Isomer volume dependence

Both the isomer shift, 5q, and the second-order Doppler shift, 6sod, are pressure dependent through the volume dependence of the electronic charge density at the nucleus. The pressure dependence of the centre shift at constant temperature can be approximated by... 

Figure 28 shows the volume dependence of the magnetic hyperfine field, the Neel temperature and the isomer shift. All three parameters change continuously by large amounts with reduced volume. Only at the highest pressure ( 49 GPa) B, seems to increase rather little (unfortunately, could not be determined for technical reasons.)... 

Fig. 28. Volume dependencies of hyperfine field (T->0), Neel temperature and isomer shift (T = 300 K) of EuAlj. Isomer shift The dashed line gives the initial slope of dS/d In K The solid line is the hyperbolic fit discussed in text. Hyperfine field and Neel temperature The solid line is a power expansion fit. The value of at highest pressure was not included in the fit, to emphasize its weak increase. [Taken from Gleissner (1992).]...

Finally let us return to the volume dependence of isomer shift. In fig. 28 (bottom) a strong deviation from the linear extrapolation of initial slope dS/dln V = 15mm/s is apparent. The change in contact density by the compression of conduction electrons can be described by (Kalvius et al. 1974)... 

The volume dependence of p(0) is expected to be hyperbolic and indeed such a fit connects very well the experimental points (solid line in fig. 28, bottom). Volume reduction simply compresses the conduction electron gas. This result questions somewhat the suggested break around 15GPa in the S(F) dependence of EuO (see Abd-Elmeguid and Taylor 1990) which had been derived from linear fits. In one sense this point is academic since a valence change was excluded from the lack of temperature variation. But one may ask why the occurrence of an insulator-metal transition is not reflected in the isomer shift. 

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

As was shown by Floryl), starting from a certain concentration, it is impossible in principle (for purely geometric reasons) to fill a larger fraction of the volume with these chains when they are randomly arranged. This critical concentration depends on chain flexibility which Flory characterized by the fraction f of folded (gauche) isomers in a polymer molecule... 

In a solution where a nonzero volume change between the electronic isomers, HS and LS, is encountered, the position of the spin equilibrium will depend on pressure. The volume change, usually denoted here AF°, may be obtained from the study of the pressure dependence of equilibrium properties such as the magnetic susceptibility or the electronic spectrum. In favorable cases, A F° values may be derived from the amplitude of sound absorption observed in ultrasonic relaxation measurements of a spin equilibrium as will be shown in the... 

It has been stated above that the difference of partial molar volumes of the LS and HS isomers AK° can be obtained from the relaxation amplitude A of ultrasonic absorption. An independent method for the determination of AE° is based on the pressure dependence of the equilibrium constant. The pressure derivative of being determined by ... 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

These techniques are of particular interest in that they provide a means of separating molecular species which are difficult to separate by other techniques and which may be present in very low concentrations. Such species include large molecules, sub-micrometre size particles, stereo-isomers and the products from bioreactors (Volume 3). The separations can be highly specific and may depend on molecular size and shape, and the configuration of the constituent chemical groups of the molecules. 

In the course of our synthetic efforts, we discovered a new, unnatural conformational isomer of the VBL piperidine ring (see Chapter 2, this volume, for details). This compound is inactive with the microtubule system in vitro and is poorly cytotoxic to cultured tumor cells (Fig. 5b). Therefore, the functional determinism of the C-20 position of VBL-like molecules mediates reactions, as yet unknown, that are dependent on the binary alkaloid structure and on the natural stereochemical configuration at C-16 and C-14 as well as on the conformation of the cleavamine moiety. 

The pressure dependence of other properties can be used to calculate AV°. Because the volume differences between the spin states are relatively large, pressures of up to only 1000-3000 atm are sufficient to cause a significant shift in the spin equilibrium. Observation of the change in the electronic absorption spectrum, for example, enables calculation of A V°, with the help of certain assumptions and ancillary experiments (19). The extinction coefficients for absorption by the two isomers must be obtained. In the simplest model they are assumed to be independent of pressure. In one approach (19) they were found by examination of the temperature dependence of the electronic absorption spectrum. This required knowledge of the temperature dependence of the spin-equilibrium constant, which was obtained from the temperature dependence of the susceptibility observed in the Evans NMR experiment. Clearly a more direct measurement is preferable. 

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). 

The relative concentrations of the two species depend on the size of the Ln3+ ion, temperature, pressure, and on the concentration of added inorganic salts [61-63]. While the twisted CSAP geometry is the isomer present with the higher percentage ( major isomer) for the complexes of the larger cations, La3+-Nd3+,the CSAP geometry becomes the most stable for the smaller cations Sm3+-Er3+ [61, 63]. In all these cases, the isomerization process is purely conformational, as shown by the near zero reaction volumes obtained by high-pressure NMR [63]. However, for the complexes of the smallest cations (Tm3+-Lu3+), the... 

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