Polydispersity definition

We shall see that measurement of the osmotic pressure of a polydisperse system permits the experimental evaluation of M (Chapter 3), and light scattering experiments enable us to measure Mw (Chapter 5). It follows from the definition of these various averages that... 

The problem of molecular weight distribution (MWD) and functionality type distribution (FTD) belongs by definition to an extensive problem of molecular heterogeneity of polymers. In the synthesis of a polymer with the requested properties, e.g. a telechelic polymer, one is always faced with different types of polydispersity the macromolecules can be of different length, they can have a different number of functional groups, i.e. be mono-, bifunctional, etc., they can be branched (star-, comb- or tree-like) and, finally, they can be cyclic. 

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

Particles used in practice for gas-solid flows are usually nonspherical and polydispersed. For a nonspherical particle, several equivalent diameters, which are usually based on equivalences either in geometric parameters (e.g., volume) or in flow dynamic characteristics (e.g., terminal velocity), are defined. Thus, for a given nonspherical particle, more than one equivalent diameter can be defined, as exemplified by the particle shown in Fig. 1.2, in which three different equivalent diameters are defined for the given nonspherical particle. The selection of a desired definition is often based on the specific process application intended. 

Only a minority of systems of industrial interest contain powders with a uniform particle size, i.e. monodisperse. Most systems generally show a distribution of sizes (polydisperse) and it is then necessary to define the average dimension. There are many different definitions of particle size,1 2 the most commonly used, particularly in fluidisation, is the so called volume-surface mean or the Sauter mean diameter. This is the... 

The ratio Mw/ Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index. Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/ Mn is in the range 1.5-2, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/ Mn = 1.00. 

The probability of formation of polyhedra (cells) of a definite shape was studied with the methods of statistical mechanics applying two variants of calculations [52], These theoretical considerations were done for a monolayer of a polydisperse foam. Both variants gave a probability curve the maximum of which was at 6 side faces of the polyhedron. The theoretical dependence fits well with the curve of probability for distribution of cell faces in a real foam monolayer [53],... 

It has not so far been possible to perform a definitive set of experiments to show whether this holds for all possible molecular weight distributions, but it seems certain from existing experimental data that this result will be adequate for the type of polydispersity normally encountered. 

Gel permeation chromatography indicates a polymodal polydispersity with a broad molecular weight distribution. Currently it is not possible to specify the definite values of the average molecular weights due to a lack of comparable standards. 

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