The pressure dependence of yield

If the pressure on a sample is increased the normal force on every plane is increased and the Coulomb criterion thus suggests that there is a dependence of yield on pressure. The pressure dependence of yield is therefore considered in the following section. 

The application of the yield criterion represented by equation (8.11) is not straightforward, however, because it is necessary to find the plane for which the LHS is a maximum under the particular system of applied stresses. It has been found that a simpler criterion, based on the von Mises criterion, is useful for describing yield in a variety of multi-axial stressing experiments. This criterion is expressed by the equation 

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Lazzeri and Bucknall [131] have proposed that the pressure dependence of yield behaviour caused by the presence of microvoids can explain the observation of dilatation bands in rubber-toughened epoxy resins [132], rubber-toughened polycarbonate [133] and styrene butadiene diblock copolymers [134]. These dilatation bands combine in-plane shear with dilatation normal to the shear plane. Whereas true crazes contain interconnecting strands, as described in Section 12.5.1 above, dilatation bands contain discrete voids that, for rubber-toughened polymers, are confined to the rubber phase. 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

If the pressure dependence of the molar volume of the liquid is neglected, integration from a flat interface (r = oo) yields... 

Somewhat surprisingly, the pressure dependence of quantum yields from the photolysis of NO at 1236 A, where the primary process is almost entirely photoionization199, is very similar to that observed for 1470-1650 A198. Clearly, recombination of the ionic fragments must lead to an excited state of NO which predissociates upon collision. However, the neutralization reaction... 

In kinetics, similar relationships apply, but the volume of activation AV can be determined only from the pressure dependence of the rate coefficient k, since the partial molal volumes V of transition states are not directly measurable. Conversely, however, equation 4 can yield values of V. ... 

Fig. 8. Data showing (a) the pressure dependence of the quantum yield of H2 produced in the 184.9 nm pyi dysis of borazine and (b) the build-up of solid polymer during the pyrolysis reaction...

Olzmann, M Th. Benter, M. Liesner, and R. N. Schindler, On the Pressure Dependence of the N02 Product Yield in the Reaction of N03 Radicals with Selected Alkenes, Atmos. Enriron., 28, 2677-2683 (1994). 

Size and Yield as a Function of Flow Rate and Gas Pressure. The effect of gas pressure on the size of particles prepared by the gas evaporation method was noticed at an early period of the development of this method (17). It was reported that to obtain the same size, the pressure of helium had to be about 10 times as large as that of argon, and the size was larger under high-pressure gas. More quantitative work was done by Yatsuya et a). (18) on the pressure dependence of the size of the Al fine particle. In these studies, particles were sampled in the gas phase. 

The photodecomposition of perfluoro diethyl-62 and perfluoro-di-w-propyl63 ketones has been shown to follow a course similar to that of hexa-fluoroacetone. The fluorescence is weaker in the case of the perfluoro-diethyl ketone and almost absent in the case of the perfluorodi-n-propyl ketone, and the pressure dependence of the quantum yields of carbon monoxide is consistent with this behavior. It is proposed that in the more complex structures, the energy may more easily be accommodated and lost by internal conversion, thereby reducing the contribution made by fluorescence and by Collisional quenching of the excited molecule. 

The measured rate constant for unimolecular reactions, association reactions, and certain bi-molecular reactions to be considered in the next section can have a complex dependence on total pressure, in addition to the strong temperature dependence of Eq. 9.83. This section introduces the theory of the pressure-dependence of the rate constant kmj the same theory follows to yield the pressure dependence of kassoc. Because kuni and kassoc are related by the equilibrium constant, which is independent of pressure, for a given reaction... 

The pressure dependence of the NMR spectrum of a nickel(II) complex which undergoes a coordination-spin equilibrium has been used to obtain the volume difference between the planar and octahedral isomers (118). In this case both the temperature and pressure dependence of the NMR spectra were analyzed simultaneously to yield five parameters, AH0, AS0, A V°, and the chemical shifts of the two isomers. Subsequent determinations from the electronic spectra and ultrasonics relaxation are in good agreement with the NMR result (13). 

A theoretical calculation shows that 80 kcal/mol is required to form oxirene from ketene (73). The fact that hot ground-state ketene has no low-energy decomposition pathway available may make the explanation of the pressure dependence of photodecomposition yields plausible. The thresholds for 3g and A production have been measured as 75.7 1.0 kcal/mol and 84.0 0.6 kcal/ mol, respectively (225). These high barriers should therefore make the decomposition relatively slow for a molecule this size at low excitation energies, and thus subject to pressure quenching at moderately high pressures (10-100 torr). 

If the reaction mixture is contained in an internal poly(tetrafluoroethylene) cell transmitting IR radiation (see Sec. 6.7.2), quantitative analysis via high-pressure spectroscopy (Figures 6.7-16 to 6.7-18)) yields precise values of the rate coefficients of these Diels-Alder reactions. As an example, the pressure dependence of the rate coefficient k of the cycloaddition of 2 (with R = CF3) and 3 in CH2CI2 solution at 45 °C (Buback et al., 1989) is shown in Fig. 6.7-19. 

The quantum yield is too insensitive to k y to determine the pressure dependence of that rate coefficient. Nearly the same results are obtained if reaction (45 ) is second or third order. However, [M] is in actuality of the form [H2]+ai[HCl]+ fl2[Cl2]+U3[02], so that ai[C 2]+a [02 must have been approximately 140 in all the relevant experiments. A re-examination of the data shows, in fact, that for most of the pertinent experiments [O2 ] -I- [CI2] varied between 93 and 175 torr. The best estimate for 3 is 0.33. If we set 02 = 2.0, then we can re-calculate the predicted quantum yields using eqn. (ee) for those conditions where the effects of Cl 2 and/or O2 should be most pronounced. The results are shown in Table 4. The re-computed values are not unreasonable, but they do not fit the data nearly as well as those computed from eqn. (cc). Nevertheless, our current understanding of the H-I-O2 recombination requires that we reject eqn. (cc) in favor of (ee). Perhaps other estimates of 2 and would give somewhat better agreement. By equating the constants in eqn. (ee) to the parameters in eqn. (cc), we find that 67/ 68 = 9.4x10 torr, = 0.93x10" , and = 1-7. Norrish... 

Fig. 11. The pressure dependence of the quantum yields of ihemain products of acetone photolysis at 2800 A and at high intensities (/ 10 quanta.l". sec" ).------,P torr acetone ------,...

There is significant disagreement between some of the results obtained in different laboratories. The conclusions given above are mainly based on only one kind of information, i.e. on the pressure-dependence of the product quantum yields, for which more than one equally reasonable explanation often exists. Since phosphorescence is not observed with cyclic ketones, the method of phosphorescence quenching—which is one of the main sources of information about the role of the triplet state—cannot be used here. These facts clearly indicate that further studies are required before a reliable scheme for the photo-physical processes can be formulated. 

The pressure dependence of the fluorescence yield for the 337 nm line is shown in Fig. 4. The fluorescence yield is decreasing with increasing pressure. This is due to the fact that the mean time between molecular collisions is decreasing at higher pressure and therefore the quenching of the excited states is getting stronger. 

Pt(III) intermediates. The pressure dependence of the quantum yield for the reductive elimination of azide from [frans-Pt(CN) (N,)2] to give [Pt(CN) ] has been exeunined auid the results interpreted in terms of formation of a caged radical species via simultaneous scission of both Pt-N, bonds in the charge-treuisfer excited state. - Alcohols have been oxidised in a two electron process at room temperature by O2 in the presence of a H PtCl /CuCl catalyst. A cyclic process incorporating a Pt(III) species % ich undergoes a redox reaction with Cu(II) to regenerate the Pt(IV) catalyst appears to be involved. 14. Copper... 

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