Rayleigh ratio, solution

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 ... 

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). ... 

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... 

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)]. 

Use of Eq. (76) requires determinations of the isotropic Rayleigh ratio for mixtures of various concentrations c2. The density fluctuation Rd differs slightly for each solution and is determined from the following expression [Eq. (77)], which is obtained by comparing the forms of Eq. (71) for pure liquid 1 and a mixture, and in which Ri denotes the isotropic Rayleigh ratio for pure liquid 1 ... 

Difference between the Rayleigh ratio for a dilute solution and for pure solvent. 

Note If the scattering intensity is not reduced to the Rayleigh ratio, the difference between the scattering intensities for a dilute solution and that for pure solvent is named excess scattering . 

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. 

Fig. 3.3 Example of plot of KcIRg, where K is an optical constant and Re is difference between the Rayleigh ratio of the solution and that of the pure solvent, vs. concentration. From an SLS experiment on a PS-PI diblock (W = 43 kg mol-1, 81% PS) in dimelhylacetamide at 26.5 °C (Booth et al. 1978).

In static LLS [43], the angular dependence of the excess absolute time-averaged scattering intensity, known as the Rayleigh ratio Rw(< )> is measured. For a dilute solution measured at a relatively small angle (6), Rw(q) can be related to the weight average molar mass (Mw), the root mean square... 

Static Light Scattering. For a solution of polydisperse nonabsorbing particles, the Rayleigh ratio Rvv(9) is the excess absolute scattered intensity of the solution over that of the pure... 

Figure 5. Collective diffusion coefficient D c= Tlq1 (left) and Rayleigh ratio Rdyn (right) from dynamic light scattering intensity in PNIPA gels at 20°C at equilibrium with aqueous solutions containing different concentrations ce of phenols. Symbols are the same as in Figure 1.

---