Reduced Intensity of Scattering

One of the most satisfactory types of apparatus yet developed is that of Zimm (1948 b). In his arrangement, the cell containing the liquid under study is a small thin-walled glass bulb, immersed in an outer cell containing a liquid of approximately the same refractive index as that in the inner cell. The scattered light is received on a photomultiplier tube, while a portion of the incident beam falls on a phototube of much lower sensitivity. The currents produced in the two tubes are balanced in a precision potentiometer at balance, the setting of the potentiometer shows the ratio of the currents. Details of the electronic circuit are given 

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With the scattering function P(d), the concentration dependence of the reduced intensities of scattered light is given as... 

In the determination of M , the intensity of scattered light is measured at different concentrations and at different angles 6). The incident light sends out a scattering envelope that has four equal quadrants (Figure 3.11a) for small particles. The ratio of scattering at 45° compared with that at 135° is called the dissymmetry factor or dissymmetry ratio Z. The reduced dissymmetry factor Z is the intercept of the plot of Z as a function of concentration extrapolated to zero concentration. 

The reduced intensity of the SAXRD pattern of the silica/carbon composite is probably due to a similar scattering power between the silica framework and the pore filling carbon [15]. On the other hand, the observed decrease of the unit cell parameter of the silica/carbon composite might be caused by condensation of the SiOH groups in the pore walls during carbonization at 800 °C. Therefore, the hexagonal mesoporous structure is probably preserved in the composite and only collapses after dissolution of the silica framework. 

E. Calibration with reference to pure benzene as a standard scatterer reduced intensity of benzene assumed as 48.4 X 10-6 at 4358 A. 

X is the wavelength in vacuo, N is Avogadro s number, while A and A are the second and third virial coefficients. The term P(9 is the form factor which is a function of the size and shape of the macromolecule in solution and represents the modulation of the intensity of scattered radiation due to the finite size of the molecule and to its deviation from sphericity. The term dn/dc is the specific refractive index increment and represents the change in solution refractive index as a function of solute concentration. If experiments are conducted in the limit of zero scattering angle where P(9) = 1 as well as at sufficiently low concentrations where only the second virial coefficient need be considered, then eq. (1) reduces to... 

For gases, Rayleigh showed that the reduced intensity of the scattered light Rg at any angle 0 to the incident beam of wavelength X could be related to the molar mass of the gas M, its concentration c, and the refractive index increment (dnidc) by... 

Figure 3.7 Schematic of the scattering phenomenon. When the waves are out of phase, the intensity of scattered iight is reduced.

Figures 8 a) and b) display an Arrhenius plot and a plot of the concentration dependence of the reduced intensity of the solutions and the pure liquid. We see that we obtain a common activation energy in all cases and that the reduced intensity increases proportionally to the concentration of the molecules, indicating that the single molecules are the scatterers according to equation 16.

Fig 10 Reduced intensities of the depolarized light scattering A 1,5-pentanediol o 2,4-pentanediol... 

This is in contrast to the situation in 1,5-pentanediol where intramolecular hydrogen bonding is less favored by the molecular structure. These results can provide an estimate of the free energy of the formation of the relevant, structures. In a more realistic approximation, however, the anisotropic scattering in the alcohols can be-described by a distribution of the local aniso- tropy rather than to well defined structures with an equally well defined anisotropy. Dilution eriments with CHCl have confirmed this picture and have shown that the reduced intensity of 2,4-pentane-diol decreases with the solvent content. We can understand this, as the solvent will probably decrease the ratio of intermolecular to intramolecular hydrogen bonding in the same manner, as the increase of the temperature does. 

Fig. 6, Excitation and emission spectra of Calcein in NaOH. The concentration was approximately 80 fjL g/ml and a 1P21 photomultiplier tube was used. The spectra were obtained on an Amineo-Bowman l ctrophotofluorometer equipped with polarizers in the excitation and emission beams to reduce the intensity of scatter peaks, which interfere when the excitation and emission wavelengths are equal.

The above result is for solute molecules that are much smaller than the wavelength of light. When the solute consists of large molecules such as polymers, the intensity of scattered light is reduced due to interference caused by phase differences in the scattered light coming from different parts of the molecule. In this case, the expression for the scattered light becomes... 

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... 

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