Alternation even-odd

The phenomenon of odd-even alternations in the fragmentation process of excited Na = 3 l0 clusters can be explained as follows There are mainly two different dissociation channels. The Na clusters with even n dissociate into an odd-numbered cluster and one Na atom,... 

The data recently published by Ouchi and Imuta (15) on a chloroform extract of Yubari coal also indicates similarities to petroleum. Branching is greater at the low carbon numbers and drops off at higher carbon numbers as in crudes (II) and Fischer-Tropsch product (17). The other similarity to crude oil is noted in the odd-even alternation of normal alkanes from Cm to C25 with the odd carbon number alkanes predominating. 

Rings and chains of C atoms up to 18 atoms have been examined by Hoffmann (57). He found chains to be more stable than rings up to about 10 atoms, and then on rings have better stability. There is an odd-even alternation in the BEIn observed for C clusters. The gap between HOMO and LUMO was found to diminish with increasing size of the cluster. These properties are similar to the ones described earlier for Ag clusters. 

The abundances are a consequence of how the elements were synthesized by atomic fusion in the cores of stars with heavy elements only made in supernovae. Synthesis of heavier nuclei requires higher temperature and pressures and so gets progressively harder as the atomic number increases. The odd/even alternation (often referred to as the Oddo-Harkins rule) is again general, and reflects the facts that elements with odd mass numbers have larger nuclear capture cross sections and are more likely to take up another neutron, so elements with odd atomic number (and hence odd mass number) are less common than those with even mass number. Even-atomic-number nuclei are more stable when formed. 

The most interesting of the four series is exhibited by the Cl(CH2)nH series [163] the data for the liquids with n < 8 of this series (Fig. 31) exhibit a pronounced odd-even alternation above and below a line given by Cn = 1.67 — 0.04n. The Cn data for liquids with n > 7 deviate negatively from linearity in the manner exhibited by the other series with phenyl, iodo or bromo in the 1 position (Figs. 29-30). 

The odd-even alternations displayed in half of the above studies (Figs. 29 and 31) are not yet fully understood. It is well known [166] however, that the molar refractions of Z(CH2) H liquids exhibit odd-even alternation, and a variety of paraffin chain compounds [167] exhibit odd-even alternation in their melting points and heats of fusion, which of course also involves transition from the solid crystalline state to the liquid state. Such alternations have also been exhibited in... 

It would be misleading, however, to interpret how well the molecular structure of the sorbed species is accommodated by the molecular structure of the monomer unit on the basis of the observed swelling power, C, because this parameter is proportional to the product of two variables, namely the number of adsorbed molecules per accessible phenyl group (a), and the molar volume of the sorbed liquid (V = M/d), where M and d are the molecular weight and density of the sorbed liquid). Since the density of the liquid reflects how well the molecules in that liquid are accommodated by one another, this effect would be superimposed on the adsorption data. This point of view is consistent with the observations of Fajans [166], who reported that the density of Z(CH2) H liquids exhibit odd-even alternation especially in the lowest three members of a given series. These results amplify the observation made earlier, i.e. that it is more meaningful to interpret on the basis of a how well the molecular structure of the adsorbed species is accommodated by the molecular structure of the monomer unit, rather than on the basis of C from which at is derived (Eq. 15). 

Odd-even alternations have not been directly observed in k[A) curves, at least not in the G, LE and LC state. However, Sims and Zografi ), who systematically studied the pressure loss as a function of time upon keeping the film at constant A below the collapse pressure for the CjgCOOH- C20COOH series, found differences in film stability between odd and even-fatty acids. The odd-numbered ones were more resilient against pressure loss. On the other hand, up to the transition pressure, at any rate of compression there is a gradual increase of this pressure with the chain length ). 

Mukerjee, R, Odd-even alternation in chain length variation of micellar properties — evidence of some solid-like character of micellar core, Kolloid Z. Z. Polym., 236, 76, 1970. 

In contrast to the findings for a+ (and temperature dependence. The latter results from the robustness of the initially occupied, low-lying levels in the cluster (where the electron producing Cs- has to come from) against structural changes, whereas the orbitals involved in the normal ct process yielding Cs+ reflect structural changes more distinctly. 

The mono-valent metals have also been found to show a certain type of periodicity dominated by an odd-even alternation. One example of the odd-even alternation is abundance spectra, where the even clusters are more abundant than the neighbouring odd ones. Ionization potentials have also been measured for clusters of Cu [99] to be higher for the even than for the odd sizes. Fig. 11. In addition to the odd-even alternation in the ionization energies, as shown in the figure there is an additional periodicity with high values for sizes 20, 34 and 40, which are the very numbers found for clusters of alkali elements. Values obtained are strongly dependent on the temperature of the cluster and a prerequisite for resolving this type of odd-even alternation is that the clusters are sufficiently cold. 

Superimposed on the smooth behavior described by Eq. (I), the experimental data for the ionization potentials of small clusters of. s-cicetron metals show an even odd alternation N-even clusters systematically have slightly larger (0.1-0.2 cV) ionization potentials than their N-odd neighbours [25]. An inverse effect is observed for the electron affinity, with N-odd cluster anions having higher photodetachment thresholds [36]. The odd-even alternation also appears in the mass abundance spectra [25]. This odd-even effect is observed up to some limiting cluster size, which depends on the particular element. 

The temperature of crystalline melting of tactic SCLCPs also decreases as the spacer length increases (Fig. 15), albeit in an odd-even alternation as in low molar mass liquid crystals as a function of the length of the... 

The thermotropic behavior of both the isotactic and syndiotactic poly n-[4 -(4"-methoxyphenyl)phenoxy]alkyl methacrylate s is summarized in Table 11. All of the tactic polymers crystallize. With the exception of poly 2-[4 -(4"-methoxyphe-nyl)phenoxy]ethyl methacrylate] (n=2), the melting temperature of the isotactic polymers is almost independent of the spacer length. In contrast, the syndiotactic polymers melt with a large odd-even alternation. However, only the syndiotactic polymers with at least four carbons in the spacer exhibit an enantiotropic smectic mesophase, which occurs over only a very narrow temperature range. The greater order of the isotactic polymers is evidently due to the greater segmental mobility of isotactic versus syndiotactic polymethacrylate backbones [246, 247]. 

---