Polydispersity dispersity

Figures 19 and 20 show experimental data recently obtained by Siebenburger et al. [33] on polydisperse dispersions of the thermosensitive core-shell particles introduced in Sect. 3.1.2 [31]. In all cases stationary states were achieved after shearing long enough, proving that ageing could be neglected even for glassy states. Because of the appreciable poyldispersity in particle size (standard deviation 17%) crystallization could efficiently be prevented and flow curves over extremely wide windows could be obtained. Two flow curves from their work can be used to test the asymptotic results.

Finally, the precipitation and redispersion of the silver nanocrystals was found to be nearly reversible. After precipitating the largest nanocrystals of a polydisperse dispersion by lowering the system pressure from 414 bar to 276 bar, and then repressurizing to 414 bar, 90% of the silver nanocrystals redispersed. Reversible nanocrystal flocculation has potential value in fine-tuning size-dependent separations with minor variations in pressure. Reversible solvation conditions are difficult to achieve using a conventional anti-solvent approach. 

Particle size distribution also affects viscoelastic behavior. Monodispersed. noninteracting particles exhibit a measurable elastic modulus for volume fractions of 0.64. near the critical packing fraction (25). Polydispersed dispersions may reach higher volume fractions before C is delectable. 

Pirog, T., Dynamics of Destabilization of Food Emulsions Measurement and Simulation of Gravity Driven Particle Velocities in Polydisperse Dispersions, Ph.D. Thesis, Purdue University, 1998. 

There are many factors that usually favour emulsion stability such as low interfacial tension, high viscosity of the bulk phase and relatively small volumes of dispersed phase. A narrow droplet distribution of droplets with small sizes is also advantageous, since polydisperse dispersions will result in a growth of large droplets on the expense of smaller ones. The potent stabilization of the emulsion is achieved by stabilization of the interface Ps- 27). 

In the bidisperse case. Figure 4.4(b), fi ctionation does occur. The large droplets cream faster than the small ones and two sharp boundaries form at the base and rise to die top at two discrete rates. The two creaming rates allow two hydrodynamic sizes to be inferred fiom eqn. (4.1). The rates at which die boundary rises at two volume fiacdons (ordinates yi and 2) are sufficient to define completely the cumulative size distribution of a bidisperse dispersion. Polydisperse dispersions are treated as an extension of the bidisperse case, the number of ordinates examined being increased as required until die size distribution is sufficiendy well defined. However, this simplistic analysis is only applicable to very dilute emulsions, where Stokes law is valid (i.e at infinite dilution in an infinite medium). In closed concentrated emulsions, droplets will interfere with one another and the effect of back-flow by the continuous phase becomes significant. 

For polydisperse dispersions, the measured Kght transmission is the inverse geometric mean of the relative transmissions LTj, LT2,. .. of the respective mass fractions mj, m2,... ... 

Okubo et al. [87] used AIBN and poly(acrylic acid) (Mw = 2 X 10 ) as the initiator and the stabilizer, respectively, for the dispersion polymerization of styrene conducted within the ethyl alcohol/water medium. The ethyl alcohol-water volumetric ratio (ml ml) was changed between (100 0) and (60 40). The uniform particles were obtained in the range of 100 0 and 70 30 while the polydisperse particles were produced with 35 65 and especially 60 40 ethyl alcohol-water ratios. The average particle size decreased form 3.8 to 1.9 /xm by the increasing water content of the dispersion medium. 

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]. 

According to the concepts, given in the paper [7], a significant difference between the values of yield stress of equiconcentrated dispersions of mono- and polydisperse polymers and the effect of molecular weight of monodisperse polymers on the value of yield stress is connected with the specific adsorption on the surface of filler particles of shorter molecules, so that for polydisperse polymers (irrespective of their average molecular weight) this is the layer of the same molecules. At the same time, upon a transition to a number of monodisperse polymers, properties of the adsorption layer become different. 

The dispersity is also commonly called the polydispersity index or the polydispersiiy. 

For a polymer consisting of molecules all of the same molar mass = M, but in all other cases, is greater than M . We can thus use the ratio of to Mjj as an indication of the spread of molar masses in a particular polymer sample. This ratio is called the polydispersity of the polymer where M Mjj = 1 the sample is said to be homo- or mono-disperse. 

SteU, G Rikvold, PA, Polydispersity in Elnids, Dispersion, and Composites Some Theoretical Results, Chemical Engineering Commnnications 51, 233, 1987. 

In order to cadculate a particle size distribution directly from the output chromatogram for a polydisperse system, the integral, dispersion equation for the chromatogram signal, F(V), as a function of elution volume, V, needs to be evaluated (27) ... 

A modification of the method proposed by Ishige, Lee, and Kamielec (29) has been shown to work well for calculating W(y) to compute a PSD (27). This iterative method starts with a first estimate of W(yT obtained from the polydisperse chromatogram assuming no axial dispersion. Equation (8) is then evaluated from which the computed chromatogram F (V) is obtained. From... 

Because of chromatographic dispersion, the sample fraction in the detector cell is polydisperse. The weight-average and number-average molecular weights of the polydisperse fraction are calculated as... 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

An important by-product of the development of this approach is that Orthogonal Chromatography provides a direct method of estimating the shape of the chromatogram for extremely narrow molecular weight distributions. This shape function is fundamental information for axial dispersion evaluation and is not otherwise easily obtained. Even commercially available monodisperse standards synthesized by anionic polymerization are too polydisperse. 

As a rule, the dispersed catalysts are polydisperse (i.e., contain crystallites and/or crystalline aggregates of different sizes and shapes). For particles of irregular shape, the concept of (linear) size is indehnite. For such a particle, the diameter d of a sphere of the same volume or number of metal atoms may serve as a measure of particle size. 

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