Polydispersity index weight distribution

It may be shown that M > M. The two are equal only for a monodisperse material, in which all molecules are the same sise. The ratio MI /MI is known as the polydispersity index and is a measure of the breadth of the molecular weight distribution. Values range from about 1.02 for carefully fractionated samples or certain polymers produced by anionic polymerization, to 20 or more for some commercial polyethylenes. 

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

The micro-mixed reactor with dead-polymer model was developed to account for the large values of the polydispersity index observed experimentally. The effect of increasing the fraction of dead-polymer in the reactor feed while maintaining the same monomer conversion is to broaden the product polymer distribution and therefore to increase the polydispersity index. As illustrated in Table V, this model, with its adjustable parameter, can exactly match experiment average molecular weights and easily account for values of the polydispersity index significantly greater than 2. 

A micro-mixed, seeded reactor will produce a broad polymer distribution with a high molecular weight tail and polydispersity index that approaches 2 at large degrees of polymerization. 

A measure of the breadth of the molecular mass distribution is given by the ratios of molecular mass averages. The most commonly used ratio Mw/Mn — H, is called the polydispersity index. Wiegand and Kohler discuss the determination of molecular masses (weights) and their distributions in Chapter 6. 

Tab. 5.7 Polyethers from isosorbide and 1,8-dibromo- or dimesyloctane yield and distribution data for the microwave procedure (Mn and Mw are, respectively, the number average and weight average molecular weights, the ratio Mw/Mn being the polydispersity index).

The hydroboration/oxidation sequence does not change the molecular-weight distribution. Gel permeation chromatography (GPC) measurements in dimethyl-formamide (DMF) with the resulting polystyrene-ft-polyalcohol polymers show very similar polydispersity indexes (Table 10.2). Here, the hydroboration/oxidation sequence is clearly superior to the epoxidation reaction, which leads to a... 

The distribution of molecular weights of each generation was determined from measurements on about 50 molecules, with results shown in Figure 12.19 (the weight fraction is the percent dendrimer in each interval of molecular weight under consideration). Based on these distributions, the polydispersity index (.MJMa) of G5 to G10 can be calculated, with results shown in Table 12.1 [39], They are all less than 1.08, which means that the particle size distribution is very uniform for each generation. 

These observations require a detailed explanation. After several unsuccessful attempts a satisfying answer was finally found. A first step was made by the ingenious derivation of the molar mass distributions of randomly branched or randomly cross-linked materials [14]. The equation, that was later rederived by Elory [13], will be given in the next section. Here it suffices to point out that the width of the distribution, or the polydispersity index MJM , increases asymptotically with the weight average degree of polymerization... 

For polymerizations carried out to high conversions where the concentrations of propagating centers, monomer, and transfer agent as well as rate constants change, the polydispersity index increases considerably. Relatively broad molecular-weight distributions are generally encountered in cationic polymerizations. 

The molecular weight distribution obtained from SEC analysis was also shown in Fig. 8. In order to check the effect of the estimated exponent a(-0.55) on molecular weight distribution for Ei branched PVAc, we used another a(-0.58) value to compute a new calibration curve as shown in Fig. 9. The two calibration curves almost overlapped with each other. The results are listed in Table 2. In both cases, we obtained the same weight-average molecular weight and the polydispersity index (M /M ). Thus, we could confirm that in using a two-point (Bq and %l) estimate for a, we have not introduced an appreciable error in the determination of molecular weight distribution of branched PVAc. 

The GPC analysis of block copolymers is handicapped by the difficulty in obtaining a calibration curve. A method has recently been suggested to circumvent this difficulty by using the calibration curves of homopolymers. This method has been extended so that the calibration curves of block copolymers of various compositions can be constructed from the calibration curve of one-component homopolymers and Mark-Houwink parameters. The intrinsic viscosity data on styrene-butadiene and styrene-methyl methacrylate block polymers were used for verification. The average molecular weight determined by this method is in excellent agreement with osmometry data while the molecular weight distribution is considerably narrower than what is implied by the polydispersity index calculated from the GPC curve in the customary manner. 

Another important characteristic of a polymeric material deals with the molecular weight (MW), more precisely its number and weight averages, Mn and Mw, respectively and, in order to get an estimate of the broadness of the MW distribution, the polydispersity index I = Mw/Mn. 

The simplest measure of the breadth of a distribution is the ratio of two different types of average molecular weight. Specifically the ratio of Mw to Mn is by far the most widely used for this purpose, and is called the polydispersity index. It has a minimum value of unity (for a monodisperse material in which all the chains have exactly the same length). The extent to which it exceeds unity is a measure of the breadth of the distribution. Typical values are in the range 1.5-2.0, but many polymerizations yield considerably larger values. 

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. 

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