A theoretical prediction of the ions distribution in an amphoteric polymer gel

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Abstract

In order to obtain the optimum design for the realization of a high performance gel actuator, the ion distribution profiles in the gel are obtained theoretically by solving the Poisson–Bolzmann equation. Regardless of the types of ions (mobile cation, immobile cation, mobile anion and immobile anion), ion concentration is found to change abruptly at the electrode–gel interface. Based on this result, we found that gel could be deformed only in this interface region. Then we concluded that: (i) the use of an amphoteric gel rather than a cationic or an anionic gel; (ii) applying high voltage to gel; and (iii) the import of the electrode–gel interface as many as possible are promising strategies for the design of practical use gel actuator.

Introduction

Application of the polymer to the actuator such as an artificial muscle was pioneered by Kachalsky et al. [1]. They built a mechanochemical turbine made of collagen in LiBr solution. In 1970s, the phase transition of polymer gel characterized by its abrupt high volume change was found by Tanaka [2]. Then the polymer gels attracted a broad attention. Especially, this material was considered to be promising material to imitate the muscle. Therefore, the intensive investigations on polymer gel properties have been performed since then, which clarified that the phase transition could be induced by a number of different types of environmental stimuli such as type of solvents, pH temperature, electric field etc. [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13].

Ionic gels show the higher order of volume change ratio rather than neutral gels on account of the existence of ions in the gel network, and some ionic gels shows thousand times of volume change ratio. The deformation of such polymer gels is extremely high, compared with other materials such as piezoelectric materials. This unique property is considered to be applicable to a numerous kinds of industrial products such as drug delivery devices, soft but largely deformable actuators etc.

Our research project aims at application of electrically driven polymer gel to the high deformation actuator, since the electrical actuation is a quite convenient way as compared with solution exchange, pH change and etc. As described above ionic gels exhibit a larger deformation compared with neutral gels. Therefore we are going to design ionic polymer gel for our purpose. Tanaka et al. reported that partially hydrolyzed acrylamide could be deformed significantly by applying electric field, since acrylamide groups were converted to acrylic acid groups [13]. However, the gel actuators for practical use have not been synthesized successfully yet. Mainly two problems remain to be overcome; first, slow response of the polymer gels to the environmental stimuli, second, fragile structure of gels. The former problem can be overcome to some extent by the scaling down of unit gel size, since the volume change heavily depends on the diffusion of the solvent. The latter can also be overcome to some extent by adding high amount of crosslinkers. However, users need right size actuators, and adding crosslinkers results in slow response time. For the first step, we focus on the former problem as to how the response time can be improved.

For the actuation of an ionic gel, the distributions of ions contained in a gel network are expected to play a key role. Thus, it is quite important to obtain the ion distributions theoretically in order to obtain the required gels. And as an actuator material, homogeneously deformable gel is preferable than heterogeneously deformable one (Fig. 1). Cationic or anionic gel may display the heteregeneous deformation, since its electronic structure is heterogeneous. For example, cationic gel contains the immobile cations fixed on the polymer network and the mobile anions as shown in Fig. 2. Without electric field, both cations and anions distribute homogeneously. But by applying electric field, the mobile anions are attracted towards one side, which results in the heterogeneous ion distribution. This phenomenon must cause a heterogeneous gel deformation. This is also the case with an anionic gel. Thus, amphoteric polymer gel is preferable than a cationic or an anionic gel. Ion distributions in an amphoteric gel is expected to be symmetric. Namely, even the mobile anions are attracted towards one side by electric field, the same amount of cations are expected to be attracted towards the other side, and then the symmetric ion distribution is expected from the macroscopic view (Fig. 3). This phenomenon must cause a homogeneous deformation. Therefore, in this paper, we show the analytical model for the ions distribution in an amphoteric polymer gel, and suggest a promising design for the high performance gel actuator.

Section snippets

Analytical model for gel potential

The derivation method of the potential in an amphoteric polymer gel is explained. The coordinate system is set to the cylindrical polymer gel, and for simplicity, the potential behavior is supposed to be anti-symmetric in relationship to z=0 as shown in Fig. 4. Since the potential behavior is anti-symmetric, only the derivation methods of the potentials in region I, II and III are explained. It is not necessary to derive the potential of region IV and V.

If the concentration of the mobile anion

Results and discussions

Fig. 9, Fig. 10 show the z dependence of potential and each ion concentration. Through total amount of MC and MA should be same as that of IC and IA, these results do not fulfill that requirement. Therefore, these results are not so accurate quantitatively. However, based on these results, we cold qualitatively predict the optimum design for the electrically driven gel actuators. Hereafter imagine that IC, MA, IA and MC are CH2NH3+, OH, COO and H+, respectively. Then chemical reactions are

Conclusion

We obtained the potential and ion concentration behavior theoretically, and predicted the expected properties of gel actuator. It was pointed out that the variation of the mobile ion distribution gives rise to the formation and the breaking of the hydrogen bonding. Namely if we can build an actuator by use of gel whose volume change is dominated by hydrogen bonding, we can deform it deliberately by adjusting the applied voltage. In addition to the use of such a kind of gel the importance of

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