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Research Papers

Salt-Induced Swelling and Volume Phase Transition of Polyelectrolyte Gels

[+] Author and Article Information
Yalin Yu, Chad M. Landis, Rui Huang

Department of Aerospace Engineering
and Engineering Mechanics,
University of Texas,
Austin, TX 78712

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 29, 2016; final manuscript received February 28, 2017; published online March 24, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(5), 051005 (Mar 24, 2017) (12 pages) Paper No: JAM-16-1629; doi: 10.1115/1.4036113 History: Received December 29, 2016; Revised February 28, 2017

A theoretical model of polyelectrolyte gels is presented to study continuous and discontinuous volume phase transitions induced by changing salt concentration in the external solution. Phase diagrams are constructed in terms of the polymer–solvent interaction parameters, external salt concentration, and concentration of fixed charges. Comparisons with previous experiments for an ionized acrylamide gel in mixed water–acetone solvents are made with good quantitative agreement for a monovalent salt (NaCl) but fair qualitative agreement for a divalent salt (MgCl2), using a simple set of parameters for both cases. The effective polymer–solvent interactions vary with the volume fraction of acetone in the mixed solvent, leading to either continuous or discontinuous volume transitions. The presence of divalent ions (Mg2+) in addition to monovalent ions in the external solution reduces the critical salt concentration for the discontinuous transition by several orders of magnitude. Moreover, a secondary continuous transition is predicted between two highly swollen states for the case of a divalent salt. The present model may be further extended to study volume phase transitions of polyelectrolyte gels in response to other stimuli such as temperature, pH and electrical field.

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Figures

Grahic Jump Location
Fig. 1

Schematic of a polyelectrolyte gel in equilibrium with an external salt solution, with an electrical double layer at the interface

Grahic Jump Location
Fig. 2

Free swelling of a polyelectrolyte gel (Nυ=10−3, υCfix=0.02, and χ=0.5) immersed in an ionic solution with varying ion concentration. (a) Stretch, (b) electrical potential, (c) and (d) nominal concentrations of counter-ions and co-ions.

Grahic Jump Location
Fig. 3

(a) Equilibrium stretch as a function of ion concentration in the external solution for polyelectrolyte gels with different values of χ, showing continuous and discontinuous transitions. (b) A phase diagram with two distinct phases, highly swollen and collapsed, and the transition lines in between (thick solid line for discontinuous transition and dashed lines for continuous transition with λ= 3, 2.5, and 2).

Grahic Jump Location
Fig. 4

(a) Normalized stress–stretch relations for a polyelectrolyte gel (χ=0.7, Nυ=10−3, and υCfix=0.02) with different ion concentrations, and (b) normalized mechanical work

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Fig. 5

(a) Lines of discontinuous transition for different concentrations of fixed charges and (b) a diagram of phase transitions for Nυ=10−3

Grahic Jump Location
Fig. 6

Effects of the composition dependent polymer–solvent interaction. (a) Equilibrium stretch for polyelectrolyte gels with Nυ=10−3, υCfix=0.02, and χ0=0.9; (b) lines of discontinuous transition (Nυ=10−3 and υCfix=0.02); (c) a diagram of phase transitions in terms of the two interaction parameters (Nυ=10−3 and υCfix=0.02); and (d) a diagram of phase transitions in terms of υCfix and χ0 (Nυ=10−3 and χ1=0.4), in comparison with the case for composition independent interaction (χ1=0).

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Fig. 7

(a) The relative volume ratio (ρ=λ03/λ3) versus NaCl concentration for mixed solvents with various volume fractions of acetone, comparing theoretical predictions (lines) with the data (symbols) from the experiments by Ohmine and Tanaka [32]. (b) The relative volume ratio versus MgCl2 concentration, with symbols for φ=60% from the experiments by Ohmine and Tanaka [32]. The same set of parameters are used in the calculations for both (a) and (b).

Grahic Jump Location
Fig. 8

(a) Improved agreement for continuous volume transition of acrylamide gels in a pure water solvent (φ=0%) with varying NaCl concentrations. (b) Improved agreement for the discontinuous volume transitions of acrylamide gels in a mixed solvent (φ=60%) with either NaCl or MgCl2. Experimental data (symbols) are taken from Ohmine and Tanaka [32].

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