Multiobjective optimization of PPy based trilayer
actuators and mechanical sensors
by
Nazanin Khalili
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
Copyright © 2014 by Nazanin Khalili
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Abstract
Multiobjective optimization of PPy based trilayer actuators and mechanical sensors
Nazanin Khalili
Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
2014
Polypyrrole (PPy) as a conducting polymer has exhibited great potential for the
fabrication of bending type actuators and conjugated polymer based mechanical sensors.
Considering the structure and performance of any actuating or sensing device, it is of
pivotal importance to study the roles and relationships of associated decision variables
to design a device with a desired performance. In this thesis, proper modeling
methodologies are presented to capture responses of a PPy trilayer actuator and
mechanical sensor considering their main characteristic outputs. As the central focus,
constrained nonlinear multiobjective optimization models for these actuators and sensors
are accordingly developed to obtain the optimal range of their designated design
variables. Moreover, incorporation of a layer of multi-walled carbon nanotubes into the
structure of a neat PPy actuator is investigated to overcome one of its main
shortcomings, low electrical conductivity. The accuracy of the numerical results were
then determined using their experimental counterparts.
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Acknowledgments
I would like to express my sincere gratitude to my supervisors, Professor Hani E.
Naguib and Professor Roy H. Kwon. Within the last two years, their support and
guidance have awarded me a unique opportunity to experience a high level of academic
research environment and engage brilliant ideas in the multidisciplinary field of
conducting polymers as well as multiobjective optimization.
I would also like to thank all members of the Smart and Adaptive Polymers
Laboratory (SAPL) whose instructive feedbacks and friendships have motivated and
inspired me throughout my MASc research program. Finally, my special appreciation
goes to my family for their encouragement, patience, and unconditional support.
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Contents
1 Introduction 1
1.1 Research objectives and contributions ................................................................ 3
1.2 Thesis outline ...................................................................................................... 5
2 Background and literature survey 6
2.1 A brief review on electroactive polymers ............................................................. 6
2.2 Polypyrrole based actuators ................................................................................ 8
2.2.1 Actuation mechanism in polypyrrole ............................................................ 8
2.3 Configurations of conjugated polymer based actuators ..................................... 12
2.3.1 Actuators operating in wet mediums .......................................................... 12
2.3.2 Actuators operating in dry mediums .......................................................... 13
2.3.3 Micro-scale actuators .................................................................................. 14
2.4 Limitations and shortcomings ........................................................................... 15
2.5 Application of carbon nanotubes in actuator structures ................................... 15
2.6 Mathematical Modelling of CP based actuators ................................................ 16
2.6.1 Non-frequency based models ....................................................................... 16
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2.6.2 Frequency based models ............................................................................. 18
2.7 A brief review on conjugated polymer based mechanical sensors ...................... 22
2.8 Sensing mechanism ........................................................................................... 23
2.9 Modeling approaches and strategies .................................................................. 24
2.10 A brief review on multiobjective optimization procedures and algorithms ..... 31
2.10.1 Optimization techniques ............................................................................. 33
3 PPy based trilayer actuators 36
3.1 Mathematical modeling and optimization model formulation ........................... 36
3.1.1 Electromechanical model ............................................................................ 38
3.1.2 Electrochemomechanical Model .................................................................. 45
3.2 Optimization algorithms ................................................................................... 56
3.3 Experimental procedure and analysis ................................................................ 60
3.3.1 Actuator fabrication ................................................................................... 60
3.3.2 Microstructure of the fabricated trilayer actuators ..................................... 62
3.3.3 Measurements ............................................................................................. 63
3.4 Optimization results .......................................................................................... 67
4 PPy/MWCNT layered actuators 77
4.1 MWCNT layer incorporation into the structure of a neat PPy actuator .......... 77
4.2 Mathematical modeling ..................................................................................... 79
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4.3 Optimization modeling procedure ..................................................................... 84
4.4 Fabrication process ........................................................................................... 89
4.5 Characterization ................................................................................................ 92
4.5.1 Morphology ................................................................................................ 92
4.5.2 Fourier transform infrared spectroscopy ..................................................... 94
4.5.3 Numerical analysis and verification ............................................................ 96
4.5.4 Optimization results ................................................................................. 100
5 PPy based trilayer mechanical sensors 110
5.1 Structure of the multilayered sensor ............................................................... 111
5.2 Description of the mathematical modeling and its verification ....................... 111
5.3 Optimization results ........................................................................................ 124
6 Concluding remarks and future work 127
6.1 Conclusions ..................................................................................................... 127
6.2 Future Work ................................................................................................... 129
Bibliography 132
vii
List of Tables
2-1 Comparison of the general properties of EAPs, EACs, and SMAs ........................ 7
2-2 List of parameters and variables used in the transmission line model ................. 19
2-3 The effect of increasing the geometrical variables of the trilayer sensor on its
output behaviors .................................................................................................. 28
2-4 List of modeling parameters ................................................................................ 29
3-1 The optimal set of design variables and their resulting objective functions
obtained from electromechanical model. .............................................................. 72
3-2 The theoretical values of the average, standard deviation, and the
confidence interval for the two objective functions .............................................. 73
4-1 Values of modeling parameters ............................................................................ 96
5-1 Values of modeling parameters .......................................................................... 117
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List of Figures
2-1 Schematic of different states of polypyrrole. .......................................................... 9
2-2 Schematic of the energy stages in polypyrrole quinoid structure. ........................ 10
2-3 Schematic configuration of two types of bimorph actuators, (a) bending type
with a rocking chair motion, and (b) extensional type with a linear motion. ...... 14
2-4 The equivalent circuit of the interface of a conjugated polymer layer with an
electrolyte solution. ............................................................................................. 21
2-5 The transmission line circuit of a PPy/PVDF/PPy trilayer actuator. ................ 21
2-6 The feasible set of a multiobjective optimization problem. .................................. 33
2-7 Flowchart representing the Multiobjective Genetic Algorithm. ........................... 34
2-8 Flowchart of the active set algorithm. ................................................................. 35
3-1 Schematic of the trilayer actuator with its geometric variables. .......................... 39
3-2 Length correction of the theoretical bending curve of the actuator for
various applied voltages....................................................................................... 42
3-3 Variation of (a) tip vertical displacement, and (b) blocking force of an
actuator based on the electromechanical model for different values of length
and PPy thickness with V=2V and w=1mm. ..................................................... 44
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3-4 Schematic of the equivalent circuit for the DEM model. ..................................... 46
3-5 Variation of the poles and zeros of the curvature transfer function with
respect to different PPy thicknesses. ................................................................... 53
3-6 Frequency response of the bending curvature using (a) reduced DEM
models, (b) mathematically estimated Bode diagrams of the reduced models. .... 54
3-7 Variation of tip vertical displacement for different input frequencies. ................. 55
3-8 The electrochemomechanical model’s (a) feasible set, (b) Pareto front of the
two competing objective functions. ...................................................................... 57
3-9 Semi definite condition for optimality of the objective functions of the
electrochemical model. ......................................................................................... 59
3-10 Schematic configuration of the fabrication and electropolymerization setup. ...... 61
3-11 The cross sectional microstructure of a PPy trilayer actuator............................. 62
3-12 SEM micrographs illustrating the cross-sectional morphology of trilayer
actuators with various PPy thicknesses obtained after (a) 18-hour, (b) 15-
hour, (c) 9-hour, and (d) 6-hour electropolymerization of pyrrole monomers. ..... 63
3-13 The experimental setup depicting the process of tip displacement
measurement. ...................................................................................................... 64
3-14 The measured tip vertical deflections of a trilayer actuator over the
actuation time for different applied voltages and frequencies, (a) 0.1 Hz, (b)
0.2 Hz, (c) 0.3 Hz, and (d) 0.4 Hz. ...................................................................... 65
3-15 The measured variation of the tip vertical displacement of the actuator with
the applied frequency for different applied voltages ............................................ 66
x
3-16 Schematic of the experimental setup for the force measurement of the
actuator under different input voltages. .............................................................. 67
3-17 Effect of design parameters on the objective functions based on the
described models. ................................................................................................. 68
3-18 Results obtained from the two optimization algorithms for (a)
electromechanical, (b) electrochemomechanical models. ...................................... 70
3-19 Blocking force and tip displacement optimal region resulted from the
optimization of the electromechanical model. ...................................................... 71
3-20 Results attained from actuating a trilayer actuator with =10 m, and
=5 mm under different applied potentials and with a varying length: (a)
and (b) electromechanical model, (c) and (d) experimental. ............................... 74
3-21 Experimental vs. numerical values of the blocking force of an actuator for
different effective lengths and applied voltages. .................................................. 75
3-22 Results attained from actuating a trilayer actuator with =30 m, and
=3 mm under different applied potentials and with a varying length: (a)
and (b) electrochemomechanical model, (c) and (d) experimental. ..................... 76
4-1 Schematic of the trilayer bending actuator with an incorporated layer of
MWCNT and its geometrical variables. .............................................................. 79
4-2 The developed algorithm to define the bending curvature of the trilayer
actuator for each segment of its corresponding Bode plot. .................................. 83
4-3 Variation of the response time utility function with and with the
contour lines demonstrating the indifference curves ............................................ 86
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4-4 The indifference curves of the designated response time utility function for
the two time constants ........................................................................................ 87
4-5 Schematic of the fabrication process of the PPy/MWCNT actuators. ................ 91
4-6 Captured images of the actuator’s tip vertical deflection measurement. ............. 92
4-7 The micrograph of (a) the cross section of the trilayer configuration of the
actuators, (b) the surface morphology of MWCNT, (c) and (d) the surface
texture of electropolymerized PPy film. .............................................................. 93
4-8 FTIR spectroscopy of each layer of the trilayer actuator. ................................... 95
4-9 Variation of the tip blocking force and vertical displacement with different
applied frequencies obtained from the mathematical model for a neat PPy
vs. a PPy/MWCNT actuator. ............................................................................. 97
4-10 Variation of the tip vertical deflection of the actuator for different values of
widths, effective lengths, and applied voltages, (a) = 20mm (exp.), (b)
= 25mm (exp.), (c) = 1mm (exp. vs. model), and (d) = 2mm (exp. vs.
model). ................................................................................................................ 99
4-11 The measured blocking force of an actuator with varying effective lengths
and applied voltages vs. their modeling counterparts. ....................................... 100
4-12 Variation of the tip vertical displacement with the applied voltage for a neat
PPy vs. a PPy/CNT actuator for an effective length of 20mm. ........................ 100
4-13 The optimum points obtained from the three-objective optimization process. .. 101
4-14 The 2D projections of the Pareto optimum points of the three-objective
optimization; (a) blocking force vs. tip deflection, (b) response time utility
vs. blocking force, and (c) response time utility vs. tip deflection. .................... 103
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4-15 (a) Pareto fronts obtained for a 2-objective optimization problem, (b) The
design variables corresponding to two of the optimal solutions. ........................ 103
4-16 The 2D projections of the Pareto optimum points of the 3-objective vs. 2-
objective optimization; (a),(d), and (g) blocking force vs. tip vertical
deflection, (b), (e), and (h) response time utility vs. tip vertical deflection,
and (c), (f), and (i) response time utility vs. blocking force. ............................. 105
4-17 The optimum range of the decision variables for (a) maximum tip vertical
displacement, and (b) maximum blocking force. ............................................... 107
4-18 The optimum range of the decision variables for (a) applied voltage, (b)
applied frequency, (c) actuator effective length, (d) actuator width, (e)
MWCNT layer thickness, and (f) PPy layer thickness, for the 3-objective
optimization. ..................................................................................................... 108
5-1 Schematic of the equivalent transmission line circuit of the trilayer
mechanical sensor .............................................................................................. 112
5-2 Comparison of the frequency response of the sensor with different orders of
transfer function. ............................................................................................... 116
5-3 Variation of the output voltage of the sensor with the amplitude of tip
deflection for different input frequencies using (a) Equation (5-8), and (b)
the approximated bending curvature. ................................................................ 118
5-4 Frequency response of the sensor (MATLAB plot vs. approximated
diagram) ............................................................................................................ 119
5-5 Variation of the voltage output with the input amplitude of the sensor tip
deflection, (a) experimental, (b) numerical results. ........................................... 123
5-6 The Pareto frontiers of the optimization problem ............................................. 124
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5-7 Variation of the objective functions with the PPy thickness optimal values. .... 126
1
Chapter 1
Introduction
In a wide range of emerging engineering applications, actuators have been the key points
for development of various systems namely control systems where a set of devices are
linked to manage, command or direct the behavior of a system, equipment or machine.
Although actuators have a history dated back to the very early development of basic
machines as well as mechanical equipment, the modern actuators have been developed
and commercialized within the last few decades parallel to the astonishing advances in
different fields of science and technology. Similar to the information technology which
has been revolutionized partially due to the miniaturization of its related electronic and
optical devices, many applications including mechanical and biological ones have been
benefitted from the same miniaturization occurred for sensors and actuators [1]. As new
technologies or applications have emerged, new challenge has been formed for designing
and developing their related and required devices. Therefore, these days many industrial
and research groups direct their attention to develop proper devices conforming to those
requirements defined according to the inputs set by any particular emerging technology.
Specifically, in the design and development of actuators, due to their applications and
working environments, different research themes and directions have been established
such as biomedical and biomimetic robotics along with micromanipulation systems. In
particular, some of the potential applications of the trilayer actuators studied in this
2
thesis are in surgical tools including Laparoscopic surgeries, a propulsion element for a
swimming device or a robotic fish, and various prototype applications such as an
electronic Braille screen [2], a rehabilitation glove [3], tremor suppression [4] and a
variable camber propeller [5].
However, due to various mechanical characteristics of actuators and their
constituent materials, there are a large number of variables which have to be taken into
account throughout their design and fabrication process. Regarding these characteristics,
although for many applications developing required actuators have reached to a level of
maturity within last few decades, finding and evaluating the best design among all
possibilities have still remained a challenge. Analyzing and fabricating all potential
candidates can be a time consuming as well as costly task. Nevertheless, in today’s
highly competitive environment, cost and performance efficiency of a system are crucial
elements which are to be considered in addition to its main desired technical
performance. Therefore, it is of critical importance to design the best system which is
efficient, versatile and at the same time cost effective. This can be achieved through
optimization of a new design or process. However, due to the required numerical
analysis and data processing, particularly for a complex and multivariable system, the
optimization process had been a difficult, costly, time consuming and for many cases an
impossible process. This has been changed within last few decades owing to the
impressive advances in computers, and consequently numerical analysis. Optimization
methods have been evolved from a mainly theoretical tool to a practical tool employed
in a wide range of different fields and both engineering and non-engineering applications.
However, in an optimization process, one challenge is to develop a robust and
comprehensive, yet realistic, mathematical model that can capture the main features of
the system or design intended to be optimized. The other main challenge is to develop a
solution strategy and algorithm to be able to solve the mathematical model without
compromising its main characteristics. One of the main characteristics of the
optimization models of multidisciplinary systems or engineering devices such as
3
actuators is their multi-criteria design decision making. This characteristic can be taken
into account through defining a nonlinear multiobjective optimization problem. In this
type of models, the optimal decision should be made through trade-offs among two or
more objectives. Ultimately, the acceptable result is achieved when the final system or
design can perform its desired tasks without violation of its prescribed characteristics or
considerations. These prescribed as well as essential considerations are taken into
account through the constraints of the defined optimization model.
In order to provide a general perspective of this work, it should be mentioned that
the actuator and mechanical sensor investigated in this thesis have bending type layered
configurations comprising two layers of PPy deposited on a porous membrane of
Polyvinylidene fluoride (PVDF). The dimensions of the strips along with the applied
voltage and its frequency are considered as the decision variables.
1.1 Research objectives and contributions
Conjugated polymers and their actuating and sensing properties have been the focus of
many research programs in recent years. Along with these endeavours, the main
objective of this thesis is to develop a multiobjective optimization model of layered
conjugated polymer based actuators. This is performed in order to obtain the optimal
design variables so that the designed actuator meets its desired performance. To achieve
this goal properly, it is crucial to gain a comprehensive understanding of the
performance of this type of actuators as well as their underlying electrochemomechanical
mechanism of actuation. Another main objective of this work aims to demonstrate a
new modeling and optimization procedure for the CP based mechanical sensors with a
laminate structure.
The main contribution of this work lies in exploiting the optimization procedure to
design more efficient and desired actuators and sensors considering their predefined
4
output responses. In more detail, the key and novel contributions of this research can
be summarized as follows
i. Development of a two-objective optimization model for trilayer conjugated
polymer based actuators: A mathematical modeling is developed to capture the
two main output responses, tip vertical displacement and blocking force, of
trilayer PPy bending actuators. The derived mathematical expressions
representing these two characteristic behaviors of the actuator are then used as
the objective functions of a subsequent optimization process. In order to attain
comprehensive yet practical results, in this work, two modeling methodologies
(i.e., electrochemical and electrochemomechanical) are employed to define the
multivariable objective functions.
ii. Fabrication of a trilayer PPy based actuator with an incorporated conductive
layer of multi-walled carbon nanotubes: To investigate the effect of the actuator’s
conductivity on its performance, an extra layer of electrophoretically deposited
MWCNT is incorporated into the structure of a neat PPy actuator.
iii. Development of a three-objective optimization model for the PPy/MWCNT
actuator: To capture the response time of the actuator in the presence of the new
layer, a utility function indicating its response time is formulated as the third
objective function of the optimization model.
iv. Development of a mathematical model capturing the sensing response of a PPy
based mechanical sensor along with representing its corresponding optimization
model: The frequency response of a conjugated polymer mechanical sensor is
captured through a novel transmission line circuit. Due to the wide range of the
sensor’s outputs resulted from its structural characteristics; an optimization
procedure is designed to arrive at the optimal design variables.
5
1.2 Thesis outline
This thesis comprises six chapters. The first chapter provides a brief introduction to the
actuators and their design process. The main objectives, motivations, and contributions
of this research are outlined in the first chapter as well. In Chapter 2, Background and
literature survey, a brief overview of electroactive polymers and more specifically
polypyrrole as one of the mainly applied conjugated polymers in fabrication of layered
CP based actuators is presented along with their actuation mechanism. Previously
proposed novel modelings of these actuators as well as an overview of the multiobjective
optimization procedures and algorithms are addressed. This chapter concludes with a
brief description of the CP based mechanical sensors and their corresponding modeling
methodologies. Chapter 3, PPy based trilayer actuators, explores the fabrication process
of PPy trilayer actuators working on the basis of the inherent electrical conductivity of
conjugated polymers. Two modeling methodologies capturing the electroactive response
of the actuator are presented in detail along with their associated multiobjective
optimization procedures. Chapter 4, PPy/MWCNT layered actuators, focuses more
specifically on the fabrication, and influence of incorporating a layer of multi-walled
carbon nanotubes into the structure of the aforementioned PPy trilayer actuator. It also
describes the mathematical modeling of the PPy/MWCNT actuator and exhibits the
optimization procedure along with the optimal results obtained from the proposed
model. Chapter 5, PPy based trilayer mechanical sensors, provides an introductory
study on the sensing mechanism of a trilayer PPy mechanical sensor and explicitly
elaborates on a suggested modeling methodology based on the equivalent transmission
line circuit of the sensor. Finally in Chapter 6, Concluding remarks and future work, the
main conclusions of this work are summarized and some recommendations for future
work are outlined.
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Chapter 2
Background and literature survey
To model and design conjugated polymer based actuators and mechanical sensors, and
consequently optimize their performances, it is required to obtain a thorough knowledge
regarding their structures as well as their constituent materials. Therefore, this chapter
provides an overview of different aspects and characteristics of conjugated polymer
based actuators and mechanical sensors along with the recent investigations and their
contributions to this field.
2.1 A brief review on electroactive polymers
Since the early 90s, much attention has been focused on an emerged group of
electroactive polymers (EAP) that can significantly change in their size, shape, or color
in response to an electric stimulus. The recently developed EAP materials are able to
induce large strains which are nearly two orders of magnitude greater than those
induced by electroactive ceramics (EAC). Moreover, EAPs have higher response speed,
lower density, and greater resilience in comparison with shape memory alloys (SMA). A
comparison between EAPs, EACs, and SMAs is given in Table 2-1, showing the
advantage of EAP materials in terms of their actuation strain, density, and power. EAP
materials have exhibited great potential for a wide range of applications in both
engineering and bioengineering fields such as biomimetic robotics, biomedical and
7
micromanipulation systems. EAPs possess the ability to emulate the function of
biological muscles regarding their large strain, high fraction toughness, and vibration
damping. They are effectively capable of mimicking the movements of biological muscles
and this has led to significant research efforts dedicated to studying the behavior of
electroactive polymers [6, 7, 8, 9].
Table 2-1. Comparison of the general properties of EAPs, EACs, and SMAs [6]
Property EAP EAC SMA
Actuation strain over 300% Typically 0.1-0.3% <8% short fragile
life
Force (MPa) 0.1-40 30-40 200
Reaction speed sec to min sec to min msec to min
Density 1-2.5 g/cc 6-8 g/cc 5-6 g/cc
Driving voltage 1-7 V for ionic EAP, and 10-150 V/µm for
electronic EAP 50-800 V 5 V
Consumed
power* m-Watts Watts Watts
Fracture behavior Resilient, elastic Fragile Resilient, elastic
*Note: the power consumption was estimated for the macro devices that are driven by such actuators.
Based on their actuation mechanism, EAPs are generally categorized into two major
groups: electronic, and ionic. The activation voltage of the electronic electroactive
polymers is relatively high (>150 V/ m) which is close to their breakdown level and
they are activated by electrostatic forces. Moreover, they respond to the electric
stimulus faster and are capable of operating in air without any major limitations.
Electroresistive, electrostatic, piezoelectric, and ferroelectric materials are considered as
electronic EAPs. On the other hand, in the ionic EAPs the activation results from the
electrically driven transport of ions and molecules. They can be actuated by applying a
low driving voltage (1-5 V). However, this type of polymers mostly requires to be in an
8
aqueous environment in order to operate. Ionic EAPs are classified into three principal
material groups: ionic polymer-metal composites (IPMC), carbon nanotubes (CNT), and
conducting polymers (CP) [6].
Conducting polymers (CPs), also known as conjugated polymers can be utilized in
the structure of actuating devices and their function is more analogous to that of a
natural muscle [8]. Some of the most prominent features of these actuators are namely
their low operating voltage, simple construction, light weight, no acoustic noise, and
mostly low cost. In addition, some of their properties can be reversibly manipulated
such as color, conductivity, volume, and porosity [6, 7, 10].
2.2 Polypyrrole based actuators
Many research efforts in the area of electroactive polymers have been dedicated to
conjugated polymer based actuators in which mechanical work is obtained through
direct conversion of electrical energy [6]. The linear or biaxial dimensional changes of a
conducting polymer layer are employed to attain the desired mechanical work. These
changes are either related to a single electrode or the ones associated with the relative
dimensional changes of two or more connected electrodes [8]. More specifically,
polypyrrole (PPy) films have been the key components of many actuating devices due to
their intrinsic properties explicitly their high conductivity, biocompatibility, high
environmental stability with large volume change, reasonably high strain (>2%), as well
as their ease of fabrication [5, 7, 11, 12].
2.2.1 Actuation mechanism in polypyrrole
The structure of polypyrrole consists of a one-dimensional polyene backbone in which
the alternating single and double bonds are located on its extended -conjugated system
[13]. This structure results in a delocalized positive charge in case of electron removal
from the polymer [14]. Different oxidation levels of PPy, as depicted in Figure 2-1, can
be electrochemically obtained by applying a low positive voltage.
9
Figure 2-1. Schematic of different states of polypyrrole.
The local deformations of the polymer lattice results in the movement of the
existing -bonds and consequently, the charge mobility within the polymer arises [15].
The underlying mechanism of conduction within PPy stems from its electronic band
structure. There is a band-gap energy of 3.2 eV between the polymer’s valence band and
conduction band which causes the polymer to be inherently non-conductive [15, 16, 17].
Moreover, pyrrole (Py) monomers possess different geometries in their ionized state and
ground state, an aromatic geometry vs. a quinoid structure, respectively. Figure 2-2
illustrates different stages of band-gap energy changes within the polymer listed as
follows
a. Total ionization energy of pyrrole ( )
b. Relaxation energy ( ) gained by the monomer during its quinoid state (ionized
state).
c. Distortion energy ( ) released in the ground state of the monomer so that it
assumes the quinoid structure.
d. Ionization energy of the quinoid geometry ( ).
10
Figure 2-2. Schematic of the energy stages in polypyrrole quinoid structure.
Altering the oxidation state of a conjugated polymer affects several features of its
structure such as the length of C-C bonds on the backbone of the polymer [18, 19], the
interactions between the solvent and polymer chains [20], as well as the inter-chain
interactions [21]. However, the main mechanism that accounts for the volume change of
the polymer layer is the mass transport within the polymer. The level of charge on the
conjugated backbone of the conducting polymer marginally changes upon a change in
the oxidation state of the polymer. When a driving voltage is applied to the polymer,
the flow of a current through the electrolyte initiates and the accretion of ionic charge in
the polymer/electrolyte interface imposes a positive charge on the oxidized conducting
polymer backbone. This positive charge is the result of electron removal from the chains
of the polymer which modifies the allocation of the double bonds and bond angles [22].
In order to maintain charge neutrality, mobile ions move throughout the -conjugated
system of the polymer. Consequently, a change in the volume of the polymer film occurs
due to the movement of free ions into and out of the polymer structure. The oxidation
and reduction process (redox) of the polymer is demonstrated by Equation (2-1) and
Equation (2-2), respectively [23].
(2-1)
(2-2)
11
where , and correspond to the oxidized (doped) and reduced (undoped) states
of the polymer, respectively. signifies the incorporation of the counter-ion, , in
the polymer as a dopant, whereas the term shows that a cation, also called co-
ion, has been introduced to the structure of the polymer during the reduction process
[7]. It can be inferred from these equations that maintaining charge neutrality within
the polymer requires a change in both electronic and ionic charge. The former is
accompanied by the mass transport between the electrolyte and the polymer.
In systems with mobile anions and large cations, expansion of the polymer layer
occurs during its oxidation owing to the movement of mobile anionic dopants into the
polymer structure, while the immobile and large cations are not able to effectively
diffuse through the polymer chains. Therefore, the process in Equation (2-1) dominates
and the conjugated polymer expands during the oxidation process and contracts while
being reduced. On the other hand, in polymers prepared with large anions, and small
and mobile cations, the polymer expands upon reduction since the ion movement is
derived primarily by incorporation of cations to compensate the charge. In some systems
both anions and cations are medium-sized and mobile, causing an expansion followed by
a contraction of the polymer structure attributed to the ‘salt draining’ process which is
clearly an undesirable process [24, 25]. In these systems, both ions can diffuse into and
out of the CP layer, and the effects of their influx and outflow will be canceled out,
therefore, the maximum attainable volume change cannot be occurred [26].
When a conducting polymer layer is in contact with an electrolyte, its volume
change is also associated with the solvent transport resulted from either ion salvation or
osmotic processes [7]. Accordingly, the main cause of the volumetric change and
consequently, the electromechanical actuation of the conducting polymer is the redox
process which occurs in a continuous and reversible manner [27, 28]. This process leads
to some concurrent changes in conductivity [29, 30], color [31, 32], and volume of the
12
polymer layer. All these changes are associated with the flow of both ions and solvent in
and out of the conducting polymer.
2.3 Configurations of conjugated polymer based actuators
There are various types of conjugated polymer actuators most of which have been
designed to operate in liquid electrolytes. Fabrication of actuating devices operating in
air has also been reported, expanding the range of applications of CP based actuators.
Synthesis of bending bilayer and trilayer conjugated polymer actuators, linear
contracting actuators, and the ones in which the swelling occurs in the direction of their
thickness have been established. Moreover, conjugated polymer actuators in the micron-
scale have also been fabricated. Conducting polymer based actuators can be mainly
categorized into three major groups, as briefly discussed in the following sections [7]. In
order to obtain a reversible conjugated polymer actuator, three circuit elements are at
least required namely a cathode, an anode, and an ion source [8].
2.3.1 Actuators operating in wet mediums
This type of conjugated polymer actuators includes different configurations two of which
are the bilayer (unimorph) and trilayer (bimorph), both considered as bending
actuators. A unimorph actuator comprises a single film of conjugated polymer adhered
to an electro-mechanically inert layer. Its performance is confined to aqueous
environments since an electrolyte solution is required as an ion source and sink in which
the actuator is immersed [33, 34, 35]. Upon ion exchange with electrolyte solution, there
will be an electrochemically induced strain throughout the polymer leading to the
bending movement of the bilayer. The study and analysis of bilayer configurations of
conjugated polymer actuators have been considerably carried out by Otero et al. [36,
37], and Pei et al. [38, 39]. On the other hand, a trilayer (bimorph) conjugated polymer
actuator consists of a middle inert layer with a film of polymer deposited on its both
sides. In this configuration one film of CP acts as the working electrode while the other
13
one is the counter electrode. Linear conjugated polymer based actuators are another
configuration of actuators operating in wet environments. They are constituted of free
standing films and fibers clamped at one end and are found to generate greater
actuation stresses [7, 40].
2.3.2 Actuators operating in dry mediums
The range of applications of conjugated polymer actuators was further broadened by
introducing the actuators able to operate in dry environments. Using a polymer
electrolyte as a separator of two films of conjugated polymer, bending type actuators
and linear (extensional) actuators can be achieved [41]. Figure 2-3 schematically shows
the two types of dry actuators configurations. Fabrication of a bending type conjugated
polymer actuator operating in air for a short time was first reported by MacDiarmid et
al. in 1994 [42, 43]. They applied two films of polyaniline as the conducting polymer
layers separated by either an HCl-soaked piece of paper or a polymer gel electrolyte. In
this type of configuration, two CP layers are deposited onto an inner electrolyte film
which acts as an ion tank as well as an electrochemically insulating film between the
two layers. The active layers are constrained by the middle electrolyte layer and
therefore, they act analogous to a cantilevered multi-layer structure [44]. In a bending
type actuator one polymer film is oxidized while the other one is being reduced due to
the movement of ions during the electrochemical switching. This leads to generating a
rocking-chair motion of the actuator.
In a linear actuator, one of the conducting polymer films acts as an anion-exchanger
whereas the other layer is a cation-exchanger resulting in a linear (extensional) motion
of the actuator. Oxidation of the anion-exchanger and reduction of the cation-exchanger
occur upon insertion of ions from the electrolyte to the CP films. This leads to
expansion of both polymer films and elongation of the actuator. When the voltage is
switched, the conjugated polymer films drive out the ions and contract. Lewis et al. [45]
14
fabricated a PPy based linear contracting actuator using an acrylamide hydrogel as a
solid ion source of the actuator.
Figure 2-3. Schematic configuration of two types of bimorph actuators, (a) bending type
with a rocking chair motion, and (b) extensional type with a linear motion.
2.3.3 Micro-scale actuators
There are some shortcomings to the large-scale conjugated polymer actuators that limit
their performance. The speed of these actuators is confined due to relatively high values
of the ion diffusion and RC (resistance capacitance) time constants. Moreover, the
large amount of charge consumed by conducting polymers during the electrochemical
switching process has to be taken into account [46]. One solution to tackle these
problems is to fabricate a microactuator in which application of thinner polymer films
leads to a higher speed of the actuator as well as a higher efficiency in converting
electrical energy to mechanical work. A microactuator with a bilayer structure was the
first actuator fabricated in micro-scale reported in 1993 by Smela et al. [47, 48].
Different fabrication techniques can be applied to fabricate a bilayer microactuator as
well as small diameter, fiber-based actuators.
15
2.4 Limitations and shortcomings
Despite all aforementioned remarkable properties of PPy actuators, there are also a
number of shortcomings in their performance entailing further considerations. For
instance, their actuation response time is not as fast as desired due to the movement of
ions into or out of the polymer during actuation [7, 49]. Another drawback of PPy
actuators is the decrease of their electronic conductivity by two or three orders of
magnitude as a result of the reduction process within the polymer. Therefore, only a
small part of the polymer would be actively actuated [50]. This can be one of the main
causes of the low response speed which noticeably restricts the performance of the
actuator. In order to partially overcome or alleviate this limitation, an additional
electron conductor such as an ultra-thin layer of gold or platinum is added to the
actuator structure [51, 52, 53].
2.5 Application of carbon nanotubes in actuator structures
One of the major groups of ionic EAPs is the carbon nanotubes (CNTs) which have
received considerable attention due to their eye-catching chemical and mechanical
features. The use of CNTs in the structure of mechanical actuators was first introduced
by Baughman et al. [8]. Further, Mukai et al. [54, 55] reported the fabrication of an
actuator with a bimorph configuration in which a polymer-supported ionic liquid
electrolyte was sandwiched by two bucky gel electrodes containing single-walled carbon
nanotubes (SWCNT). Incorporating SWCNTs into the structure of multi-layer
actuators have been reported by several research groups; however, these nanoparticles
are very expensive and require special preparation techniques. Contrarily, Multi-walled
carbon nanotubes (MWCNT) are low in cost and are mostly applied in battery
electrodes [56]. Therefore, many studies have been focused on using MWCNT based
bending actuators such as that of Biso et al. [57] who fabricated a polymer actuator
comprising a MWCNT-gel electrode and an ionic liquid. Moreover, it has been
demonstrated that higher electrochemical capacitance can be acquired using activated
16
(acid-treated) carbon nanotubes as double-layer capacitors than non-treated CNTs [58].
This superiority is owing to the changes imposed on the structure of CNTs and their
surface characteristics throughout the acid-treating process. In another study, the
electrochemical and electromechanical properties of polymer actuators containing
activated and non-activated MWCNTs were compared with a SWCNT based actuator.
2.6 Mathematical Modelling of CP based actuators
The performance of CP based actuators is difficult to predict due to their unique
mechanical and chemical properties which leads to their nonlinear behavior. Therefore,
employing such actuators in different fields of engineering and providing a more
comprehensive insight into their underlying electrochemomechanical mechanisms of the
actuation process entails further establishment of a valid mathematical model. This
leads to a better perception and predictability of their nonlinear behavior. Hence, in
recent years a great number of research groups developed different mathematical models
and methodologies predicting the output behavior of multilayer actuators in response to
a stimulus. Most of these models were designated to estimate the tip displacement of the
actuator along with its generated blocking force.
2.6.1 Non-frequency based models
The nonlinear behavior of CP based actuators has been extensively studied by Alici et
al. whose work has made great contributions to this field. In one of their studies, they
reported a lumped-parameter mathematical model describing the bending mechanism of
PPy multi-layer actuators. The results acquired from their modeling approach estimate
the bending angle and bending moment of such actuators for a range of applied
voltages. This model can be used to optimize the geometry of the polymer layers in
order to design and fabricate an actuator with efficient performances [59]. The force
output of these trilayer CP based actuators operating in non-liquid environments has
also been studied by Alici et al. [60] investigating two special cases in their force model;
17
free deflection and zero deflection. The model was experimentally verified through
fabricating a robotic finger and the obtained results were shown to be in good agreement
with their proposed mathematical model. Study of the shape, tip deflection angle, and
deflected length of a trilayer PPy actuator was then further pursued via another
developed model by Alici et al. [61] in which a nonlinear least square optimization
algorithm was applied to estimate the deflected length and tip deflection angle of the
actuator. In other studies conducted by Shapiro et al. [62] and Du et al. [63] a
multilayer model was introduced based on the classic beam bending theory in which the
thickness of the beam is considered small compared to the lowest radius of curvature
attained by the trilayer strip while being actuated. Moreover, the relationship between
the stress and strain induced in the actuator is assumed to be linear.
Regarding large deformations of conducting polymer actuators, Fang et al. [64]
established a nonlinear elastic model in which the nonlinear stress-strain relationship
was captured using Neo-Hookean type strain energy functions. The model was
experimentally demonstrated to possess more capability in terms of predicting the
nonlinear behavior of the conjugated polymer trilayer actuators for higher applied
voltages in comparison with the developed models based on the linear elasticity theory.
In this model the driving voltage is considered as the input while the bending radius is
the designated output of the model. Equation (2-3) and Equation (2-4) express the force
and moment balance of the trilayer actuator, respectively [64].
(2-3)
18
(2-4)
where is the radius at the inner surface of the bent strip, is the radius of the
boundary between the reduced PPy layer and the middle PVDF membrane, is the
radius of the boundary between the PVDF layer and the oxidized PPy layer, and is
defined as the radius of the outer surface of the bent trilayer actuator. Furthermore,
and represent the swellings of the reduced and oxidized PPy layers, respectively.
The shear moduli of PPy and PVDF are respectively denoted by and .
Finally, is the ratio of the bending angle of the strip to the position of the actuator
along the longitudinal axis. These two equations were then numerically solved by
applying the Newton’s method and the two parameters (i.e., and defining the
deformed configuration of the bending actuator were found simultaneously.
2.6.2 Frequency based models
One of the main approaches that have been recently employed to predict the response of
an electrochemically driven trilayer actuator is the use of the transmission line models.
These models capture the charging of the conducting polymer layer through time and
19
space [65]. In a transmission line model, the equivalent circuit of a conducting polymer
immersed in an electrolyte is developed to obtain the electrochemical impedance of the
layer. Shoa et al. [65] modeled the charge distributions in a polypyrrole layer in two
dimensions (i.e., through the length and the thickness of the strip). The elements of
which their 2-D distributed transmission line circuit is composed are the ionic and
electronic resistance of a segment of the polymer layer, the electrolyte resistance, and
the capacitance of the designated section of the polymer. Using an equivalent circuit,
the impedance of the transmission line was analytically derived. This calculated
impedance predicts the current produced in the polymer layer submitted to a driving
voltage. Furthermore, the generated current results in obtaining the amount of charge
transferred through the CP layer which is a time dependant variable. Equation (2-5)
illustrates the 2-D impedance of the 2-D transmission line described by Shoa et al. [65].
The variables and parameters used in the model are listed in Table 2-2.
Table 2-2. List of parameters and variables used in the transmission line model
Symbol Description
Electronic conductivity of the polymer
Ionic conductivity of the polymer
h Total thickness of the polymer
L Length of the polymer layer
A The area of the conducting polymer layer
d Distance between the reference electrode
and the conducting polymer
Volumetric capacitance of the polymer
Appling this model, the dynamic actuation response of the conjugated polymer
based actuators can be analytically predicted. Furthermore, the effects of different
20
variables on the response of these electrochemically driven actuators are demonstrated
by the model which facilitates the design process of an optimized actuating device.
(2-5)
As pointed out, one of the most envisioned fields in which the conducting polymer
based actuators are applied is the medical and biomedical applications. These areas
require a high accuracy in the positioning of the actuator due to their intricate
applications which make the use of implemented sensory controls practically impossible.
Therefore, there is a growing need of applying feedback and open-loop control
techniques based on an inversion-based model of the CP based multilayer actuator in
order to have control over their bending displacement as well as bending angle [66, 67].
Developing a valid electrochemomechanical model, Nguyen et al. [66] estimated the
control input required to obtain the desired bending displacement through inverting the
mathematical model. The nonlinear behavior of a PPy based trilayer actuator was
captured in their experimentally verified modeling methodology. An inversion based
controller was further implemented based on their proposed modeling methodology. The
model was built upon an electronic equivalent circuit of the trilayer conducting polymer
actuator in which the diffusion impedance ( ) was connected in series to the electronic
capacitance of the actuator ( ). It was assumed that the trilayer actuator consisted of
n-element of impedance throughout its length. Their proposed model for one element of
PPy/PVDF layers is schematically presented in Figure 2-4. The electronic resistance of
21
one element of PPy layer and one element of PVDF layer are shown by and ,
respectively.
Figure 2-4. The equivalent circuit of the interface of a conjugated polymer layer with an
electrolyte solution [66].
Considering the equivalent electrical circuit of the interface between the conducting
polymer layer and the middle PVDF membrane, the transmission line circuit
corresponding to the total trilayer actuator (PPy/PVDF/PPy) is illustrated in Figure
2-5. Furthermore, the total impedance corresponding to each element of the actuator
and consequently, the total impedance of the entire trilayer actuator were obtained
using its equivalent electrical circuit [66].
Figure 2-5. The transmission line circuit of a PPy/PVDF/PPy trilayer actuator [66].
22
2.7 A brief review on conjugated polymer based mechanical sensors
Electroactive polymers possess many promising features that can also be exploited in
sensing devices. Although conjugated polymer based actuators have been significantly
studied and characterized by a large number of research groups, slight amount of work
has been dedicated to analysis and modeling of conjugated polymer based mechanical
sensors.
Mechanical energy can be converted to electrical potential energy through the
application of polymeric materials. Mechanical sensors based on piezoelectric polymers
have been commercially available. However, through conjugated polymer based sensors,
force and displacement can be measured at relatively higher strain which is 10 times
larger than those typical of piezoelectric polymers [68]. Moreover, CP based sensors have
the potential to be utilized in different devices and instruments owing to their relatively
low mechanical impedance and elastic moduli (<1 Gpa).
Some polymers contain free ions such as polyelectrolyte gels, ionic polymer-metal
composites (IPMC), and conjugated polymers (CP). They have the potential to generate
electrical energy when a mechanical stimulus is applied. Upon the application of a
compressive load, the pH level of a polyelectrolyte gel changes reversibly which is
ascribed to the ionization of the carboxyl groups of the polymer. A lateral expansion will
be induced in the gel resulting in the dilatation of the polymer network in one
dimension. This will lead to a decrease in the entropy level of the polymer and hence,
the chemical free energy of the polymer chain increases. An increase in the degree of
ionization of the gel will simultaneously compensate the boosted level of the free energy
[69]. Ionic polymer transducers are reported to have charge sensing abilities similar to
those of materials with piezoelectric properties [70]. The induced mechanical
deformation results in a change in the dipole moment of the polymer and therefore,
produces a capacitive discharge in the polymer [71].
23
Conducting polymers as a group of ionic electroactive polymers contain -
conjugated systems, the electrical conductivity of which can be altered and approach to
that of metal [72]. It has been shown that there is a connection between the
mechanically induced deformations of conjugated polymers and their associated
electrical properties. Recently, it has been found that these polymers are capable of
generating an output current or voltage upon an induced mechanical deformation or
force. This observed behavior in polymer based mechanical sensors is considered as the
reverse actuation process. Many outstanding properties of the conjugated polymer
actuators including their light weight, biocompatibility, and the potential to be
fabricated in micro-scale are still retained by these sensors [7]. Sensors with a trilayer
configuration are capable of operating in air in response to a mechanically induced
bending deformation.
2.8 Sensing mechanism
The sensing effect of conjugated polymers was first identified by Takashima et al. [73].
A mechanically induced electrochemical current was observed in a free standing film of
conjugated polymer, polyaniline (PAni) under a tensile load. The amount of the induced
current was reported to be proportional to the applied tensioning load, dimensions of
the polymer film, and the oxidation degree of the conjugated polymer. It was pointed
out that upon stretching the polymer film, its main chain stretches and consequently,
the density of state (DOS) near the chemical potential changes. This leads to inducing a
redox current within the conjugated polymer. More recently, it was found that the
voltage required to actuate a PPy based trilayer (bimorph) actuator increases by
applying a mechanical load, as stated by Otero and Cortes [12]. They showed that the
consumed electric energy of the trilayer actuator (artificial muscle) changes linearly with
the associated studied variables namely temperature, the electrolyte concentration, and
trailed load. Under galvanostatic conditions, trilayer PPy based configurations would
simultaneously act as an actuator and sensor. It was also suggested that the voltage
24
generated by these film-type conjugated polymer sensors is resulted from the
mechanically induced ion flux within the polymer [10, 74]. Accordingly, when an
external load is applied to the conjugated polymer layer the concentration of ions
changes due to the volume change of the film. This induced ion concentration gradient
leads to a change in the Donnan equilibrium (i.e., the behavior of ion species in the
presence of a membrane across which the charged particles are unevenly distributed).
The perturbation of Donnan equilibrium results in an ion flux throughout the interface
between the layer and the electrolyte. This phenomenon renders the charge/discharge of
the capacitance considered at the polymer/electrolyte interface. In other words, applying
a mechanical input to the polymer sensor results in a temporary change in the
concentration of the dopant ions within the polymer layers. Therefore, the ion
concentration gradient between the polymer layer and the electrolyte changes which
generates a potential difference across the sensor [75]. Wu et al. [76] also indicated that
expansion of the polymer upon applying tensile stress results in reduction of the force
required for the ions to enter the polymer expanded network. Therefore, the ions and
solvent are inserted into the polymer by a lower voltage.
2.9 Modeling approaches and strategies
Some of the mathematical modeling methodologies capturing the output behavior of the
conjugated polymer based mechanical sensors are put forward in this section.
The electrochemomechanical responses of the conjugated polymer based actuators
and sensors can be estimated using a thermodynamic approach. The energy provided by
the power supply, is stored as either electrochemical energy (
) or
mechanical (elastic) energy (
) in an actuator, where is the actuation strain,
is the elastic modulus of the PPy layer, is the applied voltage, and is the
volumetric capacitance of PPy. The same methodology can be applied for a CP based
sensor. When the sensor in operating in an open circuit, the redox state of the
25
conjugated polymer layers will remain constant and therefore, the input energy resulted
from the elastic deformation ( ) is equal to the energy transferred to the external
circuit ( as follows
(2-6)
where is the charge density of the polymer layers. Using Equation (2-6) and the
strain to charge density ratio ( , one can obtain the output voltage of the sensor
as
(2-7)
Upon the elastic deformation of the trilayer PPy based sensor, a voltage difference
will be induced in the open circuit. Consequently, a current will flow between the PPy
films in the short circuit, the amount of which can be estimated using the values of the
volumetric capacitance and the open circuit voltage ( ). This proposed model
was experimentally proven to be a promising methodology to predict the output
behavior of the trilayer CP based sensors in response to a mechanical deformation [76].
Moreover, it was demonstrated that the generated voltage of the sensor is related to the
redox state of the polymer layers as well as the nature of the counter ions. This
phenomenon was captured through a “Deformation Induced Ion Flux” model by Wu et
al. [76]. The size of the dopant ion greatly influences the polarity of the generated
voltage as well as its magnitude. When the dopant ion is mobile and small in size, it
leads to a negative voltage (out of phase voltage), whereas a large and immobile dopant
ion produces a positive (in phase) voltage. It is also worth noting that opposing to
piezoelectric materials and generators, conjugated polymers are superior in terms of
charge generating whereas the voltage they produce is low [30]. This implies the fact
that while using a conducting polymer as a mechanical sensor, it is more sensitive when
the output is current (potentiostatic mode) than when there is a voltage output
(galvanostatic mode).
26
In another study conducted by Alici et al. [77] the experimental frequency response
of a PPy based trilayer laminate structured sensor along with its impulse results have
been demonstrated. The sensor operates in a dry medium and a mechanical deformation
was applied to the free end of the sensor as its stimulus. They used the experimental
frequency response of the trilayer sensor in order to model its output/input behavior as
a transfer function given by Equation (2-8).
(2-8)
The coefficients of the assumed transfer function have been then estimated using the
experimental transfer functions as follows
(2-9)
where is the number of amplitude ratio and phase measurements and its value is
greater than the total number of variables in Equation (2-8). Setting the assumed
theoretical transfer function to the obtained experimental one, a set of equations can be
obtained as
(2-10)
27
This set of equations can also be demonstrated in a matrix-vector format, as given
in Equation (2-11), and using a classical least squares estimation, the unknown
coefficient vector will be determined. Moreover, in order to obtain a reasonable fit
between the theoretical and experimental transfer functions, a cost function has been
described and finally, an empirical transfer function with minimum possible number of
poles and zeros was chosen.
(2-11)
It was further shown that this proposed transfer function is able to predict the
electrical output behavior of the conjugated polymer based sensor for frequencies up to
20 Hz. Moreover, the voltage output of the sensor resulted from the mechanical
deflection was estimated using a methodology based on the energy balance which was
experimentally validated. The experimental results obtained by the same research group
in another study [75] show that the resistance of the conjugated polymer based sensor
increases until the applied displacement frequency of 2 Hz. However, for frequencies
higher than 2 Hz, the sensor resistance increases resulting in a sharp decrease of the
current passing through the polymer layer regardless of the polymer effective length.
Moreover, in all their conducted experiments, the thickness of the sensor was remained
constant.
The effect of geometry on the output behavior of a trilayer conjugated polymer
based sensor was further investigated by John et al. [78]. The generated voltage and
current of the sensor were reported to vary by changing the geometrical variables of the
28
trilayer bender, and they were identified up to a maximum frequency of 300 Hz. Using
the experimental results, they proposed a methodology to optimize the output response
of the sensor. Two main characteristics of the output signal of the sensor namely the
bandwidth and the sensitivity were targeted for the optimization process. The range of
frequencies within which the gain of the sensor does not significantly change is the
bandwidth of the sensor, whereas sensor sensitivity is defined as the output signal
magnitude for a specific input signal. The effect of increasing different geometrical
variables (i.e., the effective length and the width of the sensor along with the thicknesses
of the PPy and PVDF layers) are presented in Table 2-3. It was also demonstrated that
the current generated by the CP based sensor increases by increasing the volume of the
conjugated polymer layers.
Table 2-3. The effect of increasing the geometrical variables of the trilayer sensor on its
output behaviors [78]
Parameter Bandwidth Sensitivity
Length Decrease frequency of upper limit Displacement: decrease Strain: increase
Width No change Increase
PPy thickness Increase frequency of lower limit Increase
PVDF
thickness Increase frequency of upper limit Increase
The change in the load applied to a bending type PPy sensor results in a change in
the capacitance of the polymer, as shown by Mirfakhrai et al. [79]. This change was
further applied in order to capture the sensing effect of the polymer through a
mathematical model. In their modeling methodology, the variation of the Young’s
modulus of the polymer due to the change in its oxidation state has also been taken into
account. This important effect is mostly disregarded in the studies conducted in this
field. Their obtained experimental results exhibited close agreement with their modeling
29
predictions. This mathematical modeling procedure is briefly described below and the
parameters used are listed in Table 2-4.
Table 2-4. List of modeling parameters
Parameter Description
Initial applied force
Final applied force
Stiffness of the polymer at its uncharged state
(zero charge level)
Stiffness of the polymer at an applied voltage of V
Initial displacement of the polymer
Final displacement of the polymer
Bias voltage applied between the sensor and a
reference electrode
It should be mentioned that , , and , where is
the input of the system and is the output. The electrical energy of the system
(
) changes at an open circuit upon applying a force to the sensor,
where and are respectively the initial and final potential between the working
electrode and the reference electrode minus the potential at which the stored charge in
the sensor is zero ( ). Moreover, and denote the initial and final capacitance of
the sensor, the values of which were estimated performing cyclic voltammograms at
various rates and potentials. The current work done by the sensor arises from the
change in the stored electrical energy of the system as well as the mechanical energy
that would have been stored at the uncharged state of the sensor ( ), as expressed
by Equation (2-12).
(2-12)
30
where is the applied force, and is the stored charge. The mechanical energy and the
total work done by the sensor are then calculated and the final expression accounting
for the output voltage of the conjugated polymer based sensor is given by
(2-13)
Equation (2-13) can approximately be simplified as the following equation which implies
that there is no sensing voltage when , and also the output voltage varies
linearly with the bias potential.
(2-14)
Along with the load sensing ability of polypyrrole, it is shown that this conjugated
polymer is capable of responding to an applied mechanical force while it is itself being
actuated [12, 80]. This sensing ability makes polypyrrole a promising candidate as a
feedback loop controller for the applications in which detection of an extra load on the
actuator is required. As an example, navigating a catheter within an artery can be
carried out using a PPy artificial muscle. When the catheter strikes the arterial wall, a
sharp increase in the applied load to the polymer occurs. Therefore, it is of critical
importance to detect this extra loading in order to prevent any internal bleeding caused
by a puncture in the arterial walls [79]. In order to verify this phenomenon, Mirfakhrai
et al. [79] conducted an experiment in which a cyclic external force was applied on a
film-type polypyrrole based actuator with a step voltage as its stimulus. The current
resulting from the combined effect of the applied voltage and external load was
monitored and then further processed to detect the changes in the load.
31
2.10 A brief review on multiobjective optimization procedures and
algorithms
Applying a mathematical model which leads to an optimized design of conjugated
polymer based actuators is of crucial importance since changing the design variables is
greatly influential on the performance of the actuator. Hence, along with the endeavors
made to obtain a precise, yet efficient, methodology to predict the performance of these
actuators, it is essential to optimize their physical configuration so as to meet their
designated performance specifications. The effects of changing design variables on the
performance of a film type trilayer actuator have been studied by several research
groups in order to obtain experimentally optimized actuators. The influence of different
actuator thicknesses for a uniform width and length was investigated by Minato et al.
[81]. They reported that higher thickness of the PPy layer in certain areas of the
actuator length results in improving its performance. Therefore, a geometrically
optimized actuator can be synthesized for desired applications. Alici et al. [82] further
demonstrated that for a bending actuator with constant length and width, a larger
bending moment can be obtained through actuating a strip with a higher thickness at
its root (i.e., the clamped end of the actuator). The characteristic output behaviors of
these actuators are mainly their tip vertical displacement, bending curvature, bending
angle, and tip generated blocking force as well as their response time. Each of these
outputs can be defined as an objective function in a multiobjective optimization problem
so as to be maximized/minimized, simultaneously.
Multiobjective optimization is of great practical importance considering the fact
that most optimization problems existing in real world include multiple conflicting
objectives. Applying classical methodologies, these problems were solved by artificially
converting the multiobjective problem into a single-objective one. This essentially
stemmed from lack of appropriate optimization techniques to find several optimal
solutions. However, the evolutionary means suggest solving such problems as they are,
32
without scalarizing them into a single-objective problem [83]. The major challenge with
multiobjective problems is their arising set of trade-off optimal solutions, known as
Pareto-optimal solutions. Since any two of these Pareto-optimal solutions comprise a
trade-off between the objective functions, it is of critical importance to obtain not only
one optimal solution but as many as possible. When such trade-offs are presented, one
can make a more precise choice for the final solution. Over the past 20 years the rise of
evolutionary algorithms (EAs), through which multiple Pareto-optimal solutions are
found simultaneously, has offered new horizons for research and applications in a wide
range of fields [83]. It is worth noting that in a multiobjective problem it is not intended
to find an optimal solution corresponding to each objective function. Generally, there
are two main goals sought in a multiobjective optimization namely: i) converging to the
Pareto-optimal solutions, and ii) maintaining a set of Pareto-optimal solutions which are
maximally spread.
Multiobjective algorithms mostly use the concept of dominance and try to find the
dominated solutions in a finite-sized population. Based on this concept, one can choose
the best solution among any two given ones in terms of all objective functions. This
leads to a final set of solutions, none of which dominate the others. Moreover, for any
solution outside of this specific set (known as non-dominated set), there exists a solution
inside the set that dominates the one outside. A point x* is considered as the Pareto
optimum or efficient solution of the problem if and only if there exists no x such that
for all . The image of all Pareto optimum points (all efficient
solutions) is called Pareto front or Pareto curve on which the optimum points are
consistently distributed [84]. Figure 2-6 shows an example of a feasible set C obtained in
which the Pareto front is defined by the points between ( , ,) and ( ,
).
33
Figure 2-6. The feasible set of a multiobjective optimization problem.
2.10.1 Optimization techniques
There are different algorithms and techniques one can use to solve a multiobjective
optimization problem two of which are briefly addressed in the following section.
a. Multiobjective optimization using Genetic Algorithm (GA): Both constrained and
unconstrained optimization problems can be solved using the Genetic Algorithm (GA).
It is suitable for objective functions with high nonlinearities and even non-
differentiabilities. It applies a natural selection process simulating the biological
evolution including an iterative process starting from a randomly generated population
of individuals. In each iteration the population is called a generation in which the fitness
of each individual is evaluated by solving the objective function designated in the
optimization problem. The more fitted individuals are randomly (stochastically) selected
as the parents of the next generation. Finally, an optimal solution will be found based
on two stopping criteria: i) the number of maximum generations has been reached, or ii)
the program has reached an adequate level of fitness for the population. This algorithm
is schematically depicted in Figure 2-7.
34
Figure 2-7. Flowchart representing the Multiobjective Genetic Algorithm.
b. Constrained nonlinear minimization using active-set algorithm: This algorithm is
designed to minimize a single nonlinear multivariable function subject to both linear and
nonlinear constraints. It is highly dependent on the nature of the imposed constraints of
the optimization problem. Opposed to the interior point methods, an active-set method
does not attempt to assure that the algorithm remains interior regarding the inequality
constraints ( . However, it determines the constraints that actively influence
the final result of the optimization. A constraint is considered as an active constraint at
if the value of the inequality constraint at is equal to zero ( ), whereas in a
non-active constraint this value is greater than zero ( ). This implies the fact
that all equality constraints are inherently active constraints. Furthermore, in each
iteration, the Lagrange multipliers of the detected active constraints are calculated and
35
the ones with negative Lagrange multipliers are removed from the subset. The general
structure of the active-set algorithm is illustrated by Figure 2-8.
Figure 2-8. Flowchart of the active set algorithm.
36
Chapter 3
PPy based trilayer actuators
Polypyrrole based trilayer actuators convert the input electrical energy into mechanical.
Consequently, they can be employed in many cutting edge applications owing to their
inherent properties, as discussed in Chapter 2. Along with the fabrication of different
configurations of PPy actuators, many modeling methodologies have been proposed.
These modelings assist to capture the actuation behaviour of the actuators and
explicitly predict their outputs. However, obtaining the most relatively desired output of
these actuators entails performing an optimization procedure based on a developed
mathematical model which is the main objective explored in this chapter.
3.1 Mathematical modeling and optimization model formulation
Recent studies on conjugated polymers have noticeably contributed in further
development of several aspects of CP based actuators such as their maximum attainable
strain, operating stress, work per cycle, and operating lifetime. However, these
improvements have been reported in different types of conjugated polymer actuators
under dissimilar conditions. Hence, attaining one single conducting polymer actuator
that simultaneously produces high blocking force, low response time, and high strain
rate is now of critical importance [10]. As pointed out in preceding sections, different
research groups have investigated polypyrrole (PPy) actuators, one of the most applied
CP based trilayer actuators with key properties such as low actuation voltage, large and
37
mechanically stable strain, high strength, high reversibility, and scalability to micro-
scale [7, 85]. PPy actuators are also biocompatible and light in weight, operating in air
and liquid environments [86].
In order to fabricate more comprehensive conjugated polymer based actuators, in
terms of their applications and performance predictability, a realistic mathematical
model is required to investigate, and consequently, improve the determining
characteristics of these actuators [59]. Hence, in recent years, several research groups
have proposed different mathematical models along with their experimental analyses.
Most of these models are designed to calculate the tip displacement of the actuator as
well as the blocking force in response to a stimulus. These modeling approaches have
been briefly addressed in Section 2.6.1. However, the described models mostly considered
the electromechanical behavior of trilayer actuators while their electrochemical
properties have a major impact on their output as well. Accordingly, it is of critical
importance to develop a model that describes the electrochemomechanical behavior of
the actuator along with prediction of its outputs under different actuating conditions.
Madden [30] developed a diffusive elastic metal (DEM) model to illustrate the
impedance of CP actuators. The relationship between the current across the CP layer
and the input voltage can be characterized through this model. Different mathematical
models have been formulated based on the proposed DEM model including the one
developed by Fang et al. [87]. They designed a self-tuning regulator considering the
simplified DEM model for conjugated polymer actuators. In another study conducted by
Hguyen et al. [88], the curvature and current response of a conducting polymer trilayer
actuator was captured through a model developed based on a diffusive impedance and a
double layer capacitance along with its charge transfer resistance. However, since the
linear elasticity theory is only applicable for low actuation voltages, the DEM model
may not be adequately appropriate in predicting the mechanical outputs of an actuator
with relatively larger strains. In this regard, Fang et al. [64] developed a nonlinear
mechanical model based on the nonlinear elasticity theory. The results were compared
38
with their counterparts obtained from the linear model showing that their nonlinear
approach is capable of demonstrating the actuator performance under a wider range of
applied voltages.
Reviewing the investigations conducted in this field indicates the importance of
optimizing the output behaviors of CP based actuators. An optimization process can
assist to achieve the actuators’ optimal geometrical characteristics using a mathematical
model, the results of which can efficiently be used to fabricate an actuator fulfilling the
performance desired for its designated applications. For this purpose, a multiobjective
non-linear optimization approach is developed based on two mathematical modeling
approaches. The first modeling strategy mostly stems from the electrical and mechanical
characteristics of the conjugated polymer layer with experimentally adjustable
parameters. The second approach is developed on the basis of fundamental principles of
a conjugated polymer film in contact with an electrolyte such as mechanical and
electrochemical. The developed models can then be employed to optimize the two most
significant outputs of trilayer actuators: their generated tip vertical displacement and
blocking force. In the next sub-sections the two modeling strategies, electrochemical and
electrochemomechanical models, are introduced accounting for the two outputs of
conjugated polymer based trilayer actuators and mathematically developed in order to
predict their nonlinear behavior. The characteristics and basis of these modeling
approaches as briefly pointed out in the preceding section will be discussed in more
detail in the following sub-sections.
3.1.1 Electromechanical model
The electromechanical behavior of a trilayer actuator is formulated considering the
model developed by Alici et al. [89]. In this model, geometric parameters as well as
mechanical properties of the PPy trilayer actuators are taken into account. There are
three main assumptions considered in this model:
39
i. Material properties of platinum (Pt) are neglected since the thickness of the Pt
layer is small compared to those of PPy and PVDF films.
ii. Expansion/contraction of the PPy layers is the main cause of induced stresses in
the conducting polymer actuator. It is assumed that these stresses are only in the
lateral direction, and are uniform in the two PPy layers. The uniformity in
distribution of the stresses indicates that the thickness of the PPy layers cannot
go beyond a certain limit.
iii. The strain distribution along the thickness of the actuator with respect to the
neutral axis is linear. In addition, each of the plane cross-sections is still
considered as a plane after the bending movement occurs.
In this work, since the thickness of the PVDF membrane utilized in all performed
experiments is the same, it is assumed to be a predetermined constant in the model. In
Figure 3-1, the geometric variables of a trilayer strip are depicted in which denotes
the effective length of the actuator, is its width, h1 is half of the thickness of the
middle PVDF layer, is the thickness of each PPy layer, and is the voltage applied
across the actuator.
Figure 3-1. Schematic of the trilayer actuator with its geometric variables.
The differential equation representing the vertical deflection of the bending actuator
is given by Equation (3-1) as reported by Alici et al. [89]. This equation is solved with
proper initial conditions to obtain the vertical deflection as a function of the horizontal
40
position of the actuator as well as the decision variables reflected in the optimization
process.
(3-1)
where is the vertical displacement, is the horizontal position of the actuator, is
the applied voltage, and are the elastic moduli of PPy and PVDF layers,
respectively, and is the capacitance obtained through dividing the electrical charge by
the applied voltage. In addition, is a coefficient which relates the stress induced in the
PPy layers to the exchanged charge density as follows
(3-2)
where is the stress, is the exchanged charge, is the volume of a PPy layer,
and denotes the CP layer transferred charge density. The induced stress is also given
by
(3-3)
where is the induced in-plane strain. Substituting Equation (3-2) into Equation (3-3),
the strain to charge density ratio () can be obtained by
(3-4)
The value of is experimentally estimated to be in terms of the applied voltage and
this estimation is reported to be valid for applied voltages from 0.05V to 0.6V as [88]
(3-5)
41
The vertical position of the strip, , is then given by the following expression through
solving Equation (3-1) with regard to the horizontal position of the actuator
(3-6)
Another characteristic output of the actuator is its generated blocking force
intended to be maximized in order to gain a more enhanced performance by the
actuator, and is estimated by [89]
(3-7)
According to the described electromechanical model, an actuator with larger width
produces a higher blocking force due to an increase in its overall stiffness. However, the
increase of the actuator rigidity results in reduction of the tip vertical displacement. On
the other hand, longer actuators with the same width and input voltage have higher
maximum tip deflection while they exhibit lower value of force output. It can also be
inferred from Equation (3-7) that by increasing the length of the actuator, its blocking
force decreases. Therefore, it is evident that there is a trade-off between the two
outputs, and the optimum variables should be obtained using a multiobjective
optimization process. Multivariable objective functions representing the outputs of the
actuator should be maximized, simultaneously. Equation (3-6) and Equation (3-7)
determine the tip vertical displacement and blocking force, respectively, and on that
account they are considered as the two multivariable objective functions of the
optimization procedure. The decision variables selected for the electromechanical model
are the geometric dimensions of the trilayer strip along with the applied voltage. These
42
geometrical variables are the effective length ( ), and width ( ) of the actuator as well
as the thickness of PPy layers ( ).
The nonlinear objective functions are subject to boundary constraints, giving an
upper and lower bound for each decision variable. In addition, a nonlinear equality
constraint should also be considered in order to set the curve-length of the actuator
equal to its effective length. This is due to the fact that it is assumed that the length of
the strip remains unchanged during actuation. For any given vertical position of the
actuator’s tip, its curve-length is set equal to through this nonlinear equality
constraint. Figure 3-2 illustrates the length correction of the bending curves of the
actuator for different applied voltages.
Figure 3-2. Length correction of the theoretical bending curve of the actuator for various
applied voltages.
43
The mathematical formulation of the objective functions along with their
corresponding imposed constraints can be expressed as follows
(3-8a)
(3-8b)
(3-8c)
where
where , and are the vertical deflection and blocking force of the tip, respectively. All
design variables are in the SI units. This mathematical model is then solved using two
different optimization algorithms. In both proposed methods, a set of optimum feasible
solutions are found stemming from the nonlinear multiobjective nature of the problem.
44
Any point within the feasible domain (satisfying all the constraints) can be considered
as one of the optimal solutions. The trade-off between the two multivariable functions
can clearly be observed in Figure 3-3. The maximum displacement of the actuator tip
occurs at the upper bound of its length and the lower bound of the PPy thickness,
Figure 3-3(a), while these values result in the minimum blocking force as seen in Figure
3-3(b).
(a)
(b)
Figure 3-3. Variation of (a) tip vertical displacement, and (b) blocking force of an
actuator based on the electromechanical model for different values of length and PPy
thickness with V=2V and w=1mm.
45
As pointed out, it should be noted that the proposed modeling methodology
constitutionally originates from the physical, electrical, and mechanical properties of the
conjugated polymer layer (PPy). The strain to charge density ratio parameter, , can
also be empirically adjusted in order to obtain an acceptable tracking ability with the
experimental results. Therefore, this modeling methodology is regarded as a physical
and electromechanical model with possible adjustable parameters.
3.1.2 Electrochemomechanical Model
This section describes the second optimization model developed in this study which
considers the electrochemical aspects of the trilayer actuator as well. This modeling
methodology mainly focuses on the frequency response of the CP based actuator. In
addition, the blocking force and curvature generated by the PPy actuator are defined as
the objective functions of the optimization problem.
3.1.2.1 Curvature
The diffusive elastic metal (DEM) model is a fundamental comprehensive modeling
strategy through which the electrochemomechanical behavior of the layered CP based
actuators can fully be captured. This modeling approach originates from the impedance
of an actuator in which a conducting polymer film is in contact with an electrolyte
solution on one side. As pointed out, it formulates the relationship between the applied
voltage and the current flowing through the conducting polymer films. The movement of
mobile ions initiates when the actuating voltage is applied across the polymer layer. The
porous PVDF membrane in the middle allows the ions and molecules to diffuse within
the film. However, not all mobile ions can diffuse through the interface between the CP
layer and the electrolyte. As a result, an electrochemically charged double layer will be
formed at the polymer/electrolyte interface considered as a parallel plate capacitor. The
DEM model is derived in the Laplace domain and its electrical admittance can then be
written as [30]
46
(3-9)
where denotes the diffusion coefficient, is the double layer thickness, is the
thickness of the CP layer, is the contact resistance and the resistivity of the middle
PVDF membrane containing the electrolyte, is the double layer capacitance, and
finally is the Laplace variable. The 1/2 multiplier arising in the equation is due to the
fact that a trilayer actuator consists of two CP layers with a double layer at each
polymer/electrolyte interface; hence, there are two double layers across which the
voltage is applied. Figure 3-4 depicts the diffusive model configuration and its elements
[30, 90]. This equivalent circuit characterizes the impedance of the polymer where is
the double layer capacitance, is the contact resistance along with the resistivity of
the electrolyte, and refers to the diffusion impedance for a film of finite thickness.
The diffusive impedance and the double layer capacitor are assumed to have a parallel
connection while the resistance of the middle polymer layer containing the electrolyte is
in series with the two former elements.
Figure 3-4. Schematic of the equivalent circuit for the DEM model.
In addition, the movement of ions through the polymer layer is assumed to be driven by
their diffusion, and the ions migration and convection are not taken into account [98].
47
Considering the relatively high conductivity of the conjugated polymer, the existing
ionic charge will rapidly be cancelled out by the electronic charge. Therefore, the
movement of ions is not rendered by the electric field within the polymer, and the
expansion/contraction of the CP layers is diffusion-driven. It is also assumed that no
electron transfer (Faradaic reaction) occurs between the electrolyte and the polymer
layer. Moreover, the effects of ion depletion near the polymer/electrolyte interface can
be neglected, since mass transport within the polymer is assumed to be much lower than
in the electrolyte. The main assumptions held in the DEM model can then be
summarized as [30]
i. The elastic moduli of the polymer layers are assumed to remain constant through
the actuation process.
ii. The PVDF membrane is porous and therefore, the ions and molecules can diffuse
within the polymer network.
iii. The migration effects of ions and solvent molecules are negligible.
iv. Comparing with the value of the applied voltage, potential drops along the
polymer are negligible.
v. Due to the fact that mass transport is assumed to be much slower than that of
the electrolyte, ion depletion near the polymer/electrolyte interface is assumed to
be insignificant.
vi. The double layer capacitor at the polymer interface is expressed by a parallel
plate model.
vii. At constant stress, the strain induced in the polymer is linearly proportional to
the polymer charge density.
The pure bending strain of the polymer layer can be determined using the following
equation while there is no external force applied on the beam.
(3-10)
48
where is the distance between the CP layer and the reference plane, is the bending
angle, is the radius of curvature, and is the curvature of the bending actuator. In
addition to the bending strain, the actuation effect is also taken into consideration. The
fundamental mechanical relations of the polymer are assumed to be linear elastic, with
the actuation strain linearly proportional to the exchanged charge density, , as given
by [32, 91]
(3-11)
where is the strain to charge density ratio. Therefore, the stress induced in a film-type
bending actuator can be obtained by superimposing the actuation effect term upon the
term indicating the bending effect as follows
(3-12a)
(3-12b)
In Equation (3-12a), the positive and negative signs refer to the contracted and
expanded layers, respectively. Assuming that there is no external force applied on the
beam (free bending), one can obtain the bending curvature as a function of the
exchanged charge density by setting the net force and net moment equal to zero as
shown successively in the following equations.
(3-13a)
(3-13b)
49
Solving Equation (3-13a) and Equation (3-13b) simultaneously, the curvature is
given by
(3-14)
where
The double layer capacitance has a minor effect on the total exchanged charge
comparing with the bulk capacitance of the PPy layers, and hence, the charge induced
in the actuator is mainly due to the conjugated polymer layers [30]. The charge density
in the Laplace domain is obtained as follows
(3-15)
Substituting Equation (3-15) into Equation (3-14), one can obtain the bending
curvature as
(3-16)
The system represented by Equation (3-16) tends to be dimensionally infinite due to
the arising hyperbolic tangent term; hence, it is not appropriate for real-time control
applications [87]. An alternative for circumventing this problem is to replace the
associated hyperbolic term by Taylor series expansion of hyperbolic tangent to simplify
the model. This expansion is subject to a constraint which results in an upper and lower
50
bound for the input frequency, and thus, it confines the model to low-range applied
frequencies. The first three terms of the series expansion used are as follows with
denoting the nth Bernoulli number and equal to
.
(3-17)
Equation (3-18) expresses an equality commonly used in previous studies to replace
the hyperbolic tangent terms [30]. Although this equality does not restrict the applied
frequency within a specific range, it imposes unnecessary complexity. In addition, the
effect of applied voltage frequency cannot be observed in low-frequency applications.
Using the two aforementioned equalities, the admittance is then simplified and used as
the transfer function for obtaining the frequency response of the bending curvature.
(3-18)
where , and . For low-frequency applications, the value of the
summation term replaced for the hyperbolic tangent does not significantly vary by
increasing , thus the terms associated with large values of can be ignored. Using the
first three terms of the series expansion ( ), one can obtain a third order
approximation for the bending curvature generated by the polymer actuator as given by
(3-19)
where and
are the zeros and poles of the simplified curvature transfer
function, respectively. They are in terms of decision variables and fixed parameters
considered in the optimization model.
51
3.1.2.2 Blocking Force
Subjecting the tip of the actuator to an applied force, maximum blocking force can be
obtained when there is no tip displacement (zero curvature). Given that the net
moments should be equal to zero, the moment generated by the external force cancels
out the effect of the induced bending moment at a fixed position as expressed by
(3-20)
Solving for , one can substitute (3-20), and (3-15) into Equation (3-9), and obtain
the generated tip blocking force as
(3-21)
where
A third order approximation can also be obtained
for the generated blocking force by implementing the simplification method similar to
that applied to the bending curvature.
(3-22)
where
and
are respectively the zeros and poles of the simplified transfer
function corresponding to the blocking force. The two objective functions defined in the
Laplace domain are then transformed into the frequency domain to obtain their
frequency response. To transform from Laplace domain to frequency domain, Bode plots
are used to determine the output transfer functions in terms of the applied frequency.
52
Therefore, the final objective functions of the optimization problem are defined by
assembling equations approximately representing their corresponding Bode diagrams.
The first step is to determine the zeros and poles of both transfer functions. In this
regard, the frequency range for each segment of the diagram is obtained and its
correspondent straight line is formulated. Furthermore, the proper equation is used as
the objective function according to the applied voltage frequency range. The input
frequency is assumed to be in the range of 0.01 Hz to 100 Hz. The objective functions
are formulated for each frequency range depending on the zeros and poles of the transfer
functions. The following is the mathematical expressions associated with the last
frequency range. Each logarithmic term arises due to one of the poles or zeros of the
transfer function. The lower bound of the frequency for this specific segment of the plot
is the largest absolute value amongst the zeros and poles while its upper limit is 100 Hz.
(3-23a)
(3-23b)
When a small step voltage is applied to the actuator, the generated vertical
deflection and blocking force is highly dependent on the frequency by which the driving
voltage varies between positive and negative values. As discussed, the range of input
frequency for each segment of the Bode plot is determined based on the poles and zeroes
of the transfer function. Figure 3-5 illustrates the variation of the poles and zeros
53
corresponding to the applied Taylor series expansion for various PPy thicknesses. The
remaining design variables are assumed to be predetermined since they do not affect the
values of poles and zeroes. It can be inferred from the figure that smaller ranges of
frequency are obtained by increasing the thickness of PPy layers. In order to observe the
effect of frequency on the actuator outputs through the simplified models, the
mathematical terms of which the objective functions are constituted should be acquired
from the second or higher segments of the Bode plot.
Figure 3-5. Variation of the poles and zeros of the curvature transfer function with
respect to different PPy thicknesses.
The Bode diagrams corresponding to the two reduced electrochemomechanical
models of a trilayer film-type actuator with specified dimensions, applied voltage, and
electrochemical properties are depicted in Figure 3-6a. As seen, the resultant Bode plots
of the simplifying strategies agree well. Each segment of these plots refers to a particular
mathematical equation in terms of the zeros and poles of the transfer function. The
appropriate curvature and blocking force equations are selected for a given frequency
54
range. They will then be subject to proper boundary constraints which confine the
optimal solutions to a feasible domain. Figure 3-6b implies that the approximately
formulated straight lines are in good agreement with the actual Bode plots. The largest
deviation is observed at the breakpoints of the plots (i.e., ),
while smaller deviations occur at points where a new segment of the graph initiates.
(a)
(b)
Figure 3-6. Frequency response of the bending curvature using (a) reduced DEM
models, (b) mathematically estimated Bode diagrams of the reduced models.
55
The tip vertical deflection of the actuator can be obtained in terms of its bendin
curvature through solving Equation (3-24) for which is derived from geometric
calculations for a cantilever beam.
(3-24)
Figure 3-7 represents the variation of the tip vertical displacement resulted from the
reduced model using Taylor series expansion. The input signal frequency is ranged from
0.88 Hz to 1.49 Hz corresponding to the second segment of the objective functions with
specific values of the remaining design variables.
Figure 3-7. Variation of tip vertical displacement for different input frequencies.
Having obtained the mathematical formulations for the segments of the Bode plots
of the actuator bending curvature and blocking force, the optimization model for the
second segment of the model is expressed as
56
(3-25a)
(3-25b)
(3-25c)
(3-25d)
where
It is also worth considering that the electrochemomechanical modeling methodology
stems from the basic polymeric, mechanical, and electrochemical principles of a
conjugated polymer film in contact with an electrolyte. Starting from these basic
principles, the multi-aspect behavior of the described trilayer conjugated polymer based
actuator is modeled with appropriate imposed constraints.
3.2 Optimization algorithms
As pointed out in Chapter 2, there are different optimization algorithms and
methodologies applied to solve an optimization problem two of which were briefly
addressed, multiobjective optimization using Genetic Algorithm (GA), and constrained
57
nonlinear minimization using active-set algorithm. Using these two algorithms, the
described optimization models are solved and the optimum range for the specified
decision variables is obtained. Figure 3-8a represents the feasible set obtained for the
electrochemomechanical model in which the Pareto front is defined by the points
between ( , ) and ( , ). The obtained Pareto front of the two defined objective
functions considered in the electrochemomechanical model is then shown in Figure 3-8b.
The values for both objectives are negative considering that the input functions are
minimized by the solver; however, their absolute values are maximized.
(a)
(b)
Figure 3-8. The electrochemomechanical model’s (a) feasible set, (b) Pareto front of the
two competing objective functions.
58
The active-set algorithm is used for a single-objective optimization problem and
given that there are two separate objective functions in the proposed model; the
multiobjective optimization problem is converted into a single-objective. One objective
function is considered as the main objective and the problem is solved for different
initial points. The value of the second objective is evaluated through a non-equality
constraint and the solutions relatively close to the optimal points are listed as the final
results of the optimization problem. It should be noted that before applying this
algorithm, the existence of an optimal point in both objective functions has to be
verified. Concavity or convexity of a function is a sufficient condition for its optimality.
In this regard, the Hessian matrix of the multivariable functions should be
definite/semi-definite and therefore, the quadratic form of their Hessian matrix is
calculated. In the positive semi-definite condition, ( ), is a non-zero column
vector of decision variables, is the Hessian matrix, and is the transpose matrix of
. The values of for the objective functions of the electrochemical model are
plotted with respect to their given range of design variables, (Figure 3-9). It can be
observed that the sufficient optimality condition is satisfied within the specified range of
design variables. The objective functions are positive semi-definite in their corresponding
feasible set which indicates their convexity. The optimality of the second model is also
examined using the same procedure.
59
(a) (b)
(c) (d)
(e) (f)
Figure 3-9. Semi definite condition for optimality of the objective functions of the
electrochemical model.
60
3.3 Experimental procedure and analysis
Fabrication of the trilayer actuators along with the performed experiments in order to
verify the mathematical models are described in this section.
3.3.1 Actuator fabrication
PPy films are produced by means of electrochemically polymerizing pyrrole (Py)
monomers on a substrate. This process consists of three major steps as follows
i) Preparation of the electropolymerization solution: the main solvent in the
electropolymerization solution is propylene carbonate (PC) due to its low vapor
pressure which allows the actuator to operate in air for a longer time period. In order
to provide dopant ions for the redox reaction, using different salts has been reported
such as: tetrabutylammonium hexafluorophosphate ( ), and bis
(trifluoromethane) sulfonimide lithium salt (LiTFSI). The experimental results from
previous studies show that the latter results in higher strain rates and consequently
in both higher displacement and force output. Furthermore, the response time of
/ actuator is shorter leading to stronger resonance amplification [10].
Another composition of the electrolyte is Py that was distilled prior to the deposition
on the core membrane of the actuator. Water was finally added to the solution so
that the electropolymerization process would be improved at colder temperatures.
Both Py and LiTFSI were added at a concentration of 0.2 M.
ii) Sputter coating of the PVDF layer with platinum: the core membrane (i.e.,
polyvinylidine fluoride) with a thickness of 110 m was made electrically conductive
by sputter coating an ultra-thin layer of platinum on each side of the membrane.
This incorporated layer increases the electrical conductivity between the electrolyte
and PPy layers.
iii) Electropolymerization process: the final step is to galvanostatically
electropolymerize Py monomers onto the faces of the sputter coated PVDF. In order
61
to minimize the unavoidable curling of the samples, the membrane was soaked
overnight in pure propylene carbonate solution after it was cut to size to fit the
Teflon electropolymerization vessel and sputter coated. Once it uptakes the PC and is
placed flat for a while, it relaxes to a more flat state. This is also helpful to reduce
any wrinkling that might otherwise occur if the membrane is installed dry into the
frame of the vessel and then immersed into the electropolymerization solution. Since
the membrane grows in size upon wetting while the edges are constrained by the
frame, it tends to buckle out of the plane providing that it was not initially wet. It is
also worth mentioning that there will be some curling unavoidable if a unimorph
actuator is being fabricated (single conductive polymer layer on a membrane) due to
the induced eccentric strain upon deposition. This is considered as one of the several
reasons that bimorphs are a superior design; however some applications entail the use
of a unimorph design which is inevitable. The electropolymerization process was
performed with a current density of 0.1 mA/cm2 and for durations of 6, 9, 15, and 18
hours and therefore, different thicknesses of PPy layers were obtained. Two stainless
steel plates were placed inside the vessel as the counter electrodes, whereas the PVDF
membrane acted as the working electrode. A schematic configuration of the
experimental setup for the samples fabrication is illustrated in Figure 3-10.
Figure 3-10. Schematic configuration of the fabrication and electropolymerization setup.
62
Following the electropolymerization process, the samples were rinsed with acetone
to remove any un-deposited remaining polymer. They were then cut into proper
dimensions and stored in a solution of PC and well dissolved LiTFSI for future
experiments.
3.3.2 Microstructure of the fabricated trilayer actuators
The cross sectional microstructures of PPy trilayer strips are indicated in Figure 3-11
and Figure 3-12. The porous structure of the middle PVDF layer can be observed in the
Scanning Electron Microscopy (SEM) image and its thickness is measured to be 110 m.
Figure 3-11 depicts the cross sectional image of a sample after 6 hours of
electropolymerization with an approximate PPy thickness of 10 m. Various PPy
thicknesses are obtained by changing the duration of electropolymerization process. It
can be noticed that increasing duration of the reaction process results in thicker PPy
films.
Figure 3-11. The cross sectional microstructure of a PPy trilayer actuator.
63
(a)
(b)
(c)
(d)
Figure 3-12. SEM micrographs illustrating the cross-sectional morphology of trilayer
actuators with various PPy thicknesses obtained after (a) 18-hour, (b) 15-hour, (c) 9-
hour, and (d) 6-hour electropolymerization of pyrrole monomers.
3.3.3 Measurements
The force and displacement measurements should be carried out once the actuator has
reached its steady state which normally occurs after the first 20 cycles [32].
64
3.3.3.1 Displacement
A step voltage was applied as an input to initialize the bending movement of the
fabricated actuators. The voltage amplitude was set to 1 V, 0.8 V, 0.6V, and 0.4 V and
the frequency of the applied voltage varied between 0.2 Hz and 1 Hz. Dimension of each
strip alters corresponding to the results obtained from the optimization process. The
actuator bending movement was recorded by a digital camera with a grid paper placed
behind the strip. Several images with a proper number of frames per second were
captured from the actuators’ recorded bending movement. Using an image processing
software (imageJ), the maximum tip vertical displacements were measured for different
widths, lengths, and applied step voltages. Figure 3-13 shows the schematic of the
displacement measurement setup.
Figure 3-13. The experimental setup depicting the process of tip displacement
measurement.
Using the abovementioned setup, the vertical deflection generated by the tip of the
trilayer actuator was measured over a specific period of time for different applied
frequencies as well as different values of input square voltages. Figure 3-14 clearly shows
that after a number of cycles the tip displacement of the trilayer strip reaches its steady
state.
65
(a) (b)
(c) (d)
Figure 3-14. The measured tip vertical deflections of a trilayer actuator over the
actuation time for different applied voltages and frequencies, (a) 0.1 Hz, (b) 0.2 Hz, (c)
0.3 Hz, and (d) 0.4 Hz.
66
The frequency response of the actuator regarding its tip vertical deflection is also
depicted in Figure 3-15 for a range of applied voltages. It is evident that higher
frequencies and higher applied actuation voltages result in higher vertical displacement
of the tip of the actuator.
Figure 3-15. The measured variation of the tip vertical displacement of the actuator
with the applied frequency for different applied voltages.
3.3.3.2 Blocking Force
The force generated by the actuator was measured under the conditions similar to those
applied for the displacement measurements. The tip displacement was remained at zero
and the tip blocking force was monitored using a force gauge with a resolution of 0.005
mN as schematically shown in Figure 3-16. Using a software interface, the values of the
measured blocking force of the conjugated polymer actuator were recorded from the
force gauge.
67
Figure 3-16. Schematic of the experimental setup for the force measurement of the
actuator under different input voltages.
3.4 Optimization results
The effects of design variables on the two multivariable objective functions of the
optimization problems are represented in Figure 3-17. Additionally, the performance of
the proposed models (i.e., the electromechanical model (1), the reduced form of the
electrochemomechanical model using Taylor series expansion (2), and the conventional
equality (3)), can be compared. As illustrated in the figures, there is good agreement
between the models in terms of their prediction of the actuator’s outputs. The value of
the blocking force generated by the tip of the actuator is highly dependent on the
effective length of the bending actuator. For a predetermined induced bending moment
of the actuator, a longer geometry results in a lower value of the tip blocking force as
depicted in Figure 3-17b. According to both models (i.e., electromechanical, and
electrochemomechanical), the value of the actuator’s blocking force is independent of the
width of the strip while its tip displacement decreases for wider geometries due to an
increase in its overall stiffness. Furthermore, a higher input voltage results in increasing
the rate of the redox process owing to the higher diffusion rate of the ions into and out
of the polymer films. Consequently, the contraction and expansion of the conjugated
polymer layers will initialize faster. This implies the fact that by increasing the applied
68
driving voltage, the value of both objective functions increase as shown in Figure 3-17e,
and Figure 3-17f.
(a) (b)
(c) (d)
(e) (f)
Figure 3-17. Effect of design parameters on the objective functions based on the
described models.
69
The results acquired from both solution strategies are depicted in Figure 3-18. In
the optimization process carried out for the electromechanical model, due to the highly
nonlinear equality constraint associated with the curve length, the fmincon solver
(www.mathworks.com) did not find an optimal point within the selected value of the
constraint tolerance. Therefore, the optimization was performed considering the
boundary constraints, and accordingly, the related errors were calculated. The
maximum error of the obtained optimal points is less than 2%, implying an acceptable
distance of the points from the actual solutions. This error is essentially due to the
assumed bending movement of the actuator. As the tip of the strip initiates to bend, its
horizontal position is no longer equal to the effective length of the actuator.
Each point on the curves corresponds to a particular set of values for decision
variables. Therefore, by defining an appropriate region on the graphs in which both
objective functions are within the intended domains, a range for each decision variable
can be determined. The results show that the active set algorithm and multiobjective
GA are following the exact same trend; however, there is a slight difference between the
values obtained from the two algorithms. The multiobjective GA generates higher
values for the two objective functions as one can observe in Figure 3-18.
70
(a)
(b)
Figure 3-18. Results obtained from the two optimization algorithms for (a)
electromechanical, (b) electrochemomechanical models.
71
In order to determine an optimal region in the obtained set of solutions, the mean
values of the resulted blocking force ( ), and tip vertical deflection ( ) along with
their corresponding standard deviations, and , are calculated. An optimal interval
of is chosen for each set, and the decision variables belonging to both
intervals are selected to be the final optimal solutions of the optimization problem.
Figure 3-19 shows the optimum region selected for the electromechanical model resulted
from the multiobjective GA. The set of solutions obtained from multiobjective GA is
illustrated in Table 3-1, and the optimal values of each decision variable within the
confidence interval are highlighted. A similar procedure can be performed for the results
obtained from the electrochemomechanical model. It should be noted that all the points
on the Pareto curve are non-dominated solutions of the problem signifying that if one
goes from one solution to another one, it is not possible to improve on one objective
without weakening the other one. Therefore, it is of critical importance to ensure that a
set of optimal solutions within an acceptable range will be reached and chosen by the
decision maker.
Figure 3-19. Blocking force and tip displacement optimal region resulted from the
optimization of the electromechanical model.
72
Table 3-1. The optimal set of design variables and their resulting objective functions
obtained from electromechanical model
Y
(mm)
F
(mN)
L*
(mm)
w*
(mm)
h2*
( m)
V*
(V)
2.12 0.202 20.0 3.77 50.0 0.998
2.33 0.201 20.0 3.46 49.7 0.997
2.36 0.198 20.1 3.48 48.7 0.998
2.55 0.195 20.1 3.29 46.6 0.997
2.71 0.191 20.4 3.10 47.8 0.994
2.85 0.191 20.2 3.05 43.9 0.997
3.08 0.173 20.8 3.10 37.8 0.994
3.18 0.173 20.5 3.10 32.5 0.994
3.32 0.168 20.6 3.06 30.8 0.995
3.78 0.142 21.5 3.04 20.6 0.993
3.81 0.140 21.7 3.04 21.0 0.993
3.97 0.130 22.6 3.02 21.5 0.993
4.15 0.122 22.7 3.03 15.5 0.990
4.25 0.111 24.2 3.07 19.3 0.993
4.40 0.103 25.2 3.06 20.7 0.992
4.63 0.095 26.1 3.07 17.8 0.994
4.91 0.087 26.9 3.03 15.0 0.990
5.17 0.078 28.6 3.02 17.3 0.991
5.47 0.070 30.2 3.04 15.5 0.990
5.57 0.068 30.4 3.03 15.0 0.991
5.76 0.063 31.7 3.03 15.5 0.992
6.18 0.054 34.8 3.05 18.7 0.992
6.31 0.052 35.3 3.05 17.5 0.993
6.44 0.051 35.0 3.03 14.2 0.992
6.55 0.049 35.8 3.03 14.9 0.990
6.70 0.047 37.0 3.01 17.4 0.992
6.95 0.044 38.4 3.01 17.4 0.995
7.08 0.042 39.1 3.02 17.0 0.992
7.38 0.039 40.0 3.02 13.8 0.992
7.38 0.039 40.0 3.02 13.8 0.991
73
Table 3-2. The theoretical values of the average, standard deviation, and the confidence
interval for the two objective functions
Average ( ) STD ( )
Y(mm) 4.71 1.68 6.40 3.03
F(mN) 0.110 0.059 0.170 0.050
The outputs of fabricated actuators with different lengths and PPy thicknesses were
measured under a range of applied step voltages. The trend of experimental results was
in good agreement with their modeling counterparts as depicted in Figure 3-20, and
Figure 3-22. Since it was assumed that the strain to charge density ratio is a function of
applied voltage, the proportionality of the blocking force to input voltage is not linear,
and this can be observed in Figure 3-22a. Moreover, a higher input voltage leads to a
higher amount of charge passed through the PPy layers, and consequently, results in
larger tip displacement and blocking force owing to a higher rate of reduction and
oxidation of the conjugated polymer. However, it should be noticed that the applied
voltage is required to maintain within a small range (less than 2V) so that the Young’s
modulus of PPy remains unchanged. Changing the effective length of the actuator, the
reverse and nonlinear behavior of the output tip deflection and blocking force is
illustrated in Figure 3-20a.
74
(a)
(b)
(c)
(d)
Figure 3-20. Results attained from actuating a trilayer actuator with =10 m, and
=5 mm under different applied potentials and with a varying length: (a) and (b)
electromechanical model, (c) and (d) experimental.
75
The experimentally measured generated blocking force of the trilayer actuators are
compared in Figure 3-21 with the ones resulted from the electromechanical model. As
discussed, the electromechanical modeling methodology suggests that the generated
blocking force of the tip of the actuator linearly varies with the applied driving voltage.
This linearity can also be observed through the obtained experimental results depicted
in Figure 3-21.
Figure 3-21. Experimental vs. numerical values of the blocking force of an actuator for different effective lengths and applied voltages.
As pointed out, the strain to charge density ratio is assumed to be in terms of the
applied voltage. Using Equation (3-5), the values of the output blocking force for
different effective lengths are represented as dashed lines in Figure 3-22a, while the solid
lines are plotted using the average value of this coefficient. It can be observed that there
is a deviation between the resulted values of the blocking force which occurs at an input
voltage of 0.6V and higher. This is due to the estimated equation applied for the strain
to charge density ratio which is applicable for voltages within the range of 0.05 V to 0.6
V.
76
(a)
(b)
(c)
(d)
Figure 3-22. Results attained from actuating a trilayer actuator with =30 m, and
=3 mm under different applied potentials and with a varying length: (a) and (b)
electrochemomechanical model, (c) and (d) experimental.
77
Chapter 4
PPy/MWCNT layered actuators
Despite the advantageous features of conjugated polymer actuators as briefly addressed
in the preceding chapters, they also have some shortcomings. For instance, their low
electrical conductivity while they are in their discharged state results in degrading their
rate performance. This chapter describes an investigation intended to overcome the
aforementioned shortcoming of the neat PPy actuators through incorporating a layer of
MWCNT into their laminate structures.
4.1 MWCNT layer incorporation into the structure of a neat PPy actuator
The low electrical conductivity of neat PPy trilayer actuators could suppress their
performance and limit their strain rates. Moreover, the rate of mass transport of ions
into and out of the polymer layer is relatively low in CP based actuators [92]. To tackle
and overcome this problem, it is possible to use a highly conductive layer in the
structure of the actuator to improve its electric charge delivery across its length [93].
One of the potential candidates for this purpose is a thin layer of multi-walled carbon
nanotubes (MWCNT). This layer can be placed as a conductive film in the structure of
the actuator owing to its high electrical conductivity, high Young’s modulus, high
strength, fast response, and good chemical stability [94]. Therefore, by applying this
design configuration, the mechanical and electrochemical properties of the trilayer
actuator are expected to be improved.
78
On the other hand, one of the main design characteristics of a multidisciplinary
system or process such as a CP trilayer actuator is the trade-off among several design
variables. This trade-off can improve or most of the time can compromise the main
performance of the designed systems if it is not systemically controlled. Therefore, to
design and fabricate actuators with a large number of variables stemming from their
various mechanical characteristics and constituent materials, it is a determining key to
develop a system that can capture all these variables and their interconnected relations
in a unique framework. Furthermore, this developed system or mathematical model not
only can effectively assist to gain a better understanding of the underlying design
variables and their relationships, can also reduce the time and cost associated with the
design of experimental analysis. In view of this fact, therefore in this work, a
mathematical model is developed to optimize the designated decision variables
corresponding to the actuators’ desired behaviors. For the conjugated polymer based
actuators, these desired behaviors are considered as their tip vertical displacement,
generated blocking force, and response time. As pointed out, the main characteristic of
this type of systems is their multi-criteria design decision making process which is taken
into account through defining a nonlinear multiobjective optimization problem. In this
regard, the trade-offs existing among the aforementioned behaviors of the actuators
captured through the multiobjective functions are methodically employed through
obtaining the corresponding optimal design variables. Along with the analytical
investigations conducted in this work, a bending-type trilayer actuator was fabricated
comprising a film of PVDF sandwiched by two outer PPy electrode layers on which a
thin film of MWCNTs was electrophoretically deposited. The CNT layer acts as a
conductive interface between the inert non-conductive PVDF membrane and the
conjugated polymer electrodes. The experimental results are then used to discuss their
numerical counterparts and findings.
79
4.2 Mathematical modeling
The configuration of the trilayer conjugated polymer based actuator is schematically
depicted in Figure 4-1, where and are the width and effective length of the actuator,
respectively, is half of the thickness of the PVDF membrane, is the CNT layer
thickness, is the PPy layer thickness, and is the applied voltage.
Figure 4-1. Schematic of the trilayer bending actuator with an incorporated layer of
MWCNT and its geometrical variables.
Upon immersion in an electrolyte solution, the DEM model can be applied to obtain
the admittance of the polymer strip in order to relate the current passing through the
polymer to the applied driving voltage. Similar to the previous chapter, based on the
equivalent circuit of the trilayer actuator in which the polymer/electrolyte interface is
considered as a parallel plate capacitor, the admittance is given by Equation (3-9). In
addition, convection and migration of ions and solvent within the polymer are negligible
and the movement of ions through the polymer layer is assumed to be diffusion-driven.
The internally induced stress in each CP layer of the actuator and the PVDF
membrane is analogous to those given by Equation (3-12a) and Equation (3-12b). When
the conjugated polymer layer is expanded or contracted, the actuation strain
proportional to the strain-to-charge ratio ( of the polymer will be generated arising
from the transferred charges in the CP layers. Therefore, the total strain will be the
80
summation of the strains induced by the actuation as well as the geometry of the
actuator. However, since there is no actuation in the PVDF and CNT layers, their
generated strain originates only from their geometry. The induced stress in the CNT
layer is then given by Equation (4-1) as follows
, (4-1)
where is the bending curvature of the actuator, is the induced strain in the
CNT layer, is the elastic modulus of the multi-walled carbon nanotube layer,
and denotes the distance between the film and the reference plane. Moreover, the
strain-to-charge ratio is shown to be a function of the applied voltage for low operating
voltages as presented by Equation (3-5) [88].
The bending curvature of the trilayer actuator can be obtained via the balance of
moment at equilibrium, when the actuator undergoes a free deflection. This will result
in a mathematical expression for the actuator bending curvature in terms of its
exchanged charge density. Equation (4-2) signifies the summation of the moments
generated by each layer of the actuator as: two PPy layers ( = 1 and 5), two MWCNT
layers ( = 2 and 4), and one PVDF film ( = 3).
(4-2)
When the actuation voltage is applied to the trilayer actuator, the bulk capacitance
of the polymer demonstrates the total exchanged charge which is considered as an
indicator for the maximum contraction and expansion of the polymer strips. This
electrochemical phenomenon can be captured through the mathematical equation:
, and therefore using the DEM model, the final expression for the
bending curvature in the Laplace domain is
81
(4-3)
The following equation defines as
(4-4)
where , and . A similar procedure can be
employed to obtain the maximum tip blocking force of the actuator when there is no
bending (zero tip displacement) while a vertical force is being applied on the tip.
Equation (4-5) is the mathematical expression representing the tip blocking force in the
Laplace domain.
(4-5)
where . The hyperbolic tangent terms
appearing in Equation (4-4) and Equation (4-5) result in a dimensionally infinite system
and therefore, the model is reduced using the same procedure as explicitly explained in
the previous chapter. The hyperbolic tangent terms are replaced by the first three terms
of the equivalent series expressed by Equation (3-18). The reduced form of the model is
then given by Equation (4-6a) and Equation (4-6b).
(4-6a)
82
(4-6b)
where and
are the zeros, and
and
are the poles of the
curvature and blocking force transfer functions, respectively. In addition, these poles
and zeros are functions of the specified design variables. The frequency responses of the
two transfer functions are defined in order to formulate the objective functions for the
optimization model. For this purpose, their corresponding Bode plots are
mathematically derived, and set as the multivariable objective functions of the model. It
should be noted that the derived objective functions are in essence dependent on the
values of the zeros and poles of the described transfer functions. Each segment of the
Bode plots corresponds to a different frequency range, and can mathematically be
represented by a specific formulation. In order to obtain the appropriate objective
function for each segment, the algorithm portrayed in Figure 4-2 has been developed for
a transfer function including two zeros and three poles. This algorithm leads to a six-
segment Bode plot, and the frequency of each segment ranges between two of the poles
and zeroes depending on their values. For instance, in segment 2 the range of the
applied frequency, , can be decided based on four different scenarios as follows
If and then
If and then
If and then
If and then .
The first segment of the estimated graph is a straight line with a value including all the
zeroes and poles of the transfer function as pointed out in the figure. Starting from the
mathematical expression corresponding to this straight line, the value of the minimum
zero of the transfer function is compared to that of the minimum pole, and the lowest
83
one will be replaced by the frequency ( ) term in the expression of the subsequent
segment. This procedure will continue until all six segments are formulated. Therefore,
implementing this algorithm, the mathematical formulation of the bending curvature of
the actuator can be obtained in terms of the applied frequency regarding the following
two main principles; the order of the zeros and poles values, and the designated
frequency segment number of the corresponding Bode plot (which ranges from 1 to 6, as
indicated in Figure 4-2). Ultimately, the final mathematical expression of the tip vertical
displacement of the actuator is developed through converting the bending curvature of
the strip into its vertical deflection. The same algorithm is applied to derive the
frequency-dependant tip blocking force.
Figure 4-2. The developed algorithm to define the bending curvature of the trilayer
actuator for each segment of its corresponding Bode plot.
84
Another crucial characteristic of conjugated polymer actuators is their response time
to the actuation stimulus. Improving the response time of CP based actuators can
furnish a better performance and more applicability. A sluggish response to the applied
voltage results in diminishing their possible usage in many fields where instantaneous
response is a decisive factor. Two time constants accounting for two different physical
interpretations were reported in the literature [30].
(4-7a)
(4-7b)
Equation (4-7a) demonstrates the time required by the double layer capacitance to
be charged. The rate of diffusion of ions decreases as the double layer charging time
increases. As a result, if the time by which the voltage is applied across the polymer is
shorter than , the double layer remains uncharged, and thus, there will be no bending
movement. In the DEM model, the double layer capacitance is related to its thickness
through the solvent dielectric constant ( ) using the parallel plate or Helmholtz model
[98] as expressed by: , where is the electric constant with a value of
. The second time constant, , corresponds to the time span required
for the diffusion of ions into the polymer layer. At times shorter than , the ions do not
essentially acquire a uniform concentration through the polymer film thickness.
Accordingly, these two time constants contribute to evaluating the response time of the
CP based actuators and are intended to be minimized, simultaneously.
4.3 Optimization modeling procedure
In order to justify the structure of the optimization model, it should be pointed out that
due to the aforementioned trade-off among the three characteristic behaviors of the
trilayer actuator (i.e., the tip vertical deflection, generated blocking force, and response
time) they do not change toward their desired direction simultaneously, although they
85
all appear at the same time. It is intended to reach the maximum possible tip vertical
deflection, maximum tip blocking force, and minimum response time at the same time.
This signifies the need for a multiobjective optimization which imposes boundaries at
certain dimensions for the selected design variables and defines their nonlinear
relationships. The optimization algorithm employed to determine the optimal values of
each decision variable considered in this study is a multiobjective Genetic Algorithm
(GA). As pointed out in the preceding chapters, by applying this algorithm a range of
optimal solutions to the problem, each called a Pareto optimum point, is obtained
through imposing a set of appropriate constraints. Since three multivariable objective
functions are considered in this proposed model, their corresponding image of Pareto
optimum solutions form a surface on which these points are consistently distributed. All
points on this surface map to a specific value for each design variable as well as
objective function. Depending on the desired values of the objective functions, each
Pareto optimum point can be picked by the decision maker as the final solution to the
optimization problem.
As discussed, the first two objective functions are the frequency-dependant tip
vertical deflection of the trilayer actuator and its generated blocking force. Due to the
trade-off existing between these two objective functions, increasing one will result in
decreasing the other. They are both defined in the frequency domain using their
corresponding Bode diagrams. The mathematical expressions associated with these two
objectives are dependent on the range of the applied frequency. Therefore, a particular
multivariable objective function will be used for each frequency range. As for the third
objective function of the optimization problem, the two time constants described in the
preceding sections are to be minimized at the same time. In order to define a single
objective function as an indicator of the response time of the actuator including both
time constants, a utility function has been defined. Utility functions represent the
relative preferences or sensitivities of the objective functions by assigning a specific
ranking to each of them. Regarding the two time constants, since the range of is
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lower than that of by four orders of magnitude, the final result of the optimization
problem will be highly affected by the latter one. To make the results equally sensitive
to both time constants, a utility function is defined as
(4-8)
where and are constant numbers, the values of which are assigned in accordance
with the range of the two time constants. The indifference curves of the defined utility
function are illustrated in Figure 4-3 and Figure 4-4 in which each contour line
represents a rank of utility. Given the value of each time constant, the corresponding
level of utility can be obtained from the figure. Any two points lying on the same
contour are associated with the same level of utility. This implies that the choice of any
combination of the two time constants is indifferent provided that they are on the same
level curve. However, since both time constants are in terms of design variables, each of
their combination results in a different value for the decision variables, although they
possess equal ranks of utility.
Figure 4-3. Variation of the response time utility function with and with the
contour lines demonstrating the indifference curves.
87
Figure 4-4. The indifference curves of the designated response time utility function for
the two time constants.
The decision variables in the optimization model are the width and effective length
of the actuator, the corresponding thicknesses of the PPy and CNT layers, along with
the applied actuation voltage and its frequency. The mathematical formulation of the
multiobjective problem is represented by Equation (4-9a). The objective functions are
subject to three types of constraint:
i. A set of boundary constraints, Equation (4-9d), defining upper and lower bounds for
each design variable.
ii. A nonlinear non-equality constraint, Equation (4-9b), to determine the range
of the driving voltage frequency corresponding to the second segment of the
Bode plot. Therefore, the objective functions designed in this model are the
ones defined for this specific frequency range using the described algorithm.
iii. A nonlinear equality constraint, Equation (4-9c), that sets the curve-length of
the actuator equal to its effective length. The horizontal position of the tip of
88
the actuator is represented by . Moreover, all parameters and decision
variables are defined in the SI unit system. During the actuation process, it is
assumed that the trilayer layer actuator does not elongate and its effective
length remains constant.
(4-9a)
(4-9b)
(4-9c)
(4-9d)
where
89
4.4 Fabrication process
Deposition of a thin layer of MWCNTs on an electrode surface has been reported by
several research groups employing different methodologies and experimental set-ups.
Electrophoretic deposition (EPD) of multi-walled carbon nanotubes is known to be a
promising technique to produce a homogeneous and uniform film of MWCNTs on a
metallic substrate [95]. EPD has gained increasing attention due to its versatile
applicability as well as simplicity. It has been shown to be a cost-effective technique
through which the thickness of the coating can be controlled, and different types of
conductive substrates can be employed as the deposition electrode [96]. Synthesis of a
bilayer bending-type actuator composed of an electrochemically deposited CP layer on a
film of super-growth single-walled carbon nanotubes (SG-SWNT) has been reported by
Mukai et al. [97].
The PPy trilayer actuators synthesized for this study are analogous to those
fabricated for the previous study with an extra layer of MWCNT incorporated into their
structure. As pointed out in Chapter 3, the middle porous PVDF membrane acts as an
electrolyte tank as well as an insulator while the actuation occurs in the two CP layers
through applying a low driving voltage. In order to fabricate the strips, the PVDF film
was made electrically conductive by sputter coating of a very thin layer of platinum on
its both sides. Subsequently, a layer of MWCNTs was electrophoretically deposited on
the platinum coated PVDF membrane. Electrophoretically deposited films are generally
produced through applying a DC electric field to a well dispersed and stable solution of
powder material in a suitable solvent. The charged particles are forced to move towards
an oppositely charged deposition electrode which results in a homogeneous
microstructure and coherent deposition of the particles [99]. Prior to initializing the
90
deposition of nanotubes, it is required to purify and functionalize the nanoparticles due
to their probable impurities such as amorphous carbon or catalyst particles [100, 101].
In order to remove these impurities, oxygen functional groups were introduced onto the
surface of the CNT particles through an oxidation process. It was reported that the
density of these acidic sites is related to the mixture ratio of the acid solution [102]. The
acid treatment process was carried out by refluxing 0.8 g of multi-walled carbon
nanotubes in 60 ml mixture of nitric acid and sulfuric acid of 1:3 by volume ratio. The
solution was magnetically stirred at 130 for 30 min, and subsequently, a PH of 7 was
obtained by washing the nanotubes for several times [103]. Functionalization of CNTs
using this method results in a better solubility in water as well as stability of their
electronic and mechanical properties [104]. In order to prepare the solution for the EPD
process, an aqueous suspension of surface treated MWCNTs with a concentration of 0.55
mg/ml was prepared. Finally, 0.5 g of sodium dodecyl sulfate solution (SDS) as a
surfactant was added to the suspension. The solution was sonicated for an overall time
of 30 min with different frequencies so as to obtain a well dispersed and stable solution.
Two stainless steel sheets with a distance of 20 mm from both sides of the PVDF
membrane were used as the electrodes of the EPD process. The MWCNT coated PVDF
membrane was cut into small films of 10 40mm and placed into a one-compartment
Teflon cell. The deposition was performed potentiostatically with an applied voltage of
40 V for the duration of 20 min. The samples were dried for 24 hours and prepared for
the electropolymerization of pyrrole monomers. The electropolymerization process is
similar to that explained in Section 3.3.1. The synthesized films were then cut into small
strips with different dimensions and stored in a solution containing PC and LiTFSI after
rinsing with acetone. The configuration of the described fabrication process is
schematically depicted in Figure 4-5.
91
(a) Functionalization of the nanotubes
(b) Preparation of a well dispersed solution
using a sonicator
(c) EPD of nanotubes as well as electropolymerization of pyrrole
Figure 4-5. Schematic of the fabrication process of the PPy/MWCNT actuators.
The tip vertical displacements of the fabricated trilayer actuators with different
dimensions were measured using the same setup as described in Chapter 3 with a digital
camera and a grid paper placed behind the moving actuators. The trilayer strips were
actuated using a step voltage with various amplitudes and a constant frequency of
0.2Hz. Several images with a proper number of frames per second were captured from
92
the actuators’ recorded bending movement. Some of the images captured while
measuring the tip vertical deformation are presented in Figure 4-6.
Figure 4-6. Captured images of the actuator’s tip vertical deflection measurement.
4.5 Characterization
The morphology of the synthesized layered samples and the related infrared spectrum of
each layer are presented and discussed in the following.
4.5.1 Morphology
The cross sectional microstructure of a fabricated trilayer strip is depicted in Figure
4-7a using a scanning electron microscope (SEM). The laminate structure of the
actuator can be observed as well as the porous structure of the middle PVDF
membrane. The thickness of the MWCNT and PPy layers can be altered by controlling
the duration of the EPD and electropolymerization processes, respectively. Figure 4-7b
shows the surface morphology of the homogeneous and randomly oriented
93
electrophoretically deposited multi-walled carbon nanotubes. In the EPD process, the
packing density of the nanotubes and their alignment is highly dependent on the
solution used for the deposition procedure. This could be attributed to the fact that
different EPD suspensions result in different degrees of CNT agglomerations [99]. The
surface texture of the electropolymerized PPy layer is illustrated in Figure 4-7c and
Figure 4-7d, with two different magnifications, in which the nodular characteristic of
PPy can be observed. The extreme polarization of Py monomers while being reduced
during the electropolymerization process highly affects the density of the PPy nodules,
and their size as well as the film porosity.
Figure 4-7. The micrograph of (a) the cross section of the trilayer configuration of the
actuators, (b) the surface morphology of MWCNT, (c) and (d) the surface texture of
electropolymerized PPy film.
94
4.5.2 Fourier transform infrared spectroscopy
In order to characterize each layer of the fabricated trilayer strips, their corresponding
Fourier transform infrared spectroscopy (FTIR) results are presented in Figure 4-8 and
are addressed as follows
i. The main characteristic peaks associated with the -phase of neat PVDF
membrane appear at 615 cm-1 and 763 cm-1 attributed to bending, and also
975 cm-1 resulted from twisting [105].
ii. In the FTIR spectroscopy of the platinum sputter coated PVDF membrane no
new peaks were detected and the previous ones remained with lower
absorptions. This stems from the ultra-thin film of platinum through which the
infrared radiation was absorbed by the PVDF membrane but with a lower
intensity.
iii. The modified MWCNT layer exhibited the functional groups of –COOH and –
OH, indicating that the acid treatment of as-received nanotubes was effectively
performed. The absorption peaks at 1717 cm-1 and 1663 cm-1 are in
correspondence to the C=O stretching vibrations in the carboxyl group whereas
the peak at 1559 cm-1 is assigned to C=C stretching [106]. The strong band at
1088 cm-1 is due to the existence of hydroxyl groups (–OH) on the surface of the
nanotubes which can be attributed to either the atmospheric moisture or
oxidation during modification of the MWCNTs. This characteristic peak can
also be assigned to the C–O stretching of alcohols [107]. Finally the two peaks
appearing at 2847 cm-1 and 2916 cm-1 are associated with C–H stretching.
iv. The absorption bands of the outer PPy layer of the actuator are also depicted
in Figure 4-8. The characteristic peak observed at 1542 cm-1 is attributed to the
fundamental vibrations of the five-membered pyrrole ring and stretching of
C=C band. In addition, the peak at 1458 cm-1 is indicative of stretching
vibrations of C–N in the pyrrole ring. The in-plane vibration of =C–H is
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indicated by the peaks at 1302 cm-1 and 1125 cm-1 which is the result of PPy
doping during the electropolymerization process. The peak at 1041 cm-1 is
corresponding to the out-of-plane =C–H vibrations [108].
The abovementioned peak assignments detected in the FTIR spectroscopy verify the
formation of PPy on the MWCNT coated PVDF membrane.
Figure 4-8. FTIR spectroscopy of each layer of the trilayer actuator.
96
4.5.3 Numerical analysis and verification
The estimated values of the parameters used in the modeling procedure are listed in
Table 4-1. The diffusion coefficient is an uncertain parameter in the model with an
expected range of 1 to 2 /s [109]. This coefficient tends to decrease
as the solvent evaporates.
Table 4-1. Values of modeling parameters
Parameter Value
2
25
15
65 at 25
110
80
440
900
The frequency response of the actuator in terms of its vertical tip displacement and
generated blocking force is obtained using the numerical model as briefly pointed out in
the preceding sections. Figure 4-9 compares the frequency responses of a neat PPy based
trilayer actuator with the one with an incorporated thin layer of MWCNT. As seen, by
increasing the frequency of the applied step voltage, the tip blocking force of the two
actuators non-linearly decreases. Figure 4-9 also indicates that adding a thin layer of
electrophoretically deposited MWCNT results in a better performance of the CP based
trilayer actuator with respect to its vertical deflection and blocking force.
97
Figure 4-9. Variation of the tip blocking force and vertical displacement with different
applied frequencies obtained from the mathematical model for a neat PPy vs. a
PPy/MWCNT actuator.
The PPy trilayer actuators with an incorporated film of MWCNT were fabricated
with different widths and effective lengths, and stimulated by an applied step voltage.
Their generated tip vertical displacement in response to varying driving voltages is
shown in Figure 4-10. As expected, the tip displacement of the samples increased by
increasing both the applied voltage and their effective length while increasing the width
resulted in the reduction of their tip deformation. Higher effective length of the bending
actuator leads to a higher bending moment generated by its tip, and consequently, the
actuator’s tip deflection increases. Moreover, applying a higher voltage results in a
higher rate of reduction and oxidation of the CP layers, and therefore, the rate by which
the ions diffuse into the polymer films increases. This in return causes both the blocking
force and tip vertical deflection to increase, accordingly. Furthermore, for a constant
thickness and effective length of the actuator, a higher width results in decreasing its tip
vertical deflection, as depicted in Figure 4-10a and Figure 4-10b for = 1, 2, and 3mm.
This can be interpreted through the fact that by having a wider actuator a larger
98
volume of the strip is being actuated. In addition, the overall rigidity of the actuator
increases for higher widths. These results are compared with their experimental
counterparts in Figure 4-10c and Figure 4-10d, indicating a good tracking ability of the
proposed model. Regarding the generated blocking force of the actuator, Figure 4-12
signifies the variation of the blocking force for different applied actuation voltages and
actuator lengths obtained from the simulation results and their corresponding measured
values. As expected, longer actuators stimulated with lower actuating voltages generate
lower blocking force. Figure 4-12 compares the experimental results for the tip vertical
displacements of a neat PPy actuator with a PPy/MWCNT actuator with an effective
length of 20mm for different actuating voltages. It can be observed that by depositing a
thin layer of MWCNTs on the platinum coated PVDF membrane, the tip vertical
displacement of the actuator increases for a similar geometry and applied voltage. This
can be justified due to an increase in the overall electrical and ionic conductivity of the
polymer. The ohmic potential drop along the length of the actuator decreases by
improving its electrical conductivity [98]. However, it is worth noting that by
incorporating another layer into the structure of the film type actuator, its overall
rigidity also increases due to the high Young’s modulus of the added MWCNT layer.
Therefore, including an extra layer in the configuration of the actuator has to be carried
out with additional care so as to make a sense of balance between the differing effects
arising from this layer.
99
(a)
(b)
(c)
(d)
Figure 4-10. Variation of the tip vertical deflection of the actuator for different values of
widths, effective lengths, and applied voltages, (a) = 20mm (exp.), (b) = 25mm
(exp.), (c) = 1mm (exp. vs. model), and (d) = 2mm (exp. vs. model).
100
Figure 4-11. The measured blocking force of an actuator with varying effective lengths
and applied voltages vs. their modeling counterparts.
Figure 4-12. Variation of the tip vertical displacement with the applied voltage for a
neat PPy vs. a PPy/CNT actuator for an effective length of 20mm.
4.5.4 Optimization results
The results obtained from solving the developed multiobjective optimization problem
are shown in Figure 4-13. Using Genetic Algorithm, a Pareto surface can be interpolated
through these points on which the optimal points found are spread consistently. Each
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point maps to a specific value for each decision variable, and accordingly to a specific
value for each objective function.
Figure 4-13. The optimum points obtained from the three-objective optimization
process.
Due to the existing trade-off between the generated blocking force and tip vertical
deflection of the actuator, the final solution to the problem will be in accordance with
the significance of each of the three objective functions. Figure 4-14 illustrates the 2D
projections of the Pareto surface. The Pareto curve (Pareto Front) resulted from
performing a two-objective optimization process is shown in Figure 4-14a as well. It is
evident that the outer curve of the 2D projected Pareto surface corresponding to the
vertical displacement of the actuator and its blocking force is close to that obtained
from the two-objective optimization problem on which the non-dominated optimal
points are located. None of these points are dominated by the ones positioned under the
curve inside the feasible region of the Pareto surface. These dominated points have
arisen owing to the third objective function (response time) incorporated into the
optimization problem. The slight difference between these two curves could also be
102
attributed to the random number generation of the GA, and on that account, the results
are slightly different every time that the algorithm is executed. This can also be inferred
from Figure 4-15a depicting the Pareto curves for a 2-objective optimization with the
tip deflection and blocking force as the objective functions. Each optimal point on the
Pareto front corresponds to a set of values for the design variables as shown for two of
the optimal points in Figure 4-15b.
(a)
(b)
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(c)
Figure 4-14. The 2D projections of the Pareto optimum points of the three-objective
optimization; (a) blocking force vs. tip deflection, (b) response time utility vs. blocking
force, and (c) response time utility vs. tip deflection.
(a) (b)
Figure 4-15. (a) Pareto fronts obtained for a 2-objective optimization problem, (b) The
design variables corresponding to two of the optimal solutions.
Considering the trade-offs between the generated blocking force, tip vertical
deflection, and response time of the actuator, the final solution to the problem will be in
104
accordance with the significance of each objective function. Figure 4-16 depicts the
Pareto frontiers of the 2D projections of the results shown in Figure 4-13 along with the
results obtained from their corresponding 2-objective optimization. It should be noted
that these Pareto frontiers are extracted from the 2D projections by performing a
separate GA optimization on the two objective functions of each projection. Since there
are three objective functions defined in this work, three sets of 2-objective optimization
are designed and performed. Consequently, the obtained results can be compared to
their corresponding optimum points acquired from the 3-objective optimizations. It is
evident that the optimums of 2-objective optimizations are close to those of a 3-
objective (Figure 4-16a, 4-16e, and 4-16i). However; the results obtained for the third
objective function (the one that is not included in the 2-objective optimization) do not
show an optimal behavior (Figure 4-16b, 4-16c, 4-16d, 4-16f, 4-16g, and 4-16h) and they
are mostly at the non-desired end of their designated range. This stems from the
aforementioned trade-offs among the three objective functions. The results also
demonstrate that the optimal points obtained from the 3-objective optimization cover a
wider range of values associated with the third objective function. This indicates that a
3-objetive optimization process delivers relatively more optimal solutions to the problem
than a 2-objective one. Moreover, in order to narrow down the choices of the resulted
optimal points, a confidence interval of [ ] is indicated for each objective
function where and are the average and standard deviation of the optimal points,
respectively. The points within this interval are considered as the final results of the
optimization each of which maps to a specific value for the allocated design variables.
Therefore, in order to choose the final results of the optimization process, one can select
the specified interval of the objective functions from any of the three scenarios (i.e.,
Figure 4-16a, 4-16e, and 4-16i) depending on the two most desired objective functions.
105
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 4-16. The 2D projections of the Pareto optimum points of the 3-objective vs. 2-
objective optimization; (a),(d), and (g) blocking force vs. tip vertical deflection, (b), (e),
and (h) response time utility vs. tip vertical deflection, and (c), (f), and (i) response
time utility vs. blocking force.
106
The optimal ranges acquired for the assigned decision variables are given in Figure
4-17 for the tip vertical displacement of the actuator and its generated blocking force so
as to gain a more comprehensive insight into their relationship and trade-off. It can be
observed that for both objective functions, the optimal value of the applied voltage is
close to its upper bound as expected. The effective lengths of the strips have been
respectively optimized at their lower and upper bounds for a higher blocking force and
vertical deflection, whereas this trend is the opposite for the actuators’ width. Moreover,
increasing the thickness of the incorporated MWCNT layer increases the overall stiffness
of the actuator. Hence, the generated tip blocking force also increases while this results
in a decrease in the tip vertical deflection.
(a)
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(b)
Figure 4-17. The optimum range of the decision variables for (a) maximum tip vertical
displacement, and (b) maximum blocking force.
In addition, the optimal ranges acquired for the assigned decision variables are
compared in Figure 4-18 for each set of the two objective functions (i.e., Y-F, Y-T, and
F-T). It can be observed that the optimal values of the applied voltage and frequency
are respectively close to their upper and lower bounds, as expected (Figure 4-18a, and
Figure 4-18b). The feasible range of the applied frequency for the solved optimization
problem corresponds to the second segment of the graph ( ) which is between 0.1523
to 4.4981 Hz. Figure 4-18b shows the high concentration of the optimal applied
frequencies at the lower values of their specified range. The optimized range of the
effective length of the actuator varies depending on the two assigned objective functions
(Figure 4-18c). For instance, in the case of F-T, the desired range of both functions
inclines to the lower values of while in the Y-F optimization, the actuator length
optimal range is more distributed through its entire feasible range.
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(a)
(b)
(c)
(d)
(e)
(f)
Figure 4-18. The optimum range of the decision variables for (a) applied voltage, (b)
applied frequency, (c) actuator effective length, (d) actuator width, (e) MWCNT layer
thickness, and (f) PPy layer thickness, for the 3-objective optimization.
109
Regarding the actuator’s width, the results shown in Figure 4-18d are right skewed
indicating that the overall optimality of the width of the actuator occurs at its higher
values. Figure 4-18e and Figure 4-18f demonstrate that the thickness of the incorporated
MWCNT layer and the PPy layer are mostly optimized at their lower values. However,
the results obtained for the thickness of the MWCNT layer is more scattered through its
overall specified range. It is also worth mentioning that the largest number of entities
belongs to the F-T optimization set in each figure. This could be due to the fact that
the trend of the blocking force of the trilayer actuator is analogous to that of the
response time utility function with respect to the decision variables, and therefore, this
set covers a larger number of optimal decision variables.
110
Chapter 5
PPy based trilayer mechanical
sensors
Many efforts have been devoted to modeling the diffusive impedance of conjugated
polymer based actuators using their equivalent electrical circuits. Their corresponding
equivalent transmission lines are applied to model the actuator’s main outputs as
explicitly discussed in the preceding chapters. Using the same methodology, CP based
mechanical sensors can also be treated by an equivalent transmission line circuit and
their overall impedance can be modeled, correspondingly. The capacitive behaviors of
conjugated polymer based actuators and mechanical sensors are described by many
engineers, physicists, and electrochemists implementing the transmission line approach.
Due to the large number of resources to study the electrical circuits, this technique is a
practical tool. Therefore, in this study, an equivalent RC-circuit model including
electrochemical parameters is determined in order to obtain a better perception of the
sensing mechanism of a multilayer PPy based mechanical sensor.
111
5.1 Structure of the multilayered sensor
The structure of the mechanical sensor considered in this chapter is analogous to that of
a PPy trilayer actuator which comprises three main layers: two outer layers of PPy
acting as the working electrodes, and a middle layer of PVDF as an electrically
insulating and ionically conductive porous membrane acting as an electrolyte tank.
The fabrication process of the layered sensor consists of the same three steps
described in Chapter 3, as follows: i. preparation of the electropolymerization solution
containing propylene carbonate, LiTFSI, Py monomers, and water, ii. Sputter coating of
a thin layer of platinum on both sides of the PVDF membrane, and iii.
Electropolymerization of Py monomers onto the faces of the platinum coated PVDF
using a galvanostatic process in a one-compartment Teflon vessel. The membrane was
affixed to a built-in frame so that the tension remains constant. The frame was then
submerged into the electropolymerization solution. It is worth mentioning that the
thickness of the deposited conjugated polymer layer is directly proportional to the
amount of charge passed during the electropolymerization process. Since a galvanostatic
process was employed, the thickness of the PPy film is proportional to the duration of
polymerization. Once the electropolymerization process was performed, the samples were
rinsed with acetone to remove any undeposited polymer. They were then cut into
desired dimensions and stored in a well dissolved solution of PC and LiTFSI.
5.2 Description of the mathematical modeling and its verification
Assuming that the trilayer sensor consists of n-elements of impedance connected in
series along its length, the transmission line circuit of PPy/PVDF/PPy elements of the
strip can be modeled using electrical elements as depicted in Figure 5-1. Upon
immersion of the conjugated polymer layer in the electrolyte, the interface between the
CP layer and the middle PVDF membrane acts as a parallel plate capacitor. Therefore,
in the equivalent electrical circuit, this interface consists of a double layer capacitance
112
( ) in series with a diffusion impedance ( ). The electronic resistance of each element
of the PPy layer and the PVDF membrane are respectively denoted by
( is the ionic conductiity of the PPy layer), and ( is the
electrolyte conductivity) [65]. The impedance element of the sensor can be considered as
a charge generator in which a variable load resistor ( ) is in parallel with the two
aforementioned electrical elements. When a mechanical load is applied to the sensor
which has been previously charged to a voltage, , the load resistor changes. This
results in an increase in the voltage of the sensor. It is assumed that the variable resistor
varies linearly with the applied mechanical load and correspondingly with the
mechanically induced deflection of the tip of the trilayer sensor as where the
coefficient is considered as a fitting parameter to be empirically determined.
Figure 5-1. Schematic of the equivalent transmission line circuit of the trilayer
mechanical sensor
113
The total impedance of the i-element of the sensor is then given by Equation (5-1)
as follows
(5-1)
The diffusion element ( ) is considered as the finite-length Warburg diffusion element
characterized by the diffusional time constant (
), and the diffusional pseudo-
capacitance ( ). Macdonald [110] described this element using the following expression.
(5-2)
where is the angular frequency, and is the unit imaginary number. Replacing
with the Laplace variable ( ), the diffusion element can be obtained in the Laplace
domain. Moreover, the impedance response of a finite-length open transmission line with
the phase angle shifted from 45 to 90° due to the finite diffusion length is analogous to
that of the diffusion element ( ) [110].
Using the equivalent circuit presented in Figure 2, one can obtain the total
impedance of the trilayer sensor as given by Equation (5-3).
(5-3)
Substituting Equation (5-1) and Equation (5-2) into Equation (5-3), the final impedance
of the designated transmission line is expressed as
114
(5-4)
Equation (5-4) relates the output voltage of the sensor to the current flowing
through the polymer network. Using an electrochemical coupling the flowing current will
be related to the mechanically induced strain and finally the vertical tip displacement of
the sensor will be obtained via geometric relations. The mathematical expression
corresponding to the overall impedance of the sensor is not suitable for real-time control
applications due to the arising hyperbolic tangent terms and therefore, a reduced model
is required to obtain a dimensionally finite model. For this reason, the hyperbolic
tangent terms are approximated using the following series as
(5-5)
The X and Y terms for each of the two arising hyperbolic tangents are specifies as
. The overall impedance of the
sensor is then reduced to an approximated transfer function as given by
(5-6)
where and
are constant numbers arising from the predetermined
parameters, and denotes the order of the approximated transfer function expressed by
115
Equation (5-6). In order to obtain the transfer function relating the mechanically
induced vertical deflection of the sensor’s tip to its output voltage, the current flowing
through the polymer network is translated into the tip vertical deflection of the trilayer
bender via the following relations.
where is the current flowing through the polymer network, is the CP layer
transferred charge density, is the strain to charge density ratio, is the elastic
modulus of each layer, is the mechanically induced strain, is the mechanical stress,
is the bending curvature, and denotes the input tip vertical deflection of the sensor.
The coefficient arises from setting the net bending moment of the sensor equal to
zero and it is obtained using
.
These relations yield to the final expression for the output voltage of the sensor over its
mechanically induced tip vertical deflection in the Laplace domain. Figure 5-2
116
demonstrates the frequency response of the transfer function for different values of . It
is evident that by increasing , the frequency response remains relatively constant.
Therefore, using the first three terms of the series ( ), a third order approximation
transfer function is obtained as
(5-7)
where and the coefficients and
are in terms of the
dimensions of the trilayer actuator, diffusion coefficient, load resistor, double layer
capacitance, and strain to charge density ratio. The parameters used in the modeling
and their corresponding estimated value are listed in Table 5-1.
Figure 5-2. Comparison of the frequency response of the sensor with different orders of
transfer function.
117
Table 5-1. Values of modeling parameters
Parameter Value
2
25
8
110
80
440
In order to convert the mechanically imposed tip vertical deflection of the sensor
into its bending curvature, the following expression stemmed from the geometrical
relations can be employed. However, in most cases the tip deflection of the trilayer
bender is small compared to its effective length ( ), and the bending curvature can
be approximated as .
(5-8)
The approximated bending curvature results in a linear relationship between the input
tip deflection of the sensor and the generated voltage (Figure 5-3a), while Equation (5-
8) leads to a nonlinear relation as depicted in Figure 5-3b. The former mirrors the
trends presented in the literature [76].
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(a)
(b)
Figure 5-3. Variation of the output voltage of the sensor with the amplitude of tip
deflection for different input frequencies using (a) Equation (5-8), and (b) the
approximated bending curvature.
119
Applying the same algorithm described in Chapter 4, the approximated Bode
diagram is plotted and compared with the exact Bode plot in Figure 5-4. It can be
inferred from the graph that the approximated straight lines follow the same trend as
the Bode diagram with the exception of the breakpoints occurring at the zeros and poles
of the transfer function. Therefore, along with maximizing the output voltage, it is also
intended to obtain the best possible and most smooth approximation of the frequency
response of the sensor by minimizing the difference between the two sets of poles and
zeroes that are located at the plot’s breakpoints. This results in increasing the
sensitivity of the proposed model to the applied frequency of the input displacement.
Figure 5-4. Frequency response of the sensor (MATLAB plot vs. approximated diagram)
Two mathematical expressions accounting for the length of the two straight lines
shown in the figure are formed (i.e., and ). However, since they
exhibit the same trend and there exists no trade-off between them, the optimal points
minimizing one will result in the other’s minimization as well. Therefore, only one of the
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aforementioned equations along with the sensor’s output voltage are set as the objective
functions of the optimization problem.
(5-9a)
(5-9b)
(5-9c)
where
The presented optimization model accounts for the second segment of the
approximated Bode diagram. Therefore, the frequency range associated with this part of
the graph is: . Equation (5-10a) and Equation (5-10b) represent the
mathematical expressions for the pole and zero of the transfer function corresponding to
the two ends of the line whose length is to be minimized.
(5-10a)
(5-10b)
121
where
122
The derived mathematical modeling which describes the output behavior of the
conjugated polymer mechanical sensor is verified using experimental results presented in
the literature. Figure 5-5a and Figure 5-5b illustrate respectively the experimental and
numerical results corresponding to variation of the output voltage with the amplitude of
the input tip deflection of a sensor with dimension of 10 1 0.17mm and an applied
frequency of 0.1Hz. The experimental results presented by Alici et al. [77] are used to
support the dynamic behavior of the proposed modeling methodology for the trilayer
bender described in this chapter. As seen, the trend and the magnitude of the output
voltage of the sensor obtained from the model are relatively close to those of the
experimental ones. More specifically, the related average error between the numerical
points and their experimental counterparts shown in Figure 5-5 is 10.45 percent. This
error can be the result of the numerical approximation of the predetermined parameters
such as the strain to charge density ratio, diffusion coefficient, and the ionic
conductivity of the layers. Moreover, the elastic modulus of the polymer is assumed to
be constant in the modeling procedure which could be another source of error. However,
more experimental analysis specifically designed to determine the aforementioned
parameters can efficiently reduce the associated error. It should be also noted that a
fraction of this error can be attributed to the inherent errors incorporated with the
experimental measurements.
As seen in the figure, the relationship between the output voltage and the
mechanically induced displacement of the sensor is approximately linear, as already
discussed for the modeling outcomes. Therefore, increasing the amplitude of the tip
displacement of the bender leads to a higher magnitude of the output voltage. The same
trend can be expected for the induced strain and stress of the sensor [74, 78].
123
(a)
(b)
Figure 5-5. Variation of the voltage output with the input amplitude of the sensor tip
deflection, (a) experimental, (b) numerical results.
124
5.3 Optimization results
In real-world applications, it is very unlikely that a problem concerns only a single value
or objective. Therefore, the challenge of identifying variables that simultaneously
optimize multiple objectives is encountered in many engineering problems and other
domains. This signifies the fact that generally there is not a unique optimal solution, out
of a pool of possible designs, which excels in all objectives. This leads to selection of an
entire set of (Pareto-)optimal solutions with optimal trade-offs in the objectives. The
optimization problem defined herein identifies a 2-objective problem with different
candidate designs that trade the multivariable objectives. The same optimization
procedure employed in the previous two chapters is applied to obtain the Pareto
optimal points. A multiobjective Genetic Algorithm is performed resulting in a set of
optimal values for the designated decision variables (i.e., the width and effective length
of the trilayer strips, thickness of the PPy layers, and the mechanically induced tip
vertical displacement of the sensor). The resulted Pareto frontiers corresponding to the
output voltage of the sensor and the two length corrections are depicted in Figure 5-6.
As pointed out, each solution point on the graph maps to a specific optimal value for
each design variable.
Figure 5-6. The Pareto frontiers of the optimization problem.
125
A summary of the final results of optimization is as follows
i. Effective length: The magnitude of the output voltage of the sensor increases
as the effective length increases. However, it should be noted that the induced
strain into the polymer layers decreases by increasing the length of the sensor for
a given input displacement.
ii. Width: Increasing the width of the sensor results in an increase in the volume of
the polymer and thus it results in a higher output voltage. It is also worth
mentioning that the magnitude of the sensor output is most practically affected
by altering the width rather than its length or thickness. This is due to the fact
that the induced strain and resonance of the sensor are anticipated to remain
constant and the transverse bending is not taken into account.
iii. PPy thickness: Increasing the thickness of the conducting polymer layers leads
to an increase in the overall volume of the sensor and therefore the magnitude of
the output signal also rises. The mechanically induced strain into the two PPy
layers also increases by increasing the PPy thickness. However, the flexural
rigidity of the sensor increases with an increase in the conducting polymer
thickness. This requires a larger amount of force for a specified input
displacement. On the other hand, the optimal range of the PPy thickness resulted
from the optimization problem indicates that higher thicknesses decrease the
sensitivity of the model to the applied frequency, as illustrated in Figure 5-7.
Therefore, based on the application and the frequency range of the input
displacement, one can choose the most practical thickness for the polymer layer.
iv. Tip displacement: As the input amplitude of the sensor tip displacement
increases, the magnitude of the output voltage increases correspondingly.
It should be noted that increasing the width and length of the trilayer sensor does not
considerably affect the path of dopant ions through the polymer network. This causes
126
only the magnitude of the output voltage to change and its phase remains constant as
reported by John et al. [78].
Figure 5-7. Variation of the objective functions with the PPy thickness optimal values.
127
Chapter 6
Concluding remarks and future work
6.1 Conclusions
Conducting polymers have exhibited unique properties which make them promising
candidates for many applications ranging from solar cells to mechanical sensors and
actuators. Given their low input voltage, biocompatibility, and ease of fabrication, PPy
actuators are one of the most applied layered conducting polymer actuators. In this
thesis, an optimization modeling approach was proposed in order to attain the most
relatively optimum outputs of PPy bender actuators and mechanical sensors. Applying
two different modeling methodologies, the tip vertical displacement and blocking force of
a trilayer PPy actuator were mathematically formulated. The electromechanical features
of the actuator were reflected in the first model whereas its frequency response was
taken into account in the second model by applying two different model reduction
methodologies. It was demonstrated that there is a trade-off between the two outputs,
implying that increasing one will result in decreasing the other one at the same time.
One of the main design characteristics of a multidisciplinary system or process such as a
CP trilayer actuator is the trade-off among its several design variables. This can
improve or most of the time compromise the main performances of the designed systems
provided that it is not systemically controlled. For this reason, the two main
characteristic behaviors of the actuator were optimized through defining a nonlinear
128
multiobjective optimization problem with proper constraints. Two optimization
techniques were methodically performed and the corresponding optimal design variables
were obtained. Comparing the experimental results with their modeling counterparts, it
can also be concluded that the electrochemical modeling approach provides a better
insight into the vertical displacement of the actuator’s tip. This is mainly due to the
imposed nonlinear equality constraint restricting the effective length of the trilayer strip.
On the other hand, the frequency response of the actuator was reflected by the
electrochemomechanical model through which the bending movement of the actuator for
different driving voltage frequencies was predicted. The range of the applied frequency
considered in the model was 0.01 Hz to 100 Hz. However, the electrochemomechanical
model was observed to have a better tracking ability for low frequency applications.
Regarding the blocking force generated by the actuator, the second model suggested a
nonlinear relation between the force and the applied voltage, whereas the
electrochemical model predicted a linear variation of the generated blocking force. This
stems from the assumption held in the modeling procedure that the strain to charge
ratio is a function of the applied actuation voltage.
As pointed out, one of the main shortcomings of a neat PPy actuator is decreasing
its electronic conductivity by two or three orders of magnitude as a result of the
reduction process within the polymer. This results in the actuation of only a small part
of the polymer. As an alternative to tackle this shortcoming, a layered PPy actuator
was fabricated with an extra layer of electrophoretically deposited MWCNT on the
conducting polymer layers. The MWCNT layer acts as a conductive interface between
the inert non-conductive PVDF membrane and the conjugated polymer electrodes. The
two mentioned output behaviors were then formulated in the frequency domain for a
PPy/MWCNT actuator along with a utility function accounting for the response time of
the actuator. To obtain the optimum points within a feasible range, appropriate
constraints were imposed on the multivariable objective functions. Using a
multiobjective Genetic Algorithm, the three competing objective functions were solved
129
simultaneously. The results were shown on a Pareto surface, and a set of optimal
solutions corresponding to a specific set of values for the design variables were acquired.
It was also demonstrated that a single 3-objective optimization results in a wider range
of optimal solutions than three sets of 2-objective optimization problems. In addition,
both the experimental and theoretical results indicated that incorporating a very thin
layer of MWCNTs into the structure of the bending type trilayer actuator effectively
improves its desired performances.
Finally, a study was conducted on PPy based trilayer mechanical sensors. The
overall impedance of such sensors was modeled based on their equivalent transmission
line circuit. Employing the developed model, the output voltage resulted from the
mechanically induced tip deflection was obtained. In order to increase the sensitivity of
the trilayer bender to an input displacement, the output voltage is to be increased
across the frequency response of the sensor. Therefore, two objective functions
accounting for the output voltage of the sensor and sensitivity of the model to the
applied frequency were set as the objectives of an optimization model with proper
imposed constraints. It was shown that increasing the overall volume of the conjugated
polymer layer (i.e., increasing its width, effective length, and thickness) increases the
output magnitude. This is the same trend reflected in the literature. However, the final
optimal selection of the geometry depends on the application of the sensor. Thus, there
should be a sense of balance between the output magnitude, the force required to induce
the tip deflection, and the factors restraining the functionality of the device.
6.2 Future Work
Considering the research presented in this thesis, there are a number of directions with
prominent potential to peruse for the future investigations in the area of conjugated
polymer based actuators and mechanical sensors. On this point, some of the main and
most relevant novel directions can be summarized as follows
130
i. One of the main parts of this research was to investigate the effect of a highly
conductive layer incorporated into the structure of an actuator in order to
improve its electric charge delivery. However, application of other conductive
layers incorporated into the structure of the neat PPy actuator such as graphene
can be of crucial importance for investigating their effect on the ionic and
electrical conductivity of the actuator. In addition, more attention has to be
drawn towards the potential means of facilitating ion diffusion through the
polymer network. Moreover, in order to further enhance the performance of the
actuator, the ionic conductivity of the multilayered actuator can be
characterized through electrical impedance spectroscopy (EIS) of the samples.
ii. Considering the outcomes of this research, one of the potential novel directions
for future study in this field is to employ the combined effect of actuation and
sensing of polypyrrole in a single device in order to design a feedback loop
controller. This coupling effect can efficiently be exploited to detect the extra
loading applied on a polymer actuator. This could be helpful in many biomedical
applications one of which is navigating a catheter through an artery to avoid
puncturing the arterial walls by detecting a sudden increase in the load applied
to the polymer. The applied load implies that the catheter has struck the wall of
the artery.
iii. Since PPy actuators have the potential to be manufactured in micro scale, it
would be a great contribution to apply the optimization modeling procedure to a
PPy multilayered actuator with a micro scale geometry. This can be used to
more comprehensively study the effects of different variables associated with the
fabrication of an actuator and ultimately to improve its desired performances.
iv. In order to find a real life application for any proposed device or tool, its
applicability over a long period of time has to be verified. Therefore, it is of
critical importance to investigate the life time of the studied PPy mechanical
sensors. Moreover, the parameters affecting the number of load cycles the sensor
can take without a remarkable change in the output current are to be identified
131
and optimized. In addition, the parameters associated with the modeling
methodology can be obtained more precisely through experimental analysis
explicitly designed for this purpose.
132
Bibliography
1. E.W.H. Jager, E. Smela, O. Inganas, Microfabricating conjugated polymer
actuators, Science 290 (2000) 1540-1545.
2. J. Ding, L. Liu, G.M. Spinks, D. Zhou, G.G. Wallace, J. Gillespie, High
performance conducting polymer actuators utilizing a tubular geometry and
helical wire interconnects, Synthetic Metals 138 (2003) 391-398.
3. G.M. Spinks, G.G. Wallace, L. Liu, D. Zhou, Conducting polymers and carbon
nanotubes as electromechanical actuators and strain sensors, Materials Research
Society Symposia Proceedings 698 (2002) 5-16.
4. M. Manto, M. Topping, M. Soede, J. Sanchez-Lacuesta, W. Harwin, J. Pons, J.
Williams, S. Skaarup, L. Normie, Dynamically responsive intervention for tremor
suppression, Engineering in Medicine and Biology Magazine 22 (2003) 120-132.
5. J.D.W. Madden, N.A. Vandesteeg, P.A. Anquetil, P.G.A. Madden, A. Takshi,
R.Z. Pytel, S.R. Lafontaine, P.A. Wieringa, I.W. Hunter, Artificial muscle
technology: Physical principles and naval prospects, IEEE Journal of Oceanic
Engineering 29 (2004) 706-728.
6. Y. Bar-Cohen, EAP history, current status, and infrastructure, Electroactive
Polymer (EAP) actuators as artificial muscles: Reality, potential, and challenges,
SPIE Press, (2004).
7. E. Smela, Conjugated polymer actuators for biomedical applications, Advanced
Materials 15 (2003) 481-494.
133
8. R. Baughman, Conducting polymer artificial muscles, Synthetic Metals 78 (1996)
339-353.
9. U. Kosidlo, M. Omastova, M. Micusik, G. Ciric-Marjanovic, H. Randriamahazaka,
T. Wallmersperger, A. Aabloo, I. Kolaric, T. Bauernhansl, Nanocarbon based
ionic actuators – a review, Smart Materials and Structures 22 (2013) 104022
(30pp).
10. Y. Wu, G. Alici, G.M. Spinks, G.G. Wallace, Fast trilayer polypyrrole bending
actuators for high speed applications, Synthetic Metals 156 (2006) 1017-1022.
11. X. Wang, X. Gu, C. Yuan, S. Chen, P. Zhang, T. Zhang, J. Yao, F. Chen, G.
Chen, Evaluation of biocompatibility of polypyrrole in vitro and in vivo, Journal
of Biomedical Materials Research 68 (2004) 411–422.
12. T.F. Otero, M.T. Cortes, A sensing muscle, Sensors and Actuators B: Chemical
96 (2003) 152-156.
13. M. Gerard, A. Chaubey, B.D. Malhorta, Review: Application of conducting
polymers biosensors, Biosensors & Bioelectronics 17 (2002) 345-359.
14. T.A. Skotheim, R.L. Elsenbaumer, J.R. Reynolds, Handbook of conducting
polymers, New York (1998).
15. J.L. Bredas, G.B. Street, Polarons, bipolarons, and solitons in conducting
polymers, Accounts of Chemical Research 18 (1985) 309-315.
16. J.L. Bredas, B. Themans, J.M. Andre, Bipolarons in polypyrrole chains, Physical
Review B 27 (1983) 7827-7830.
17. J.L. Bredas, J.C. Scott, K. Yakushi, G.B Street, Plarons and bipolarons in
polypyrrole: Evolution of the band structure and optical spectrum upon doping,
Physical Review B 30 (1984) 1023-1025.
134
18. N.S. Murthy, L.W. Shacklette, R.H. Baughman, Effect of charge transfer on chain
dimension in trans-polyacetylene, Journal of Chemical Physics 87 (1987) 2346-
2348.
19. R.H. Baughman, N.S. Murthy, H. Eckhardt, Charge oscillations and structure for
alkali-metal-doped polyacetylene, Physical Review B 46 (1992) 10515-10539.
20. Q. Pei, O. Inganas, conjugated polymers as smart materials, gas sensors and
actuators using bending beams, Synthetic Metals 57 (1993) 3730-3735.
21. M. Lahav, C. Durkan, R. Gabai, E. Katz, I. Willner, M.E. Welland, Redox
activation of a polyaniline-coated cantilever: an electro-driven microdevice,
Angewandte Chemie International Edition 40 (2001) 4095-4097.
22. T.F. Otero, J. Padilla, Anodic shrinking and compaction of polypyrrole blend:
Electrochemical reduction under conformational relaxation kinetic control. Journal
of Electroanalytical Chemistry 561 (2004) 167–171.
23. R. John, G.G. Wallace, Doping-dedoping of polypyrrole: a study using current-
measuring and resistance-measuring techniques, Journal of Electroanalytical
Chemistry 35 (1993) 145-160.
24. M.R. Gandhi, P. Murray, G.M. Spinks, G.G. Wallace, Mechanism of
electrochemical actuation in polypyrrole, Synthetic Metals 73 (1995) 247-256.
25. Q. Pei, O. Inganas, Electrochemical applications of the bending beam method. 1.
Mass transport and volume changes in polypyrrole during redox, Journal of
Physical Chemistry 96 (1992) 10507-10514.
26. P.G.A. Madden, J.D.W. Madden, P.A. Anquetil, N.A. Vandesteeg, I.W. Hunter,
The relationship of conducting polymer actuator material properties to
performance, IEEE Journal of Oceanic Engineering 29 (2004) 696-705.
135
27. Y. Fang, X. Tan, Y. Shen, N. Xi, G. Alici, A scalable model for trilayer
conjugated polymer actuators and its experimental validation, Materials Science
and Engineering: C 28 (2008) 421–428.
28. B. Gaihre, G. Alici, G.M. Spinks, J.M. Cairney, Effect of electrolyte storage layer
on performance of PPy-PVDF-PPy microactuators, Sensors and Actuators B:
Chemical 155 (2011) 810–816.
29. K. Naoi, M.M. Lien, W.H. Smyrl, Quartz crystal microbalance analysis: Part I.
Evidence of anion or cation insertion into electropolymerized conducting polymers,
J. Electroanal. Chem. 272 (1989) 273-275.
30. J.D.W. Madden, Conducting polymer actuators, Ph.D. thesis Massachusetts
Institute of Technology, Cambridge MA. (2000).
31. F. Garnier, G. Tourillon, Organic conducting polymers derived from substituted
thiophenes as electrochromic material, Journal of Electroanalytical Chemistry 148
(1983) 299-303.
32. G.M. Spinks, B. Xi, D. Zhou, V.T. Truong, G.G. Wallace, Enhanced control and
stability of polypyrrole electromechanical actuators, Synthetic Metals 140 (2004)
273-280.
33. J.M. Sansinena, V. Olazabal, T.F. Otero, C.N. Polo da Fonseca, M.A. De Paoli, A
solid state artificial muscle based on polypyrrole and a solid polymeric electrolyte
working in air, Chemical Communications 22 (1997) 2217–2218.
34. G. Alici, V. Devaud, P. Renaud, G. Spinks, Conducting polymer microactuators
operating in air, Journal of Micromechanics and Microengineering 19 (2009) 1-9.
35. R. Kiefer, X. Mandviwalla, R. Archer, S.S. Tjahyono, H. Wang, B. MacDonald,
G.A. Bowmaker, P.A. Kilmartin, J. Travas-Sejdic, The application of polypyrrole
trilayer actuators in microfluidics and robotics, Proceedings of SPIE on
Electroactive Polymer Actuators and Devices, (2008).
136
36. T.F. Otero, E. Angulo, J. Rodriguez, C. Santamaria, Electrochemomechanical
properties from a bilayer: polypyrrole/ non-conducting and flexible material -
artificial muscle, Journal of Electroanalytical Chemistry 341 (1992) 369-375.
37. T.F. Otero, J. Rodriguez, E. Angulo, C. Santamaria, Artificial muscles from
bilayer structures, Synthetic Metals 55-57 (1993) 3713-3717.
38. Q. Pei, O. Inganas, Electrochemical applications of the bending beam method. 2.
electroshrinking and slow relaxation in polypyrrole, Journal of Physical Chemistry
97 (1993) 6034-6041.
39. Q. Pei, O. Inganas, I. Lundstrom, Bending bilayer strips built from polyaniline for
artificial electrochemical muscles, Smart Materials and Structures 2 (1993) 1-6.
40. P. Chiarelli, A. Della Santa, D. De Rossi, A. Mazzoldi, Actuation properties of
electrochemically driven polypyrrole free-standing films, Journal of Intelligent
Material systems and Structures 6 (1995) 32-37.
41. R.H. Baughamn, L.W. Shacklette, R.L. Elsenbaumer, E.J. Plichta, C. Becht,
Micro electromechanical actuators based on conducting polymers, Molecular
Electronics, Springer (1991).
42. Y. Min, A.G. MacDiarmid, K. Kaneto, Electromechanical actuators using
polyaniline-polyaniline films, Polymeric Materials Science Engineering, 71 (1994)
713-727.
43. K. Kaneto, M. Kaneko, Y. Min, A.G. MacDiarmid, Artificial muscle:
Electromechanical actuators using polyaniline films, Synthetic Metals 71 (1995)
2211-2212.
44. S. John, G. Alici, C. Cook, Frequency response of polypyrrole trilayer actuator
displacement, Proceedings of SPIE on Electroactive Polymer Actuators and
Devices, (2008).
137
45. T.W. Lewis, L.A.P. Kane-Maguire, A.S. Hutchison, G.M. Spinks, G.G. Wallace,
Development of an all-polymer, axial force electrochemical actuator, Synthetic
Metals 102 (1999) 1317-1318.
46. J.D.W. Madden, P.G.A. Madden, I.W. Hunter, Conducting polymer actuators as
engineering materials, Proceedings of SPIE on Electroactive Polymer Actuators
and Devices, (2002).
47. E. Smela, O. Inganas, I. Lundstrom, Conducting polymers as artificial muscles:
challenges and possibilities, Journal of Micromechanics and Microengineering 3
(1993) 203-205.
48. E. Smela, O. Inganas, Q. Pei, I. Lundstrom, Electrochemical muscles:
Micromachining fingers and corkscrews, Advanced Materials 5 (1993) 630-632.
49. E. Smela, M. Kallenbach, J. Holdenried, Electrochemically driven polypyrrole
bilayers for moving and positioning bulk micromachined silicon plates, Journal of
Microelectromechanical Systems 8 (1999) 373-383.
50. L. Bay, K. West, N. Vlachopoulos, S. Skaarup, Potential profile in a conducting
polymer strip, Proceedings of SPIE on Smart Structures and Materials, (2001).
51. L. Bay, K. West, P. Sommer-Larsen, S. Skaarup, M. Benslimane, A conducting
polymer actuator with 12% linear strain, Advanced Materials 15 (2003) 310–313.
52. J. Ding, L. Liu, G.M. Spinks, D. Zhou, G.G. Wallace, J. Gillespie, High
performance conducting polymer actuators utilizing a tubular geometry and
helical wire interconnects, Synthetic Metals 138 (2003) 391–398.
53. S. Hara, T. Zama, W. Takashima, K. Kaneto, Polypyrrole–metal coil composite
actuators as artificial muscle fibers, Synthetic Metals 146 (2004) 47–55.
138
54. T. Fukushima, K. Asaka, A. Kosaka, T. Aida, Layer-by-layer casting fabrication
of soft actuator based on single-walled carbon nanotubes and ionic liquids.
Angewandte Chemie International Edition 44 (2005) 2410–2413.
55. K. Mukai, K. Asaka, K. Kiyohara, T. Sugino, I. Takeuchi, T. Fukushima, T.
Aida, High performance fully plastic actuator based on ionic-liquid-based bucky
gel, Electrochimica Acta 53 (2008) 5555-5562.
56. N. Terasawa, N. Ono, K. Mukai, T. Koga, N. Higashi, K. Asaka, A multi-walled
carbon nanotube/polymer actuator that surpasses the performance of a single-
walled carbon nanotube/polymer actuator, Carbon 50 (2012) 311-320.
57. M. Biso, D. Ricci, Multi-walled carbon nanotubes plastic actuator, Physica Status
Solidi (b) 246 (2009) 2820-2823.
58. C. Li, D. Wang, T. Liang, X. Wang, L. Ji, A study of activated carbon nanotubes
as double-layer capacitors electrode materials, Materials Letters 58 (2004) 3774-
3777.
59. G. Alici, P. Metz, G.M. Sinks, A mathematical model to describe bending
mechanics of polypyrrole (PPy) actuators, Proceedings of the IEEE/ASME
International Conference on Advanced Intelligent Mechatronics, (2005).
60. G. Alici, N.N. Huynha, Predicting force output of trilayer polymer actuators,
Sensors and Actuators A: Physical. 132 (2006) 616–625.
61. G. Alici, An effective modeling approach to estimate nonlinear bending behavior
of cantilever type conducting polymer actuators, Sensors and Actuators B:
Chemical 141 (2009) 284–292.
62. B. Shapiro, E. Smela, Bending actuators with maximum curvature and force and
zero interfacial stress, Journal of Intelligent Material Systems and Structures 18
(2007) 181–186.
139
63. P. Du, X. Lin, X. Zhang, A multilayer bending model for conducting polymer
actuators, Sensors and Actuators A: Physical 163 (2010) 240–246.
64. Y. Fang, T.J. Pence, X. Tan, Nonlinear elastic modeling of differential expansion
in trilayer conjugated polymer actuators, Smart Materials and Structures 17
(2008) 065020 (10pp).
65. T. Shoa, D.S. Yoo, K. Walus, J.D.W. Madden, A dynamic electrochemical model
for electrochemically driven conducting polymer actuators, IEEE/ASME
Transactions on Mechatronics 16 (2011) 42-49.
66. C.H. Nguyen, G. Alici, G. Wallace, An advanced mathematical model and its
experimental verification for trilayer conjugated polymer actuators, IEEE/ASME
Transactions on Mechatronics 19 (2013) 1279-1288.
67. X. Wang, G. Alici, X. Tan, Modeling and inverse feedforward control for
conducting polymer actuators with hysteresis, Smart Materials and Structures 23
(2014) 025015 (9pp).
68. T. Shoa, J.D.W. Madden, T. Mirfakhrai, G. Alici, G.M. Spinks, Electromechanical
coupling in polypyrrole sensors and actuators, Sensors and Actuators A: Physical
161 (2010) 127-133.
69. Y. Osada, J.P. Gong, Soft and wet materials: polymer gels, Advanced Materials
10 (1998) 827-837.
70. K.M. Newbury, D.J. Leo, Electromechanical modeling and characterization of
ionic polymer benders, Journal of Intelligent Material Systems and Structures 13
(2002) 51-60.
71. K. Farinholt, D.J. Leo, Modeling of electromechanical charge sensing in ionic
polymer trancducers, Mechanics of Materials 36 (2004) 421-433.
140
72. C.K. Chiang, C.R. Fincher, Y.W. Park, A.J. Heeger, H. Shirakawa, E.J. Louis,
A.G. MacDiarmid, Electrical conductivity in doped polyacetylene, Physical
Review Letters 39 (1977) 1098-1101.
73. W. Takashima, T. Uesugi, M. Fukui, M. Kaneko, K. Kaneto,
Mechanochemoelectrical effect of polyaniline film, Synthetic Metals 85 (1997)
1395-1396.
74. W. Takashima, K. Hayasi, K. Kaneto, Force detection with Donnan equilibrium
in polypyrrole film, Electrochemistry Communications 9 (2007) 2056-2061.
75. G. Alici, G.M. Spinks, J.D.W. Maden, Y. Wu, G.G. Wallace, An investigation
into behavior of electro active polymers as mechanical sensors, Proceedings of the
IEEE/ASME International Conference on Advanced Intelligent Mechatronics,
(2007).
76. Y. Wu, G. Alici, J.D.W. Madden, G.M. Spinks, G.G. Wallace, Soft mechanical
sensors through reverse actuation in polypyrrole, Advanced Functional Materials
17 (2007) 3216-3222.
77. G. Alici, G.M. Spinks, J.D.W. Madden, Y. Wu, G.G. Wallace, Response
characterization of electroactive polymers as mechanical sensors, IEEE/ASME
Transactions on Mechatronics 13 (2008) 187-196.
78. S.W. John, G. Alici, G.M. Spinks, J.D.W. Madden, G.G. Wallace, Towards fully
optimized conducting polymer bending sensors: the effect of geometry, Smart
Materials and Structures 18 (2009) 085007 (8pp).
79. T. Mirfakhrai, T. Shoa, N. Fekri, J.D.W. Madden, A model for mechanical force
sensing in conducting polymers, ECS Transactions 28 (2010) 59-71.
80. T.F. Otero, M.T. Cortes, Artificial muscles with tactile sensitivity, Advanced
Materials 15 (2003) 279-282.
141
81. R. Minato, G. Alici, S. McGovern, G. Spinks, Tri-layer conducting polymer
actuators with variable dimensions, Proceedings of SPIE on Electroactive Polymer
Actuators and Devices, (2007).
82. G. Alici, P. Metz, G.M. Spinks, A methodology towards geometry optimization of
high performance polypyrrole (PPy) actuators, Smart Materials and Structures 15
(2006) 243–252.
83. E.K. Burke, G. Kendall, Search methodologies: Introductory tutorials in
optimization and decision support techniques, Springer, (2006).
84. M. Caramia, P. Dell’Olmo, Multiobjective management in freight logistics,
Springer, (2008).
85. U.L. Zainudeen, M.A. Careem, S. Skaarup, PEDOT and PPy conducting polymer
bilayer and trilayer actuators, Sensor and Actuators B: Chemical 134 (2008) 467-
470.
86. N.N. Huynhl, G. Alici, G.M. Spinks, Force analysis and characterization of
polymer actuators, Proceedings of the IEEE/RSJ International Conference on
Intelligent Robots and Systems, (2006).
87. Y. Fang, X. Tan, G. Alici, Robust Adaptive control of conjugated polymer
actuators, IEEE Transactions on Control Systems Technology 16 (2008) 600-612.
88. C.H. Nguyen, G. Alici, G.G. Wallace, Modeling trilayer conjugated polymer
actuators for their sensorless position control, Sensors and Actuators A: Physical
185 (2012) 82-91.
89. G. Alici, B. Mui, C. Cook, Bending modeling and its experimental verification for
polymer actuators dedicated to manipulation applications, Sensors and Actuators
A: Physical 126 (2006) 396–404.
142
90. Y. Fang, X. Tan, G. Alici, Redox level-dependent impedance model for
conjugated polymer actuators, Sensors and Actuators B: Chemical 132 (2008)
182–190.
91. T.F. Otero, J.M. Sansinena, Bilayer dimensions and movement in artificial
muscles, Bioelectrochemistry and Bioenergetics 42 (1997) 117-122.
92. J.D.W. Madden, Electroactive polymers for robotics applications, Springer,
(2007).
93. W. Zheng, J.M. Razal, P.G. Whitten, R. Ovalle-Robles, G.G. Wallace, R.H.
Baughman, Artificial muscles based on polypyrrole/carbon nanotube laminates
Advanced Materials 23 (2011) 2966-2970.
94. T.W. Ebbesen, H.J. lezec, H. Hiura, J.W. Bennett, H.F. Ghaemi, T. Thio,
Electrical conductivity of individual carbon nanotubes, Nature 382 (1996) 54–56.
95. B.J.C. Thomas, A.R. Boccaccini, M.S.P. Shaffer, Multi-walled carbon nanotube
coatings using electrophoretic deposition (EPD), Journal of the American Ceramic
Society 88 (2005) 980-982.
96. A.R. Boccaccini, I. Zhitomirsky, Application of electrophoretic and electrolytic
deposition techniques in ceramics processing, Current Opinion in Solid State &
Material Science 6 (2002) 251-261.
97. K. Mukai, K. Yamato, K. Asaka, K. Hata, H. Oike, Actuator of double layer film
composed of carbon nanotubes and polypyrroles, Sensors and Actuators B:
Chemical 161 (2012) 1010-1017.
98. P.G.A. Madden, J.D.W. Madden, P.A. Anquetil, N.A. Vandesteeg, I.W. Hunter
The relation of conducting polymer actuator material properties to performance,
IEEE Journal of Oceanic Engineering 29 (2004) 696-705.
143
99. A.R. Boccaccini, J. Cho, J.A. Roether, B.J.C. Thomas, E.J. Minay, M.S.P.
Shaffer, Electrophoretic deposition of carbon nanotubes, Carbon 44 (2006) 3149-
3160.
100. C. Singh, M.S.P. Shaffer, A.H. Windle, Production of controlled architectures of
aligned carbon nanotubes by an injection chemical vapour deposition method,
Carbon 41 (2003) 359-368.
101. T.W. Ebbesen, P.M. Ajayan, Large-scale synthesis of carbon nanotubes, Nature
358 (1992) 220-222.
102. C. Li, D. Wang, T. Liang, W. Wang, L. Ji, A study of activated carbon
nanotubes as double-layer capacitors electrode materials, Materials Letters 58
(2004) 3774-3777.
103. M.S.P. Shaffer, X. Fan, A.H. Windle, Dispersion and Packing of Carbon
Nanotubes, Carbon 36 (1998) 1603-1612.
104. J. Zhang, H. Zou, Q. Qing, Y. Yang, Q. Li, Z. Liu, X. Guo, Z. Du, Effect of
chemical oxidation on the structure of single-walled carbon nanotubes, Journal of
Physical Chemistry B 107 (2003) 3712–3718.
105. G.H. Kim, S.M. Hong, Y. Seo, Piezoelectric properties of poly(vinylidene fluoride)
and carbon nanotube blends: -phase development, Physical Chemistry Chemical
Physics 11 (2009) 10506-10512.
106. J.H. Choi, J. Jegal, W.N. Kim, Fabrication and characterization of multi-walled
carbon nanotubes/polymer blend membranes, Journal of Membrane Science 284
(2006) 406-415.
107. J. Kathi, K.Y. Rhee, Surface modification of multi-walled carbon nanotubes using
3-aminopropyltriethoxysilane, Journal of Materials Science 43 (2008) 33-37.
144
108. A. Joshi, S.A. Gangal, S.K. Gupta, Ammonia sensing properties of polypyrrole
thin films at room temperature, Sensors and Actuators B: Chemical 156 (2011)
938-942.
109. E.D. Blanchard, M.J. Smith, C.H. Nguyen, Parameter identification study of
frequency response data for a trilayer conjugated polymer actuator displacement
model, Proceedings of the IEEE/ASME International Conference on Advanced
Intelligent Mechatronics, (2013).
110. J.R. Macdonald, Impedance spectroscopy: Emphasizing solid materials and
systems, Wiley, (1987).
