Fraunhofer scattering

In the case of He-Ne laser, the wavelength value is 0.63 p. Using this, particle sizes in the range of 2-100 p can be measured. The measurement by this technique gives rise to good accuracy and speed. The sample size needed is 5g. The method can be automated. 

Results of Coulter counter measurements for two particle sizes A and B R is the resistance between the electrodes, shown as shaded squares. 

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Left Elastic scattering angular distribution for illustrating Fraunhofer scattering (Hiebert... 

A particle size analyzer determines the particle size distribution of powders either dry or dispersed in solvent by laser light scattering based on the Fraunhofer scattering theory. This type of equipment has an optical bench whose combined dynamic range is nominally 0.7-2000 pm. The instrument calculates mean diameters and distribution data. An interfaced computer generates sample histograms. This technique has been applied to the study of particle size and particle size distributions for polymer powders and polymer suspensions in a variety of solvents. 

Fraunhofer scattering has become a popular optical sizing tool for particles substantially larger than a micrometre in diameter. In this case each particle behaves similarly to a pinhole aperture, and the low angle scattered light is a superposition of Fraunhofer diffraction patterns. This technique is widely used for the analysis of commercial food-based emulsions and sauces. 

Figure 2.13. A 3-D display of Fraunhofer scattering intensity. All three axes are plotted in log scale [62] (by permission of Medpharm Scientific Publishers).

Particle Size Laser Refractometiy is based upon Mie scattering of particles in a liquid medium. Up until about 1985, the power of computers supplied with laser diffraction instruments was not sufficient to utilize the rigorous solution for homogeneous spherical particles formulated by Gustave Mie in 1908. Laser particle instrument manufacturers therefore used approximations conceived by Fraunhofer. 

According to the Fraunhofer approximation of kinematic scattering theory the real space and the reciprocal space are related to each other by an integral transform known by the name Fourier transform, which shall be indicated by the operator The n-dimensional (nD) Fourier transform of h (r) is defined by... 

The vesicle size is an important parameter not only for in-process control but particularly in quality assurance, because the physical stability of the vesicle dispersion depends on particle size and particle size distribution. An appropriate and particularly quick method is laser light scattering or diffraction. Laser light diffraction can be applied to particles > 1 pm and refers to the proportionality between the intensity of diffraction and the square of the particle diameter according to the diffraction theory of Fraunhofer. 

For particles below 200 nm, Rayleigh s theory holds, which considers the scattering intensity to be proportional to the 6th potency of the particle diameter. Both Fraunhofer s and Rayleigh s theories are only approximations of Mie s theory which claims that the scattering intensity depends on the scattering angle, the absorption, the size of the particles as well as on the refractive indices of both the particles and the dispersion medium. 

Conditions (2) and (3) are equivalent to the Fraunhofer or far-field approximations in ordinary optics. The coherently illuminated region with usual laboratory X-ray sotuces is a few micrometres across. We therefore expect this theory to be useful in the cases of weak scattering but to be seriously awry for strong scattering. 

Capillary hydrodynamic chromatography Fraunhofer diffraction Light-scattering photometry Phase Doppler anemometry Ultrasonic spectroscopy... 

The Mie theory (actually Mie s solution to Maxwell s equations for spheres) can be applied to spherical particles that are smaller than, similar in size to, and larger than the wavelength of light used (Mie, 1908). With particles much larger than the wavelength, the Mie theory can be simplified to the Fraunhofer theory. The mathematics of scattering is complicated for other than spherical shapes, and that is why the assumption that particles are spherical is often made. 

Figure 10.24 Angular distribution for 12C +160 elastic scattering, showing Fraunhofer diffraction and the elastic scattering of 160 with 208Pb, which shows Fresnel diffraction. [From Valentin (1981).]...

The value of 10 is determined by molecular and particulate (cloud and aerosol) scattering, and surface reflection. A small fraction of the molecular scattering is the non-conservative Rotational Raman scattering (RRS) that partially fills the solar Fraunhofer lines in the scattered radiation, creating what is commonly known as the Ring effect [15] As a result, the ratio Iq/F, where F is the extraterrestrial solar flux, contains structure that is correlated with solar Fraunhofer lines. By separating these effects, one can write... 

In this book, particles larger than 1 pm are of primary interest, and thus, only the Fraunhofer diffraction method, which can account for particles larger than 2-3 pm, is discussed here. The Fraunhofer diffraction theory is derived from fundamental optical principles that are not concerned with scattering. To obtain the Fraunhofer diffraction, two basic requirements must be satisfied. First, the area of the particle or aperture must be much smaller than the product of the wavelength of light and the distance from the light source to the particle or aperture. Second, this area must also be smaller than the product... 

Fraunhofer diffraction theory combines the above results to compute the light scattered at small angles from large particles. Such a particle is pictured in Figure 4.15. 

Fraunhofer, W., G. Winter and C. Coester (2004). Asymmetrical flow field-flow fractionation and multiangle light scattering for analysis of gelatin nanoparticle drug carrier systems. Anal Chem 76(7) 1909-20. 

D < 500 pm, Fraunhofer Diffraction Pattern Analysis (FDPA) can be employed in measuring particle size distributions (4,5). For the particles in the intermediate range, 0.7 pm < D < 10 pm, Mie theory of scattering holds and Turbidity Spectra (TS) can furnish information about particle sizes (6). 

The more complex Mie Theory (lj must be invoked to analyze particles with dimensions near the wavelength of light. Fraunhofer theory is an interference phenomenon, and is described in various optics text books (.2,3.). It is adequate for most particle sizing applications and will be discussed in detail. Mie Theory requires a knowledge c the refractive index of the material. A unique use of polarized side scatter at several wavelengths is employed to obtain particle size channels in the submicron region. 

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