Sensors and Actuators B 124 (2007) 6–11

Charge quantity as a sole factor quantitatively governing
curvature of Selemion
Hirohisa Tamagawa ∗ , Fumio Nogata, Minoru Sasaki
Department of Human and Information Systems, Faculty of Engineering,
Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan
Received 2 August 2006; received in revised form 21 November 2006; accepted 21 November 2006
Available online 13 December 2006

Abstract
It was reported previously that the curvature of largely dehydrated silver-plated Selemion had a quantitatively direct correlation to the charge
given to it, as long as the redox reaction of silver layers was induced. It was interpreted such that the control of charge quantity given to Selemion led
to the precise control of its bending curvature, which was a quite preferable characteristic for the actuator. On the other hand, it was found previouslythat the curvature of Selemion was largely influenced by the environmental humidity. Therefore, such a quantitative correlation between the charge
quantity and curvature might change once the environmental humidity changes. This paper discusses the limits of validity of this correlation. We
derived a conclusion that the Selemion curvature was solely governed by the charge quantity, despite the occurrence of significant alteration of
Selemion’s electric property in accordance with environmental humidity change. Based on this conclusion, we further proposed a mathematicalmodel which related the charge quantity with the Selemion bending curvature.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Selemion; Actuator; Curvature; Charge; Redox reaction

1. Introduction
Fabricating a practical polymer actuator has been an attractive theme these years [1–13]. Ion exchange polymer membranes
have been regarded as a promising polymer material for fabricating the bending mode actuators. For instance, it was foundthat one of ion exchange polymer membranes called Nafion(DuPont) exhibited bending upon a small applied voltage, when
it was sandwiched by thin metal layers and in the hydrated state[2–6,9–10,13]. Later, other types of ion exchange polymer membranes were found to exhibit large bending, too [10,12]. Amongthem, we have studied the bending characteristics especially of
Selemion (Asahi glass Co. Ltd., Japan) [14–18].
Largely dehydrated silver-plated Selemion exhibits precisely
controllable bending behavior under applied voltage [14,17,18].
Previously, we found that its bending curvature was quantitatively governed by the charge quantity given to it, as longas the redox reaction of silver layers on the Selemion sur-∗ Corresponding author. Tel.: +81 58 293 2529; fax: +81 58 293 2529.

E-mail address: tmgwhrhs@gifu-u.ac.jp (H. Tamagawa).
0925-4005/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.snb.2006.11.038

faces was induced [17,18]. It was interpreted such that theapplication of quantitatively controlled charge to Selemion
resulted in its quantitatively controllable bending curvature. It
is a quite preferable characteristic for the purpose of employing Selemion as an electrically controllable polymer actuatormaterial.
For the precise control of Selemion bending, the large dehydration (not complete dehydration) treatment to Selemion isnecessarily employed. Only a minute quantity of water isessential to be retained in Selemion [17,18], contrary to ourconventional treatment that the ion exchange membrane should
be largely hydrated for this sort of experiment. However, we
reported that such a largely dehydrated Selemion bending curvature was quite susceptible to the environmental humidity [15].
A practical actuator should not be largely influenced by the environmental conditions, otherwise it will results in an improper
operation.
This paper addresses the limits of validity of quantitative
correlation between the Selemion curvature and the quantity ofcharge given to it under the influence of environmental humidity change and discusses if the Selemion bending is precisely
controllable under the varying humidity conditions.

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Fig. 1. (a) Structure of specimen. (b) Experimental setup for measuring the Selemion tip displacement.

2. Specimen preparation
The surfaces of Selemion containing –SO3 H groups, witha thickness of 140 ␮m, were roughened with sandpaper. The
surfaces were plated with silver by the silver mirror reaction,
where the plating procedure is detailed in ref. [11]. It was washedwith water and stored in a desiccator so as to be dehydrated.
3. Measurements
The curvature of Selemion was measured by the following
procedure. Before starting measurement, Selemion was cut into
strips with a dimension of 20 mm × 2 mm × 140 ␮m (Fig. 1(a)).
This strip shape Selemion was left in the air of well controlled
humidity for a few hours so that it could absorb a minute quantityof water from the air. After the completion of water absorption,
this Selemion strip was horizontally clamped with electrodes as
illustrated in Fig. 1(b), where the top and bottom electrodes
were designated as negative and positive electrodes, respectively. Upon a given voltage, the tip displacement of Selemion
was measured as a function of time with a laser displacement
meter. The tip displacement data was converted into the curvature by the same computational procedure as employed in ref.
[11].
4. Result and discussion

voltage (V) increasing from 0 to 1200 mV at a rate of 15 mV s−1
by the power supply in the air with the humidity (H) of 70, 80 and
90%. Fig. 2 shows V versus I, where I was obtained as the current per 1 mm-width of Selemion strip. Namely, the measured
data of current was divided by the width of Selemion strip. I
decreased with a decrease of H. This trend must be caused by
the decrease of ion concentration in the Selemion due to thedecrease of water contained in Selemion, resulting in a decreasein charge flow rate. Namely, the electric property of Selemion
was altered with the change of humidity. However, an abrupt
increase of I was observed around at V = 700 mV irrespectiveof H. At the same time, the surface of the Selemion strip connected to the positive electrode blackened around V = 700 mV,
irrespective of H. The blackened surface suggests the creationof Ag2 O by the reaction of 2Ag + (1/2)O2 → Ag2 O [15,16].
Once the polarity of 700 mV applied voltage was reversed, theblackened surface returned to the original white surface. The
reoccurrence white surface suggests the creation of Ag by thereaction Ag2 O → 2Ag + (1/2)O2 . These observations strongly
suggest that the silver redox reaction started occurring aroundV = 700 mV.
4.2. Correlation of charge versus curvature
At H = 90%, the charge (Q) dependence of curvature (C) of
Selemion was obtained under a constant V value of 1000, 1100
and 1200 mV, that was above the voltage at which the redox

In order to see if the bending curvature of Selemion was
controllable by the charge quantity given to it under varying environmental humidity conditions, we measured the timedependence of Selemion curvature, current and charge, in the
air with humidity 70, 80 and 90% upon the applied voltage.
4.1. Occurrence of Ag redox reaction
As touched upon earlier, the predominance of charge quantity to the bending curvature of Selemion emerges, only when
the redox reaction of silver layers on the Selemion surfaces is
induced. Before making measurement of Selemion curvature, it
was necessary to determine the voltage in need for the inductionof redox reaction of silver. Firstly, current (I), bending curvature(C) and charge (Q) of Selemion were measured under the applied

Fig. 2. Voltage vs. current of Selemion in the air of humidity H = 70, 80 and
90%.

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Fig. 3. Charge vs. curvature of Selemion under a constant applied voltage of
V = 1000, 1100 and 1200 mV.

reaction started occurring.
 Q was calculated by the numericalcomputation from Q = I dt. Fig. 3 shows Q versus C, andirrespective of the applied voltage, all curves fall on the almost
same linear line. It is interpreted as the curvature C is governedby the charge Q. It is a quite useful property for the actuator,
since the curvature is precisely controllable merely by the control of charge. However, such a simple correlation might break
down, if the environmental humidity changes. Such a concern
was brought up due to the experimental fact that at least the electric property was heavily influenced by the humidity as seen in
Fig. 2. Fig. 4 shows the influence of humidity on the curvatureof Selemion investigated under a constant V of 1000 mV. All
curves fall on the almost same linear line irrespective of humidity, although the electric property of Selemion was largely alteredin accordance with the humidity. With this result in mind alongwith the result given in Fig. 3, we can derive the conclusionthat the curvature of largely dehydrated silver-plated Selemionis governed purely by the quantity of charge.
Previously, we proposed a bending mechanism of Selemion[16]. That bending mechanism rests on the creation and loss ofAg and Ag2 O on the Selemion surfaces by the redox reactionof 2Ag + (1/2)O2 = Ag2 O. Now, we discuss if our experimental
observation so far shown agrees with that bending mechanism.
Firstly, we consider solely the redox reaction of Ag andAg2 O. The quantity of Ag and Ag2 O created and vanished by
the redox reaction has a quantitatively direct correlation to thecharge quantity. For instance, the creation of Ag is represented
by Ag+ + e− → Ag. Namely, the creation of one Ag atom takes

Fig. 4. Charge vs. curvature of Selemion under a constant applied voltage of1000 mV in the air of humidity H = 70, 80 and 90%.

one electron exactly. Therefore, the quantity of charge is directly
associated with the quantity of Ag and Ag2 O created and vanished, as long as the whole charge flowing through the Selemion
body is involved in the silver redox reaction.
The conclusion we derived earlier in this paper is that what
determines the Selemion curvature is merely the quantity ofcharge. Since the quantity of charge is translated into the quantity of Ag and Ag2 O created and vanished as described here, it
is concluded that the quantity of Ag and Ag2 O created and vanished determines the Selemion curvature. This conclusion agrees
with the bending mechanism we proposed previously, since thatbending mechanism claims that the Ag and Ag2 O creation andloss cause the Selemion bending [16].
How the quantity of Ag and Ag2 O created and vanished determines the Selemion curvature is detailed in the next section,
too.
4.3. Bending mechanism of Selemion
Prior to explaining the bending mechanism of Selemion we
proposed previously, we would like to show the widely accepted
existing bending mechanism for the commonly studied ion
exchange polymer membranes as below.
One of ion exchange polymer membranes, called Nafion,
exhibits bending upon an applied voltage, when it is sandwiched by two thin metal layers just like Selemion illustrated
in Fig. 1 and highly hydrated. Although the bending mechanism of Nafion has not been completely elucidated yet, it has
been widely believed that the shift of hydrated ions containedin Nafion causes its bending [16]. Once the voltage is applied
to Nafion, the hydrated mobile ions inside Nafion are dragged
toward one side, and such an ions shift generates the volume
gradient in the thickness direction, resulting in the bending(Fig. 5(a)). However, at the same time, it is believed that the
backward flow of water molecules occurs, causing the bending relaxation (Fig. 5(b)) [16]. This bending mechanism cannot
explain the bending of Selemion, since Selemion never exhibits
the bending relaxation.
Now, we explain the bending mechanism of Selemion
we proposed previously [16]. Selemion bends in the positive electrode direction. Whenever the Selemion was bent,
we observed the occurrence of the following reactions
2Ag + (1/2)O2 → Ag2 O and Ag2 O → 2Ag + (1/2)O2 at the
Selemion surfaces which were connected to the positive andnegative electrodes, respectively [16]. First, we focus on thereaction 2Ag + (1/2)O2 → Ag2 O occurring at the Selemion surface connected to the positive electrode. The surface of Selemionis quite roughly concave and is coated with silver atoms as illustrated in Fig. 6(a). When the oxidation reaction is induced at thesurface connected to the positive electrode, silver atoms associate with one another through the intermediary of an oxygen
atom to form Ag2 O. Formation of Ag2 O narrows the neighboring surfaces of Selemion, surface-␣ and surface-␤, which
are illustrated in Fig. 6(b), causing the gap narrowing. At the
Selemion surface connected to the negative electrode, the opposite phenomenon must be induced, that is the gap widening by thereaction Ag2 O → 2Ag + (1/2)O2 . Consequently, the redox reac-

H. Tamagawa et al. / Sensors and Actuators B 124 (2007) 6–11

9Fig. 5. (a) The bending of Nafion caused by the volume gradient in its thickness direction due to the shift of hydrated mobile ions. (b) The bending relaxation of
Nafion due to the backward flow of hydration water molecules.

tion results in the bending of Selemion in the direction of positiveelectrode. This bending mechanism describes that the bending
curvature of Selemion is directly related to the quantity of Ag
and Ag2 O created and vanished, in other words the quantity ofcharge. Next, we propose a mathematical model of Selemion
bending which associates the curvature with the quantity of Ag
and Ag2 O created and vanished (or quantity of charge).
4.4. Mathematical model of Selemion bending
It is assumed that the angle δ is generated by the onetime
reactions 2Ag + (1/2)O2 → Ag2 O and Ag2 O → 2Ag + (1/2)O2
which occurred on the Selemion surfaces at the right end ofelectrodes – the original point “o” – as illustrated in Fig. 7(see Fig. 1(b) as well). Namely, it is assumed that the onetime redox reaction corresponds to the generation of angle δ.
Actual bending phenomenon is accompanied by a number ofredox reactions. Therefore, we assume the uniform distributionof onetime redox reactions at N individual positions (N  1) on
the Selemion surfaces which produces the bending of Selemion
as illustrated in Fig. 8(a). Selemion bends, since the angle δis formed at individual redox reaction positions as illustrated
in Fig. 8(a). Since N is an extremely large number, we canregard the thick solid line representing Selemion illustrated inFig. 6. Bending mechanism of Selemion. (a) Surface structure of Selemion. (b)Gap narrowing at the concave point of Selemion surface by the oxidation ofsilver atoms.

Fig. 8(a) as a smooth curve in a macroscopic view represented
by the dashed thick line as illustrated in Fig. 8(b). Defining
angle θ brings θ/N (=2δ) as the central angle of individual sector form as illustrated in Fig. 8(b). In this case, the curvatureof Selemion, ρN , is given by ρN = 1/rN = [(θ/N) × N]/L = θ/L,
where rN is the curvature radius and L is the length of Selemion
from the original point “o” to the free end. If totally 2N redox
reactions occurs at 2N positions on the Selemion surfaces,
ρ2N is given by ρ2N = 1/r2N = [(θ/N) × 2N]/L = 2(θ/L) = 2ρN .
This model is extended to the occurrence of nN reactions at nN positions on the Selemion strip, and ρnN
is given by ρnN = 1/rnN = [(θ/N) × nN]/L = n(θ/L) = nρN ∝ n(ρN = constant) ∝ nN (N = constant). This equation is interpreted
in a way that the curvature, ρnN , is proportional to the numberof reactions, nN, in other words, the number of Ag and Ag2 O
creation and loss or the number of charge involved in this reaction. This conclusion agrees with our experimental observations

Fig. 7. Mathematical model of Selemion bending with the coordinate system,
where the original point “o” is defined as the right end of electrodes clamping
Selemion. Onetime reduction and oxidation reactions occur at the top and bottom
surfaces of Selemion, respectively, at “o”.

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of charge quantity can lead to the precise control of Selemion
bending curvature. Based on this finding that the curvature has
a quantitative dependence on the quantity of charge, we could
put forward a quantitative mathematical model associating the
Selemion bending curvature with the quantity of charge.
Acknowledgment
This research was conducted under the financial support by
The Joint Research Development Study on Smart Material Systems.
References

Fig. 8. (a) Mathematical model of Selemion bending, when the onetime redox
reaction occurs at N positions on the Selemion surfaces at the regular interval.
(b) Central angle, θ, formed by onetime redox reaction occurring at individual
N positions.

shown in Figs. 3 and 4. Furthermore, the occurrence of no bending relaxation of Selemion, which is touched upon in Section
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Without the induction of redox reaction, Selemion can exhibit
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5. Conclusion
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Biographies
Hirohisa Tamagawa obtained PhD from Tokyo Institute of Technology, Japan
in 1997. He is a research assistant in Gifu University in Japan and currently
involved in the research on the biomaterials, especially polymer gels.

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Fumio Nogata obtained PhD from Tohoku University, Japan in 1988. He isa professor in Gifu University, Japan. Although his early interest was in thenondestructive test, currently he is involved in the development of new medical
diagnosis methods employing ultrasound.
Minoru Sasaki obtained PhD from Tohoku University, Japan in 1985. He is a
professor in Gifu University, Japan and currently involved in the research on
robotics and control theory.