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APS March Meeting 2012 Padden Award Symposium February 28, 2012. Influence of Charge and Network Inhomogeneities on the Swollen-Collapsed Transition in Polyelectrolyte Nanogels. Prateek Jha (Northwestern University) Jos Zwanikken (Northwestern University)
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APS March Meeting 2012 Padden Award Symposium February 28, 2012 Influence of Charge and Network Inhomogeneities on the Swollen-Collapsed Transition in Polyelectrolyte Nanogels PrateekJha(Northwestern University) JosZwanikken (Northwestern University) François Detcheverry (University de Lyon) Juan de Pablo (University of Wisconsin-Madison) Monica Olvera de la Cruz (Northwestern University) This material is based upon work supported by NSF under Award numbers DMR-0907781 and DMR-0520513.
Polymer Nanogels • Finite-sized, solvent-permeated polymer networks • Highly responsive materials • High volume changes by absorbing/releasing solvent • Small size (10-1000 nm) enables rapid kinetic response • Ionic (Polyelectrolyte) nanogels superior than neutral nanogels Kabanov and Vinogradov, AngewChemInt Ed Engl. 2009 ; 48(30): 5418–5429
PolyelectrolyteNanogels as Drug Delivery Carriers and in Anti-Cancer Therapy • Can easily incorporate oppositely charged drugs/biomacromolecules • e.g. oligonucleotides, siRNA, DNA, proteins, … Kabanov and Vinogradov, AngewChemInt Ed Engl. 2009 ; 48(30): 5418–5429 • High swelling of nanogelused in killing cancer cells Park et al., Journal of Controlled Release 135 (2009) 89–95
Classical Description of Gel Swelling • 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: Rubber Elasticity Flory-Huggins Theory Donnan Membrane Equilibrium • Solve for Flory, Principles of Polymer Chemistry
Charge and Network Inhomogeneities in Nanogels • Nanogels are not homogeneous • Crosslinkinginhomogeneities (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 ? Polymer Volume Fraction Distance from center [nm] J Ramos et al; Soft Matter, 2011, 7, 5067-5082
Poisson-Boltzmann Description • Mobile ion concentrations by mean-field approximation • Dielectric mismatch between solvent and polymer can be incorporated by a solvation term: Network charge fixed and homogeneous PK Jha et al, Current Opinion in Solid State and Materials Science, 15(6), 271-276 (2011)
Smaller, collapsed, and gels at low salt concentration or in high dielectric solvent have larger excess charge Donnan theory fails PK Jha et al, Current Opinion in Solid State and Materials Science, 15(6), 271-276 (2011) • Excess charge may be used to self-assemble nanogels to crystalline structures Gottwald et al, Phys. Rev. Lett. 92, 068301 (2004) • Dielectric mismatch can give rise to re-entrant behavior: re-swelling at high salt concentration Salt Concentration
Theoretically Informed Coarse-Grained Simulations (TICG) • Detailed swelling behavior • Crosslink Inhomogeneities • Fluctuations • Few physical invariants • Free of discretization effects • Computationally Efficient • 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 Detcheverry et al, Macromolecules, 2008, 41 (13), pp 4989–5001; Soft Matter, 2009, 5, 4858-4865; Faraday Discuss., 2010, 144, 111-125
Effect of Polymer Charge • Very high swelling for ionic nanogels (Coulomb repulsions) • Discontinuous volume transition for ionic nanogels GOOD SOLVENT POOR SOLVENT PK Jha et al, Soft Matter, 7, 5965-5975 (2011)
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), 271-276 (2011)
Summary • Density and Charge Inhomogeneities strongly contributes to the nanoscalegel behavior • New Simulation Scheme for swelling behavior of polyelectrolyte nanogels • Discontinuous volume transition for ionic nanogels