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Spinodal
In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero. : 0 The locus of these points (the inflection point within a G-x or G-c curve, Gibbs free energy as a function of composition) is known as the spinodal curve.G. Astarita: ''Thermodynamics: An Advanced Textbook for Chemical Engineers'' (Springer 1990), chaps 4, 8, 9, 12.Sandler S. I., ''Chemical and Engineering Thermodynamics''. 1999 John Wiley & Sons, Inc., p 571.Koningsveld K., Stockmayer W. H., Nies, E., ''Polymer Phase Diagrams: A Textbook''. 2001 Oxford, p 12. For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via spinodal decomposition. Outside of the curve, the solution will be at least metastable with respect to fluctuations. In other words, outside the spinodal curve some careful process may obtain a single phase system. Insi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spinodal Decomposition
Spinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). Decomposition occurs when there is no thermodynamic barrier to phase separation. As a result, phase separation via decomposition does not require the nucleation events resulting from thermodynamic fluctuations, which normally trigger phase separation. Spinodal decomposition is observed when mixtures of metals or polymers separate into two co-existing phases, each rich in one species and poor in the other. When the two phases emerge in approximately equal proportion (each occupying about the same volume or area), characteristic intertwined structures are formed that gradually coarsen (see animation). The dynamics of spinodal decomposition is commonly modeled using the Cahn–Hilliard equation. Spinodal decomposition is fundamentally different from nucleation and growth. When there is a nucleation barrier to the formation of a second phase, time i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Free Energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy change , measured in joules in SI) is the ''maximum'' amount of non-expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces. The Gibbs energy is the thermodynamic potential that is minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Derivative
In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of . Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of the object, or the rate at which the velocity of the object is changing with respect to time. In Leibniz notation: :\mathbf = \frac = \frac, where ''a'' is acceleration, ''v'' is velocity, ''t'' is time, ''x'' is position, and d is the instantaneous "delta" or change. The last expression \tfrac is the second derivative of position (x) with respect to time. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the opposite way. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locus (mathematics)
In geometry, a locus (plural: ''loci'') (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.. In other words, the set of the points that satisfy some property is often called the ''locus of a point'' satisfying this property. The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be ''located'' or may move. History and philosophy Until the beginning of the 20th century, a geometrical shape (for example a curve) was not considered as an infinite set of points; rather, it was considered as an entity on which a point may be located or on which it moves. Thus a circle in the Euclidean plane was defined as the ''locus'' of a point that is at a given dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Composition
A chemical composition specifies the identity, arrangement, and ratio of the elements making up a compound. Chemical formulas can be used to describe the relative amounts of elements present in a compound. For example, the chemical formula for water is H2O: this means that each molecule of water is constituted by 2 atoms of hydrogen (H) and 1 atom of oxygen (O). The chemical composition of water may be interpreted as a 2:1 ratio of hydrogen atoms to oxygen atoms. Different types of chemical formulas are used to convey composition information, such as an empirical or molecular formula. Nomenclature can be used to express not only the elements present in a compound but their arrangement within the molecules of the compound. In this way, compounds will have unique names which can describe their elemental composition. Composite mixture The chemical composition of a mixture can be defined as the distribution of the individual substances that constitute the mixture, called "compon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of matter nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, while not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. A thermodynamic sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Vapor Deposition
Physical vapor deposition (PVD), sometimes called physical vapor transport (PVT), describes a variety of vacuum deposition methods which can be used to produce thin films and coatings on substrates including metals, ceramics, glass, and polymers. PVD is characterized by a process in which the material transitions from a condensed phase to a vapor phase and then back to a thin film condensed phase. The most common PVD processes are sputtering and evaporation. PVD is used in the manufacturing of items which require thin films for optical, mechanical, electrical, acoustic or chemical functions. Examples include semiconductor devices such as thin-film solar cells, microelectromechanical devices such as thin film bulk acoustic resonator, aluminized PET film for food packaging and balloons, and titanium nitride coated cutting tools for metalworking. Besides PVD tools for fabrication, special smaller tools used mainly for scientific purposes have been developed. The source material i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binodal
In thermodynamics, the binodal, also known as the coexistence curve or binodal curve, denotes the condition at which two distinct phases may coexist. Equivalently, it is the boundary between the set of conditions in which it is thermodynamically favorable for the system to be fully mixed and the set of conditions in which it is thermodynamically favorable for it to phase separate.IUPAC binodal curve definition http://old.iupac.org/goldbook/BT07273.pdf accessed 2/20/13 In general, the binodal is defined by the condition at which the chemical potential of all solution components is equal in each phase. The extremum of a binodal curve in temperature coincides with the one of the spinodal In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero. : 0 The locus of these points (the inflection point within a G-x or G- ... curve and is known as a critical point. Bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miscibility Gap
A miscibility gap is a region in a phase diagram for a mixture of components where the mixture exists as two or more phases – any region of composition of mixtures where the constituents are not completely miscible. The IUPAC Gold Book defines ''miscibility gap'' as "Area within the coexistence curve of an isobaric phase diagram (temperature vs composition) or an isothermal phase diagram (pressure vs composition)." A miscibility gap between isostructural phases may be described as the ''solvus'', a term also used to describe the boundary on a phase diagram between a miscibility gap and other phases. Thermodynamically, miscibility gaps indicate a maximum (''e.g.'' of Gibbs energy) in the composition range. Named miscibility gaps A number of miscibility gaps in phase systems are named, including * The ''huttenlocher'' (found in bytownite, anorthite composition An55-95.), ''boggild'' (in labradorite, An39-48 and An53-63.) and peristerite (in oligoclase, ~An5-15.) miscibility g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper Critical Solution Temperature
The upper critical solution temperature (UCST) or upper consolute temperature is the critical temperature above which the components of a mixture are miscible in all proportions. The word ''upper'' indicates that the UCST is an upper bound to a temperature range of partial miscibility, or miscibility for certain compositions only. For example, hexane-nitrobenzene mixtures have a UCST of , so that these two substances are miscible in all proportions above but not at lower temperatures. Examples at higher temperatures are the aniline-water system at (at pressures high enough for liquid water to exist at that temperature), and the lead-zinc system at (a temperature where both metals are liquid). A solid state example is the palladium-hydrogen system which has a solid solution phase (H2 in Pd) in equilibrium with a hydride phase (PdHn) below the UCST at 300 °C. Above this temperature there is a single solid solution phase. In the phase diagram of the mixture components, the UC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
