Mechanoelectric Transduction in Ionic Polymer-Metal CompositeSupplemental Material

1. Experimental set-up

Experiments were performed for validation of both the ionic and electrostatic model. IPMC

electroded with platinum on both sides was used for experimental purposes. The dimension of

the sample used was 50 mm (length) X 10 mm (width) X 0.2 mm (thickness). Typical thickness of

platinum layer is 1 to 5 microns with the average particle size of 47 nm that has been reported

previously [1]. IPMC samples were vibrated using a shaker assembly (TIRA Vibration System,

TV52110) that was excited using a sine wave (open-loop) signal with the amplitude of 1 V and

frequency of 10 Hz. The amplitude of vibration was fixed to 0.5 inch. Data acquisition purchased

from National Instruments (SCB 68) was employed for the measurement of the voltage on the

sample. Simulation was performed in MATLAB/SIMULINK.

Fig. A: Experimental set-up schematic for parametric study using Electrostatic-Ionic model to analyze mechanoelectric effect in IPMC.

2. Model parameter definition

Table A: Defining parameters in electrostatic modelParameter Definition Units Representative Value

Me Equivalent weight of Nafion® kg/mol 1.2ρd Density of dry membrane kg/m3 2075

Δ Fractional volume change of % 69.7

membrane due to water absorptionΔ ’ (NAVi)/( Me/ ρd) 0.0708

β Constant m2.mol/kg 1.08 X 10-17

γ Specific surface energy J/m2 0.0065NA Avagadro’s constant mol-1 6.022 X 1023

K Boltzmann’s constant J/K 1.38066 X 10-23

T Absolute temperature K 300Vi Volume of a single ion exchange site m3 6.8 X 10-29

ρw Density of water kg/m3 1000

Table B: Defining parameters in ionic modelParameter Definition Units Value

F Faraday’s constant C/mol 96487R Gas constant J/mol/K 8.3143Y Young’s modulus Pa 50 X 106

h Thickness μm 100D Ionic diffusivity m2/s 3.32 X 10-11

C- Anion concentration mol/m3 1091κe Dielectric permittivity F/m 1.88 X 10-3

Ψ Coupling constant J/C 104

3. Cluster formation in IPMC

Nafion®, manufactured by Dupont de Nemours, is one of the most widely used proton

exchange membrane. The membrane consists of hydrophobic fluorocarbon and hydrophilic ionic

cluster. Anions are attached to the polymer chain while cations are free to move upon hydration

(Choi et al., 2005). Hydrophilic group forms a pendent like structure in the membrane. Upon

hydration water molecules penetrate inside pendants, resulting in a reverse micelle structure as

illustrated in Figure B (Liu et al., 2006). The structure of Nafion® is shown in Figure B.

Fig. B: Nafion® is perfluorinated polymer with ionic functional group. Illustration showing reverse micelle structure of clusters inside Nafion®. These clusters are formed due to the hydrophobic

SO3- group.

4. Cross-section SEM of IPMC showing different IPMC layers

Electrode layer

Interfacial layer

Polymer layer

Fig. C: Cross-section of the IPMC showing the electrode, the interfacial and the polymer layers.

The cross section of the IPMC is shown in the figure. This shows the polymer layer, the electrode layer and the interfacial or composite layer that is resultant of the electroless deposition. All three layers are crucial and have impact on the mechanoelectric transduction. These layers are accounted for in the model as impedance.

References

[1] M. Shahinpoor and K. J. Kim, Smart Mater. Struct. 9, 543 (2000).