Factor Deceleration

While increasing anion solvation by protic solvents has an accelerating effect on SnI reactions as described above, it is often a decelerating factor in Sn2 reactions. Thus, reaction (5-103) between (iodomethyl)benzene and radioactively labeled sodium iodide in acetone is clearly decelerated by the addition of protic solvents such as water, ethanol or phenol, as demonstrated in Fig. 5-16 [266]. 

If the addition of alcohols (or additives) causes deceleration, this factor is termed deceleration factor (DF) [121],... 

Observed and calculated deceleration factor by sodium polyacrylate of the NH OCN"-urea conversion (50 °C)... 

The strong retardation by NaPSt is due to the simultaneous contribution of the hydrophobic and electrostatic interactions between the polyanions and dye cations (deceleration factor 10 ). The OH is repelled by the electrostatic repulsion by the polyanions. Other polyanions, which lack the hydrophobic groups, decelerate the reactions much more moderately than NaPSt, because only the electrostatic interactions are operating. The strength of the hydrophobic interactions depends on the hydrophobicity of the dye cations. Thus, the ratio of the highest rate in the presence of CTABr to the lowest one in the presence of NaPSt amounts to 10 . The ratio for MG, which is least hydrophobic among the dyes studied, is about 10 . 

Figure 13.28 Plot to give creep rate deceleration factor (CROP). (Reproduced from Cawood, M.J., Channell, A.D. and Capaccio, C. (1993) Crack initiation and fiber creep in polyethylene. Polymer, 34, 423. Copyright (1993) Elsevier Ltd.)...

Figure 13.29 Correlation between creep rate deceleration factor (CRDF) and notched pipe test (NPT) failure times. (Reproduced from Clutton, E.Q., Rose, L.j. and Capaccio, C. (1998) Slow crack growth and impact mechanisms in polyethylene. Plast. Rubber Comp. Proc. Appl., 27, 478. Copyright (1998) Maney Publishing.)...

When a wire rope is operated close to the minimum design factor, the rope and related equipment should be in good operating condition. At all times, the operating personnel should minimize shock, impact, and acceleration or deceleration of loads. Successful field operations indicate that the following design factors should be regarded as minimum ... 

As recently as 1965, Thoma and Stewart predicted that alterations in reaction rates [in the presence of the cycloamyloses] should be anticipated whose magnitude and sign will fluctuate with the reaction type, and added that at the present juncture, it is impossible to sort out confidently. . . which factors may contribute importantly to raising or lowering the activation energy of the reaction. In the short interval between 1965 and the present, a wide variety of cycloamylose-induced rate accelerations and decelerations have, indeed, been revealed. More importantly, rate alterations imposed by the cycloamyloses can now be explained with substantially more confidence. The reactions of derivatives of carboxylic acids and organo-phosphorus compounds with the cycloamyloses, for example, proceed to form covalent intermediates. Other types of reactions appear to be influenced by the dielectric properties of the microscopic cycloamylose cavity. Still other reactions may be affected by the geometrical requirements of the inclusion process. 

However, the behaviour near m = raB needs some other explanation. My proposal involves the specific solvation of the backside of the carbenium ion by the strong dipole of the solvent this displaces the monomer molecule which is located there in the absence of the solvent, so that the 7t-bond to the monomer at the front is weakened and the unimolecular isomerization-propagation becomes accelerated, despite the statistical factor which, alone, would produce a deceleration, as explained at the end of Section 3a. As the dilution proceeds from m = raB downwards, the polymerization goes through a dieidic phase, in... 

On the other hand, there is now a good deal of evidence that the solvolysis of most cyclobutyl derivatives does lead directly to the cyclopropylcarbinyl cation. For example, orbital symmetry considerations (Section 11.3) indicate that the conversion of cyclobutyl cations into cyclopropylcarbinyl cations should occur by disrotatory ring opening as shown in Figure 6.11 but any steric factors that would hinder such a process decelerate most cyclobutyl solvolyses. Thus 86 See note 84(b). 

A number of cases of steric deceleration of solvolysis have been reported. For example, the nonbonded strain in 87 is approximately 1.9 kcal mole-1 greater than that in 86. Assuming that the strain is fully relieved in the transition state for ionization, one would predict that the rate of solvolysis of the endo-tosylate (87) should exceed that of the exo-tosylate (86) by a factor of 25. 

Here, we shall discuss the implications of cosmological expansion for the searches of a quantum-gravity-induced refractive index and a stochastic effect. We will consider Friedman-Robertson-Walker (FRW) metrics as an appropriate candidate for standard homogeneous and isotropic cosmology. Let R be the FRW scale factor, and a subscript 0 will denote the value at the present era. Ho is the present Hubble expansion parameter, and the deceleration parameter qo is defined in terms of the curvature k of the FRW metric by k ( 2[Pg.588]

On one hand, solid materials to be processed with an impinging stream device have various sizes, while, on the other hand, the relative velocity between gas and particles varies from time to time in acceleration and deceleration stages of particle motion. Both factors make the value for Rep vary continuously with considerably large amplitude, which may be across various flow regimes. So, the variation of the drag coefficient, Cd, in various flow regimes has to be taken into account in the solution of the motion equations for the particle in various stages. 

The velocity based on the hole area is v . The pressure Pi is the pressure upstream of the orifice, typically about 1 pipe diameter upstream, the pressure P2 is the pressure at the vena contracta, where the flow passes through a minimum area which is less than the orifice area, and the pressure P3 is the pressure downstream of the vena contracta after pressure recovery associated with deceleration of the fluid. The velocity of approach factor 1 — (AJA)2 accounts for the kinetic energy approaching the orifice, and the orifice coefficient or discharge coefficient C accounts for the vena contracta. The location of the vena contracta varies with AJA, but is about 0.7 pipe diameter for AJA < 0.25. The factor 1 — AJA accounts for pressure recovery. Pressure recovery is complete by about 4 to 8 pipe diameters downstream of the orifice. The permanent pressure drop is Pi — P3. When the orifice is at the end of pipe, discharging directly into a large chamber, there is negligible pressure recovery, the permanent pressure drop is Pi — P2, and the last equality in Eq. (6-111) does not apply. Instead, P2 = P3. Equation (6-111) may also be used for flow across a perforated plate with open area A and total area A. The location of the vena contracta and complete recovery would scale not with the vessel or pipe diameter in which the plate is installed, but with the hole diameter and pitch between holes. 

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