Digital Signal Transmission Line with Carbon

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Ultra-stretchable Analog/Digital Signal Transmission Line with Carbon Nanotube Sheets Yourack Lee, Min-Kyu Joo, Viet Thong Le, Raquel Ovalle-Robles, Xavier Lepró, Márcio D. Lima, Daniel G. Suh, Han Young Yu, Young Hee Lee, and Dongseok Suh ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b04406 • Publication Date (Web): 20 Jul 2017 Downloaded from http://pubs.acs.org on July 21, 2017

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ACS Applied Materials & Interfaces

Ultra-stretchable Analog/Digital Signal Transmission Line with Carbon Nanotube Sheets

Yourack Lee||,§, Min-Kyu Joo||,†,§, Viet Thong Le||,§, Raquel Ovalle-Robles‡, Xavier Lepró‡, Márcio D. Lima‡, Daniel G. Suh¶, Han Young YuҰ, Young Hee Lee||,†,*, and Dongseok Suh||,*

||

Department of Energy Science, Sungkyunkwan University, Suwon 16419, Republic of Korea

†

Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Suwon 16419,

Republic of Korea ‡

The Alan G. MacDiarmid NanoTech Institute, University of Texas at Dallas, Richardson, TX

75083, USA ¶

Department of Chemistry, Brown University, Providence, RI 02912, USA

Ұ

IT Convergence Technology Research Laboratory, Electronics and Telecommunications

Research Institute (ETRI), Yuseong-gu, Daejeon 34129, Republic of Korea

*

E-mails (Y. H. Lee and D. Suh): [email protected] and [email protected]

§

These authors (Y. Lee, M-K. Joo, and V. T. Le) contributed equally to this work.

1

ACS Paragon Plus Environment


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ABSTRACT Stretchable conductors can be used in various applications depending on their own characteristics. Here, we demonstrate simple and robust elastomeric conductors that are optimized for stretchable electrical signal transmission line. They can withstand strains up to 600% without any substantial change in their resistance (≤ 10% as is and ≤ 1% with passivation), and exhibit suppressed charge fluctuations in the medium. The inherent elasticity of a polymeric rubber and the high conductivity of flexible, highly oriented carbon nanotube sheets were combined synergistically, without losing both properties. The nanoscopic strong adhesion between aligned carbon nanotube arrays and strained elastomeric polymers induces conductive wavy folds with microscopic bending of radii on the scale of a few micrometers. Such features enable practical applications such as in elastomeric length-changeable electrical digital and analog signal transmission lines at above MHz frequencies. In addition to reporting basic DC, AC, and noise characterizations of the elastomeric conductors, various examples as a stretchable signal transmission line up to 600% strains are presented by confirming the capability of transmitting audio and video signals, as well as low-frequency medical signals without information distortion.

KEYWORDS: Carbon nanotube sheet, Stretchable conductor, Signal transmission line, Wearable electronics, Low-frequency noise 2


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1. INTRODUCTION Stretchable electronics devices, which have been the subject of increasing interest, are aimed at meeting future demand for flexible and wearable devices. Recent progress on flexible, highly stretchable electronic conductors has exploited several structural design possibilities. Examples include

wrinkled,

quasi-two-dimensional

conductors1-5,

and

porous

three-dimensional

conducting networks that are backfilled with elastomer6. Nanoscale conducting materials such as silver nanowires7, 8, gold nanoparticles9, graphenes10, and carbon nanotubes1, 5, 11-18 have been used with various elastomers. A common finding from all previously considered concepts indicates a significant increase in the electrical resistance of the devices upon stretching. Two major factors affect changes in the static resistance of such devices in response to stretching. The first is the charge transport mechanism of elastomeric composites that use percolation-based conduction1, 8, 9, 13, 19. Irrespective of the initial metallic conductivity before stretching, the variation in resistance cannot be suppressed because contacts between conducting particles along a percolation path are affected by external stresses. The second contributor is a geometric effect. As in the case of liquid metal alloy-based fibers20, a change in conductor dimensions (i.e., an increase in the sample length and a decrease in the cross-sectional area) inevitably results in a large increase in resistance upon stretch. If such a length-dependent change in resistance is noticeable and can be consistently reproduced, the device can serve as a sensor that reliably measures mechanical strains or pressure10, 16, 17, 19, 21. However, such variation in resistance is a critical disadvantage for applications in elastomeric signal transmission lines that transmit electric signals. 3



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Applications of stretchable conductors can be simply classified into three different categories based on their electrical and mechanical properties; these categories are schematically illustrated in Figure 1a. During elongation and contraction of stretchable conductors, a wide-range change in resistance can be useful for strain sensor applications10, 12, 13, 16, 17, 20-22, and moderately varying resistance with high electrical conductivity may be suitable for conventional electrical connections where substantial variation in electrical resistance is allowed4, 6, 7, 11, 19, 23-25. On the contrary, a few groups reported stretchable signal transmission lines with strain-insensitive resistance that remains nearly constant even when these lines are subjected to large strains8, 26-28 (Relevant research trends are compared in Supporting Information (SI) Figure S1). Such properties are desired for transmitting analog voltage or current signals, for example, which may contain vital information from sensors attached to or implanted in a human body. Combined with high signal to noise ratios (SNRs), these stretchable conductors are likely to be very promising in health care and wound-monitoring systems, or related applications29,30. In this study, we designed and characterized stretchable carbon nanotube (CNT) sheets based signal transmission line (STL) that exhibits minimal variations in resistance and low electric noise in response to elastomeric deformations of up to 600%. The basic idea is schematized in Figure 1b, where a highly flexible and highly conducting layer is significantly extended in the horizontal direction via formation of small wavy folds. In addition, as an improvement of this approach, we considered alumina passivation on stretchable STL. The unwavering original length of the STL makes our prototype system a highly suitable candidate for resistanceinvariant stretchable STLs for digital and analog STLs operating in the supra MHz frequency 4


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range. In addition, the system can be used in wearable electronic devices and patient monitoring systems. 2. RESULTS AND DISCUSSION The detailed fabrication process of this stretchable conductor is described in SI Figure S2. Highly aligned free-standing CNT sheets were transferred to a largely pre-strained elastomer (subject to strains reaching 600%) by placing the CNT sheets on the surface of the elastomer (Figure S3 in SI). When the tension applied to the elastomer decreased until the strain vanished, the elastomer with the CNT sheets on it shrank to its initial length. As the elastomer is released from its pre-strained state, the CNT layer is forced to fold and exhibits a wavy shape for releasing the compressive pressure owing to the shrinkage of the elastomer substrate (Figures S2c and S6 in SI). The photographs of a sample subject to the strains of 600% and 0% are shown in Figure 1b. (In the following part, NX indicates a sample consisting of “X” CNT sheets, and

εY% is defined as Y% of a pre-strained sample.). The stability of the sample’s electrical resistance during stretching/relaxation cycles was examined and the results are shown in Figure 1c for (N10, ε600%). Variations in resistance from four-probe DC measurement during different cycles were nearly identical, without any significant degradation in the overall performance, which is advantageous for a good signal transmission line. In addition, the digital signal transmission capability of the sample (N10, ε600%) was tested by comparing its performance with that of a commercial Bayonet Neill–Concelman (BNC) cable. The sheet resistance (along the alignment direction) as a function of the number of 5



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CNT sheet layers (n) are presented in SI Figure S4, which is relatively larger than nominal resistance value of BNC cable. In order to ensure electrical noise suppression and stable signal transmission, another CNT sheet (N10, ε600%) was placed underneath the sample to form a signalground configuration. Generated voltage signals with frequencies ranging from 1 Hz to 100 MHz were separately passed through the sample (N10, ε600%) subject to different strains (0% and 600%), and the selected frequency responses are shown in Figures 1d to 1g. Square-wave digital signals were transmitted without serious distortion, even when the sample was subject to the strain of 600% and for frequencies reaching up to 10 MHz. A proper measurement setup, addressing frequencies above 10 MHz, seems to require the impedance matching procedures. The bandwidth of the voltage gain (= VOutput/VInput) and the frequency ratio (=fOuput/fInput) for the strain of 300% are shown in SI Figure S5. These performance characteristics suggest that the proposed concept is suitable as a stretchable STL for use in medical/health care systems and/or audio and video information collection systems. Figure 2 demonstrates the applicability of the proposed device with respect to the transmitted signal frequency via the resistance-invariant and stretchable STL (N100, ε600%). An electrocardiogram (ECG) pattern covering frequencies in the 0.05–100 Hz range was first considered. The ECG signal, acquired using the proposed stretchable STL by employing a socalled “three leads ECG” method, was very similar to the reference ECG signal recorded using standard Cu wires, as shown in Figure 2a. In addition to a high signal consistency, a normal sinus rhythm (including features such as PR intervals, PR segments, QRS complexes, QT intervals,

6


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and ST segments) is clear, independent of the strain magnitude, demonstrating the practicality of the proposed device as a stretchable bio-medical signal STL (see Video S1 in SI)29. Figures 2b and 2c show audio and video signals recorded using the proposed stretchable STL, and compare those with signals obtained using a reference commercial BNC cable. In general, relevant frequencies range from 20 Hz to 20 kHz for acoustic electronics devices and are on the order of a few MHz for composite video signals; these frequencies are much higher than those considered in Figure 2a. As shown in Figures 2b and 2c, the audio and video source signals were respectively split into the sample and a reference line for estimating the signals’ similarity. In all cases, i.e., up to the frequency of a few MHz, the transmitted signals passing through the sample were almost identical, even for video signals, and were not distorted by straining the device. In principle, transmission of video signals requires much higher accuracy in terms of the signal period (or frequency) and amplitude, because the information on brightness, color, and synchronization of a signal is delivered at the same time. To be more particular, various significant signals such as horizontal synchronization, color reference burst, active pixel region (period, 52.66 µs), and front and back porch should be respectively transmitted without delay and distortion, as shown in Figure 2c30. Thus, the proposed stretchable STL can transmit not only biomedical time series (such as ECG), but also audio and video signals, even when the device is subject to relatively high strains, without distorting the original information in terms of its resistance and frequency (videos S2 and SI Figure S5). The operational stability with respect to stretching/relaxation cycles, which is critical for various practical applications, was confirmed in Figure 3a. The electrical resistance did not vary 7



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significantly even after 32000+ stretching cycles, for strains in the 100–300% range. In addition, the final failure occurred owing to the elastomer and not owing to the CNT sheet layer. In many experiments, it was confirmed that the endurance is mainly limited not by the attached CNT sheets, but rather by the mechanical integrity of the elastomer substrate (see inset photographs in Figure 3a), indicating the high durability of the CNT sheet layer. The structural stability of the proposed stretchable conductor was also checked by direct optical microscopy observations before and after 1000 stretching/relaxation cycles (Figure 3b), for the (N10, ε400%) sample. After the attachment of the CNT sheets to a pre-strained elastomer (strain, 400%), well-aligned CNT bundles were initially observed, as shown in the first image in Figure 3b. During the first shrinkage process, several depression lines, i.e., thick black lines roughly normal to the sheet orientation at the strain of 300%, started to appear. This may reflect early evolution of wavy wrinkles to mitigate the structural stress arising from the different contraction rates of the conducting CNT layer and the elastomer’s surface. As the strain decreased to zero, depressions evolved and appeared throughout the sample. The sample was imaged again after 1000 stretching cycles, with strains in the 0–400% range. Surprisingly, the final state (with the strain of 400%) exhibited well-aligned CNT arrays, as shown in the last image in Figure 3b, implying

that

charge

conduction

was

not

noticeably

affected

even

after

1000

stretching/relaxation cycles. In the case of the micrometer-scale mechanical deformation, the Raman analysis (results shown in Figure 3c) further indicated that the formation of small tiny folds did not degrade the structural quality of the CNT sheet layer, i.e., in the Raman spectrum the peak positions of the D, G, and G′ 8


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bands did not move and the D-to-G peak intensity ratio was almost the same (Ecoflex contribution to total Raman intensity with respect to the cycling test process and strain is discussed in Figure S7 in SI). This result is interesting because each CNT was expected to bend more than 10 times to form wrinkles when the length of a single CNT (equivalent to the height of the initial CNT forest, which was 160 µm in this sample), the height of the highly packed folds (10–15 µm in SI Figure S6a), and the roughly estimated bending radius (2–3 µm) obtained as a half of the distance between the white arrows in Figures 3d (N30, ε100%) and 3e (N30, ε600%) were considered. In addition, the sample after 32000+ cycles did not exhibit any noticeable differences in its Raman spectrum, proving that the CNT sheets were not damaged, even after a large number of stretching/relaxation cycles. Therefore, resistance invariance and negligible Raman peak shifts in response to strain suggest that folded wrinkles do not significantly affect the device’s resistance. To further improve the proposed STL concept, we examined the effects of alumina (AlOx) passivation of stretchable CNT sheets. Intuitively, a minimal change in the device resistance in response to large strains indicates that the lengths of conduction paths are not affected by stretching/relaxation, as conceptualized in Figure 1b. This subsequently raises questions about the morphology of conducting layers on the elastomer’s surface. For a fixed number of CNT sheets (30 sheets for the results shown in Figures 3d and 3e), different pre-straining scenarios yield different surface morphologies. For the sample with ε100% in Figure 3d, wrinkles were not densely packed and almost individually separated. However, for the sample with ε600% in Figure 3e, all wrinkles were in contact with adjacent wrinkles. 9



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This finding indicates the possibility of lower resistance at lower strains owing to the formation of conductive “shortcut pathways” by contacts between wrinkles (highlighted in red in the inset of Figure 4a)31, which is consistent with the data in Figure 4a (and the schematic in its inset) for the non-passivated sample. This figure also shows the resistance-strain curves for the nonpassivated sample and for the alumina-passivated sample, with respect to different strain sweep directions. There is a hysteresis only for the non-passivated sample between the curves of elongation and contraction, especially for strains in the 0–300% range, and such hysteresis is related to the contact between folded regions. Specifically, when contacts were established in the low strain region, they persisted even at relatively high strains, resulting in the slow increase of resistance with increasing the strain. In the alumina-passivated sample, however, the variation in the resistance with strain was suppressed down to ∼1% and the hysteresis was not observed (The detailed SEM morphologies of CNT bundles inside alumina-passivated before and after strain are presented in SI Figures S8 and S9, respectively.) Estimating charge fluctuations in wearable electronic devices is essential, because flexible and stretchable passive components determine the minimal detectable signal amplitude for highspeed analog circuits and flexible electronics20,29-33. To characterize the proposed stretchable conductor for determining its ability to transmit weak electrical signals in the face of large strokes, we studied the low-frequency (LF) electric noise characteristics for frequencies ranging from 10 Hz to 10 kHz, and for a variety of strains. Two pre-strained samples (N10, ε400%), with and without the alumina passivation layer, were simultaneously loaded and measured under the same condition (Figure S10 in SI). Noise-wise, it is difficult to predict whether the passivation 10


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layer will enforce or reduce charge fluctuations, because noise characteristics of the contact between the CNT bundles and the deposited alumina layer are not known. To address this issue in detail, the LF current noise power spectrum density (SI) curves, for a fixed voltage bias V = 5 mV, are shown in Figure 4b for the non-passivated and passivated samples, for 0% and 400% strains, respectively. In all cases, a clear thermal noise behavior appeared, the so-called Johnson–Nyquist noise, in addition to a partial 1/f noise contribution at frequencies below 100 Hz. These results suggest that this LF noise can be mostly attributed to the intrinsic thermal noise. In general, this trend has been interpreted using the following noise analytical model,

SI =

4 k BT I2 +A γ R f

(1),

where A is the noise amplitude, I is the driving current, and kB and γ are the Boltzmann constant and the frequency exponent, respectively32-34. The parameter γ was generally found to be close to 1 in a condensed matter system including semiconductor transistors in the quasi-equilibrium state35. For the proposed stretchable STL, this parameter ranged from 0.9 to 1.5, depending on the strain. The amplitude of the thermal noise current, represented by the frequency-independent term in Equation (1), was estimated to be ∼1.68 × 10−23 A2/Hz and ∼1.95 × 10−23 A2/Hz with and without the passivation, respectively. These values are quite comparable to the theoretically expected values corresponding to their resistances, which are 1.04 × 10−23 A2/Hz for the aluminapassivated sample and 1.08 × 10−23 A2/Hz for the non-passivated one, respectively. 11



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Besides, the tendency toward noise reduction by a factor of 10–100, especially at high strains, is clearly observed in the passivated sample compared with the non-passivated one (Figure 4b). This was not expected, because the passivation layer in the proposed resistance-invariant stretchable STL was thought to exert significant effects only at low strains, where electrical contacts between folded CNT layers do not occur owing to the passivation. One possible explanation for noise suppression in the passivated sample subject to high strains could be that conduction paths are not exposed to air and/or moisture, which are known to induce surface charge fluctuations in the conduction path4, 34, 36, 37. But the fact that alumina passivation did not fully cover the CNT bundles inside the sheet make the above explanation less plausible. Instead, the protection of connected parts between CNTs having van-der-Waals interaction may also reduce the noise under the assumption that the majority of stresses at high strains are focused on those junctions potentially generating charge fluctuations due to, for example, varying contact resistances. The current normalized SI curves (SI/I2) were plotted with respect to the strain in Figure 4c for f = 10 Hz to gain clear insights into the strain effect on the LF noise. With increasing strain, the non-passivated sample exhibited an increasing fluctuation in conductance, while the passivated one exhibited a smaller noise amplitude (i.e., A in Equation (1)). The minimal detectable voltage ranges, limited mainly by the 1/f trend (the second frequency-dependent term on the right hand side in Equation (1)), were estimated as 22–70 nV/√Hz for the non-passivated sample and 12–16 nV/√Hz for the passivated sample, respectively. This result indicates that the passivation of CNT sheets can help increase the signal transmission bandwidth due to a lower SNR, and ensures 12


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more reliable operation of flexible electronics devices that utilize the proposed stretchable conductor. 3. CONCLUSION In conclusion, we demonstrated that alumina-passivated non-percolating conduction through aligned CNT sheets on an elastomer significantly suppresses an electrical resistance variation in response to varying strains and reduces a low frequency noise, which is advantageous for stretchable electrical signal transmission line. In addition to the examples presented here, other useful variants of such a conductor-on-elastomer system include the use of metal nanoparticles for higher electrical conductivity or a cylindrical, wire-shaped elastomer matrix covered by CNT sheets38. Such alternative forms can be explored for future use in implantable or portable medical devices to make the experience of patients wearing these devices and using them in their daily life more comfortable. 4. EXPERIMETAL SECTION 4.1 Carbon nanotube sheets and elastomer: Sheets consisting of aligned arrays of carbon nanotubes (CNTs) were drawn from multi-walled carbon nanotube forests grown using the chemical vapor deposition technique. The height of a typical forest was ~160 µm, and each individual nanotube typically had ~9 walls with an outer diameter of ~10 nm, as described previously39. Highly stretchable elastomers (Ecoflex 0010, smooth-on) consisted of platinumcatalyzed silicones, which are commercially available at low cost. Strains for repetitive elongation or contraction operations with negligible creep were typically in the 0–600% range, 13



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the same range as that for which the results are shown in Figure 4a. The thickness of the elastomeric substrate was ∼1 mm. When the CNT sheets were attached to the elastomeric substrate, they were tightly stuck to each other without needing any further treatment. One droplet of ethanol was added onto the CNT side for densification. 4.2 Cross-sectional images: Samples for cross-section analysis in Figure S6a in SI were prepared after elastomer passivation. Initially uncured liquid-phase elastomer material was used to cover the surface of the CNT sheets on the pre-strained elastomeric substrate. Subsequently, the strain decreased slowly from the pre-strained value to zero before the elastomer curing was finished, which resulted in a conformal coating. After curing, the substrate and coating (i.e., passivation) layer consisted of identical elastomeric material, such that the elastic properties of the CNT sheets on the elastomeric substrate were not altered by the elastomer passivation layer. Cross-sectional images in SI Figure S6a were captured using an optical microscope (Axio Imager 2, ZEISS) for the elastomer-passivated samples, cut along a stretch direction after freezing and breaking in a liquid nitrogen environment to obtain sharp cross-sections. 4.3 Passivation by the alumina (AlOx) layer: The sample passivated by the alumina layer in Figure 4a was prepared by the evaporation of AlOx (with a nominal thickness of 20 nm) on the free-standing CNT layer consisting of 10 sheets before their attachment to the elastomeric substrate pre-strained at 600%. 4.4 Low frequency noise measurements: LF noise measurements were conducted using a customized LF noise measurement system40 and a network signal analyzer (HP3562A, Agilent 14


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Technologies) in a metal shielding box at room temperature. The current was supplied by a homemade battery box and was converted to a voltage signal using a low noise current-tovoltage pre-amplifier (SR570, Stanford Research Systems). 4.5 Scanning electron microscopy (SEM) and Raman spectroscopy measurements: SEM images in SI Figures S4, S6, S8, and S9 were acquired using JSM7000F, JEOL. Raman spectroscopy was performed using a Renishaw, inVia Raman microscope with a laser excitation wavelength of 532 nm and a laser spot size of ∼1 µm. ASSOCIATED CONTENT Supporting Information Supplementary figures and discussion contains sample preparation procedures from a CNT forest to CNT sheets on elastomers, bandwidth of voltage gain and frequency ratio in CNT sheets STL, structural properties of a CNT-sheet-on-elastomer stretchable conductor, AlOx passivation for the suppression of the resistance variation upon stretching, and sample preparation for low-frequency noise measurement, respectively. Additional video clips for the bio-medical ECG signal transmission test using the CNT sheet STL, audio signal transmission test using the CNT sheet STL, video signal transmission test using the CNT sheet STL are also prepared. This material is available online at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *

E-mails (Y. H. Lee and D. Suh): [email protected] and [email protected] Author Contribution

§

These authors (Y. Lee, M-K. Joo, and V.T. Le) contributed equally to this work. 15



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Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was supported by the Institute for Basic Science (IBS-R011-D1) and the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT & Future Planning (No. NRF-2016R1A2B2012336).

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Figure 1. (a) Application diagram for a stretchable signal transmission line showing variation in resistance with respect to strain (green x axis) as well as frequency (orange x axis). (b) Photographs of a stretchable signal transmission line (N10, ε600%) subject to the strain of 600% (right) and subject to the strain of 0% (relaxation, left). (c) Repetitive variations in resistance corresponding to the strain cycles between the strain of 0% and the specified value for the sample (N10, ε600%). (d-g) Various AC frequency responses of the signal transmission line (N100, ε600%) subject to the alternating strains of 0% and 600%, for (d) 1 Hz, (e) 1 MHz, (f) 10 MHz, and (g) 100 MHz, respectively.

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Figure 2. Various applications of resistance-invariant and stretchable signal transmission line (N100, ε600%): (a) vital signs (0.05–100 Hz) from a sample electrocardiogram (ECG) measurement; (b) audio signals (frequency, 20 Hz–20 kHz) in case of acoustic electronics; (c) video graphics array (VGA) signals (frequency on the order of a few MHz) for composite video, respectively. In all cases, the reference signals were recorded via commercial BNC cables.

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Figure 3. (a) Endurance test during repetitive stretching or relaxation, up to +32000 cycles, for strains ranging from 100% to 300% for the sample (N10, ε400%), at the stretching rate of 2.5 mm/s. The photographs show the images of the tested samples immediately before (①) and after (②) failure. (b) Optical microscope images of the sample (N10, ε400%) subject to stretching. The images correspond to the strain sequence 400% (left) → 300% → 200% → 0% → 1000 cycles between 0% and 400% (not shown) → 0% → 300% → final 400% (right), respectively. (c) Raman spectra for the sample (N10, ε400%) subject to different strains. (d-e) Top-view SEM images of the samples: (d) ε100%, (e) ε600% (with the same N30). All scale bars are 50 µm.

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Figure 4. (a) Resistance-strain curves for the non-passivated sample and no hysteresis for the alumina-passivated sample. (b) LF current noise power spectrum density (SI) curves vs. frequency, for the bias voltage fixed at 5 mV, for non-passivated and alumina-passivated samples (N10, ε400%) subject to the strains of 0% and 400%, respectively. The two cyan lines represent the frequency-dependent 1/fγ (with γ = 1) model, and the Johnson–Nyquist noise model independent of frequency, respectively. The bottom blue dotted line indicates the system noise limitation. (c) The current normalized SI (SI/I2 (= A/f)) with f = 10 Hz, for different strains. The shaded area and the dotted green and red lines are shown for guiding the eye only.

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Digital Signal Transmission Line with Carbon

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