GrapheneGraphene (ˈgræfiːn) is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds. Each atom in a graphene sheet is connected to its three nearest neighbors by σ-bonds and a delocalised π-bond, which contributes to a valence band that extends over the whole sheet.
Surface plasmon resonanceSurface plasmon resonance (SPR) is a phenomenon that occurs where electrons in a thin metal sheet become excited by light that is directed to the sheet with a particular angle of incidence, and then travel parallel to the sheet. Assuming a constant light source wavelength and that the metal sheet is thin, the angle of incidence that triggers SPR is related to the refractive index of the material and even a small change in the refractive index will cause SPR to not be observed.
Potential applications of graphenePotential graphene applications include lightweight, thin, and flexible electric/photonics circuits, solar cells, and various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials. In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample the area of a cross section of a human hair costing more than 1,000asofApril2008(about100,000,000/cm2). Since then, exfoliation procedures have been scaled up, and now companies sell graphene in large quantities. Surface plasmonSurface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such as a metal sheet in air). SPs have lower energy than bulk (or volume) plasmons which quantise the longitudinal electron oscillations about positive ion cores within the bulk of an electron gas (or plasma). The charge motion in a surface plasmon always creates electromagnetic fields outside (as well as inside) the metal.
Localized surface plasmonA localized surface plasmon (LSP) is the result of the confinement of a surface plasmon in a nanoparticle of size comparable to or smaller than the wavelength of light used to excite the plasmon. When a small spherical metallic nanoparticle is irradiated by light, the oscillating electric field causes the conduction electrons to oscillate coherently. When the electron cloud is displaced relative to its original position, a restoring force arises from Coulombic attraction between electrons and nuclei.
Graphene nanoribbonGraphene nanoribbons (GNRs, also called nano-graphene ribbons or nano-graphite ribbons) are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine the edge and nanoscale size effect in graphene. Large quantities of width-controlled GNRs can be produced via graphite nanotomy, where applying a sharp diamond knife on graphite produces graphite nanoblocks, which can then be exfoliated to produce GNRs as shown by Vikas Berry.
Multi-parametric surface plasmon resonanceMulti-parametric surface plasmon resonance (MP-SPR) is based on surface plasmon resonance (SPR), an established real-time label-free method for biomolecular interaction analysis, but it uses a different optical setup, a goniometric SPR configuration. While MP-SPR provides same kinetic information as SPR (equilibrium constant, dissociation constant, association constant), it provides also structural information (refractive index, layer thickness). Hence, MP-SPR measures both surface interactions and nanolayer properties.
Surface plasmon polaritonSurface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal ("surface plasmon") and electromagnetic waves in the air or dielectric ("polariton"). They are a type of surface wave, guided along the interface in much the same way that light can be guided by an optical fiber.
PlasmonIn physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quantization of plasma oscillations, just like phonons are quantizations of mechanical vibrations. Thus, plasmons are collective (a discrete number) oscillations of the free electron gas density. For example, at optical frequencies, plasmons can couple with a photon to create another quasiparticle called a plasmon polariton.
Single-layer materialsIn materials science, the term single-layer materials or 2D materials refers to crystalline solids consisting of a single layer of atoms. These materials are promising for some applications but remain the focus of research. Single-layer materials derived from single elements generally carry the -ene suffix in their names, e.g. graphene. Single-layer materials that are compounds of two or more elements have -ane or -ide suffixes. 2D materials can generally be categorized as either 2D allotropes of various elements or as compounds (consisting of two or more covalently bonding elements).
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Bilayer grapheneBilayer graphene is a material consisting of two layers of graphene. One of the first reports of bilayer graphene was in the seminal 2004 Science paper by Geim and colleagues, in which they described devices "which contained just one, two, or three atomic layers" Bilayer graphene can exist in the AB, or Bernal-stacked form, where half of the atoms lie directly over the center of a hexagon in the lower graphene sheet, and half of the atoms lie over an atom, or, less commonly, in the AA form, in which the layers are exactly aligned.
Carbon nanotubeA carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometer range (nanoscale). They are one of the allotropes of carbon. Single-walled carbon nanotubes (SWCNTs) have diameters around 0.5–2.0 nanometers, about 100,000 times smaller than the width of a human hair. They can be idealized as cutouts from a two-dimensional graphene sheet rolled up to form a hollow cylinder. Multi-walled carbon nanotubes (MWCNTs) consist of nested single-wall carbon nanotubes in a nested, tube-in-tube structure.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
AbsorbanceAbsorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)". Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample". The term is used in many technical areas to quantify the results of an experimental measurement. While the term has its origin in quantifying the absorption of light, it is often entangled with quantification of light which is “lost” to a detector system through other mechanisms.
TransmittanceTransmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field. Internal transmittance refers to energy loss by absorption, whereas (total) transmittance is that due to absorption, scattering, reflection, etc.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Runge–Kutta methodsIn numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".
