Solution radiation scattering

When a polymer absorbs very strongly in the visible region, near IR incident radiation is used. In a very coloured solution the scattered intensity is reduced by a factor exp(—e)2) where e is the absorption coefficient of the solvent. Hence i0 must be multiplied by exp(+e ) in order to obtain the true scattered intensity undiminished by absorption effects. For small values of efi, the quantity exp(efi) approximates well to (1 + e2) so that Eq. (42) becomes38. ... 

As emphasized earlier, the weakness of the difference intensity is a specific difficulty with this sort of experiment. The ratio between the difference and the full scattering intensity is on the order of 10 -10 This is particularly problematic in solution work, where the radiation scattered by the solute is buried in that from the solvent. A further complication arises from the interference between X-ray and optical manipulations. In fact, the intensity of... 

For a two-component system (macromolecule, component 2, dissolved in pure solvent, e.g., water, component 1), application of the fluctuation theory of scattering (15, 16) shows that in a volume element of volume SV (of the order of s z at the lowest angles of measurement), the intensity of radiation scattered by the solution in excess of the solvent, I(s) = /(s)solution — I(s)solvent, is proportional to the fluctuations in the number of electrons, n ... 

As the latter effect, which is comparable to the inner-filter effect during photolysis experiments in solution, does not always occur, radiation scattering problems are inherent to all solid-state photoreactions and are particularly relevant to the photostability testing of solid-state drugs, such as tablets, pills, or powders. Thus in this section, we will discuss three experimental approaches for the determination of solid-state photochemical quantum yields utilizing chemical actinometers. 

We can also determine the value of interaction b from the second virial coefficient A2, a basic quantity associated with osmotic pressure as well as radiation scattering. Hence, for a monodisperse solute of molecular mass M, the... 

The solute structure function H(q) is determined experimentally by radiation scattering. The interval gmin, < m in which H(q) is measured depends upon the nature of the radiation used in the experiment [see (15.1.22) and (15.1.23)]. The choice of such a radiation is imposed by the choice of the interval which best suits the study of the observed structure. 

The RTE is a simplified form of the complete Maxwell equations describing the propagation of an electromagnetic wave in an attenuating medium. The simplified RTE does not include the effects of polarization of the radiation or the influence of nearby particles on the radiation scattered or absorbed by other particles (dependent scattering or absorption). For example, if polarization effects are present (as they are when reflections occur at off-normal incidence from polished surfaces or in reflections from embedded interfaces), then the analyst should revert to complete solution of the Maxwell equations, which is a formidable task in complex geometries Delineating the bounds of applicability of the radiative transfer equation is an area of active research. 

All three types of radiation scattering techniques light. X-ray and neutrons, have been used to measure the interaction parameters and study the phase equilibria. Using the relations derived for polymer solutions (see Eqs 2.31-2.36), the methods can be used to measure M, < s and Aj, thus Xj2 ... 

Microemulsions and most surfactants in dilute solutions and dispersions self-assemble into a variety of microstructures spherical or wormlike micelles, swollen micelles, vesicles, and liposomes. Such systems are of biological and technological importance, e.g., in detergency, drug delivery, catalysis, enhanced oil recovery, flammability control, and nanoscale particle production. The macroscopic properties—rheology, surface tension, and conductivity—of these systems depend on their microstructure. As these microstructures are small (1-1000 nm) and sometimes several microstructures can coexist in the same solution, it is difficult to determine their structure. Conventional techniques like radiation scattering, although useful, provide only indirect evidence of microstructures, and the structures deduced are model-dependent. 

When radiation of type a and wavelength A is scattered from the solution, the intensity of the radiation scattered through the angle 6 where... 

In equation (11), 6 is the scattering angle, and X is the radiation wavelength in the polymer solution. The scattered light spectrum produced by a polymer solution depends upon the mass, polarizability and number of polymer coils in the solution, and the magnitude of the scattering field vector. 

Radiation scattering from dilute polymer solution 54... 

Radiation Scattering from Solutions of Star Polymers 63... 

The intensity of radiation scattered from solutions of star-branched polymers in good or 6 solvent can be presented... 

The intensity of radiation scattered by semidilute solution of star polymers can be decomposed into two contributions ... 

Definition of terms relating to individual macromolecules, their assemblies, and dilute solution.This document includes the recommended definitions for molecular weight, molecular weight averages, distribution functions, radius of gyration, end-to-end-distance vector, the Flory-Huggins-Staverman theory, solution viscosity, scattering of radiation by polymers and polymer solutions, fractionation, separation techniques, and so on. The document on dispersity is an important extension of this recommendation. 

The particles in a solution which scatter light by diffraction are small compared to the wavelength of the light incident on them. In a solution of macromolecules, the dimensions of the solute molecules are of a considerable magnitude and therefore they cannot behave as point sources (see Fig.1). Individual centers within a particle scatter light in their own fashion resulting in interference of the radiation scattered. The scattering envelope in such a case is asymmetric. 

In a collection scattered photons will be emitted in all directions, and the atoms will appear to be acting (approximately) as secondary sources of spherical waves. The spherical wave solution to the Helmholtz equation gives an electric field, E,(r,t), dependent upon the distance, r, between the point of observation, P, and a source located at the origin, according to ... 

In a typical Raman experiment, a laser beam is passed through the sample and the radiation scattered from the front face of the sample is monitored (Fig. 12.5). This detection geometry allows for the study of gases, pure liquids, solutions, suspensions, and solids. 

In the previous expression, gf indicates a form factor that describes possible effects due to radiation scattering within the jet, d is the jet thickness and a is the absorption coefficient at the probed point. One way to compare experimental transmission with the developed model passes through assuming the same form factor for measurements and for wave propagation simulations carried out for a homogeneous solution (the latter providing a transmission, This... 

G. Fairweather, A. Karageorghis, P.A. Martin, The method of fundamental solutions for scattering and radiation problems, Eng. Anal. Bound. Elem. 27, 759 (2003)... 

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