Rayleigh turbidities

The behavior of hafnium chloride in aqueous IM NaCl has been studied over the temperature interval 25°-73°C. Total hafnium concentration was varied from 0.60 to 30 mM, and hydroxyl number was varied from 0 to 3. Rayleigh turbidities and pH values were measured as functions of time. The existence of polynuclear species was confirmed, but the measured properties change slowly with time, the most rapidly at the highest temperature. The rate of hydrolysis is related analytically to total hafnium concentration, hydroxyl number, and temperature. 

Experimentally the Rayleigh ratio for benzene at 90° has been observed to equal about 1.58 X 10 m" under the conditions described in this example. By Eq. (10.6), r = (167t/3) so the value of R corresponding to this calculated turbidity is Rg = 5.41 X lO" m". The ratio between the observed value of Rq and that calculated in the example is called the Cabannes factor and equals about 2.9 in this case. 

As the attenuation of the incident beam per unit path through the solution, the turbidity is larger than the Rayleigh ratio by the factor Ibrr/S, since T is obtained by integrating Rg over a spherical surface. Thus, if Eq. (10.54) is written in terms of Rg rather than r, the proportionality constant H must also be decreased by l6n/3, in which case the constant is represented by the symbol K ... 

Thus the turbidity may be calculated directly from the Rayleigh ratio. Both of these quantities enter into the subsequent discussion, where it is to be borne in mind that either one is readily calculated from the other. 

The empirical values of the parameter F2 found using uncorrected Rayleigh ratios or turbidities should be angle-dependent and do not necessarily represent the customary thermodynamic parameter F2. 

Note For small particles direct proportionality exists between turbidity and the Rayleigh ratio. 

Next, we introduce the theory of Rayleigh scattering (Section 5.3), the first of many models covered in the chapter. The Rayleigh theory for dilute systems and solutions is developed here, with illustrative examples of the determination of molecular weight and the second virial coefficient. This is followed by a brief description of some of the basic experimental considerations and an introduction to absorbance and turbidity (Section 5.4). 

The Rayleigh ratio as defined by Equation (24) has a precise meaning, yet it is a quantity somewhat difficult to visualize physically. After we have discussed the experimental aspects of light scattering, we shall see that Re is directly proportional to the turbidity of the solution when turbidity is the same as the absorbance determined spectrophotometrically. 

The formal similarity between Equations (27) and (39) helps us understand somewhat better the physical significance of the Rayleigh ratio Re. It is directly proportional to the attenuation of the light per unit optical path, measured as absorbance, when the attenuation is due to scattering alone. In this case absorbance is more properly called turbidity. 

Rayleigh X Rs, particle size Applicable for (R/X) < 1/20 extension of the Rayleigh equation to solutions allows the measurement of osmotic pressure, molecular weight, and turbidity of colloidal or polymer solutions see Section 5.3... 

What is meant by turbidity of a dispersion How is the turbidity related to the Rayleigh ratio ... 

The scan of a fluorescence emission spectrum should routinely include the region of the Rayleigh peak (see Fig. B3.6.1). This provides a built-in indicator of turbidity of the buffer and protein solutions. The height of the peak for the protein solution should not differ greatly from that obtained for the solvent from the equivalent buffer blank scan it will increase markedly if there is dust or aggregate in the solution. 

In the present work with a laser source and photon counting detection we were able to make measurements at concentrations lower than the work of Heller and Tabibian where multiple scattering and particle turbidity were negligible and single scattering could be directly observed. It was possible to make direct measurements of IQ and utilize the Rayleigh ratio Vv and Mie theory coefficient (ii)A by... 

Therefore, in principle, the parameters of the particle size distribution can be estimated from specific turbidity measurements at different wavelengths. This is not true, however, in the Rayleigh regime (i.e. small particles, (D/Am) less than 0.1). In this case, the extinction coefficient is proportional to (D/Am)4 and... 

Combining SEC with MAES to produce absolute molar mass data without molecular calibration standards also requires prior calibration of the concentration detector as well as calibration of the MAES detector itself. The latter calibration involves the determination of all geometrical contributions such that the MAES detector measures the Rayleigh excess ratio at each scattering angle. This is most easily achieved by using a turbidity standard such as toluene. Details are found in Ref. 2. Once the refractive index of the mobile phase is entered, the software [4] performs the required calibration. 

Fig. 5.48 shows the extraterrestrial spectrum Ex°n and the associated pattern of EXn. The upper edge of this curve represents the irradiance reduced purely by Rayleigh scattering. The deteriorations marked in black are caused by the absorption by the gases 03, 02, H20 and C02. Further diagrams of this type, which show the variation in the influencing quantities (water vapour and ozone content, turbidness due to aerosols, different optical masses), are available in M. Iqbal [5.34]. 

By combining the Rayleigh theory with the Smoluchowski-Fuchs theory of flocculation kinetics [7, 8], the following expression can be obtained for the variation of turbidity with time. 

A comparison of Eqs. (4.86) and (4.75) shows that the relationship between the turbidity and the Rayleigh ratio is... 

---