Rayleigh ratios

The excess Rayleigh ratio Rq can be derived from the raw galvanometer readings Ig and Ig when the sample cell contains the solution and the solvent, respectively, with the photocell of Fig. 4.9 positioned at an angle Q in both cases. The equation used is 

If lo and I are the intensities of the beam before and after passing through a length I of the medium, they can be related in terms of Beer s law for the absorption of light as follows (Rudin, 1982)  

Noting that I = Io Is, where Is is the total intensity of light that is scattered by the solution, Eq. (4.67) may be written in the form (Allcock and Lampe, 1990)  

The value of the product of the definite integrals is 167t/3 (Rudin, 1982 Allcock and Lampe, 1990), so that we obtain the following relationship involving turbidity and the total scattered intensity  

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A modified fonn of equation (B 1.9.16) is usually used to express the scattering power of a system in tenns of the Rayleigh ratio defined as... 

The second method to calculate the scattered intensity or R the Rayleigh ratio) is to square the sum in I... 

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. 

The Rayleigh ratio combines the intensity factors with those associated with the geometry of the experiment ... 

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 ... 

Hence, the value of I/Iq is dependent on relative molar mass of the molecules involved in the light scattering. The Rayleigh ratio, Rg, may be defined as ... 

From this definition, equation (6.8) may be rewritten in terms of the Rayleigh ratio ... 

Equation (6.12) is important it shows that we can determine the relative molar mass of the molecule from the experimental measurement of the Rayleigh ratio in fight scattering. 

Values of are obtained partly by previous calibration using a series of standard light scatterers whose Rayleigh ratios have been precisely determined. Typical standards used in practice are poly(methyl methacrylate) blocks, colloidal silica suspensions, or tungsto-silicic acid, H4SiW 2O40-... 

The variable quantities in the K term, i.e. rig, (AnMcf, and X, must be determined. Values of are available for most solvents from the literature X is obtained by dividing the value of X by the refractive index of the solution. The refractive index increment, (dn/dcj, must be determined to within 10 in dn using a differential refractometer. The choice of solvent is limited if dn/dc = 0, there is no scattering if dn/dc is greater than 0.3 cm g the Rayleigh ratio is no longer proportional to (dn/dc). ... 

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. 

If the scattering intensity can be measured with sufficient accuracy down to very small angles, the Rayleigh ratio at zero angle may be... 

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. 

As will be demonstrated later, LS can be quantified by an experimental quantity termed the excess Rayleigh ratio between solution and solvent, R, which is related to the concentration and molecular weight of solute by the following expression... 

The total polarisability per unit volume of solute plus solvent has been invoked in Eq. (22) so that the dimensions of the Rayleigh ratio R0 in Eq. (23) are not cm2 as it appears, but actually cm 1. For pure liquids and polymers of small-moderate molecular weight, scattering at an angle of 90° is used and the Rayleigh ratio in such instances is given simply as... 

The expressions for scattered light intensity (and Rayleigh ratio) must be corrected by dividing by the appropriate Cabannes factor. Effectively this is equivalent to replacing the optical constant K as defined in Eq. (24) by Kf and by 2 Kfj for unpolarised and vertically polarised incident light respectively. 

Some Rayleigh ratios at less common wavelengths have been assembled with cognate refractometric data in Table 2. 

Here the symbols R, P and G denote respectively the Rayleigh ratio, particle scattering function and instrument scattering reading. It is possible to take other angles such as 60° and 120°, which are also symmetrical about 90°. However, the angles 45° and 135° are most frequently selected, and the widely used Brice-Phoenix photo-... 

One of the most elegant LS studies on liquid mixtures is that of Sicotte and Rinfret17 and it will be instructive to summarise their approach solely with regard to that aspect which is concerned with molecular weight determination. Liquid 1 will be considered as solvent and liquid 2 (of ostensibly unknown molecular weight M2) as solute. The Rayleigh ratios implied are the isotropic ones, which are obtained for liquid 1 as well as for solutions (subscript 12) via the measured Cabannes factors [Eqs. (44) and (45)]. 

For pure liquid 1 the Rayleigh ratio Rd arises from density fluctuations in accord with Einstein theory ... 

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