NanoparticleA nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At the lowest range, metal particles smaller than 1 nm are usually called atom clusters instead.
Platinum nanoparticlePlatinum nanoparticles are usually in the form of a suspension or colloid of nanoparticles of platinum in a fluid, usually water. A colloid is technically defined as a stable dispersion of particles in a fluid medium (liquid or gas). Spherical platinum nanoparticles can be made with sizes between about 2 and 100 nanometres (nm), depending on reaction conditions. Platinum nanoparticles are suspended in the colloidal solution of brownish-red or black color. Nanoparticles come in wide variety of shapes including spheres, rods, cubes, and tetrahedra.
Silver nanoparticleSilver nanoparticles are nanoparticles of silver of between 1 nm and 100 nm in size. While frequently described as being 'silver' some are composed of a large percentage of silver oxide due to their large ratio of surface to bulk silver atoms. Numerous shapes of nanoparticles can be constructed depending on the application at hand. Commonly used silver nanoparticles are spherical, but diamond, octagonal, and thin sheets are also common. Their extremely large surface area permits the coordination of a vast number of ligands.
Nanoparticle–biomolecule conjugateA nanoparticle–biomolecule conjugate is a nanoparticle with biomolecules attached to its surface. Nanoparticles are minuscule particles, typically measured in nanometers (nm), that are used in nanobiotechnology to explore the functions of biomolecules. Properties of the ultrafine particles are characterized by the components on their surfaces more so than larger structures, such as cells, due to large surface area-to-volume ratios. Large surface area-to-volume-ratios of nanoparticles optimize the potential for interactions with biomolecules.
DerivativeIn mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Generalizations of the derivativeIn mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, geometry, etc. The Fréchet derivative defines the derivative for general normed vector spaces . Briefly, a function , an open subset of , is called Fréchet differentiable at if there exists a bounded linear operator such that Functions are defined as being differentiable in some open neighbourhood of , rather than at individual points, as not doing so tends to lead to many pathological counterexamples.
Fréchet derivativeIn mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued function of multiple real variables, and to define the functional derivative used widely in the calculus of variations. Generally, it extends the idea of the derivative from real-valued functions of one real variable to functions on normed spaces.
Logarithmic derivativeIn mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f. When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f.
Nanomaterial-based catalystNanomaterial-based catalysts are usually heterogeneous catalysts broken up into metal nanoparticles in order to enhance the catalytic process. Metal nanoparticles have high surface area, which can increase catalytic activity. Nanoparticle catalysts can be easily separated and recycled. They are typically used under mild conditions to prevent decomposition of the nanoparticles. Functionalized metal nanoparticles are more stable toward solvents compared to non-functionalized metal nanoparticles.
Gateaux derivativeIn mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René Gateaux, a French mathematician who died at age 25 in World War I, it is defined for functions between locally convex topological vector spaces such as Banach spaces. Like the Fréchet derivative on a Banach space, the Gateaux differential is often used to formalize the functional derivative commonly used in the calculus of variations and physics.
Partial derivativeIn mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function with respect to the variable is variously denoted by It can be thought of as the rate of change of the function in the -direction.
Directional derivativeA directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given point. The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. The directional derivative of a scalar function f with respect to a vector v at a point (e.g.
Energy consumptionEnergy consumption is the amount of energy used. In the body, energy consumption is part of energy homeostasis. It derived from food energy. Energy consumption in the body is a product of the basal metabolic rate and the physical activity level. The physical activity level are defined for a non-pregnant, non-lactating adult as that person's total energy expenditure (TEE) in a 24-hour period, divided by his or her basal metabolic rate (BMR): Topics related to energy consumption in a demographic sense are: Wo
Allotropes of oxygenThere are several known allotropes of oxygen. The most familiar is molecular oxygen (), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (). Others are: Atomic oxygen (), a free radical. Singlet oxygen (O2*), one of two metastable states of molecular oxygen. Tetraoxygen (), another metastable form. Solid oxygen, existing in six variously colored phases, of which one is octaoxygen (,red oxygen) and another one metallic (ζ-oxygen).
Solid oxygenSolid oxygen forms at normal atmospheric pressure at a temperature below 54.36 K (−218.79 °C, −361.82 °F). Solid oxygen O2, like liquid oxygen, is a clear substance with a light sky-blue color caused by absorption in the red part of the visible light spectrum. Oxygen molecules have attracted attention because of the relationship between the molecular magnetization and crystal structures, electronic structures, and superconductivity. Oxygen is the only simple diatomic molecule (and one of the few molecules in general) to carry a magnetic moment.
Reaction progress kinetic analysisIn chemistry, reaction progress kinetic analysis (RPKA) is a subset of a broad range of kinetic techniques utilized to determine the rate laws of chemical reactions and to aid in elucidation of reaction mechanisms. While the concepts guiding reaction progress kinetic analysis are not new, the process was formalized by Professor Donna Blackmond (currently at Scripps Research Institute) in the late 1990s and has since seen increasingly widespread use.
