Behaviour of Anionic and Cationic Hydrogels

Abstract

Ionic polyelectrolytic gels in an aqueous solution, i.e. hydrogels -also known as smart materials -react to different kinds of environmental changes, e.g. chemical, electrical, mechanical, and thermal stimulation. As a reaction, they show enormous swelling capabilities resulting from the delivery or uptake of ions and solvent. These properties make them attractive for chemo-electro-mechanical energy converters and for the application as actuators or sensors. The applied multi-field formulation consists of the chemical, electrical, and mechanical field and is capable of giving local concentrations, electric potential distributions and displacements. In this excerpt the reaction of a modelled hydrogel finger gripper under electrical stimulation is shown. The swelling ratio is assumed to be in the regime of small volume changes and corresponding displacements.

Recent advances in various stimuli-responsive hydrogels: from synthetic designs to emerging healthcare applications

“…165 pH sensitive hydrogels can be divided into two types according to the type of the existing functional moiety in the hydrogel: one is cationic and the other is anionic. 166 The swelling and shrinking performances of anionic hydrogels mainly depend on the dissociation of the anionic functionalities of the hydrogel which breaks only when the adjacent medium pH surpasses the acid dissociation constant (p K a ) of the anionic hydrogel concerned. The hydrogel become negatively charged by eliminating protons.…”

Direct interaction approximation for non-Markovianized stochastic models in the turbulence problem

“…Here we apply Keller's perturbation procedure [10] to the second order equation governing the wave propagation in a random medium,…”

“…The DIA procedure is then applied to the problem of wave propagation in a random medium -this exploration is of relevance to the propagation of radio waves through the ionosphere and laser beams through the atmosphere (Tatarskii [7], Chernov [8]) 2 . This problem is described by a stochastic differential equation with the characteristics of the medium represented by stochastic coefficients (Bourret [9], Keller [10], van Kampen [11], Shivamoggi et al [12]), d 2 E dξ 2 + k 2 [1 + µ(ξ)]E = 0 (1) where E is the electric field of a monochromatic wave, k is the wavenumber of the wave, µ(ξ) represents the fluctuations in the refractive index of the medium (which is assumed to be a centered random function of position), and ξ is the distance measured along the propagation direction.…”

“…4 )kt. (A.52) (A.52) agrees with the previous results (A.20) and (A.36b) from the first and second approximations, respectively, except for the slight numerical discrepancy with the wavenumber shift.A.2 First Order System for the Non-Markovian Stochastic Model EquationWe may write the second order equation (A.6) as a system of first order equations by introducing, s[10] perturbation procedure, eqn(A.54) leads to the following matrix equation, have f = e −αt (d 1 cos βt + d 2 sin βt). for c 1 and c 2 from (A.60), we haveα = σ 2 λ 4(λ 2 + 4ν) β = ν − σ 4 λ 2 16(λ 2 + 4ν) 2 − σ 2 λ 2 4(λ 2 + 4ν) (A.67)In the large-λ limit, (A.66) becomesf ∼ e − σ 2 4λ t (a 1 cos βt + a 2 sin βt), β ≈ ν − σ 2 (A.68)On the other hand, in the small-λ limit, (A.66) becomes…”