Scattering Lorentz-Lorenz

Figure 47 shows taken from Equation 20 versus Vj. It shows that S. is quite sensitive to Vp and is therefore a good means to evaluate v, with the numerical values of Fig. 47. It can be estimated that the tensile modulus E of the bulk PMMA is not affected by the very low pressure toluene gas environment during the short duration of the experiment. The optical craze index in PMMA in air without load is known as n = 1.32, which corresponds to v = 0.6. From the optical interferometry, it is known that the craze just before breakage is twice as thick as unloaded, (v, = 0.3) and hence using Lorentz-Lorenz equation its optical index is n = 1.15. From Figs. 46 and 47 it can be concluded that the bulk modulus around the propagating crack is about 4400 MPa, which is a somewhat high value, in view of the strain rates at a propagating crack tip (10 to s" ). Using the scatter displayed in Fig. 46, it can be concluded from Fig. 47 that the fibril volume fraction is constant, v = 0.3, within a scatter band of 0.08, and is therefore not sensitive to the toluene gas.

The refractive index of the ethane/propane mixture, needed for calculation of the scattering vector, was determined from experimental density measurements and an empirical Lorentz-Lorenz relationship (12). Incorporating the errors from the viscosity and refractive index calculations into the Stokes-Einstein relation results in a maximum error in the hydrodynamic radius of approximately 5%. 

In 1906, J. C. Maxwell Garnett used the Maxwell Garnett theory, equation (12), for the first time to descibe the color of metal colloids glasses and of thin metal films. Equation (12) can be deviated from the Rayleigh scattering theory for spherical particles [21], or from the Lorentz-Lorenz assumption for the electrical field of a sphere and the Clausius-Mossotti Equation by using the polarizability of an metal particle if only dipole polarization is considered [22]. 

The relationship between a and the concentration of scattering centers is derived next (Tanford, 1961). The Lorentz-Lorenz formula (another aspect of electromagnetic theory) is... 

Thus, the procedure is to first find the singular solution of the Lorentz-Lorenz law together with the dispersion relation for the effective wave number Kg, and then to determine the arbitrary constant from the scalar equations (2.190) or (2.191). After the conditional average of the scattered field coefficients has been evaluated, the coherent reflected field can be computed by taking the configurational average of (2.171), i.e.,... 

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