Micro-Electro-Mechanics of Ionic Polymeric Gels As Electrically Controllable Artificial Muscles (1995)

Ionic polymeric gels are three-dimensional networks of cross-linked macromlecular polyelectrolytes that swell or shrink in aqueous solutions on addition of alkali or acids, respectively. Reversible dilation and contraction of the order of more than 1000 percent have been observed in our laboratory for polyacrylonitrile (PAN) fibers. Furthermore, it has been experimentally observed that swelling and shrinking of ionic gels can also be induced electrically. Thus, direct computer control of large expansions and contractions of ionic polymeric gels by means of a voltage gradient appears to be possible. These gels possess an ionic structure in the sense that they are generally composed of a number of fixed ions (polyions) pertaining to sites of various polymer cross-links and segments and mobile ions (counter ions or unbound ions) due to the presence of a solvent which is electrolytic. Electrically-induced dynamic deformation of ionic polymeric gels such as polyacrylic acid plus sodium acrylate cross-linked with bisacrylamide (PAAM), or poly(2-acrylamido-2-methylpropanesulfonic acid) or PAMPS or various combinations of chemically-doped polyacrylic acid plus polyvinyl alcohol (PAA-PVA) can be easily observed in our laboratory. Such deformations give rise to an internal molecular network structure with bound ions (polyions) and unbound or mobile ions (counterions) when submerged in an electrolytic liquid phase. In the presence of an electric field, these ionic polymeric networks undergo substantial contraction accompanied by exudation of the liquid phase contained within the network. Under these circumstances, there are generally four competing forces acting on such ionic networks: the rubber elasticity, the polymer-liquid viscous interactions due to the motion of the liquid phase, inertial effects due to the motion of the liquid through the ionic network, and the electrophoretic interactions. These forces collectively give rise to dynamic osmotic pressure and network deformation and subsequently determine the dynamic equilibrium of such charged networks. On the other hand there are situations in which a strip of such ionic polymeric gels undergoes bending in the presence of a transverse electric field with hardly any water exudation. Under these circumstances there are generally three competing forces acting on the gel polymer network: the rubber elasticity, the polymer-polymer affinity and the ion pressure. These forces collectively create the osmotic pressure which determines the equilibrium state of the gel. The competition between these forces changes the osmotic pressure and produces the volume change or deformation. Rubber elasticity tends to shrink the gel under tension and expand it under compression. Polymer-polymer affinity depends on the electrical attraction between the polymer and the solvent. Ion pressure is the force exerted by the motion of the cations or anions within the gel network. Ions enter the gel attracted by the opposite charges on the polymer chain while their random motions tend to expand the gel like an ionic (Fermionic) gas. Two mechanisms are presented for the reversible nonhomogeneous large deformations and in particular contraction/expansion with water exudation as well as bending of strips of ionic polymeric gels in the presence of an electric field. An analytical model is first presented for the dynamics of contraction of ionic polymeric gels with liquid exudation in the presence of an electrical field. The proposed model considers the dynamic balance between the internal forces during the contraction. These forces are assumed to be due to the viscous effects caused by the motion of the liquid, the inertial forces due to the motion of the liquid in and out of the network, and the electrophoretic forces due to the motion of the charged ions in the solvent as it exudes from the ionic polymeric gel network. The effects of rubber elasticity of the network as well as ion-ion interactions have been assumed negligible in this case compared with the inertial, viscous and electrophoretic effects. The governing equations, thus obtained are then solved exactly for the velocity of liquid exudation from within the network as a function of time and radial distance in cylindrical samples. The relative weight of the gel sample is then related to this velocity by an integral equation. This integral equation is then numerically solved to obtain a relationship between the amount of contraction as a function of time, electric field strength and other pertinent material and geometrical parameters. The results of the numerical simulations are compared with some experiment results on PAMPS contractile fibers and satisfactory agreements are observed. Next, the case of electrically-induced bending of strips of ionic polymeric gels is considered. Exact expressions are given relating the deformation characteristics of the gel to the electric field strength or voltage gradient, gel dimensions and other physical parameters such as the resistance and the capacitance of the gel strip. It is concluded that direct voltage control of such nonhomogeneous large deformations in ionic polymeric gels is possible.