Physical chemistryPhysical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics, analytical dynamics and chemical equilibria. Physical chemistry, in contrast to chemical physics, is predominantly (but not always) a supra-molecular science, as the majority of the principles on which it was founded relate to the bulk rather than the molecular or atomic structure alone (for example, chemical equilibrium and colloids).
Computational chemistryComputational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form.
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.
Quantum chemistryQuantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties.
Potential energy surfaceA potential energy surface (PES) describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy curve or . An example is the Morse/Long-range potential. It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g.
SurfaceA surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".
Surface (topology)In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
Riemann surfaceIn mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together.
OrientabilityIn mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable.
Algebraic surfaceIn mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dimension four as a smooth manifold. The theory of algebraic surfaces is much more complicated than that of algebraic curves (including the compact Riemann surfaces, which are genuine surfaces of (real) dimension two).
Differential geometry of surfacesIn mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface.
Surface (mathematics)In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space. The exact definition of a surface may depend on the context.
Boy's surfaceIn geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space. Boy's surface was first parametrized explicitly by Bernard Morin in 1978. Another parametrization was discovered by Rob Kusner and Robert Bryant. Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.
Surface tensionSurface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged. At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). There are two primary mechanisms in play.
Surface energyIn surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material (the atoms on the surface have more energy compared with the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see sublimation).
Capillary lengthThe capillary length or capillary constant, is a length scaling factor that relates gravity and surface tension. It is a fundamental physical property that governs the behavior of menisci, and is found when body forces (gravity) and surface forces (Laplace pressure) are in equilibrium. The pressure of a static fluid does not depend on the shape, total mass or surface area of the fluid. It is directly proportional to the fluid's specific weight – the force exerted by gravity over a specific volume, and its vertical height.
Thermodynamic stateIn thermodynamics, a thermodynamic state of a system is its condition at a specific time; that is, fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables. Once such a set of values of thermodynamic variables has been specified for a system, the values of all thermodynamic properties of the system are uniquely determined. Usually, by default, a thermodynamic state is taken to be one of thermodynamic equilibrium.
Minimal surfaceIn mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame.
Thermodynamic cycleA thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine.
Thermodynamic systemA thermodynamic system is a body of matter and/or radiation, considered as separate from its surroundings, and studied using the laws of thermodynamics. Thermodynamic systems may be isolated, closed, or open. An isolated system exchanges no matter or energy with its surroundings, whereas a closed system does not exchange matter but may exchange heat and experience and exert forces. An open system can interact with its surroundings by exchanging both matter and energy.
