Distribution chord length

If we consider the chord length distribution, we can express the alternating chords and I2 as ... 

In the Lasentec instruments a chord-length distribution is generated, from a rotating infrared beam, and this is converted to a size distribution. Since highly concentrated systems can be interrogated this system can be used for on-hne size analysis. 

Cylindrical Filaments. If cylindrical filaments are studied, the last-mentioned assumption is not be fulfilled. In this case it is more suitable to cross an elongated24 primary beam and the fiber in such a way that the irradiated height of the beam, Bgo, is constant. Then the irradiated volume becomes V = Bbo nrj, with /y being the radius of the fiber. In many practical applications the studied fiber is very thin, and the effective absorption coefficient can be approximated by exp (—fiteff) 1. If this approximation is not feasible, the absorption factor exp (—ji ) must be integrated for the chord length distribution gc ( ) of a circle with radius ry (cf. p 168) in order to yield the effective absorption. 

The isotropic chord length distribution (CLD) is of limited practical value if soft matter with only short-range order is studied. Nevertheless, the related notions have been fruitful for the development of new methods for topology visualization from SAXS data. 

Figure 8.23. The chord length distributions g (r) and g (—r) found in the 2nd derivative y" (r) of the radial correlation function. The example shows g(r) of a suspension of 10 wt.-% of silica (reproduced from a handout of DENISE TCHOUBAR)...

Figure 8.24. Demonstration of the edge-enhancement principle built into the chord length distribution, (a) Two-phase structure intersected by a straight line, (b) The density along the line, (c) The derivative of the density is a sequence of 5-functions which are marking the positions of the domain edges...

Figure 8.35. The homogeneous sphere of radius R. Radial correlation function, ys (r), distance distribution function (DDF) ps (r) and chord length distribution (CLD) gs (r)...

FBRM provides a real time chord length distribution within the crystallizer. The technique is excellent for determining the onset of nucleation and in following general growth rate and rate transitions associated with polymorphic transformation, reaching equilibrium and attrition effects. 

Fig. 4 Chord-length distribution Y (d), 0.5 nm < d < 5 nm, inset the corresponding SAXS curve obtained for the microporous glass membrane...

Based on the curvature behaviour of the SAS correlation function y(r), the distribution laws of random distances between the interfaces were analyzed [12]. This is examplified for a sequence of 4 pores and 3 walls in Fig. 5. Furthermore, the appearance of all minima and maxima in the chord-length distribution, see Fig. 4, at d= 2.1 nm, 2.5 nm, 2.9 nm,... is traced back to the mean chord lengths <1> and . 

Fig. 3. Theoretical two-point probability (left) and chord-lengths distribution right) for a rartdom ensemble A of mono-disperse penetrable solid spheres compared to the same descriptors recalculated from A s reconstruct B.

Chord length distribution and pore size distribution of porous VYCOR glass... 

Nitrogen adsorption (NA) experiments yield diameter distribution densities V d) of the random pore diameter d. Based on the assumed particle shape (circular cylinder, random diameter d), the function V d) can be transformed into a chord length distribution density (CLD) A 1). CLDs are connected with the porosity p of the material. The direct transformation step,... 

Lasentec Partec 100 was found to give reasonably accurate data for the chord length distribution of sherical particles but the accuracy deteriorated progressively as the shape became more ellipsoidal [123],... 

Lasentec s Focussed Beam Reflectance Measurement Model (FBRM M400L) operates at a wavelength of 791 nm and the beam rotates 75 s at a peripheral speed of 1.9 ms .to describe a circle of diameter 8 mm. It has been used with a 3D-model of chord length distribution for particles of a general shape as well as particles with the same shape but different sizes [124]. The focal point can be changed in the axial position but it is... 

Fig. 4 Chord length distribution of latex particles suspended in water (- - -) and actual particle size distribution (—). (From Ref. ". )...

Fig. 5 Theoretical chord length distribution for single crystal from orientation averaging.

Focused beam reflectance measurement (FBRM) particle size (chord length) distribution... 

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