Modeling Investigation of Hydrogel Volume Transition

Wu, Shixin; Li, Hua; Chen, Jiaping; Lam, K.Y.

doi:10.1002/mats.200300013

Cited by 79 publications

(65 citation statements)

References 150 publications

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“…The dynamics of polyelectrolyte gels has also received a great deal of attention, and systems of evolution equations have been proposed by many authors [18,16,19,31,34,49,48,52,32,9,1,23]. A standard approach, which we adopt in this paper, is to treat polyelectrolyte gels as a two phase medium of polymer network and fluid, with the ions being treated as solute species dissolved in the fluid.…”

mentioning

confidence: 99%

A Dynamic Model of Polyelectrolyte Gels

Mori¹,

Chen

Micek³

et al. 2013

SIAM J. Appl. Math.

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Abstract. We derive a model of the coupled mechanical and electrochemical effects of polyelectrolyte gels. We assume that the gel, which is immersed in a fluid domain, is an immiscible and incompressible mixture of a solid polymeric component and the fluid. As the gel swells and de-swells, the gel-fluid interface can move. Our model consists of a system of partial differential equations for mass and linear momentum balance of the polymer and fluid components of the gel, the NavierStokes equations in the surrounding fluid domain, and the Poisson-Nernst-Planck equations for the ionic concentrations on the whole domain. These are supplemented by a novel and general class of boundary conditions expressing mass and linear momentum balance across the moving gel-fluid interface. Our boundary conditions include the permeability boundary conditions proposed in earlier studies. A salient feature of our model is that it satisfies a free energy dissipation identity, in accordance with the second law of thermodynamics. We also show, using boundary layer analysis, that the well-established Donnan condition for equilibrium arises naturally as a consequence of taking the electroneutral limit in our model.

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mentioning

confidence: 99%

A Dynamic Model of Polyelectrolyte Gels

Mori¹,

Chen

Micek³

et al. 2013

SIAM J. Appl. Math.

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“…In a highly charged and highly crosslinked hydrogel, [13,17] each strand between the consecutive crosslinks in the network would satisfy the conditions of both a short contour length and a strong electrostatic repulsion. This makes the finite-extensibility correction necessary in order to construct a correct theory for this system.…”

Section: Resultsmentioning

confidence: 99%

“…Specifically, with the Gaussian stretching term in Flory's theory [13] modified to a non-Gaussian form accounting for the finite-extensibility effect, we can obtain a qualitative consistence between the modeling and the experiment for the swelling process of hydrogels. Motivated by this and based on the fact that the physics of the hydrogel network is effectively reduced to a single-chain problem within a mean-field theory, in the present paper, we focus our attentions on the statistical behavior of one single chain and address the finiteextensibility effect on the equilibrium size of the chain theoretically.…”

Section: Introductionmentioning

confidence: 98%

Effect of Finite Extensibility on the Equilibrium Chain Size

Miao

Vilgis

Poggendorf

et al. 2010

Macro Theory & Simulations

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We investigate the finite‐extensibility effect on the equilibrium size of a single polymer chain by using a Flory‐type calculation. The finite extensibility of the chain is effectively taken into account by modifying the Gaussian stretching energy to a non‐Gaussian form which recovers the harmonic spring behavior in the limit of weak stretch and diverges when the chain extension approaches the total contour length. In general, the finite extensibility decreases the equilibrium size of the chain compared to that obtained from Flory's classic theory, due to a steeper free energy or effective potential of the chain generated by the finite‐extensibility effect. It is illustrated clearly that, for a chain with a short contour length and/or with strong repulsions between monomers, the finite‐extensibility correction is important and necessary to be taken into account. A typical system where the finite extensibility plays an important role is suggested to be the highly charged and highly crosslinked hydrogel.magnified image

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“…These changes can be used to determine and monitor the physiological state of the part of interest, and can also be used in the design of targeted and controlled drug delivery systems. [15][16][17][18][19] In this paper, a chemo-electromechanical formulation, referred to as the multieffect-coupling pH-stimulus (MECpH) model previously developed by the present authors, [20][21][22][23] is refined here to investigate the effects of the Young modulus on the responsive behavior of the pH-sensitive hydrogel to the concurrent environmental changes in the solution pH and externally applied electric field. In the MECpH model, the transport mechanism of diffusive ionic species in a solution is described mathematically by Nernst-Planck equations.…”

Section: Full Papermentioning

confidence: 99%

Meshless Modeling of pH‐Sensitive Hydrogels Subjected to Coupled pH and Electric Field Stimuli: Young Modulus Effects and Case Studies

Yew

et al. 2007

Macro Chemistry & Physics

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The effect of Young's modulus on the behavior of pH‐sensitive hydrogels is studied when subjected to coupled stimuli of solution pH and externally applied electric field. The study is the first instance for coupled stimuli numerical analysis of the hydrogels, in which a multieffect‐coupling pH‐stimulus (MECpH) model is presented. The model considers ionic diffusion, electric potential, and large mechanical deformation. A correlation between diffusive hydrogen ion and charge groups fixed onto the hydrogel polymeric chains by the Langmuir absorption isotherm is incorporated into the model. To validate the model, the computed results by the meshless Hermite‐Cloud technique are compared well with experimental data available from the literature. Then several case studies are conducted for the swelling hydrogel immersed in buffered solution subject to applied electric voltage, especially for the Young modulus effects on the volume variations of the hydrogels.magnified image

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Modeling Investigation of Hydrogel Volume Transition

Cited by 79 publications

References 150 publications

A Dynamic Model of Polyelectrolyte Gels

A Dynamic Model of Polyelectrolyte Gels

Effect of Finite Extensibility on the Equilibrium Chain Size

Meshless Modeling of pH‐Sensitive Hydrogels Subjected to Coupled pH and Electric Field Stimuli: Young Modulus Effects and Case Studies

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