Method for calculation of Young’s Modulus of IPMCs by loaded actuation experiments 

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Empirical (Black Box) Models

Based purely on the empirical responses, black-box models offer minimal insight into the governing mechanisms within the IPMC. While these models are simple in nature, they are often sample-dependent and not scalable in dimensions. One earlier method matches the responses of a transducer modeled with various parameters to measured responses. The parameters are found by fitting the modeled and measured responses. These models were first developed when there was very little knowledge of ionic polymer dynamics but a need for a model to evaluate implementation of EAPs into various possible applications. Most early models focused on the modeling of actuation.

Kanno et al. (1994)

An example of this type is the work of Kanno et al. (1994)[1] where only input and output relationships are modeled by a time-series where the parameters are determined for each transducer. This model is therefore only applicable to a particular experimental scenario and must be recomputed and used separately for other transducers, inputs and/or outputs. The tip displacement Yt of a cantilevered bender is modeled with the expression where A through E and α through δ are constants, and t represents time. The authors used experimental tip displacement data with voltage step inputs in conjunction with a least squares algorithm to determine values for the constants. First, data from experiment done with an excitation with a 1.5V voltage step was used to determine values for all of the constants. Then, the experiment was repeated with step inputs ranging from 0.5V to 1.5V, in 0.1V increments, and parameter values from A through E were determined at each voltage level. The reported values of A through E did not vary linearly with input voltage; in fact, two of the constants underwent a sign change as the input level was varied. The lack of a linear relationship suggests that ionic polymer actuator behavior cannot be modeled using a linear, time-invariant system, at least in the input range considered.

Modeling of Electric Double Layer: Bockris et al. (1963)

This modeling work which is never mentioned in the bibliographies of IPMC modeling is a very important prerequisite to modeling of polymer composite structures. It considers the interface that should be created between two media (in the case of IPMC we can interpret this as Nafion and Platinum). The electrically neutral system that occurs at the interface, at which a layer of positive charges faces a layer of negative charges, surrounded by oriented polar molecules, is called an electric double layer (EDL), (Figure 2.1) (Sparnaay, 1972). Sadeghipour et al., (1992) showed that an electric double layer is formed in IPMC at the interface between Nafion and platinum. Capacitance and the charge motion in IPMC transducers attest the presence of this electric double layer, according to one approach we present in section 2.3.3.

De Gennes et al. (2000)

Asaka and Oguro (2000) [16] had proposed an IPMC model, in which the bending response was attributed to the electro-osmotic flow in the ion gel film, taking into account only the water flow in the membrane. In the same year, de Gennes et al. (2000) [17] gave a more comprehensive model analyzing the static case. The underlying actuation mechanism was explained by the water (Solvation) dragged by the migrating ions, causing a volume differential which is responsible for the induced curvature. The polymer backbone responds to the volume differential of solvent by expanding on cation-rich region, in order to maintain the regional volume. It responds by shrinking on the opposite cation-poor region. Using linear irreversible thermodynamics based on flux-force relations, the transducer behavior was described by the standard Onsager formulation.

Comparative Explanation of IPMC Actuation Mechanisms with Different Physical Models

Successive photos of actuation help to investigate the mechanisms underlying actuation (Figure 2.7, presented with a zoom at the tip on the right hand side). Under a DC step voltage excitation, the sample quickly bends from A to B, and then slowly relaxes back to C, overshooting the initial position. Upon shorting the electrodes at stage C, the sample responds by a fast motion to D followed by a slow relaxation back to E, leaving a permanent deformation.

Gray Box Macroscopic Models using Physical Laws and Empirical Parameters

Kanno and Tadokoro (1996) [20] represented the ionic polymer actuator using three stages that were connected in series, an electrical stage, a stress-generation stage, and a mechanical stage (Fig. 2.14).
For the analysis of the electrical stage, the actuator was divided into discrete, one mm long elements along its length. For the stress-generation and mechanical stages, the actuator was further divided into three layers through its thickness (two electrode layers and a Nafion layer in between). In the electrical stage, each set of elements along the length was modeled using the equivalent circuit shown in Figure 2.15; Ra an Rb are surface resistances of the actuator, Rx is the resistance of the polymer gel layer as an electric conductor. Rc and C express the characteristics of the exponential step response curve of the current, which decreases with the decreasing cation migration rate as a result of cations’ being saturated at the cathode side.

Table of contents :

List of Figures
List of Tables
1. General Review: From the Biological Muscle to the Biomimetic Actuators
1. Biological Muscle as an Actuator
2. Various Types of Biomimetic Actuators
2.1. Actuators driven by biological material
2.2. Mc Kibben Pneumatic Muscles
2.3. Shape Memory Alloys (SMAs)
2.4. Magneto-active and photo-active gels
2.5. Electro-active materials based actuators
2.5.1. Electroactive Ceramics
2.5.2. Carbon nanotubes (CNTs)
2.5.3. Electro-Active Polymers (EAPs) Electronic EAPs Electro-strictive polymers Dielectric Elastomer Actuators Ionic EAPs Poly-electrolyte gels 4 Electronically Conducting Polymers (ECPs) Ionic Polymer Metal Composites (IPMCs)
3. Ionic Polymer Metal Composites 
3.1. Historical Background of Ionic Polymer Actuators
3.2. Ion Exchange Polymers: Nafion Structure
3.3. Description and Actuation Mechanism
3.4. Relaxation Mechanism
3.5. Fabrication Methods of Ionic Polymer Metal Composites
3.6. Historical Background of Characterization
4. Conclusions
References for Chapter 1
2. General Review on Modeling of IPMC 
2.1. Introduction
2.2. Empirical (Black Box) Models
2.2.1. Kanno et al. (1994)
2.3. Physical Models
2.3.1. Modeling of Electric Double Layer: Bockris et al. (1963)
2.3.2. Tadokoro et al. (2000)
2.3.3. Nemat-Nasser et al. (2000)
2.3.4. De Gennes et al. (2000)
2.3.5. Comparative Explanation of IPMC Actuation Mechanisms with Different Physical Models
2.4. Gray Box Macroscopic Models using Physical Laws and Empirical Parameters
2.4.1. Kanno and Tadokoro (1996)
2.4.2. Newbury-Leo Equivalent Circuit Model (2002)
2.4.3. Xiao and Bhattacharya, Nonlinear Euler Bernoulli Beam Model Augmented for Eigencurvature (2001)
2.5. Discussion on Modeling of IPMC
References for Chapter 2
3. Fabrication and Morphological Characterization of IPMC 
3.1. Introduction
3.2. Fabrication of IPMC
3.2.1. General Review on Fabrication methods Surface roughening the membrane material Membrane conditioning and fabrication of the composite structure Membrane treatment with HCl or HNO3 Preparing the ion exchange solution containing metal salts Reducing the metal salt cations to metallic state under the form of nanoparticles Developing of electrode by metal coating of surface Cation Exchange Number of Cycles of Fabrication
3.2.2. Fabrication at ANIM with Conventional Electroless Plating Method Fabrication Procedure
a. Surface Roughening of the Membrane
b. Ion-exchange to Platinum
c. Primary Plating (Reduction)
d. Secondary Plating (Developing)
e. Cation Exchange Fabrication Setup Fabrication Results: Form of deposited electrodes
3.2.3. Fabrication at LISE with Plasma Treatment followed by Electroless Plating method Plasma Etching Rugosity Observation of pre-treated Nafion samples Fabrication with Electroless Plating Fabrication Results: Form of deposited electrodes Surface Dimension Measurements Introduction
a. The Concept of Dimension
b. Self Similarity
c. Box counting dimension Results of Surface Dimension Observations
3.3. Cross section of IPMC
3.4. Sheet Resistance Characterization
3.4.1. Definitions of Surface Resistance and Surface Resistivity
3.4.2. Surface Electrode Resistance Measurement Method
3.4.3. Surface Resistivity Maps Obtained after First Cycle of Platinum Plating
3.4.4. Relation between Fractal Dimension and Resistivity
3.5. Conclusions
References for Chapter 3
4. Characterization of Mechanical and Electrical Properties of IPMC
4.1. Introduction
4.2. Experimental Setup
4.2.1. Characterization Setup at INSERM U742-ANIM 104 First experimental setup with reference grating 105 Experimental setup with laser displacement sensor 106
4.2.2. Characterization Setup at LISE-MPIA-LMT Cachan 108
1- Actuation assembly
2- Power supplying platform using a computer controlled potentiostat
3- Measuring system using laser displacement sensor and precise positioning assembly
4- Acquisition system using acquisition hardware and computer
4.3. Results of Characterization Experiments
4.3.1. Explanation of experimental graph with an example
4.3.2. Preliminary Tests of IPMC
4.3.3. Free deflection response of fabricated IPMCs doped with different cations
4.3.4. Time dependent shape of IPMC under actuation
4.3.5. Current Response of IPMC under low step Voltage
4.3.6. Length dependent deflection of IPMC observed at different voltages of actuation
4.3.7. Voltammetry Measurements
4.3.8. Curvature Measurements
4.3.9. Loaded Deflection Measurements
4.4. Young Modulus of IPMC: Two New Methods of characterization
4.4.1. Method for calculation of Young’s Modulus of IPMCs by loaded actuation experiments Evaluation of the Young’s modulus Experiments
4.4.2. Method for calculation of Young’s Modulus of IPMCs by Eigenfrequency analysis
4.5. Impedance Analysis of IPMC fabricated using plasma treatment
4.5.1. Introduction
4.5.2. Experimental Conditions
4.5.3. Results of EIS Measurements and Discussion Deflection Evidence in the Time Domain Results on and Transfer Functions V/iu/
4.6. Conclusions
References for Chapter 4
5. Modeling of biomimetic artificial Muscles (Mc Kibben and IPMC) 
5.1.1 Skeletal Muscle and Linear Model of Static Force
5.1.2 Mc Kibben Pneumatical Muscle
5.1.3 Modeling of a Segment Movement Actuated by Mc Kibben Pneumatical Artificial Muscles
5.1.4 Testing the Model on Experimental Setup
5.1.5 Index Finger Model
5.1.6 Robotic Representation of Forward Kinematic Equations of Robots for
3 degrees of freedom
5.1.7 Application for the Finger
5.1.8 3D finger model actuated by pneumatic muscles using Robotic Coordinates
5.1.9 Section Conclusion
5.2.1. Introduction
5.2.2. Static Deflection Model
5.2.3. Nonlinear Euler Bernoulli Beam Model augmented for Eigencurvature
5.2.4. Simulator of Bending Movement
5.2.5. Comparison of simulation results with Experiments
5.2.6. Proposed Longitudinal Contractile IPMC Actuator and its modeling
5.2.7. Prototype of the Proposed Contractile Actuator
5.2.8. Section Conclusion
References for Chapter 5
6. Conclusions and Future Work 
6.1. Conclusions
6.2. Recommended Future Work

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