Polydispersity index, discussion

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. 

The ratio Xw/Xn is synonymous with the ratio MwfMn discussed in Sec. 1-4. It is a measure of the polydispersity of a polymer sample. The value of Xw/Xn increases with the extent of reaction and approaches 2 in the limit of large extents of reaction. The ratio XwfX is also referred to as the polydispersity index (PDI). 

A consideration of the preceding equations indicates that high polymer (i.e., large values of X and Xw) will be produced only if p is close to unity. This is certainly what one expects from the previous discussions in Sec. 3-5. The distributions described by Eqs. 2-86, 2-88, and 2-89 have been shown in Figs. 2-9 and 2-10. The breadth of the size distribution Xw/X [also referred to as the polydispersity index (PDI)] has a limiting value of two as p approaches unity. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

A polymerization that provides a transition into a discussion of gelation is the condensation of an excess of A-B with a small amount of an /-functional monomer, R-A/, that contains / equivalent functional groups of Type A, but no functional groups of Type B.[3 Linear chains are obtained when / is 1 or 2, but multichain condensation polymers are produced when/>2. At high conversion the polydispersity index depends only on/. 

Before we leave molecular weight discussion mention should be made of the heterogeneity index (HI), or polydispersity index. This is defined as the weight average molecular weight divided by the number average molecular weight ... 

Equation 5.1 is applicable to polyolefins made with single-site catalysts, such as metallocenes, and predicts a polydispersity index of 2.0. It is discussed later how this equation can also be used to model the CLD of polyolefins made with multiple-site catalysts, such as heterogeneous Ziegler-Natta and Phillips catalysts. Despite its simplicity, this equation can be used to predict the complete CLD of single-site polyolefins instantaneously using an easy-to-estimate parameter, t. 

The chemical structure of BP-AZ-CA can be seen in Fig. 5.1. The sample used in the following discussion has a number-averaged molecular weight of 41,000, with a polydispersity index of 2.2. The colloidal spheres of the azo polymer were prepared by gradual hydrophobic aggregation scheme as discussed earlier. The sizes of the colloidal spheres were estimated by both TEM and DLS measurement. The average hydrodynamic diameter (Z>h) was measured to be 223 nm, with a polydispersity index of 0.04. The 2-D arrays of the close-packed colloidal spheres were fabricated by the vertical deposition method. 

PHEMA, the theoretical value iWntheo calculated with the monomer-to-initiator molar ratio and the conversion was used (for selected samples, the validity of this assumption was confirmed by GPC with a multiangle laser light-scattering (MALLS) detector). The following discussion will be based on M theo for absolute M and /Ww,PEG/Afn,PEG fot absolute polydispersity index. 

The synthesis of polymers, with attendant aspects of the thermodynamics and kinetics of polymerization that occupy entire textbooks (62,63), is to a very significant extent beyond the coverage of this text. Indeed, organic polymer science is often taught as a mate course to physical polymer science. However, since the thermodynamics and kinetics of polymerization affect both the molecular weights and the polydispersity index obtained, the most salient features of these areas will be explored. Polymer synthesis itself was briefly discussed in Section 1.4. 

The value of is sensitive to the presence of higher molecular masses, whereas the value of ilf, is sensitive to the lower molecular masses. The ratio of M and Jlf, is often used as a measure of the breadth of the molecular-weight distribution (MWD) and times is referred to as the polydispersity index. In monodisperse systems, MJM = 1, whereas in the examples discussed in Sections 1.1.2A and 1.1.2B, MJMn = 2.5 (550,000/220,000), indicating that it is a polydisperse system. 

The breadth of the molecular weight distrihution is often discussed in terms of the dispersity ( )) (also commonly called the polydispersity index or the polydispersity) and is expressed in terms of the moments as shown in eqn [41] ... 

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