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Micellar Cubic
{{unreferenced, date=April 2017 A micellar cubic phase is a lyotropic liquid crystal phase formed when the concentration of micelles dispersed in a solvent (usually water) is sufficiently high that they are forced to pack into a structure having long-ranged positional (translational) order. For example, spherical micelles a subic packing of a body-centred cubic lattice. Normal topology micellar cubic phases, denoted by the symbol I1, are the first lyotropic liquid crystalline phases that are formed by type I amphiphiles. The amphiphiles' hydrocarbon tails are contained on the inside of the micelle and hence the polar-apolar interface of the aggregates has a positive mean curvature, by definition (it curves away from the polar phase). Inverse topology micellar cubic phases (such as the Fd3m phase) are observed for some type II amphiphiles at very high amphiphile concentrations. These aggregates, in which water is the minority phase, have a polar-apolar interface with a negative mean ...
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Lyotropic Liquid Crystal
A liquid crystalline mesophase is called lyotropic (a portmanteau of lyo- "dissolve" and -tropic "change" ) if formed by dissolving an amphiphilic mesogen in a suitable solvent, under appropriate conditions of concentration, temperature and pressure. A mixture of soap and water is an everyday example of a lyotropic liquid crystal. Historically, the term was used to describe the common behavior of materials composed of amphiphilic molecules upon the addition of a solvent. Such molecules comprise a water-loving hydrophilic head-group (which may be ionic or non-ionic) attached to a water-hating, hydrophobic group. The micro-phase segregation of two incompatible components on a nanometer scale results in different type of solvent-induced extended anisotropic arrangement, depending on the volume balances between the hydrophilic part and hydrophobic part. In turn, they generate the long-range order of the phases, with the solvent molecules filling the space around the compounds to pro ...
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Micelles
A micelle () or micella () (plural micelles or micellae, respectively) is an aggregate (or supramolecular assembly) of surfactant amphipathic lipid molecules dispersed in a liquid, forming a colloid, colloidal suspension (also known as associated colloidal system). A typical micelle in aqueous solution, water forms an aggregate with the hydrophilic "head" regions in contact with surrounding solvent, sequestering the hydrophobic single-tail regions in the micelle centre. This phase is caused by the Lipid bilayer phase behavior, packing behavior of single-tail lipids in a lipid bilayer, bilayer. The difficulty filling all the volume of the interior of a bilayer, while accommodating the area per head group forced on the molecule by the hydration of the lipid head group, leads to the formation of the micelle. This type of micelle is known as a normal-phase micelle (oil-in-water micelle). Inverse micelles have the head groups at the centre with the tails extending out (water-in-oil ...
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Normal Topology
Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Normal'' (2009 film), an adaptation of Anthony Neilson's 1991 play ''Normal: The Düsseldorf Ripper'' * ''Normal!'', a 2011 Algerian film * ''The Normals'' (film), a 2012 American comedy film * "Normal" (''New Girl''), an episode of the TV series Mathematics * Normal (geometry), an object such as a line or vector that is perpendicular to a given object * Normal basis (of a Galois extension), used heavily in cryptography * Normal bundle * Normal cone, of a subscheme in algebraic geometry * Normal coordinates, in differential geometry, local coordinates obtained from the exponential map (Riemannian geometry) * Normal distribution, the Gaussian continuous probability distribution * Normal equations, describing the solution of the linear least ...
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Type I Amphiphiles
Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Type (Unix), a command in POSIX shells that gives information about commands. * Type safety, the extent to which a programming language discourages or prevents type errors. * Type system, defines a programming language's response to data types. Mathematics * Type (model theory) * Type theory, basis for the study of type systems * Arity or type, the number of operands a function takes * Type, any proposition or set in the intuitionistic type theory * Type, of an entire function ** Exponential type Biology * Type (biology), which fixes a scientific name to a taxon * Dog type, categorization by use or function of domestic dogs Lettering * Type is a design concept for lettering used in typography which helped bring about modern textual printin ...
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Mean Curvature
In mathematics, the mean curvature H of a surface S is an ''extrinsic'' measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The concept was used by Sophie Germain in her work on elasticity theory. Jean Baptiste Marie Meusnier used it in 1776, in his studies of minimal surfaces. It is important in the analysis of minimal surfaces, which have mean curvature zero, and in the analysis of physical interfaces between fluids (such as soap films) which, for example, have constant mean curvature in static flows, by the Young-Laplace equation. Definition Let p be a point on the surface S inside the three dimensional Euclidean space . Each plane through p containing the normal line to S cuts S in a (plane) curve. Fixing a choice of unit normal gives a signed curvature to that curve. As the plane is rotated by an angle \theta (always containing the normal line) that curvatur ...
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Inverse Topology
Inverse or invert may refer to: Science and mathematics * Inverse (logic), a type of conditional sentence which is an immediate inference made from another conditional sentence * Additive inverse (negation), the inverse of a number that, when added to the original number, yields zero * Compositional inverse, a function that "reverses" another function * Inverse element * Inverse function, a function that "reverses" another function **Generalized inverse, a matrix that has some properties of the inverse matrix but not necessarily all of them * Multiplicative inverse (reciprocal), a number which when multiplied by a given number yields the multiplicative identity, 1 ** Inverse matrix of an Invertible matrix Other uses * Invert level, the base interior level of a pipe, trench or tunnel * ''Inverse'' (website), an online magazine * An outdated term for an LGBT person; see Sexual inversion (sexology) See also * Inversion (other) Inversion or inversions may refer to: Ar ...
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Type II Amphiphiles
Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Type (Unix), a command in POSIX shells that gives information about commands. * Type safety, the extent to which a programming language discourages or prevents type errors. * Type system, defines a programming language's response to data types. Mathematics * Type (model theory) * Type theory, basis for the study of type systems * Arity or type, the number of operands a function takes * Type, any proposition or set in the intuitionistic type theory * Type, of an entire function ** Exponential type Biology * Type (biology), which fixes a scientific name to a taxon * Dog type, categorization by use or function of domestic dogs Lettering * Type is a design concept for lettering used in typography which helped bring about modern textual printin ...
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Non-ionic Surfactants
An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convention. The net charge of an ion is not zero because its total number of electrons is unequal to its total number of protons. A cation is a positively charged ion with fewer electrons than protons while an anion is a negatively charged ion with more electrons than protons. Opposite electric charges are pulled towards one another by electrostatic force, so cations and anions attract each other and readily form ionic compounds. Ions consisting of only a single atom are termed atomic or monatomic ions, while two or more atoms form molecular ions or polyatomic ions. In the case of physical ionization in a fluid (gas or liquid), "ion pairs" are created by spontaneous molecule collisions, where each generated pair consists of a free electron and a ...
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Micellar Solutions
A micellar solution consists of a dispersion of micelles in a solvent (most usually water). Micelles consist of aggregated amphiphiles, and in a micellar solution these are in equilibrium with free, unaggregated amphiphiles. Micellar solutions form when the concentration of amphiphile exceeds the critical micellar concentration (CMC) or critical aggregation concentration - CAC, and persist until the amphiphile concentration becomes sufficiently high to form a lyotropic liquid crystal A liquid crystalline mesophase is called lyotropic (a portmanteau of lyo- "dissolve" and -tropic "change" ) if formed by dissolving an amphiphilic mesogen in a suitable solvent, under appropriate conditions of concentration, temperature and pr ... phase. Although micelles are often depicted as being spherical, they can be cylindrical or oblate depending on the chemical structure of the amphiphile. Micellar solutions are isotropic phases. Micellar originates from France, with its usage in skin ...
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Phases Of Matter
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See ) The term ''phase'' is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the term ''phase'' is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Becau ...
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