Stretchable Active Matrix Temperature Sensor Array of Polyaniline Nanofibers for Electronic Skin

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1 Stretchable Active Matrix Temperature Sensor Array of Polyaniline Nanofibers for Electronic Skin Soo Yeong Hong, Yong Hui Lee, Heun Park, Sang Woo Jin, Yu Ra Jeong, Junyeong Yun, Ilhwan You, Goangseup Zi, and Jeong Sook Ha* Recently, there has been remarkable accomplishment in the field of stretchable electronics including display panels, [1 ] radio frequency (RF) electronics, [2 ] light emitting diodes (LEDs), [3,4 ] acoustic devices, [5 ] strain, [6 ] and pressure sensors. [7 ] Stretchable devices are required to ensure that no performance deterioration occurs due to body movements when electronics are applied to noncoplanar surfaces such as the human body. In the fabrication of stretchable devices, stretchable electrical interconnections are considered a challenge. Successful demonstrations of serpentine interconnections of a polymer-encapsulated metal thin film have been reported; these interconnections are effective tools for relieving strain when strain is externally applied onto the entire electronic device. [8 10 ] Recently, it was also reported that liquid metal interconnections embedded into a deformable polymer substrate can be widely applied as stretchable and highly conductive electrical interconnections with a simple fabrication process and high fill factor of active devices. [11 14 ] Among wearable devices, electronic skins (e-skin) have been thoroughly investigated with the development of novel sensors for monitoring applications, such as the strain sensor, [6 ] pressure sensor, [15 ] temperature sensor, [16,17 ] and oximeter. [18 ] Although both passive- and active-matrix (AM) designs can be used for enabling the proposed user-interactive e-skins, AM designs have the advantage of minimizing signal crosstalk and thereby offering a better spatial resolution and contrast, and a faster response. [19 ] An AM backplane is composed of individual pixels that can be controlled by thin film transistors (TFT). Among the channels of the TFT, single-walled carbon nanotubes (SWCNTs) have a promising material platform, and SWCNT TFTs with a high conductivity, transparency, and S. Y. Hong, Y. H. Lee, H. Park, Y. R. Jeong, J. Yun, Prof. J. S. Ha Department of Chemical and Biological Engineering Korea University Seoul , Korea jeongsha@korea.ac.kr S. W. Jin, Prof. J. S. Ha KU-KIST Graduate School of Converging Science and Technology Korea University Seoul , Korea I. You, Prof. G. Zi Department of Civil Environmental and Architectural Engineering Korea University Seoul , Korea flexibility are fabricated via both solution [20,21 ] and chemical vapor deposition (CVD) methods. [22 ] As one of the important sensing components for the e-skin, the temperature sensor has also been investigated with various materials including carbon nanotube (CNT), [23 ] graphene, [18 ] and conductive polymer. [24,25 ] In particular, conductive polymers can be easily synthesized, and their conductivity can be tuned by doping and chemical treatments. [26 ] Recently, polyaniline nanofibers were reported to be easily synthesized using electrochemical polymerization, i.e., the potentiodynamic method. [27 ] Electrochemical polymerization has advantages of uniform morphology and cost effectiveness. [28,29 ] Even though stretchable temperature sensor with embedded silver nanowire (Ag NW) electrodes and graphene detection channels was recently reported, [16 ] fabricating a stretchable temperature sensor which maintains a stable performance under an applied strain up to 50% was found challenging because the sensitivity of the temperature sensor changed during stretching. Here, we report on the fabrication of a stretchable polyaniline nanofiber temperature sensor array with an AM consisting of the SWCNT TFTs. In order to achieve mechanical stability under an externally applied strain, a specially designed soft Ecoflex substrate is used with locally implanted SWCNT TFTs and temperature sensors on stiff poly(ethylene terephthalate) (PET) films. Thus, the SWCNT TFTs are protected from the applied strain, and they are electrically connected via embedded interconnections of Galinstan, an eutectic alloy liquid metal consisting of gallium (68.5%), indium (21.5%), and tin (10%). [30 ] Owing to the embedded Galinstan interconnections, SWCNT TFTs, LED arrays, and temperature sensors maintain their performance under the deformations such as bending and stretching. In addition, the fabricated 5 5 AM temperature sensor array can be easily attached to the skin owing to its thin film structure and use of the soft and sticky Ecoflex. The temperature sensor exhibits a high resistance sensitivity of 1.0% C 1 and a response time of 1.8 s in the temperature range from 15 to 45 C. The integrated temperature sensor array with the SWCNT TFT-based AM backplane on the stretchable substrate gives mechanical stability under biaxial stretching of 30%, and the resultant spatial temperature mapping does not show any mechanical or electrical degradation. Our stretchable substrate with a multilayered structure was fabricated by assembling several component layers as shown in Figure 1a. Ecoflex (Ecoflex 0030, Smooth-On) was poured in a steel mold with Fe wires (dia. 300 µm) protruding from the bottom surface and then it was cured. After detaching the 500 µm thick cured Ecoflex layer from the mold, microchannels were opened at the bottom of the layer (Layer WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 1

2 Figure 1. a) Schematic of the fabrication process for the stretchable AM temperature sensor array. b) Assembly of prepared layers, liquid metal injection, and formation of electrical contacts with the Ag NW sticker. Red and yellow dotted regions correspond to SEM images in Figure S1b,c (Supporting Information) (red: SWCNTs, yellow: polyaniline nanofi bers). c) Circuit diagram of the stretchable AM temperature sensor array. and Layer 3). 300 µm thick Layer 1 and Layer 4 were prepared by spin-coating the Ecoflex. Next, fabricated 25 SWCNT TFTs and polyaniline nanofiber temperature sensors on PET films were attached onto Layer 1 and Layer 4, respectively, using the uncured Ecoflex. The detailed fabrication process of the stretchable temperature sensor array is described with Figure S1 (Supporting Information). The more detailed properties of PDMS, Ecoflex, and PET film are shown in Table S1 (Supporting Information). The adhesion of polyaniline nanofibers on the PET film after etching of Au film is confirmed in scanning electron microscope (SEM) images of Figure S2 (Supporting Information). Figure 1 b illustrates the stacked AM temperature sensor array on a deformable Ecoflex substrate with the embedded Galinstan interconnections and Ag NW sticker contacts. Ag NWs are confirmed to be partially embedded in PDMS through the peeling test using a 3M scotch tape. After being peeled off, the tape is slightly stained with Ag NWs. However, almost no change in the optical images of the Ag NW sticker after peeling test is observed as shown in Figure S3 (Supporting Information). The circuit diagram of AM temperature sensor array is given in Figure 1 c. The electrical performance of the SWCNT TFT AM backplane was obtained as shown in Figure S4 (Supporting Information). To fabricate the stretchable AM temperature sensor array, the SWCNT TFT should be stable during thermal heating at the temperatures where sensing is carried out. Thus, the thermal stability of the SWCNT TFT was confirmed by measuring the temperature-dependent drain current ( I DS ). I DS remained constant from 25 to 45 C, as indicated by the normalized current ( I DS /I DS0 ) of 1.0 in Figure S5 (Supporting Information). Here, I DS and I DS0 are the drain currents at temperatures from 25 to 45 C and at 25 C, respectively. Strain distribution on the stretchable substrate under bending and biaxial stretching was calculated by the finite element method (FEM). In Figure 2 a, the applied biaxial strain is defined as ε applied = ( l l ) 0, where l 0 and l are the lengths of a l0 unit module before and after the deformation, respectively. The stretchable substrates are modeled by a commercial finite element program, ABAQUS. [11 13,31] The neo-hookean constitutive models are used for the Ecoflex. To minimize the strain applied to the active devices, they were fabricated on stiff PET films; owing to the PET film that has a higher Young s modulus ( GPa) [32] than the Ecoflex film (69 kpa), [33] the strain of the active devices on the PET film can be dramatically suppressed compared to that of the soft Ecoflex between the devices. The optical image and FEM analysis of the stretchable substrate bent over a radius of 14 mm are shown in Figure 2 b. Strain is concentrated on the soft Ecoflex film between the implanted PET films while the strain on the surface of the implanted PET films is 0%, as expected for our design. Figure 2 c also shows an optical image and FEM analysis of the stretchable substrate under the biaxial strain of 30%. Again, 2 wileyonlinelibrary.com 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

3 Figure 2. a) Defi nition of applied biaxial strain ( ε applied ) on the stretchable substrate. Optical images (left) and FEM analyzes (right) of the stretchable AM temperature array upon b) bending with a radius of 14 mm and c) stretching with applied strain of 30%. The inset of (c) shows an enlarged optical image and FEM analysis. because the Young s modulus of the PET film is much higher than that of the Ecoflex film between the neighboring PET films, the strain on the Ecoflex is as high as 240% while that on the PET is 0% under ε applied = 30%. Therefore, the fabricated active devices positioned on top of the PET film are expected to be mechanically stable upon external deformation. Furthermore, high fill factors can be obtained by the use of embedded liquid metal interconnections and the SWCNT TFT backplanes as shown in Figure S6 (Supporting Information). The fill factor of our stretchable substrate without any applied strain is 85.7%, and that under the 30% biaxial strain is 62.7%, respectively. The spatial distribution of the current on/off ratio for the 5 5 SWCNT TFT AM backplane on the stretchable substrate with deformations is plotted in Figure S7 (Supporting Information). The transfer curves of a representative TFT on the stretchable substrate measured with deformations of bending with a bending radius of 14 mm and biaxial stretching by 30% show no noticeable change. Figure 3 shows fabricated stretchable AM µ-leds, where a 2 5 array of µ-leds on PET film is positioned on each pixel. Following the circuit diagram of Figure 3 a, each commercial µ-led array is implanted on top of the stretchable substrate above the SWCNT TFT backplane. Thus, the individual µ-led arrays in the stretchable substrate can be addressed by the SWCNT TFT backplane as shown in Figure 3 b,c. Under bending and biaxial stretching of 30%, the AM µ-led arrays exhibit a stable operation without any noticeable degradation in brightness as clearly seen in Figure 3 d f. Furthermore, 1000 repeated cycles of bending and biaxial stretching by 30% do not deteriorate the brightness of µ-leds as shown in Figure S8 (Supporting Information). A resistor-type temperature sensor (1 1 cm 2 ) was fabricated with a polyaniline nanofiber film prepared using Figure 3. a) Circuit diagram of the stretchable AM µ-led array. b f) Optical images showing operation of the stretchable AM µ-led array under selective control by scanning b) two dots and c) a line. d) µ-led array on bending. µ-led array e) before and f) after biaxial stretching by 30% WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 3

4 Figure 4. a) Normalized resistance change (Δ R /R 0 ) of the sensor versus temperature. Here, Δ R = R R 0, where R 0 and R are the resistances at 25 C and at temperatures between 15 and 45 C, respectively. b) Normalized drain current (Δ I DS /I DS0 ) of the SWCNT TFT-sensor versus 1000/ T, with temperature ranging from 288 to 318 K at the gate voltage of 10 V and the drain voltage of 10 V. Here, Δ I DS = I DS I DS0, where I DS0 and I DS are the drain currents at 298 K and at temperatures between 288 and 318 K, respectively. c) Δ R /R 0 versus temperature under biaxial strain up to 30%. d) Δ R /R 0 as a function of number of stretching cycles under a strain of 30%, where R 0 is the resistance at 25 C taken for the fi rst cycle. electrochemical polymerization. With the polyaniline sensor, temperature was measured in the range between 15 and 45 C. Prior to the measurement, the thermal stability of the polyaniline nanofibers was confirmed by taking Raman spectra as shown in Figure S9 (Supporting Information). The Raman peaks of the polyaniline nanofibers exhibited almost no difference at 25 and 45 C. Figure 4 a indicates a decrease (increase) in the resistance with heating (cooling) at a fixed voltage of 1 V, which is a clear indication of a negative temperature coefficient (NTC). [34] There appears no hysteresis. Here, the normalized resistance change is defined as Δ R/ R 0 = ( R R 0 )/R 0, where R and R 0 are the resistances at temperature T from 15 to 45 C and at room temperature of 25 C, respectively. The resistance change exhibits linear dependence on the temperature, and the resistance sensitivity ( 0 ) ( S ) is defined as S = δ Δ R/ R 100/ δt, indicating the slope of the curve. Here, δt is the change in the applied temperature. The sensitivity of our sensor is estimated to be 1.0% C 1 ( R 2 = 0.998) via the linear least squares fitting, which is better than that of the previously reported temperature sensors. [24,25,35] We attribute the excellent sensitivity of our temperature sensor to the use of electrochemically synthesized homogeneous 1D structured [36,37] conducting polyaniline nanofiber film [38] as channel material. The detailed properties of temperature sensor and the temperature-dependent change in current are demonstrated in Figure S10 (Supporting Information). The small error bars in Figure 4 a are the standard deviations taken from five sensors, showing very high reproducibility. To protect the sensor against unintentional damages and direct contact with the skin, the sensors are encapsulated with a polydimethylsiloxane (PDMS) film. Figure S11 (Supporting Information) shows that the temperature sensor with encapsulation exhibited a behavior similar to that without encapsulation. Figure 4 b shows the normalized change in the drain current of a single pixel in the temperature array, where the source electrode of the SWCNT TFT is connected to a ground through the temperature sensor. The temperature sensor is driven as a variable resistor. The current sensitivity of a single pixel is estimated to be 0.97% K 1 ( R 2 = 0.974) in the temperature ranging from 288 (15 C) to 318 K (45 C); however, it is slightly lower compared to that of the temperature sensor as shown in Figure S10d (Supporting Information). Such reduced sensitivity could be attributed to the extra contact resistance due to the silver paste and copper wires used for measuring the change in the drain current in the case of the AM-based temperature sensor. Δ R /R 0 of the sensor versus temperature with varying biaxial strain up to 30% is shown in Figure 4 c. During the cycles of heating and cooling under biaxial stretching up to 30%, no performance degradation was observed in the entire device, including the sensors and embedded Galinstan interconnection as expected from the previously conducted FEM analysis for stretchable substrate (Figure 2 ). In additional measurement under biaxial stretching up to 50%, the temperature sensor did not show any noticeable change in electrical performance as 4 wileyonlinelibrary.com 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

5 Figure 5. a) Optical image of the stretchable 5 5 AM temperature sensor array, showing that the surface of the array is locally touched by fi ngers in the shape of X under the applied biaxial strain of 30%. Normalized drain current mapping and corresponding temperature distribution under b) 0% strain and c) 30% strain, respectively. Here, I DS0 is the drain current at 25 C before stretching and I DS are the drain currents at temperature T b) before and c) after 30% biaxial stretching, respectively. Optical images of the temperature array on the stretchable substrate attached onto the right palm where a heart-shaped cold water container ( 15 C) was positioned: d) before and g) after stretching. e,h) The corresponding mapping of the temperature distribution via the measurement of the normalized drain current. Corresponding temperature distribution to the normalized drain current using a cold water container at 15 C on top of the palm under f) flat and i) stretched palm conditions, respectively. Here, I DS0 and I DS are the drain currents at skin temperature of 35 C and at temperature measured on each pixel, respectively. shown in Figure S12 (Supporting Information). In Figure 4 d, Δ R /R 0 values taken after repeated 30% biaxial stretching of the whole device are shown. Even after 1000 cycles, the variation is within 3%. These results clearly suggest that our fabricated temperature sensor on the stretchable substrate be very stable under repetitive biaxial stretching. To model the temperature mapping on the entire sensor array, several fingers are touched on top of the temperature sensor array in the shape of X, simultaneously, as shown in Figure 5 a. Figure 5 b,c compares the temperature distribution exhibited in a 3D-shaped matrix form of a normalized drain current (Δ I DS /I DS0 ) under 0% and 30% strain, respectively. Here, I DS0 is the drain current at 25 C before stretching and I DS are the drain currents at temperature T before (Figure 5 b) and after (Figure 5 c) 30% biaxial stretching, respectively. The variation in normalized current change due to 30% stretching is negligible, which indicates the mechanical strength of our stretchable sensor array. The temperature was calculated using the temperature-dependent behavior of drain current shown in Figure 4 b. The finger temperature measured using an infrared radiation thermometer, 29.9 C shown in Figure S13 (Supporting Information) is close to that measured by our polyaniline sensor, 30 ± 0.13 C. These results demonstrate the potential application of our stretchable AM temperature sensor array as a wearable device that can measure the temperature and identify the shape of the object under body movement. Owing to the stretchable thin film structure and the sticky Ecoflex of our AM temperature sensor array, it could be easily attached onto the palm. To conduct temperature mapping, a heart-shaped aluminum container filled with cold water (15 C) was positioned on top of the encapsulated sensor array that was attached to the right palm. Optical images taken before (Figure 5 d f) and after stretching (Figure 5 g i) the palm, and the corresponding temperature mapping for the same via measurement of the normalized change in the current are shown. Here, I DS0 and I DS are the drain currents at skin temperature of 35 C and at temperature measured on each pixel, respectively. The mapping was carried 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 5

6 out by applying 10 V to both the drain and gate electrodes of the SWCNT TFTs. With a common ground for each pixel, the larger change of current in the area contacting the aluminum container with cold water was measured, as expected. Figure 5 f,i indicates the estimated temperature distribution corresponding to those of Figure 5 e,h, respectively. It is shown that a nearly constant normalized drain current is observed under the deformation of palm stretching and our stretchable AM temperature sensor array provides reliable temperature detection. In conclusion, we demonstrate a successful fabrication of stretchable polyaniline nanofiber temperature sensor arrays with an AM consisting of the SWCNT TFTs, which clearly suggests the high potential application to high-performance skin attachable e-skin devices. Supporting Information Supporting Information is available from the Wiley Online Library or from the author. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Grant No. NRF-2013R1A2A1A ). This work was also partly supported by Institute for Information and Communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (B , the core technology development of light and space adaptable energysaving I/O platform for future advertising service). It was partially supported by Korea University Grant. The authors also thank the KU-KIST graduate school program of Korea University. Received: September 22, 2015 Revised: October 29, 2015 Published online: [1] T. Sekitani, H. Nakajima, H. Maeda, T. Fukushima, T. Aida, K. Hata, T. Someya, Nat. Mater. 2009, 8, 494. [2] S. Cheng, Z. Wu, Lab Chip 2010, 10, [3] R.-H. Kim, M.-H. Bae, D. G. Kim, H. Cheng, B. H. Kim, D.-H. Kim, M. Li, J. Wu, F. Du, H.-S. Kim, S. Kim, D. Estrada, S. W. Hong, Y. Huang, E. Pop, J. A. Rogers, Nano Lett. 2011, 11, [4] X. Hu, P. Krull, B. de Graff, K. Dowling, J. A. Rogers, W. J. Arora, Adv. Mater. 2011, 23, [5] S. W. Jin, J. Park, S. Y. Hong, H. Park, Y. R. Jeong, J. Park, S.-S. Lee, J. S. Ha, Sci. Rep. 2015, 5, [6] Y. R. Jeong, H. Park, S. W. Jin, S. Y. Hong, S. S. Lee, J. S. Ha, Adv. Funct. Mater. 2015, 25, [7] S. Jung, J. H. Kim, J. Kim, S. Choi, J. Lee, I. Park, T. Hyeon, D.-H. Kim, Adv. Mater. 2014, 26, [8] J. W. Jeong, W. H. Yeo, A. Akhtar, J. J. Norton, Y. J. Kwack, S. Li, S. Y. Jung, Y. Su, W. Lee, J. Xia, H. Cheng, Y. Huang, W.-S. Choi, T. Bretl, J. A. Rogers, Adv. Mater. 2013, 25, [9] G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, J. A. Rogers, Small 2010, 6, 851. [10] D. Kim, G. Shin, Y. J. Kang, W. Kim, J. S. Ha, ACS Nano 2013, 7, [11] J. Yoon, S. Y. Hong, Y. Lim, S. J. Lee, G. Zi, J. S. Ha, Adv. Mater. 2014, 26, [12] S. Y. Hong, J. Yoon, S. W. Jin, Y. Lim, S.-J. Lee, G. Zi, J. S. Ha, ACS Nano 2014, 8, [13] Y. Lim, J. Yoon, J. Yun, D. Kim, S. Y. Hong, S.-J. Lee, G. Zi, J. S. Ha, ACS Nano 2014, 8, [14] S. Zhu, J.-H. So, R. Mays, S. Desai, W. R. Barnes, B. Pourdeyhimi, M. D. Dickey, Adv. Funct. Mater. 2013, 23, [15] L. Pan, A. Chortos, G. Yu, Y. Wang, S. Isaacson, R. Allen, Y. Shi, R. Dauskardt, Z. Bao, Nat. Commun. 2014, 5, [16] C. Yan, J. Wang, P. S. Lee, ACS Nano 2015, 9, [17] T. Someya, Y. Kato, T. Sekitani, S. Iba, Y. Noguchi, Y. Murase, H. Kawaguchi, T. Sakurai, Proc. Natl. Acad. Sci. USA 2005, 102, [18] K.-I. Jang, S. Y. Han, S. Xu, K. E. Mathewson, Y. Zhang, J.-W. Jeong, G.-T. Kim, R. C. Webb, J. W. Lee, T. J. Dawidczyk, R. H. Kim, Y. M. Yeo, S. Kim, H. Cheng, S. I. Rhee, J. Chung, B. Kim, H. U. Chung, D. Lee, Y. Yang, M. Cho, J. G. Gaspar, R. Carbonari, M. Fbriani, G. Gratton, Y. Huang, J. A. Rogers, Nat. Commun. 2014, 5, [19] C. Wang, D. Hwang, Z. Yu, K. Takei, J. Park, T. Chen, B. Ma, A. Javey, Nat. Mater. 2013, 12, 899. [20] C. Wang, J. Zhang, C. Zhou, ACS Nano 2010, 4, [21] C. Wang, J.-C. Chien, K. Takei, T. Takahashi, J. Nah, A. M. Niknejad, A. Javey, Nano Lett. 2012, 12, [22] J. Yoon, G. Shin, J. Kim, Y. S. Moon, S. J. Lee, G. Zi, J. S. Ha, Small 2014, 10, [23] Y. Zeng, G. Lu, H. Wang, J. Du, Z. Ying, C. Liu, Sci. Rep. 2014, 4, [24] W. Honda, S. Harada, T. Arie, S. Akita, K. Takei, Adv. Funct. Mater. 2014, 24, [25] S. Harada, W. Honda, T. Arie, S. Akita, K. Takei, ACS Nano 2014, 8, [26] D. Kumar, R. Sharma, Eur. Polym. J. 1998, 34, [27] P. D. Gaikwad, D. J. Shirale, V. K. Gade, P. A. Savale, H. J. Kharat, K. P. Kakde, S. S. Hussaini, N. R. Dhumane, M. P. Shirsat, Bull. Mater. Sci. 2006, 29, 169. [28] R. Ansari, M. Keivani, J. Chem. 2006, 3, 202. [29] S. Virji, J. Huang, R. B. Kaner, B. H. Weiller, Nano Lett. 2004, 4, 491. [30] T. Liu, P. Sen, C.-J. C. Kim, J. Micorelectromech. Syst. 2012, 21, 443. [31] ABAQUS Version 6.10 User s Manual, Hibbit, Karlson & Sorensen, Inc., Providence, RI [32] R. Nakahara, M. Uno, T. Uemura, K. Takimiya, J. Takeya, Adv. Mater. 2012, 24, [33] Y.-L. Park, B.-R. Chen, R. J. Wood, IEEE Sens. J. 2012, 12, [34] A. Feteira, J. Am. Ceram. Soc. 2009, 92, 967. [35] D.-H. Kim, N. Lu, R. Ghaffari, Y.-S. Kim, S. P. Lee, L. Xu, J. Wu, R.-H. Kim, J. Song, Z. Liu,, J. Viventi, B. D. Graff, B. Elolampi, M. Mansour, M. J. Slepian, S. Hwang, J. D. Moss, S.-M. Won, Y. Huang, B. Litt, J. A. Rogers, Nat. Mater. 2011, 10, 316. [36] K. I. Winey, T. Kashiwagi, M. Mu, MRS Bull. 2007, 32, 348. [37] A. Henry, G. Chen, S. J. Plimpton, A. Thompson, Phys. Rev. B: Condens. Matter 2010, 82, [38] E. Fermi, J. Pasta, S. Ulam, Studies of Nonlinear Problems, Los Alamos Report LA-1940, wileyonlinelibrary.com 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim