pubs.acs.org/NanoLett
Temperature-Induced Reversible Dominoes in Carbon Nanotubes Tienchong Chang* and Zhengrong Guo Shanghai Institute of Applied Mathematics and Mechanics, Institute of Low Dimensional Carbon and Device Physics, Shanghai University, Shanghai 200072, People’s Republic of China ABSTRACT We show by molecular dynamics simulations that there exists a reversible domino process in single walled carbon nanotubes (SWCNTs). SWCNTs with one end collapsed and the other circular are chosen for demonstration. At a low temperature, the collapsed zone spreads over the whole tube, while at a higher temperature, the collapsed zone shrinks, and the circular zone extends along the tube. The reason for the reversible domino process is that the temperature modifies the stable state of the tube. The temperature-induced reversible domino process of SWCNTs provides opportunities for the design of nanoscale heat engines, rechargeable expelling devices, temperature-sensitive devices, mechanical oscillators, and pulse generators, etc.
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the previous work,12 but a time step of 0.5 fs is used in all calculations. The initial configuration of all tubes considered in the calculation is semicollapsed, i.e., with one end collapsed and the other circular. During the simulations, two rings of atoms at the edge of the collapsed end are held fixed, and another two rings of atoms of the circular end are radially constrained. Shown in Figure 1 are the typical snapshots of the temperature-induced reversible domino process of a (30, 30) SWCNT. The tube is originally designed with one end collapsed into a ribbon-like shape and the other end kept circular. At room temperature (300 K), the collapsed zone
evelopment of new energy sources and conversion technologies is very important for human life.1 Since the invention of the steam engine, there has been, and still is, a continuous effort to create new energy conversion techniques, especially for converting thermal into mechanical energy.2-4 Nowadays, the miniaturization of electronic and mechanical devices has stimulated a great deal of particular interest in the development of nanoscale energy conversion devices.5-10 Carbon nanotubes (CNTs), due to their small size and unique physical properties, have been used to convert chemical,6 electrical,7-11 and van der Waals potential12 energies into mechanical energy at the nanoscale. However, the development of nanoscale heat engines that may continuously convert thermal into mechanical energy is yet an important challenge facing nanotechnology. Previously, we have shown that van der Waals energy stored up in single walled carbon nanotubes (SWCNTs) can be converted into mechanical energy via an interesting domino process,12 earlier discussed as collapse propagation.13 Here we demonstrate by molecular dynamics simulations that such a domino process may be reversed at a higher temperature, and thermal energy may be converted into van der Waals energy during the reverse process. The reversible domino process can thus form a thermodynamic cycle in which conversion between thermal and mechanical energies can be accomplished. This study could be a starting point for the design of CNT-based heat engines. In addition, we show that the structural stability of a SWCNT cannot be determined by simply comparing the potential energies of different configurations but should be resolved by taking thermal effect into consideration. All simulations are carried out using the classical molecular dynamics based on Brenner’s second generation reactive empirical bond order potential,14 as has been used in
FIGURE 1. (color online) Temperature-induced reversible domino process in a (30, 30) single walled carbon nanotube (see movie 1 in the Supporting Information). (a) The initial configurations (they are totally the same) of the tube. (b-d) Configurations at 9.5, 18.5, and 27 ps, respectively. At a low temperature (300 K, left panel), successive collapse of carbon rings forms a domino wave, while at a high temperature (900 K, right panel), the collapsed zone shrinks, and a reverse domino wave develops. (e) Schematics of dominoes in different states.
* Email address:
[email protected]. Received for review: 05/7/2010 Published on Web: 08/03/2010 © 2010 American Chemical Society
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critical temperature. With a further increase in temperature, an opening wave develops in the reverse direction, and its wave speed increases. In other words, lower temperature leads to faster collapse wave propagation below the critical temperature; while higher temperature leads to faster opening wave propagation over the critical temperature. This finding shows that we can control the domino wave speed by controlling the tube temperature. Both the collapse and opening wave speeds can be up to 0.8 km/s, which is very important for constructing super fast nanomechanical devices. Our results indicate also that the critical temperature is a highly sensitive and approximately linear function of tube diameter ranging from 3.39 to 4.34 nm. As shown in Figure 2b, a small increase in tube diameter can cause a remarkable linear increase in the critical temperature, e.g., with increasing tube diameter from 3.66 to 4.34 nm, the critical temperature increases from 245 to 915 K. The narrowest tube we calculated is (25, 25), with a diameter of about 3.39 nm, having a critical temperature of 35 K. In the light of the approximately linear dependence between critical temperature and diameter, we estimate that only tubes with a diameter larger than about 3.35 nm have critical temperatures (see Figure 2b). For smaller tubes, the circular state is always favored, and no collapse propagation can occur even if the temperature is down to 0. It is important to understand why the propagating direction of the domino wave is dependent on temperature. From an energetic point of view, the domino wave propagates along the direction of decreasing system free energy because the tube tends to adopt a lower energy configuration (see Figure 1e for illustration). Therefore the reason for the reversible domino process is that the temperature modifies the stable state of the tube. At lower temperatures, the collapsed configuration is stable, while at higher temperatures, the circular configuration is stable. Based on an analysis of the system potential energy, many previous works13,15-17 have shown that the stable state of a SWCNT is diameter dependent. For small tubes, the circular configuration possesses a lower potential energy and is thus stable, while for large tubes, the collapsed configuration is stable (and the circular configuration becomes metastable). The present finding shows for the first time that the stable configuration of a SWCNT is dependent also on temperature. However, we find that the stable state of a SWCNT cannot be identified solely by simply comparing the system potential energies between the circular and collapsed configurations, as demonstrated in the previous works.15-17 As shown in Figure 3a, even at a high temperature at which the opening wave is favored, the system potentials of the circular configurations of (50, 0) and (30, 30) tubes are yet higher than those of the collapsed configurations. It is obvious that we cannot clarify the mechanism of reversible domino process based on a simple potential energy analysis, but the thermal effect must be taken into account.
FIGURE 2. (color online) (a) Temperature-dependent domino wave speed of single walled carbon nanotubes. A positive value of the speed means the wave propagates from the collapsed toward circular zone, and a negative value represents a reverse propagation. It should be noted that the values at 300 K are slightly lower than those obtained in a previous work12 because an radial constraint is imposed on the circular ends of all tubes. (b) Critical temperature (shown with symbol + line) as a function of tube diameter of SWCNTs. The figure can be regarded as temperature versus diameter phase diagram in which the critical temperature shows in fact the phase boundary between collapsed and circular tubes. The blue dashed line represents the previous understanding based solely on a potential energy analysis.
spreads over the whole tube, just like the successive toppling of a row of standing dominoes (Figure 1e), as has been discussed by Yakobson et al.13 and demonstrated by Chang.12 However, at a higher temperature (e.g., 900 K), the process is quite different: The collapsed zone shrinks, and the circular zone extends along the tube. This indicates that the propagating direction of the domino wave in a SWCNT is reversible, depending on tube temperature. In other words, one can control the shape of the tube, i.e., making it circular or collapsed by heating or cooling the tube. This may offer a new technique to open collapsed CNTs observed in experiments.15 To give a clearer understanding of the reversible domino process in a SWCNT, we show in Figure 2a the temperaturedependent propagation speed of the domino wave of the (50, 0) and (30, 30) tubes. It is seen that, with increasing temperature, the collapse wave speed decreases to 0 at a © 2010 American Chemical Society
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be regarded as a phase transition, and the critical temperature is just the phase transition temperature. Figure 2b is thus actually a phase diagram of temperature versus diameter for SWCNTs. Below the curve, the collapsed tubes are favored, while the circular tubes are favored above the curve. This is quite different from the previous understanding that the stable state of the SWCNTs is dependent only on the tube diameter (as the blue dashed line shows). Our findings of the temperature-induced reversible domino process have broad applications potential. It has been shown that the domino-like collapse of a SWCNT can be used to design nanogun in nanoscale expelling or injecting systems,12 i.e., the molecules or particles inside the tube may be expelled out of the tube when the collapse wave arrives, and the van der Waals potential is converted in part into mechanical energy. Since a collapsed tube can be restored to its circular shape at higher temperatures, the dominodriven expelling systems can thus be rechargeable. This is very important for device design because the domino-driven device is simply a one-time device if the process is irreversible. In particular, during an opening process, the thermal energy is stored up as van der Waals pontenial energy in a SWCNT. The reciprocation between the collapse and opening processes could thus form thermodynamic cycles in which conversion between thermal and mechanical energy is accomplished. This offers possibilities for future design of nanotube-based heat engines. In particular, unlike existing heat engines, which use fluids (e.g., steam and Stirling engines),2 radiation (e.g., quantum heat engine3), or electrons (e.g., thermoelectric devices)4 to work, the CNT-based heat engines are driven by the CNTs’ structural transition, and no working material is required. In addition, the conductance of a collapsed structure of a semiconductor SWCNT may be quite higher than that of a circular structure,21-25 and the tube could be heated when an electric current flows through it.11 Suppose a constant voltage is applied to a semiconductor SWCNT with one end collapsed and the other circular. At a low temperature, the tube may be collapsed, and thus the current is larger, which could heat the tube to a higher temperature. If the tube temperature increases beyond its critical temperature, then the opening process occurs and would finally make the tube circular, and the tube conductance would be lowered. If the heat generated in the circular tube in this case cannot compensate the heat loss to the surroundings, then the tube temperature may be decreased below its critical temperature, and the whole tube will collapse again. This forms a cycle of the change in the current (resulting from the change in the conductance) of the tube, and thus shows the possibility of using SWCNT to generate electric pulse. Meanwhile, during such a cycle, the domino wavefront shuttles between the two tube ends, making the device behave like a mechanical oscillator.26-28 Since the domino wave speed can be controlled by the tube temperature, the frequency of the oscillator is thus tunable. This is a very important
FIGURE 3. (color online) (a) System potential energy versus temperature of (50, 0) and (30, 30) tubes. (b) The variation of free energy versus temperature, respectively.
Based on the theory of thermodynamics, here we qualitatively elucidate the existence of the critical temperature and the mechanism of the reversible domino process in a SWCNT. Since the collapsed tube is more constrained and has less freedom in the phase space (Ω), which consequently lowers the entropy S because S is proportional to ln Ω. This means that the entropy per unit length of the collapsed configuration is always smaller than that of the circular configuration. At low temperatures, if a collapse wave could spontaneously propagate in a SWCNT, the free energy per unit length of the collapsed configuration should be smaller than that of the circular configuration. With increasing temperature, both of the free energies decrease, but the one for the collapsed configuration decreases slower (because of its lower entropy). There must therefore exist a critical temperature Tc at which the two free energies are equal to each other (See Figure 3b for illustration). With a further increase in temperature, the free energy per unit length of the collapsed configuration becomes larger than that of the circular configuration, which consequently results in an opening process in the reverse direction. To further understand the temperature-induced reversible domino process in a SWCNT, the phase equilibrium concept is very helpful. If we view the circular and collapsed configurations of a SWCNT as its two phases (the reason is that, for a SWCNT with a moderate diameter, both circular and collapsed configurations are stable or metastable),12,13,17-20 the temperature-induced reversible domino process could © 2010 American Chemical Society
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feature for device design, as has been pointed out by Sazonova et al.28 In summary, temperature-induced reversible domino process of carbon nanotubes is investigated using molecular dynamics simulations. The finding shows for the first time that the stable configuration of a single walled carbon nanotube (SWCNT) is dependent not only on tube diameter but also on temperature. A simple potential energy analysis is not sufficient to determine the stable state of a SWCNT, and a thermodynamic analysis must be performed. A phase diagram of temperature versus diameter for SWCNTs is presented. We show that one can control the propagating direction as well as the propagating speed of the domino wave in a SWCNT by controlling tube temperature. During a thermodynamic cycle formed by reversible domino process, conversion between thermal and mechanical energy, which is the primary base of heat engines, can be accomplished. The finding provides broad applications potential for carbon nanotubes.
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Acknowledgment. Financial support from the National Science Foundation (10872120, 10732040) and 973 Program (2007CB936204) of China, the Fok Ying Tung Education Foundation (121005), the Shanghai Shuguang Program (08SG39), the Shanghai Rising Star Program (09QH1401000), the Innovation Program of Shanghai Municipal Education Commission (09ZZ97), and the Shanghai Leading Academic Discipline Project (S30106) are gratefully acknowledged.
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Supporting Information Available. A movie for the temperature-induced reversible domino process in a (30, 30) single-walled carbon nanotube. This material is available free of charge via the Internet at http://pubs.acs.org.
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