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  • 1
    Electronic Resource
    Electronic Resource
    A mathematical model for a dissolving polymer (1995)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 41 (1995), S. 2345-2355 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In certain polymer-penetrant systems, nonlinear viscoelastic effects dominate those of Fickian diffusion. This behavior is often embodied in a memory integral incorporating nonlocal time effects into the dynamics; this integral can be derived from an augmented chemical potential. The mathematical framework presented is a moving boundary-value problem. The boundary separates the polymer into two distinct states: glassy and rubbery, where different physical processes dominate. The moving boundary condition that results is not solvable by similarity solutions, but can be solved by perturbation and integral equation techniques. Asymptotic solutions are obtained where sharp fronts move with constant speed. The resultant profiles are quite similar to experimental results in a dissolving polymer. It is then demonstrated that such a model has a limit on the allowable front speed and a self-regulating mass uptake.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690411102
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  • 2
    Electronic Resource
    Electronic Resource
    Sorption of a finite amount of swelling solvent in a glassy polymerThis work was supported in part by the U.S. Army Research office (Durham) under Contract DAAG29-85-K-0092, by the national Science Foundation under Grant DMS84-00885, and by the Department of Energy under Grant 7405/ENG-36 at the Center for Nonlinear Studies at Los Alamos. (1987)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 25 (1987), S. 611-617 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: We study the time history of a diffusing front when a polymer is exposed to a finite amount of penetrant which becomes used up. A class of polymers is considered for which slow molecular relaxation occurs only at or near the glass-gel interface with instantaneous relaxation both ahead of and behind the progressing front. We show that the position of the penetrant front versus time undergoes a long smooth transition from standard Fickian t1/2 behavior to exponential time decay onto a final equilibrium position attained when all the penetrant is used up.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1987.090250312
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  • 3
    Electronic Resource
    Electronic Resource
    The evolution of steep fronts in non-fickian polymer-penetrant systems (1992)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 30 (1992), S. 145-161 
    Details
    ISSN: 0887-6266
    Keywords: diffusion, non-Fickian, in polymer-penetrant systems ; transport of penetrants in polymers, model involving flux and relaxation in ; penetrant diffusion in polymers, evolution of steep fronts in ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: We adapt a recently proposed model for non-Fickian diffusion of penetrants into polymers and use it to study a drug-delivery problem. The model modified Fick's diffusion equation by the addition of stress-induced flux. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The relaxation time in the polymer is taken as a function of the penetrant concentration. The system is studied under the assumption that the diffusivity is large. Singular perturbation techniques are used to show that the concentration and stress evolve diffusively for small time, but exhibit steep fronts in a narrow region within the domain for larger time. These predictions are verified numerically for specified parameter values. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1992.090300204
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  • 4
    Electronic Resource
    Electronic Resource
    A mathematical model for stress-driven diffusion in polymers (1989)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 27 (1989), S. 589-602 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1989.090270308
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  • 5
    Electronic Resource
    Electronic Resource
    Sharp fronts due to diffusion and stress at the glass transition in polymers (1989)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 27 (1989), S. 1731-1747 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: We derive and analyze a model for sharp fronts in glassy polymers. We take the major effect of a diffusing penetrant on the polymer entanglement network to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms, via a relaxation parameter, to account for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state owing to slow response to changing conditions. We produce concentration profiles in good agreement with observations on sharp front formation. In addition the model can account for the phenomenon of sorption overshoot.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1989.090270811
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  • 6
    Electronic Resource
    Electronic Resource
    Theoretical models for diffusion in glassy polymers. II (1984)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 22 (1984), S. 1001-1009 
    Details
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The author refines and generalizes a model for diffusion in glassy polymers which he previously introduced. The model unifies many diverse observations by explicity formulating the common property of a glassy polymer in all its various modes, namely the finite relaxation time due to its slow response to changing conditions. An integral approximation method is used to study the motion of the penetrant front and the glass-gel interface and a useful polynomial approximation method is introduced for use in special simple situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1984.180220606
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  • 7
    Electronic Resource
    Electronic Resource
    Theoretical models for diffusion in glassy polymers (1983)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 21 (1983), S. 2057-2065 
    Details
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A model is derived which incorporates and unifies many of the diverse observations occurring in diffusion in glassy polymers. This unification is made possible by explicitly formulating the common property of a glassy polymer in all its various modes, namely the finite relaxation time due to its slow response to changing conditions. The application and use of the model in various situations is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1983.180211016
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