Nonlinear swelling of polymer gels

Durning, C. J.; Morman, K. N.
March 1993
Journal of Chemical Physics;3/1/1993, Vol. 98 Issue 5, p4275
Academic Journal
We present a continuum theory for the nonlinear swelling of polymer gels. The approach is to solve the continuity equations for the network and liquid under the constraint that the instantaneous free energy be minimal. Constitutive relations are needed for the free energy density of the gel, W, and for the liquid diffusion current, J. The James–Guth phantom network model and Bastide’s scaling model are used for W; Fick’s law is used for J which is tantamount to neglecting the gel’s shear modulus relative relative to its osmotic compressive modulus. The theory is applied to the free swelling of networks in good solvents to a semidilute gel for three geometries: sphere, long cylinder, and thin slab. We find a geometry-dependent, nonlocal effect influencing the measurables (gel shape and liquid uptake). This arises from the dependence of the network’s deformation at the gel/liquid interface on the whole deformation field for the sample. The theory gives reasonable agreement with experiment; discrepancies are likely due to nonlocal effects in J not accounted for by Fick’s law.


Related Articles

  • Doping-dependent evolution of low-energy excitations and quantum phase transitions within an effective model for high-Tc copper oxides. Korshunov, M. M.; Ovchinnikov, S. G. // European Physical Journal B -- Condensed Matter;Jun2007, Vol. 57 Issue 3, p271 

    In this paper a mean-field theory for the spin-liquid paramagnetic non-superconducting phase of the p- and n-type high-Tc cuprates is developed. This theory applied to the effective t-t'-t′′-J* model with the ab initio calculated parameters and with the three-site correlated...

  • Field theory and segmental alignment analysis for a solution of sequence disordered liquid crystalline polymers. Gutman, Lorin; Shakhnovich, Eugene // Journal of Chemical Physics;2/15/2002, Vol. 116 Issue 7, p3134 

    A field theory for the many-chain mesogen/flexible sequence model is developed. The theory is solved using a creation–annihilation formalism based on a reference state that recovers the Gupta–Edwards solution for the many-chain homopolymer system. Orientational averages are...

  • Relationship between local molecular field theory and density functional theory for non-uniform liquids. Archer, A. J.; Evans, R. // Journal of Chemical Physics;1/7/2013, Vol. 138 Issue 1, p014502 

    The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of...

  • Multi-reference vibration correlation methods. Pfeiffer, Florian; Rauhut, Guntram // Journal of Chemical Physics;2/14/2014, Vol. 140 Issue 6, p064110-1 

    State-specific vibration correlation methods beyond the vibrational multi-configuration selfconsistent field (VMCSCF) approximation have been developed, which allow for the accurate calculation of state energies for systems suffering from strong anharmonic resonances. Both variational...

  • Analytical solutions describing the phase separation driven by a free energy functional... Ohnishi, Isamu; Nishiura, Yasumasa; Imai, Masaki; Matsushita, Yushu // Chaos;Jun99, Vol. 9 Issue 2, p329 

    Provides analytical solutions describing the phase separation driven by a free energy functional containing a long-range interaction term. Thermodynamic equilibrium state of the phase separation phenomenon; Characterization of the periodic structure of the global minimizer of the functional.

  • Free energy and size distributions of micelles in solution. Christopher, P. S.; Oxtoby, David W. // Journal of Chemical Physics;3/22/2003, Vol. 118 Issue 12, p5665 

    This paper presents a new derivation of the free energy of micellar solutions. From this free energy a micelle size distribution can be calculated. By using a density functional model for the bulk contribution to the free energy, and a simple approximation for the micelle (proper) contribution,...

  • Oscillatory femtosecond relaxation of photoexcited organic molecules. Wise, F. W.; Rosker, M. J.; Tang, C. L. // Journal of Chemical Physics;3/1/1987, Vol. 86 Issue 5, p2827 

    The ultrafast relaxation of large organic molecules in solution has been investigated with the transmission correlation technique. The existence of damped sinusoidal decays after photoexcitation has been verified for several organic dyes. This behavior (the first such decay observed on a...

  • Solution of the Percus–Yevick equation for hard spherocylinders. I. The entire pair correlation function. Lago, S.; Sevilla, P. // Journal of Chemical Physics;10/1/1988, Vol. 89 Issue 7, p4349 

    The Percus–Yevick equation for hard spherocylinders has been numerically solved using a recent algorithm to calculate the shortest distances between rods proposed by ourselves. The equation is solved for four different reduced densities to η=0.3879 and length-to-breadth ratio L*=1.0....

  • Calculating the hopping rate for diffusion in molecular liquids: CS[sub 2]. Gezelter, J. Daniel; Rabani, Eran; Berne, B.J. // Journal of Chemical Physics;2/15/1999, Vol. 110 Issue 7, p3444 

    Extends the cage correlation function method for calculating the hopping rate in Zwanzig's model of self-diffusion in liquids to liquids composed of polyatomic molecules. Vibrational density of states of inherent structures in liquids; Calculation of diffusion constants.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics