Influence of Charge and Network Inhomogeneities on the Swollen-Collapsed Transition in Polyelectrolyte Nanogels Prateek Jha (Northwestern University) Jos Zwanikken (Northwestern University) François Detcheverry (University de Lyon) Juan de Pablo (University of Wisconsin-Madison) Monica Olvera de la Cruz (Northwestern University) APS March Meeting 2012 Padden Award Symposium February 28, 2012 This material is based upon work supported by NSF under Award numbers DMR and DMR

Polymer Nanogels Finite-sized, solvent-permeated polymer networks Highly responsive materials – High volume changes by absorbing/releasing solvent – Small size ( nm) enables rapid kinetic response – Ionic (Polyelectrolyte) nanogels superior than neutral nanogels Kabanov and Vinogradov, Angew Chem Int Ed Engl ; 48(30): 5418–5429

Polyelectrolyte Nanogels as Drug Delivery Carriers and in Anti-Cancer Therapy Can easily incorporate oppositely charged drugs/biomacromolecules e.g. oligonucleotides, siRNA, DNA, proteins, … High swelling of nanogel used in killing cancer cells Park et al., Journal of Controlled Release 135 (2009) 89–95

Classical Description of Gel Swelling Rubber ElasticityFlory-Huggins Theory Donnan Membrane Equilibrium Homogeneous deformation  uniform volume fraction, Charge neutrality in gel and solvent bath  No Coulomb interactions Electrostatic contribution from mobile ion entropy (Donnan) – Mobile ion concentrations from association  dissociation equilibrium of salt Free Energy of gel: Condition of Mechanical Equilibrium: Solve for  Flory, Principles of Polymer Chemistry

Nanogels are not homogeneous – Crosslinking inhomogeneities (during preparation) – Excess Charge due to presence of surfaces Excess Charge  Coulomb Interactions (Neglected in the Donnan picture) Important when nanogel size is comparable to screening length Influence on Swelling behavior ? Charge and Network Inhomogeneities in Nanogels J Ramos et al; Soft Matter, 2011, 7, Polymer Volume Fraction Distance from center [nm]

Poisson-Boltzmann Description Mobile ion concentrations by mean-field approximation Dielectric mismatch between solvent and polymer can be incorporated by a solvation term: PK Jha et al, Current Opinion in Solid State and Materials Science, 15(6), (2011) Network charge fixed and homogeneous

PK Jha et al, Current Opinion in Solid State and Materials Science, 15(6), (2011) Excess charge may be used to self-assemble nanogels to crystalline structures Gottwald et al, Phys. Rev. Lett. 92, (2004) Dielectric mismatch can give rise to re-entrant behavior: re-swelling at high salt concentration Salt Concentration Smaller, collapsed, and gels at low salt concentration or in high dielectric solvent have larger excess charge  Donnan theory fails

Theoretically Informed Coarse-Grained Simulations (TICG) Detailed swelling behavior Crosslink Inhomogeneities Fluctuations Few physical invariants Free of discretization effects Computationally Efficient Detcheverry et al, Macromolecules, 2008, 41 (13), pp 4989–5001; Soft Matter, 2009, 5, ; Faraday Discuss., 2010, 144, Construct the free energy functional: Bonded (Elastic) Contribution from Gaussian Chain Approximation Non-Bonded Contribution = Solvent + Entropy + Coulomb Monte Carlo using the free energy functional

Effect of Polymer Charge PK Jha et al, Soft Matter, 7, (2011) Very high swelling for ionic nanogels (Coulomb repulsions) Discontinuous volume transition for ionic nanogels GOOD SOLVENTPOOR SOLVENT

Effect of Salt Concentration Swelling decreases with increase in salt concentration (screening) PK Jha et al, Current Opinion in Solid State and Materials Science, 15(6), (2011)

Summary Density and Charge Inhomogeneities strongly contributes to the nanoscale gel behavior New Simulation Scheme for swelling behavior of polyelectrolyte nanogels Discontinuous volume transition for ionic nanogels SWOLLENCOLLAPSED Good SolventBad Solvent Highly ChargedNeutral/Weakly Charged Low saltHigh salt Loosely crosslinkedTightly Crosslinked