Degree of polydispersity

Alternatively, the one-step polymerization of branched monomers results in what is called a hyperbranched polymer [53] possessing a higher degree of polydispersity and lower degree of branching compared to the analogous dendrimer. 

In the past few decades, a specific kind of colloidal system based on monodis-perse size has been developed for various industrial applications. A variety of metal oxides and hydroxides and polymer lattices have been produced. Monodisperse systems are obviously preferred since their properties can be easily predicted. On the other hand, polydisperse systems will exhibit varying characteristics, depending on the degree of polydispersity. 

As can be seen, many factors affect the geometry of HIPEs. Generally, a degree of polydispersity and some cell distortion is shown in real systems and very rarely, if ever, will a truly monodisperse system be observed1. The extent of deviation from monodispersity will depend on the experimental conditions and on the physical properties of the HIPE. 

NP diameters observed through are 6.2 1.7nm showing some degree of polydispersity. 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

For any polydispersed system, Mx (mass average) > Mt (number average), and only when the system is monodispersed will these averages coincide. The ratio Mr (mass average)/Mr (number average) is a measure of the degree of polydispersity. 

The sedimentation process gives rise to a solvent phase and a concentrated polymer solution phase which are separated by a boundary layer in which the polymer concentration varies. There is, therefore, a natural tendency for backward diffusion of the molecules in order to equalise the chemical potentials of the components in the different regions of the cell, and this causes broadening of the boundary layer. The breadth of the boundary layer also increases with the degree of polydispersity because molecules of higher molar mass sediment at faster rates. The windows in the cell enable the radial variation in polymer concentration to be measured during ultracentrifugation typically... 

Figure 17.4 Angular intensity ratio, I/I0, for lognormal aerosols with different degrees of polydispersity, X = 550 nm.

Geometrical shape of gas bubbles in foam depends on the ratio of gas and liquid volumes, on the degree of polydispersity and on bubble packing. The results discussed below apply also for concentrated emulsions (considering density and interfacial tension). 

The average foam dispersity in the experiments performed varied within the limits of aVL = 6.10"2-3.5.10 1 mm the degree of polydispersity significantly increased in the process of foam coarsening. It can be seen that curves 1 and 2 fit well at expansion ratio n > 300. At low expansion ratio (20 < n < 40) the difference between rjr (n) and rjrn(n) grows to 15% but if the longitudinal curvature is accounted for then this difference is about 7%. This means that the difference in size of the individual bubbles in a polydisperse foam does not influence strongly the course of the ra lrn (n) dependence as compared to the monodisperse model system. 

Subsequently Crabtree et al. developed a model according to which polymerization would take place with the encapsulation of catalyst sub-particles. Such a model provides for a rapid increase in the degree of polydispersity to a maximum and then a slow drop with increasing polymer yield or reaction time. 

Polyethylene with an even lower degree of polydispersity was recently obtained by Greco et al. by studying high yield magnesium chlorotitanate-based... 

---