Inhomogeneous Swelling of a Gel In Equilibrium With a Solvent and Mechanical Load (original) (raw)

Transient analysis of swelling-induced large deformations in polymer gels

Journal of the Mechanics and Physics of Solids, 2013

The purpose of the research is to describe the swelling-induced large deformations in polymer gels: a theoretical model is developed, and then implemented and solved using the finite element method. The model is firstly assessed with two well-known benchmark problems; moreover, the proposed approach is benchmarked against a recent experiment involving localized exposure of the gel boundary to a solvent, where large bending deformations appear during solvent absorption. In both cases, our results are quite satisfying.

Incipient Dynamics of Swelling of Gels

SIAM Journal on Applied Mathematics, 2008

In this article, we analyze a model of the incipient dynamics of gel swelling, and perform numerical simulations. The governing system consists of balance laws for a mixture of nonlinear elastic solid and solvent yielding effective equations for the gel. We discuss the multiscale nature of the problem and identify physically realistic regimes. The mixing mechanism is based on the Flory-Huggins energy. We consider the case that the dissipation mechanism is the solid-solvent friction force. This leads to a system of weakly dissipative nonlinear hyperbolic equations. After addressing the Cauchy problem, we propose physically realistic boundary conditions describing the motion of the swelling boundary. We study the linearized version of the free boundary problem. Numerical simulations of solutions are presented too.

Swelling Dynamics of a Disk-Shaped Gel

Macromolecules

When a gel absorbs a solvent from the surrounding, a stress field is created in the gel, and this causes complex dynamics of the swelling behavior. Here, we study this effect for a diskshaped gel by rigorously solving the diffusio-mechanical coupling equation. We show that (a) while the macroscopic thickness and the radius of the gel increase monotonically in time, the gel is compressed near the midplane, and that (b) while the swelling time depends on the shear modulus G of the gel, its dependence is weak, and the time is mainly determined by the friction constant of the gel network and the osmotic bulk modulus of the gel. We also show that these characteristic features are reproduced accurately by a simple variational calculation for the gel deformation. An analytical expression is given for the swelling time.

Modeling Approaches to the Dynamics of Hydrogel Swelling

Journal of Computational and Theoretical Nanoscience, 2010

We consider a gel as an immiscible mixture of polymer and solvent, and derive governing equations of the dynamics. They include the balance of mass and linear momentum of the individual components. The model allows to account for nonlinear elasticity, viscoelasticity, transport and diffusion. The total free energy of the system combines the elastic contribution of the polymer with the Flory-Huggins energy of mixing. The system is also formulated in terms of the center of mass velocity and the diffusive velocity, involving the total and the relative stresses. This allows for the identification of special regimes, such as the purely diffusive and the transport ones. We also obtain an equation for the rate of change of the total energy yielding decay for special choices of boundary conditions. The energy law motivates the Rayleghian variational approach discussed in the last part of the article. We consider the case of a gel in a one-dimensional strip domain in order to study special features of the dynamics, in particular, the early dynamics. We find that the monotonicity of the extensional stress is a necessary condition to guarantee the propagation of the swelling interface between the gel and its solvent. Such monotonicity 0-1 condition is satisfied for data corresponding to linear entangled polymers. However, for polyssacharide gels the monotonicity of the stress fails at a critical volume fraction, suggesting the onset of de-swelling. The weak elasticity is responsible for the loss of monotonicity of the stress. The analysis also suggests that type II diffusion is a hyperbolic phenomenon rather than a diffusive one. One goal is to compare the derivation method, assumptions and resulting equations with other models available in the literature, and determine their regimes of validity. The stress-diffusion coupling model by Yamaue and Doi [26] is one main benchmark. We assume that the gel is non-ionic, and neglect thermal effects.

Swelling and de-swelling of gels under external elastic deformation

Polymer, 2013

We show that the equilibrium Poisson ratio of electrically neutral gels depends on their shear modulus. When immersed in a good solvent, gels increase their volume on imposed external deformation, but stiffer gels swell less and exhibit a larger Poisson ratio, closer to 0.5, while the gels with a higher solvent content (and correspondingly lower shear modulus) approach a Poisson ratio of 0.25. We monitor the full process of stress and shape relaxation after an instantaneous deformation by using the technique of digital image correlation (DIC), and show that the amount of stress relaxation in uniaxially strained gels is proportional to the shear modulus of the free swollen state and a change in effective strain. Experiments were conducted on polyacrylamide (PAAm) gels in a custom built setup to give the Poisson ratio to high accuracy and time resolution, as well as verification of homogeneous deformation in equilibrium. In addition to water, hydrophilic gels were stretched in three poor solvents: silicone oil, mineral oil, and in air. All three exhibited water loss on imposed deformation and a resulting increase in stress, with mineral oil presenting the smallest change due to its lower permeability to water. Mineral oil and silicone oil are of particular interest as they are often used in mechanical testing to prevent solvent loss.

Swelling Equilibrium of a Binary Polymer Gel

Macromolecules, 2011

The swelling properties of a new class of biohybrid gels made of heparin and 4-arm starpoly(ethylene glycol) (PEG) were studied using mean-field concepts. Heparin acts as a multifunctional crosslinker and is highly charged in aqueous environments allowing for the functionalization of the gels with a plethora of biologically active molecules. The elasticity of the gels is provided by the flexible arms of the PEG. Varying the mole fraction of the heparin at preparation changes both the elasticity and the charge of the gel. We combine the classical Flory-Rehner model with a free energy contribution due to trapped counterions and derive a general equation for the equilibrium swelling of the gel as a function of the heparin-content at preparation, size of PEG molecules and salt concentration of the solvent. Varying the heparin content in the state of preparation results in opposite tendencies of the swelling behavior in the limit of low and high salt concentrations. At intermediate salt concentrations we find a regime where the heparin concentration at equilibrium swelling is almost independent of the heparin concentration at preparation. This provides access to novel gel-based biomaterials where physical stimuli (modulus) and biomolecular signals (modulated by the heparin concentration) can be varied independently. Our results are in good agreement with experimental data obtained at various gel compositions and salt concentrations of the aqueous environments.

Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core

2008

Abstract A polymer network can imbibe water from environment and swell to an equilibrium state. If the equilibrium is reached when the network is subject to external mechanical constraint, the deformation of the network is typically anisotropic and the concentration of water inhomogeneous. Such an equilibrium state in a network constrained by a hard core is modeled here with a nonlinear differential equation. The presence of the hard core markedly reduces the concentration of water near the interface and causes high stresses.

A theory of constrained swelling of a pH-sensitive hydrogel

2010

Many engineering devices and natural phenomena involve gels that swell under the constraint of hard materials. The constraint causes a field of stress in a gel, and often makes the swelling inhomogeneous even when the gel reaches a state of equilibrium. This paper develops a theory of constrained swelling of a pH-sensitive hydrogel, a network of polymers bearing acidic groups, in equilibrium with an aqueous solution and mechanical forces.

Inhomogeneous Large Deformation Kinetics of Polymeric Gels

International Journal of Applied Mechanics, 2013

This work examines the dynamics of nonlinear large deformation of polymeric gels, and the kinetics of gel deformation is carried out through the coupling of existing hyperelastic theory for gels with kinetic laws for diffusion of small molecules. As finite element (FE) models for the transient swelling process is not available in commercial FE software, we develop a customized FE model/methodology which can be used to simulate the transient swelling process of hydrogels. The method is based on the similarity between diffusion and heat transfer laws by determining the equivalent thermal properties for gel kinetics. Several numerical examples are investigated to explore the capabilities of the present FE model, namely: a cube to study free swelling; one-dimensional constrained swelling; a rectangular block fixed to a rigid substrate to study swelling under external constraints; and a thin annulus fixed at the inner core to study buckling phenomena. The simulation results for the const...

Mechanical Instabilities of Gels

Annual Review of Condensed Matter Physics, 2012

Although the study of gels undoubtedly takes its roots within the field of physicochemistry, the interest in gels has flourished and they have progressively become an important object in the study of the mechanics of polymeric materials and volumetric growth, raising some fascinating problems, some of them remaining unsolved. Because gels are multiphase objects, their study represents an important step in the understanding of the mechanics of complex soft matter as well as for the process of shape generation in biological bodies. The scope of this article is to review the understanding we have of the mechanical behavior of gels, with a strong focus on the development of instabilities in swelling gels.