Using carbon nanotubes as propellant for nano-particle field extraction thrusters

• Stefan Seuleanu

Introduction

Carbon nanotubes have been a research focus for more than two decades due to their unique physical properties and have been used so far in a variety of appli- cations. A possible application of carbon nanotubes is their use as propellant for an electric propulsion prototype, the nano-particle field extraction thruster (nanoFET). The nanoFET accelerates and ejects conductive particles in order to provide thrust1 . Its main advantage over other electric propulsion systems, such as ion or arcjet thrusters, is its variable specific impulse and thrust, while maintaining a high internal efficiency1 . Theoretically, the nanoFET propulsion system can be used for a large range of orbital and deep space exploration sit- uations, offering the possibility of decoupling the spacecraft design from the propulsion system4 . However, to date, nanoFETs have not been researched ex- tensively and much of the experimental work is still to be expected. This paper will investigate the possibility of using carbon nanotubes as nanoFET propel- lant by considering their relevant physical properties. By understanding how the nano-particle field extraction thruster works,this account also motivates the use of carbon nanotubes as propellant, despite their current high price.

Properties and characteristics of CNTs

Firstly, it is important to understand the relevant characteristics that make CNTs desirable for the nanoFET propulsion system. A carbon nanotube is a tubular/cylindrical structure that can be visualized as a wrapped sheet of graphene (one atom thick, two dimensional carbon based hexagonal lattice). Their size is typically a couple of nanometers in diameter and can span many micrometers in length. Carbon nanotubes can be single-walled (SWNTs) or multi-walled (MWNTs). These two characteristics will determine their aspect ratio (ratio between length and diameter), which is generally very high. As will be explained later on, the aspect ratio is a determinant factor that influences the nanoFET performance2,3 .

The geometric structure of the nanotube determines its electrical properties. Based on the chiral vector (n,m), illustrated below, there are three main types of CNTs: zigzag, armchair and chiral. When n − m is a multiple of three, then the CNT is metallic, and semiconducting otherwise. Due to their geometry, armchair CNTs are always metallic, while the other types can be metallic only with the right choice of (n,m). Because there is no exact way to synthesize carbon nanotubes of only one geometry, as expected, generally one third of the synthesized CNTs are metallic and the rest are semiconducting 2,3 .

Figure 1: CNT type depends on the chiral vector2 .

Regarding the nanoFETs, the desired CNTs are the metallic type which implies the necessity for prior sorting before use. Moreover, the synthesized CNTs can contain geometrical ”defects” that can be manipulated to improve the thruster’s performance3 .

Due to the fact that the CNTs’ structure/geometry minimizes the collisions between conducting electrons, the resulting metallic tubes are highly conductive. Another characteristic is determined by the strong carbon bonds that allow high current to flow at low resistivity. This properties will become relevant when explaining the charging stage of the nanoFET 2,3 .

The stages of a nanoFET

The acceleration of a particle by a nanoFET can be divided into several stages. By assuming that the particles have been already sorted for the desired thrust, the first stage is the transportation of the particles to the charging pad. The transportation of the particles can be achieved either trough a dielectric fluid or through back pressure, hence the difference between wet nanoFETs and dry nanoFETs. For the purpose of this paper only the wet nanoFETs will be con- sidered, as the research done into dry nanoFETs has so far been minimal. The transportation liquid used for the proof-of-concept tests was silicon oil. After

the particle is transported to the charging pad, the next stage is the charging process . Here the conductive particle is electrostatically charged to a desired level 5,6,8 .

Figure 2: Single nanoFET emission channel – cross section5

The next phase is the lift-off and extraction, which represents the application of an electric field, a potential bias between the electrode and the acceleration gates, such that the particle leaves the charging pad and moves upwards towards the liquid’s surface. At the surface, the particle must overcome the surface tension and get extracted from the liquid. After the extraction, the next stage is the acceleration of the particle trough several stacked gates. The gates have alternating insulating and conductive layers, each providing in theory an electric potential of 1000V, leading to a total of 10,000V potential that accelerates a particle to approximately 10km/s. The particle is finally ejected out of the nanoFET and thrust is produced5,6,7 .

Particle behavior in nanoFETs

In order to understand the behavior of the particle in a gravitational setting compared to a micro-gravitational setting, it is important to identify the forces that act on the particle at different stages in the nanoFET. The four main forces acting on a particle in a gravitational setting are the electrostatic force, the buoyant force, gravitational force and the drag force. As the cylindrical particle is transported to the charging pad, the liquid provides a horizontal inertial force. This horizontal inertial force is assumed to be low and therefore ignored in the calculations. After the nanoparticles are transported to the charging pad (electrode), they are electrostatically charged; thus contact with the electrode is necessary. If the contact is horizontal, along the length, then the charge of the particle is described by6 .:

q0,cy−h = 2πrlεl El

However if the contact is at either ends, so the particle is vertical on the electrode, the charge is the following6 .:

l2

q0,cy−v = π ln( 2l

εl El

When the cylindrical particle is vertical on the charging pad, it gains more charge and it also requires less electric field to move upwards, as seen in the figure below6 .

Figure 3: Vertically vs horizontal oriented particles – a) ratio of acquired particle charge; b) ratio of required lift-off electric field6

In order to orient a particle from horizontal to vertical on the charging pad, an intense electric field focused only at one of the particle’s ends is applied. The fabrication defects that are usually present at the ends of CNTs may help to change the orientation of the particle on the electrode, requiring less electric field to create a moment that rotates the CNTs vertically. Additionally to the gravitational force, while still on the charging pad, the particle has to overcome the adhesion and electric image force in order to achieve vertical lift-off5,6 .

After the particle leaves the charging pad, it has to move vertically trough the viscous liquid to the liquid surface. Therefore, the adhesion force and the electric image are no longer present; however the drag force now slows the particle’s movement. For a cylindrical particle the formula for the fluid drag used in the nanoFET calculations is given by6 :

2πµl lv

D = ln( l ) + 0.193

While moving through the liquid, the particle loses charge as described by

q(t) = q0 exp(− t ), where τ = εl

5,6 . Because the particle moves fast through

τ σl

the liquid, the charged loss is overall assumed to be negligible. Generally, the

particle’s equation of motion is described by6 :

dv

(mp + K ml ) dt = q(t)El − D + Fbuoyant − W.

The above equation also takes in account the added mass that is accelerated with the particle where K is a coefficient that depends on the geometry of the particle, while mp is the mass of the particle and ml is the mass of the liquid. In a laboratory gravitational environment the gravitational forces are minimal compared to the dominant drag and electrostatic forces. In a micro-gravitational environment the gravitational force and the buoyant force can be neglected5,6 .

Performance and particle size

For characterizing the performance of the nanoFET electric propulsion system, the space industry uses specific impulse and thrust-to-power ratio as indica- tors of performance. The specific impulse is the impulse delivered per unit of propellant consumed. In order to achieve a certain thrust, the systems that have higher specific impulse consume less propellant than the ones with lower specific impulse. For the nanoFET system the specific impulse increases as the charge-to-mass ratio of the particle increases. Thurst-to-power ratio describes the amount of thrust outputted for a specific power provided4,6 .

1 q 1

T 2 mp 1

Isp =

0

(2Vo

p

) 2 ;

= ( ) 2

P Vo q

Moreover, the internal efficiency is given by4,6 :

1 T

ηint = 2 g0 P Isp

There are several factors that can influence the performance or the mode of operation of the nanoFET. First of all, the horizontal inertial force that the particle gains from the transportation liquid is assumed to be negligible. How- ever, this is not necessarily the case and further research needs to be conducted in order to determine its influence. Another important factor is the presence of Taylor cones and surface instability when a high electric field is present near the liquid’s surface. These cones can eject droplets and reduce the performance of the nanoFET. In order to mitigate the surface instability and the ejection of droplets, an experiment has been done to analyze how different particle shapes influence the minimum electric field needed for the extraction process. The ex- periment consists of various vacuum electric fields applied to spherical 800µm and cylindrical 300µm diameter and 1.5mm length aluminium particles with a total silicon oil fluid gap of 12.7mm. As seen in the figure below, cylindrical particles can be extracted before the Taylor cones form5,6,7, .

Figure 4: Taylor cone formation and particle extraction6

Furthermore, further study into the charge-to-mass ratio revealed that, for cylindrical particles, charge-to-mass ratio increases as aspect ratio increases. Therefore, at large aspect ratios, the needed extraction electric field decreases as seen in the following figure. For this reason increasing the aspect ratio of the particles increases in turn the Isp and the overall internal efficiency6 .

A good candidate for further research are the CNTs due to their cylindrical

Figure 5: Cylindrical particles’ vacuum extraction field simulations6

shape, high aspect ratio, good charge-to-mass ratio and fast charging. By choos- ing different CNT sizes to be used with variable gate potentials, the nanoFETs’ Isp range is theoretically very large compared to other electric propulsion sys- tem such as ion thrusters or hall thrusters. Similarly, the thrust-to-power varies greatly, which offers the flexibility of using the same propulsion system for mul- tiple missions or to perform unplanned trajectory changes at a low propellant expense. These are theoretically achieved while maintaining a high internal efficiency that is usually above 85%. For the following CNTs: nanoFET par- ticle1 – 16nm diameter, 3µm length; nanoFET particle2 – 4nm diameter, 3µm length; nanoFET particle3 – 1nm diameter, 3µm length, the expected Isp and Thrust-to-Power ratio is illustrated4,5 .

Figure 6: Thrust-to-power ratio for large specific impulse range4

Figure 7: Internal efficiency for large specific impulse range4

Discussion

Apart from the large specific impulse range at high internal efficiency that pro- vides great flexibility to design a multitude of mission phases based on just one propulsion system and to accommodate for unforeseen scenarios, the nanoFETs have other important advantages over other electric propulsion system, such as potential longer operational lifetime, their geometric scalability and the fact that the system is highly integrated. The longer operational lifetime is due to the fact that the CNT particles or any other conductive particles are charged electro- statically and not ionized which eliminates the need for cathodes and eliminates charge exchange collisions that are the main lifetime reduction factors5,6 . However, there are still a multitude of challenges ahead until a fully functional prototype will be achieved. First of all, the experiments done so far that demon- strated particle transportation, charging and lift-off were conducted using mi- crometer size particles such as Aluminum, Titanium and Indium. Although theoretically the CNTs can greatly increase the performance, no nano-size par- ticles have been experimentally used so far. Experimenting at the nanoscale might sometime reveal new problems that were not present at the micron level. Also, it is generally desirable that a quantitative experimental analysis is done in order to understand how a multitude of particles with different character- istics perform. In this way it could be determined what particle shows the most promise, although CNTs have a strong theoretical advantage mainly due to their charge-to-mass ratio. Another important factor to investigate is how the charging process changes as the size of the particle decreases to the several nanometers; the main concerns being conductivity and the contact area with

the electrode. Furthermore, an investigation should also be conducted regard- ing the transportation liquid. So far, it is uncertain if a fully dielectric liquid is always desired over a slightly conductive liquid. Moreover, different liquids should be tested in order to experimentally understand how the viscosity of the liquid influences the space charge current5,6,7,8 .

Finally, from an academic point of view it would be desirable that both the theoretical and experimental papers are published in a peer-reviewed journal.

Conclusion

Overall, the nanoFET propulsion system shows great promise due to its high specific impulse range and inherent scalability. Although it is a new concept, the most important processes such as particle transportation and charging have been already demonstrated. However, there are still a multitude of experiments that need to be conducted in order to fully understand the behavior of the system under a wide range of factors. Another interesting prospect for the nanoFET technology is their possible use , not only in the space industry, but also in medicine. The nanoFET technology can also be used to accelerate particles and inject them through cellular walls to deliver drugs. For these reasons, the nanoFET technology is an exciting and potentially rewarding research subject.

References

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