Dilute concentration, scattering

Resonance Raman spectroscopy has been applied to studies of polyenes for the following reasons. The Raman spectrum of a sample can be obtained even at a dilute concentration by the enhancement of scattering intensity, when the excitation laser wavelength is within an electronic absorption band of the sample. Raman spectra can give information about the location of dipole forbidden transitions, vibronic activity and structures of electronically excited states. A brief summary of vibronic theory of resonance Raman scattering is described here. 

To uniquely identify the intrinsic feature of the material, one method of sample preparation is to pelletize the explosive powders or crystals [14], It is standard practice in far-infrared (THz) spectroscopy to press samples into pellet form to measure the THz transmission spectra. When the sample is a powder with a grain size comparable to the THz wavelength (about 300 microns), the powder strongly scatters the THz radiation. Another method of sample preparation is to mix the material (e.g., RDX) with an inert matrix or filler material to create a pellet. The filler is typically a material that is transparent in the THz such as polyethylene. This allows dilute concentrations of a highly absorbing agent to be measured. 

For non-dilute concentrations (Cp > 1/vN2), a binary interaction between two macromolecules can occur either through a direct contact, or through a series of contacts [29] with other chains (third, fourth, etc.). If k chains are involved, the scattering function is ... 

The Debye function describes the q dependence of scattering data from dilute solutions of ideal chains. Such dilute solutions can either be obtained in a (9-solvent or by having a dilute solution of ordinary chains in a melt of perdeuterated chains. Small-angle neutron scattering data for four dilute concentrations of poly(methyl methacrylate) (PMMA with 2.50 000 g/mol ) in perdeuterated PMMA are shown to be fit by the Debye... 

Tanahatoe JJ, Kuil ME. Dynamic light scattering of a flexible highly charged polyelectrolyte in the dilute concentration regime. Macromolecules 1997 30 6102-6106. 

The extinction of light is a characteristic behaviour of particle systems, which is governed by particle size and concentration—apart from material properties. For dilute, weakly scattering particle systems, the extinction obeys Lambert-Beer law, which states a linear dependency between turbidity r and particle concentration ... 

Inelastic scattering techniques monitor correlations of concentration and/or density fluctuations. In dilute and semi-dilute concentrations, concentration fluctuations are related to the mutual diffusion coefficients by fluctuation-dissipation theories, whereas density fluctuations are generally neglected. 

Dynamic Ught scattering from an appropriate ternary mixture (a solvent, a perhaps-concentrated matrix polymer that is isorefiractive with the solvent and hence scatters no light, and a dilute, intensely-scattering polymer) determines a single-chain S(q, t) of the dilute, scattering polymer species. Many authors have exploited this outcome at small q to study chain tracer diffusion, as discussed in Chapter 8. 

K includes the refractive index of the solvent as well as the change in refractive index with polymer concentration for the particular system being investigated. The values of these properties for an extensive list of polymer/solvent systems are tabulated in Polymer Handbook [26]. They can also be measured in separate experiments using a refractometer and a differential reliactometer. The intensity of scattered light is measured at various angles 0 and for various dilute concentrations c. Both P(0) and Q Q) go to unity as 0 approaches zero. A double extrapolation of the data to 0 = 0 and c = 0 allows for the determination of M, the second virial coefficient A2, and a complex function of molecular shape P(0). We can see that in these two limits. Equation 6.47 reduces to... 

It is important to recognize the approximations made here the electric field is supposed to be sulficiently small so that the equilibrium distribution of velocities of the ions is essentially undisturbed. We are also assuming that the we can use the relaxation approximation, and that the relaxation time r is independent of the ionic concentration and velocity. We shall see below that these approximations break down at higher ionic concentrations a primary reason for this is that ion-ion interactions begin to affect both x and F, as we shall see in more detail below. However, in very dilute solutions, the ion scattering will be dominated by solvent molecules, and in this limiting region A2.4.31 will be an adequate description. 

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