Modeling and Simulation of the Swelling Behavior of pH-Stimulus-Responsive Hydrogels

Abstract

The modulation of the swelling ability of the hydrogel matrix by pH-stimulus enables the dynamic control of the swelling forces, thereby obtaining effective diffusivity and permeability of the solutes, or mechanical energy from the hydrogel. In this work, a chemo-electro-mechanical model describing hydrogel behavior, based on multi-field effects, is developed to simulate the swelling and shrinking of these fascinating bio-materials, and it is termed the multi-effect-coupling pH-stimulus (MECpH) model. This model accounts for the ionic fluxes within both the hydrogel and solution, the coupling between the electric field, ionic fluxes, and mechanical deformations of the hydrogel. The main contribution of this model is to incorporate the relationship between the concentrations of the ionized fixed-charge groups and the diffusive hydrogen ion, which follows a Langmuir isotherm, into the Poisson-Nernst-Planck system. To validate this MECpH model, one-dimensional steady-state simulations under varying pH solution are carried out via a meshless Hermite-Cloud methodology, and the numerical results are compared with available experimental data. It is shown that the presently developed MECpH model is accurate, efficient, and numerically stable.

A Dynamic Model of Polyelectrolyte Gels

“…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.…”

2D simulation of the deformation of pH-sensitive hydrogel by novel strong-form meshless random differential quadrature method

“…Also, the osmotic pressure is applied normal to the hydrogel thickness such that the stress in the direction normal to the hydrogel cross-section is assumed to be negligible. The basic model to solve the 2D hydrogel domain can be found in [5,19]. Figure 3 shows the schematics of hydrogel and solution domains, where L , W and R are the hydrogel length, width and boundary radius, respectively.…”

“…After computing the concentration of H + ions, the other ionic concentrations were computed by Donnan membrane theory and subsequently the osmotic pressure is computed. Li et al [5,6] developed a chemo-electro-mechanical model using Poisson-NernstPlank (PNP) equations by incorporating the relationship between the concentrations of ionized fixed-charge groups and the diffusive hydrogen ion using Langmuir isotherm. They also validated the model by 1D simulation via the meshless Hermite-cloud method.…”

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

“…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.…”