J. deClaville Christiansen

Modeling the effects of pH and ionic strength on swelling of polyelectrolyte gels

A model is developed for the elastic response of a polyelectrolyte gel under unconstrained and constrained swelling in a water bath with an arbitrary pH, where a monovalent salt is dissolved. A gel is treated as a three-phase medium consisting of an equivalent polymer network, solvent (water), and solute (mobile ions). Transport of solvent and solute is thought of as their diffusion through the network accelerated by an electric field formed by mobile and fixed ions and accompanied by chemical reactions (self-ionization of water molecules, dissociation of functional groups attached to polymer chains, and formation of ion pairs between bound charges and mobile counter-ions). Constitutive equations are derived by means of the free energy imbalance inequality for an arbitrary three-dimensional deformation with finite strains. Adjustable parameters in the governing relations are found by fitting equilibrium swelling diagrams on several hydrogels. The effects of pH, ionic strength of solution, and constraints on equilibrium water uptake are studied numerically.

Self-limiting lithiation of electrode nanoparticles in Li-ion batteries

A model is derived for the viscoplastic behavior of a host medium driven by stress-induced diffusion of guest atoms. The constitutive equations are applied to study development of stresses in a spherical electrode particle subjected to insertion of lithium. Numerical simulation demonstrates the ability of the model to capture basic phenomena observed in anode nanoparticles under lithiation: formation of a sharp interphase between a Li-poor core and a Li-rich shell, slowing down of the interphase motion revealed as self-limiting lithiation, and growth of tensile hoop stresses near the outer surface of a particle leading to its fracture.

Time-dependent response of hydrogels under constrained swelling

Constitutive equations are developed for the viscoplastic behavior of covalently cross-linked hydrogels subjected to swelling. The ability of the model to describe the time-dependent response is confirmed by comparison of results of simulation with observations on partially swollen poly(2-hydroxyethyl methacrylate) gel specimens in uniaxial tensile tests with a constant strain rate and tensile relaxation tests. The stress–strain relations are applied to study the kinetics of unconstrained and constrained swelling. The following conclusions are drawn from numerical analysis: (i) maximum water uptake under constrained swelling a viscoplastic hydrogel is lower than that for unconstrained swelling of its elastic counterpart and exceeds maximum water uptake under constrained swelling of the elastic gel, (ii) when the rate of water diffusion exceeds the rate of plastic flow in a polymer network, swelling curves (mass uptake versus time) for viscoplastic gels under constraints demonstrate characteristic features...

The Effects of pH and Ionic Strength of Swelling of Cationic Gels

A model is reported for the mechanical response of a cationic polyelectrolyte gel subjected to swelling in a water bath with an arbitrary pH and an arbitrary concentration of a monovalent salt. A gel is treated as a three-phase medium consisting of a polymer network, solvent (water), and solute (mobile ions). Transport of solvent and solute is thought of as their diffusion through the network accelerated by the electric field formed by mobile ions and bound charges and accompanied by chemical reactions (self-ionization of water molecules, protonation of functional groups, and formation of ion pairs between fixed cations and mobile anions). Material constants in the governing equations are determined by fitting equilibrium swelling diagrams on several copolymer gels with vinylimidazole component. Simulation demonstrates that the anti-polyelectrolyte effect (nonmonotonic changes in degree of swelling with molar fraction of salt) can be observed in cationic gels and core-shell microgels.

A simplified model for equilibrium and transient swelling of thermo-responsive gels

A simplified model is developed for the elastic response of thermo-responsive gels subjected to swelling under an arbitrary deformation with finite strains. The constitutive equations involve five adjustable parameters that are determined by fitting observations in equilibrium water uptake tests and T-jump transient tests on thin gel disks. Two scenarios for water release under heating are revealed by means of numerical simulation. When the final temperature in a T-jump test is below the volume-phase transition temperature, deswelling is characterized by smooth distribution of water molecules and small tensile stresses. When the final temperature exceeds the critical temperature, a gel disk is split into three regions (central part with a high concentration of water molecules and two domains near the boundaries with low water content) separated by sharp interfaces, whose propagation is accompanied by development of large (comparable with the elastic modulus) tensile stresses.

Double-network gels with dynamic bonds under multi-cycle deformation

Application of double-network (DN) gels with dynamic bonds as implants for repair of damaged and degenerate cartilage tissue and their use as synthetic non-degradable scaffolds for growth, proliferation and differentiation of stem cells requires understanding of the mechanical behavior of these materials under cyclic deformation. A constitutive model is developed for the viscoelastic and viscoplastic responses of DN gels with covalent and non-covalent junctions under multi-cycle loading. Viscoelasticity is treated as breakage and reformation of temporary junctions driven by thermal fluctuations. Viscoplasticity is thought of as sliding of permanent junctions with respect to their initial positions in the polymer network. Adjustable parameters in the governing equations are found by fitting observations in tensile loading-unloading tests with various maximum strains and multi-cycle tests with monotonically increasing maximum elongation ratios per cycle on two DN gels with physical junctions formed due to hydrogen bonds and ionic complexation. Numerical analysis demonstrates the ability of the model not only to describe observations correctly, but also to predict the mechanical response in multi-cycle tests with sophisticated deformation programs. Quantitative and qualitative effects of metal-coordination bonds on the mechanical behavior of supramolecular gels are revealed by simulation.