Nanoscale Pattern Formation in Polyelectrolyte Gels
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Nanoscale pattern formation in polyelectrolyte gels Prateek K. Jha1, Francisco J. Solis4, Juan J. de Pablo5, and Monica Olvera de la Cruz1, 2, 3* 1 Department of Chemical and Biological Engineering, 2Department of Materials Science and Engineering, and 3Department of Chemistry, Northwestern University, Evanston IL 60201, 4 Department of Integrated Natural Sciences, Arizona State University, Glendale, AZ 85306, and 5 Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706 * Corresponding author. E-mail: [email protected]
ABSTRACT Polyelectrolyte (PE) gels exhibit complex phase behavior that includes the existence of nanostructures in poor-solvent conditions. The formation of these inhomogeneous structures is made possible by the competition between the short-range hydrophobic, elastic, and entropic interactions and the long-range electrostatic forces. We develop a theoretical framework that describes the effect of monomer and charge inhomogeneities in PE gels. Numerical calculations performed on a salt-free PE gel with one-dimensional heterogeneities demonstrate the presence of nanophases for a finite range of physical parameters. INTRODUCTION Polyelectrolyte (PE) gels are versatile materials that find applications in super absorbents (e.g. diapers, contact lenses), cosmetics, “on-off”-actuators, electro-active materials, artificial muscles, tissue engineering, as well as drug-delivery devices.1-6 Their network structure that can adapt to tunable physical interactions contributes to their rich phase-behaviors. In particular, they can swell to large extents while retaining their network structure in good-solvent conditions and may give rise to finite-sized nano-domains or nanostructures in poor-solvent conditions. Such multi-functionality can be achieved by a variety of stimuli such as temperature, pH, and electric field. Indeed, aspects of physiological functionality are provided by biological gels that closely resemble PE gels.7-9 Theories of PE gels10-13 have primarily focused on the swelling-collapse mechanism described for homogeneous gels by the classical theory of rubber elasticity combined with the Flory-Huggins model of polymers. In the formalism, ionic effects enter through the translational entropy of mobile ions and through a Donnan potential that relates to the associationdisassociation equilibrium of salt. However, recent experimental findings14-17 indicate the importance of static inhomogeneities and dynamic fluctuations on the phase behavior of gels that are both not properly accounted for in the classical model. One important outcome is the formation of nanophases similar to the microphase separation observed for polyelectrolytes in poor-solvent conditions: the electrostatic and van der Waals forces compete and result in formation of alternating rich and depleted regions of polymer, though the presence of crosslinks in PE gels further constrains the domain size, and consequently, the length scales of microphase separation are much sm
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