Heterogeneous distribution

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

This argument is confirmed by the study of CO pulse chemisorption by Biffis at al., mentioned above. In this piece of investigation, the authors prepared a 2% (w/w) palladium catalyst supported by Lewatit UCP 118, a macroreticular resin (nominal cld = 18 %) from Bayer. Its TEM characterization showed a remarkably heterogeneous distribution of the metal nanoclusters, which are apparently located close to the surface of the polymer nodules [62] (Figure 9). 

Spatially heterogenous distributions of crop protection products, within and among test sites, will result from well controlled applications. The soil CEF concentrations ranged from a high of 2.3 qgg at one station on site 1 Day 0 to none detected in 10 samples from various stations several days post-application. The measured mean soil CEF concentrations were between 0.2 and 1.0qgg on Day 0. The theoretical CEF concentration immediately after application was calculated to be... 

Figure 7.6 Heterogeneous distribution of additives in (a) 0.728 mg, (b) 0.580 mg, and (c) 0.494 mg PE samples determined by SFE-HPLC, according to Hirata and Okamoto [127]. Reprinted from Y. Hirata and Y. Okamoto, Journal of Microcolumn Separations, 1, 46-50, Copyright (1989, John Wiley Sons, Inc.). This material is used by permission of John Wiley Sons, Inc.

Radiological Background. The surface of the earth contains a very heterogeneous distribution of the naturally occurring elements. 

Protein kinase C (PKC) exists as a family of closely related kinase subspecies with a heterogeneous distribution in the brain 897... 

The data from 3529-45 can also be interpreted as reflecting an initially heterogeneous distribution of 26A1. Melilite and hibonite may have formed from different reservoirs with enequal 26A1 contents in which case the different (26A1/27A1)Q ratios for... 

The effect of the exponent rtf is to predict progressively less effective sorption as concentration increases. Where f approaches one, the isotherm reverts to the K model, in which sorption is equally effective at any concentration. For n less than one, a smaller fraction of a component sorbs at high than at low concentration. This effect is taken as reflecting a heterogeneous distribution of sorbing sites in... 

RET can be used to investigate the lateral organization of phospholipids (range of 100 A) in gel and fluid phases. Indeed, information can be obtained on the probe heterogeneity distribution the donors sense various concentrations of acceptor according to their localization. A continuous probability function of having donors with a mean local concentration CA of acceptors in their surroundings should thus be introduced in Eq. (9.36) written in two dimensions ... 

A 50% functionalization evokes the interesting question, bearing in mind facile transesterification, of how the fluoroalkyl chains will be distributed over the molecules and how they will be distributed on one particular molecule This question has been examined in detail for dendrimers of the poly(propyleneimine) type functionalized with stearic acid [33]. It was proven that the compositional heterogeneity (distribution of degree of substitution) is random, but the positional heterogeneity (spatial distribution of the substituents over the dendrimer molecule) is not random. However, due to flexibility, no particular effect of the spatial distribution can be observed. Unlike the dendrimers, we expect the hyperbranched polyesteramides to be stiffer, so that spatial distribution could lead to interesting effects if the molecule were composed of a functionalized side and a non-func-tionalized side (Fig. 28), as shown possible for dendrimers via a convergent synthesis [34]. 

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