Theory Rayleigh,

The Rayleigh scattering theory which culminates in Eq. (10.60) as its most pertinent form for our purposes is based on the explicit assumption that interference effects are absent. The objective of the present section is to correct the Rayleigh theory to allow for interference effects. There are several assumptions-limitations that are implied by our approach ... 

We assume that the Rayleigh theory can be corrected by subdividing the actual solute particle into an array of scattering sites which, considered individually, obey the Rayleigh theory. It can be shown that this approach is a valid approximation so long as (47rR/X)(n2/fii - 1) 1, where R is... 

We assume that the observed interference is the cumulative effect of the contributions of the individual polymer molecules and that solute-solute interactions do not enter the picture. This effectively limits the model to dilute solutions. This restriction is not particularly troublesome, since our development of the Rayleigh theory also assumes dilute solutions. 

We assume that there exists a function which we represent by P(0)-in recognition of the fact that it is angle dependent-which can be multiplied by the scattered intensity as predicted by the Rayleigh theory to give the correct value for i, even in the presence of interference. That is. 

In applying the Rayleigh theory to large polymer molecules, we had to extrapolate results measured at different 0 s to 0 = 0 to eliminate the interference effect. 

Prepare a log-log plot of rx versus X and evaluate the slope as a test of the Rayleigh theory applied to air. The factor M/pN in Eq. (10.36) becomes 6.55 X 10 /No, where Nq is the number of gas molecules per cubic centimeter at STP and the numerical factor is the thickness of the atmosphere corrected to STP conditions. Use a selection of the above data to determine several estimates of Nq, and from the average, calculate Avogadro s number. The average value of n - 1 is 2.97 X 10" over the range of wavelengths which are most useful for the evaluation of N. ... 

E. Schrodinger, Ann. Phys. 80 (1926), 437. The quantal formalism substantially follows the classical method developed by Lord Rayleigh (Theory of Sound [1894]) and is commonly referred to as Rayleigh-Schrodinger perturbation theory. ... 

For spheres sufficiently small that Rayleigh theory (Chapter 5) is applicable, or for arbitrarily shaped particles that satisfy the requirements of the Rayleigh-Gans approximation (Chapter 6), incident light with electric field components parallel and perpendicular to the scattering plane may be scattered with different amplitudes however, there is no phase shift between the two components. Hence, the amplitude scattering matrix has the form... 

The particles may not be small enough for the Rayleigh theory to be valid. For larger particles, the relation between absorption and size is more complicated. 

Some insight into how departures from Rayleigh theory affect linear polarization can be obtained from calculations of Asano and Sato (1980) for randomly oriented oblate spheroids with refractive index 1.33, which is near enough to that of ice, axial ratio a/c = 5, and size parameter 2ma/ = 5 for a... 

Although the indium particles are not small compared with the wavelength in all directions, they are sufficiently small (368 A) along the direction of propagation of the incident light that Rayleigh theory is a good approximation. The unobserved feature calculated for 1390-A spheres is therefore easy to... 

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). 

Section 5.5 moves on to an extension of the Rayleigh theory essential for colloid science, namely, the Debye theory for particles of the order of the wavelength of the radiation source. The important concept of interference effects, the form factor, the Zimm plot, and... 

The Rayleigh theory does not apply when the scattering molecules are absorbing or when the atmosphere contains dust particles, water drops, or other particles with dimensions that are larger than ordinary gas molecules. 

The Rayleigh approximation shows that the intensity of scattered light depends on the wavelength of the light, the refractive index of the system (subject to the limitation already cited), the angle of observation, and the concentration of the solution (which is also restricted to dilute solutions). In the Rayleigh theory, the size and shape of the scatterers (M and B) enter the picture through thermodynamic rather than optical considerations. 

What is meant by Rayleigh scattering What are the important assumptions and limitations of the Rayleigh theory ... 

Lord Rayleigh, Theory of Sound, Vol. I, Dover, New York, 1945, reprint. 

From Rayleigh theory, the intensity of light scattered from each droplet or particle depends largely on its size and shape, and on the difference in refractive index between the particle and the medium. For a dispersion, each spherical droplet, bubble, or particle scatters unpolarized light having an intensity l[Pg.24]

Rayleigh theory gives another relation from which particle sizes can be obtained [13,25], In the limit as the particle concentration goes to zero,... 

The jet stability and break-off behavior with respect to the fluid properties are stated in well-known theories such as Navier-Stokes equations and the Rayleigh theory. During recent years many computer simulations have aimed at predicting the jetting process in specific print heads and, more importantly, for establishing a methodology for selection of ink additives. ... 

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