The very large measuring range from 0.01 [micro]m to 2100 [micro]m of the Analysette 22 NanoTec results from the combination of two lasers with two different measuring cell detector spacings: Large particles are detected using an infrared laser with a large distance to the measuring cell, for small particles a green laser with a small distance to the cell is used, which permits the detection of the forward scattered light up to a scattering angle
of 65 degrees.
Although the spherical geometry poses some technical complications, the solution is given in terms of the coefficients of a Legendre polynomial [P.sub.l]([x.sub.L]) expansion of the differential scattering cross section, where [x.sub.L] = cos [theta] and [theta] is the polar scattering angle
. Sharp features are smoothed more rapidly than slowly varying ones.
where [THETA] is the scattering angle
and [U.sub.n] is the second kind of Chebyshev function.
The scattering angle
is [[theta].sub.s] = -90[degrees] ~90[degrees].
For the MC-simulations in this work, we sort BSEs into bins according to their scattering angle
and monitor the BSE energy in addition to the BSE number.
The incident angle and scattering angle
at fixed at [[theta].sub.i] = 20[degrees], [[theta].sub.s] = 40[degrees] with a surface roughness of [k.sub.l] = 6.28, [k.sub.[sigma]] = 0.628.
where R is the average spherulitic radius, [[lambda].sub.0] is the wavelength of light in air, n = 1.42 is the refractive index of the sample, and [[theta].sub.m] is the corrected scattering angle
for maximum intensity, which is related to the actual scattering angle
, [[theta].sub.m] as, sin [[theta].sub.m] = sin([[theta].sub.m]/n) .
The scattering intensity I is measured as a function of the scattering vector g = (4[pi] sin [theta])/[lambda], where [lambda] is the wavelength of the incident radiation and [theta] is half of the scattering angle
. 1(g) for a polydisperse system of noninteracting particles in a uniform media can be expressed as follows :
However, the photon degree of polarization undergoes greater variation for large values of scattering angle
DLS data taken at one scattering angle
enable measurement of the hydrodynamic radius of the protein while simultaneously measuring molar mass by MALS.
In Equation (9), [u'.sub.0_h] and [u'.sub.0_V] are the amplitude of the horizontal polarization component and the vertical polarization component of the incident wave on dV, respectively; [f.sub.12], [f.sub.21], and [f.sub.22] are the elements of the scattering amplitude function matrix for the raindrop with the diameter D, which are the functions of scattering angle
[THETA] (cos = [THETA] = [[??].sub.0] X [??]), and are related to the scattering functions [S.sub.1], [S.sub.2], [S.sub.3] and [S.sub.4] used by Van de Hulst and in Mie solution for a sphere [48, 50]; [??] is the unit vector of a scattering direction in the coordinate axes xyz.
He further added that by measuring the scattering angle
and understanding the physics of Coulomb multiple scattering, one can assess the locations and amount of the melted fuel in the reactor.