Concentration and scattering

By measurement of light scattering (A = 436 nm) from toluene solutions of a polystyrene sample [D. Rahlwes and R. G. Kirste, Makromol. Chem., 178, 1793 (1977)], the following results were obtained for the Rayleigh ratio, R(9), at various concentrations and scattering angles ... 

Intensity of Scattered Light. From measurements of scattered light intensity as a function of concentration and scattering angle, we can determine the weight averaged molecular weight, where is the number of scatterers... 

The sxmimation over ij is over all atomic species and sublattices, and the sxmimation over represents all interatomic vectors. The N is the number of unit cells c and / are the concentration and scattering factors for the species, respectively. The C/ , are short-range order (SRO) parameters that may alternatively be called correlation eoeffieients. 

The partial pair correlation functions, gap(r), are just the probability of finding any atom of type a at a distance r from any central atom p. It should be noted that for the purposes of this thesis the concentration and scattering length factor in (3.12) will be referred to as the prefactor. The definition of a corresponding polyatomic coordination number, the average number of p atoms that are situated in the spherical shell between two distances ri and r2 around an a atom, follows ... 

Further work with application to large molecules or particles in solution was done by Smoluchowski (J), Einstein (4), Debye (5, 6) and Zimm (7). For many years now the measurement of the intensity of the light scattered from dilute solutions of macromolecules as a function of concentration, and scattering angle has provided much important information on the size, shape, and thermodynamic properties of these... 

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. 

The domain is small compared to the wavelength of visible light, so Eq. (10.33) describes the scattering, provided that we can find appropriate values for the concentration and polarizability of these domains. 

Other measurements important to visual air quality are pollutant related, i.e., the size distribution, mass concentration, and number concentration of airborne particles and their chemical composition. From the size distribution, the Mie theory of light scattering can be used to calculate the scattering coefficient (20). Table 14-2 summarizes the different types of visual monitoring methods (21). 

As a second example, results from a TOP ERDA measurement for a multi-element sample are shown in Fig. 3.65 [3.171]. The sample consists of different metal-metal oxide layers on a boron silicate glass. The projectiles are 120-MeV Kr ions. It can be seen that many different recoil ions can be separated from the most intense line, produced by the scattered projectiles. Figure 3.66 shows the energy spectra for O and Al recoils calculated from the measured TOF spectra, together with simulated spectra using the SIMNRA code. The concentration and thickness of the O and Al layers are obtained from the simulations. 

Artifact removal and/or linearization. A common form of artifact removal is baseline correction of a spectrum or chromatogram. Common linearizations are the conversion of spectral transmittance into spectral absorbance and the multiplicative scatter correction for diffuse reflectance spectra. We must be very careful when attempting to remove artifacts. If we do not remove them correctly, we can actually introduce other artifacts that are worse than the ones we are trying to remove. But, for every artifact that we can correctly remove from the data, we make available additional degrees-of-freedom that the model can use to fit the relationship between the concentrations and the absorbances. This translates into greater precision and robustness of the calibration. Thus, if we can do it properly, it is always better to remove an artifact than to rely on the calibration to fit it. Similar reasoning applies to data linearization. 

Figure 7-2 shows the vertical profiles of temperature, dew point, light scattering (a measure of aerosol concentration) and the concentrations of O3 and SO2. Here we see that up to about 1.5 km, the temperature, dew point, light scattering... 

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