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Autocatalytic
In chemistry, a chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same reaction. Many forms of autocatalysis are recognized.Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) pp. 151–2 A ''set'' of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set). Examples Acid-catalyzed hydrolysis of esters produces carboxylic acids that also catalyze the same reaction. Indeed, the observation of an accelerating hydrolysis of gamma valerolactone to gamma-hydroxyvaleric acid led to the introduction of the concept of autocatalysis in 1890. The oxidation of hydrocarbons by air or oxygen is the basis of autoxidation. Like many radic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autocatalytic Set
An autocatalytic set is a collection of entities, each of which can be created catalytically by other entities within the set, such that as a whole, the set is able to catalyze its own production. In this way the set ''as a whole'' is said to be autocatalytic. Autocatalytic sets were originally and most concretely defined in terms of molecular entities, but have more recently been metaphorically extended to the study of systems in sociology, ecology, and economics. Autocatalytic sets also have the ability to replicate themselves if they are split apart into two physically separated spaces. Computer models illustrate that split autocatalytic sets will reproduce all of the reactions of the original set in each half, much like cellular mitosis. In effect, using the principles of autocatalysis, a small metabolism can replicate itself with very little high level organization. This property is why autocatalysis is a contender as the foundational mechanism for complex evolution. Pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Induction Period
An induction period in chemical kinetics is an initial slow stage of a chemical reaction; after the induction period, the reaction accelerates. Ignoring induction periods can lead to runaway reactions. In some catalytic reactions, a pre-catalyst needs to undergo a transformation to form the active catalyst, before the catalyst can take effect. Time is required for this transformation, hence the induction period. For example, with Wilkinson's catalyst, one triphenylphosphine ligand must dissociate to give the coordinatively unsaturated 14-electron species which can participate in the catalytic cycle: : Similarly, for an autocatalytic reaction, where one of the reaction products catalyzes the reaction itself, the rate of reaction is low initially until sufficient products have formed to catalyze the reaction. Reactions generally accelerate when heat is applied. Where a reaction is exothermic, the rate of the reaction may initially be low. As the reaction proceeds, heat is gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation f(x) = \frac where The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L. The exponential function with negated argument (e^ ) is used to define the standard logistic function, depicted at right, where L=1, k=1, x_0=0, which has the equation f(x) = \frac and is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse function of the logit. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. There are various generalizations, depending on the field. History The logistic function was introduced in a series of three papers by Pier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brusselator
The Brusselator is a theoretical model for a type of autocatalytic reaction. The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. It is a portmanteau of Brussels and oscillator. It is characterized by the reactions : A \rightarrow X : 2X + Y \rightarrow 3X : B + X \rightarrow Y + D : X \rightarrow E Under conditions where A and B are in vast excess and can thus be modeled at constant concentration, the rate equations become :\left\ = \left\ + \left\^2 \left\ - \left\ \left\ - \left\ \, :\left\ = \left\ \left\ - \left\^2 \left\ \, where, for convenience, the rate constants have been set to 1. The Brusselator has a fixed point at :\left\ = A \, :\left\ = \,. The fixed point becomes unstable when : B>1+A^2 \, leading to an oscillation of the system. Unlike the Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autoxidation
Autoxidation (sometimes auto-oxidation) refers to oxidations brought about by reactions with oxygen at normal temperatures, without the intervention of flame or electric spark. The term is usually used to describe the gradual degradation of organic compounds in air at ambient temperatures. Many common phenomena can be attributed to autoxidation, such as food going rancid, the ' drying' of varnishes and paints, and the perishing of rubber. It is also an important concept in both industrial chemistry and biology. Autoxidation is therefore a fairly broad term and can encompass examples of photooxygenation and catalytic oxidation. The common mechanism is a free radical chain reaction, where the addition of oxygen gives rise to hydroperoxides and their associated peroxy radicals (ROO•). Typically, an induction period is seen at the start where there is little activity; this is followed by a gradually accelerating take-up of oxygen, giving an autocatalytic reaction which can on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alcohol (chemistry)
In chemistry, an alcohol (), is a type of organic compound that carries at least one hydroxyl () functional group bound to a Saturated and unsaturated compounds, saturated carbon atom. Alcohols range from the simple, like methanol and ethanol, to complex, like sugar alcohols and cholesterol. The presence of an OH group strongly modifies the properties of Hydrocarbon, hydrocarbons, conferring Hydrophile, hydrophilic (water-loving) properties. The OH group provides a site at which many reactions can occur. History The flammable nature of the exhalations of wine was already known to ancient natural philosophers such as Aristotle (384–322 BCE), Theophrastus (–287 BCE), and Pliny the Elder (23/24–79 CE). However, this did not immediately lead to the isolation of alcohol, even despite the development of more advanced distillation techniques in second- and third-century Roman Egypt. An important recognition, first found in one of the writings attributed to Jabir ibn Hayyan, J� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carboxylic Acid
In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an Substituent, R-group. The general formula of a carboxylic acid is often written as or , sometimes as with R referring to an organyl group (e.g., alkyl, alkenyl, aryl), or hydrogen, or other groups. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion. Examples and nomenclature Carboxylic acids are commonly identified by their trivial names. They often have the suffix ''-ic acid''. IUPAC-recommended names also exist; in this system, carboxylic acids have an ''-oic acid'' suffix. For example, butyric acid () is butanoic acid by IUPAC guidelines. For nomenclature of complex molecules containing a carboxylic acid, the carboxyl can be considered position one of the parent chain even if there are other substituents, such as 3-chloropropanoic acid. Alternately, it can be named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ester
In chemistry, an ester is a compound derived from an acid (either organic or inorganic) in which the hydrogen atom (H) of at least one acidic hydroxyl group () of that acid is replaced by an organyl group (R). These compounds contain a distinctive functional group. Analogues derived from oxygen replaced by other chalcogens belong to the ester category as well. According to some authors, organyl derivatives of acidic hydrogen of other acids are esters as well (e.g. amides), but not according to the IUPAC. Glycerides are fatty acid esters of glycerol; they are important in biology, being one of the main classes of lipids and comprising the bulk of animal fats and vegetable oils. Lactones are cyclic carboxylic esters; naturally occurring lactones are mainly 5- and 6-membered ring lactones. Lactones contribute to the aroma of fruits, butter, cheese, vegetables like celery and other foods. Esters can be formed from oxoacids (e.g. esters of acetic acid, carbonic acid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is any mathematical function whose graph of a function, graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula :\sigma(x) = \frac = \frac = 1 - \sigma(-x). Other sigmoid functions are given in the #Examples, Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as a synonym for "logistic function". Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of ''x'') and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (''y'' axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ralph Pearson
Ralph Gottfrid Pearson (January 12, 1919 – October 12, 2022) was an American physical inorganic chemist best known for the development of the concept of hard and soft acids and bases (HSAB). He received his Ph.D. in physical chemistry in 1943 from Northwestern University, and taught chemistry at Northwestern faculty from 1946 until 1976, when he moved to University of California at Santa Barbara (UCSB). He retired in 1989 but remained active in research in theoretical inorganic chemistry until his death. In 1958 Pearson and Fred Basolo, his colleague at Northwestern wrote the influential monograph "Mechanisms of Inorganic Reactions", which integrated concepts from ligand field theory and physical organic chemistry and signaled a shift from descriptive coordination chemistry to a more quantitative science. With another Northwestern colleague, Arthur Atwater Frost, Pearson wrote in 1961 another classic text, ''Kinetics and Mechanism: A Study of Homogeneous Chemical Reactions'' ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macroscopic
The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena and bodies, the macroscopic scale describes things as a person can directly perceive them, without the aid of magnifying devices. This is in contrast to observations ( microscopy) or theories ( microphysics, statistical physics) of objects of geometric lengths smaller than perhaps some hundreds of micrometres. A macroscopic view of a ball is just that: a ball. A microscopic view could reveal a thick round skin seemingly composed entirely of puckered cracks and fissures (as viewed through a microscope) or, further down in scale, a collection of molecules in a roughly spherical shape (as viewed through an electron microscope). An example of a physical theory that takes a deliberately macroscopic viewpoint is thermodynamics. An exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
