<title>Relationship between the volumetric strain and the pH in ionic polymeric gels</title>

Abstract

A theoretical model is presented for the derivation of a mathematical relationship between the volumetric strain, c, of an ionic polymeric gel and its pH. The model presented also applies to polyelectrolytes in aqueous solutions. The derivation uses an expression for the total electrostatic free energy per single polyelectrolyte molecule which involves a quasi-Debye curvature, the local absolute temperature, the geometric features of polyelectrolyte molecule, the dielectric constant of the gel as well as the local ionic concentrations for the fixed and the mobile charges. The gradient of the free energy with respect to the number of fixed ions is then related to the pH, i.e., the local concentration of hydrogen ions H+, the absolute temperature T and the degree of ionization a which is defined as the ratio of the number of moles of 11+ to the number of moles of the ionizable groups fixed to the ionic gel network. Subsequently, the gradient of the free energy is related to the volumetric strain, v' of the ionic gel network. The relationship obtained between the pH and the volumetric strain, v' of the ionic gel is highly nonlinear and does depict a trend compatible with experimental evidence on rapid phase transformation in ionic gels at certain critical values of the pH. For infinitesimal strains, the derived expression between the pH and the volumetric strain fv is shown to become approximately linear. 2-INTRODUCTIONIonizable polymeric gels composed of ionic networks of randomly cross-linked macromolecules of polyelectrolytes have recently been investigated as electrically controllable artificial muscles and smart materials for medical, robotic, and other engineering applications. A polymer gel is defined as a cross-linked polymer network swollen in a liquid medium. These gels possess an ionic structure in the sense that they are generally composed of a number of fixed ions pertaining to sites of various polymer cross-links and segments and mobile ions (counter ions) due to the presence of a solvent which is electrolytic. Figure 1 below depicts a very simplistic molecular picture of such ionic gels. Katchalsky [1], and Kuhn[2] originally reported on the possibility that certain copolymers . can be chemically contracted or swollen like a synthetic muscle (pH muscle) by changing the pH of the solution containing them. As originally reported by Kuhn, Horgitay, Katchalsky, and Eisenberg [3], a three-dimensional network, consisting of polyacrylic acid, can be obtained by heating a foil of polyacrylic acid containing a polyvalent alcohol such as glycerol or polyvinyl alcohol. The resulting three-dimensional networks are insoluble in water but swell enormously in water on addition of alkali and contract enormously on addition of acids. Linear reversible dilations and contractions of the order of more than 1000 percent has been observed for ionic gel muscles made with polyacrylonitrile (PAN) fibers (Shahinpoor and Mojarrad [4]). Furthermore, as reported recently by Li and Tanaka [5], the structural deformation (swelling ...

<title>Nonhomogeneous large-deformation theory of ionic polymeric gels in electric and pH fields</title>

“…A recent paper by Shahinpoor [25] has presented an analysis on the dependence of volumetric strain in (8) where a and b are material parameters that generally depend on the activity coefficients, degree of ionization, temperature, Debye curvature, dielectric constant and molecular dimensions of the gel as discussed by Shahinpoor [25]. Current experimental data (see for example Tanaka, et.al., [26] and Umemoto, Okui and Sakai [27]) on the dependence of either linear strain c or volumetric strain v ionic gels as a function of pH indicate that there exists a phase transition in which the gel undergoes large expansion or contraction as the pH of the solvent and subsequently the ionic gel itself is changed.…”

“…1916 Q being the current i through the gel strip across its thickness. Equation (25) can be readily solved to yield Q=Cgv[1xP. ((t/RgCg))] (26) assuming at t=O, Q=O.…”

“…No inductive properties may be attributed to ionic gels at this stage of investigation. However, it is quite conceivable that an ionic gel possesses a capacitance Cg and a resistance Rg Note that the Kirchhoff's law can be written for a gel strip in the following form: V C1 Q+ RgQ =i, (25) where v is the voltage across the thickness of the gel, and Q is the charge accumulated in the gel, 48/SPIE Vol. 1916 Q being the current i through the gel strip across its thickness.…”

<title>Design and modeling of a novel spring-loaded ionic polymeric gel actuator</title>

“…[7], ICIM'92 [8] and Wada 9. Applications particularly relevant to army research have been presented by Crowson and Ghirardelli [10], Crowson and Anderson [11], Wu [12] and Anderson, Crowson and Chandra [13]. For further references see [14]- [20].…”