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Lennard–Jones Potential
The Lennard-Jones potential (also termed the LJ potential or 12-6 potential) is an intermolecular pair potential. Out of all the intermolecular potentials, the Lennard-Jones potential is probably the one that has been the most extensively studied. It is considered an archetype model for simple yet realistic intermolecular interactions. The Lennard-Jones potential models soft repulsive and attractive ( van der Waals) interactions. Hence, the Lennard-Jones potential describes electronically neutral atoms or molecules. It is named after John Lennard-Jones. The commonly used expression for the Lennard-Jones potential is V_\text(r) = 4\varepsilon \left \left(\frac\right)^ - \left(\frac\right)^6 \right, where r is the distance between two interacting particles, \varepsilon is the depth of the potential well (usually referred to as 'dispersion energy'), and \sigma is the distance at which the particle-particle potential energy V is zero (often referred to as 'size of the particle'). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Of Lennard-Jones Potential
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties * Graph (topology), a topological space resembling a graph in the sense of discrete mathematics * Graph of a function * Graph of a relation * Graph paper * Chart, a means of representing data (also called a graph) Computing * Graph (abstract data type), an abstract data type representing relations or connections * graph (Unix), Unix command-line utility * Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy The English suffix -graphy means a "field of study" or related to "writing" a book, and is an anglicization of the French ''-graphie'' inherited from the Latin ''-graphia'', which is a transl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pauli Exclusion Principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940. In the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: ''n'', the principal quantum number; ', the azimuthal quantum number; ''m'', the magnetic quantum number; and ''ms'', the spin quantum number. For example, if two electrons reside in the same orbital, then their ''n'', ', and ''m'' values are the same; therefore their ''ms'' must be different, and thus the electrons must have opposite half-integer spin projections of 1/2 and −1/2. Particles with an integer spin, or boson ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid-state Physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Background Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and elasticity), thermal, electrical, magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern (crystalline solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can be both fluid and solid. Viscoelastic fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers any liquid constituent of the body (body fluid), whereas "liquid" is not used in this sense. Sometimes liquids given for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chemistry
Quantum 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. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics. Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hard Spheres
Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong ("infinitely elastic bouncing") repulsion that atoms and spherical molecules experience at very close distances. Hard spheres systems are studied by analytical means, by molecular dynamics simulations, and by the experimental study of certain colloidal model systems. The hard-sphere system provides a generic model that explains the quasiuniversal structure and dynamics of simple liquids. Formal definition Hard spheres of diameter \sigma are particles with the following pairwise interaction potential: :V(\mathbf_1,\mathbf_2)=\left\{ \begin{matrix}0 & \mbox{if}\quad , \mathbf{r}_1-\mathbf{r}_2, \geq \sigma \\ \infty & \mbox{if}\quad, \mathbf{r}_1-\mathbf{r}_2, < \sigma \end{matrix} \right. where and are th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observable
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. Physically meaningful observables must also satisfy transformation laws that relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations that preserve certain mathematical properties of the space in question. Quantum mechanics In quantum physics, observables manifest as linear operators on a Hilbert space representing the state space of quantum states ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: * Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mie Potential
The Mie potential is an intermolecular pair potential, i.e. it describes the interactions between particles at the atomic level. The model is attributed to the German physicist Gustave Mie. The Mie potential is the generalized case of the Lennard-Jones (LJ) potential, which is perhaps the single most widely used pair potential. The Mie potential V(r) is a function of r, the distance between two particles, and is written as V(r) = C \, \varepsilon \left \left(\frac \right)^- \left( \frac\right)^m \right,~~~~~~ (1) with C = \frac \left( \frac\right)^ . The Lennard-Jones potential corresponds to the special case where n=12 and m=6 in Eq. (1). In Eq. (1), \varepsilon is the dispersion energy, and \sigma indicates the distance at which V = 0 , which is sometimes called the "collision radius." The parameter \sigma is generally indicative of the size of the particles involved in the collision. The parameters n and m characterize the shape of the potential: n describes the cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exchange Interaction
In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier. The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing sign (antisymmetric) when two particles are exchanged. Both bosons and fermions can experience the exchange interaction. For fermions, this interaction is sometimes called Pauli repulsion and is related to the Pauli exclusion principle. For bosons, the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation. The exchange interaction alters the expectation value of the distance when the wave functions of two or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
