Poly dispersability

On the basis of the concepts and notation introduced here, we see that there are several ways of describing a poly disperse system ... 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

If the poorer solvent is added incrementally to a system which is poly-disperse with respect to molecular weight, the phase separation affects molecules of larger n, while shorter chains are more uniformly distributed. These ideas constitute the basis for one method of polymer fractionation. We shall develop this topic in more detail in the next section. 

The solute molecular weight enters the van t Hoff equation as the factor of proportionality between the number of solute particles that the osmotic pressure counts and the mass of solute which is known from the preparation of the solution. The molecular weight that is obtained from measurements on poly disperse systems is a number average quantity. 

Table 9,4 Data for the Analysis of the Gel Permeation Chromatogram of a Poly disperse Polymer Used in Example 9.7...

A mass of polymer will contain a large number of individual molecules which will vary in their molecular size. This will occur in the case, for example, of free-radically polymerised polymers because of the somewhat random occurrence of ehain termination reactions and in the case of condensation polymers because of the random nature of the chain growth. There will thus be a distribution of molecular weights the system is said to be poly disperse. 

Z. Tang, L. E. Scriven, H. T. Davis. Size selectivity in adsorptions of poly-disperse hard-rod fluids in micropores. J Chem Phys 97 5732-5737, 1992. 

For additional evaluation of the effect of hydrophobization and the molecular weight of the polymers on the biological immuno-stimulating activity, we investigated the ex vivo cytokine (interIeukin-6 [IL-6], and tumor necrosis factor [TNFj-inducing activity from human peripheral whole blood cells of hydrophobized polymers by use of fractionated poly(M A-CDA) with narrow poly-dispersity. Since this assay uses the intact human cells, it shows more accurate results than in vitro assay using cultured cell line [25]. 

Data of Figs 8-10 give a simple pattern of yield stress being independent of the viscosity of monodisperse polymers, indicating that yield stress is determined only by the structure of a filler. However, it turned out that if we go over from mono- to poly-disperse polymers of one row, yield stress estimated by a flow curve, changes by tens of times [7]. This result is quite unexpected and can be explained only presumably by some qualitative considerations. Since in case of both mono- and polydisperse polymers yield stress is independent of viscosity, probably, the decisive role is played by more fine effects. Here, possibly, the same qualitative differences of relaxation properties of mono- and polydisperse polymers, which are known as regards their viscosity properties [1]. 

There are two types of multicomponent mixtures which occur In polymer phase equilibrium calculations solutions with multiple solvents or pol ers and solutions containing poly-disperse polymers. We will address these situations In turn. 

For zero conversion, /jv = /ip = 1 since only monomers are present initially. At high conversion, Equation (13.18) approaches Equation (13.4). The poly-dispersity for the complete conversion case is... 

For example, the parameters g = 0.77, h = 0.94, p = 1.4, and C = 0.158 measured for a polymer sample and compared with the plots in Figures 7.11 through 7.13 were most consistent with athree-arm star monodisperse polymer a poly disperse three-arm star would have g= 1.12,/ = 1.05,p= 1.6, and C close to 0.2. °° The second example was poly(vinyl acetate) (PVAc) prepared by emulsion polymerization. Since no data for linear equivalent were available, g and h were not calculated. At lower conversion/MW p= 1.84 was found, only slightly higher than the theoretically expected p = 1.73 for a randomly branched architecture, p slightly decreased with increasing M, indicating... 

Interpretation of pubhshed data is often comphcated by the fact that rather complex catalytic materials are utilized, namely, poly disperse nonuniform metal particles, highly porous supports, etc., where various secondary effects may influence or even submerge PSEs. These include mass transport and discrete particle distribution effects in porous layers, as confirmed by Gloaguen, Antoine, and co-workers [Gloaguen et al., 1994, 1998 Antoine et al., 1998], and diffusion-readsorption effects, as shown by Jusys and co-workers for the MOR and by Chen and Kucemak for the ORR [Jusys et al., 2003 Chen and Kucemak, 2004a, b]. Novel approaches to the design of ordered nanoparticle arrays where nanoparticle size and interparticle distances can be varied independently are expected to shed hght on PSEs in complex multistep multielectron processes such as the MOR and the ORR. 

J. Bibette, 1991, (Depletion interactions and fractionated crystallization for poly-disperse emulsion purification), J. Colloid Interface Sci. 147, 474. 

Strictly speaking, monodisperse samples would be required for the determination of the Mark-Houwink coefficients. Since, however, the poly-dispersities of the nine individual fractions are only moderate (Mw/Mn 2) and since both Mw and [tj] are measured as weight averages with the same statistical weights, the error introduced by the incorrect treatment of the polydispersity could be neglected. 

A method has also been developed for treating poly disperse particles (Kwauk, 1964c). 

Bandi, F., A. Khan, and C.R. Phillips, Effects of Aerosol Poly-dispersity on Theoretical Calculation of Unattached Fractions of Radon Progeny, this volume (1987). 

An exhaustive theoretical characterization of the chemical structure of poly-disperse block copolymers suggests knowledge of the distributions of ... 

---