Density functional theoryDensity-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.
Theoretical chemistryTheoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation. Theoretical chemistry unites principles and concepts common to all branches of chemistry. Within the framework of theoretical chemistry, there is a systematization of chemical laws, principles and rules, their refinement and detailing, the construction of a hierarchy.
Kinetic theory of gasesThe kinetic theory of gases is a simple, historically significant classical model of the thermodynamic behavior of gases, with which many principal concepts of thermodynamics were established. The model describes a gas as a large number of identical submicroscopic particles (atoms or molecules), all of which are in constant, rapid, random motion. Their size is assumed to be much smaller than the average distance between the particles. The particles undergo random elastic collisions between themselves and with the enclosing walls of the container.
Reaction rateThe reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second.
Collision theoryCollision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the reactant hit each other with the correct orientation, only a certain amount of collisions result in a perceptible or notable change; these successful changes are called successful collisions. The successful collisions must have enough energy, also known as activation energy, at the moment of impact to break the pre-existing bonds and form all new bonds.
ElectrophoresisElectrophoresis is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. Electrophoresis of positively charged particles (cations) is sometimes called cataphoresis, while electrophoresis of negatively charged particles (anions) is sometimes called anaphoresis. The electrokinetic phenomenon of electrophoresis was observed for the first time in 1807 by Russian professors Peter Ivanovich Strakhov and Ferdinand Frederic Reuss at Moscow University, who noticed that the application of a constant electric field caused clay particles dispersed in water to migrate.
Einstein relation (kinetic theory)In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is where D is the diffusion coefficient; μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = vd/F; kB is the Boltzmann constant; T is the absolute temperature.
Brownian motionBrownian motion is the random motion of particles suspended in a medium (a liquid or a gas). This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena).
Macromolecular crowdingThe phenomenon of macromolecular crowding alters the properties of molecules in a solution when high concentrations of macromolecules such as proteins are present. Such conditions occur routinely in living cells; for instance, the cytosol of Escherichia coli contains about 300–400mg/ml of macromolecules. Crowding occurs since these high concentrations of macromolecules reduce the volume of solvent available for other molecules in the solution, which has the result of increasing their effective concentrations.
ColloidA colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols and gels. The term colloidal suspension refers unambiguously to the overall mixture (although a narrower sense of the word suspension is distinguished from colloids by larger particle size).
Theoretical physicsTheoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.
Zeta potentialZeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in colloidal dispersions. In the colloidal chemistry literature, it is usually denoted using the Greek letter zeta (ζ), hence ζ-potential. The usual units are volts (V) or, more commonly, millivolts (mV).
Electroacoustic phenomenaElectroacoustic phenomena arise when ultrasound propagates through a fluid containing ions. The associated particle motion generates electric signals because ions have electric charge. This coupling between ultrasound and electric field is called electroacoustic phenomena. The fluid might be a simple Newtonian liquid, or complex heterogeneous dispersion, emulsion or even a porous body. There are several different electroacoustic effects depending on the nature of the fluid.
MacromoleculeA macromolecule is a very large molecule important to biological processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The most common macromolecules in biochemistry are biopolymers (nucleic acids, proteins, and carbohydrates) and large non-polymeric molecules such as lipids, nanogels and macrocycles. Synthetic fibers and experimental materials such as carbon nanotubes are also examples of macromolecules.
Local-density approximationLocal-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT) that depend solely upon the value of the electronic density at each point in space (and not, for example, derivatives of the density or the Kohn–Sham orbitals). Many approaches can yield local approximations to the XC energy. However, overwhelmingly successful local approximations are those that have been derived from the homogeneous electron gas (HEG) model.
DiffusionDiffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Cross section (physics)In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns.
TheoryA theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
Homotopy groups of spheresIn the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry. Unlike homology groups, which are also topological invariants, the homotopy groups are surprisingly complex and difficult to compute.
