Dispersity
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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 Po ...
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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 cha ...
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Colloid
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols and gels. The term colloidal suspension refers unambiguously to the overall mixture (although a narrower sense of the word ''suspension'' is distinguished from colloids by larger particle size). A colloid has a dispersed phase (the suspended particles) and a continuous phase (the medium of suspension). The dispersed phase particles have a diameter of approximately 1 nanometre to 1 micrometre. Some colloids are translucent because of the Tyndall effect, which is the scattering of light by particles in the colloid. Other colloids may be opaque or have a slight color. Colloidal suspensions are the subject of interface and colloid science. This field of study was introduced in 1845 by Itali ...
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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 ''weight ...
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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 ''weight ...
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Polyelectrolyte
Polyelectrolytes are polymers whose repeating units bear an electrolyte group. Ion#Anions and cations, Polycations and polyanions are polyelectrolytes. These groups dissociation (chemistry), dissociate in aqueous solutions (water), making the polymers charge (physics), charged. Polyelectrolyte properties are thus similar to both electrolytes (salts) and polymers (high molecular weight compounds) and are sometimes called polysalts. Like salts, their solutions are electrically conductive. Like polymers, their solutions are often viscosity, viscous. Charged molecular chains, commonly present in soft matter systems, play a fundamental role in determining structure, stability and the interactions of various molecular assemblies. Theoretical approaches to describing their statistical properties differ profoundly from those of their electrically neutral counterparts, while technological and industrial fields exploit their unique properties. Many biological molecules are polyelectrolytes. ...
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Fulvic Acid
Humic substances (HS) are organic compounds that are important components of humus, the major organic fraction of soil, peat, and coal (and also a constituent of many upland streams, dystrophic lakes, and ocean water). For a long era in the 19th and 20th centuries, humic substances were often viewed through a lens of acid–base theory that described humic acids (HA), as organic acids, and their conjugate bases, humates, as important components of organic matter. Through this viewpoint humic acids were defined as organic substances extracted from soil that coagulate (form small solid pieces) when a strong-base extract is acidified, whereas fulvic acids (FA) are organic acids that remain soluble (stay dissolved) when a strong-base extract is acidified. The remaining alkali-insoluble part of humus would be termed humin. Humic matter in isolation is the result of a chemical extraction from the soil organic matter or the dissolved organic matter and represent the humic molecules dist ...
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Damköhler Numbers
The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale ( reaction rate) to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköhler. The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka. In its most commonly used form, the Damköhler number relates the reaction timescale to the convection time scale, volumetric flow rate, through the reactor for continuous (plug flow or stirred tank) or semibatch chemical processes: : \mathrm = \frac In reacting systems that include interphase mass transport, the second Damköhler number (DaII) is defined as the ratio of the chemical reaction rate to the mass transfer rate : \mathrm_ = \frac It is also defined as the ratio of the characteristic fluidic and chemical time scales: : \mathrm = \frac Since the reaction timescale is determined by the reaction rate, the exact formula for the Damköhler number v ...
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Geometric Distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: * The probability distribution of the number ''X'' of Bernoulli trials needed to get one success, supported on the set \; * The probability distribution of the number ''Y'' = ''X'' − 1 of failures before the first success, supported on the set \. Which of these is called the geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometric distribution is adopted for the former one (distribution of the number ''X''); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly. The geometric distribution gives the probability that the first occurrence of success requires ''k'' independent trials, each with success probability ''p''. If the probability of succe ...
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Degree Of Polymerization
The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule. For a homopolymer, there is only one type of monomeric unit and the ''number-average'' degree of polymerization is given by DP_n\equiv X_n=\frac, where Mn is the number-average molecular weight and M0 is the molecular weight of the monomer unit. For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired. This number does not reflect the variation in molecule size of the polymer that typically occurs, it only represents the mean number of monomeric units. Some authors, however, define DP as the number of repeat units, where for copolymers the repeat unit may not be identical to the monomeric unit.Fried J.R. "Polymer Science and Technology" (Pearson Prentice-Hall, 2nd edn 2003), p.27 For example, in nylon-6,6, the repeat unit contains the two monomeric units —NH(CH2)6NH— and —OC(CH2)4CO—, so that a chain ...
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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 reacto ...
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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 volu ...
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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 from t ...
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