Polydispersity parameters

The width of a molecular-weight distribution can, because of equation (8-43), always be described by the ratio of two molecular weight averages. The polydispersity index 

Combinations of other molecular weight averages are also possible to give analogous Q and U values. For a monodisperse material Q = 1 and U = 0. 

The width of the molecular-weight distribution increases with increasing Q and U values. However, Q and U are not very sensitive to the distribution width for narrow molecular-weight distribution. Of course, according to equation (8-18), U is also given by 

the molecular inhomogeneity U and, consequently, the value of Q depend also on the number-average molecular weight. The standard deviation remains as a more sensitive measure of the distribution width than either Q or U, but with one exception, it is not an absolute measure of the width of the distribution (see also Section 8.3.2.1). To be an absolute measure of the width of the molecular-weight distribution, the standard deviation must encompass a fraction of the original material that is independent of the width of the distribution, and this only holds for a Gaussian distribution. 

Peebles, Molecular Weight Distributions in Polymers, Wiley-Interscience, New York, 1971. 

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Based on the plots in Figure 5 it follows that sonication, in contrast to mixing, allows effective size regulation of microspheres. Microspheres with decreasing from 27.5 to 15.4 juim were obtained when the sonication power was increased from 150 to 300 W. However, variation of sonication power did not provide poly(Lc) microspheres with narrow diameter distribution. With sonication at 150 W, the diameter polydispersity parameter D /D was equal to 1.94. With increasing power of sonication values. 

The number average diameter of microspheres obtained from polymers synthesized, by emulsification of polymer solutions followed by solvent extraction and/or solvent evaporation methods, can be controlled by choosing the appropriate conditions at which particles are produced. However, by this method particles with 15 p,m and with D D > 1.9 are produced. Spray drying did not provide poly(L-Lc) particles with regular spherical shape. Direct synthesis of poly(L-Lc) microspheres by ring-opening polymerization with stepwise monomer addition can be used as a method of choice for the production of microspheres with diameters controlled to ca. 6 p.m and with diameter polydispersity parameter < 1.20. 

Figure 8. Graph of Y(1)/Y(0) vs. the molecular parameter b for various values of the polydispersity parameter z of the Schulz...

Fig. 28. Plot of G (Eq. (62)) vs. reduced chain length x = 2 L/A for fractions of ladder polydichloro-phenylsiloxane in tetrabromoethane (1), bromoform (2), and benzene (3) and cellulose carbanilate in dioxane (4) Theoretical curves are plotted according to Ref. at the following values of polydispersity parameter U = U = 1 (I), 1.4 (II), 1.6 (III), 1.8 (IV)...

The size distribution of the particles, expressed as the standard deviation over the number-average diameter (polydispersity parameter in percentage), is shown in Figure 3. The size distribution is narrower at... 

The SANS data were modeled [34, 35] as a system of particles with an inner core radius (/ core) and outer shell radius (/ sheii) assuming that there are no orientational correlations, using the same methodology [26, 27, 34] as that developed for aqueous aggregates. For dilute solutions, interparticle interactions may be neglected [4] and several particle shapes were used. The best fits were given by a spherical core-shell model with a Schultz distribution [35] of particle sizes, with a breadth (polydispersity) parameter (Z) and an aggregation number (i.e. the number of molecules per micelle) A agg- A comparison of independently calibrated... 

Because under all practical situations, adsorbing particle populations are to some degree polydisperse, it is vital to estimate the influence of the polydispersity parameter on the jamming coverage. This was done in Ref 137 by performing RSA simulations for polydisperse particle mixtures characterized by the Gauss and uniform size distributions characterized by the relative standard deviation (polydispersity parameter). 

The results plotted in Fig. 29 (for uniform particle size distribution) indicate that the jamming coverage increases with the polydispersity parameter, which can be well reflected by the fltting functions [137]... 

FIG. 29 The dependence of the jamming coverage on the polydispersity parameter for polydisperse mixtures of hard particles characterized by a uniform size distribution curve 1, calculated as n a) N curve 2, calculated as re (true surface coverage). The broken lines denote the... 

A special logarithmic distribution function separates the influence of the size (e.g. radius for spheres, radius of gyration for coils) and polydispersity parameter a on the scattering curve. 

Shroff and Mavridis [56] examined the simpler problem of inferring a single polydispersity parameter from various types of rheological data. They considered several parameters in addition to the polydispersity index MJMJ, including the polydispersity index of relaxation times originally defined by Graessley [57]. This is the ratio of average relaxation times defined by Eqs. 4.56 and 4.57. 

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