Activation volume

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

If, in analogy to equation (A3.6.5). one denotes the change of activation volume with respect to some... 

Schmidt R 1998 Interpretation of reaction and activation volumes in solution J. Rhys. Ohem. A 102 9082-6... 

In summary, it seems that for most Diels-Alder reactions secondary orbital interactions afford a satisfactory rationalisation of the endo-exo selectivity. However, since the endo-exo ratio is determined by small differences in transition state energies, the influence of other interactions, most often steric in origin and different for each particular reaction, is likely to be felt. The compact character of the Diels-Alder activated complex (the activation volume of the retro Diels-Alder reaction is negative) will attenuate these eflfects. The ideas of Sustmann" and Mattay ° provide an attractive alternative explanation, but, at the moment, lack the proper experimental foundation. 

Activation energy Activation of cellulose Activation parameters Activation volume Activators... 

Activation volumes may be either positive or negative, corresponding to the fact that reactions may become either slower or faster at high pressures. 

The activation volume can be positive or negative, and its sign is a valuable piece of mechanistic information. Although the measurement of AV is not commonly... 

It is conventional to take as the activation volume the value of AV when P = 0, namely —bRT. (This is essentially equal to the value at atmospheric pressure.) Pressure has usually been measured in kilobars (kbar), or 10 dyn cm 1 kbar = 986.92 atm. The currently preferred unit is the pascal (Pa), which is 1 N m 1 kbar = 0.1 GPa. Measurements of AV usually require pressures in the range 0-10 kbar. The units of AV are cubic centimeters per mole most AV values are in the range —30 to +30 cm moP, and the typical uncertainty is 1 cm moP. Rate constant measurements should be in pressure-independent units (mole fraction or molality), not molarity. ... 

Asano and co-workers have reported die kinetic effects of pressure, solvent, and substituent on geometric isomerization about die carbon-nitrogen double bond for pyrazol-3-one azomethines 406 (R = H), 406 (R = NO2) and 407, (Scheme 93). The results demonstrate the versatility of die inversion mechanism. The rotation mechanism has been invalidated. First-wder rate constants and activating volumes for diermal E-Z isomerization for 406 (R = H) and 406 (R = NO2) are given at 25°C in benzene and methanol (89JOC379). 

Vset = active volume of settler occupied by one of the phases, cu ft... 

The factor p, having the dimensions of volume, is identified as the activation volume for the reaction. 

Fig. 6.4. Energy barrier between occupied and empty molecular sites u activation energy. The applied shear stress t deforms the energy barrier analogous to Eyring s theory of viscosity v activation volume...

Accordingly, the activation volume v can be determined from yield experiments performed at various shear rates. 

Fig. 6.5. Yield strengths from flexural tests are plotted against strain rates at the surface of the samples. Tests were performed on polymers A, B, and E test temperature 23 °C. The slope of the three lines correspond to similar activation volumes v = 2 0.1 nm3...

Fig. 6.6. Comparison of activation volume and average volume of the strands between crosslinks. The effective molecular mass Mc between crosslinks is varied from 0.1 to 10 kg/mol. The cubes represent the activation volume of 2 nm3.

Left-hand side Sic < 1 kg/mol the activation volume contains several molecular junctions. Right-hand side Sic > 1 kg/mol the volume of one strand is much larger than the activation volume... 

Activation volumes of the polymers according to Eq. (6.5) were calculated with t, = 0.5ay and plotted in Fig. 6.6 versus the average molecular mass Mc of network strands. The volume of a molecular strand is plotted also... 

The activation volume of the three polymers turned out to be v 2 nm3, independent of their crosslink density. In the crosslinked polymer A the strands are short and about five of them fit into the activation volume. In contrast, one strand of polymer E requires a volume five times larger than the activation volume ... 

Apparently, crosslinks between the molecular chains do not interfere with the yield process in the activation volume. Yielding involves the cooperative movement of about 10 to 20 chain segments, if the average volume of one segment measures about 0.15 nm3. Such a volume seems to be reasonable according to molecular parameters [73-75]. 

Differentiation between inner- and outer-sphere complexes may be possible on the basis of determination of activation volumes of dediazoniations catalyzed by various metal complexes, similar to the differentiation between heterolytic and homolytic dediazoniations in DMSO made by Kuokkanen, 1989 (see Sec. 8.7). If outer-sphere complexes are involved in a dediazoniation, larger (positive) volumes of activation are expected than those for the comparable reactions with inner-sphere complexes. Such investigations have not been made, however, so far as we are aware. 

Szele and Zollinger (1978 b) have found that homolytic dediazoniation is favored by an increase in the nucleophilicity of the solvent and by an increase in the elec-trophilicity of the P-nitrogen atom of the arenediazonium ion. In Table 8-2 are listed the products of dediazoniation in various solvents that have been investigated in detail. Products obtained from heterolytic and homolytic intermediates are denoted by C (cationic) and R (radical) respectively for three typical substituted benzenediazonium salts and the unsubstituted salt. A borderline case is dediazoniation in DMSO, where the 4-nitrobenzenediazonium ion follows a homolytic mechanism, but the benzenediazonium ion decomposes heterolytically, as shown by product analyses by Kuokkanen (1989) the homolytic process has an activation volume AF = + (6.4 0.4) xlO-3 m-1, whereas for the heterolytic reaction AF = +(10.4 0.4) x 10 3 m-1. Both values are similar to the corresponding activation volumes found earlier in methanol (Kuokkanen, 1984) and in water (Ishida et al., 1970). 

The activation volume for homolytic dediazoniations in methanol as measured by Kuokkanen (1984, 1989, AV = 5.4 x 103 m-1) does not, however, allow one to differentiate between the various mechanisms discussed in this section. 

Activation volumes of the reactions of transition metal compounds in solution. D. A. Palmer and H. Kelm, Coord. Chem. Rev., 1981, 36, 89-152 (225). 

Role of activation volume in the elucidation of reaction mechanisms in octahedral coordination complexes. G. A. Lawrance and D. R. Stranks, Acc. Chem. Res., 1979,12,403-409 (50). 

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