Electrostatic control of nanoscale phase behavior of polyelectrolyte networks Prateek K. Jha a , Jos W. Zwanikken b , Juan J. de Pablo d , Monica Olvera de la Cruz a,b,c,⇑ a Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60201, USA b Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60201, USA c Department of Chemistry, Northwestern University, Evanston, IL 60201, USA d Department of Chemical and Biological Engineering, University of Wisconsin, Madison, WI 53706, USA article info Article history: Received 15 April 2011 Accepted 11 June 2011 Available online 25 June 2011 Keywords: Ionic gel Nanogel Polyelectrolyte network Theoretically informed coarse-grained simulations Poisson–Boltzmann theory abstract Polyelectrolyte gels are intelligent materials that undergo large reversible volume changes for a range of environmental stimuli. Although the strength of electrostatic interactions have a strong influence on the gel response, these interactions are not properly accounted in the classical mean-field theories that assume a homogeneous charge-neutral gel. Using Poisson–Boltzmann theory and theoretically informed coarse-grained simulations, we emphasize the importance of charge inhomogeneities and the associated Coulomb interactions in determining the response of gels. Our analysis reveals that nanometer-sized gels, collapsed gels, and gels in media with low salinity or high dielectric constant, have large regions of excess charge. We also observe that the addition of salt can induce collapse in swollen gels by compensating the polymer charge. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Gels are solvent-permeated soft solids, formed by physical/ chemical crosslinking of polymer chains [1,2]. They can absorb large amounts of solvent, while maintaining high flexibility, owing to their three-dimensional network structure. This solvent uptake behavior is reversible and can be controlled by a wide range of stimuli such as temperature [3], pH [4], light [5–7], chemical reac- tions [8,9], and electric field [10]. Polyelectrolyte gels are superior to neutral gels in the extent of swelling [11], and show striking similarities with many biological networks, such as those found in mitotic chromosomes [12] and cornea [13]. This has prompted great interest in the use of polyelectrolyte gels as soft active mate- rials in a variety of applications such as: superabsorbers [14], drug delivery carriers [15], muscle-like actuators [16], battery electro- lytes [17], and tissue engineering [18]. Swelling of gels results from an interplay of physical interac- tions, such as the short-ranged van der Waals forces and the long-ranged electrostatic interactions; which couple with the elas- ticity of the network. For instance, gels with hydrophilic and highly charged polymer backbones are usually swollen, because of an effective repulsion between the polymer strands constituting the network. On the other hand, gels with hydrophobic and neutral polymer backbones are usually collapsed, because of an effective attraction between the polymer strands. Further, the network elas- ticity, entropic in nature, pose limits on the maximum swelling that can be achieved. This was the motivation behind the classical mean-field theories of polymer gels, [1,2,11,19] that treats the swelling phenomenon as an osmotic equilibrium of a homoge- neous network with a solvent bath. The net osmotic pressure due to the gel mass was assumed to be a sum of an elastic contribution, a mixing contribution, and an ion-entropic contribution. The elas- tic contribution was derived using the continuum theories of rub- ber elasticity [2] and the mixing contribution was derived using the Flory–Huggins theory of polymer solutions [1]. Since they as- sume a homogeneous charge-neutral gel with no excess charge, the Coulomb interactions are absent in these theories. Instead, the electrostatic effects are included through an ion entropic con- tribution, derived in analogy with the Donnan membrane equilib- rium [20]. Classical mean-field theories of gels have met considerable suc- cess in the qualitative prediction of the swelling behavior, includ- ing the discontinuous phase transitions observed in polyelectrolyte gels [21,22]. However, the effects of inhomogeneities in the den- sity, charge, and dielectric constant, are completely neglected. In particular, they fail to explain mesoscopic phenomena that re- quires an explicit treatment of Coulomb interactions or a detailed treatment of polymer elasticity and van der Waals forces [23– 27]. As an example of such phenomenon, polyelectrolyte gels with hydrophobic backbones are known to nanophase segregate [28– 31] to form co-existing domains dense and dilute in polymer, as observed by a peak at a finite wave-vector in scattering experi- 1359-0286/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cossms.2011.06.002 ⇑ Corresponding author at: Department of Chemistry, Northwestern University, Evanston, IL 60201, USA. E-mail address: m-olvera@northwestern.edu (M. Olvera de la Cruz). Current Opinion in Solid State and Materials Science 15 (2011) 271–276 Contents lists available at ScienceDirect Current Opinion in Solid State and Materials Science journal homepage: www.elsevier.com/locate/cossms