Scattering vector, Rayleigh

Figure 8. Rayleigh factor as a function of the square of the scattering vector for But 27, But 24, But 22, and 1. Key q, units of scattering vector, (fan) 1.

Fig. 23 Angular dependence of Rayleigh ratio (Rw(q)) of segmented PNIPAM-seg-St copolymer chains in water measured from static LLS, where K is a constant, q is the scattering vector and polymer concentration (C) was 7.2 x 10-7 g/mL. The inset shows the temperature dependence of the hydrodynamic radius distribution /(Rh) determined from dynamic LLS [94]...

R - Rq) = the Reduced Rayleigh ratio neglecting intramolecular effects s = Sq - s = the propagation or scattering vector Sq = the unit vector in the incident ray direction s, = the unit vector in the scattered ray direction Tj = the vector to the y scattering element... 

Fig. 22. Plot of Rayleigh ratio versus scattering vector showing a maximum following quenching of a 1% agarose solution to between 32-5 and 19°C. (Reprinted with permission from G. T. Feke and W. Prins, Macromolecules,...

The excess Rayleigh ratio can also be calculated for the general case of a dilute solution at all scattering angles. The scattering function at finite scattering vector is defined as ... 

Figure 17.18. Variation of the excess Rayleigh ratio. A/ , extrapolated to zero scattering vector, as a function of the droplet volume fraction, 0. The solid line is the best two-parameter fit using the Carnahan-Starling equation for the hard-sphere equation of state. The two fitted parameters were rHs = 86 A and rhc = 76 A (data taken from ref. (17))...

In a static fight scattering experiment the effective structure factor, S(0) at zero scattering vector was obtained from the extrapolated forward scattering. In Fig. 4 is shown the variation of the excess Rayleigh ratio dR(0) extrapolated zero scattering vector with the volume fraction of droplets, (f> [3]. In the monodisperse case, S(0) is finked to the osmotic compressibility for which, in the case of hard spheres, an accurate expression exists due to Carnahan and Starling [17]. The experimental data were... 

In the Rayleigh-Debye-approximation the argument of the scattering function is the product of the size parameter and the length of the scattering vector h h = 4nX sin 0/2). Therefore the size dependence can be represented by one scattering curve. 

As the macromolecule and its constituting elements change their orientation at any moment, it is necessary to consider the average value of cos(cpj - cpj) over all the orientations taken by the vector with respect to the scattering vector (k). Vectors fij and k respectively, express the possible conformations of the macromolecule and a specific orientation of the chain with respect to the scattered and incident beams. Introduction of the relation (cp - (p, = 2 k /y/X) into the expression of the Rayleigh ratio, after calculation of the average (which will not be done here) gives... 

The important question in EFISHG, especially in the light of the complementarity with hyper-Rayleigh scattering (HRS), is What is actually experimentally determined The expression for the rotational contribution is determined by the scalar product of the dipole moment vector with the vector part of the third-rank hyperpolarizability tensor (Eq. (13)). 

In Equation 14.22 the subscripts RDG and R denote Rayleigh-Debye-Gans and Rayleigh. In Equation 14.23b q is the scattering wave vector to be discussed below. 

The electron clouds of a molecule irradiated with visible light will orient themselves to some extent in line with the electric vector of the light. If the light is plane polarised, scattered light is visible only in one plane, and if the dimensions of the molecule are small compared with the wavelength of the light, the Rayleigh equation, eqn. (4.21), holds ... 

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