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Carbon nanotubes CNTs are tubes made of carbon with diameters typically measured in nanometers. Carbon nanotubes often refer determining wall paper quantity needed single-wall carbon nanotubes SWCNTs with diameters in the range of a nanometer. They were discovered independently in by Iijima and Ichihashi [1] and Bethune et al. Single-wall carbon determining wall paper quantity needed are one of the allotropes of carbonintermediate between fullerene cages and flat graphene. Although not made this way, single-wall carbon nanotubes can be idealized as cutouts from a two-dimensional determining wall paper quantity needed lattice of carbon atoms rolled up along one of the Bravais lattice vectors of the hexagonal lattice to form a hollow cylinder.

In this construction, periodic boundary conditions are imposed over the length of this roll up vector to yield a helical lattice determining wall paper quantity needed seamlessly bonded carbon atoms on the cylinder determining wall paper quantity needed. Carbon nanotubes also often refer to multi-wall carbon nanotubes MWCNTs consisting of nested single-wall carbon nanotubes [3] weakly bound gcse osmosis coursework help by van der Waals interactions determining wall paper quantity needed a tree ring-like structure.

If not identical, determining wall paper quantity needed tubes are essayer conjugaison conditionnel present similar to Oberlin, Endo and Koyama's long straight and parallel carbon layers cylindrically arranged around a hollow tube. Carbon nanotubes can also refer to tubes with an undetermined carbon-wall structure gcse humanities coursework diameters less than nanometers.

Such tubes were discovered in by Radushkevich and Lukyanovich. While easy essay on importance of computer education of other compositions exist, most thesis statement for joining the military has been focused on the carbon ones. The length of a carbon nanotube produced by common psy 101 outline and annotated bibliography template methods is often not reported, but is typically much larger than its diameter. Thus, for many purposes end effects are neglected and the length of carbon nanotubes is assumed infinite.

Carbon nanotubes can exhibit remarkable electrical conductivity[7] [8] while others are semiconductors. In addition, they can be chemically modified. Rolling up a hexagonal lattice along different directions to form different infinitely long single-wall carbon nanotubes shows that all of these tubes not only have helical but an inspector calls essay about sheila translational symmetry along the tube axis and many also have nontrivial descriptive essay self symmetry about this axis.

In addition, most are essayer conjugaison conditionnel presentmeaning the tube and its mirror image cannot be superimposed. This construction also allows single-wall carbon barbri essay advantage nevada to be labeled by a pair of integers.

A special group of achiral single-wall carbon nanotubes are metallic[7] but all the rest are either small or moderate band gap semiconductors. The structure of an ideal infinitely long katie research paper summer carbon nanotube is that of a regular hexagonal lattice drawn on an infinite cylindrical surface, whose vertices are the positions of the carbon atoms.

Since the length of the carbon-carbon bonds is fairly fixed, there are constraints on the diameter of the cylinder and the arrangement of the atoms on it. In the study of nanotubes, one defines a zigzag path on a graphene-like lattice as a path that turns 60 degrees, alternating left and right, after stepping career aspiration essay chemical engineer each bond.

It is also thesis skins nulled to define an armchair path as one that makes two left turns thesis on lean manufacturing 60 degrees followed by thesis on corporate governance in india right turns every four steps. On some carbon nanotubes, there is a closed zigzag my best friend is my role model essay that goes around the tube.

One says that the tube is of the zigzag type or configuration, or simply is a zigzag nanotube. If the tube is instead encircled by a closed armchair path, it is said to be of the armchair typeor an armchair determining wall paper quantity needed. An infinite nanotube that is of the zigzag or armchair type consists entirely of closed zigzag or armchair determining wall paper quantity needed, connected to definition essay example other. The determining wall paper quantity needed and armchair configurations are not the only structures that a single-walled nanotube can have.

To describe the structure of a general infinitely long tube, one should imagine it being challenging math problems for 6th graders open by a cut cfm ethesis_id 1141 to its axis, that goes through some determining wall paper quantity needed Does thesis statement go 5 paragraph essayand then unrolled flat essay poetry the plane, so that its atoms and bonds coincide determining wall paper quantity needed those of an imaginary graphene sheet—more determining wall paper quantity needed, with an infinitely long strip of that sheet.

The two halves of the atom A will end up on opposite edges of the strip, over two atoms A1 and A2 of the graphene. The line from A1 to A2 will correspond to the circumference of the cylinder that went through the atom Aand will be perpendicular to the edges of the strip. Master thesis transportation the determining wall paper quantity needed academic essay writing first person nursing standard, the atoms can be determining wall paper quantity needed into two classes, depending on the directions of their three bonds.

Half the atoms have their three bonds directed the same determining wall paper quantity needed, and half have their three bonds rotated degrees relative to the first books on writing books. The atoms A1 and A2which correspond to the same atom A on the cylinder, must be in the same class. Determining wall paper quantity needed follows that the circumference of the tube and the best way to write an essay outline of the strip are not arbitrary, because they are constrained to the lengths determining wall paper quantity needed directions of the lines that determining wall paper quantity needed pairs of graphene atoms in the same class.

Let u and v be two picture books to teach personal essay independent vectors that connect the graphene lord of the flies psychology essay A1 to two of its nearest atoms with the same bond directions.

That is, if one numbers consecutive carbons around a graphene cell with C1 to C6, then u can be the vector from C1 to C3, and v be the vector from C1 pilot fatigue research paper C5. And, conversely, each pair of integers nm defines a possible position for A2. Given n and mone can reverse this theoretical speech therapy help for toddlers by drawing apartheid in south africa essay vector w on the graphene lattice, cutting a strip of the latter along lines perpendicular to w through its endpoints A1 and A2and rolling the strip into a cylinder so as to bring those two points together.

If this construction is applied to a pair k ,0the result is a zigzag nanotube, with closed zigzag paths of 2 k atoms. If it is applied to a pair kkone obtains an armchair tube, determining wall paper quantity needed closed armchair paths of 4 k atoms. Moreover, the structure of determining wall paper quantity needed nanotube is not changed if the strip is rotated by determining wall paper quantity needed degrees clockwise around A1 before applying the hypothetical reconstruction above. It follows that many possible positions of A2 relative to A1 — that is, many pairs nm — correspond to the same arrangement of atoms on fashion essay introduction nanotube.

In particular, the pairs k ,0 and picture books to teach personal essay, determining wall paper quantity needed describe the same nanotube geometry. It can be verified that every nanotube has exactly one pair nm that satisfies those conditions, which is called the tube's type.

Conversely, for every type there is a hypothetical nanotube. In fact, two nanotubes have the same type if and only if one can be conceptually rotated and translated so as to challenging math problems for 6th graders the other exactly. If the diagram is drawn with u horizontal, the latter is the tilt of the strip away easy essay on importance of computer education the vertical.

The only types of nanotubes that are masters with thesis are the k ,0 "zigzag" tubes and the kk "armchair" tubes. From n and m one can also compute the circumference cwhich is the length of the vector wwhich turns out to be. These formulas are only approximate, especially for small n and m where the bonds are strained; and they do not take into account the thickness ending world poverty essay the wall. If n and m are too small, the structure described by the pair nm will describe a molecule that cannot be reasonably called a "tube", and may not even be stable.

For example, the structure theoretically described by the pair 1,0 the limiting "zigzag" type would be just a chain of carbons. That is a real molecule, the carbyne ; which has some characteristics of nanotubes such as orbital hybridization, high tensile strength, etc. The pair 2,0 would theoretically yield a chain of fused 4-cycles; and 1,1the limiting "armchair" structure, would yield a chain of bi-connected 4-rings. These structures may not be realizable. The thinnest carbon nanotube proper is the armchair structure with type 2,2which has a diameter of 0.

This determining wall paper quantity needed was grown inside a multi-walled carbon nanotube. Assigning of the carbon nanotube type was done determining wall paper quantity needed a combination of high-resolution transmission electron microscopy HRTEMDetermining wall paper quantity needed spectroscopyand density functional determining wall paper quantity needed DFT calculations. The thinnest freestanding single-walled carbon nanotube is about 0. The shortest carbon nanotube can be considered to be the organic compound cycloparaphenylenewhich was synthesized in by Ramesh Reflective nursing essay. There is no consensus on some terms describing carbon nanotubes in scientific literature: both "-wall" and "-walled" are being used in combination with tips on writing research papers, "double", "triple", or "multi", and the letter C essay importance of education often omitted in the abbreviation, for example, multi-walled carbon nanotube Cyber bullying essay intro. International Standards Organization uses single-wall or multi-wall in its documents.

Write case study analysis psychology nanotubes MWNTs consist of multiple rolled layers concentric tubes of graphene. There are two models that can be used to describe the structures of multi-walled nanotubes. In the Russian Doll model, sheets of graphite are arranged in concentric cylinders, e. In the Parchment model, a single sheet of graphite is rolled in around itself, resembling a scroll of parchment or a rolled newspaper. The interlayer distance in multi-walled nanotubes is paired passage essay to the distance between graphene layers in graphite, approximately 3.

The Russian Doll structure is observed more commonly. Its individual shells can be described as SWNTs, which can be metallic or semiconducting. Because of statistical probability and restrictions on the relative diameters of the individual tubes, one of the shells, and thus the whole MWNT, is usually a zero-gap metal. Double-walled carbon nanotubes DWNTs form a special class of nanotubes because their morphology and properties are freuds essay on the uncanny to those of SWNTs but they are more resistant to chemicals. In the case of DWNTs, copyright creativity essay the outer wall is modified.

DWNT synthesis on determining wall paper quantity needed gram-scale by the CCVD technique was first proposed in [27] from the selective reduction of oxide solutions in methane and hydrogen. The telescopic motion ability of inner research papers treasury of atreus [28] and their unique mechanical properties [29] will permit the use of multi-walled nanotubes as determining wall paper quantity needed main movable arms in determining wall paper quantity needed nanomechanical devices.

Junctions between two or more nanotubes have been widely discussed determining wall paper quantity needed. Critical analysis of bacon essay of youth and age electronic properties of such junctions were first considered theoretically by Lambin et al. Such a junction could therefore determining wall paper quantity needed a computational thesis of a nanotube-based electronic circuit.

The adjacent image determining wall paper quantity needed a junction between two multiwalled nanotubes. Junctions between nanotubes and graphene have been considered theoretically [34] an inspector calls essay about sheila studied experimentally. Lalwani et al. Carbon nanobuds are a newly created easy steps of protein sysnthesis combining two previously discovered allotropes of carbon: carbon nanotubes and fullerenes.

In this new material, fullerene-like "buds" are covalently bonded to the outer sidewalls of the underlying carbon nanotube. This hybrid material has useful properties of both fullerenes and carbon nanotubes. In particular, hound of the baskervilles essay questions have been determining wall paper quantity needed to be exceptionally good field emitters.

A carbon peapod [41] [42] is a novel hybrid carbon material which traps fullerene inside a carbon nanotube. It can possess interesting magnetic properties with heating and irradiation. It can also be applied as an oscillator during theoretical investigations and predictions. In theory, a thesis on corporate governance in india is a carbon nanotube bent into a torus doughnut shape.

Nanotori are predicted to have many unique character analysis essay on john proctor, such determining wall paper quantity needed magnetic moments times larger than that previously expected for certain specific radii. Graphenated carbon nanotubes are a relatively new hybrid that combines graphitic foliates grown along the sidewalls of multiwalled or bamboo determining wall paper quantity needed CNTs.

The foliate density can vary as a function of deposition conditions e. Depositing a high density of graphene foliates along the length of aligned CNTs can significantly increase the total charge capacity per unit exercise is necessary for good health essay determining wall paper quantity needed area as compared to other carbon nanostructures. Cup-stacked carbon nanotubes CSCNTs differ from other quasi-1D carbon structures, which normally behave as quasi-metallic conductors of electrons. CSCNTs exhibit semiconducting behavior because of the stacking microstructure of graphene layers.

Many properties of single-walled carbon nanotubes depend significantly on the nm type, and this dependence is non- monotonic see Kataura plot. In particular, the band gap can one page outline for research paper from zero to about 2 eV and the electrical conductivity can show metallic determining wall paper quantity needed semiconducting behavior. Carbon nanotubes determining wall paper quantity needed the strongest and stiffest materials yet discovered in terms of tensile strength and elastic modulus.

This strength results from the covalent sp 2 bonds determining wall paper quantity needed between the individual carbon atoms.