Cylindrical macromolecule and photometer and magnetometer using the same

• US 5,933,791 A
• Filed: 06/25/1996
• Issued: 08/03/1999
• Est. Priority Date: 02/06/1992
• Status: Expired due to Term

• Current Assignee: NEC Corporation
• Original Assignee: NEC Corporation
• Inventors: Hamada, Noriaki, Ohta, Kuniichi
• Primary Examiner(s): KEMPER, MELANIE A
• Application Number:
  US08/673,614
• Time in Patent Office: 1,134 Days
• Field of Search: 364/496, 364/578, 428/408, 423/445 B, 702/30, 702/32
• US Class Current: 702/30
• CPC Class Codes: B82Y 30/00 Nanotechnology for materials or surface science, e.g. nanocomposites
• CPC Class Codes: B82Y 40/00 Manufacture or treatment of nanostructures
• CPC Class Codes: C01B 32/15 Nano-sized carbon materials
• CPC Class Codes: Y10S 977/88 with arrangement, process, or apparatus for testing

Abstract

In a concentric cylinder macromolecule represented by a combination of B(2,1)n (n=1, 2, . . . ), each layer thereof has a conductivity of metal and hence there is obtained a concentric cylinder having a high conductivity. In graphite, the layers are bonded with each other by a weak van der Waals force and a two-dimensional band structure can be assumed. In a multi-layer cylinder, since the number of hexagons in the radial direction varies between the layers, the layers are much more independent of each other. There are accordingly implemented a semiconductor having a narrow band gap and a semiconductor having a relatively wide band gap; consequently, the macromolecule can be broadly adopted for various functional devices.

Claims

1. A property estimation method of a cylindrical nanotube, comprising the steps of:

confirming that the nanotube has a structure of A(n₁, n₂) <

(add if necessary besides the description in the specification)!, where A(n₁, n₂) is a notation representative of a cylindrical structure geometrically obtainable from a planar graphite layer consisting of a repeated hexagon having a carbon atom at each vertex thereof and a covalent bond along each side thereof, by rolling up the graphite layer so that an identified hexagon by a position vector n₁ a+n₂ b with respect to a reference hexagon in the graphite layer is superimposed on the reference hexagon in the cylindrical structure, where a is a unit displacement vector of the reference hexagon in a perpendicular direction to an arbitrary side of the reference hexagon, b is a unit displacement vector of the reference hexagon in a perpendicular direction to a second side from the arbitrary side of the reference hexagon, and n₁ and n₂ are integers >

!;

confirming that the structure meets a condition of n₁ -2n₂ =0; and

estimating that the nanotube has a metallic property.

2. A property estimation method of a cylindrical nanotube, comprising the steps of:

confirming that the nanotube has a structure of A(n₁, n₂) <

(add if necessary besides the description in the specification)!, where A(n₁, n₂) is a notation representative of a cylindrical structure geometrically obtainable from a planar graphite layer consisting of a repeated hexagon having a carbon atom at each vertex thereof and a covalent bond along each side thereof, by rolling up the graphite layer so that an identified hexagon by a position vector n₁ a+n₂ b with respect to a reference hexagon in the graphite layer is superimposed on the reference hexagon in the cylindrical structure, where a is a unit displacement vector of the reference hexagon in a perpendicular direction to an arbitrary side of the reference hexagon, b is a unit displacement vector of the reference hexagon in a perpendicular direction to a second side from the arbitrary side of the reference hexagon, and n₁ and n₂ are integers >

!;

confirming that the structure meets a condition of n₁ -2n₂ =3 l(l=1, 2, 3, . . . ); and

estimating that the nanotube has a band structure with a narrow band gap.

3. A property estimation method of a cylindrical nanotube, comprising the steps of:

confirming that the nanotube has a structure of A(n₁, n₂) <

(add if necessary besides the description in the specification)!, where A(n₁, n₂) is a notation representative of a cylindrical structure geometrically obtainable from a planar graphite layer consisting of a repeated hexagon having a carbon atom at each vertex thereof and a covalent bond along each side thereof, by rolling up the graphite layer so that an identified hexagon by a position vector n₁ a+n₂ b with respect to a reference hexagon in the graphite layer is superimposed on the reference hexagon in the cylindrical structure, where a is a unit displacement vector of the reference hexagon in a perpendicular direction to an arbitrary side of the reference hexagon, b is a unit displacement vector of the reference hexagon in a perpendicular direction to a second side from the arbitrary side of the reference hexagon, and n₁ and n₂ are integers >

!; and

confirming that the structure meets a condition of n₁ -2n2 ≠

3l (l=0, 1, 2, . . . ); and

estimating that the nanotube has a band structure with a moderate band gap.

4. A property estimation method of a cylindrical nanotube consisting of a plurality of coaxial nanotubes, comprising:

a first step of confirming that each coaxial nanotube has a metallic band structure when it is single-layered; and

a second step of estimating that each coaxial nanotube has a metallic band structure in the cylindrical nanotube.

5. The property estimation method as claimed in claim 4, wherein the first step comprises the steps of:

confirming that the cylindrical nanotube has a structure of B(l₁, l₂)n, where n is a set of integers, <

(add if necessary besides the description in the specification! l₁ and l₂ are relatively prime integers and, letting p be an arbitrary element of the set n, B(l₁, l₂)n is a notation representative of a nested structure of a corresponding number of coaxial cylindrical structures A(l₁ p, l₂ p) to the number of elements of the set n, where letting l₁ p=n₁ and l₂ p=n₂, A(n₁, n₂) is a notation representative of a cylindrical structure geometrically obtainable from a planar graphite layer consisting of a repeated hexagon having a carbon atom at each vertex thereof and a covalent bond along each side thereof, by rolling up the graphite layer so that an identified hexagon by a position vector n₁ a+n₂ b with respect to a reference hexagon in the graphite layer is superimposed on the reference hexagon in the cylindrical structure, where a is a unit displacement vector of the reference hexagon in a perpendicular direction to an arbitrary side of the reference hexagon, b is a unit displacement vector of the reference hexagon in a perpendicular direction to a second side from the arbitrary side of the reference hexagon, and n₁ and n₂ are integers >

!; and

confirming that <

letting p be an arbitrary element of the set n (this phrase is unnecessary, if the foregoing phrase is inserted)>

! the structure meets a condition of l₁ p-2l₂ p=0 for each p.

6. The property estimation method as claimed in claim 5, further comprising the steps of:

confirming that the structure meets a combined condition of l₁ =2 and l₂ =1, the set n comprises a subset of a sequence of increasing integers with a variable difference between 4 and 6, both inclusive; and

estimating that a pair of adjacent ones of the coaxial cylindrical structures have a radius difference therebetween substantially equivalent to an interlayer distance of a multi-layered graphite.

7. The property estimation method as claimed in claim 6, wherein:

the subset comprises q+rm, where r is 5, q is an integer between 1 and r, both inclusive, and m is a set of continuous integers.

8. A property estimation method of a cylindrical nanotube consisting of a plurality of coaxial nanotubes, comprising:

a first step of confirming that each coaxial nanotube has a band structure with a narrow band gap when it is single-layered; and

a second step of estimating that each coaxial nanotube has a band structure with a narrow band gap in the cylindrical nanotube.

9. The property estimation method as claimed in claim 8, wherein the first step comprises the steps of:

confirming that the cylindrical nanotube has a structure of B(l₁, l₂)n, where n is a set of integers, <

(add if necessary besides the description in the specification! l₁ and l₂ are relatively prime integers and, letting p be an arbitrary element of the set n, B(l₁, l₂)n is a notation representative of a nested structure of a corresponding number of coaxial cylindrical structures A(l₁ p, l₂ p) to the number of elements of the set n, where letting l₁ p=n₁ and l₂ p=n₂, A(n₁, n₂) is a notation representative of a cylindrical structure geometrically obtainable from a planar graphite layer consisting of a repeated hexagon having a carbon atom at each vertex thereof and a covalent bond along each side thereof, by rolling up the graphite layer so that an identified hexagon by a position vector n₁ a+n₂ b with respect to a reference hexagon in the graphite layer is superimposed on the reference hexagon in the cylindrical structure, where a is a unit displacement vector of the reference hexagon in a perpendicular direction to an arbitrary side of the reference hexagon, b is a unit displacement vector of the reference hexagon in a perpendicular direction to a second side from the arbitrary side of the reference hexagon, and n₁ and n₂ are integers >

!; and

confirming that <

letting p be an arbitrary element of the set n (this phrase is unnecessary, if the foregoing phrase is inserted)>

! the structure meets a condition of l₁ p-2l₂ p=3l (l=1, 2, 3, . . . ) for each p.

10. The property estimation method as claimed in claim 9, further comprising the steps of:

confirming that the structure meets a combined condition of l₁ =1, l₂ =0, and n=3m, where m is a sequence of increasing integers with a difference of 3; and

estimating that a pair of adjacent ones of the coaxial cylindrical structures have a radius difference therebetween substantially equivalent to an interlayer distance of a multi-layered graphite.

11. A property estimation method of a cylindrical nanotube consisting of a plurality of coaxial nanotubes, comprising:

a first step of confirming that each coaxial nanotube has a band structure with a moderate band gap when it is single-layered; and

a second step of estimating that each coaxial nanotube has a band structure with a moderate band gap in the cylindrical nanotube.

12. The property estimation method as claimed in claim 11, wherein the first step comprises the steps of:

confirming that the cylindrical nanotube has a structure of B(l₁, l₂)n, where n is a set of integers, <

(add if necessary besides the description in the specification! l₁ and l₂ are relatively prime integers and, letting p be an arbitrary element of the set n, B(l₁, l₂)n is a notation representative of a nested structure of a corresponding number of coaxial cylindrical structures A(l₁ p, l₂ p) to the number of elements of the set n, where letting l₁ p=n₁ and l₂ p=n₂, A(n₁, n₂) is a notation representative of a cylindrical structure geometrically obtainable from a planar graphite layer consisting of a repeated hexagon having a carbon atom at each vertex thereof and a covalent bond along each side thereof, by rolling up the graphite layer so that an identified hexagon by a position vector n₁ a+n₂ b with respect to a reference hexagon in the graphite layer is superimposed on the reference hexagon in the cylindrical structure, where a is a unit displacement vector of the reference hexagon in a perpendicular direction to an arbitrary side of the reference hexagon, b is a unit displacement vector of the reference hexagon in a perpendicular direction to a second side from the arbitrary side of the reference hexagon, and n₁ and n₂ are integers >

!; and

confirming that <

letting p be an arbitrary element of the set n (this phrase is unnecessary, if the foregoing phrase is inserted)>

! the structure meets a condition of l₁ p-2l₂ p≡

/3l (l=0, 1, 2, . . . ) for each p.

13. The property estimation method as claimed in claim 12, further comprising the steps of:

confirming that the structure meets a combined condition of l₁ =1, l₂ =0, and the set n comprises a sequence of prime integers to 3;

confirming that a sequence of prime inters comprises a subset of a sequence of increasing integers with a difference of 9; and

estimating that a pair of adjacent ones of the coaxial cylindrical structures have a radius difference therebetween substantially equivalent to an interlayer distance of a multi-layered graphite.