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Praseodymium is a chemical element with the symbol Pr and atomic number 59. It is the third member of the lanthanide series and is traditionally considered to be one of the rare-earth metals. is a soft, silvery, malleable and ductile metal, valued for its magnetic, electrical, chemical, and optical properties. It is to...
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Praseodymium Aqueous praseodymium ions are yellowish-green, and similarly praseodymium results in various shades of yellow-green when incorporated into glasses. Many of praseodymium's industrial uses involve its ability to filter yellow light from light sources. is the third member of the lanthanide series. In the peri...
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Praseodymium Like most other metals in the lanthanide series, praseodymium usually only uses three electrons as valence electrons, as afterwards the remaining 4f electrons are too strongly bound: this is because the 4f orbitals penetrate the most through the inert xenon core of electrons to the nucleus, followed by 5d ...
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Praseodymium This isotope has 82 neutrons, a magic number that confers additional stability. This isotope is produced in stars through the s- and r-processes (slow and rapid neutron capture, respectively). All other praseodymium isotopes have half-lives under a day (and most under a minute), with the single exception o...
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Praseodymium 25, but at 400–700 °C the oxide defects are instead ordered, creating phases of the general formula PrO with "n" = 4, 7, 9, 10, 11, 12, and ∞. These phases PrO are sometimes labelled α and β′ (nonstoichiometric), β ("y" = 1.833), δ (1.818), ε (1.8), ζ (1.778), ι (1.714), θ, and σ. is an electropositive ele...
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Praseodymium Although praseodymium(V) in the bulk state is unknown, the existence of praseodymium in its +5 oxidation state (with the stable electron configuration of the preceding noble gas xenon) under noble-gas matrix isolation conditions was reported in 2016. The species assigned to the +5 state were identified as ...
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Praseodymium There are also a few mixed oxides and fluorides involving praseodymium(IV), but it does not have an appreciable coordination chemistry in this oxidation state like its neighbour cerium. However, the first example of a molecular complex of praseodymium(IV) has recently been reported. In 1751, the Swedish mi...
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Praseodymium While lanthanum turned out to be a pure element, didymium was not and turned out to be only a mixture of all the stable early lanthanides from praseodymium to europium, as had been suspected by Marc Delafontaine after spectroscopic analysis, though he lacked the time to pursue its separation into its const...
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Praseodymium Although not particularly rare, praseodymium is never found as a dominant rare earth in praseodymium-bearing minerals. It is always preceded by cerium, lanthanum and usually also by neodymium. The Pr ion is similar in size to the early lanthanides of the cerium group (those from lanthanum up to samarium an...
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Praseodymium The acidic filtrates are partially neutralised with sodium hydroxide to pH 3–4, during which thorium precipitates as a hydroxide and is removed. The solution is treated with ammonium oxalate to convert rare earths to their insoluble oxalates, the oxalates are converted to oxides by annealing, and the oxide...
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Praseodymium They are then precipitated as their insoluble oxalates, burned to form the oxides, and then reduced to the metals. Leo Moser (son of Ludwig Moser, founder of the Moser Glassworks in what is now Karlovy Vary in the Czech Republic, not to be confused with the mathematician of the same name) investigated the ...
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Praseodymium The following more modern applications involve praseodymium specifically, or at least praseodymium in a small subset of the lanthanides: Due to its role in permanent magnets used for wind turbines, it has been argued that praseodymium will be one of the main objects of geopolitical competition in a world r...
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Potion A potion (from Latin "potio" "drink") is a magical type of liquified medicine or drug. The term philtre is also used, often specifically for a love potion, "supposed to be capable of exciting sexual attraction or love". In mythology and literature, a potion is usually made by a magician, dragon, fairy or witch a...
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Potion Yusufzai witches, for example, would bathe a recently deceased leatherworker and sell the water to those seeking a male partner; this practice is said to exist in a modified form in modern times.
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Stercobilin is a tetrapyrrolic bile pigment and is one end-product of heme catabolism. It is the chemical responsible for the brown color of human feces and was originally isolated from feces in 1932. (and related urobilin) can be used as a marker for biochemical identification of fecal pollution levels in rivers. resu...
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Stercobilin An analysis of two infants suffering from cholelithiasis observed that a substantial amount of stercobilin was present in brown pigment gallstones. This study suggested that brown pigment gallstones could form spontaneously in infants suffering from bacterial infections of the biliary tract. A 1996 study by...
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Gerty Cori Gerty Theresa Cori (née Radnitz; August 15, 1896 – October 26, 1957) was a Austro-Hungarian-American biochemist who in 1947 was the third woman—and first American woman—to win a Nobel Prize in science, and the first woman to be awarded the Nobel Prize in Physiology or Medicine, for her role in the discovery ...
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Gerty Cori With her husband Carl and Argentine physiologist Bernardo Houssay, received the Nobel Prize in 1947 for the discovery of the mechanism by which glycogen—a derivative of glucose—is broken down in muscle tissue into lactic acid and then resynthesized in the body and stored as a source of energy (known as the C...
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Gerty Cori Her uncle, a professor of pediatrics, encouraged her to attend medical school, so she studied for and passed the university entrance examination. She was admitted to the medical school of the Karl-Ferdinands-Universität in Prague in 1914, an unusual achievement for women at that time. While studying, she met...
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Gerty Cori In 1922, the Coris both immigrated to the United States (Gerty six months after Carl because of difficulty in obtaining a position) to pursue medical research at the State Institute for the Study of Malignant Diseases (now the Roswell Park Cancer Institute) in Buffalo, New York. In 1928, they became naturali...
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Gerty Cori Carl refused a position at the University of Buffalo because the school would not allow him to work with his wife. In 1931, they moved to St. Louis, Missouri, as Washington University offered both Carl and Gerty positions, although Gerty's rank and salary were much lower than her husband's. Despite her resea...
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Gerty Cori It can also be the last step in the conversion of blood glucose to glycogen, as it is a reversible step. also studied glycogen storage disease, identifying at least four forms, each related to a particular enzymatic defect. She was the first to show that a defect in an enzyme can be the cause of a human gene...
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Gerty Cori Gerty was also a member of the American Society of Biological Chemists, the American Chemical Society and the American Philosophical Society. She and her husband were presented jointly with the Midwest Award (American Chemical Society) in 1946 and the Squibb Award in Endocrinology in 1947. In addition, Cori ...
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Gerty Cori The 41-cent stamp was reported by the Associated Press to have a printing error in the chemical formula for glucose-1-phosphate (Cori ester), but was distributed despite the error. Her description reads: "Biochemist (1896–1957), in collaboration with her husband, Carl, made important discoveries—including a ...
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Gerty Cori Later, her son erected a cenotaph for Gerty and Carl Cori in Bellefontaine Cemetery in St. Louis, Missouri. She was survived by her husband and their only child, Tom Cori, who married the daughter of conservative activist Phyllis Schlafly. Carl Cori remarried in 1960 to Anne Fitzgerald-Jones. The two later m...
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Yuan T. Lee Yuan Tseh Lee (; born 19 November 1936) is a Taiwanese chemist and a Professor Emeritus at the University of California, Berkeley. He was the first Taiwanese Nobel Prize laureate who, along with the Hungarian-Canadian John C. Polanyi and American Dudley R. Herschbach, won the Nobel Prize in Chemistry in 198...
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Yuan T. Lee He earned his MS from National Tsing Hua University in 1961 and his PhD from the University of California, Berkeley in 1965 under the supervision of Bruce H. Mahan. He was a member of the Chemistry International Board from 1977 to 1984. In February 1967, he started working with Dudley Herschbach at Harvard ...
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Yuan T. Lee Swedish chemist Svante Arrhenius studied this phenomenon during the late 1880s, and stated the relations between reactive molecular encounters and rates of reactions (formulated in terms of activation energies). Other scientists at the time also stated a chemical reaction is fundamentally a mechanical event...
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Yuan T. Lee To do so, Professor Lee used a breakthrough laboratory technique at the time, called the ""crossed molecular beams technique"", where the information derived from the measurements of angular and velocity distributions allowed him and his team to understand the dynamics of elementary chemical reactions. Duri...
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Yuan T. Lee Lee's sister, Chi-Mei Lee has served as a professor in National Chung Hsing University. In 2003, he was one of 22 Nobel Laureates who signed the Humanist Manifesto. Lee played an important role during the 2000 Presidential Election and since then has been a supporter of the Pan-green coalition which advocat...
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Yuan T. Lee He was elected President of the International Council for Science in 2008, to start his term in 2011. During the 2012 Republic of China presidential elections, Lee expressed his support for DPP candidate Tsai Ing-wen. In early 2016, he appeared and addressed a rally by New Power Party-a party formed by stud...
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Michaelis–Menten kinetics In biochemistry, is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate formula_1 (rate of formati...
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Michaelis–Menten kinetics This may be represented schematically as where formula_8 (forward rate constant), formula_9 (reverse rate constant), and formula_10 (catalytic rate constant) denote the rate constants, the double arrows between S (substrate) and ES (enzyme-substrate complex) represent the fact that enzyme-subs...
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Michaelis–Menten kinetics The value of the Michaelis constant formula_6 is numerically equal to the <chem>[S]</chem> at which the reaction rate is at half-maximum, and is an inverse measure of the substrate's affinity for the enzyme—as a small formula_6 indicates high affinity, meaning that the rate will approach formu...
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Michaelis–Menten kinetics have also been applied to a variety of spheres outside of biochemical reactions, including alveolar clearance of dusts, the richness of species pools, clearance of blood alcohol, the photosynthesis-irradiance relationship, and bacterial phage infection. The equation can also be used to describ...
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Michaelis–Menten kinetics They assumed that the concentration of the intermediate complex does not change on the time-scale of product formation – known as the quasi-steady-state assumption or pseudo-steady-state-hypothesis. Mathematically, this assumption means formula_34. This is mathematically the same as the previo...
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Michaelis–Menten kinetics The Michaelis–Menten equilibrium analysis is valid if the substrate reaches equilibrium on a much faster time-scale than the product is formed or, more precisely, that By contrast, the Briggs–Haldane quasi-steady-state analysis is valid if Thus it holds if the enzyme concentration is much less...
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Michaelis–Menten kinetics The typical method for determining the constants formula_5 and formula_6 involves running a series of enzyme assays at varying substrate concentrations formula_49, and measuring the initial reaction rate formula_50. 'Initial' here is taken to mean that the reaction rate is measured after a rel...
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Michaelis–Menten kinetics Nonetheless, their use can still be found in modern literature. In 1997 Santiago Schnell and Claudio Mendoza suggested a closed form solution for the time course kinetics analysis of the based on the solution of the Lambert W function. Namely, where "W" is the Lambert W function and The above ...
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Carbonation is the chemical reaction of carbon dioxide to give carbonates, bicarbonates, and carbonic acid. In chemistry, the term is sometimes used in place of carboxylation, which refers to the formation of carboxylic acids. In inorganic chemistry and geology, carbonation is common. Metal hydroxides (MOH) and metal o...
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DNA computing is a branch of computing which uses DNA, biochemistry, and molecular biology hardware, instead of the traditional silicon-based computer technologies. Research and development in this area concerns theory, experiments, and applications of DNA computing. The term "molectronics" has sometimes been used, but...
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DNA computing On April 28, 2004, Ehud Shapiro, Yaakov Benenson, Binyamin Gil, Uri Ben-Dor, and Rivka Adar at the Weizmann Institute announced in the journal "Nature" that they had constructed a DNA computer coupled with an input-and-output module which would theoretically be capable of diagnosing cancerous activity wit...
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DNA computing Therefore, about 1000 petaFLOPS could be reached, while today's most powerful computers do not go above much (200 petaFLOPS being the current record). The slow processing speed of a DNA computer (the response time is measured in minutes, hours or days, rather than milliseconds) is compensated by its poten...
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DNA computing The remains are the solution to the problem, but overall, the experiment lasted a week. However, current technical limitations prevent the evaluation of the results. Therefore, the experiment isn’t suitable for the application, but it is nevertheless a proof of concept. First results to these problems wer...
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DNA computing The corresponding bin becomes fluorescent, indicating which box is being played by the DNA computer. The DNA enzymes are divided among the bins in such a way as to ensure that the best the human player can achieve is a draw, as in real tic-tac-toe. Kevin Cherry and Lulu Qian at Caltech developed a DNA-bas...
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DNA computing This is because with instructions in fast cache memory, there is no need swap them in and out of main memory which can be slow. Similarly, in localized DNA computing, the DNA strands responsible for computation are fixed on a breadboard like substrate ensuring physical proximity of the computing gates. Su...
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DNA computing Jian-Jun Shu and colleagues built a DNA GPS system and also conduct an experiment to show that magnetic fields can enhance charge transport through DNA (or protein), which may allow organisms to sense magnetic fields. does not provide any new capabilities from the standpoint of computability theory, the s...
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DNA computing The DNAzyme logic gate changes its structure when it binds to a matching oligonucleotide and the fluorogenic substrate it is bonded to is cleaved free. While other materials can be used, most models use a fluorescence-based substrate because it is very easy to detect, even at the single molecule limit. Th...
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DNA computing Enzyme based DNA computers are usually of the form of a simple Turing machine; there is analogous hardware, in the form of an enzyme, and software, in the form of DNA. Benenson, Shapiro and colleagues have demonstrated a DNA computer using the FokI enzyme and expanded on their work by going on to show aut...
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DNA computing In this system, an input DNA strand binds to a sticky end, or toehold, on another DNA molecule, which allows it to displace another strand segment from the molecule. This allows the creation of modular logic components such as AND, OR, and NOT gates and signal amplifiers, which can be linked into arbitrar...
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Double bond A double bond in chemistry is a covalent bond between two atoms involving four bonding electrons as opposed to two in a single bond. Double bonds occur most commonly between two carbon atoms, for example in alkenes. Many double bonds exist between two different elements: for example, in a carbonyl group bet...
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Double bond For maximum overlap, the p-orbitals have to remain parallel, and, therefore, rotation around the central bond is not possible. This property gives rise to cis-trans isomerism. Double bonds are shorter than single bonds because p-orbital overlap is maximized. With 133 pm, the ethylene C=C bond length is shor...
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Double bond The distannene (MeSi)CHSn=SnCH(SiMe) has a tin-tin bond length just a little shorter than a single bond, a trans bent structure with pyramidal coordination at each tin atom, and readily dissociates in solution to form (MeSi)CHSn: (stannanediyl, a carbene analog). The bonding comprises two weak donor accepto...
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Galvanic cell A galvanic cell or voltaic cell, named after Luigi Galvani or Alessandro Volta, respectively, is an electrochemical cell that derives electrical energy from spontaneous redox reactions taking place within the cell. It generally consists of two different metals immersed in electrolytes, or of individual ha...
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Galvanic cell He built it entirely out of non-biological material to challenge Galvani's (and the later experimenter Leopoldo Nobili)'s animal electricity theory in favor of his own metal-metal contact electricity theory. Carlo Matteucci in his turn constructed a battery entirely out of biological material in answer to...
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Galvanic cell It was suggested by Wilhelm König in 1940 that the object known as the Baghdad battery might represent galvanic cell technology from ancient Parthia. Replicas filled with citric acid or grape juice have been shown to produce a voltage. However, it is far from certain that this was its purpose—other schola...
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Galvanic cell In the copper half-cell, the copper ions plate onto the copper electrode (reduction), taking up electrons that leave the external conductor. Since the Cu ions (cations) plate onto the copper electrode, the latter is called the cathode. Correspondingly the zinc electrode is the anode. The electrochemical r...
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Galvanic cell The difference between the metals' ionization energies in water is the other energetic contribution that can drive the reaction in a galvanic cell; it is not important in the Daniell cell because the energies of hydrated Cu and Zn ions happen to be similar. Both atom transfer, e.g. of zinc from the metal ...
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Galvanic cell Inside an isolated half-cell, there is an oxidation-reduction (redox) reaction that is in chemical equilibrium, a condition written symbolically as follows (here, "M" represents a metal cation, an atom that has a charge imbalance due to the loss of ""n"" electrons): A galvanic cell consists of two half-ce...
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Galvanic cell For instance, a typical 12V lead–acid battery has six galvanic cells connected in series with the anodes composed of lead and cathodes composed of lead dioxide, both immersed in sulfuric acid. Large battery rooms, for instance in a telephone exchange providing central office power to user's telephones, ma...
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Galvanic cell The polarity of the cell is determined as follows. Zinc metal is more strongly reducing than copper metal because the standard (reduction) potential for zinc is more negative than that of copper. Thus, zinc metal will lose electrons to copper ions and develop a positive electrical charge. The equilibrium ...
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Galvanic cell These calculations are based on the assumption that all chemical reactions are in equilibrium. When a current flows in the circuit, equilibrium conditions are not achieved and the cell voltage will usually be reduced by various mechanisms, such as the development of overpotentials. Also, since chemical re...
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Cathodic protection (CP) is a technique used to control the corrosion of a metal surface by making it the cathode of an electrochemical cell. A simple method of protection connects the metal to be protected to a more easily corroded "sacrificial metal" to act as the anode. The sacrificial metal then corrodes instead of...
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Cathodic protection Since excess marine growth affected the performance of the ship, the Royal Navy decided that it was better to allow the copper to corrode and have the benefit of reduced marine growth, so cathodic protection was not used further. Davy was assisted in his experiments by his pupil Michael Faraday, who...
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Cathodic protection Galvanic systems are "constant potential" systems that aim to restore the concrete's natural protective environment by providing a high initial current to restore passivity. It then reverts to a lower sacrificial current while harmful negative Chloride ions migrate away from the steel and towards th...
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Cathodic protection ASTM International publishes standards on the composition and manufacturing of galvanic anodes. In order for galvanic cathodic protection to work, the anode must possess a lower (that is, more negative) electrode potential than that of the cathode (the target structure to be protected). The table be...
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Cathodic protection The output DC negative terminal is connected to the structure to be protected by the cathodic protection system. The rectifier output DC positive cable is connected to the anodes. The AC power cable is connected to the rectifier input terminals. The output of the ICCP system should be optimised to p...
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Cathodic protection The power supply is then taken away and the anodes simply attached to the steel as a galvanic system. More powered phases can be administered if needed. Like Galvanic systems corrosion rate monitoring from polarisation tests and half-cell potential mapping can be used to measure corrosion. Polarizat...
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Cathodic protection The positive DC output terminal would be connected via cables to the anode array, while another cable would connect the negative terminal of the rectifier to the pipeline, preferably through junction boxes to allow measurements to be taken. Anodes can be installed in a groundbed consisting of a vert...
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Cathodic protection Since ships are regularly removed from the water for inspections and maintenance, it is a simple task to replace the galvanic anodes. Galvanic anodes are generally shaped to reduced drag in the water and fitted flush to the hull to also try to minimize drag. Smaller vessels, with non-metallic hulls,...
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Cathodic protection In cases like this, aluminium or zinc galvanic anodes can be used to offset the potential difference between the aluminium hull and the steel fixture. If the steel fixtures are large, several galvanic anodes may be required, or even a small ICCP system. Marine cathodic protection covers many areas, ...
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Cathodic protection However, in a typical atmospherically exposed concrete structure such as a bridge, there will be many more anodes distributed through the structure as opposed to an array of anodes as used on a pipeline. This makes for a more complicated system and usually an automatically controlled DC power source...
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Cathodic protection Vessels, pipelines and tanks which are used to store or transport liquids can also be protected from corrosion on their internal surfaces by the use of cathodic protection. ICCP and galvanic systems can be used. A common application of internal cathodic protection is water storage tanks and power pl...
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Cathodic protection Several companies market electronic devices claiming to mitigate corrosion for automobiles and trucks. Corrosion control professionals find they do not work. There is no peer reviewed scientific testing and validation supporting the use of the devices. In 1996 the FTC ordered David McCready, a perso...
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Cathodic protection Hydrogen atoms, however, are small enough to pass through the crystalline steel structure, and lead in some cases to hydrogen embrittlement. This is a process of disbondment of protective coatings from the protected structure (cathode) due to the formation of hydrogen ions over the surface of the pr...
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Cathodic protection A 1999 report concerning a spill from a Saskatchewan crude oil line contains an excellent definition of the cathodic shielding problem: Cathodic shielding is referenced in a number of the standards listed below. Newly issued USDOT regulation Title 49 CFR 192.112, in the section for "Additional desig...
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Alkoxy group In chemistry, the alkoxy group is an alkyl (carbon and hydrogen chain) group singularly bonded to oxygen; thus R–O. The range of alkoxy group is vast, the simplest being methoxy (CHO–). An ethoxy group (CHCHO–) is found in the organic compound ethyl phenyl ether, CHOCHCH which is also known as ethoxybenzen...
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Nondestructive testing (NDT) is a wide group of analysis techniques used in science and technology industry to evaluate the properties of a material, component or system without causing damage. The terms nondestructive examination (NDE), nondestructive inspection (NDI), and nondestructive evaluation (NDE) are also comm...
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Nondestructive testing NDT methods rely upon use of electromagnetic radiation, sound and other signal conversions to examine a wide variety of articles (metallic and non-metallic, food-product, artifacts and antiquities, infrastructure) for integrity, composition, or condition with no alteration of the article undergoi...
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Nondestructive testing Contrast and probability of detection for a visual examination by the unaided eye is often enhanced by using liquids to penetrate the test article surface, allowing for visualization of flaws or other surface conditions. This method (liquid penetrant testing) (PT) involves using dyes, fluorescent...
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Nondestructive testing Because these connections may encounter loads and fatigue during product lifetime, there is a chance that they may fail if not created to proper specification. For example, the base metal must reach a certain temperature during the welding process, must cool at a specific rate, and must be welded...
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Nondestructive testing This verifies the weld as correct to procedure prior to nondestructive evaluation and metallurgy tests. Structure can be complex systems that undergo different loads during their lifetime, e.g. Lithium-ion batteries. Some complex structures, such as the turbo machinery in a liquid-fuel rocket, ca...
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Nondestructive testing Technological improvements or upgrades in these NDT methods have migrated over from medical equipment advances, including digital radiography (DR), phased array ultrasonic testing (PAUT), and endoscopy (borescope or assisted visual inspection). "(Basic Source for above: Hellier, 2001) Note the nu...
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Nondestructive testing NDT professionals and managers who seek to further their growth, knowledge and experience to remain competitive in the rapidly advancing technology field of nondestructive testing should consider joining NDTMA, a member organization of NDT Managers and Executives who work to provide a forum for t...
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Nondestructive testing Certifications issued by a national NDT society which is a member of the European Federation of NDT (EFNDT) are mutually acceptable by the other member societies under a multilateral recognition agreement. Canada also implements an ISO 9712 central certification scheme, which is administered by N...
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Nondestructive testing A common error in POD tests is to assume that the percentage of flaws detected is the POD, whereas the percentage of flaws detected is merely the first step in the analysis. Since the number of flaws tested is necessarily a limited number (non-infinite), statistical methods must be used to determ...
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Fluorophore A fluorophore (or fluorochrome, similarly to a chromophore) is a fluorescent chemical compound that can re-emit light upon light excitation. Fluorophores typically contain several combined aromatic groups, or planar or cyclic molecules with several π bonds. Fluorophores are sometimes used alone, as a tracer...
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Fluorophore The absorbed wavelengths, energy transfer efficiency, and time before emission depend on both the fluorophore structure and its chemical environment, as the molecule in its excited state interacts with surrounding molecules. Wavelengths of maximum absorption (≈ excitation) and emission (for example, Absorpt...
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Fluorophore Most fluorophores are organic small molecules of 20 - 100 atoms (200 - 1000 Dalton - the molecular weight may be higher depending on grafted modifications, and conjugated molecules), but there are also much larger natural fluorophores that are proteins: Green fluorescent protein (GFP) is 27 kDa and several ...
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Fluorophore They can be attached to protein to specific functional groups, such as - amino groups (Active ester, Carboxylate, Isothiocyanate, hydrazine) - carboxyl groups (carbodiimide) - thiol (maleimide, acetyl bromide) - azide (via click chemistry or non-specifically (glutaraldehyde)). Additionally, various function...
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Fluorophore Abbreviations: <br> Ex (nm): Excitation wavelength in nanometers <br> Em (nm): Emission wavelength in nanometers<br> MW: Molecular weight<br> QY: Quantum yield Abbreviations: <br> Ex (nm): Excitation wavelength in nanometers <br> Em (nm): Emission wavelength in nanometers<br> MW: Molecular weight <br> QY: Q...
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Anodyne An anodyne is a drug used to lessen pain through reducing the sensitivity of the brain or nervous system. The term was common in medicine before the 20th century, but such drugs are now more often known as analgesics or painkillers. The name derives from Greek "anōdynos" (), from "an-" (, "without") and "odynē"...
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Principal quantum number In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to all electrons in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. Apart from the principal quantum number, the other quan...
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Principal quantum number The principal quantum number was first created for use in the semiclassical Bohr model of the atom, distinguishing between different energy levels. With the development of modern quantum mechanics, the simple Bohr model was replaced with a more complex theory of atomic orbitals. However, the mo...
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Principal quantum number In the Bohr model, the allowed orbits were derived from quantized (discrete) values of orbital angular momentum, "L" according to the equation where "n" = 1, 2, 3, … and is called the principal quantum number, and "h" is Planck's constant. This formula is not correct in quantum mechanics as the...
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Principal quantum number The definite total energy for a particle motion in a common Coulomb field and with a discrete spectrum, is given by: where formula_5 is the Bohr radius. This discrete energy spectrum resulted from the solution of the quantum mechanical problem on the electron motion in the Coulomb field, coinci...
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Azimuthal quantum number The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. It is also known as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ (p...
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Azimuthal quantum number In the illustration, the letters s, p, and d (a convention originating in spectroscopy) describe the shape of the atomic orbital. Their wavefunctions take the form of spherical harmonics, and so are described by Legendre polynomials. The various orbitals relating to different values of "ℓ" are ...
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Azimuthal quantum number In more complex atoms these energy levels split for all "n" > 1, placing states of higher "ℓ" above states of lower "ℓ". For example, the energy of 2p is higher than of 2s, 3d occurs higher than 3p, which in turn is above 3s, etc. This effect eventually forms the block structure of the periodic...
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Azimuthal quantum number These therefore change over time. However the total angular momentum J does commute with the one-electron Hamiltonian and so is constant. J is defined through L being the orbital angular momentum and S the spin. The total angular momentum satisfies the same commutation relations as orbital angu...
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