Molecular weight distribution dispersion index

They are discrete transforms and can therefore operate directly on the separate equations for each species, reducing them to one expression. Nonlinear terms arising from condensation polymerization can be handled and, with some difficulty, so can realistic terminations in free radical polymerization. They are a special case of the generating functions and can be used readily to calculate directly the moments of the distribution, and thus, average molecular weights and dispersion index, etc. Abraham (2) provided a short table of Z-transforms and showed their use with stepwise addition. 

In summary, the attributes of the elastomer that contribute to the enhanced impact strength of a plastic in plastic mbber blend include the type of mbber, plastic to mbber ratio, particle size, particle size distribution, cross-Unk density, and degree of grafting, if any. Molecular weight and molecular weight distribution of the plastic also exert some influence. For example, for high-impact PS, the optimal molecular weight of PS is between 170,000 and 220,000. The dispersity index is... 

The polydispersity of dendritic molecules, expressed in the form of their poly-dispersity index (PDI), is directly related to their structural perfection. The PDI is a measure of molecular weight distribution. 

The ratio MJM is called the polydispersity index (also known as heterogeneity index and dispersity index) and is an indication of the broadness of molecular weight distribution. As polydispersity index increases, MWD broadens. If the polymer were a single macromolecule, the polydispersity would be 1.0 and the polymer would be said to be monodisperse. 

The theoretical molecular weight distributions for cationic chain polymerizations (see Problem 8.30) are the same as those described in Chapter 6 for radical chain polymerizations terminating by disproportionation, i.e., where each propagating chain yields one dead polymer molecule. The poly-dispersity index (PDI = DP /DPn) has a limit of 2. Many cationic polymerizations proceed with rapid initiation, which narrows the molecular weight distribution (MDI). In the extreme case where termination and transfer reactions are very slow or nonexistent, this would yield a very narrow MDI with PDI close to one (p. 681). 

The polymers produced by Ziegler-Natta polymerization normally have very wide molecular weight distributions. The polydispersity index PDI (= Myj/Mn) is 5-20 for polyethylene and 5-15 for polypropylene. The cause of the wide dispersity is not precisely known. Some workers believe that the propagation reaction becomes diffusion controlled after a few percent conversion and it is this which is responsible for the large dispersity. Some other workers believe that the rate constants are dependent upon the molecular size. 

Molecular weight distributions are predicted to be of the Flory type with a dispersion index equal to 2.0. The numerical results show that the dispersion index has a value of 4/3 at the beginning of the reaction, very quickly approaching a value of 2.0. These results are in complete agreement with the predictions of Saidel and Katz (5). They are the same whether or not the polymer particle size distribution has been considered. 

By contrast with other chromatographic methods, GPC (gel permeation chromatography) or SEC (size exclusion chromatography) separates according to the size of the specimen molecule in solution. This is a simple way of utilizing the exclusion principle. This very specific separation mechanism enables the determination of molecular weight distribution and dispersion index. 

Influence from multiple extrusion of high-molecular polystyrene on molecular weight, dispersion index, and molecular weight distribution [20]... 

A key term in the standard deviation is the ratio of Mw to Mn. This term is known as the polydispersivity index and it is used as a measure of the breadness of the molecular weight distribution. The polydispersity index or dispersity D is commonly used to measure the distribution of molecular mass in a given polymer sample ... 

The stable free radical polymerization technique is characterized by the growing polymer chains that are reversibly capped by a stable free radical [e.g., 2,2-tetramethyl-l-piperidynyloxy nitroxide (TEMPO)]. For example, stable polystyrene dispersions were prepared by the stable free radical polymerization of styrene conducted in miniemulsion polymerization at 135 C [62]. Sodium dodecylbenzene sulfonate, hexadecane, and potassium persulfate/ TEMPO were used as the surfactant, costabihzer, and initiator system, respectively. Prodpran et al. [63] studied the styrene miniemulsion polymerization stabilized by Dowfax 8390 and hexadecane and initiated by benzoyl peroxide at 125 °C. A molar ratio of TEMPO to benzoyl peroxide equal to 3 to 1 resulted in polystyrene with the lowest polydispersity index (1.3) of polymer molecular weight distribution. 

A series of COOH-flinctionalized PCs were synthesized via an organocatalytic ROP pathway under mild conditions. The polymers exhibited moderate molecular weight (A4 = 3100-9700) and were very narrowly distributed (dispersity index=1.07-1.15). Aliphatic amines with different chain lengths (triethylenete-traamine, tetraethylenepentamine, or pentaethylenehexamine)... 

The dispersity in chain lengths (often referred to as the polydispersity index or PDI) is very low, implying that the width of the molecular weight distribution... 

The variance measures the absolute breadth of the distribution, but properties that depend on the width of the distribution would depend on the width relative to the average. For this reason the dispersion index is defined as the ratio of the weight to the number average molecular weight, which is related to the variance as follows ... 

Continuous Stirred Tank Reactors. Biesenberger (8) solved for the MWD with condensation polymerization in a CSTR, analogous to the treatment Denbigh (14) provided for the other two mechanisms. In this case, the variable residence time distribution leads to an extremely broad MWD with even the maximum weight fraction at the lowest molecular weight (monomer). The dispersion index approaches infinity as the condensation is driven to completion in a stirred tank reactor. A sequential analytical solution of the algebraic equations was obtained with a numerical evaluation of the consecutive equations. 

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