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.

Swelling of thermo-responsive hydrogels.

A model is developed for the elastic response and solvent diffusion through a thermo-responsive gel under an arbitrary deformation with finite strains. The constitutive equations involve the stress-strain relation, the nonlinear diffusion equation for solvent molecules, the heat conduction equation, and the Allen-Cahn equation for an order parameter (proportional to the concentration of hydrophilic segments in polymer chains). Material constants are found by fitting swelling diagrams for PNIPA gels under uniaxial tension. Numerical analysis demonstrates good agreement between predictions of the model and observations in tests with stress- and strain-controlled programs.

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.

Lifetime Predictions for High-Density Polyethylene under Creep: Experiments and Modeling.

Observations are reported in uniaxial tensile tests with various strain rates, tensile relaxation tests with various strains, and tensile creep tests with various stresses on high-density polyethylene (HDPE) at room temperature. Constitutive equations are developed for the viscoelastoplastic response of semicrystalline polymers. The model involves seven material parameters. Four of them are found by fitting observations in relaxation tests, while the others are determined by matching experimental creep curves. The predictive ability of the model is confirmed by comparing observations in independent short- and medium-term creep tests (with the duration up to several days) with the results of numerical analysis. The governing relations are applied to evaluate the lifetime of HDPE under creep conditions. An advantage of the proposed approach is that it predicts the stress-time-to-failure diagrams with account for the creep endurance limit.

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.

Modulation of the volume phase transition temperature of thermo-responsive gels.

Thermo-responsive (TR) gels swell substantially below their volume phase transition temperature Tc and shrink above this temperature. Applications of TR gels in controlled drug delivery and their use as biosensors and temperature-triggered soft actuators require fine tuning of Tc. As the critical temperature is independent of the preparation conditions and molar fractions of monomers and cross-linkers, it is modulated by incorporation of (neutral or ionic) monomers and polymer chains into pre-gel solutions for TR gels. A model is developed for the mechanical response and equilibrium swelling of TR gels. Analytical formulas are derived for the effect of molar fraction of comonomers on the volume phase transition temperature Tc in copolymer gels and gels with semi-interpenetrating networks. Adjustable parameters are found by fitting equilibrium swelling diagrams on poly(N,N-diethylacrylamide) gels. Good agreement is demonstrated between predictions of the model and experimental data.

Tension-compression asymmetry in the mechanical response of hydrogels.

Two factors play the key role in application of hydrogels as biomedical implants (for example, for replacement of damaged intervertebral discs and repair of spinal cord injuries): their stiffness and strength (measured in tensile tests) and mechanical integrity (estimated under uniaxial compression). Observations show a pronounced difference between the responses of hydrogels under tension and compression (the Young's moduli can differ by two orders of magnitude), which is conventionally referred to as the tension-compression asymmetry (TCA). A constitutive model is developed for the mechanical behavior of hydrogels, where TCA is described within the viscoplasticity theory (plastic flow is treated as sliding of junctions between chains with respect to their reference positions). The governing equations involve five material constants with transparent physical meaning. These quantities are found by fitting stress-strain diagrams under tension and compression on a number of pristine and nanocomposite hydrogels with various kinds of chemical and physical bonds between chains. Good agreement is demonstrated between the experimental data and results of simulation. The influence of volume fraction of nanoparticles, concentration of cross-links, and topology of a polymer network on material parameters is analyzed numerically.

Equilibrium swelling of thermo-responsive copolymer microgels.

Thermo-responsive (TR) hydrogels with a lower critical solution temperature swell strongly at temperatures below their volume phase transition temperature T c and collapse above T c. Biomedical application of these materials requires tuning the critical temperature in a rather wide interval. A facile method for modulation of T c is to polymerize the basic monomers with hydrophilic or hydrophobic comonomers. Although the effectiveness of this method has been confirmed by experimental data, molar fractions of comonomers necessary for fine tuning of T c in macroscopic gels and microgels are unknown. A simple model is developed for the equilibrium swelling of TR copolymer gels. Its adjustable parameters are found by fitting swelling diagrams on several macro- and microgels with N-isopropylacrylamide as a basic monomer. Good agreement is demonstrated between the experimental swelling curves and results of numerical analysis. An explicit expression is derived for the volume phase transition temperature as a function of molar fraction of comonomers. The ability of this relation to predict the critical temperature is confirmed by comparison with observations.

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.

Swelling of glucose-responsive gels functionalized with boronic acid.

A model is developed for the elastic response of a glucose-sensitive gel functionalized with boronic acid under swelling in aqueous solutions of glucose with various pH. A gel is treated as a three-phase medium composed of a solid phase (partially ionized polymer network), solvent (water), and solute (mobile glucose molecules and ions). Constitutive equations are derived by means of the free energy imbalance inequality for three-dimensional deformation with finite strains. Numerical analysis demonstrates the ability of the model to describe the effects of pH, molar fraction of glucose, and concentration of functional groups on equilibrium water uptake diagrams under unconstrained and constrained swelling.

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.

[Profilament actin in muscle cells of starfish ambulacra]. / Profilamentnyi aktin v myshechnykh kletkakh ambulaktal'nykh nozhek morskoi zvezdy.

In gelatinated extracts of starfish ambulacral podia the actin polymerized during gel formation exists as oligomers incapable of binding to rabbit myosin. Actin is also the major protein extractable from the cells by glycerol- and Triton-containing solutions, which do not destroy the contractile mechanism of the cells. The weakly bound gel proteins washed from gel by low ionic strength solutions comprise a factor hampering the polymerization of rabbit actin. The data obtained suggest that the ambulacral sarcoplasmic proteins contain actin (profilament form) coupled to the factor preventing its polymerization.