1、 A Nano-Tuneable Pressure Switch System Design Based On Single Wall Carbon Nanotubes S.S.Hosseini Yazdi and M.Mousavi Mashadi Faculty of Mechanical Engineering,University of Tehran, Iran Abstract:Under hydrostatic pressure, the cross section of a Single Wall Carbon Nanotube(SWNT) reduces uniformly a
2、nd proportionally to the applied pressure until it reaches to SWNTs first transition pressure.In addition, SWNT kinks,becomes unstable and collapses on a ground plane due to bending loads.This phenomenon is a function of SWNT diameter. Bending loads can be generated by inducing a voltage between SWN
3、T and a conductive ground plane. Therefore ,by inducing a certain Pull-in voltage relative to a certain diameter(pressure), SWNT does not collapse until the applied pressure reaches to a certain amount which causes a certain SWNT diameter reduction.In this case, because of SWNT collapse on the groun
4、d plane, there will be a connection between them closing an electric circuit.In this study, these characteristics are employed to introduce a tuneable pressure switch. This type of pressure switch,in comparison to previous presented one, uses only one SWNT for switching, is able to sense pressure wi
5、th higher resolution and has a much simpler system. Key words:Single wall carbon nanotube, pull-in voltages, electrostatic bending forces, kink, phase transition, transient pressure INTRODUCTION Single Wall Carbon Nanotubes(SWNTs) has novel mechanical properties and behaviors which have attracted ma
6、ny considerations and studies recently. Under hydrostatic Pressure, SWNTs cross section is reduced uniformly and proportionally to applied pressure, until it reaches SWNTs first transient pressure. In this case the SWNT physical properties change and its cross section becomes elliptical. This charac
7、teristics has been used in previous presented nano pressure sensors by Wu et al.(2004), When applied pressure reaches to one of the SWNTs transition pressure, its cross section shape changes, turning SWNT into a semi-conductive material.The pressure sensing system has the ability to sense the change
8、 of SWNT from a conductive material to a semi- conductive substance for switching. Therefore, in this way, pressure sensor needs a number of SWNTs. However, the number of used SWNTs is restricted because Gao et al.(1998)bsowed when SWNT diameter exceeds a limit, its natural shape is collapsed form.
9、Thus, it is imposssible to use them in this system. Consequently, the pressure sensor only is able to sense retricted number of pressure(SWNTs transition pressures) （ Fig.1 and 2） . To overcome the pressure sensing range restriction of the previous introduced switch, in this study, a tuneable pressu
10、re switch system has been introduced which can switches with higher resolution using much simpler system. It consists of a fixed ends SWNT and a graphite ground plane which are conductive. When various Pull-in voltage are induced, SWNT collapses on the ground plane only if the relative hydrostatic p
11、ressures are applied. The upper bound of pressure sensing range of this switch is the first SWNTs traansition pressure. To understand the mechanism of the switch on which the design is based, SWNT transition pressure and pull-in phenomenon are illuminated in the follow sections. TRANSITION PRESSURE
12、Zang et al.(2004), Sun et al.(2004) and Sood (2004) showed that SWNTs under applied hydrostatic pressure encounter phase transition. This phase transition is due to difference between energy which is needed to alter Carbon-Carbon bond length and Carbon-Carbon-Carbon angle. At first stage, the SWNT c
13、ross section reduces uniformly and proportionally under pressure, which is the result of Carbon-Carbon bond uniform length reduction. At a certain point, the cross section shape collapses from circular to elliptical. In this case, the SWNT deformation is much lager than previous. The reason is: Carb
14、on-Carbon-Carbon angle variation needs much less energy in comparison to Carbon-Carbon bond length variation. Thus, SWNT undergoes a greater deformation after facing pressure higher than its first transition pressure. As a result, the isotropic SWNT turns into an anisotropic SWNT which is semi-condu
15、ctive substance. The first SWNT transition pressure is obtained by (Fig.3): Where R0 is SWNT initial radius and D is SWNT elastic constant. For SWNTs, D=0.76eV which is obtained by Molecular Dynamics. In consequence, the dimension of Pt1 is: PULL-IN PHENOMENON Dequensnes ey al.(2004) has demonstrate
16、d when a voltage is include between a SWNT and a conductive ground plane, the SWNT deflects. When the deflection reaches to a certain amount, SWNT becomes unstable and collapses. This phenomenon is called Pull-in and the relative voltage, Pull-in voltage. The applied electrostatic force per length i
17、s found by classic capacitance model as: Where 0 is vacuum permittivity, V is include voltage, Rnt is SWNT radius and r is SWNT and ground plane distance. Wang and Varadan(2005) prove that this instability is because of SWNT kink under bending conditions, which has been observed by high resolution t
18、ransmission electron, when the strain energy at the inner wall of the compressive side reaches the critical value. Since stress and strain follow a linear distribution in radial direction, it is reasonable to assume that kink instability happens when in-plane strain under uniformly distributed compr
19、ession. The kink slope being a function of dnt can be found by: That L is SWNT length, dNT, is its diameter and h is SWNT effective thickness. DEFINITION OF TUNEABLE PRESSURE SWITCH By combining the above mentioned concepts about Pull-in phenomenon and transition pressure of SWNTs, the tuneable pres
20、sure switch mechanism can be defined. As it can be seen, from Eq.3, the er is a function of SWNT diameter. While a hydrostatic pressure is applied on SWNT, its diameter reduces uniformly and proportionally to the applied pressure: WheredNT0 is SWNTs initial diameter (at zero pressure) and E is its e
21、ffective young Modulus (Fig.5) To calculate the Pull-in voltage, elastic and electrostatic domains should be considered. Van der Waals forces are quite small in comparison to electrostatic force； therefore, they are neglected in this study. The system obeys the classical beam equation Which is highl
22、y none-linear. Therefore, it has no analytical solution. Without losing the generality, it is possible to use lump model derived by Dequensenes et al.(2002) which assumes bending electrostatic force distribution is uniform before Pull-in phenomenon happens. The pull-in voltage for a lump model is ca
23、lcuated by: That rinit is the initial distance between SWNT and ground plane and rpl=2rinit/3 is the distance which Pull-in happens. By considering RNT as a function of applied pressure, the relation between Pull-in voltage and applied pressure is obtained(Fig.6). In consequence, the mechanism of su
24、ggested pressure switch consists of a both end fixed SWNT, a conductive ground plane and a tuneable voltage source to induce voltage between the SWNT and the ground plane(Fig.7). CONCLUSIONS In summary, a tuneable pressure switch has been obtained which uses only one SWNT and its mechanism run as fo
25、llowing: When a Pull-in voltage related to a certain pressure is induced to the system, the SWNT does not kink and does not on the ground plane, until the applied pressure reaches to that certain amount.When due to the application of pressure and voltage, SWNT collapses on the ground plane, because
26、both of them are conductive, an electric circuit is closed and the switch is considered ON.As a result, its sensing and switching mechanism is much simpler in comparison to previous presented pressure sensor because a complicated system which is able to sense the difference between a conductive and
27、semi conductive material is eliminated. The recent system, also, is able to switch at any desire pressure which is obtainable by its resolution within is sensing range(Its pressure sensing range is between zero and used SWNT the first transition pressure). Hence, it is not restricted to few pressure
28、 of limited numbers of SWNTs transition pressure. The resolution of voltage inducement, determines the resolution of pressure switching which is Pt V. Here for such a typical system, the kink and deflection graphs for two pressure conditions are brought. The SWNT effective physical properties are as followings, which was calculated by authors based on inter-atomic force field constants for Carbon lattice presented by Leamy(2005)；L=27.14nm,dNT0=1.88nm,rinit=6nm,h=0.34nm and Eeffective=1.03nm(Fig.8 and 9).
