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Dispersity
In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform. The objects can be in any form of chemical dispersion, such as particles in a colloid, droplets in a cloud, crystals in a rock, or polymer macromolecules in a solution or a solid polymer mass. Polymers can be described by molecular mass distribution; a population of particles can be described by size, surface area, and/or mass distribution; and thin films can be described by film thickness distribution. IUPAC has deprecated the use of the term ''polydispersity index'', having replaced it with the term ''dispersity'', represented by the symbol Đ (pronounced D-strokeStepto, R. F. T.; Gilbert, R. G.; Hess, M.; Jenkins, A. D.; Jones, R. G.; Kratochvíl P. (2009).Dispersity in P ...
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Weight Average Molecular Weight
The molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation. Definitions of molar mass average Different average values can be defined, depending on the statistical method applied. In practice, four averages are used, representing the weighted mean taken with the mole fraction, the weight fraction, and two other functions which can be related to measured quantities: *''Number average molar mass'' (Mn), also loosely referred to as ''number average molecular weight'' (NAMW). *''Mass average molar mass'' (Mw), where ''w'' stands for weight; also commonly referred to as ''weight average'' or ''w ...
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Number Average Molecular Weight
The molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation. Definitions of molar mass average Different average values can be defined, depending on the statistical method applied. In practice, four averages are used, representing the weighted mean taken with the mole fraction, the weight fraction, and two other functions which can be related to measured quantities: *''Number average molar mass'' (Mn), also loosely referred to as ''number average molecular weight'' (NAMW). *''Mass average molar mass'' (Mw), where ''w'' stands for weight; also commonly referred to as ''weight average'' or ''wei ...
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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 ...
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Living Polymerization
In polymer chemistry, living polymerization is a form of chain growth polymerization where the ability of a growing polymer chain to terminate has been removed. This can be accomplished in a variety of ways. Chain termination and chain transfer reactions are absent and the rate of chain initiation is also much larger than the rate of chain propagation. The result is that the polymer chains grow at a more constant rate than seen in traditional chain polymerization and their lengths remain very similar (i.e. they have a very low polydispersity index). Living polymerization is a popular method for synthesizing block copolymers since the polymer can be synthesized in stages, each stage containing a different monomer. Additional advantages are predetermined molar mass and control over end-groups. Living polymerization is desirable because it offers precision and control in macromolecular synthesis. This is important since many of the novel/useful properties of polymers result ...
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Polymer
A polymer (; Greek ''poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compounds, produces unique physical properties including toughness, high elasticity, viscoelasticity, and a tendency to form amorphous and semicrystalline structures rather than crystals. The term "polymer" derives from the Greek word πολύς (''polus'', meaning "many, much") and μέρος (''meros'', mean ...
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Carothers' Equation
In step-growth polymerization, the Carothers equation (or Carothers' equation) gives the degree of polymerization, , for a given fractional monomer conversion, . There are several versions of this equation, proposed by Wallace Carothers, who invented nylon in 1935. Linear polymers: two monomers in equimolar quantities The simplest case refers to the formation of a strictly linear polymer by the reaction (usually by condensation) of two monomers in equimolar quantities. An example is the synthesis of nylon-6,6 whose formula is from one mole of hexamethylenediamine, , and one mole of adipic acid, . For this case :\bar_n=\frac In this equation * is the number-average value of the degree of polymerization, equal to the average number of monomer units in a polymer molecule. For the example of nylon-6,6 \bar_n = 2n ( diamine units and diacid units). *p=\tfrac is the extent of reaction (or conversion to polymer), defined by ** is the number of molecules present initially as monome ...
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Polymerization
In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. There are many forms of polymerization and different systems exist to categorize them. In chemical compounds, polymerization can occur via a variety of reaction mechanisms that vary in complexity due to the functional groups present in the reactants and their inherent steric effects. In more straightforward polymerizations, alkenes form polymers through relatively simple radical reactions; in contrast, reactions involving substitution at a carbonyl group require more complex synthesis due to the way in which reactants polymerize. Alkanes can also be polymerized, but only with the help of strong acids. As alkenes can polymerize in somewhat straightforward radical reactions, they form useful compounds such as polyethylene and polyvinyl chloride (PVC), w ...
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Block Copolymer
In polymer chemistry, a copolymer is a polymer derived from more than one species of monomer. The polymerization of monomers into copolymers is called copolymerization. Copolymers obtained from the copolymerization of two monomer species are sometimes called ''bipolymers''. Those obtained from three and four monomers are called ''terpolymers'' and ''quaterpolymers'', respectively. Copolymers can be characterized by a variety of techniques such as Nuclear magnetic resonance spectroscopy, NMR spectroscopy and size-exclusion chromatography to determine the molecular size, weight, properties, and composition of the material. Commercial copolymers include acrylonitrile butadiene styrene (ABS), styrene/butadiene co-polymer (SBR), nitrile rubber, styrene-acrylonitrile, styrene-isoprene-styrene (SIS) and ethylene-vinyl acetate, all of which are formed by chain-growth polymerization. Another production mechanism is step-growth polymerization, which is used to produce the nylon-12/6/66 co ...
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Gel Permeation Chromatography
Gel permeation chromatography (GPC) is a type of size-exclusion chromatography (SEC), that separates analytes on the basis of size, typically in organic solvents. The technique is often used for the analysis of polymers. As a technique, SEC was first developed in 1955 by Lathe and Ruthven.Lathe, G.H.; Ruthven, C.R.J. The Separation of Substance and '1956', ''62'', 665–674. The term ''gel permeation chromatography'' can be traced back to J.C. Moore of the Dow Chemical Company who investigated the technique in 1964. The proprietary column technology was licensed to Waters Corporation, who subsequently commercialized this technology in 1964.Moore, J.C. Gel permeation chromatography. I. A new method for molecular weight distribution of high polymers. ''J. Polym. Sci.'', 1964, ''2'', 835-84 GPC systems and consumables are now also available from a number of manufacturers. It is often necessary to separate polymers, both to analyze them as well as to purify the desired product. When ...
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Plug Flow Reactor Model
The plug flow reactor model (PFR, sometimes called continuous tubular reactor, CTR, or piston flow reactors) is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of chemical reactors of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated. Fluid going through a PFR may be modeled as flowing through the reactor as a series of infinitely thin coherent "plugs", each with a uniform composition, traveling in the axial direction of the reactor, with each plug having a different composition from the ones before and after it. The key assumption is that as a plug flows through a PFR, the fluid is perfectly mixed in the radial direction but not in the axial direction (forwards or backwards). Each plug of differential volume is considered as a separate entity, effectively an infinitesimally small continuous stirred tank reactor, limiting to zero vo ...
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Continuous Stirred-tank Reactor
The continuous stirred-tank reactor (CSTR), also known as vat- or backmix reactor, mixed flow reactor (MFR), or a continuous-''flow'' stirred-tank reactor (C''F''STR), is a common model for a chemical reactor in chemical engineering and environmental engineering. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. The mathematical model works for all fluids: liquids, gases, and slurries. The behavior of a CSTR is often approximated or modeled by that of an ideal CSTR, which assumes perfect mixing. In a perfectly mixed reactor, reagent is instantaneously and uniformly mixed throughout the reactor upon entry. Consequently, the output composition is identical to composition of the material inside the reactor, which is a function of residence time and reaction rate. The CSTR is the ideal limit of complete mixing in reactor design, which is the complete opposite of a plug flow react ...
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