Strain phenomenon in carbon nanotube buckpaper actuator: Experiments and modeling

Sensors and Actuators A 194 (2013) 252–258

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

Strain phenomenon in carbon nanotube buckpaper actuator: Experiments and modeling P.-J. Cottinet, M.-Q. Le, J. Degraff, C. Souders, Z. Liang ∗ , B. Wang, C. Zhang High-Performance Materials Institute, Florida State University, 2005 Levy Ave, Tallahassee, FL 32310, United States

a r t i c l e

i n f o

Article history: Received 18 December 2012 Received in revised form 4 February 2013 Accepted 9 February 2013 Available online 24 February 2013 Keywords: Buckypaper Smart material Electroactive polymer Carbon nanotube Actuator

a b s t r a c t Carbon nanotube buckypapers and Nafion composites demonstrate the potential to offer a combination of sensing and actuating abilities for lightweight and flexible applications. These materials have a promising future in the applications of robotic and biomedical systems. This paper describes the modelling of the electromechanical conversion phenomena pertaining to buckypaper/Nafion actuators. The physical properties of buckypaper and Nafion, including Young’s modulus and electrical double layer capacitance, serve as key factors in the actuators’ performance. Moreover, established by a convolution procedure, the proposed approach is able to study the hysteresis under an electric field. The generated displacement of the cantilevered buckypaper/Nafion actuators were calculated and show an excellent agreement between the computed tip strains and the measured data over a wide frequency range. Published by Elsevier B.V.

1. Introduction Over the past decade, electro-active polymers (EAPs) have received tremendous interest for their potential applications in sensing, actuation and energy storage [1]. Electro-active polymers have created a unique opportunity to provide greater flexibility and degrees of freedom to design biologically-inspired robots. The unique properties of biological muscles are large strain generation, moderate stress, quick response, improved efficiency and a long life cycle. Prior research has shown that EAPs have similar properties and function similar to biological muscles [1]. Indeed, ionic electro-active polymers (I-EAP) have shown many new opportunities in robotic actuation technologies because of their low electric field requirements and relatively large deformations. In particular, the I-EAPs can be applied to an arbitrary shape and size, with proper intelligent and biomimetic shape-changing control schemes. Such polymeric actuators demonstrate a clear advantage towards developing a more intelligent biomimetic robotic system in comparison to traditional electromechanical actuators [2,3]. In the past, robots mobilized by smart (piezoelectric) material have been limited in practical applications due to the lack of technology that can mimic complex movements. Even though recent research on animal motions has made tremendous progress towards a better understanding of their complex motions [4–8], using I-EAP for robotics or micromanipulations has remained an

∗ Corresponding author. E-mail address: [email protected] (Z. Liang). 0924-4247/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.sna.2013.02.014

obstacle. In most of these applications, EAP actuators were dynamically driven. The back-relaxation phenomenon in I-EAP [9] has led to uncertainty as to whether I-EAPs are suitable for some applications, for example DC actuation. To establish some clarity, this paper describes a model able to predict the strains under an electric field. The actuator is composed of carbon nanotube (CNT) buckypaper and a Nafion electrolyte. The discovery of CNTs and their electromechanical actuations introduced a unique technology enabling the conversion of an electrical stimulus to mechanical displacement due to a novel quantum mechanical mechanism [10]. The activation mechanism was based on a double-layer charge injection working in a liquid electrolyte [11]. Together with the quantum chemical effect, this double layer of ions creates large dimension changes in the covalent bonds of the nanotubes. This paper reports on the investigation behavior of buckypaper under a quasistatic input. A number of dynamic processes (e.g., ion migration, water diffusion) takes place in I-EAP actuation; however, the exact mechanisms of actuation are still a subject of active research [9,12,13]. A hysteretic relationship between the steadystate curvature and the applied voltage were observed. Many models have been presented to describe the behaviour of EAP. Newbury classified these into three categories, physical model, black box models, and gray box models [1,14]. However, their models did not sufficiently reflect the hysteresis nonlinearity of EAP. Some researchers assumed that EAP is a mechanical and electrical linear system and the other assumed that EAP is a partially nonlinear system with hysteresis [15–17]. The Preisach Model was proposed by F. Preisach in the 1930s to explain magnetic hysteresis [18]. Preisach hysteresis model sufficiently ferromagnetism hysteresis

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253

0.02 0.015

Strain (%)

0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -100

-50

0

50

100

Electric field (V/mm) Figure 2. Strain versus electric field at 0.1 Hz. Figure 1. Scheme of the experimental test bench.

sufficiently [19]. Subsequently, this model has been applied in various smart materials such as piezoelectric actuators, EAP and shape memory alloys to described their hysteresis behaviour [20–22]. However, this model does not relate to the physical parameters of the system, since identifying the main reason of the hysteresis in the material is difficult [23]. In this paper, a model was developed to take into account of the hysteresis and relationships with the intrinsic parameters of the actuator. This paper describes the effects of an applied electric field on the strain properties of buckypaper. A specific experimental bench was developed to allow for the measurement of the buckypapers’ strain under a quasi-static sinusoidal electric field at low frequencies. As a result, this article proposes a model able to predict the hysteris of the strain under an electric field. 2. Experimental procedure 2.1. Actuators preparation In this study, randomly orientated multi-wall nanotube (MWNT) buckypapers were used to fabricate buckypaper/Nafion actuators. The fabrication process was previously presented [24] and is summarized in this paper. The MWNT buckypapers were were produced using CNTs by CNano Technology (San Francisco, CA). The buckypaper fabrication procedures were documented in detail by the research groups of Smalley [25] and Wang [26,28]. The buckypaper actuator is a bimorph structure fabricated with Nafion, a solid electrolyte layer capable of ion diffusion, sandwiched between two buckypaper electrode layers. Purchased from DuPont, the Nafion NRE-212 is an electrically conducting polymer membrane used as the medium between the two buckypaper strips. This polymer was chosen because of its proven ion mobility and environmental stability [27]. The Nafion was sandwiched between the two buckypaper layers and hot-pressed at 110 ◦ C while undergoing an applied pressure of 120 psi for 10 min. Before combining the buckypaper and Nafion membrane, a Nafion solution was coated onto the two sheets of buckypapers to increase the interfacial bonding of the structure [24]. 2.2. Experimental set-up Fig. 1 shows the experimental setup for sample characterization. As displayed, the buckypaper/Nafion actuators were tested using a cantilever configuration and would bend when stimulated by an applied voltage. One end was fixed by a rigid clamp fitted

with copper foil electrodes that were connected to the outside buckypaper sample surface. The deflection of the free end was measured with a laser displacement sensor. The tip displacement can be expressed in terms of strain (S1 ) using simple geometry and Eq. (1), where ı denotes the tip displacement (zero-to-peak), t denotes the sample thickness (t = 100 ␮m), and L denotes the free length of the sample (L = 30 mm). This equation assumes that the actuator deforms with a uniform curvature [24,28]. S1 =

ıt L2

(1)

The displacement of the buckypaper/Nafion actuators was measured using a Microtrak II laser displacement sensor (MTI Instrument, Inc.). Test cells were produced to characterize the electrochemical properties of buckypaper/Nafion. As shown in Fig. 1, the sinusoidal wave potentials were applied between the working and counter electrodes using a function generator (Agilent 2310A). The clamp that supports the actuators was mounted to a breadboard from ThorLabs. The breadboard was housed in a Plexiglas enclosure with a door mounted on top to prevent any air flow from disturbing the results. The breadboard was mounted to an Iso-Plate Passive Isolation System to dampen any vibrations in the room. The time history of the tip displacement and input voltage was measured using an oscilloscope. The uncertainty of the displacement is 20 ␮m. Moreover, for each sample, measurement was performed three times and for three samples. The deviation of the displacement response was indicated by error bars in the different figures. This principal deviation of the displacement measurement was due to the thickness change of each sample. 3. Results and discussions 3.1. Electromechanical measurement Fig. 2 depicts the electromechanical responses of the buckypaper/Nafion/buckypaper bimorph cantilever structure under various electric fields. Under low electric fields (e.g. E3 = 20 V/mm), a linear relationship between the voltage and the displacement was observed. However, when the electric field was higher than the saturated value (i.e. Esat = 45 V/mm), a nonlinear characteristic occurred between the strain and the electric field. The mechanisms of actuation and saturation effect have been reported in previous works [24]. The saturation of the strain versus electric field can be attributed to the oxidation of the oxygen-containing functional groups located on the carbon nanotube surface in the buckypaper

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0

-50

0

0

10

20

30

-3

S

-5 50

40

time (s)

Strain (%)

5

x 10

x 10 15

60

-3

(b)

10 63%.S

max

20

5

0

0

-30

-20

-10

0

10

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-20

40

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10

20

Electric field (V/mm)

[29,30]. This could also be attributed to nanotubes having different chirality, which is analogous to the chemoselectivity demonstrated by Strano et al. [31]. To further analyze the mechanical and electrical characteristics of the buckypaper/Nafion/buckypaper, Fig. 3(a) displays the temporal evolution of the electric field and generated strain. A phase-shift was observed between the strain and electric field. This is due to the transported charge being the key-governing factor of the electromechanical conversion in the electroactive actuators [24,32]. Also, the sample required a certain period of time to relax and return back to its initial position when the electric field was off. Fig. 3(b) illustrates the measured strain vs. the electric field input. A hysteresial relationship existed between the input and output as the oscillating sine waves were not in phase. Similar to magnetic materials, magnetostrictives, piezoceramics, shape memory alloys and other materials, buckypaper/Nafion has the disadvantage of hysteresis and creep or drift behaviors. These behaviors are inherent in piezoelectric actuators as they may deteriorate the system’s performance and lead to vibration or instability. This especially occurs in high-precision positioning systems, such as atomic force microscopes and micro-manipulators. 3.2. Modeling hysteresis in buckypaper/Nafion actuators In order to understand the observed hysteresis cycle of the strain versus the electric field, a modeling of the buckypaper/Nafion actuator was developed. The electrical charge-induced strain in the buckypaper/Nafion film can be represented by [33–36] S1 = ˛31 3

(2)

where ˛31 denotes the coupling constant between the electric charge density (3 ) and the strain S1 . Eq. (2) shows a linear relationship between the electric field and the electric charge. As previously demonstrated, this behavior is more accurate in the case of low electric fields [24]. The electric charge can be given by 3 = C0 E3

(3)

where E3 denotes the applied voltage across the sample, and C0 denotes the double layer capacitance of the buckypaper/Nafion. The hysteresis presented in Fig. 3 was modeled by introducing the function h(t) convolved by the expression of strain in Eq. (2). = h(t) ∗ S1

30

40

-5 50

Time (s)

Figure 3. (a).Measured strain and applied electric field in function of time, (b) measured strain versus electric field.

hys

max

40

0

-5 -40

S1

-3

Strain (%)

(a)

x 10 5

Electric field (V/mm)

50

Strain (%)

Electric field (V/m)

254

(4)

Figure 4. Response of BP/Nafion actuator under a step voltage excitation.

Based on [37,38], the buckypaper/Nafion actuator is equivalent to a first order system. As shown in Fig. 4, the generated strain exponentially increases in transient without overshoot when the sample was experimentally driven by a step electric field of 20 V/mm. At steady state, the strain response remained constant and near the desired values of 0.01%. This behavior represents the typical signature of a first order system, in which the function h(t) can be defined as

 t

h(t) = exp −

(5)



where t denotes the time, and  denotes the time constant, which can also be called the relaxation time. The relaxation time  was empirically deduced from the strain response of a first order system presented in Fig. 4. Actually,  represents the time necessary for the step response to reach 63% of its final value at steady state [39]. The value of  is experimentally found to be 3.2 s. Table 1 summarizes the different values of the parameters used in the model. The effective coefficient ˇ31 can be calculated from the curve S1 = f(E3 ) (see Fig. 2) by assuming that S1 = ˇ31 E3 before reaching saturation. Based on the experiments, measuring the coefficient ˇ31 was easier than measuring ˛31 [24]. Indeed, the coefficient ˛31 was calculated from ˇ31 using ˛31 = ˇ31 /C0 , where C0 was obtained using an impedance-meter (Solartron SI1260 Impedance/GainPhase Analyser). Fig. 5 displays the input electric field versus time (Fig. 5(a)), as well as the measured and simulated strain versus time (Fig. 5(b)). As observed in Fig. 5(c), the strain error between the measurements and the simulations was relatively low, confirming agreement between the experimental and theoretical values. This indicates that the model reflects the major conversion mechanism. It is interesting to note that the model reported in this paper allows to take into account the creep effect, which is a common property existing in many kinds of EAPs. The creep phenomenon entails that a response that cannot maintain a steady value when a time-invariant signal is applied to the system, but the response changes slowly over time [40]. In the case of the buckypaper/Nafion actuator, when a sinusoidal electric field signal of 35 V/mm was Table 1 Parameters of the BP/Nafion actuator at 0.1 Hz. ˇ31 (m/V)

 (s)

C0 (F/m)

˛31 (m2 /C)

16 × 10−10

3.2

4.16

3.84 × 10−10

Electric field (V/mm)

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255

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(a)

0 -50

0

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Time (s) -5

Strain (m/m)

x 10 5

(b)

0

data modelling

-5 0

5

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Time (s)

Error (m/m)

-5

2

x 10

0

(c) -2

0

5

10

15

20

25

30

35

40

45

50

Time (s) Figure 5. Evolution of measured and modelled strain of BP/Nafion actuator at 0.1 Hz.

chosen as the input, the output displacement somewhat deviates with time, as illustrated in Fig. 5(a). Different reasons for the creep phenomenon in the ionic polymer have been reported in literature. Chen et al. argued that the mismatch of internal stresses in the buckypaper/Nafion interface could lead to delamination and/or spontaneous creep of the actuator [41]. Another cause was proposed by Hao et al. noting the degradation of the Nafion due to the electrolyze [42]. In any case, the proposed model reported in this paper considers the creep and hysteresis effects and also quantify the relaxation time (), which is an interesting element for the material characterizations. In order to complete the characterization study of the buckypaper/Nafion actuator, an analysis of the strain behavior in the frequency domain was conducted. Fig. 6 shows the evolution of the measured and modeling strains in terms of the electrical field with a frequency range of 0.1–5 Hz. For a given electric field amplitude of 35 V/mm, four sinusoidal excitation signals with frequencies of 0.1 Hz, 0.5 Hz, 1 Hz, and 5 Hz were chosen for characterizing the buckypaper/Nafion actuator. Such a frequency range was utilized due to the high deformation or strain capacity of the buckypaper/Nafion actuator over a low bandwidth. On the other hand, when the frequencies increased, the actuator would produce very little strain, which is a limit in several applications, particularly in robotic and biomedical domains [35]. The results in Fig. 6 confirm that the experimental results are in agreement with the modelling results for a low bandwidth range. Finally, the proposed model in terms of strain and electric field for the EAP actuator can be validated in both time and frequency domains. Table 2 presents the model parameters calculated using the aforementioned frequency values. As was observed, the relaxation time, , was constant for the given bandwidth. This is due to the parameter  intrinsically representing the mechanical and electrical losses, which can be considered independent of the frequency

Table 2 Evolution of the modelling parameters for different frequencies. f (Hz) 0.1 0.5 1 5

ˇ31 (m/V) −10

16 × 10 7.5 × 10−10 3.9 × 10−10 2.1 × 10−10

 (s)

C0 (F/m)

˛31 (m2 /C)

3.2 3.2 3.2 3.2

4.16 3.33 2.77 2.15

3.84 × 10−10 2.25 × 10−10 1.40 × 10−10 0.99 × 10−10

[43,44]. Therefore, the time constant  can be used in characterizing the hysteresis and the creep properties of the material induced by the mechanical and electrical losses. The electromechanical conversion coefficients (i.e., ˇ31 and ˛31 ) highly varied subject to the excited frequency. When frequency increased, the strain generated for a given electric field decreased. This can be explained by the fact that the electromechanical activity of the material reduces over higher frequency ranges, relating to the principle of the EAP actuator conversion based on the ions’ movements. Actually, the cations’ mobility depends on the ion size and the ionic interaction between the counter cations and the sulfonic acid groups [45,46] that strongly vary with the frequency. Such a property may provide limitations of the actuation frequencies characterized by the electrical double layer (C0 ) [44]. Indeed, C0 determines the voltage needed to generate a given concentration at the electrolyte, Nafion surface. When the frequency increases, the double layer capacitance decreases, even when the double layer thickness is unchanged. In this case, a minimal charge per volt in the double layer would cause the concentration of ions per volt to be reduced. A minimal charge in the double layer at the maximum voltages should also reduce the maximum expansion of the polymer [33]. To better understand the above phenomenon, Fig. 7 shows the trend of the electrical double layer C0 (F/m) in terms of the frequency. The capacitance was calculated by the expression C = −1/(2fZ ) where Z denotes the imaginary component of the impedance. As expected, the curve of the capacitance shows a decreasing behavior as frequency increases. These results are clearly indicative of the diminution of the ions’ mobility, as reported in [44]. For instance, when the frequency increased from 0.1 Hz to 5 Hz, the electromechanical coefficient (˛31 ) decreased about four times, whereas the capacitance of C0 was reduced by half (see Table 2). Furthermore, the global diminution of ˛31 was due to an increase of the sample’s modulus with frequency [43]. In fact, some recent works show that the electromechanical coefficient is proportional to the ratio of the electrical double layer to the Young’s modulus [33,47]. Smart materials, e.g., magnetostrictives, piezoelectric polymers and shape memory alloys (SMAs), exhibit strong couplings between applied electric–electromagnetic–thermal fields and strains that can be exploited for actuation. Hysteresis in smart materials, however, poses a significant challenge for applications. Table 3 provides

256

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Figure 6. Comparison between experimental and modelling data for different frequency (the blue dash lines are the modelling and solid green lines are experimental data). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 3 Comparison of hysteresis in different smart material. Type of material

SMA [21]

Magnetostrictive [49]

IPMC [50]

Piezoelectric polymer [51]

Electrostrictive polymer [52]

BP actuator

Hysteresis

High

Average

Average

Average

Low

Average

a comparison of different types of actuators in term of hysteresis. Compared to shape memory polymers, a great advantage of using BP actuator comes from the fact that there was almost no hysteresis. These properties are clearly shown in Fig. 3, where the strains were plotted vs. electric fields. The area of the loop was very small as the actuator was closely passing by the same path upon high and low electric fields, which facilitates controlling the displacement and force [40,48].

4.5 4 3.5

C0 (F/m)

3 2.5 2 1.5 1 0.5 0 -1 10

10

0

10

1

frequency (Hz) Figure 7. Electrical double layer capacitor versus frequency for BP/Nafion actuator.

4. Conclusion This paper reported on the actuation performance of the buckypaper/Nafion material composites. A model was proposed to account for the hysteresis in the material under cyclic electric fields. The modelling results are in good agreements with the experimental measurements, as they confirmed an approximate linear relationship between the strain per unit voltage and the capacitance of the actuator over a wide range of frequencies. These results demonstrate a strong dependence between the charge accumulation at the Nafion-buckypaper interface and the electromechanical performance. Moreover, the macroscopic model parameters, such as the double layer capacitor C0 and the Young’s modulus Y, were considered in the electro-mechanical conversion of the buckypaper/Nafion composite material. The hysteresis effect could be introduced as a simple mathematical function. The global model was then empirically validated, and the specific values of the system parameters were found to correspond with the physical phenomena. These parameters are considered to be some of the most important elements as they pertain to the characterization of the materials’ properties. In conclusion, future work can be extended in several directions. The model could be used to develop an open-loop controller. An investigation could be conducted to determine if the hysteresis effect and the actuation characteristics could be associated with the temperature changes. The development of the electro-active actuators with increased electrical double layers for a large bandwidth may also be included. A study to determine if the capacitance may achieve high performance of the actuators (e.g. maximum

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displacement) would be challenging, but this is a priority in our future works.

Acknowledgments This research was supported by the US Army Research Laboratory (ARL) through the Nanotubes Optimized for Lightweight Exceptional Strength (NOLES) Composite Materials Program. Dr. Shawn Walsh’s management of this program is greatly appreciated.

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Biographies Dr. Pierre-Jean Cottinet graduated from the Institut National des Sciences Appliquées de Lyon (INSA Lyon), Lyon, France, in 2008. He received a Ph.D. degree in

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Acoustics in 2008 from the Institut National des Sciences Appliquées de Lyon (INSA) France for his thesis on electrostrictive polymer for energy harvesting and actuation. During 2011, he was at Florida State University as a post-doctoral and working on buckypaper in HPMI (High-Performance Materials Institute). Currently, he is an associate professor at INSA de Lyon, with research interests concerning electroactive materials (polymers, CNT. . .) and smart structures. Dr. Minh-Quyen Lê received her electrical engineering and MSc degrees in Acoustics from the Institut National des Sciences Appliquées de Lyon (INSA de Lyon), France, in 2008. She then received her Ph.D. degree in Electronics, Electrotechnics and Automatics from INSA de Lyon in 2011. In 2011–2012, she was a post-doctoral research at the Montpellier Laboratory of Informatics, Robotics, and Microelectronics (LIRMM), France where she worked on the European ARAKNES project. She is now working at EKIUM company in the process control and automation production line. She also collaborates with the HPMI of Florida State University for the design and characterization of smart structure with Buckypaper. Her research interests are haptic teleoperation system, birateral control, robotics for minimally invasive surgery, smart materials and morphing. Joshua DeGraff is an Industrial and Manufacturing Engineering Masters Student at the Florida A&M/Florida State University College of Engineering. He obtained his Bacheleor’s degree in the same field from Florida State University. His research experiences have been geared towards the advancement of the ionic polymer composite membrane, Nafion. His current research pertains to improving the blocking force and displacement generated by Nafion/Buckypaper actuators. He is currently employed at Florida State’s High Performance Materials Institute. Corey Souders graduated with a degree in Industrial Engineering from Florida State University. As an undergrad he performed research in bucky paper – Nafion actuators and windmill power generation. He is currently employed by Duke Energy. Dr. Zhiyong (Richard) Liang is a professor at Dept. of Industrial and Manufacturing, FAMU-FSU College of Engineering. He also serves as the Director of the FSU

High-Performance Materials Institute (HPMI). He received his Ph.D. degree in Materials Science and Engineering from the Beijing University of Aeronautics and Astronautics, and then jointed the school as a faculty member and rise to the professor and program director of polymers and composites materials. His research experience and expertise are nanoparticle dispersion, nanotube film or buckypaper materials and high-performance composites and nanocomposites, including synthesis, chemical functionalization, processing–structure–property relationships, property characterization and process modeling. His researches were sponsored by various government agencies (ARL, AFRL, AFOSR and ONR etc.) and leading industrial corporations. He has published more than 95 refereed journal papers. He advised 23 MS, 9 Ph.D. and 6 honors thesis students, as well as 17 postdoc follows since he joined FSU in 2001. Dr. Ben Wang recently joined the Georgia Tech’s Stewart School of Industrial and Systems Engineering. Until 2011, Dr. Wang was the director of the High-Performance Materials Institute and professor at Dept of IME at FSU. With a primary research interest in applying emerging technologies to improve manufacturing competitiveness, He specializes in process development for affordable composite materials and is widely acknowledged as a pioneer in the growing field of nano-materials. He has published more than 160 papers in referred journals and is an inventor or co-inventor of over 25 patents or patent applications. Dr. Chun (Chuck) Zhang is a professor at High-Performance Materials Institute (HPMI) and Department of Industrial and Manufacturing Engineering (IME). He received his Ph.D. in industrial engineering from the University of Iowa. He has been with Florida FSU since 1993. His research interests include scalable nanomanufacturing, modeling, simulation and optimization of composites and nanomaterials manufacturing processes, multifunctional materials development and geometric tolerancing and metrology. He has published over 120 referred journal articles and 170 conference papers and is an inventor or co-inventor of over 25 patents or patent applications.