A theory for species migration in a finitely strained solid with application to polymer network swelling

Journal of the Mechanics and Physics of Solids

Volumn 58, Issue 4, 2010, Pages 515-529

  Duda, Fernando P ^a   Souza, Angela C ^b   Fried, Eliot ^c  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b FLUMINENSE FEDERAL UNIVERSITY   (Brazil)

^c MCGILL UNIVERSITY   (Canada)

Author keywords

Mechanochemistry; Phase coexistence; Swelling

Indexed keywords

BASIC EQUATIONS; CHEMICAL INTERACTIONS; CHEMICAL PROCESS; CHEMICAL SPECIES; CONSTITUTIVE RELATIONS; DYNAMICAL PROCESS; EQUILIBRIUM STATE; FLORY INTERACTION; INDUCED PHASE TRANSITION; LIQUID MOLECULES; MECHANICAL FORCE; MECHANICAL PROCESS; MECHANO-CHEMISTRY; MOLECULAR VOLUME; PER UNIT; PHASE CO-EXISTENCE; POLYMER NETWORKS; SWOLLEN MEMBRANES; TRANSPORT BALANCE; TWO PARAMETER; VIRTUAL POWER;

CROSSLINKING; SWELLING;

PHASE TRANSITIONS;

EID: 77349105709     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2010.01.009     Document Type: Article

References (35)

1. Baek S., and Srinivasa A.R. Diffusion of a fluid through an elastic solid undergoing large deformation. Int. J. Non-Linear Mech. 39 (2004) 201-218
2. Baierlein R. The elusive chemical potential. Am. J. Phys. 69 (2001) 423-434
3. Barriere B., and Leibler L. Kinetics of solvent absorption and permeation through a highly swellable elastomeric network. J. Polym. Sci. B Polym. Phys. 41 (2003) 166-182
4. Coleman B.D., and Noll W. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13 (1963) 167-178
5. Crank J. The Mathematics of Diffusion. second ed. (1990), Oxford University Press, New York
6. Doi M. Gel dynamics. J. Phys. Soc. Jpn. 78 (2009) 052001-1-052001-19
7. Duda F.P., and Souza A.C. Continuum mechanics, inelastic behavior and multiscale modelling in mechanics of materials. Comput. Appl. Math. 21 (2002) 485-498
8. Durning C.J., and Morman Jr. K.K. Nonlinear swelling of polymer gels. J. Chem. Phys. 98 (1993) 4275-4293
9. Dusek K., and Patterson D. Transition in swollen polymer networks induced by intramolecular condensation. J. Polym. Sci. A Polym. Chem. 6 (1968) 1200-1216
10. Ericksen J.L. Equilibrium of bars. J. Elasticity 5 (1975) 191-201
11. Flory P.J., and Rehner J. Statistical mechanics of cross-linked polymer networks II. Swelling. J. Chem. Phys. 11 (1943) 521-526
12. Flory P.J., and Rehner J. Effect of the deformation on the swelling capacity of the rubber. J. Chem. Phys. 12 (1944) 413-414
13. Flory P.J. Principles in Polymer Chemistry (1953), Cornell University Press, New York
14. Fried E., and Gurtin M. Dynamic solid-solid transitions with phase characterized by an order parameter. Phys. D 72 (1994) 287-308
15. Fried E., and Gurtin M. Coherent solid-state phase transitions with atomic diffusion: a thermomechanical treatment. J. Stat. Phys. 95 (1999) 1361-1427
16. Gibbs J.W. On the equilibrium of heterogeneous substances. Trans. Conn. Acad. Arts Sci. III (1878) 108-248 Reprinted in: The Scientific Papers of J. Willard Gibbs, Volume 1, Dover, New York, 1961
17. Hong W., Zhao X., Zhou J., and Suo Z. A theory of coupled diffusion and large deformation in polymeric gels. J. Mech. Phys. Solids 56 (2008) 1779-1793
18. Job G., and Herrmann F. Chemical potential-a quantity in search of recognition. Eur. J. Phys. 27 (2006) 353-371
19. Larché F.C., and Cahn J.W. The effect of self-stress on diffusion in solids. Acta Metall. 30 (1982) 1835-1845
20. Larché F.C., and Cahn J.W. The interactions of composition and stress in crystalline solids. Acta Metall. 33 3 (1985) 331-357
21. Lubarda V.A. Constitutive theories based on the multiplicative decomposition of deformation gradient: thermoelasticity, elastoplasticity, and biomechanics. Appl. Mech. Rev. 57 (2004) 95-108
22. Man C.S. Thermodynamics based on a work inequality. Arch. Ration. Mech. Anal. 106 (1989) 1-61
23. Neogi P., Kim M., and Yang Y. Diffusion in solids under strain with emphasis on polymer membranes. AIChE J. 32 (1986) 1835-1845
24. Onuki A. Volume-phase transitions in constrained gels. J. Phys. Soc. Jpn. 57 (1988) 1868-1871
25. Onuki A. Theory of phase transition in polymer gels. Adv. Polym. Sci. 109 (1993) 63-121
26. Paul D.R., and Ebra-Lima O.O. Pressure-induced diffusion of organic liquids through highly swollen polymer membranes. J. Appl. Polym. Sci. 14 (1970) 2201-2224
27. Podio-Guidugli P. A virtual power format for thermomechanics. Cont. Mech. Thermodyn. 20 (2009) 479-487
28. Rajagopal K.R. Diffusion through polymeric solids undergoing large deformations. Mater. Sci. Technol. 19 (2003) 1175-1180
29. Sekimoto K., and Doi M. Dynamics of interface of gels undergoing volume phase transition. J. Phys. II 1 (1991) 1053-1066
30. Suzuki A. Phase transition in gels of sub-millimeter size induced by interaction with stimuli. Adv. Polym. Sci. 110 (1993) 199-240
31. Suzuki A., and Ishii T. Phase coexistence of neutral polymer gels under mechanical constraint. J. Chem. Phys. 110 (1999) 2289-2296
32. Tanaka T., Sun S.T., Hirokawa Y., Katayama S., Kucera J., Hirose Y., and Amiya A. Mechanical instability of gels at the phase transition. Nature 325 (1987) 796-798
33. Tomari T., and Doi M. Swelling dynamics of a gel undergoing volume transitions. J. Phys. Soc. Jpn. 63 (1994) 2093-2101
34. Treloar L.R.G. The Physics of Rubber Elasticity (1975), Oxford University Press, New York
35. Truesdell C.A. A First Course in Rational Continuum Mechanics, Part I. second ed. (1991), Academic Press, Boston