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Stokes Radius
The Stokes radius or Stokes–Einstein radius of a solute is the radius of a hard sphere that diffuses at the same rate as that solute. Named after George Gabriel Stokes, it is closely related to solute mobility, factoring in not only size but also solvent effects. A smaller ion with stronger hydration, for example, may have a greater Stokes radius than a larger ion with weaker hydration. This is because the smaller ion drags a greater number of water molecules with it as it moves through the solution. Stokes radius is sometimes used synonymously with effective hydrated radius in solution. Hydrodynamic radius, ''R''''H'', can refer to the Stokes radius of a polymer or other macromolecule. Spherical case According to Stokes’ law, a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient f: F_\text = fs = (6 \pi \eta a)s where \eta is the liquid's viscosity, s is the sphere's drift speed, and a is its radius. Because ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903. As a physicist, Stokes made seminal contributions to fluid mechanics, including the Navier–Stokes equations; and to physical optics, with notable works on polarization and fluorescence. As a mathematician, he popularised "Stokes' theorem" in vector calculus and contributed to the theory of asymptotic expansions. Stokes, along with Felix Hoppe-Seyler, first demonstrated the oxygen transport function of hemoglobin and showed color changes produced by aeration of hemoglobin solutions. Stokes was made a baronet by the British monarch in 1889. In 1893 he received the Royal Society's Copley Medal, then the most prestigious scientific prize in the world, "for his researches and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Relation (kinetic Theory)
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation is D = \mu \, k_\text T, where * is the diffusion coefficient; * is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ; * is the Boltzmann constant; * is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. Two frequently used important special forms of the relation are: * Einstein–Smoluchowski equation, for diffusion of charged particles: D = \frac * Stokes–Einstein equation, for diffusion of spherical particles through a liquid with low Reynolds number: D = \frac Here * is the electrical charge of a particle; * is the electrical mobility of the charged particle; * is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ion Transport Number
In chemistry, ion transport number, also called the transference number, is the fraction of the total electric current carried in an electrolyte by a given ionic species : :t_i = \frac Differences in transport number arise from differences in electrical mobility. For example, in an aqueous solution of sodium chloride, less than half of the current is carried by the positively charged sodium ions (cations) and more than half is carried by the negatively charged chloride ions (anions) because the chloride ions are able to move faster, i.e., chloride ions have higher mobility than sodium ions. The sum of the transport numbers for all of the ions in solution always equals unity: :\sum_i t_i = 1 The concept and measurement of transport number were introduced by Johann Wilhelm Hittorf in the year 1853. Liquid junction potential can arise from ions in a solution having different ion transport numbers. At zero concentration, the limiting ion transport numbers may be expressed in ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ionic Radius
Ionic radius, ''r''ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), with 1 Å = 100 pm. Typical values range from 31 pm (0.3 Å) to over 200 pm (2 Å). The concept can be extended to solvated ions in liquid solutions taking into consideration the solvation shell. Trends Ions may be larger or smaller than the neutral atom, depending on the ion's electric charge. When an atom loses an electron to form a cation, the other electrons are more attracted to the nucleus, and the radius of the ion gets smaller. Similarly, when an electron is added to an atom, forming an anion, the added electron increases the size of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalent Spherical Diameter
The equivalent spherical diameter of an irregularly shaped object is the diameter of a sphere of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation. The particle size of a perfectly smooth, spherical object can be accurately defined by a single parameter, the particle diameter. However, real-life particles are likely to have irregular shapes and surface irregularities, and their size cannot be fully characterized by a single parameter. The concept of equivalent spherical diameter has been introduced in the field of particle size analysis to enable the representation of the particle size distribution in a simplified, homogenized way. Here, the real-life particle is matched with an imaginary sphere which has the same properties according to a defined principle, enabling the real-life particle to be defined by the diameter of the imaginary sphere. The principle used to match the real-life particle and the ima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Light Scattering
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon auto-correlation function (also known as photon correlation spectroscopy or quasi-elastic light scattering). In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions. Setup A monochromatic light source, usually a laser, is shot through a polarizer and into a sample. The scattered light ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Capillary Electrophoresis
Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter diameter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other electrophoretic techniques including capillary gel electrophoresis (CGE), capillary isoelectric focusing (CIEF), capillary isotachophoresis and micellar electrokinetic chromatography (MEKC) belong also to this class of methods. In CE methods, analytes migrate through electrolyte solutions under the influence of an electric field. Analytes can be separated according to ionic mobility and/or partitioning into an alternate phase via non-covalent interactions. Additionally, analytes may be concentrated or "focused" by means of gradients in conductivity and pH. Instrumentation The instrumentation needed to perform capillary electrophoresis is relatively simple. A basic schematic of a capillary electrophoresis system is shown in ''figure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Born Equation
The Born equation can be used for estimating the electrostatic component of Gibbs free energy of solvation of an ion. It is an electrostatic model that treats the solvent as a continuous dielectric medium (it is thus one member of a class of methods known as continuum solvation methods). It was derived by Max Born. \Delta G =- \frac\left(1-\frac\right) where: *''N''A = Avogadro constant *''z'' = charge of ion *''e'' = elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a funda ..., 1.6022 C *''ε''0 = permittivity of free space *''r''0 = effective radius of ion *''ε''r = dielectric constant of the solvent Derivation The energy U stored in an electrostatic field distribution is:U=\frac \varepsilon_0 \varepsilon_r \int , , ^2 dVKnowing the magnitude of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Charge
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell's equations. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others. The presence of an electric charge, which can be either positive or negative, produces an electric field. The movement of electric charges is an electric current and produces a magnetic field. When a charge is placed in a location with a non-zero electric field, a force will act on it. The magnitude of this force is given by Coulomb's law. If the charge moves, the electric field would be doing work on the electric charge. Thus we can speak of electric potential at a certain point in space, which is equal to the work done by an external agent in carrying a unit of posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrodynamic Radius
The hydrodynamic radius of a macromolecule or colloid particle is R_. The macromolecule or colloid particle is a collection of N subparticles. This is done most commonly for polymers; the subparticles would then be the units of the polymer. R_ is defined by : \frac \ \stackrel\ \frac \left\langle \sum_ \frac \right\rangle where r_ is the distance between subparticles i and j, and where the angular brackets \langle \ldots \rangle represent an ensemble average. The theoretical hydrodynamic radius R_ was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer, and some sources still use ''hydrodynamic radius'' as a synonym for the Stokes radius. Note that in biophysics, hydrodynamic radius refers to the Stokes radius, or commonly to the apparent Stokes radius obtained from size exclusion chromatography. The theoretical hydrodynamic radius R_ arises in the study of the dynamic properties of polymers moving in a solvent. It is often similar in magni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven " defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly . Roles of the Boltzmann constant Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure and volume is proportional to the product of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory of relativity, but he also made important contributions to the development of the theory of quantum mechanics. Relativity and quantum mechanics are the two pillars of modern physics. His mass–energy equivalence formula , which arises from relativity theory, has been dubbed "the world's most famous equation". His work is also known for its influence on the philosophy of science. He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory. His intellectual achievements and originality resulted in "Einstein" becoming synonymous with "genius". In 1905, a year sometimes described as his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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