Theoretical Simulation on the Assembly of Carbon Nanotubes Between Electrodes by AC Dielectrophoresis
© to the authors 2008
Received: 14 October 2008
Accepted: 11 November 2008
Published: 25 November 2008
The assembly of single-walled carbon nanotubes (SWCNTs) using the AC dielectrophoresis technique is studied theoretically. It is found that the comb electrode bears better position control of SWCNTs compared to the parallel electrode. In the assembly, when some SWCNTs bridge the electrode first, they can greatly alter the local electrical field so as to “screen off” later coming SWCNTs, which contributes to the formation of dispersed SWCNT array. The screening distance scales with the gap width of electrodes and the length of SWCNTs, which provides a way to estimate the assembled density of SWCNTs. The influence of thermal noise on SWCNTs alignment is also analyzed in the simulation. It is shown that the status of the array distribution for SWCNTs is decided by the competition between the thermal noise and the AC electric-field strength. This influence of the thermal noise can be suppressed by using higher AC voltage to assemble the SWCNTs.
KeywordsSingle-walled carbon nanotubes (SWCNTs) AC dielectrophoresis Simulation
Since its discovery in 1991, carbon nanotubes (CNTs) have attracted great research interests due to its unique one-dimensional structure and outstanding properties . A large amount of research has been conducted to explore both the fundamental properties [2–4] and application potentials for CNTs. In terms of applications, high-performance CNT-based field-effect transistors , solar cells , hazard gas detector , and DNA sensors  have been widely reported. It is also found that CNTs have excellent field emission properties [9, 10]. With significant advantages over their traditional counterpart, CNTs are generally believed to be an ideal building block for the next generation electronics, optoelectronics, and high-performance sensors. However, the selectable and controllable placement and patterning of this nano-scale material has remained a challenge for their practical application. Common techniques to form aligned nanostructures include microwave plasma CVD , phase transformation , thermal oxidation , and electroless deposition . Recently, researchers have shown that dielectrophoresis (DEP) is an efficient technique to manipulate carbon nanotubes [15, 16]. With no functionalization, DEP has the potential of separating metallic-single-walled carbon nanotubes (SWCNTs) and semiconducting-SWCNTs , aligning carbon nanotubes between microelectrodes , and realizing large-scale manipulation . Both experimental and theoretical work are conducted, most studies focus on the frequency-dependent DEP behavior of CNTs , and the translation and rotation of CNTs under electrical field . However, the mechanisms for controllable patterning of CNTs between electrodes are not fully understood.
Here, the assembly of SWCNTs between electrodes is analyzed with the electrophoresis model. The influences of various factors including the electrode type, DEP voltage and thermal noise on the DEP assembly are taken into consideration. Besides, the influence of already deposited SWCNTs on the alignment of succeeding ones is also studied.
In our modeling, F consists of two components: one is the deterministic DEP force due to electrical field generated by the electrodes; while the other is the random force induced by thermal noise in the surrounding medium. The latter leads to the well-known Brownian motion of microparticles.
where KB is the Boltzmann constant, T the room temperature, f the friction factor of SWCNT-bundle, and G i a Gaussian distributed random number.
The Solution of Langevin Equation
The movement of SWCNT-bundles is divided into a series of steps. For every time step, the terminal velocity is evaluated by Eq. 9. To avoid numerical errors, the time step is adjusted to make the space step constant, which means near regions with high field strength, the time step is effectively reduced. In our simulation, this time step is well above the characteristic time ∝, so the use of Eq. 9is justified. To account for Brownian motion, we superpose the Brownian displacement given by Eq. 7at every step.
To get the final SWCNT-bundles’ space distribution on the electrode, we initiate 1,000 randomly distributed SWCNT-bundles in the solution, and trace the movement of every bundle until it reaches the substrate. Considering the relatively low CNTs’ density in medium solution (in the order of μg/l in device applications), we neglect the interaction between SWCNT-bundles when they are suspended in the medium. However, once a bundle first attach to the electrode, it may severely alter the local electrical field structure. Thus, change the DEP movement of latter bundles. We numerically demonstrate this effect by solving the Poisson’s equation with one SWCNT-bundle bridge the electrode (Fig. 2c, d) and then use this field solution to simulate the subsequent SWCNT-bundles’ DEP process.
Result and Discussion
When suspended in the solution medium, the interaction between SWCNT-bundles can be neglected because of relatively low density (in the order of μg/l). On the other hand, when the interaction between two SWCNT-bundles are taken into account, we are actually dealing with the interaction between the two dipole moments and For one SWCNT-bundle, the interaction force is due to the field created by the dipole moment of another SWCNT-bundle. This interaction force can be expressed as where is the field created by dipole moment So generally, this interaction force is a secondary effect, and will not influence the DEP movement due to the fact that the DEP force produced by external field dominates. The case that the interaction between SWCNT-bundles will play a main role is when the external field is uniform, in which and there is no DEP movement. In our simulation, the use of microelectrodes will cause the generation of strong non-uniform electrical fields. So, the interaction between SWCNT-bundles will not change the results of our simulation.
The assembly of SWCNTs on the electrodes using the DEP method has been studied theoretically. The influences of electrode type, electrode voltage, thermal noise, and as-bridged nanotubes on the results of DEP assembly are analyzed. The results suggest that: (1) although the parallel and comb electrode are both effective electrode structures to align the SWCNTs, the comb electrode has a better position control of SWCNTs than the parallel electrode; (2) once a SWNCT bundle bridges on the electrode, it will change the local electrical field and “screen off” the SWCNTs that approach later; for parallel electrode this effect results in the formation of dispersed SWCNT array, while for comb electrode it guarantees that one fingertip pair collects only one SWCNT bundle; (3) the density of DEP assembled array is limited by the “screening length”, which scales with the gap width of electrodes and the length of SWCNT bundle; and (4) the thermal noise has an important influence on the DEP assembly of SWCNTs, which is more significant for the smaller electrode structures and shorter SWCNTs; by increasing the AC voltage, this influence can be effectively eliminated.
Changxin Chen and Yang Lu contributed equally to this work.
This work is supported by National Natural Science Foundation of China No. 60807008, Shanghai International Science and Technology Cooperation Foundation No. 08520741500, Shanghai Science and Technology Grant No. 0752nm015, National Natural Science Foundation of China No. 50730008 and National Basic Research Program of China No. 2006CB300406.
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