Swelling of Thermo-Responsive Gels in Aqueous Solutions of Salts: A Predictive Model.

The equilibrium degree of swelling of thermo-responsive (TR) gels is strongly affected by the presence of ions in an aqueous solution. This phenomenon plays an important role in (i) the synthesis of multi-stimuli-responsive gels for soft robotics, where extraordinary strength and toughness are reached by soaking of a gel in solutions of multivalent ions, and (ii) the preparation of hybrid gels with interpenetrating networks formed by covalently cross-linked synthetic chains and ionically cross-linked biopolymer chains. A model is developed for equilibrium swelling of a TR gel in aqueous solutions of salts at various temperatures T below and above the critical temperature at which collapse of the gel occurs. An advantage of the model is that it involves a a small (compared with conventional relations) number of material constants and allows the critical temperature to be determined explicitly. Its ability (i) to describe equilibrium swelling diagrams on poly(N-isopropylacrylamide) gels in aqueous solutions of mono- and multivalent salts and (ii) to predict the influence of volume fraction of salt on the critical temperature is confirmed by comparison of observations with results of numerical simulation.

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.

Structure-property relations in rheology of cellulose nanofibrils-based hydrogels.

Hydrogels prepared from self-assembled cellulose nanofibrils (CNFs) are widely used in biomedicine, electronics and environmental technology. Their ability to serve as inks for extrusion-based 3D printing is conventionally evaluated by means of rheological tests. A model is developed that describes the response of CNF gels in small- and large-amplitude oscillatory tests in a unified manner. The model involves a reasonably small number of material parameters, ensures good agreement between results of simulation and observations in oscillatory tests and correctly predicts the stress-strain Lissajous curves, experimental data in hysteresis loop tests, and measurements of the steady-state viscosity. The model is applied to analyze how composition and preparation conditions for CNF gels affect transition from shear thinning to weak strain overshoot in large-amplitude shear oscillatory tests. Based on the model, simple relations are derived for the fractal dimension of CNF clusters and the storage modulus of gels prepared in aqueous solutions of multivalent salts. The validity of these equations is confirmed by comparison of their predictions with observations in independent tests.

Thermo-Mechanical Behavior of Poly(ether ether ketone): Experiments and Modeling.

Observations are reported on poly(ether ether ketone) (PEEK) in uniaxial tensile tests, relaxation tests and creep tests with various stresses in a wide interval of temperatures ranging from room temperature to 180 °C. Constitutive equations are developed for the thermo-mechanical behavior of PEEK under uniaxial deformation. Adjustable parameters in the governing equations are found by matching the experimental data. Good agreement is demonstrated between the observations and results of numerical simulation. It is shown that the activation energies for the elastoplastic, viscoelastic and viscoelastoplastic responses adopt similar values at temperatures above the glass transition point.

The effect of saccharides on equilibrium swelling of thermo-responsive gels.

Mechanical and optical properties of thermo-responsive (TR) gels change drastically at their volume phase transition temperature. As the critical temperature is strongly affected by the presence of small amounts of additives in aqueous solutions, TR gels can be employed as sensors for detection and recognition of multiple analytes (from specific ions to hazardous biochemicals to pathogenic proteins) and actuators for biomedical applications. A simplified mean-field model is developed for equilibrium swelling of TR gels in aqueous solutions of additives. Its advantage is that the model involves a relatively small (compared with the conventional approaches) number of material constants and accounts for changes in the thermo-mechanical response at transition from the swollen to collapsed state. The ability of the model to describe experimental swelling diagrams and to predict the influence of additives on the equilibrium degree of swelling and the volume phase transition temperature of TR gels is confirmed by comparison of observations on poly(N-isopropylacrylamide) gel in aqueous solutions of saccharides (glucose, sucrose and galactose) with results of numerical analysis.

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.

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.

Swelling of pH-sensitive hydrogels.

A model is derived for the elastic response of polyelectrolyte gels subjected to unconstrained and constrained swelling. A gel is treated as a three-phase medium consisting of a solid phase (polymer network), solvent (water), and solutes (mobile ions). Transport of solvent and solutes is modeled as their diffusion through the network accelerated by an electric field formed by ions and accompanied by chemical reactions (dissociation of functional groups attached to the chains). Constitutive equations (including the van't Hoff law for ionic pressure and the Henderson-Hasselbach equation for ionization of chains) are derived by means of the free energy imbalance inequality. Good agreement is demonstrated between equilibrium swelling diagrams on several pH-sensitive gels and results of simulation. It is revealed that swelling of polyelectrolyte gels is driven by electrostatic repulsion of bound charges, whereas the effect of ionic pressure is of secondary importance.