Polydisperse polymer populations

Polymer populations in which all chains have identical masses are termed monodisperse. Proteins and DNA of the same type are necessarily monodisperse, as they are coded for precise monomer sequences. In general, however, polymer populations contain a wide distribution of masses. Such populations are termed polydisperse. While most synthetically produced polymers are polydisperse, many biopolymers are also produced in polydisperse populations for example, a variety of polysaccharides, glycoproteins, etc. 

The number- and weight-average chain lengths, as well as the polydispersity, of the instantaneous polymer population can be derived from eqn [61]... 

Dendrimers are nearly spherical in shape when compared to conventional linear polymers [ 17,34], The lower generation dendrimers have internal segment density distributions similar to star molecules, but even the smallest are more compact than stars. As the generation number increases, the sphere-like characteristics increase and the largest dendrimers form a population of spheres with uniform internal density (roughly half dendrimer units-half solvent) [47], sharp interfaces on the outside and a small polydispersity in shape. 

Tiopronin water soluble Au clusters have been described and their characterization by HRTEM and TGA has shown clusters of about 1.8 nm and a composition of Au2oi(Tiopronin)85 [65]. Polymer protected water soluble gold MPCs have also been synthesized using thiolated polyethyleneglycol (SH-PEG). H RTEM analysis displays a polydisperse population of clusters of 2.8 1 nm size and TGA results yields an average Au807(SH-PEG)98 composition [66]. 

In contrast, the typical polydispersity of polymers produced with Phillips catalysts varies from 6 to 20, and specialized catalyst treatments can provide polymers of PDI as low as 4.0 or as high as 100. Thus, 2 to 12 unique site types are required to reproduce the MW distribution from Phillips catalysts, because the catalyst contains a heterogeneous population of sites, differing widely in propagation and termination rate constants. Each site type generates polymer with its own characteristic MW, and consequently the polymer MW breadth reflects the heterogeneity of the site population. Differences in site reactivity no doubt derive from the... 

In a heterogeneous population of polymer chains, M is always lower than Mu, and M , is always lower than (i.e. M < Mu, < MJ. The polymolecu-larity or polydispersity index (PI) can be defined to characterise the distribution in molecular weight of the population, as shown in Equation 2.4. 

A method of describing the variation of a stable system, in which individual values are not predictable but in which the outcome as a group forms a pattern that can be described in terms of its location, spread, and shape. A differential or integral description of population. For the polymer molecular weight a mathematical description of the polydispersity. 

I-1), where (Pp is the polymer volume fraction and % is the ratio of polymer to particle size (which sets the interaction range). The density of colloidal particles is the other key parameter for the phase diagram of the system, which we will report as volume fraction (p = SfjPj, where the sum runs over populations of particles, Vj is the particle volume, and P is the number density of population i (remember that polydisperse systems are used). 

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