eng. Chem. Res. 1990, 29, 1194. Kalospiros, N. S.; Ocone, R.; Astarita, G.; Meldon, J. H. Ind. Eng. Chem. Res. 1991, 30, 851. Jou, D.; Camacho, J.; Grmela, M. Macromolecules 1991, 24, 3597.
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    • This is true of a number of other models where the Deborah number concept is not explicitly invoked; see: Carbonell, R. G.; Sarti, G. C. Ind. Eng. Chem. Res. 1990, 29, 1194. Kalospiros, N. S.; Ocone, R.; Astarita, G.; Meldon, J. H. Ind. Eng. Chem. Res. 1991, 30, 851. Jou, D.; Camacho, J.; Grmela, M. Macromolecules 1991, 24, 3597.
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    • It is curious in this regard that ref 9 is often misquoted as the work which introduced the concept of "relaxation-controlled transport". In fact, in the paper by Alfrey, Gurnee, and Lloyd the word "relaxation" appears only once: It is mentioned as an aside, while work by previous authors (who had claimed a role for it) is reviewed.
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    • The plasticized region of the material is similar from a material standpoint to a rubbery polymer. The glassy region is similar to the systems of ref 5. In both instances Fick's law is expected to hold.
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    • g the value of the storage modulus at the methanol weight fraction measured before the run may be somewhat lower than that reported in Figure 4.
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    • Toyoshima, K.1
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    • 0019581977 scopus 로고
    • We obtained similar results for the system water-EVOH in the 25-50 °C temperature range. Results for water sorption in EVOH (for different copolymer compositions from those studied here) have also been reported by: Hopfenberg, H. G.; Apicella, A.; Saleeby, D. E. J. Membr. Sci. 1981, 8, 273. We disagree with their interpretation of these results in terms of case II diffusion. In particular, we view the apparent linear regime as an artifact due to the pronounced accelerated uptake. Once the data collected by these authors are plotted vs √t (rather than vs t), they all (except for those taken at T = 0.5 °C which is very close to the freezing point of water have the sigmoidal shape shown in our figures and the initial behavior is consistent with √t uptake.
    • (1981) J. Membr. Sci. , vol.8 , pp. 273
    • Hopfenberg, H.G.1    Apicella, A.2    Saleeby, D.E.3
  • 90
    • 0020175087 scopus 로고
    • A similar increase in solvent uptake after the fronts have met is also found in case II diffusion. See the data of ref 13 and of Sarti, G. C.; Gostoli, C.; Masoni, S. J. Membr. Sci. 1983, 15, 181. However, in case II diffusion the effect on weight gain is less dramatic, due to the fact that the concentration of solvent in the plasticized region is nearly flat; in systems such as ours which follow Fick's law, there is a significant gradient (see Figure 12) in the plasticized region. In other words, when the fronts meet, a case II system is much closer to its equilibrium weight uptake than a system of the kind discussed here.
    • (1983) J. Membr. Sci. , vol.15 , pp. 181
    • Sarti, G.C.1    Gostoli, C.2    Masoni, S.3
  • 91
    • 85033814668 scopus 로고    scopus 로고
    • note
    • -1/2, and the authors describe this behavior as the transport-limited regime of the Astarita-Sarti model, e.g., the behavior is controlled by Fick's law as in our system. However, we disagree with the description given by these authors of sorption of acetone in the same material, which is interpreted as case II diffusion: No data regarding the velocity of the front are given for acetone, and the apparent linear portion in the sorption curves is, in fact, the result of an accelerated uptake regime coincident with the onset of a sudden increase in the transverse dimension of the film. As is the case with the data of ref 67, this effect is immediately apparent once the data are plotted vs √t.
  • 93
    • 0000489523 scopus 로고
    • Kwei, T. K.; Wang, T. T.; Zupko, H. M. Macromolecules 1972, 5, 645. Wang, T. T.; Kwei, T. K. Macromolecules 1973, 6, 919.
    • (1973) Macromolecules , vol.6 , pp. 919
    • Wang, T.T.1    Kwei, T.K.2
  • 94
    • 85033811523 scopus 로고    scopus 로고
    • note
    • 1.
  • 96
    • 85033817708 scopus 로고    scopus 로고
    • note
    • g will lead to similar results.
  • 97
    • 85033817782 scopus 로고    scopus 로고
    • note
    • 0 as an experimental fact.
  • 98
    • 0000067896 scopus 로고
    • Note, however, that since our front is not moving at a constant velocity, the precursor tail has the error function form of Crank (see ref 71) and not the (case II) form discussed by: Peterlin, A. Polym. Lett. 1965, 3, 1083. Peterlin, A. Makromol. Chem. 1969, 124, 136.
    • (1965) Polym. Lett. , vol.3 , pp. 1083
    • Peterlin, A.1
  • 99
    • 0001580795 scopus 로고
    • Note, however, that since our front is not moving at a constant velocity, the precursor tail has the error function form of Crank (see ref 71) and not the (case II) form discussed by: Peterlin, A. Polym. Lett. 1965, 3, 1083. Peterlin, A. Makromol. Chem. 1969, 124, 136.
    • (1969) Makromol. Chem. , vol.124 , pp. 136
    • Peterlin, A.1
  • 102
    • 85033827284 scopus 로고    scopus 로고
    • note
    • The fact that at t → 0 the solvent volume fraction at the boundary is independent of sample geometry is a manifestation of the fact discussed in the Introduction that at t → 0 every geometry is effectively semi-infinite; swelling is constrained to the direction normal to the surface, but the effect of these constraints is geometry independent.
  • 103
    • 85033830213 scopus 로고    scopus 로고
    • note
    • Note that the density of methanol is only about two-thirds the density of EVOH. As a result, the volume fraction of solvent is significantly larger than the concentration.
  • 104
    • 85033824550 scopus 로고    scopus 로고
    • note
    • This procedure is similar to that considered in ref 33. However, the way our boundary conditions change reflects the results of the constrained swelling problem for the sample geometry under consideration.
  • 105
    • 85033811194 scopus 로고    scopus 로고
    • note
    • 1(φ).
  • 106
    • 85033806091 scopus 로고    scopus 로고
    • note
    • For values of χ and N which are reasonable for our system (i.e., that produce equilibrium solvent volume fractions of the order of 0.2-0.3), the equilibrium concentration profiles within the rubber tube or shell are very fast. If this was not the case, the procedure that we adopt to deal with the kinetic problem would not be appropriate, and a potential term (which accounts for the effect of the constraint on the equilibrium profile) would have to be included in the kinetic equations. See the second of ref 30 for details.
  • 107
    • 0042374744 scopus 로고
    • In analyzing this type of result, it is important to evaluate the effect of possible morphological changes, such as solvent-induced crystallization (Kambour, R. P.; Karasz, F. E.; Daane, J. H. J. Polym. Sci., Part A-2 1967, 4, 327. Overbergh, N.; Berghmans, H.; Smets, G. Polymer 1975, 16, 703) and loss of low molecular weight components (Faulkner, D. L.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 1130) or uncross-linked chains. We note in this regard that loss of uncross-linked chains (rather than some "relaxational process") may account for the overshoots reported in: Smith, M. J.; Peppas, N. A. Polymer 1985, 26, 569. Peppas, N. A.; Urdahl, K. G. Polym. Bull. 1986, 16, 201. No attempt to check for the presence of polymer in solution at the end of the sorption experiment nor any comparison between the initial weight of the sample and a dry final weight (obtained by desorbing the sample after swelling) are reported in these papers.
    • (1967) J. Polym. Sci., Part A-2 , vol.4 , pp. 327
    • Kambour, R.P.1    Karasz, F.E.2    Daane, J.H.3
  • 108
    • 0007933140 scopus 로고
    • In analyzing this type of result, it is important to evaluate the effect of possible morphological changes, such as solvent-induced crystallization (Kambour, R. P.; Karasz, F. E.; Daane, J. H. J. Polym. Sci., Part A-2 1967, 4, 327. Overbergh, N.; Berghmans, H.; Smets, G. Polymer 1975, 16, 703) and loss of low molecular weight components (Faulkner, D. L.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 1130) or uncross-linked chains. We note in this regard that loss of uncross-linked chains (rather than some "relaxational process") may account for the overshoots reported in: Smith, M. J.; Peppas, N. A. Polymer 1985, 26, 569. Peppas, N. A.; Urdahl, K. G. Polym. Bull. 1986, 16, 201. No attempt to check for the presence of polymer in solution at the end of the sorption experiment nor any comparison between the initial weight of the sample and a dry final weight (obtained by desorbing the sample after swelling) are reported in these papers.
    • (1975) Polymer , vol.16 , pp. 703
    • Overbergh, N.1    Berghmans, H.2    Smets, G.3
  • 109
    • 0017559828 scopus 로고
    • In analyzing this type of result, it is important to evaluate the effect of possible morphological changes, such as solvent-induced crystallization (Kambour, R. P.; Karasz, F. E.; Daane, J. H. J. Polym. Sci., Part A-2 1967, 4, 327. Overbergh, N.; Berghmans, H.; Smets, G. Polymer 1975, 16, 703) and loss of low molecular weight components (Faulkner, D. L.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 1130) or uncross-linked chains. We note in this regard that loss of uncross-linked chains (rather than some "relaxational process") may account for the overshoots reported in: Smith, M. J.; Peppas, N. A. Polymer 1985, 26, 569. Peppas, N. A.; Urdahl, K. G. Polym. Bull. 1986, 16, 201. No attempt to check for the presence of polymer in solution at the end of the sorption experiment nor any comparison between the initial weight of the sample and a dry final weight (obtained by desorbing the sample after swelling) are reported in these papers.
    • (1977) Polymer , vol.18 , pp. 1130
    • Faulkner, D.L.1    Hopfenberg, H.B.2    Stannett, V.T.3
  • 110
    • 0022043614 scopus 로고
    • In analyzing this type of result, it is important to evaluate the effect of possible morphological changes, such as solvent-induced crystallization (Kambour, R. P.; Karasz, F. E.; Daane, J. H. J. Polym. Sci., Part A-2 1967, 4, 327. Overbergh, N.; Berghmans, H.; Smets, G. Polymer 1975, 16, 703) and loss of low molecular weight components (Faulkner, D. L.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 1130) or uncross-linked chains. We note in this regard that loss of uncross-linked chains (rather than some "relaxational process") may account for the overshoots reported in: Smith, M. J.; Peppas, N. A. Polymer 1985, 26, 569. Peppas, N. A.; Urdahl, K. G. Polym. Bull. 1986, 16, 201. No attempt to check for the presence of polymer in solution at the end of the sorption experiment nor any comparison between the initial weight of the sample and a dry final weight (obtained by desorbing the sample after swelling) are reported in these papers.
    • (1985) Polymer , vol.26 , pp. 569
    • Smith, M.J.1    Peppas, N.A.2
  • 111
    • 0009292261 scopus 로고
    • In analyzing this type of result, it is important to evaluate the effect of possible morphological changes, such as solvent-induced crystallization (Kambour, R. P.; Karasz, F. E.; Daane, J. H. J. Polym. Sci., Part A-2 1967, 4, 327. Overbergh, N.; Berghmans, H.; Smets, G. Polymer 1975, 16, 703) and loss of low molecular weight components (Faulkner, D. L.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18, 1130) or uncross-linked chains. We note in this regard that loss of uncross-linked chains (rather than some "relaxational process") may account for the overshoots reported in: Smith, M. J.; Peppas, N. A. Polymer 1985, 26, 569. Peppas, N. A.; Urdahl, K. G. Polym. Bull. 1986, 16, 201. No attempt to check for the presence of polymer in solution at the end of the sorption experiment nor any comparison between the initial weight of the sample and a dry final weight (obtained by desorbing the sample after swelling) are reported in these papers.
    • (1986) Polym. Bull. , vol.16 , pp. 201
    • Peppas, N.A.1    Urdahl, K.G.2


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