Molecular SimulationsThermodynamicsPolymer Physics

Nanoscience

Methods

Drug Delivery

Self-Assembly

Gels

Nanogels Polymers

Research Focus

Polymer Gels

• Solvent-permeated networks of polymer chains• Highly responsive: Large volume changes by gaining/

losing solvent with changes in T, pH, external field• Applications: Superabsorbers, Cosmetics, Contact lenses,

Drug Delivery, Tissue Engineering, Artificial Muscles, Microfluidics,

Gels

F Horkay and G McKenna; Physical Properties of Polymers Handbook; 2007, Part V, 497-523

Gels

M Shibayama; Macromol. Chem. Phys. 199, 130 (1998)

Intra-network Phase Separation in Polyelectrolyte Gels

Nanophases in polyelectrolyte (ionic) gels are similar to mesophases in block copolymers but electrostatic interactions provide the necessary competition in gels instead of connectivity constraints in the case of block copolymers.

Gels

Theory of Nanophase Separation: A one-dimensional model

• Infinite network with one-D inhomogeneities of periodicity

• Find and volume fractions by minimizing free energy density

– =0 : No phase Separation (Swollen)

– =finite: Nanophases– : Macrophase Separation

(Collapsed)

P. K. Jha, F. J. Solis, J. J. de Pablo, and M. Olvera de la Cruz; Nonlinear effects in the nanophase segregation of polyelectrolyte gels; Macromolecules, 42, 6284-6289 (2009)

GelsControl of Nanophases

• Favorable Conditions of Nanophase Formation

– Bad Solvent, Intermediate charge fractions of polymer backbone, Low salt conditions, Loosely crosslinked networks

• Results show signicant departures from linear theories

– Full Energy Minimization vs Linear Stability Analysis

– Inverse Langevin Elasticity vs Gaussian Elasticity– Nonlinear Electrostatics vs Linear Electrostatics

K.-A. Wu, P. K. Jha, and M. Olvera de la Cruz; Control of Nanophases in Polyelectrolyte Gels by Salt Addition; Macromolecules 43, 9160-9167 (2010)

GelsExtension to two-dimensions

K.-A. Wu, P. K. Jha, and M. Olvera de la Cruz; Pattern Selection in Polyelectrolyte Gels by Nonlinear Elasticity; Macromolecules, 45 (16), 6652-6657 (2012)

Nonlinearities in network elasticity and electrostatic energy are found to be the deciding factor in the thermodynamic selection of nanostructures.

Polymer Nanogels• Small size (10-1000 nm) enables rapid kinetic response• Ionic (Polyelectrolyte) nanogels superior than neutral nanogels

Nanogels

Kabanov and Vinogradov, Angew Chem Int Ed Engl. 2009 ; 48(30): 5418–5429

As Drug Delivery Carriers and in Cancer treatmentNanogels

Kabanov and Vinogradov, Angew Chem Int Ed Engl. 2009 ; 48(30): 5418–5429

• Can easily incorporate oppositely charged drugs/biomacromolecules, e.g. oligonucleotides, siRNA, DNA, proteins, …

• High swelling of nanogel can be used in killing cancer cells

Park et al., Journal of Controlled Release 135 (2009) 89–95

Poisson-Boltzmann TheoryNanogels

P. K. Jha, J. W. Zwanikken, J. J. de Pablo, and M. Olvera de la Cruz; Electrostatic Control of Nanoscale Phase Behavior of Polyelectrolyte Networks; Current Opinion in Solid State and Materials Science, 15(6), 271-276 (2011)

• Mobile ion concentrations by mean-field approximation

• Smaller, collapsed, and gels at low salt concentration or in high dielectric solvent have larger excess charge

Donnan theory fails

Modified Donnan TheoryNanogels

P. K. Jha, J. W. Zwanikken, and M. Olvera de la Cruz; Understanding Swollen-Collapsed and Re-entrant Transitions in Polyelectrolyte Nanogels by a Modified Donnan Theory; Soft Matter (Communication), 8, 9519-9522 (2012)

• For nanogels at high salt concentrations, inclusion of the excluded volume effect of ions predicts a re-entrant behavior similar to that found in mitotic chromosomes

• Effects of a neutral component, salt valence, and dielectric mismatch, on the optimal compaction of nanogels are analyzed

Theoretically Informed Coarse-Grained SimulationsNanogels

P. K. Jha, J. W. Zwanikken, F. A. Detcheverry, J. J. de Pablo, and M. Olvera de la Cruz; Study of Volume Phase Transitions in Polymeric Nanogels by Theoretically Informed Coarse-Grained Simulations; Soft Matter, 7, 5965-5975 (2011)

Detailed swelling behavior Crosslink Inhomogeneities Fluctuations Few physical invariants Free of discretization effects Computationally Efficient

• Very high swelling for ionic nanogels (decreases with salt concentration)• Discontinuous volume transition for ionic nanogels

Methods

Charges on the GPUMethods

P. K. Jha, R. Sknepnek, G. I. Guerrero-Garcia, M. Olvera de la Cruz; A Graphics Processing Unit Implementation of Coulomb Interaction in Molecular Dynamics; Journal of Chemical Theory and Computation, 6, 3058 (2010)

Yakub and Ronchi,JCP, 2003, 119, 11556

GPU implementation of long-range electrostatic interactions based on the orientation-averaged Ewald sum (ES) scheme introduced by Yakub and Ronchi (YR).

Charges on the GPUMethods

P. K. Jha, R. Sknepnek, G. I. Guerrero-Garcia, M. Olvera de la Cruz; A Graphics Processing Unit Implementation of Coulomb Interaction in Molecular Dynamics; Journal of Chemical Theory and Computation, 6, 3058 (2010)

Yakub and Ronchi,JCP, 2003, 119, 11556

GPU implementation of long-range electrostatic interactions based on the orientation-averaged Ewald sum (ES) scheme introduced by Yakub and Ronchi (YR).

Kinetic Monte Carlo SimulationsMethods

P. K. Jha, V. Kuzovkov, B. A. Grzybowski, and M. Olvera de la Cruz; Dynamic Self-Assembly of Photo-switchable nanoparticles; Soft Matter, 8, 227-234 (2012)P. K. Jha, V. Kuzovkov, and M. Olvera de la Cruz; Kinetic Monte Carlo Simulations of Flow-Assisted Polymerization; ACS Macro Letters, 2012, 1, pp 1393--1397 (2012)

• Off-lattice with fixed step size : Randomly pick spherical coordinates , in 3D

• Time-step independent of magnitude of forces (determined by the step size)

• Unphysical moves have transition probability=0 (NOT allowed)

Transition probability in kinetic Monte Carlo scheme= Transition rate in a renormalized master equation of diffusion

Light-induced Self AssemblySelf-

Assembly P. K. Jha, V. Kuzovkov, B. A. Grzybowski, and M. Olvera de la Cruz; Dynamic Self-Assembly of Photo-switchable nanoparticles; Soft Matter, 8, 227-234 (2012)

Methods

• Simple model with features representative of experiments by Klajn et al, PNAS, 104 (25), 10305-10309 (2007)

• Experimental time scales of aggregation and disassembly agree with simulations

• Energetics vs Kinetics: ”flexible”, ”frozen”, ”fluctuating” and percolated ”network-like” structures

Flow-assisted Polymerization

Polymers

P. K. Jha, V. Kuzovkov, and M. Olvera de la Cruz; Kinetic Monte Carlo Simulations of Flow-Assisted Polymerization; ACS Macro Letters, 2012, 1, pp 1393--1397 (2012)

Methods

• Model of a polymerization process in the presence of a periodic oscillatory flow to explore the role of mixing in polymerization reactors

• Flow field helps overcome the diffusive limitations that develop during a polymerization process high rates of polymerization

• “dynamic” coil–stretch transition with increase in flow-strength

Atomistic Simulations of Polymer-Drug InteractionsPolymers

Work in Progress

Drug Delivery

Acknowledgments

Gels Nanogels MethodsSelf-

Assembly PolymersDrug

Delivery

• Professor Monica Olvera de la CruzNorthwestern University

• Professor Ronald G. LarsonUniversity of Michigan-Ann Arbor