A model of ideal elastomeric gels for polyelectrolyte gels

Hydrogel-based strong and fast actuators by electroosmotic turgor pressure

Hydrogels are promising as materials for soft actuators because of qualities such as softness, transparency, and responsiveness to stimuli. However, weak and slow actuations remain challenging as a result of low modulus and osmosis-driven slow water diffusion, respectively. We used turgor pressure and electroosmosis to realize a strong and fast hydrogel-based actuator. A turgor actuator fabricated with a gel confined by a selectively permeable membrane can retain a high osmotic pressure that drives gel swelling; thus, our actuator exerts large stress [0.73 megapascals (MPa) in 96 minutes (min)] with a 1.16 cubic centimeters of hydrogel. With the accelerated water transport caused by electroosmosis, the gel swells rapidly, enhancing the actuation speed (0.79 MPa in 9 min). Our strategies enable a soft hydrogel to break a brick and construct underwater structures within a few minutes.

Equilibrium swelling of multi-stimuli-responsive copolymer gels

Copolymer gels prepared by polymerization of thermo-responsive and anionic monomers demonstrate strong sensitivity to several triggers such as temperature, pH and ionic strength of aqueous solutions. For biomedical applications of these materials (as on-off switches in controlled drug delivery and release), fine tuning of their volume phase transition temperature (VPTT) and a sharp decay in degree of swelling upon transition from the swollen to the collapsed state are needed. These requirements are fulfilled under swelling of copolymer gels and microgels in water under acidic conditions, but are violated when tests are conducted under alkaline conditions or in aqueous solutions of salts with physiological salinity. A model is developed for equilibrium swelling of multi-stimuli-responsive copolymer gels in aqueous solutions with arbitrary pH and molar fractions of a monovalent salt. Unlike conventional approaches, the model accounts for secondary interactions between chains (hydrogen bonding) to describe the kinetics of aggregation of hydrophobic segments above VPTT. Material constants are determined by fitting experimental swelling diagrams on poly(N-isopropylacrylamide-co-sodium acrylate) gels with various molar fractions of ionic monomers. The effects of temperature, pH and molar fraction of salt on the equilibrium degree of swelling below and above VPTT are studied numerically.

Carbomer microgels as model yield-stress fluids

The review presents current research results for Carbopol-based microgels as yield-stress materials, covering three aspects: chemical, physical and rheological. Such a joint three-aspect study has no analog in the literature. The chemical aspects of Carbopol polymers are presented in terms of a cross-linking polymerization of acrylic acid, their molecular structure, microgel formulation, polyacid dissociation and neutralization, osmotic pressure and associated immense microgel swelling. The physical characterization is focused on models of the shear-induced solid-to-liquid transition of microgels, which are formed of mesoscopic particles typical for soft matter materials. Models that describe interparticle effects are presented to explain the energy states of microgel particles at the mesoscale of scrutiny. Typical representatives of the models utilize attributes of jamming dispersions, micromechanical and polyelectrolyte reactions. Selected relationships that result from the models, such as scaling rules and nondimensional flow characteristics are also presented. The rheological part presents the discussion of problems of yield stress in 2D and 3D deformations, appearance and magnitude of the wall slip. The theory and characteristics of Carbopol microgel deformation in rotational rheometers are presented with graphs for the steady-state measurements, stress-controlled oscillation and two types of transient shear deformation. The review is concluded with suggestions for future research.

Experimental Verification of the Balance between Elastic Pressure and Ionic Osmotic Pressure of Highly Swollen Charged Gels

The equilibrium swelling degree of a highly swollen charged gel has been thought to be determined by the balance between its elastic pressure and ionic osmotic pressure. However, the full experimental verification of this balance has not previously been conducted. In this study, we verified the balance between the elastic pressure and ionic osmotic pressure of charged gels using purely experimental methods. We used tetra-PEG gels created using the molecular stent method (St-tetra-PEG gels) as the highly swollen charged gels to precisely and separately control their network structure and charge density. The elastic pressure of the gels was measured through the indentation test, whereas the ionic osmotic pressure was determined by electric potential measurement without any strong assumptions or fittings. We confirmed that the two experimentally determined pressures of the St-tetra-PEG gels were well balanced at their swelling equilibrium, suggesting the validity of the aforementioned relationship. Furthermore, from single-strand level analysis, we investigated the structural requirements of the highly swollen charged gels in which the elasticity and ionic osmosis are balanced at their swelling equilibrium.

Effect of Nonlinear Elasticity on the Swelling Behaviors of Highly Swollen Polyelectrolyte Gels

Polyelectrolyte gels exhibit swelling behaviors that are dependent on the external environment. The swelling behaviors of highly charged polyelectrolyte gels can be well explained using the Flory-Rehner model combined with the Gibbs-Donnan effect and Manning's counterion condensation effect (the FRGDM model). This study investigated the swelling properties of a series of model polyelectrolyte gels, namely tetra-polyacrylic acid-polyethylene glycol gels (Tetra-PAA-PEG gels), and determined the applicability of the FRGDM model. The swelling ratio (V_s/V₀) was well reproduced by the FRGDM model in the moderate swelling regime (V_s/V₀ < 10). However, in the high swelling regime (V_s/V₀ > 10), the FRGDM model is approx. 1.6 times larger than the experimental results. When we introduced the finite extensibility to the elastic free energy in the FRGDM model, the swelling behavior was successfully reproduced even in the high swelling regime. Our results reveal that finite extensibility is one of the factors determining the swelling equilibrium of highly charged polyelectrolyte gels. The modified FRGDM model reproduces well the swelling behavior of a wide range of polyelectrolyte gels.

Hydrolysis-induced large swelling of polyacrylamide hydrogels

Polyacrylamide (PAAm) hydrogels are widely used and studied. Their feature of hydrolysis is often ignored. When PAAm hydrogels are stored under alkaline conditions, they can undergo a hydrolysis reaction, which changes them from neutral hydrogels to polyelectrolyte hydrogels, resulting in significant volumetric increases. In this paper, we establish a non-equilibrium thermodynamic theory to describe hydrolysis-induced large swelling of PAAm hydrogels. In particular, a thermodynamically consistent reaction kinetics is proposed by accounting for auto-retardation of the hydrolysis reaction. As an example, hydrolysis-induced homogeneous swelling under free and constrained boundary conditions is modeled, and we show that mechanical constraints can significantly influence the swelling and reaction of the hydrogels. Our theoretical model is validated by comparing with experiments. This work provides guidelines for understanding and predicting the hydrolysis-induced swelling behavior of PAAm hydrogels under alkaline conditions, and is important for their utilization.

Electrostatic effects in collagen fibril formation

Using light scattering and Atomic Force Microscopy techniques, we have studied the kinetics and equilibrium scattering intensity of collagen association, which is pertinent to the vitreous of the human eye. Specifically, we have characterized fibrillization dependence on pH, temperature, and ionic strength. At higher and lower pH, collagen triple helices remain stable in solution without fibrillization. At physiological pH, fibrillization occurs and the fibril growth is slowed upon either an increase in ionic strength or a decrease in temperature. The total light scattering with respect to ionic strength is non-monotonic in these conditions as a result of a competing dependence of fibril concentration and size on ionic strength. Fibril concentration is the highest at lower ionic strengths and rapidly decays for higher ionic strengths. On the other hand, fibril size is larger in solutions with higher ionic strength. We present a theoretical model, based on dipolar interactions in solutions, to describe the observed electrostatic nature of collagen assembly. At extreme pH values, either very low or very high, collagen triple helices carry a large net charge of the same sign preventing their assembly into fibrils. At intermediate pH values, fluctuations in the charge distribution of the collagen triple helices around roughly zero net charge lead to fibrillization. The growth kinetics of fibrils in this regime can be adequately described by dipolar interactions arising from charge fluctuations.

On the Effect of Chemical Composition on the Desorption of Superabsorbent Hydrogels in Contact with a Porous Cementitious Material

The behavior of poly(sodium acrylate-co-acrylamide) copolymer hydrogels with varied chemical compositions in artificial pore solutions with three different pH values is examined. The absorption, chemical characteristics, mechanical stiffness, and desorption of the hydrogels in contact with a porous cementitious material were investigated. It was observed that the surface characteristics of the hydrogels play an important role in the desorption of hydrogels due to the capillary forces. It was shown that in the hydrogel systems studied here, the bonding between the hydrogels and the porous cementitious material is improved with an increase in the content of acrylamide in the hydrogels, and this results in an increased desorption rate of the hydrogels.

On the Effect of Chemical Composition on the Desorption of Superabsorbent Hydrogels in Contact with a Porous Cementitious Material

The behavior of poly(sodium acrylate-co-acrylamide) copolymer hydrogels with varied chemical compositions in artificial pore solutions with three different pH values is examined. The absorption, chemical characteristics, mechanical stiffness, and desorption of the hydrogels in contact with a porous cementitious material were investigated. It was observed that the surface characteristics of the hydrogels play an important role in the desorption of hydrogels due to the capillary forces. It was shown that in the hydrogel systems studied here, the bonding between the hydrogels and the porous cementitious material is improved with an increase in the content of acrylamide in the hydrogels, and this results in an increased desorption rate of the hydrogels.

Features of the volume change and a new constitutive equation of hydrogels under uniaxial compression

For high-water content hydrogels in compression, the water inside of hydrogels contributes to the response of hydrogels to external loads directly, but part of the water is expelled from hydrogels in the meantime to change the volume of the hydrogel and reduce the contribution. In order to consider the contribution of the water in the constitution equation, PVA (polyvinyl alcohol) hydrogels with high-water content were used as examples, and compressive experiments were carried out to measure both the stress-strain relation and the change of the volume in the meantime. By considering the effect of the difference of the contribution of water in different directions of the hydrogel, we deduced a new constitutive equation, which can pretty well depict the stress-strain of hydrogels with different water contents. The results showed that the contribution of water to the total stress increases with the compression strain and even exceed that of the polymer, although the expelled water reduces the contribution at the early loading stage, which well explains the difference of elastic moduli of hydrogels in compression and tension.

Probing the swelling-dependent mechanical and transport properties of polyacrylamide hydrogels through AFM-based dynamic nanoindentation

Hydrogels are composed of a crosslinked polymer network and water. The constitutive behaviors of hydrogels have been modeled based on Flory-Huggins theory. Within this model, the thermodynamic and kinetic parameters are assumed to be of constant values and are typically characterized through swelling tests. Since most hydrogels can absorb a large amount of solvent from the dry state to the swollen state, and the network size and solvent concentration of the hydrogels change significantly, the assumption of constant values of the thermodynamic and kinetic properties as the network swells is questionable. In this work, we have experimentally shown that even for the simple neutral polyacrylamide (PAAm) hydrogels, their mechanical responses cannot be fully described by the Flory-Huggins theory with constant thermodynamic parameters: N (number of chains per unit volume of dry polymers) and χ (polymer-solvent interaction parameter). For a more complete and precise characterization of the hydrogels, we measure the evolving properties of the gels as the network swells. Here, we use dynamic indentation to measure the poroelastic properties (shear modulus G, Poisson's ratio ν and diffusivity D) of the hydrogels under a wide range of swelling ratios. We also use linear perturbation to build the link between G, ν and N, χ, and plot the thermodynamic parameters in the Flory-Huggins theory as a function of the hydrogel swelling ratio. Consequently, the validity of the hydrogel models based on Flory-Huggins theory can be quantitatively examined.

Improved ATR-FTIR detection of hydrocarbons in water with semi-crystalline polyolefin coatings on ATR elements

In situ detection of hydrocarbons in water using ATR-FTIR with LLDPE film.

Electrostatic Swelling Transitions in Surface-Bound Microgels

Herein, electrostatic swelling transitions of poly(ethyl acrylate-co-methacrylic acid) microgels covalently bound to silica surfaces are investigated. Confined at a solid surface, microgel swelling is anisotropically hindered and the structure is flattened to an extent dictated by pH and microgel composition. Microgel deformation under applied load is also shown to depend on microgel charge density, with the highest deformation observed at intermediate charge densities. Two modes of microgel deformation under load were observed, one elastic and one viscoelastic, related to polymer strand deformation and displacement of trapped water, respectively. Results on polymer strand dynamics reveal that the microgels are highly dynamic, as the number of strand-tip interaction points increases 4-fold during a 10 s contact time. Furthermore, finite element modeling captures these effects qualitatively and shows that stress propagation in the microgel network decays locally at the rim of contact with a solid interface or close to the tip probe. Taken together, the results demonstrate a delicate interplay between the surface and microgel which determines the structure and nanomechanical properties of the latter and needs to be controlled in applications of systems such as pH-responsive surface coatings in biomaterials.

A structural model for the in vivo human cornea including collagen-swelling interaction

A structural model of the in vivo cornea, which accounts for tissue swelling behaviour, for the three-dimensional organization of stromal fibres and for collagen-swelling interaction, is proposed. Modelled as a binary electrolyte gel in thermodynamic equilibrium, the stromal electrostatic free energy is based on the mean-field approximation. To account for active endothelial ionic transport in the in vivo cornea, which modulates osmotic pressure and hydration, stromal mobile ions are shown to satisfy a modified Boltzmann distribution. The elasticity of the stromal collagen network is modelled based on three-dimensional collagen orientation probability distributions for every point in the stroma obtained by synthesizing X-ray diffraction data for azimuthal angle distributions and second harmonic-generated image processing for inclination angle distributions. The model is implemented in a finite-element framework and employed to predict free and confined swelling of stroma in an ionic bath. For the in vivo cornea, the model is used to predict corneal swelling due to increasing intraocular pressure (IOP) and is adapted to model swelling in Fuchs' corneal dystrophy. The biomechanical response of the in vivo cornea to a typical LASIK surgery for myopia is analysed, including tissue fluid pressure and swelling responses. The model provides a new interpretation of the corneal active hydration control (pump-leak) mechanism based on osmotic pressure modulation. The results also illustrate the structural necessity of fibre inclination in stabilizing the corneal refractive surface with respect to changes in tissue hydration and IOP.

Adhesion between highly stretchable materials

Recently developed high-speed ionic devices require adherent laminates of stretchable and dissimilar materials, such as gels and elastomers. Adhesion between stretchable and dissimilar materials also plays important roles in medicine, stretchable electronics, and soft robots. Here we develop a method to characterize adhesion between materials capable of large, elastic deformation. We apply the method to measure the debond energy of elastomer-hydrogel bilayers. The debond energy between an acrylic elastomer and a polyacrylamide hydrogel is found to be about 0.5 J m(-2), independent of the thickness and the crosslink density of the hydrogel. This low debond energy, however, allows the bilayer to be adherent and highly stretchable, provided that the hydrogel is thin and compliant. Furthermore, we demonstrate that nanoparticles applied at the interface can improve adhesion between the elastomer and the hydrogel.

Hyperelastic models for hydration of cellular tissue

In this paper we present hyperelastic models for swelling elastic shells, due to pressurization of the internal cavity. These shells serve as model systems for cells having cell walls, as can be found in bacteria, plants and fungi. The pressurized internal cavity represents the cell vacuole with intact membrane at a certain turgor pressure, and the elastic shell represents the hydrated cell wall. At pressurization the elastic shell undergoes inhomogeneous deformation. Its deformation is governed by a strain energy function. Using the scaling law of Cloizeaux for the osmotic pressure, we obtain approximate analytical expressions of the cell volume versus turgor pressure - which are quite comparable to numerical solutions of the problem. Subsequently, we have simulated the swelling of shells - where the cell wall material is embedded with microfibrils, leading to strain hardening and anisotropic cell expansion. The purpose of our investigations is to elucidate the contribution of cell membrane integrity and turgor to the water holding capacity (hydration) of plant foods. We conclude with a discussion of the impact of this work on the hydration of food material, and other fields like plant science and the soft matter physics of responsive gels.

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.

Mesoscale modelling of environmentally responsive hydrogels: emerging applications

We review recent advances in mesoscale computational modeling, focusing on dissipative particle dynamics, used to probe stimuli-sensitive behavior of hydrogels.

Mechanical behavior of poly(methyl methacrylate)-based ionogels

Ionogels are formed when a cross-linked polymer network absorbs an ionic liquid. Ionogels are ionic conductors and, as such, are being considered for use in stretchable electronics and artificial muscles or nerves. The use of ionogels in these applications is limited in part by their mechanical behavior. Here we present an ionogel prepared by swelling covalently cross-linked poly(methyl methacrylate) in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide. The resulting ionogel is compliant, stretchable, and relatively tough. We demonstrate that the swelling ratio, elastic modulus, stretchability, and fracture energy of the ionogel depend sensitively on the cross-link density of the polymer network. The behavior of the ionogel is well captured by the model of the ideal elastomeric gel combined with the Flory-Huggins model for the energy of mixing.