|
Langmuir Adsorption Model
The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure i.e at these conditions the adsorbate's partial pressure, p_A, is related to the volume of it, , adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of a series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate gaseous molecule A_\text and an empty sorption site, . This reaction yields an adsorbed species A_\text with an associated equilibrium constant K_\text: : A_ + S A_ From these basic hypotheses the mathematical formulation of the Langmuir adsorption isotherm can be derived in various independent and complementary ways: by the kinetics, the thermodynamics, and the statistical me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langmuir Adsorption Model
The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure i.e at these conditions the adsorbate's partial pressure, p_A, is related to the volume of it, , adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of a series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate gaseous molecule A_\text and an empty sorption site, . This reaction yields an adsorbed species A_\text with an associated equilibrium constant K_\text: : A_ + S A_ From these basic hypotheses the mathematical formulation of the Langmuir adsorption isotherm can be derived in various independent and complementary ways: by the kinetics, the thermodynamics, and the statistical me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Ensemble
In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. The system can exchange energy with the heat bath, so that the states of the system will differ in total energy. The principal thermodynamic variable of the canonical ensemble, determining the probability distribution of states, is the absolute temperature (symbol: ). The ensemble typically also depends on mechanical variables such as the number of particles in the system (symbol: ) and the system's volume (symbol: ), each of which influence the nature of the system's internal states. An ensemble with these three parameters is sometimes called the ensemble. The canonical ensemble assigns a probability to each distinct microstate given by the following exponential: :P = e^, where is the total energy of the microstate, and is the Boltzmann constant. The number is the free ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monod Equation
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910 – 1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient. The Monod equation has the same form as the Michaelis–Menten equation, but differs in that it is empirical while the latter is based on theoretical considerations. The Monod equation is commonly used in environmental engineering. For example, it is used in the activated sludge model for sewage treatment. Equation The empirical Monod equation is: : \mu = \mu_\max where: * ''μ'' is the growth rate of a considered microorganism * ''μ''max is the maximum growth rate of this microorganism * 'S''is the concentration of the limiting substrate ''S'' for growth * ''K''''s'' is the "half-velocity constant"—the value of 'S''when ''μ''/''Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michaelis–Menten Kinetics
In biochemistry, Michaelis–Menten kinetics 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 v (rate of formation of product, ce P/math>) to ce S/math>, the concentration of a substrate ''S''. Its formula is given by : v = \frac = V_\max \frac This equation is called the Michaelis–Menten equation. Here, V_\max represents the maximum rate achieved by the system, happening at saturating substrate concentration for a given enzyme concentration. When the value of the Michaelis constant K_\mathrm is numerically equal to the substrate concentration, then the reaction rate is half of V_\max. Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions. Model In 1901, French ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill Equation (biochemistry)
In biochemistry and pharmacology, the Hill equation refers to two closely related equations that reflect the binding of ligands to macromolecules, as a function of the ligand concentration. A ligand is "a substance that forms a complex with a biomolecule to serve a biological purpose" ( ligand definition), and a macromolecule is a very large molecule, such as a protein, with a complex structure of components ( macromolecule definition). Protein-ligand binding typically changes the structure of the target protein, thereby changing its function in a cell. The distinction between the two Hill equations is whether they measure ''occupancy'' or ''response''. The Hill–Langmuir equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand.For clarity, this article will use the International Union of Basic and Clinical Pharmacology convention of distinguishing between the Hill-Langmuir equation (for receptor saturation) and Hill equation (for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Everett Isotherm
Everett may refer to: Places Canada * Everett, Ontario, a community in Adjala–Tosorontio, Simcoe County * Everett Mountains, a range on southern Baffin Island in Nunavut United States * Everett, Massachusetts, in Middlesex County, Massachusetts north of Boston * Everett, Missouri, an unincorporated community * Everett, Nebraska, an unincorporated community * Everett, New Jersey, an unincorporated community * Everett, Ohio, an unincorporated community * Everett, Pennsylvania, in Bedford County, Pennsylvania ** Everett Area School District, a public school district in Bedford Country. * Everett, Washington, the county seat and largest city in Washington state's Snohomish County ** Everett Massacre, an armed confrontation between local authorities and members of the Industrial Workers of the World union ** Boeing Everett Factory, an airplane assembly building owned by Boeing * Everett Township (other), a list of townships named Everett Elsewhere * Everett Range, Ant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BET Multilayer Adsorption
Black Entertainment Television (acronym BET) is an American basic cable television channel, channel targeting African Americans, African-American audiences. It is owned by the CBS Entertainment Group unit of Paramount Global via BET Networks and has offices in New York City, Los Angeles, Chicago, and was formerly headquartered in Washington, D.C. As of February 2015, approximately 88,255,000 American households (75.8% of households with television) receive the channel. History After stepping down as a lobbyist for the cable industry, Freeport, Illinois, Freeport, Illinois native Robert L. Johnson decided to launch his own cable television network. Johnson would soon acquire a loan for $15,000 and a $500,000 investment from media executive John Malone to start the network. The network, which was named Black Entertainment Television (BET), launched on January 25, 1980. Cheryl D. Miller designed the logo that would represent the network, which featured a star to symbolize "Bla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrophobic Effect
The hydrophobic effect is the observed tendency of nonpolar substances to aggregate in an aqueous solution and exclude water molecules. The word hydrophobic literally means "water-fearing", and it describes the segregation of water and nonpolar substances, which maximizes hydrogen bonding between molecules of water and minimizes the area of contact between water and nonpolar molecules. In terms of thermodynamics, the hydrophobic effect is the free energy change of water surrounding a solute. A positive free energy change of the surrounding solvent indicates hydrophobicity, whereas a negative free energy change implies hydrophilicity. The hydrophobic effect is responsible for the separation of a mixture of oil and water into its two components. It is also responsible for effects related to biology, including: cell membrane and vesicle formation, protein folding, insertion of membrane proteins into the nonpolar lipid environment and protein-small molecule associations. Hence the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Surface Area
Specific surface area (SSA) is a property of solids defined as the total surface area of a material per unit of mass, (with units of m2/kg or m2/g) or solid or bulk volume (units of m2/m3 or m−1). It is a physical value that can be used to determine the type and properties of a material (e.g. soil or snow). It has a particular importance for adsorption, heterogeneous catalysis, and reactions on surfaces. Measurement Values obtained for specific surface area depend on the method of measurement. In adsorption based methods, the size of the adsorbate molecule (the probe molecule), the exposed crystallographic planes at the surface and measurement temperature all affect the obtained specific surface area. For this reason, in addition to the most commonly used Brunauer–Emmett–Teller (N2-BET) adsorption method, several techniques have been developed to measure the specific surface area of particulate materials at ambient temperatures and at controllable scales, including methy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal De Broglie Wavelength
In physics, the thermal de Broglie wavelength (\lambda_, sometimes also denoted by \Lambda) is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature. We can take the average interparticle spacing in the gas to be approximately where is the volume and is the number of particles. When the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this critical temperature, the thermal wavelength will be approximately equal to the interparticle distance. That is, the quantum nature of the gas will be evident for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling's Approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of n. It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: \ln(n!) = n\ln n - n +O(\ln n), where the big O notation means that, for all sufficiently large values of n, the difference between \ln(n!) and n\ln n-n will be at most proportional to the logarithm. In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to use instead the binary logarithm, giving the equivalent form \log_2 (n!) = n\log_2 n - n\log_2 e +O(\log_2 n). The error term in either base can be expressed more precisely as \tfrac12\log(2\pi n)+O(\tfrac1n), corresponding to an approximate formula for the factorial itself, n! \sim \sqrt\left(\frac\righ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication. The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names ''thermodynamic function'' and ''heat-potential''. In 1865, German physicist Rudolf Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of hea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
