Abstract:
A differential displacement sensor is disclosed that includes a pair of aligned stationary carbon nanostructures and a moveable carbon nanostructure. The moveable carbon nanostructure is configured to engage and move with respect to the pair of aligned stationary carbon nanostructures throughout a range of motion. Circuitry applies an excitation voltage across the pair of aligned stationary carbon nanostructures and the moveable carbon nanostructure to generate an output voltage proportional to a displacement of the moveable carbon nanostructure with respect to the pair of aligned stationary carbon nanostructures throughout the range of motion. Graphene sheets or carbon nanotubes may form the moveable carbon nanostructure or the pair of aligned stationary carbon nanostructures.

Description:
FIELD OF INVENTION 
     The present disclosure relates to the field of differential displacement sensors. 
     BACKGROUND 
     A position sensor is any device that permits position measurement. It can either be an absolute position sensor or a relative one (displacement sensor). Position sensors can be linear, angular, rotational or multi-axis. 
     SUMMARY 
     Carbon nanostructures are utilized to create differential displacement sensors. For example, dual-wall carbon nanotubes (DWCNT) are utilized to create linear-differential-displacement sensors. Alternatively, graphene sheets are used to create linear- and rotational-differential-displacement sensors. These differential displacement sensors achieve a doubling of the signal output which is directly proportional to displacement, and mitigation of common mode noise. 
     A differential displacement sensor is disclosed that includes a pair of aligned stationary carbon nanostructures. A moveable carbon nanostructure is configured to engage and move with respect to the pair of aligned stationary carbon nanostructures throughout a range of motion. Circuitry applies an excitation voltage across the pair of aligned stationary carbon nanostructures. The moveable carbon nanostructure generates an output voltage proportional to a displacement of the moveable carbon nanostructure with respect to the pair of aligned stationary carbon nanostructures throughout the range of motion. 
     The pair of aligned stationary carbon nanostructures can both be carbon nanotubes. The moveable carbon nanostructure may also be a carbon nanotube. The carbon nanotubes forming the pair of aligned stationary carbon nanostructures are axially aligned with the carbon nanotube forming the moveable carbon nanostructure. 
     In one embodiment, the carbon nanotubes forming the pair of aligned stationary carbon nanostructures both have the same inner diameter. In this embodiment, the carbon nanotube forming the moveable carbon nanostructure has an outer diameter smaller then the inner diameter of the carbon nanotubes forming the pair of aligned stationary carbon nanostructures. Each end of the carbon nanotube forming the moveable carbon nanostructure slides within one of the carbon nanotubes forming the pair of aligned stationary carbon nanostructures. 
     In another embodiment, the carbon nanotubes forming the pair of aligned stationary carbon nanostructures both have the same outer diameter. The carbon nanotube forming the moveable carbon nanostructure has an inner diameter larger then the outer diameter of the carbon nanotubes forming the pair of aligned stationary carbon nanostructures. Each end of the carbon nanotube forming the moveable carbon nanostructure slides over one of the carbon nanotubes forming the pair of aligned stationary carbon nanostructures. 
     The carbon nanotubes forming the moveable carbon nanostructure and the pair of aligned stationary carbon nanostructures are armchair carbon nanotubes. The sensor may also include an auxiliary nanowire secured to the moveable carbon nanostructure from which a differential output voltage is measured. The sensor may also include an auxiliary carbon nanotube secured to the moveable carbon nanostructure from which a differential output voltage is measured. The auxiliary carbon nanotube may have a zigzag configuration. The excitation voltage may be a DC voltage. The excitation voltage may also be an AC voltage. A chiral nanotube may be interposed between the carbon nanotube forming the moveable carbon nanostructure and the carbon nanotube forming the pair of aligned stationary carbon nanostructures. 
     In one embodiment, the pair of aligned stationary carbon nanostructures are both sheets of graphene. The moveable carbon nanostructure is also a sheet of graphene. The sheet of graphene forming the moveable carbon nanostructure rotates with respect to the graphene sheets forming the pair of aligned stationary carbon nanostructures. The sheet of graphene forming the moveable carbon nanostructure may move linearly with respect to the graphene sheets forming said pair of aligned stationary carbon nanostructures. In this embodiment, the sensor may also include a thin film dielectric layer. The graphene sheets forming the pair of aligned stationary carbon nanostructures are coplanar, residing in a first plane. The graphene sheet forming the moveable carbon nanostructure resides in a second plane parallel to the first plane. The thin film dielectric layer is interposed between said first and second planes. The moveable carbon nanostructure increasingly engages one of the pair of aligned stationary carbon nanostructures while simultaneously decreasingly engaging the other of one of the pair of aligned stationary carbon nanostructures when the moveable carbon nanostructure moves with respect to the pair of aligned stationary carbon nanostructures. 
     A nanotube displacement sensor is disclosed that includes a first stationary carbon nanostructure. It also includes a moving carbon nanostructure. The moving carbon nanostructure partially engages the first stationary carbon nanostructure throughout a range of motion. Circuitry applies an excitation voltage across the first stationary carbon nanostructure and the moving carbon nanostructure to generate an output voltage proportional to the displacement of the moving carbon nanostructure with respect to the first stationary carbon nanostructure throughout the range of motion. The first stationary carbon nanostructure is a carbon nanotube and the moving carbon nanostructure is a carbon nanotube in one embodiment. The first stationary carbon nanostructure is a sheet of graphene and the moving carbon nanostructure is a sheet of graphene in another embodiment. 
     Further aspects of the invention will become apparent as the following description proceeds and the features of novelty which characterize this invention are pointed out with particularity in the claims annexed to and forming a part of this specification. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The novel features that are considered characteristic of the invention are set forth with particularity in the appended claims. The invention itself; however, both as to its structure and operation together with the additional objects and advantages thereof are best understood through the following description of the preferred embodiment of the present invention when read in conjunction with the accompanying drawings, wherein: 
         FIG. 1  shows the carbon nanotube coordinate system for determining which carbon nanotubes are armchair, zigzag, or chiral; 
         FIG. 2  shows diagrams of armchair, zigzag, and chiral carbon nanotubes. 
         FIG. 3  shows which carbon nanotubes are metallic, narrow bandgap, and moderate semiconductors; 
         FIG. 4  shows two views of a DWCNT linear-differential-displacement sensor, where the larger diameter nanotube slides exterior to two smaller diameter nanotubes; 
         FIG. 5  shows two views of a DWCNT linear-differential-displacement sensor, where the smaller diameter nanotube slides interior to two larger diameter nanotubes; 
         FIG. 6  depicts auxiliary DC electrical circuitry used to convert the physical displacement of sliding nanotube into an electronic signal; 
         FIG. 7  depicts auxiliary AC electrical circuitry used to convert the physical displacement of sliding nanotube into an electronic signal; 
         FIG. 8  depicts amplification and signal conditioning of electronic voltage signals from  FIGS. 6 and 7 ; 
         FIG. 9  depicts a graphene sheet; 
         FIG. 10  depicts a graphene linear-differential-displacement sensor; 
         FIG. 11  depicts auxiliary AC electrical circuitry used to convert the physical displacement of sliding graphene sheet into an electronic signal; 
         FIG. 12  depicts a graphene rotational-differential-displacement sensor; and 
         FIG. 13  depicts auxiliary AC electrical circuitry used to convert the physical rotation of sliding graphene sheet into an electronic signal. 
     
    
    
     DETAILED DESCRIPTION 
     While the invention has been shown and described with reference to a particular embodiment thereof, it will be understood to those skilled in the art, that various changes in form and details may be made therein without departing from the spirit and scope of the invention. 
     Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure.  FIG. 1  shows the shows the carbon nanotube coordinate system  100  for determining which carbon nanotubes are armchair, zigzag, or chiral. Understanding  FIG. 1  is enhanced by simultaneously viewing nanotubes  200  in  FIG. 2 , which show armchair  202 , zigzag  204 , and chiral  206  nanotubes. In  FIG. 1 , unit vectors a 1    110  and a 2    112  are defined. A vector describing the end of the nanotube is na 1 +ma 2 , where n denotes multiples of unit vector a 1  and m denotes multiples of unit vector a 2 . Armchair nanotube  102 ,  202  is where n=m, as the end of the armchair nanotube is a linear combination of equal numbers of unit vectors a 1    110  and a 2    112 , hence the general form of an armchair nanotube is (n,n) or na 1 +na 2 . Zigzag nanotube  104 / 204  has no a 2    112  unit vectors used to describe the end of the nanotube, hence the general form of a zigzag nanotube is (n,0) or na 1 . Chiral nanotubes have an unequal number of unit vectors a 1    110  and a 2    112  used to describe the end of the carbon nanotube, na 1 +ma 2 . In  FIG. 1 , the chiral pattern  106  shown is (5,2) or C h =na 1 +ma 2 =5a 1 +2a 2 . Another way of determining which nanotubes are armchair, zigzag, or chiral is that armchair nanotubes  202  have two opposing facets of each carbon hexagon which are perpendicular to longitudinal axis  208 ; while zigzag nanotubes  204  have two opposing facets of each carbon hexagon which are parallel to longitudinal axis  208 ; and the carbon hexagons in chiral nanotubes  206  form a spiral pattern and have no facets that are either perpendicular or parallel to longitudinal axis  208 . 
     Because of the symmetry and unique electronic structure of graphene, the structure of a nanotube strongly affects its electrical properties. The chemical bonding of carbon nanotubes is composed entirely of sp 2  bonds, similar to those of graphite. As shown in Table  300 ,  FIG. 3 , for a given carbon nanotube in which n=m have electrons in their conduction bands at room temperature, conduct electricity very well, and are called metallic nanotubes. Carbon nanotubes with n−m being a nonzero multiple of 3 are semiconducting with a narrow bandgap. All other structures produce nanotubes that are true semiconductors, with a band gap typically between 0.5 and 3.5 electron-Volts. Thus all armchair (n=m) carbon nanotubes are metallic, and chiral carbon nanotubes (6,4), (9,1), etc. where n−m is not a multiple of 3 are moderately semiconducting. 
       FIG. 4  shows two views of a DWCNT differential-displacement sensor. The left view shows conductive end plates  411  and  415 , smaller diameter fixed nanotubes  412  and  414 , and larger diameter sliding nanotube  413 , where nanotubes  412 ,  413 , and  414  are drawn to show carbon atoms. Smaller diameter fixed nanotubes  412  and  414  both have the same outer diameter. The inner diameter of nanotube  413  is larger than the outer diameter of smaller diameter fixed nanotubes  412  and  414 . The right view is a block-diagram form of the left view, showing conductive end plates  421  and  425 , smaller diameter fixed nanotubes  422  and  424 , and larger diameter sliding nanotube  423 . Larger diameter nanotube  413 / 423  slides in the +/−ΔX direction, which is along the longitudinal axis of nanotubes  412 / 422 ,  413 / 423 , and  414 / 424 . Larger diameter carbon nanotube  413 / 123  slides exterior to two smaller diameter carbon nanotubes,  412 / 422  and  414 / 424 . Carbon nanotubes  412 ,  413 , and  414  are coaxial, as are carbon nanotubes  423 ,  424 , and  425 . 
     Carbon nanotube  412 / 422  is fixedly and electrically attached on one end to conducting plate  411 / 421 . Similarly, carbon nanotube  414 / 424  is fixedly attached on one end to conducting plate  415 / 425 . As nanotube  413 / 423  slides a displacement +ΔX longitudinally outside of nanotubes  412 / 422  and  414 / 424 , the exterior of nanotube  412 / 422  is covered a +ΔX and the exterior of nanotube  414 / 424  is uncovered a −ΔX. Thus a differential change of 2ΔX is physically created. 
     Similar to  FIG. 4 ,  FIG. 5  shows two views of a DWCNT differential-displacement sensor. The left view shows conductive end plates  511  and  515 , larger diameter fixed nanotubes  512  and  514 , and smaller diameter sliding nanotube  513 , where nanotubes  512 ,  513 , and  514  are drawn to show carbon atoms. Larger diameter fixed nanotubes  512  and  514  both have the same inner diameter. Smaller diameter sliding nanotube  513  has an outer diameter smaller than the inner diameter of larger diameter fixed nanotubes  512  and  514 . The right view is a block-diagram form, showing conductive end plates  521  and  525 , larger diameter fixed nanotubes  522  and  524 , and smaller diameter sliding nanotube  523 . Smaller diameter nanotube  513 / 523  slides in the +/−ΔX direction, which is along the longitudinal axis of nanotubes  512 / 522 ,  513 / 523 , and  514 / 524 . Smaller diameter carbon nanotube  513 / 523  slides interior to two larger diameter carbon nanotubes,  512 / 522  and  514 / 524 . Carbon nanotubes  512 ,  513 , and  514  are coaxial, as are carbon nanotubes  523 ,  524 , and  525 . 
     Carbon nanotube  512 / 522  is fixedly attached on one end to conducting plate  511 / 521 . Similarly, carbon nanotube  514 / 524  is fixedly attached on one end to conducting plate  515 / 525 . As nanotube  513 / 523  slides a displacement +ΔX longitudinally inside of nanotubes  512 / 522  and  514 / 524 , the interior of nanotube  512 / 522  is covered a +ΔX and the interior of nanotube  514 / 524  is uncovered a −ΔX. Thus a differential change of 2ΔX is physically created in  FIG. 5  as it was in  FIG. 4 . 
     In order that carbon nanotubes  412 / 422 ,  413 / 423 ,  414 / 424 ,  512 / 522 ,  513 / 523 , and  514 / 524  have the electrical property of being metallic, per Table  300  of  FIG. 3 , n=m. Thus, carbon nanotubes  412 / 422 ,  413 / 423 ,  414 / 424 ,  512 / 522 ,  513 / 523 , and  514 / 524  are of the armchair variety. 
       FIG. 6  depicts auxiliary DC electrical circuitry used to convert the physical displacement ΔX of sliding nanotube  423  into an electronic signal Vout  610 . Direct current (DC) voltage Vin  602  is electrically connected to conductive end plates  421  and  425 . A first end of resistor  604  is electrically connected to conductive end plate  421  and a first end of resistor  608  is electrically connected to conductive end plate  425 . A second end of resistor  604  is electrically connected a second end of resistor  608 , and that becomes the first of two points from which Vout  610  is measured. A first end of nanowire  612  is electrically connected to sliding nanotube  423 , and a second end of nanowire  612  becomes the second of two points from which Vout  610  is measured. In another embodiment, Vin  602  is an alternating voltage. This alternating voltage may be a sine-wave at a specific frequency, to allow filtering by filter  804 ,  FIG. 8 , of Vout  610  at that specific frequency to rule out as much noise as possible to improve the signal-to-noise ratio. 
     Resistor  608  is a variable resistor and is used to reduce Vout to near-zero volts when ΔX equals zero. This way, amplification of Vout shown in  FIG. 5  does not include a large DC offset voltage, the amplification of which could produce a very low signal-to-noise ratio. Variable resistor  608  may be an analog variable resistor such as a precision 10-turn potentiometer, or a digitally programmable resistor. Also shown in  FIG. 6  is optional calibration resistor  606 , which is removably connected across variable resistor  608 . Calibration resistor  606  is used to simulate a specific displacement ΔX, which can come in very handy for understanding Vout. 
     As nanotube  423  moves in the +ΔX direction, a change in resistance −ΔR between nanotubes  422  and  423  is generated. At the same time, a change in resistance +ΔR between nanotubes  424  and  423  is generated. The ratio of Vout/Vin is then proportional to −ΔR−(+ΔR) or −2ΔR. If nanotube  423  moves in the −ΔX direction, the ratio of Vout/Vin is then proportional to +ΔR−(−ΔR) or +2ΔR. Thus,  FIG. 6  registers twice the change in resistance from using one stationary nanotube and one sliding nanotube as a displacement sensor. 
       FIG. 7  depicts auxiliary AC electrical circuitry used to convert the physical displacement ΔX of sliding nanotube  423  into an electronic signal Vout  610 . Alternating current (AC) voltage Vin  702  is electrically connected to conductive end plates  421  and  425 . A first end of capacitor  704  is electrically connected to conductive end plate  421  and a first end of capacitor  708  is electrically connected to conductive end plate  425 . A second end of capacitor  704  is electrically connected a second end of capacitor  708 , and that becomes the first of two points from which Vout is measured. A first end of nanowire  612  is electrically connected to sliding nanotube  423 , and a second end of nanowire  612  becomes the second of two points from which Vout is measured. 
     Variable capacitor  708  may be an analog variable capacitor, or a digitally programmable capacitor. Also shown in  FIG. 7  is optional calibration capacitor  706 , which is removably connected across variable capacitor  708 . Calibration resistor  606  is used to simulate a specific displacement ΔX, which can come in very handy for understanding Vout. 
     Auxiliary semiconducting nanotube  712  is a dielectric cylinder that physically and electrically separates metallic nanotubes  422 ,  423 , and  424 . Per Table  300 ,  FIG. 3 , auxiliary semiconducting nanotube  612  is of the variety where n−m is neither zero nor a multiple of 3. Thus, auxiliary semiconducting nanotube  612  is not an armchair nanotube (n=m, giving n−m=0), not a zigzag (6,0) nanotube as n is a multiple of 3, and not a (5,2) chiral nanotube  106  of  FIG. 1 , as n−m is a multiple of 3. Auxiliary semiconducting nanotube  612  may be a zigzag nanotube where n is not a multiple of 3 or a chiral nanotube where n−m is not a multiple of 3, such as (6,4) or (9,1). 
     As nanotube  423  moves in the +ΔX direction, a change in capacitance +ΔC between nanotubes  422  and  423  is generated. At the same time, a change in capacitance −ΔC between nanotubes  424  and  423  is generated. The ratio of Vout/Vin is then proportional to +ΔC−(−ΔC) or 2ΔC. If nanotube  423  moves in the −ΔX direction, the ratio of Vout/Vin is then proportional to −ΔC−(−ΔC) or −2ΔC. Thus,  FIG. 7  registers twice the change in capacitance from using one stationary nanotube and one sliding nanotube as a displacement sensor. 
       FIG. 8  shows that Vout  610  enters differential amplifier  802 , to prevent signal-to-noise degrading ground-loops, and to subtract common mode noise to improve the signal-to-noise ratio. The output of differential amplifier  802  goes into frequency filter  804 . Even with differential amplifier  802 , there is 60 Hz noise from lighting, power supplies, etc, which clouds the desired measurement. Filter  804  may be set to filter out 60 Hz and its harmonics. Filter  804  may be a low pass filter, a notch filter centered at 60 Hz, or a Butterworth filter. Filter  804  may be a narrow bandpass filter to allow only the frequency of Vout  610  that matches the excitation frequency of Vin  702  to pass, thus filtering out unwanted harmonics. The output of filter  804  goes into analog-to-digital converter  806  and then into computer  808  for subsequent storage and analysis. 
       FIG. 9  shows graphene sheet  901 . There are two orientations, armchair and zigzag. Graphene sheet  901  is used in  FIGS. 10-13 . 
       FIG. 10  shows a block-diagram of a graphene linear-differential-displacement sensor  1000 , showing conductive end plates  1021  and  1025 , graphene sheets  1022  and  1024 , and graphene sheet  1023 . Graphene sheet  1023  slides in the +/−ΔX direction. Graphene sheet  1022  is fixedly and electrically attached on one end to conducting plate  1021 . Similarly, graphene sheet  1024  is fixedly attached on one end to conducting plate  1025 . As graphene sheet  1023  slides a displacement +4X longitudinally relative to graphene sheets  1022  and  1024 , graphene sheet  1022  is covered a +4X and graphene sheet  1024  is uncovered a −ΔX. Thus a differential change of 2ΔX is physically created. The side view of  FIG. 10  shows dielectric film  1028  interposed between graphene sheets  1022  and  1024 , and graphene sheets  1023 . This dielectric film  1028  is used when graphene linear-differential-displacement sensor  1000  is used in a capacitive mode, as shown in  FIG. 11 . 
       FIG. 11  depicts auxiliary AC electrical circuitry used to convert the physical displacement ΔX of sliding graphene sheet  1023  into an electronic signal Vout  610 . Alternating current (AC) voltage Vin  702  is electrically connected to conductive end plates  1021  and  1025 . A first end of capacitor  704  is electrically connected to conductive end plate  1021  and a first end of capacitor  708  is electrically connected to conductive end plate  1025 . A second end of capacitor  704  is electrically connected a second end of capacitor  708 , and that becomes the first of two points from which Vout is measured. A first end of nanowire  612  is electrically connected to sliding graphene sheet  1023 , and a second end of nanowire  612  becomes the second of two points from which Vout is measured. 
       FIG. 12  shows top and side views of graphene rotational-differential-displacement sensor  1200 . Graphene rotational-differential-displacement sensor comprises graphene semicircles  1222  and  1224 , and graphene semicircle  1223 . Graphene semicircle  1223  may rotate about optional rotational shaft  1235 . As graphene semicircle  1223  rotates, it uncovers graphene semicircle  1224 , and simultaneously covers graphene semicircle  1222 , to produce a differential change of 2ΔΘ. The side view of  FIG. 12  shows dielectric film  1228  interposed between graphene semicircles  1222  and  1224 , and graphene semicircle  1223 . This dielectric film  1228  is used when graphene rotational-differential-displacement sensor  1200  is used in a capacitive mode, as shown in  FIG. 13 . 
       FIG. 13  depicts auxiliary AC electrical circuitry used to convert the physical displacement ΔΘ of rotating graphene sheet  1223  into an electronic signal Vout  610 . Alternating current (AC) voltage Vin  702  is electrically connected to graphene sheets  1222  and  1224 . A first end of capacitor  704  is electrically connected to graphene sheet  1222  and a first end of capacitor  708  is electrically connected to graphene sheet  1224 . A second end of capacitor  704  is electrically connected a second end of capacitor  708 , and that becomes the first of two points from which Vout is measured. A first end of nanowire  612  is electrically connected to rotating graphene sheet  1223 , and a second end of nanowire  612  becomes the second of two points from which Vout is measured. 
     In an alternate embodiment, graphene sheets  1022 ,  1023 , and  1024  may themselves be rectangular, square, circular, triangular, pentagonal, or hexagonal. In an alternate embodiment, graphene sheets  1222 ,  1223 , and  1224  may themselves be square, rectangular, triangular, pentagonal, or hexagonal. Graphene sheets  1022 - 1024  and  1222 - 1224  may range from larger-sized sheets of graphene, the size that might be used to be a protective layer for an optical disk or display screen on a smart phone, down to smaller quantum-dot-sized sheets of graphene. 
     While the invention has been shown and described with reference to a particular embodiment thereof, it will be understood to those skilled in the art, that various changes in form and details may be made therein without departing from the spirit and scope of the invention.