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\confshortname{DSCC 2009} \conffullname{2009 ASME Dynamic Systems and Control Conference
and Bath/ASME Symposium on Fluid Power & Motion Control} \confdate{12-14}
\confmonth{October} \confyear{2009} \confcity{Hollywood,
California} \confcountry{USA}


\title{Modeling electric currents in the electrodes of IPMC}

%%% first author
\author{Deivid Pugal
    \affiliation{
    Active Materials and Processing Laboratory\\
    Mechanical Engineering Department\\
    University of Nevada, Reno\\
    Reno, NV, 89557\\
    Email: pugald@unr.nevada.edu
    }
    \affiliation{
    IMS Lab\\
    Institute of Technology\\
    Tartu University\\
    Estonia\\
    }
}

%%% second author
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\author{Alvo Aabloo
	\affiliation{
    IMS Lab\\
    Institute of Technology\\
    Tartu University\\
    Estonia\\
    Email: alvo.aabloo@ut.ee
    }
}

\author{Kwang J. Kim\thanks{Address all correspondence to this author.} \\
    \affiliation{Active Materials and Processing Laboratory\\
    Mechanical Engineering Department\\
    University of Nevada, Reno\\
    Reno, NV, 89557\\
    Email: kwangkim@unr.edu
    }
}

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%%% ABSTRACT %%%
\begin{abstract}
This paper presents a Finite Element Analysis (FEA) of an ionic 
polymer-metal composite (IPMC) material. The IPMC materials are 
known to bend when electric field is applied on the electrodes and
also produce a potential difference on the electrodes when bent.
Several authors have used FEA to describe that fenomenon and therefore
rather precise basic Finite Element (FE) models already exist.
However, the focus of the current study is to model the electric
currents in the electrodes. The basis of the calculations is the
Ramo-Shockley theorem, which has been used in other areas of physics
to describe the currents in a circuit due to a charge movement in a
media. We have used the theorem to calculate the current density
in the continuous electrodes of IPMC due to the ion migration
in the backbone polymer. Along the current densities we are able
to calculate exact voltage on the electrode at a given time moment.
In this stage, the electrodes are modeled as static domains, i.e.
no dynamic resistance changes have been considered. Although the
work is still in progress, we have got some physically reasonable
results to demonstrate and a section of the paper considers the
extendibility of the model. Those results have already been
previously published. However, in the paper we also consider
some possible applications of the developed model and also couple
of  concerns in regard to modeling the whole IPMC in three
dimensional domain with FE method.
\end{abstract}

\section*{INTRODUCTION}

Electroactive polymer actuators have gained a lot of attention in
many fields such as robotics and micro electronics. The advantages
of EAP actuators are relatively simple mechanics and noiseless actuation.
Additionally some EAPs, such as IPMCs\cite{shahinpoor2001ipm}, are
able to function in aqueous environments. Those qualities make the
materials possible to use as so called artificial muscles. In this
paper we consider three dimensional time dependent simulations of
IPMC type materials with the Finite Element Method.

One of the most important qualities of IPMC materials is relatively
large amplitude bending in response to electrical stimulation. An
ion exchange polymer membrane, such as Nafion, is covered
with metal layers. The metal is typically platinum or gold. During
the fabrication process the polymer membrane is saturated with certain
solvent and ions. When voltage is applied to the metal electrodes,
the ions start migrating due to the applied electric field. Migrating
ions usually drag some solvent with them, causing expansion and contractions
respectively near the surface layers. That in turn causes bending
like actuation of IPMC sheet. 

To predict the actuation, a good understanding of underlying processes
must exist. Electrostatics, mass transfer and mechanical effects must
be taken account to get a minimal functional base model which could
predict actuation. Usually two dimensional time dependent model would
be enough to get reasonable results. However, in this paper we consider
three dimensional model of IPMC. This allows to take into account
surface resistance changes for whole area of the metallic layer. Some
authors\cite{wallmersperger2004cce,nematnasser2006mer,branco2006dcm,analysisofelec}
have already simulated mass transfer and electrostatic effects. We
used similar approach in our model. Toi\cite{toi2005fea} has shown
a Finite Element model including viscosity terms in transportation
processes explicitly. The simulation is performed as time dependent
and for three dimensions. However, the basis of the described model
is a rectangular beam with 2 pairs of electrodes. 

In current work we do not explicitly calculate the bending of the
material, rather the research puts emphasis on the study of surface
currents and the voltage drops in the electrodes. The analytical surface
resistance model is derived by Chen\cite{acontrolorient} for 2D domain.
The model proposed in the current paper considers simulations both
in 2D and 3D domain. The base model is similar to the ones described
above. However, the model for a metallic surface layer is introduced,
i.e the electric currents and the voltage drop have been considered
as well.

\bibliography{paper-pugal-2009-dscc}

\end{document}