Wavelength exponent

It is important to appreciate that particular values for the wavelength exponent, n, and the attenuation index, a, at some one wave length will characterize the entire transmittancy curve in the visible spectrum of the sugar solution. When a sugar liquor is treated with a solid adsorbent, the changes in the spectrophotometric curves in the visible spectrum are adequately defined by changes in the values of n and a (see Table I). This procedure promises to be an effective tool, both in research and in applications.31... 

Fig. 5.3. (a) Plot of the turUdity as a fimctioii of wavelength for a polyfoxyethylene) stabilized latex (b) plot of the turbidity-wavelength exponent as a function of temperature for a poly(oxyethylene) stabilized latex in 0-39 M MgSO (after Dodd, 1980). 

Khlebtsov et al. (1991) have theoretically and experimentally studied the dispersion effect of the refractive indices of particles and dispersion medium in the turbidity spectrum method. A new approach is put forward to estimate the optical dispersion of the components of a colloidal system and to consider it when the system s parameters are determined from the wavelength exponent. The method has been verified on PS lattices with the particle diameter from 80 to 800 nm. The elaborated version of the turbidity spectrum method can be used as a metrological test for particle sizes, not inferior to electron microscopy in accuracy. 

Indeed, the incre2tse in the scattering intensity, when the configurative point approaches the spinodal, is accompanied by a deformation of the polar disigram of the scattered intensity (z > 1) and a decrease in the wavelength exponent (Elquation 2.1-92) to n w 2. 

Table 7.8 contains values of p,/p for the common target elements employed in X-ray work. A more extensive set of mass absorption coefficients for K, L, and M emission lines within the wavelength range from 0.7 to 12 A is contained in Heinrich s paper in T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry (eds.). The Electron Microprobe, Wiley, New York, 1966, pp. 351-377. This article should be consulted to ascertain the probable accuracy of the values and for a compilation of coefficients and exponents employed in the computations. 

Clouds of Nonblack Particles The correction for nonblackness of the particles is complicated by multiple scatter of the radiation reflected by each particle. The emissivity . of a cloud of gray particles of individual surface emissivity 1 can be estimated by the use of Eq. (5-151), with its exponent multiplied by 1, if the optical thickness alv)L does not exceed about 2. Modified Eq. (5-151) would predict an approach of . to 1 as L 0°, an impossibihty in a scattering system the asymptotic value of . can be read from Fig. 5-14 as /, with albedo (0 given by particle-surface refleclance 1 — 1. Particles with a perimeter lying between 0.5 and 5 times the wavelength of interest can be handledwith difficulty by use of the Mie equations (see Hottel and Sarofim, op. cit., chaps. 12 and 13). 

The exponent Mk depends on the mean square displacement of the atom from its equilibrium position and hence upon temperature. It is linear with (kT/m Xsin / where k is the Boltzmann constant, T the absolute temperature, the scattering angle, the wavelength and m the atomic mass (for a monatomic material). In addition there are complicated expressions dependent upon the crystal symmetry. As an example, for silicon at room temperature the /, are reduced by approximately 6%. With this correction all the equations of dynamical theory still apply. 

Furthermore, we (a) change notation of the velocity at equilibrium, v°(f) —> v(t) (b) omit kr in the exponent, since the space scale having order of a path, which a particle walks between strong collisions, is much less than the free-space wavelength A at the frequencies under investigation and (c) omit the exponential term proportional to exp[i ( f + y)], since it vanishes after integration over y. Then we have... 

The second-order hyperpolarizabilities of a series of oligothienyleneethynylenes were measured by THG at two different wavelengths. At the fundamental wavelength A=1064 nm an exponent a=3.66 [81] was found, with the harmonic wavelength in resonance. At A=1907 nm a smaller exponent a=2.4 [82] was determined. The saturation regime was reached for these oligomers at 60 linearly conjugated carbon-carbon bonds. 

For Z less than 20A, the power p(l) is almost constantly 2. When separation Z approaches the 500-A wavelength of absorption, the power grows rapidly to 3. Then the exponent remains near 3 from Z 1000 to 10,000 A before it plunges back down to 2 in the limit of large separations. Why ... 

Angstrom exponent scattering efficiency of substance X (m g ) upscatter fraction axial angle (rad) solar zenith angle (rad) wavelength (nm)... 

Another important aerosol optical property is column aerosol extinction, the vertical integral of the aerosol extinction coefficient, again a function of wavelength. This quantity is often also denoted aerosol optical thickness (AOT) or aerosol optical depth. The wavelength dependence of AOT is also often expressed as an Angstrom exponent. 

Figure 17 also shows the Angstrom exponent (cf. Section 4.04.2) evaluated from the dependence of aerosol optical thickness, r p, on wavelength A SiS a = — d log Tgp/d log A. A greater Angstrom... 

Figure 18 Global distribution of AOT t at 865 nm (upper panel) and dependence on wavelength A as the Angstrom exponent, a= — d In r/d In A (lower panel) for June 1997. The distributions were derived from radiance measurements at 18-km resolution by the POLDER (POLarization and Directionality of the Earth s Reflectance) radiometer aboard the ADEOS (ADvanced Earth Observing Satellite) platform. Retrieval is limited to the atmosphere above water surfaces. Courtesy of Laboratoire d Optique Atmospherique, Lille, France Laboratoire des Sciences du Climat et de TEnvironnement, Gif sur Yvette, France Centre National d etudes Spatiales, Toulouse, France and National Space Development Agency, Japan. For further information see http //earth-sciences.cnes.fr 8060/polder/...

In the study of the kinetics of the decay of erbium PL we used a semiconductor laser radiating at 658 nm wavelength with a variable pulse time. The energy of photons of this laser corresponds to the transitions between the tail states of the valence band and the conduction band of the amorphous silicon, but it is significantly smaller that the width of the forbidden gap of the dielectric nanocrystals of erbium silicate. The intensity decay of erbium PL after the end of the pumping pulse is well described by two exponents with the characteristic times of 27 ps for the fast component (Ifts,) and 200 ps for the slow component (Liow)- The presence in the decay kinetics of two components with strongly... 

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