Approaches to Polydispersity

The pedestrian approach to polydispersity that has been demonstrated up to here is an extension to three dimensions of the well-known rigorous treatment of polydispersity in one dimension by means of the Mellin convolution (Eq. (8.85), p. 168). 

The Tensor Approach to Polydispersity is treating the problem on a much more universal level. Here it shall at least be sketched. Instead of Eq. (2.28) we write... 

Li G, MeGown L. A new approach to polydispersity studies of sodium taurocholate and sodium taurodeoxycholate aggregates using dynamic fluorescence anisotropy. J Phys Chem 1993 97 6745-52. 

In section 9.2, the polydispersity is proven to influence strongly the phase eqnilibrium. As an example the liquid + liquid equilibrium of a polymer solution is discussed. In section 9.3, the approaches to polydispersity are treated in... 

We can extend this approach to polydisperse flexible homopolymers as the most general situation, for which Gy co) and G "(a)) may be written as (Han and Kim 1989a)... 

A similar in situ approach to alkoxide formation employs the readily accessible tris(amide)-Y(NTMS2)3, (293), and PrOI 1.881 In the absence of alcohol the polymerization of CL is fast but not controlled (Mw/Mn > 3). However, upon addition of alcohol, a controlled living system with polydispersities 1.1-1.2 results. At least 50 equivalents of PrOH may be added (the excess effects rapid chain transfer) with molecular weights in good agreement with theoretical values. Similar results have been reported using Nd(NTMS2)3, (294), and PrOH.882 The reactions of PrOH with (292) and (293) have both been studied by NMR, and in both cases Y5(/r5-0)(0 Pr)13 is not... 

Similar exercises must be performed to identify synthetic nanocomponents. Considerations include suitability for the proposed environment, synthesis and handling properties, polydispersity, structural / chemical properties, as well as amenability to assembly into higher order structures. For medical devices, tolerability and safety of the structural materials is also an issue. Current materials technology offers powerful, but limited capacity to engineer an off the shelf approach to nanostructures. 

We should note that in this introductory overview we generously ignored a number of important complications. For instance, a typical solution will be polydisperse, comprising chains of different lengths. Also the approach to the excluded volume limit ca.r follow two different paths, leading to two different, but universal, branches for functions like ag(z). All such complications will be discussed in later chapters, where a more detailed data analysis will also be presented. 

Star poly(methylmethacrylates) were synthesized via atom transfer polymerization using a small carbosilane dendrimer functionalized with a tertiary bromide moiety as an initiator core (Figure 12)100,101. a convergent approach to star polymers with a carbosilane dendrimer core was described in a report by Allgaier and coworkers102, in which living poly(butadienyl-lithium) arms were coupled with various SiCl-terminated carbosilane den-drimers. Utilizing smaller dendrimers with lower functionality was found to yield nearly ideal results in terms of substitution and polydispersity. 

Szwarc and Zimm described the consequences of transfer in the sense of eqn. (41) by means of differential equations [29], and O Driscoll simulated the system corresponding to the above scheme by the Monte Carlo method [30], Both kinds of approach produced polydispersity coefficient (PJPn) vs. time plots which were practically identical at longer times. 

In an evaluation of a range of instruments Lange [318] stated that turbidimetty appeared the most reliable approach to average size determination, whereas ultracentrifugation, DCP and TEM with image analysis were superior for determining size distributions and polydispersity. 

---