Cone angle, correlations

The Pt—P (and Pt—Cl) bond lengths correlate with the electron-donating ability of the phosphine (Tolman s Xi factor) rather than steric factors (the cone angle of the tertiary phosphine) [150b]. 

My question to Dr. J. Kochi is whether it is possible to correlate the steric factor in his equations describing the oxidation of alkylmetal compounds to some measure of the bulkiness of the alkyl groups such as cone angles similar to ones suggested by Dr. C.A. Tolman for tertiary phosphine ligands. 

Spray cleaning, of metal surfaces, 16 213 Spray coating processes, 7 23, 68-76 economic aspects, 7 75-76 Spray column absorbers, 1 27 Spray cone angle, 23 187 Spray correlations, 23 189-192 Spray deposition, of metal-matrix composites, 16 173 Spray-dried products, 11 542-543 Spray-dried resins, production of,... 

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... 

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

In order to assess steric and electronic effects on the bond enthalpies of reaction of phosphine and phosphite ligands to platinum(II), the enthalpies (AH) of reaction of these ligands L on reaction with [PtMe(PPhMe2)2(THF)]PF6 have been measured (equation 412). These authors measured the enthalpies of 34 ligands, and correlated the measured enthalpy with the ligand cone angles.1342,1343 Representative data are shown in Table 8. 

Table 8 Enthalpy and Cone Angle Correlations for the Reaction [PtMe(PPhMe2)2(THF)]PF6 + L ---> (PtMe(PPhMe2)2L]PF6 + THF...

Reasonable correlations of combustion efficiency with fuel spray momentum and spray energy in two different combustors have been shown to hold over a range of altitude-engine idling conditions 133). As different curves were obtained with different injector nozzles, spray-cone angle was thought to be a factor. Further work showed that efficiency did correlate closely with expressions representing the spray momentum or... 

Higher n/b ratios in cobalt-modified catalysts are apparently achieved as a result of the phosphine presenting more steric bulk to the insertion reaction of the alkene. The effect is predominately steric, since there is little correlation with regiochemistry and phosphine bacisity. A combination of electronic (Xi) and steric (cone angle 0) effects provide a more rational explanation of the increase in nib ratio with added phosphines.16,17... 

The enthalpy trend can be examined in terms of electronic and steric contributions to the enthalpy of reaction, the relative importance of which can be quantified in terms of the respective Ai /A2 ratios obtained in a treatment first proposed by Tolman, where enthalpies of reaction are correlated with steric (6, cone angle, see Tolman s Cone Angle) and electronic (v, carbonyl stretching frequency in Ni(CO)3L, L = tertiary phosphine) factors. A correlation factor of 0.95 is obtained when enthalpic data are fitted to equation (3) and a value of 2.32 is calculated for the A1/A2 and quantitatively denotes the overwhelming influence of steric factors. Since the steric factors have such a profound influence on the enthalpy of reaction, a direct relationship between the enthalpy of reaction and the phosphine cone angle can be established as shown in Figure 1. 

Since (a) and (b) would not apply to the lowermost part of the spout, the constant voidage values reported by these workers were presumably reached after some initial distance from the inlet orifice. Spout-voidage data obtained with different cone angles, solid materials, and H/D, ratios were correlated by the following empirical equation based on dimensional analysis ... 

This result may reflect a hampered P—H elimination in the organonickel intermediates. With other phosphanes or phosphites the yields of 4 and 5 range from 56 to 86 %. The data collected in Table 1 reveal that there is no simple correlation between product distribution and basicity or cone angle 601 of L. 

Steric effects play a role in the rate of ligand displacement. The rate of reaction for equation 7.13 has been measured for a number of phosphine ligands (PR3), and the results indicate that the rate of substitution is accelerated by bulky phosphines. A good correlation between cone angle (see Section 6-3) of the phosphine (or phosphite) ligand and rate of displacement by CO was obtained, as shown in Table 7-3. 

There is a good correlation between the logarithms of the ligand dissociation constants K (reverse of stability constant) of NiL4 and the cone angles of L. As the cone angle increases, so does the K value ... 

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