Abstract:
A method for measuring the mass of nano-substances including the steps of gripping a nano-substance with a nanotweezer gripping portion made of a plurality of nanotubes, resonating the nanotweezer gripping portion in this gripping state, measuring a resulting first characteristic frequency, and obtaining the mass of the gripped nano-substance by comparing the first and second characteristic frequencies, where the second characteristic frequency is the characteristic frequency of the nanotweezer gripping portion with no nano-substance gripped thereby. The gripping portion is caused to resonate electrically by applying an AC voltage between the nanotweezer gripping portion and an electrode disposed near the nanotweezer gripping portion. The gripping portion is caused also to resonate mechanically by way of expanding and contracting a piezo-electric element disposed on a main body that supports the nanotweezer gripping portion.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to nanotweezers that can grip and release nano-substances having a nano-scale size by opening and closing a plurality of nanotubes. More specifically, the present invention relates to a nano-substance mass measurement method and apparatus which can measure the mass of gripped nano-substances by measuring resonance frequencies of the gripping portion of the nanotweezers before and after the gripping of the nano-substances. 
     2. Prior Art 
     Generally, mass analysis methods are used as methods for measuring the mass of extremely small substances such as atoms, molecules, etc. In such mass analysis methods, a sample is ionized, and the ions are accelerated by means of an electric field so that the traveling velocity is caused to vary according to the mass. Then, the ion current is separated according to the specific charge e/m or m/e by rotation in a magnetic field, and the mass of the ions is deduced from the respective peaks in the mass spectrum. 
     The mass analysis method has the advantage of allowing precise measurements of the mass of relatively light substances such as atoms and molecules. However, this method is unsuitable for measuring the mass of nano-substances such as extremely small particles formed by the aggregation of 100 to 10,000 atoms. 
     The mass of such nano-substances is larger than the mass of atoms. Accordingly, even if these nano-substances are ionized by electron bombardment or high-frequency spark discharge, an ultra-high-intensity electric field is required in order to cause the ions to travel through space; and in order to realize such an electric field, it is inevitable that the apparatus to be used becomes excessively large in size. Furthermore, even if it is possible to cause the ions to travel through space, since the ions have a large inertia, an extremely large magnetic field is required for rotation of the ions. Consequently, the overall size of the apparatus used needs to be extremely large as in the case described above. 
     Devices that create heavy ion beams have been realized in research of atomic nuclei, etc. However, these devices are extremely large in size, and thus an extremely large apparatus is thus required even at the level of heavy ions. Accordingly, in cases where the mass of nano-substances or nano-particles that are even larger than heavy ions are to be measured by ionization, such measurements are virtually impossible when the above-described mass analysis method is used in terms of both cost and practicality. 
     SUMMARY OF THE INVENTION 
     Accordingly, the object of the present invention is to provide a nano-substance mass measurement method and apparatus in which, without using an ionizing device, electric field accelerating device or magnetic field rotating device, the mass of nano-substances is obtained in an extremely simple manner by way of griping nano-substances with nanotweezers that have nanotubes etc. at the tip ends thereof and measuring resonance frequencies of the nanotweezers before and after such gripping. 
     The present invention is a nano-substance mass measurement method characterized in that, with the use of nanotweezers that are capable of gripping and releasing nano-size nano-substances, a nano-substances is gripped by the nanotweezer gripping portion of the nanotweezers, the nanotweezer gripping portion in this gripping state is caused to resonate, the resulting characteristic frequency f m  is measured, and the mass of the gripped nano-substance is obtained by comparing two characteristic frequencies f m  and f o  where f o  is the characteristic frequency of the gripping portion of the nanotweezers which is in a state that no nano-substance is gripped. 
     In the above nano-substance mass measurement method of the present invention, the nanotweezer gripping portion is formed by the tip end portions of a plurality of nanotubes. 
     Furthermore, in the nano-substance mass measurement method according to the present invention, an external electrode is caused to approach the gripping portion of the nanotweezers, and an AC voltage is applied across the gripping portion of the nanotweezers and the external electrode so that the gripping portion of the nanotweezers is caused to resonate by AC electrostatic induction, thus measuring the characteristic frequencies f o  and f m . 
     Also in the nano-substance mass measurement method of the present invention, a piezo-electric element is provided in the nanotweezer main body which has the nanotweezer gripping portion on the tip end, and the nanotweezer gripping portion is caused to resonate by applying an AC voltage to this piezo-electric element, thus measuring the characteristic frequencies f o  and f m . 
     The present invention is also a nano-substance mass measuring apparatus which is comprised of: a nanotweezer main body to which the base end portions of a plurality of nanotubes are fastened, a nanotweezer gripping portion that is formed by the tip end portions of the nanotubes, a means which controls the nanotweezer gripping portion so that the gripping portion can be freely opened and closed, an external electrode that is disposed in close proximity to the nanotweezer gripping portion, and an AC power supply which applies an AC voltage used for resonance across the nanotweezer gripping portion and the external electrode. 
     Furthermore, the present invention is a nano-substance mass measuring apparatus which is comprised of a nanotweezer main body to which the base end portions of a plurality of nanotubes are fastened, a nanotweezer gripping portion that is formed by the tip end portions of the nanotubes, a means which controls the nanotweezer gripping portion so that the gripping portion can be freely opened and closed, a piezo-electric element which is provided in the nanotweezers, and an AC power supply which applies an AC voltage used for resonance to the piezo-electric element. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a model diagram illustrating the characteristic vibration of a cantilever beam that constitutes the principle of the present invention; 
     FIG. 2 is a model diagram illustrating the characteristic vibration of a cantilever beam that supports a mass point, constituting the principle of the present invention; 
     FIG. 3 is a schematic diagram of the nanotweezers; 
     FIG. 4 is a schematic diagram showing the nanotweezers gripping a nano-substance; 
     FIG. 5 is a structural diagram of the first embodiment of the present invention in which the nanotweezers gripping a nano-substance are caused to resonate by AC electrostatic induction; 
     FIG. 6 is a schematic waveform diagram of the AC voltage that is applied in order to cause the nanotweezers to resonate; 
     FIG. 7 is a schematic waveform diagram of the force that acts on the nanotweezers as a result of AC electrostatic induction; 
     FIG. 8 is a resonance diagram illustrating the relationship between the amplitude and frequency of the nanotweezer gripping portion; 
     FIG. 9 is a structural diagram of the second embodiment of the present invention in which the nanotweezers gripping a nano-substance are caused to resonate by a piezo-electric element; 
     FIG. 10 is a structural diagram of the third embodiment of the present invention in which nanotweezers that use three nanotubes are caused to resonate by a piezo-electric element; 
     FIG. 11 is a structural diagram of the fourth embodiment of the present invention in which nanotweezers that are also capable of an AFM operation are caused to resonate by a piezo-electric element; and 
     FIG. 12 is an explanatory diagram illustrating the operation of a nano-manipulator device which constructs nano-structures while measuring the mass of nano-substances. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The inventors of the present application have proposed nanotweezers as a device for gripping and releasing nano-substances in Japanese Patent Application Nos. 2000-112767 and 2000-404006. In these nanotweezers, the base end portions of a plurality of nanotubes are fastened to a nanotweezer main body; and by way of controlling the tip end portions of the nanotubes by means of static electricity or a piezo-electric element, the tip end portions of the nanotubes are opened and closed, thus gripping and releasing the nano-substances. 
     The inventors noted that the resonance frequency of the nanotubes varies before and after the nano-substance is gripped by the nanotweezer gripping portion and inferred that it might be possible to measure the mass of the nano-substance from the amount of such variations. 
     The mass of one H atom is 1.6×10 −24  g, and the mass of one heavy Bi atom is 3.3×10 −22  g. If nano-substances are viewed as substances formed by the aggregation of approximately 1,000 to 1,000,000 atoms, then the mass of such nano-substances can be considered to be approximately 10 −21  g to 10 −16  g. 
     On the other hand, when the mass of one carbon nanotube is considered as a typical example of a nanotube, though carbon nanotubes are hollow, if such carbon nanotubes are tentatively viewed as solid graphite rods, then the mass of a carbon nanotube that has a diameter of 20 nm and a length of 1 μm is: 
     
       
           m=ρAL= 2.3( g/cm   3 )×π×10 2 (10 −18    m   2 )×10 −6 ( m )=7.2×10 −16    g.    
       
     
     Considering that actual carbon nanotubes are hollow, and the diameter of such nanotubes can be made even smaller, the mass of one carbon nanotube can be viewed as being in the range of 10 −16  g to 10 −17  g. Meanwhile, the mass of nano-substances is 10 −21  g to 10 −16  g. Accordingly, when such nano-substances are gripped by carbon nanotubes, the resonance frequency of the nanotubes should vary significantly. Accordingly, it would appear to be possible to perform a back calculation of the mass of such a nano-substance from the amount of variation in the resonance frequency. 
     Accordingly, in order to devise a model for measuring the above-described resonance frequency, the main body of the nanotweezers developed by the inventors is viewed as a wall body, and the tip end portion of the nanotube is viewed as a cantilever beam protruding from this wall body. The characteristic frequency of this cantilever beam, i.e., the resonance frequency, is considered as described in the paragraphs below. 
     FIG. 1 is a model diagram illustrating the characteristic vibration of a cantilever beam that constitutes the principle of the present invention. A cantilever beam  1  with a volumetric density of p, a cross-sectional area of A and a length of L protrudes from the wall body W. When this cantilever beam  1  undergoes bending vibration, the solution of the Newton equations of motion indicates that the characteristic frequency f o  for n=1 is given by the following equation: 
     
       
           f   o =(½π)(1.875 /L ) 2 ( EI/ρA ) ½   
       
     
     where E is the longitudinal elastic coefficient of the material of the cantilever beam, and I is the cross-sectional secondary moment thereof. 
     FIG. 2 is a model diagram illustrating the characteristic vibration of a cantilever beam that supports a mass point, which constitutes the principle of the present invention. A mass point  1   a  of mass m is supported on the tip end of the cantilever beam  1 . When this cantilever beam  1  undergoes bending vibration, it is seen that the characteristic frequency f m  is given by the following equation when solved using the method of Rayleigh: 
     
       
           f   m =(½π)(1.875 /L ) 2 (0.246/(0.227+μ)) ½ ( EI/ρA ) ½   
       
     
     where μ=m/ρAL. 
     Accordingly, the ratio of these characteristic frequencies is given by the equation f m /f o =(0.246/(0.227+μ)) ½ . From this equation, m={0.246(f o /f m ) 2 −0.227}ρAL, so that the mass m of the nano-substance can be obtained from the characteristic frequencies f o  and f m  and the mass ρAL of the carbon nanotube. 
     The above equation can be simplified even further. If the coefficients 0.246 and 0.227 are approximated by 0.24, and f m  is set equal to f o −Δf, then the very small terms of the second order or higher can be ignored, so that m=0.48(Δf/f o )ρAL. Assuming that ρAL=10 −16  g to 10 −17  g as described above, and that Δf/f o  can be measured down to values on the order of 10 −3 , it was found that the mass can be calculated down to values of m=10 −19  g to 10 −20  g. 
     As described above, it may be predicted that the mass of nano-substances will be in the range of 10 −21  g to 10 −16  g. Accordingly, this mass range is more or less included within the above-described measurement limit (10 −20  g), thus sufficiently indicating that the mass of nano-substances can be measured by the method of the present invention. Assuming that Δf/f o  can be measured down to the order of 10 −4 , then the measurement limit for ρAL is 10 −21  g, so that the predicted range of nano-substance mass is all included in the measurable range. 
     FIG. 3 is a schematic diagram of the nanotweezers. The nanotweezers  11  are constructed by forming electrodes  4   a  and  4   b  on a main body  3  and fastening the base end portions of nanotubes  5   a  and  5   b  to the respective electrodes. A nanotweezer gripping portion  11   a  is formed by the tip end portions of the nanotubes  5   a  and  5   b.    
     FIG. 4 is a schematic diagram showing the nanotweezers gripping a nano-substance. A DC power supply E is connected between the electrodes  4   a  and  4   b  via a switch SW 1 . Positive and negative static charges are induced in the nanotubes  5   a  and  5   b  by this DC power supply E, so that the tip ends of the nanotubes  5   a  and  5   b , i.e., the gripping portion  11   a , is closed by an electrostatic attractive force, thus gripping the nano-substance  2 . 
     Carbon nanotubes are conductive nanotubes; and when the gripping portion  11   a  is constructed from such conductive nanotubes, insulating or semiconductor nano-substances  2  can be easily gripped by the electrostatic attractive force. However, when the conductive nano-substance  2  is gripped, the tip ends of the gripping portions  11   a  are electrically connected via the nano-substance  2 , and the electrostatic attractive force may drop. 
     However, by way of coating the surfaces of conductive nanotubes such as carbon nanotubes, etc. with an insulating film and by way of using these coated nanotubes as the nanotubes  5   a  and  5   b , nano-substances  2  with a broad range of electrical properties can be gripped regardless of the conductive or insulating property of the nano-substances. 
     FIG. 5 is a structural diagram of the first embodiment of the present invention which the nanotweezers gripping the nano-substance are caused to resonate by AC electrostatic induction. 
     An external electrode  6  is disposed in close proximity to the gripping portion  11   a , and an AC power supply V is attached between the external electrode  6  and the nanotweezers  11  via a switch SW 2 . When an AC voltage is applied by this AC power supply V, AC electrostatic induction occurs between the gripping portion  11   a  and external electrode  6 . As a result, the gripping portion  11   a  is forcibly caused to vibrate. 
     FIG. 6 is a schematic waveform diagram of the AC voltage that is applied in order to cause the nanotweezers to resonate. The AC voltage V(t) is given by the equation V(t)=V o sin (2πft), and an AC voltage of frequency f is applied from the external electrode  6 . 
     FIG. 7 is a schematic waveform diagram of the force that acts on the nanotweezers as a result of AC electrostatic induction. 
     When a positive charge is induced in the external electrode  6 , a negative charge is induced in the gripping portion  11   a ; and when a negative charge is induced in the external electrode  6 , a positive charge is induced in the gripping portion  11   a . In other words, an electrostatic attractive force that acts on the gripping portion  11   a  is generated twice during one period of the AC voltage; accordingly, the frequency of the AC electrostatic attractive force F(t) is 2 f. Consequently, the nanotweezer gripping portion  11   a  vibrates at a frequency of 2 f. 
     FIG. 8 is a resonance diagram illustrating the relationship between the amplitude and frequency of the nanotweezer gripping portion. 
     As the frequency of the AC voltage applied to the nanotweezers  11  is gradually increased, the gripping portion  11   a  begins a forced vibration with an amplitude of A; when the amplitude A reaches a maximum at the frequency f m , the nanotweezers  11  may be viewed as being in a resonant state. In other words, the forced vibration reaches the maximum when the frequency  2   f  applied by the AC voltage coincides with the characteristic frequency of the gripping portion  11   a . This resonant state can be confirmed under an electron microscope and can also be confirmed by observing the phase change of the current in AC electrostatic induction. 
     Accordingly, when the nanotweezers  11  are in a resonant state, a value that is twice the frequency of the AC voltage coincides with the characteristic frequency f m  of the gripping portion  11   a . In this way, the characteristic frequency f o  of the gripping portion  11   a  in a state in which a nano-substance  2  is not gripped and the characteristic frequency f m  of the gripping portion  11   a  in a state in which a nano-substance  2  is gripped are measured. 
     When the characteristic frequencies f o  and f m  are measured, the mass m of the nano-substance  2  can be obtained from the equation 
     
       
           m={ 0.246( f   0   /f   m ) 2 −0.22756 ρ AL    
       
     
     or the equation 
     
       
           m= 0.48(Δ f/f   o )}ρ AL =0.48(( f   o   −f   m )/ f   o )ρ AL    
       
     
     where ρAL is the mass of the gripping portion  11   a.    
     FIG. 9 is a structural diagram of the second embodiment of the present invention in which the nanotweezers gripping the nano-substance are caused to resonate by means of a piezo-electric element. 
     Here, a piezo-electric element  7  is formed as a coating film provided on the electrode  4   b , and an AC power supply V is connected via terminals  7   a  and  7   b  so that an AC voltage can be applied to both ends of this piezo-electric element  7 . 
     When an AC voltage V(t) is applied to the piezo-electric element  7 , the piezo-electric element  7  make a stretching vibration according to its own frequency f, and thus causes a forced vibration of the gripping portion  11   a  at this frequency f. The gripping portion  11   a  resonates at a maximum amplitude when the frequency f coincides with the above-described characteristic frequency f o  or f m . The above-described characteristic frequency f o  or f m  can be measured by reading the AC frequency in this resonant state. 
     In cases where the gripping portion  11   a  is caused to resonate mechanically by means of the piezo-electric element  7 , the material of the nanotubes is not particularly relevant. Accordingly, the gripping portion  11   a  can be caused to resonate regardless of whether the nanotubes are made of a conductive material, semiconductor material or insulating material. The reason for this is that electrical short-circuiting does not occur because an electrostatic attractive force is not used. Accordingly, not only conductive nanotubes such as carbon nanotubes, but also insulating nanotubes such as BN type nanotubes or BCN type nanotubes, can be used in the present invention. 
     Furthermore, besides the electrostatic opening-and-closing mechanism, an opening-and-closing mechanism that uses piezo-electric films can be used also as the opening-and-closing mechanism of the nanotweezer gripping portion  11   a . In such a mechanism, piezoelectric films are formed as coating films on the nanotubes  5   a  and  5   b , and the nanotubes  5   a  and  5   b  are buckled or extended by applying a voltage to these piezo-electric films so that the nanotubes  5   a  and  5   b  are caused to expand or contract. As a result, the nanotweezer gripping portion  11   a  is controlled so as to open and close. In this case, both the AC electrostatic induction shown in FIG.  5  and the mechanical vibration caused by a piezo-electric element shown in FIG. 9 can be used to measure the characteristic frequencies. 
     FIG. 10 is a structural diagram of the third embodiment of the present invention in which nanotweezers that use three nanotubes are caused to resonate by a piezo-electric element. In this embodiment, the nanotweezers  11  are constructed using an AFM cantilever. Here, “AFM” refers to “atomic force microscope”. 
     Lead electrodes  12 ,  13  and  14  are formed on a cantilever, and the base end portions of nanotubes  8 ,  9  and  10  are set so as to be in contact with the tip ends of these lead electrodes. The nanotubes are fastened in place by coating films  12   b ,  13   b  and  14   b , thus forming the nanotweezers  11 . 
     A switch SW 1  and a DC power supply E are connected to terminals  12   a ,  13   a  and  14   a  located on the rear ends of the lead electrodes  12 ,  13  and  14 ; and the negative electrode of the DC power supply E is connected to the ground EA. The nanotube tip end  8   a  is positively charged, and the nanotube tip ends  9   a  and  10   a  are negatively charged, by this DC power supply E. 
     Since the gripping portion  11   a  is constructed from three nanotube tip ends  8   a ,  9   a  and  10   a , a nano-substance  2  of any shape can be securely gripped. The nano-substance  2  is gripped and released by opening and closing the switch SW 1  and thus opening and closing the gripping portion  11   a.    
     A piezo-electric element  7  made of a piezo-electric substance formed into a film is provided in the vicinity of the coating film  13   b . An AC power supply V is connected, via a switch SW 2 , to terminals  7   a  and  7   b  located on both ends of the piezo-electric element  7 . When the AC power supply V is applied, the piezo-electric element  7  undergoes stretching vibration, and the gripping portion  11   a  is forcibly caused to vibrate. The resonant state of the gripping portion  11   a  can be observed under an electron microscope. 
     The resonance frequencies in a case where no nano-substance  2  is gripped and in a case where a nano-substance  2  is gripped give the characteristic frequencies f o  and f m  for the respective cases. Accordingly, the mass of the nano-substance  2  can be obtained from these frequencies using the above-described equations. 
     FIG. 11 is a structural diagram of the fourth embodiment of the present invention in which nanotweezers that are also capable of an AFM operation are caused to resonate by a piezo-electric element. 
     The nanotweezer gripping portion  11   a  of the nanotweezers is formed by two nanotubes  28  and  29 . The nanotube  28  protrudes further down than the nanotube  29 , and an AFM operation is performed by the tip end  28   c  of the nanotube  28 . The operation for setting the nanotube tip end portion  28   a  to a length that is longer than the length of the nanotube tip end portion  29   a  is performed under an electron microscope. 
     Nanotube lead wires  20  and  20  are connected to the base end portions  28   b  and  29   b  of the nanotubes  28  and  29 , and the upper surfaces of the lead wires are fastened to the main body  26  by coating films  21  and  21 . A piezo-electric element  7  is formed as a film on the main body  26 , and an AC voltage is applied to terminals  7   a  and  7   b  on both ends of the piezoelectric element  7 . 
     FIG. 12 is an explanatory diagram illustrating the operation of a nano-manipulator device that constructs a nano-structure while measuring the mass of nano-substances. 
     In this manipulator device, the nanotweezers  11  shown in FIG. 11 are employed using a cantilever  25 ; and the nanotube lead wires  20  are connected, via electrodes  23 , to switch SW 1 , a DC power supply E and a DC voltage control circuit EC. The open and close operation of the nanotubes  28  and  29  is controlled by varying the DC voltage. 
     A switch SW 2  and an AC power supply V are connected to the terminals  7   a  and  7   b  of the piezo-electric element  7 . 
     First, a search is made for the collection site of a nano-substance  26  by way of scanning the sample surface  24  using the nanotube tip end  28   c  as a probe needle. Once the location of the nano-substance  26  is found, the nano-substance  26  is positioned between the nanotube tip end portions  28   a  and  29   a , and the gripping portion  11   a  is closed by turning on the switch SW 1 , thus securely holding the nano-substance  26 . 
     Next, the switch SW 2  is turned on so as to resonate the gripping portion  11   a  by the AC power supply V, and the mass of the nano-substance  26  is measured, thus identifying the kind of the nano-substance  26 . Afterward, the sample surface  24  is subjected to AFM scanning by the nanotube tip end  28   c , so that the gripping portion  11   a  is moved to the position of a nano-structure  27 . After the required position of the nano-structure  27  has been found by AFM scanning, and the gripping portion  11   a  has been moved to this position, the switch SW 1  is turned off, thus releasing the nano-substance  26 . The nano-structure  27  is built by repeating this operation. 
     The present invention is not limited to the embodiments described above. Various modifications, design alterations, etc. that do not involve any departure from the technical concept of the present invention are included in the technical scope of the present invention. 
     As seen from the above, in the present invention, the characteristic frequency f m  of the nanotweezer gripping portion gripping the nano-substance is measured utilizing the phenomenon of resonance, and the mass of the nano-substance is measured merely by performing a calculation that compares this characteristic frequency f m  to the characteristic frequency f o  that is obtained by the nanotweezer gripping portion which is not gripping a nano-substance. Accordingly, the mass of nano-substances down to approximately 10 −20  g can be quickly obtained using an extremely simple structure. Thus, a nano-substance mass measurement method, which constitutes a breakthrough in the fields of semiconductors and molecular biology and in other research fields and manufacturing technology fields that handle nano-substances, can be provided. 
     Furthermore, the nanotweezer gripping portion is constructed from the tip end portions of a plurality of nanotubes. Accordingly, the respective nanotubes are freely controlled, and an efficient nano-substance mass measurement method is provided. 
     In addition, the characteristic frequencies f o  and f m  are measured merely by causing an external electrode to approach the nanotweezer gripping portion, applying an AC voltage across the external electrode and nanotweezer gripping portion, and then causing the gripping portion to resonate by means of AC electrostatic induction. Accordingly, a nano-substance mass measurement method with high utility which can handle nanotweezers of various configurations by means of an extremely simple structure is provided. 
     Also in the present invention, a piezo-electric element is provided in the main body of the nanotweezers, and the nanotweezer gripping portion is caused to resonate by applying an AC voltage to this piezo-electric element. Accordingly, a mass measurement method which makes it possible to measure the mass of nano-substances that have conductive properties, semiconductor properties and insulating properties is provided. 
     Furthermore, according to the present invention, an apparatus that allows quick measurement of the mass of nano-substances using the phenomenon of resonance caused by AC electrostatic induction is provided by an extremely simple structure that includes a nanotweezer gripping portion, an external electrode and an AC power supply. 
     Also, according to the present invention, an apparatus that allows quick and accurate measurement of the mass of nano-substances using the phenomenon of mechanical resonance caused by a piezo-electric element is provided by an extremely simple structure that includes a nanotweezer gripping portion, a piezo-electric element and an AC power supply.