Concentration scattering intensity

If we deal with a solution at very low concentrations, we can ignore the interactions between the particles and express the scattered intensity as... 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

For a more complete discussion of critical phenomena, we consider the scattering intensity S(q) from concentration fluctuations (q is the wavenumber of the scattering) which can be derived when one supplements Eq. (1) by a gradient-square term " ... 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

Since the nuclear and electronic scattering cross sections for alpha particles are well known, the relative concentrations of the elements and their depth profiles can be easily obtained. The relative element concentrations are determined by the relative scattering intensities. The depth profile is obtained from the energy spread of the scattered particles, which lose energy before and after the nuclear collision, by inelastic scattering with electrons. The knowledge of the elements areal density and of the film thickness allows the determination of film density. 

X-ray scattering intensities calculated from these models showed little variation as a function of concentration of EN, indicating that X-ray scattering will not be able to distinguish between PEBB crystalline domains with EN excluded from the domains and the situation where uniform inclusion in the crystalline domains takes place. 

In practice, the invariant can be used for the purpose of calibration to absolute scattering intensity by means of samples for which the absolute invariant can easily be computed. For this purpose colloidal suspensions of noble metals with known volume concentration are suitable [96], All the noble metal particles must be small enough so that they really contribute to the observed particle scattering. They must not agglomerate. 

Fig. 28 Top Effect of dilution on Rh and Kc/lg o of the mesoglobules ( ) formed upon heating of 0.2 gL1 aqueous solution of PVCL-g-18. Bottom Scattering intensity at 90° from polymer solution of different concentration. (Reprinted with permission from Ref. [180] copyright 2005 Elsevier)... 

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. 

In all hydrodynamic methods we have the effect of both the hydrodynamic and thermodynamic interactions and these do not contribute additively but are coupled. This explains why the theoretical treatment of [77] and of the concentration dependence of has been so difficult. So far a satisfactory result could be achieved only for flexible linear chains [3, 73]. Fortunately, the thermodynamic interaction alone can be measured by static scattering techniques (or osmotic pressure measurement) when the scattering intensity is extrapolated to zero scattering angle (forward scattering). Statistical thermodynamics demonstrate that this forward scattering is given by the osmotic compressibility dc/dn as [74,75]... 

Solutions at concentration Cq = 0.5j 1.2 and 1.6 10 g cm were prepared under vigorous stirring at 150°C and then cooled down at 23 C. It was checked by NMR and infrared experiments that no alteration nor chemical modification had occured (1+). After quenching, the intensity scattered by the solutions was recorded as a function of time. After approximately 36 h, no variation was detected for the sample Cq = 0.5 10 g cm 3 while a slow linear increase of scattered intensity with time was detected for the two other samples. In this study, the solutions were allowed to stay at room temperature for three days and then diluted at the concentration C = 10 g cm . ... 

Figure 7 Concentration dependence of the reduced light scattering intensity extrapolated to zero angle for PS-S03Li-40 in cyclohexane at 27.5°C. The solid line represents the model calculation with 3 10 (1/mol) and N 12. The dashed line indicates M] = 49,000.

As the salt concentration continues to decrease, however, matters change dramatically Q). The total scattering intensity decreases more abruptly, and the QLS autocorrelation function, which has been a simple single-exponential decay, becomes markedly two-exponential. The two decay rates differ by as much as two orders of magnitude. The faster continues the upward trend of D pp from higher salt, and is thus assigned the term "ordinary . The slower, which is about 1/10 of Dapp high salt, and appears to reflect a new mode of solution dynamics, is termed "extraordinary . 

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