0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kwon, H. J. , Osada, Y. , and Gong, J. P. , 2006, “ Polyelectrolyte Gels-Fundamentals and Applications,” Polym. J., 38(12), pp. 1211–1219. [CrossRef]
Hirotsu, S. , Hirokawa, Y. , and Tanaka, T. , 1987, “ Volume-Phase Transitions of Ionized N-Isopropylacrylamide Gels,” J. Chem. Phys., 87(2), pp. 1392–1395. [CrossRef]
Bin Imran, A. , Esaki, K., Gotoh, H., Seki, T., Ito, K., Sakai, Y., and Takeoka, Y., 2014, “ Extremely Stretchable Thermosensitive Hydrogels by Introducing Slide-Ring Polyrotaxane Cross-Linkers and Ionic Groups Into the Polymer Network,” Nat. Commun., 5, p. 5124. [CrossRef] [PubMed]
Siegel, R. A. , and Firestone, B. A. , 1988, “ pH-Dependent Equilibrium Swelling Properties of Hydrophobic Poly-Electrolyte Copolymer Gels,” Macromolecules, 21(11), pp. 3254–3259. [CrossRef]
Brannon-Peppas, L. , and Peppas, N. A. , 1991, “ Equilibrium Swelling Behavior of pH-Sensitive Hydrogels,” Chem. Eng. Sci., 46(3), pp. 715–722. [CrossRef]
Marcombe, R. , Cai, S., Hong, W., Zhao, X., Lapusta, Y., and Suo, Z., 2010, “ A Theory of Constrained Swelling of a pH-Sensitive Hydrogel,” Soft Matter, 6(4), pp. 784–793. [CrossRef]
Ricka, J. , and Tanaka, T. , 1984, “ Swelling of Ionic Gels—Quantitative Performance of the Donnan Theory,” Macromolecules, 17(12), pp. 2916–2921. [CrossRef]
Tanaka, T. , Nishio, I., Sun, S., and Uenonishio, S., 1982, “ Collapse of Gels in an Electric Field,” Science, 218(4571), pp. 467–469. [CrossRef] [PubMed]
Frank, S. , and Lauterbur, P. C. , 1993, “ Voltage-Sensitive Magnetic Gels as Magnetic-Resonance Monitoring Agents,” Nature, 363(6427), pp. 334–336. [CrossRef] [PubMed]
Mamada, A. , Tanaka, T., Kungwatchakun, D., and Irie, M., 1990, “ Photoinduced Phase Transition of Gels,” Macromolecules, 23(5), pp. 1517–1519. [CrossRef]
Suzuki, A. , and Tanaka, T. , 1990, “ Phase Transition in Polymer Gels Induced by Visible Light,” Nature, 346(6282), pp. 345–347. [CrossRef]
Shibayama, M. , and Tanaka, T. , 1993, “ Volume Phase Transition and Related Phenomena of Polymer Gels,” Adv. Polym. Sci., 109, pp. 1–62.
Dusek, K. , and Patterson, D. , 1968, “ Transition in Swollen Polymer Networks Induced by Intramolecular Condensation,” J. Polym. Sci. A, 6(7), pp. 1209–1216. [CrossRef]
Tanaka, T. , 1978, “ Collapse of Gels and the Critical Endpoint,” Phys. Rev. Lett., 40(12), pp. 820–823. [CrossRef]
Beebe, D. J. , Moore, J. S., Bauer, J. M., Yu, Q., Liu, R. H., Devadoss, C., and Jo, B. H., 2000, “ Functional Hydrogel Structures for Autonomous Flow Control Inside Microfluidic Channels,” Nature, 404(6778), pp. 588–590. [CrossRef] [PubMed]
Shahinpoor, M. , 1995, “ Micro-Electro-Mechanics of Ionic Polymeric Gels as Electrically Controllable Artificial Muscles,” J. Intell. Mater. Syst. Struct., 6(3), pp. 307–314. [CrossRef]
Miyata, T. , Uragami, T. , and Nakamae, K. , 2002, “ Biomolecule-Sensitive Hydrogels,” Adv. Drug Delivery Rev., 54(1), pp. 79–98. [CrossRef]
Qiu, Y. , and Park, K. , 2001, “ Environment-Sensitive Hydrogels for Drug Delivery,” Adv. Drug Delivery Rev., 53(3), pp. 321–339. [CrossRef]
Sun, J.-Y. , Keplinger, C., Whitesides, G. M., and Suo, Z., 2014, “ Ionic Skin,” Adv. Mater., 26(45), pp. 7608–7614. [CrossRef] [PubMed]
Yang, C. H. , Chen, B., Lu, J. J., Yang, J. H., Zhou, J., Chen, Y. M., and Suo, Z., 2015, “ Ionic Cable,” Extreme Mech. Lett., 3, pp. 59–65. [CrossRef]
Katchalsky, A. , Lifson, S. , and Eisenberg, H. , 1951, “ Equation of Swelling for Polyelectrolyte Gels,” J. Polym. Sci., 7(5), pp. 571–574. [CrossRef]
Tanaka, T. , Fillmore, D., Sun, S. T., Nishio, I., Swislow, G., and Shah, A., 1980, “ Phase Transitions in Ionic Gels,” Phys. Rev. Lett., 45(20), pp. 1636–1639. [CrossRef]
Hirotsu, S. , 1993, “ Coexistence of Phases and the Nature of First-Order Phase-Transition in Poly-N-Isopropylacrylamide Gels,” Adv. Polym. Sci., 110, pp. 1–26.
Grosberg, A. Y. , and Nechaev, S. K. , 1991, “ Topological Constraints in Polymer Network Strong Collapse,” Macromolecules, 24(10), pp. 2789–2793. [CrossRef]
Li, J. , Suo, Z. , and Vlassak, J. J. , 2014, “ A Model of Ideal Elastomeric Gels for Polyelectrolyte Gels,” Soft Matter, 10(15), pp. 2582–2590. [CrossRef] [PubMed]
Quesada-Perez, M., Maroto-Centeno, J. A., Forcada, J., and Hidalgo-Alvarez, R., 2011, “ Gel Swelling Theories: The Classical Formalism and Recent Approaches,” Soft Matter, 7(22), pp. 10536–10547. [CrossRef]
Hong, W. , Zhao, X. , and Suo, Z. , 2010, “ Large Deformation and Electrochemistry of Polyelectrolyte Gels,” J. Mech. Phys. Solids, 58(4), pp. 558–577. [CrossRef]
Li, H., Luo, R., Birgersson, E., and Lam, K. Y., 2007, “ Modeling of Multiphase Smart Hydrogels Responding to pH and Electric Voltage Coupled Stimuli,” J. Appl. Phys., 101(11), p. 114905. [CrossRef]
Feng, L., Jia, Y., Li, X., and An, L., 2011, “ Comparison of the Multiphasic Model and the Transport Model for the Swelling and Deformation of Polyelectrolyte Hydrogels,” J. Mech. Behav. Biomed. Mater., 4(7), pp. 1328–1335. [CrossRef] [PubMed]
Feng, L., Jia, Y., Chen, X., Li, X., and An, L., 2010, “ A Multiphasic Model for the Volume Change of Polyelectrolyte Hydrogels,” J. Chem. Phys., 133(11), p. 114904. [CrossRef] [PubMed]
Wallmersperger, T. , Kroplin, B. , and Gulch, R. W. , 2004, “ Coupled Chemo-Electro-Mechanical Formulation for Ionic Polymer Gels––Numerical and Experimental Investigations,” Mech. Mater., 36(5–6), pp. 411–420. [CrossRef]
Ohmine, I. , and Tanaka, T. , 1982, “ Salt Effects on the Phase Transition of Ionic Gels,” J. Chem. Phys., 77(11), pp. 5725–5729. [CrossRef]
Suo, Z. , Zhao, X. , and Greene, W. H. , 2008, “ A Nonlinear Field Theory of Deformable Dielectrics,” J. Mech. Phys. Solids, 56(2), pp. 467–486. [CrossRef]
Hong, W., Zhao, X., Zhou, J. X., and Suo, Z., 2008, “ A Theory of Coupled Diffusion and Large Deformation in Polymeric Gels,” J. Mech. Phys. Solids, 56(5), pp. 1779–1793. [CrossRef]
Kang, M. K. , and Huang, R. , 2010, “ A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints,” ASME J. Appl. Mech., 77(6), p. 061004. [CrossRef]
Ott, J. B. , and Boerio-Goates, J. , 2000, Chemical Thermodynamics: Principles and Applications, Elsevier Academic Press, London.
Khokhlov, A. R. , and Kramarenko, E. Y. , 1994, “ Polyelectrolyte/Ionomer Behavior in Polymer Gel Collapse,” Macromol. Theory Simul., 3(1), pp. 45–59. [CrossRef]
Overbeek, J. T. G. , 1956, “ The Donnan Equilibrium,” Prog. Biophys. Biophys. Chem., 6, pp. 57–84.
Fernandez-Nieves, A. , Fernandez-Barbero, A. , and Nieves, F. J. D. L. , 2001, “ Salt Effects Over the Swelling of Ionized Mesoscopic Gels,” J. Chem. Phys., 115(16), pp. 7644–7649. [CrossRef]
Okay, O. , and Sariisik, S. B. , 2000, “ Swelling Behavior of Poly(Acrylamide-co-Sodium Acrylate) Hydrogels in Aqueous Salt Solutions: Theory Versus Experiments,” Eur. Polym. J., 36(2), pp. 393–399. [CrossRef]
Shiomi, T., Suzuki, M., Tohyama, M., and Imai, K., 1989, “ Dependence of Miscibility on Copolymer Composition for Blends of Polyvinyl Chloride-Co-Vinyl Acetate) and Poly (Normal-Butyl Methacrylate-Co-Isobutyl Methacrylate),” Macromolecules, 22(9), pp. 3578–3581. [CrossRef]
Shiomi, T., Kuroki, K., Kobayashi, A., Nikaido, H., Yokoyama, M., Tezuka, Y., and Imai, K., 1995, “ Dependence of Swelling Degree on Solvent Composition of Two-Component Copolymer Networks in Mixed-Solvents,” Polymer, 36(12), pp. 2443–2449. [CrossRef]
Huang, R. , and Suo, Z. , 2012, “ Electromechanical Phase Transition in Dielectric Elastomers,” Proc. R. Soc. A, 468(2140), pp. 1014–1040. [CrossRef]
Doi, M. , 2009, “ Gel Dynamics,” J. Phys. Soc. Jpn., 78(5), p. 052001. [CrossRef]
Erman, B. , and Flory, P. J. , 1986, “ Critical Phenomena and Transitions in Swollen Polymer Networks and in Linear Macromolecules,” Macromolecules, 19(9), pp. 2342–2353. [CrossRef]
Bahar, I., Erbil, H. Y., Baysal, B. M., and Erman, B., 1987, “ Determination of Polymer-Solvent Interaction Parameter From Swelling of Networks—the System Poly(2-Hydroxyethyl Methacrylate)-Diethylene Glycol,” Macromolecules, 20(6), pp. 1353–1356. [CrossRef]
Melekaslan, D. , and Okay, O. , 2001, “ Reentrant Phase Transition of Strong Polyelectrolyte Poly(N-Isopropylacrylamide) Gels in PEG Solutions,” Macromol. Chem. Phys., 202(2), pp. 304–312. [CrossRef]
Safronov, A. P., Blyakhman, F. A., Shklyar, T. F., Terziyan, T. V., Kostareva, M. A., Tchikunov, S. A., and Pollack, G. H., 2009, “ The Influence of Counterion Type and Temperature on Flory-Huggins Binary Interaction Parameter in Polyelectrolyte Hydrogels,” Macromol. Chem. Phys., 210(7), pp. 511–519. [CrossRef]

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

Grahic Jump Location
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).

Grahic Jump Location
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].

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In