Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel

Immersed in an ionic solution, a network of polyampholytic polyelectrolyte imbibes the solution and swells, resulting in a polyampholytic pH-sensitive hydrogel, which can respond to changes in the surrounding environmental pH. The presence of fixed charges and mobile ions due to the dissociation of ionizable acidic and basic groups may give rise to a region called the electrical double layer of a thickness scaled by the Debye length. Owing to the existence of the electrical double layer, when the size of a polyampholytic pH-sensitive hydrogels is comparable to, or smaller than, the Debye length, the behavior of the gel may deviate from that of the gel of a large size. To account of the size effects, this paper develops a field theory for polyampholytic pH-sensitive hydrogels by coupling large deformation of the network, the dissociation of the functional groups and the migration of the ions and the solvent. The theory is then applied to explore the influence of pH, salt concentration, geometric constraint and the effects of the electrical double layer on swelling properties by analyzing a thin layer of a polyampholytic pH-sensitive hydrogel immersed in a solution.     

Experimental investigation of the properties of polyelectrolyte gel

A polyelectrolyte gel, e.g. polyacrylamide gel has interesting thermo-mechanical properties. It swells in solution, increasing its volume by large factors and the swelling may be induced by a change of temperature, by the acetone content of the solution or by its acidity. The swelling can be reversed, i.e. the gel may be shrunk back to its original shape. The preparation of the gel is described here and quantitative details of the swelling or shrinking are reported.Particular emphasis is placed on the effect of a load on the properties of the gel. It is shown that a tensile load significantly affects the volume changes induced by changes of acidity of the solution.Some peculiar properties of the gel emerged during the investigation, such as anisotropy in thin gels and a decrease of the electrical resistance as an immediate consequence of both loading and unloading.     

pH敏感凝胶平衡溶胀的有限元研究

1943年Flory提出第一个凝胶溶胀理论以来,凝胶溶胀理论的发展极大地促进了凝胶科学的发展．在诸多凝胶溶胀理论中,Flory-Rehner凝胶溶胀理论是最为经典的理论之一,成功地预测了聚合物胶体的诸多溶胀变形特性．但该模型是基于一种最为简单的自由连接链模型,存在精度较差的局限．因此,本文采用能够表征网络缠结拓扑等微观结构影响的弹性自由能模型,即由Edwards-Vilgis提出的Slip-Link模型,构造自由能模型并形成pH敏感凝胶的平衡溶胀理论,并基于Abaqus有限元分析了微观结构及几何限制作用对pH敏感凝胶力学行为的影响．分析结果可为微流体控制阀的设计提供参考．     

Thermodynamic considerations on a chemo-mechanical engine

A polyelectrolytic gel may possibly be used as the working medium in a chemomechanical engine of the Katchalsky, Oplatka type. The gel shrinks in a salt solution and swells in pure water.The isothermal cycle performed by the gel in the engine is investigated qualitatively and quantitatively. The material properties of the gel are those of an acrylamide-sodiumacrylate-N,N'-methylenebisacrylamide copolymer. It turns out that the gel engine cannot be run reversibly, not even in principle.     

A coupled theory of fluid permeation and large deformations for elastomeric materials

An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model for the free energy based on a Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical-mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. As representative examples of application of the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained, stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii) consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across elastomeric membranes.     

Modeling of the pH-sensitive behavior of an ionic gel in the presence of diffusion

In this paper, we develop a model for swelling of an ionic gel in a solvent of varying pH and diffusion of the solvent through the swollen gel by applying a variational method originally presented by Baek and Srinivasa (Int. J. Nonlinear Mech. 39 (2004) 201). The approach presented here, based on the balance laws of a single continuum with mass diffusion and ionic chemical reactions, delivers system equations and boundary conditions by assuming two constitutive scalar functions for the free energy of the system and the rate of dissipation, instead of assuming osmotic pressure, electrostatic repulsive force, etc. In the equilibrium case, the model describes pH-dependent behavior and the effect of other counterions on the swelling of ionic gels. In the non-equilibrium case, it accounts for the pH-dependent mass flux through ionic gels. Moreover, the model shows that the mass flux can be induced by the gradient of chemical potential, the concentration of the mobile species and ionic charges. This model is applied to a typical carboxylated copolymer gel, and compared with an experiment for equilibrium swelling, and predicts the pH-dependence for a pressure-induced mass flux.     

Thermo-Chemo-Electro-Mechanical Formulation of Saturated Charged Porous Solids

A thermo-chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from a mixture theory including the volume fraction concept. The model consists of an electrically charged porous solid saturated with an ionic solution. Incompressible deformation is assumed. The mixture as a whole is assumed locally electroneutral. Different constituents following different kinematic paths are defined: solid, fluid, anions, cations and neutral solutes. Balance laws are derived for each constituent and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics for incompressible porous media is used to derive the constitutive restrictions of the medium. The material properties are shown to be contained in one strain energy function and a matrix of frictional tensors. A principle of reversibility results from the constitutive restrictions. Existing theories of swelling media should be evaluated with respect to this principle.     

Continuum theory of swelling material surfaces with applications to thermo-responsive gel membranes and surface mass transport

Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk materials, such as the properties of spreading and absorption of liquids. In particular, polymer gel membranes experience swelling or shrinking when their solvent content change, and the non-homogeneous swelling field may be exploited to control their shape. Here, we develop a theory of swelling material surfaces to model polymer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. We also specialize the theory to thermo-responsive gels, which are made of polymers that change their affinity with a solvent when temperature varies.     

Kinetics of smart hydrogels responding to electric field: A transient deformation analysis

A multiphysics model is presented in this paper for simulation of kinetics of the smart hydrogels subject to an externally applied electric field, especially for analysis of the transient deformation of the hydrogel. The model termed the multi-effect-coupling electric stimulus (MECe) takes account of the coupled chemo-electro-mechanical multiphysics domains and the multi-phase effect of polymeric network and interstitial liquid as well as ionic species. The MECe model is validated well by transient simulation and comparison with available experimental data. Kinetics of ionic concentration of diffusive species is simulated. Parameter studies on the hydrogel displacement are conducted in detail for influences of externally applied electric voltage, initially fixed-charge density and surrounding bath solution concentration.     

Swelling and instability of a gel annulus

We study the swelling of a gel annulus attached to a rigid core when it is immersed in a solvent.For equilibrium states,the free-energy function of the gel can be converted into a strain energy function,and as a result the gel can be treated as a compressible hyperelastic material.Asymptotic methods are used to study the inhomogeneous swelling in order to obtain the leading-order solution.Some analytical insights are then deduced.Because of the compressive hoop stress in this state,at some stage instability can occur,leading to wrinkles in the gel.An incremental deformation theory in nonlinear elasticity is used to conduct a linear bifurcation analysis for understanding such instability.More specifically,the critical loading for the onset of a wrinkled state is obtained.Detailed discussions on the behaviors of various physical quantities in this critical state are given.It is found that the critical mode number,while insensitive to the material parameters,is greatly influenced by the ratio of the inner and outer radii of the gel.Also,an interesting finding is that the critical swelling ratio is an increasing function of this geometrical parameter,which implies that a thin annulus is more likely to be unstable than a thick one.     

Computational analysis of smart soft hydrogels subjected to pH-electrical coupled stimuli: Effects of initial geometry

A chemo-electro-mechanical formulation, referred to as the multi-effect-coupling pH-stimulus (MECpH) model, is presented in this paper for the analysis of the effects of the initial geometrical size on the responsive behavior of pH-sensitive hydrogels subject to the coupled stimuli of environmental solution pH and externally applied electric voltage. The model is composed of coupled nonlinear partial differential equations, and it accounts for the diffusion of ionic species, distributive electric potential and large mechanical deformation. In addition, the correlation between the diffusive hydrogen ion within the hydrogel and charge groups fixed to the polymeric network chains is incorporated quantitatively into this MECpH model. For the simulation of the response characteristics of the smart hydrogel, we solve the one-dimensional steady-state problem using the Hermite–Cloud meshless technique. For the MECpH model, the present numerical simulations were compared with experimental data available from literature to validate the accuracy and robustness of the model, and good agreement was observed. Several parameter studies were then carried out in the analysis of the hydrogel swelling when immersed in solution, and it was observed that the initial geometrical size has significant influence on the volume variations of these pH-responsive hydrogels.     

Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels

A polymer network can imbibe copious amounts of solvent and swell, the resulting state is known as a gel. Depending on its constituents, a gel is able to deform under the influence of various external stimuli, such as temperature, pH-value and light. In this work, we investigate the photo-thermal mechanics of deformation of temperature sensitive hydrogels impregnated with light-absorbing nano-particles. The field theory of photo-thermal sensitive gels is developed by incorporating effects of photochemical heating into the thermodynamic theory of neutral and temperature sensitive hydrogels. This is achieved by considering the equilibrium thermodynamics of a swelling gel through a variational approach. The phase transition phenomenon of these gels, and the factors affecting their deformations, are studied. To facilitate the simulation of large inhomogeneous deformations subjected to geometrical constraints, a finite element model is developed using a user-defined subroutine in ABAQUS, and by modeling the gel as a hyperelastic material. This numerical approach is validated through case studies involving gels undergoing phase coexistence and buckling when exposed to irradiation of varying intensities, and as a microvalve in microfluidic application.     

A theory of coupled diffusion and large deformation in polymeric gels

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.     

A chemo-electro-mechanical model for simulation of responsive deformation of glucose-sensitive hydrogels with the effect of enzyme catalysis

A multi-effect-coupling glucose-stimulus (MECglu) model is developed and solved numerically for the swelling behavior of soft smart hydrogels responding to changes in the environmental glucose concentration. The model considers the effect of the glucose oxidation reaction catalyzed by enzymes including glucose oxidase and catalase. It is composed of the Nernst-Planck equation for the mobile species in the solvent, the Poisson equation for the electric potential, and a nonlinear mechanical equation for the large deformations of the hydrogel that arise due to the conversion of chemical energy to mechanical. Based on the theory of the chemo-electro-mechanical-coupled fields, the formulation of the fixed charge groups bound onto the cross-linked polymer network is associated with the change of the ambient solution pH. The MECglu model is validated by comparison between the steady-state computation and experimental equilibrium swelling curves, and good agreement is obtained. A parameter study is then conducted by steady-state simulations to ascertain the impact of various solvent parameters on the responsive swelling behavior of the hydrogel. One key parameter is the glucose concentration, which is varied within the range of practical physiological glucose concentrations from 0 to 16.5 mM (300 mg/ml) to support the design and optimization of an insulin delivery system based on a glucose-sensitive hydrogel with immobilized glucose oxidase and catalase. The influence of oxygen and glucose concentrations in the solvent is then further studied for the distributive profiles of reacting and diffusive species concentrations, the electric potential, the displacement, as well as the swelling ratio of the glucose-sensitive hydrogel.     

数值模拟离子强度敏感水凝胶的多场特性

发展了多物理模型来研究溶液中离子强度敏感水凝胶电-力-化学多场耦合的特性. 模 型的主要控制方程包括：计算水凝胶内外离子浓度分布的Nernst-Planck化学场方程；描述 膨胀变形的力学场方程和描述电场的泊松方程. 无网格有限云团法和牛顿迭代法用来数值离 散和求解控制方程. 通过对比多场耦合的响应, 包括胶的膨胀率和胶内外离子浓度和电势的分布，探讨了影响胶体变形的主要因素. 对数值模拟结果和实验结果进行了对照.     

A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels

An elastomeric gel is a cross-linked polymer network swollen with a solvent, and certain gels can undergo large reversible volume changes as they are cycled about a critical temperature. We have developed a continuum-level theory to describe the coupled mechanical deformation, fluid permeation, and heat transfer of such thermally responsive gels. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model based on a Flory–Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical–mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. We have numerically implemented our theory in a finite element program. We show that our theory is capable of simulating swelling, squeezing of fluid by applied mechanical forces, and thermally responsive swelling/de-swelling of such materials.     

Diffusion mechanism during the swelling hidroxy-methyl cellulose membrane formation

The conduction properties of HMC polymer gel prepared by the phase inversion method were investigated through the diffusion coefficient in order to confirm the conduction mechanism. The solution introduced in the polymer is stored in the pores and then penetrates into the polymer chains. For swelling the polymer network. A model describing the swelling hidroxy-methyl cellulose is presented. The model is used to predict the type liquid–liquid phase separation (instantaneous or delayed) that occurs when HMC-PVPD-Solvent-Water casting solutions are immersed in a gelation bath. The model includes the thermodynamic interactions parameters and the transport parameters. The predictions of the model agree with the experimental observations.     

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials,electric displacements,elastic deformations,and thermoelasticity,and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures(cylinder or sphere),subjected to mechanical load and electric potential.The material properties,thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution.In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material,reinforced by elastic isotropic fibers,this material is considered as structurally anisotropic material.The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity,and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin’s approximation method.Finally,numerical results are carried out and discussed.     

Modified boundary layer analysis of an electrode in an electrostrictive material

A thin electrode embedded in an electrostrictive material under electric loading is investigated. In order to obtain an asymptotic form of electric fields and elastic fields near the electrode edge, we consider a modified boundary layer problem of an electrode in an electrostrictive material under the small scale saturation condition. The exact electric solution for the electrode is obtained by using the complex function theory. It is found that the shape of the electric displacement saturation zone is sensitive to the transverse electric displacement. A perturbation solution of stress fields induced by incompatible electrostrictive strains for the small value of the transverse electric displacement is obtained. The influence of transverse electric displacement on a microcrack initiation from the electrode edge is also discussed.