Particle scattering polydisperse

In Fig. 17 to 19 the particle-scattering factors for some regularly branched and some polydisperse molecules are shown in plots of P2(q2)-1 as function of q2 (S2)z (see also Table 2). The curves demonstrate clearly that branching causes an upturn while polydis-persity tends to balance the influence of branching34,90. ... 

Fig. 18. Reciprocal particle-scattering factors of star-molecules with polydisperse rays, where f denotes the number of rays per molecule. The same functions are obtained also for the ABC-type polycondensates, where nb denotes the number of branching points per molecule. The case f = 1 or nb = 0 is identical to linear chains obeying the most probable lengths distribution. It also represents the scattering behaviour of randomly branched f-functional polycondensates 1...

This leads to the conclusion that polydisperse Unear chains cannot be distinguished from randomly branched chains using only the shape of their scattering curves. Indeed, when the link probabilities are expressed in terms of the mean-square radius of gyration, the particle-scattering factor is given in both cases by... 

The complete balance of the upturn by the polydispersity is only obtained for random branching processes. Often the reaction is impeded by serious constraints, or the primary chains before cross-linking are monodisperse. Then the resultant final molecular-weight distribution is narrower than in the random case, and the characteristic upturn as a result of branching, develops again. A strange coincidence in behavior is observed with star-molecules, where the rays are polydisperse, and with the ABC-type polycondensates. In both cases the particle-scattering factors can be expressed as ... 

Fig. 23. Reciprocal particle-scattering factors of monodis-perse randomly branched polycondensates of functionalities f - 2,3,6. The chain curve represents the polydisperse random polycondensate83 ...

The Lagrange expansion technique can also be applied to the calculation of the particle-scattering factors Px (q) of branched or linear polymers of DP = x from the path-weight generating function of the polydisperse system. In Chap. C.I1I we have shown the equivalence... 

Polydispersity (the larger particles scatter more light and therefore appear to be brighter). 

Point charge, field strength of, 210 Poiseuille flow, 156-157 Poisson s equation, 212, 215-216 Polarization force, 218 Polarization of light, 290 incident, 282 scattered, 284 Pollen spores, 319-320 Pollution, air, 225 Polonium-210 particles, 140 Polydisperse aerosols, 3,13 and coagulation, 308 concentration of, 88 and scattering, 289-294 size of, 4... 

As opposed to the turbidity spectrum method, determination of the scattered light intensity at one or two angles does not provide correct information for the ill-defined systems due to the high sensitivity of the radiation diagram to the shape of particles, their polydispersity, and other fine structural features, not to mention multiple scattering. Such sensitivity makes it difficult to regularize the reverse problem. 

Multiple scattering is a considerable problem in extracting structural information from the dynamic light-scattering of dispersions of interacting parti-cles. " The effect of particle interactions on lg (K, t) has been studied by several authors, most notably Pusey and Ackerson. Experimentally, g K, t) is found no longer to be of a simple exponential form. The difficulty theoretically is to separate out the effects of particle interactions, polydispersity, and multiple scattering. 

Since the scattering curve from a solution is the sum of the individual particle scattering effects, it is clear that the results can only then be used to infer an unknown structure if the solution contains only one sort of identically sized particles (monodisperse system). It is instructive to consider also the other extreme case when all particles have identical and known shape but vary in size. There, the known shape function is convoluted with an unknown distribution function. In this case the results can be used to extract information about size distribution (Glatter, 1980). In intermediate cases, where neither structure nor degree of polydispersity are known, the method breaks down as a source for information on particle structure. 

Thus for a polydisperse solute, A/ <9 depends upon the weight-average molar mass and the z-average particle scattering factor. The latter can be examined further by applying Equation (3.137) and leads to... 

For particles of polydisperse size, the angular scattering intensity patterns vary according to particle size. The same argument we have made in Section 5.2, regard the necessity of multiangle measurement in a PCS experiment is completely valid in an ELS experiment. If these particles have different... 

Basic quantities and properties utilized for the characterization of macromolecules and colloidal particles are molecular mass (Al), molecular interactions (Aj), size (radius of g3uation Rg hydrodynamic radius Rh), particle scattering function (P(q)) defined by particle shape, and internal motions. Polydispersity can also be characterized by DLS. Combinations of these quantities are useful parameters to characterize maaomolecules or colloidal particles. There are a variety of monomolecular and multimolecular colloidal particles (e.g., globular proteins) flexible chain macromolecules, rigid and semifiexible rod-like macromolecules, micelles, and other self-assembled particles. We can choose suitable and efficient pathways to characterize them depending on their nature. LLS is a very powerful tool in this respect. 

Introduction. After we have discussed examples of uncorrelated but polydisperse particle systems we now turn to materials in which there is more structure - discrete scattering indicates correlation among the domains. In order to establish such correlation, various structure evolution mechanisms are possible. They range from a stochastic volume-filling mechanism over spinodal decomposition, nucleation-and-growth mechanisms to more complex interplays that may become palpable as experimental and evaluation technique is advancing. 

Order and polydispersity are key parameters that characterize many self-assembled systems. However, accurate measurement of particle sizes in concentrated solution-phase systems, and determination of crystallinity for thin-film systems, remain problematic. While inverse methods such as scattering and diffraction provide measures of these properties, often the physical information derived from such data is ambiguous and model dependent. Hence development of improved theory and data analysis methods for extracting real-space information from inverse methods is a priority. 

Light Scattering Technique. Properties of the light scattered by a large number of droplets can be used to determine droplet size distribution. Dobbins et al. 694 first derived the theoretical formulation of scattering properties of particles of arbitrary sizes and refractive indices in polydispersions of finite optical depth. Based on... 

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