Cone angles estimation

Xanthic acid metal complexes, 588 X-Ray diffraction aqueous solution, 307 cone angles estimation, 1022 hydrates... 

Using SI units, and from some literature reported values for hydroclones with D between 125 and 600 ram, and a cone angle of 38°, a value for coefficient K is 2.8 X 10. The maximum size of particles in the cleared liquid can be estimated from ... 

Various correlations for mean droplet size generated using pressure-swirl and fan spray atomizers are summarized in Tables 4.4 and 4.5, respectively. In the correlations for pressure-swirl data, FN is the Flow number defined as FN = ml/APlpl) )5, l0 and d0 are the length and diameter of final orifice, respectively, ls and ds are the length and diameter of swirl chamber, respectively, Ap is the total inlet ports area, /yds the film thickness in final orifice, 6 is the half of spray cone angle, and Weyis the Weber number estimated with film... 

Imyanitov204 has developed a method of estimating cone angles for any ligand provided that the atomic radii, van der Waals radii and the molecular geometry are known. The method involves combination of mathematical and graphical methods. From the geometry of M—AB shown in (21) the equation in terms of 0/2 was deduced (equation 50). 

For more complex and bulky ligands an accurate geometrical construction was used for measurement (22a) to estimate a value for rs and / s, where s refers to the complex substituent and r,R the sphere enclosing the complex substituent, making it equivalent to the atom B in (21). This procedure yields values for phosphorus cone angles systematically 5 higher than that of Tolman,187 undoubtedly because of the Ni—P distance of 2.23 A chosen by Imyanitov. 

Attempt to develop NMR techniques to estimate cone angle... 

Figure 13. Dimensionless absorption versus normalized frequency calculated rigorously (solid lines), from the PL-RP approximation (dashed lines), and for the hybrid model (dashed-and-dotted lines). The cone angle P = tt/8 and the reduced collision frequency y = 0.2. The reduced well depth u = 3.5 (a) and 5.5 (b). Left and righ vertical lines mark the frequency peaks estimated, respectively, in the rotational and librational ranges.

A quantitative estimation of the steric demand of L can be made in terms of its cone angle. As shown in Fig. 2.2, it is the angle of a cone with its vertex at the metal atom and a metal-phosphorus distance of about 22.8 nm. The cone is created by the surface that just encloses all the ligand atoms for all orientations resulting from the rotation around the metal-phosphorus bond. 

The steric demand of a monophosphine ligand is difficult to define precisely, especially for those with more than one kind of group attached to the P atom. A rough but useful estimate of the solid angle subtended at the metal atom to which the ligand is bound is the so-called cone angle, 0, defined as follows ... 

Table 3.3 Cone Angles of Tertiary Phosphine Ligands (Cone Angles of Bidentate Ligands [7]. Cone Angles of Ph2p(CH2) PPh2 are Estimated by Assuming PMP Angles of 74, 85,90° for n = 1,2,3, Respectively)...

In order to demonstrate the performance of the Doppler-burst envelope integral value method for the estimation of the instantaneous particle velocity vector and the particle mass flux or concentration, measurements were performed in a liquid spray issuing from a hollow cone pressure atomizer (cone angle 60°) and a swirling flow which exhibits complex particle trajectories (Sommerfeld and Qiu 1993). All the measurements were conducted using the one-component phase-Doppler anemometer. The integration of the mass flux profiles provided the dispersed phase mass flow rate which agreed to 10 % with independent measurements of the mass flow rate (Sommerfeld and Qiu 1995). 

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