Phase resonance

Upon oxidation of the reduced samples, an additional resonance is obtained. At X-band this resonance is symmetrical in shape, has a y-factor of 1.967 0.003, and has a width between points of maximum slope of 50 gauss. The intensity of this resonance, henceforth referred to as the y-phase resonance, is shown in Fig. 31 as a function of concentration of chromium. A maximum in intensity appears near 2 wt. % Cr corresponding to... 

X 10 spins per gram. This amounts to one such spin for every 14 Cr nuclei in the sample. These concentrations are based on the assumption that the spin of the species giving rise to the y-phase resonance is that is, there is one unpaired electron per absorber rather than three as in Cr +... 

Justification for this assumption is given below. At K-band the 7-phase resonance increases in width to about 80 gauss and the derivative becomes slightly asymmetric. No changes were observed in the width or position of the 7-phase resonance at —196°. 

The peak in the derivative of the 5-phase resonance does not change drastically in intensity upon oxidation. The /8-phase resonance, however, does change considerably in intensity in the intermediate concentration range (0.5-3.6 wt. %) upon oxidation. Upon exposure of reduced chromia-on-alumina samples of low concentration to air at room temperature, a rapid color change from blue to green occurs and the EPR characteristic of the 7-phase immediately appears, although reduced in intensity in comparison to the 7-phase resonance intensity after oxidation at 600°. 

Fig. 31. Concentration of unpaired electrons in 7-phase resonance of chromia-on-alumina versus weight per cent chromium (17S).

The 5-phase resonance can be fairly well represented by the spin-Hamil-tonian corresponding to Cr + in an axially symmetric crystal field. 

The relatively sharp y-phase resonance which appears upon oxidation of the reduced chromia-on-alumina is possibly due to single electrons trapped on Cr + ions, i.e., Cr + ions. 

One would expect the presence of trapped electrons in the oxidized samples to give rise to n-type conductivity, conduction possibly taking place by jump migration of the odd electron in the lattice of Cr + ions in a somewhat similar manner to the mechanism discussed by Heikes 174) for the migration of Ni + holes in lithia-doped NiO. The observed p-type conductivity of chromia in an oxygen atmosphere is presumably due to electron holes in a solid which is predominantly CraOs for the low concentrations of chromia-on-alumina where the 7-phase resonance intensity is maximum, the chromium is predominantly in the d-6 valence state 167). 

The 5-phase resonance is not affected appreciably by oxidation at 500 and appears to be relatively stable as Cr +. Matsunaga 167) on the basis of susceptibility data at concentrations only as low as 1 wt. % Cr, concluded that at infinite dilution, all chromium in the -1-3 valence state would be converted to the d-6 state upon oxidation. EPR data indicate that this is not true the 5-phase predominates at low concentration and is stable towards oxidation. On the other hand, the /3-phase at high concentration is apparently rather stable towards complete oxidation at 500°C this indicates that the chromia is most susceptible to oxidation when in rather small clusters. 

A plot of the energies of the two configurations, R X and R+ X, in the gas phase as a function of the reaction co-ordinate is illustrated by the bold lines in Fig. 5. Each curve shows a minimum, the R X configuration because of the out-of-phase resonance, R X <— R, X (the in-phase resonance describing one of the triplet forms of the R—X bond), while R + X " shows a minimum due to the electrostatic attraction between cation and anion. 

Most of the early work concentrated on an ESR signal that appears when the hexavalent catalyst is partially reduced by H2 or CO. This y-phase resonance is generally attributed to a Cr(V) surface species (25, 26), although some insist that it involves a combination of Cr(VI) and Cr(III) (10,11,27). Usually these studies found either a correlation or a reverse correlation between this signal and some measure of polymerization activity, often from a catalyst bearing little resemblance to those used commercially. This was indirect evidence at best, and the issue was always clouded by the simultaneous presence of several oxidation states. This work has already been summarized adequately (28-30). 

Krauss and Stach (31) demonstrated that the hexavalent catalyst can be quantitatively reduced by CO at 350°C to divalent chromium. This material has no y-phase resonance but is active for ethylene polymerization, indicating that Cr(II) is definitely an active valence.1 These results have since been confirmed by several other laboratories, including this one (30). In fact, Hogan concluded, as early as 1959 from similar reduction studies, that the active species must be divalent. The CO-reduced catalyst polymerizes ethylene in a high-pressure autoclave much like its hexavalent parent, and produces almost identical polymer. Since the polymer properties are extremely sensitive to the catalyst pretreatment, this is a strong endorsement for the conclusion that Cr(II) is probably also the active species on the commercial catalyst after reduction by ethylene. 

Auzinsh, M.P. (1990). Nonlinear phase resonance of quantum beats in the dimer ground state, Opt. Spectrosc. (USSR), 68, 750-752. 

When no study of the temperature dependence of the quadrupole coupling constant is available, phase transitions may be detected by observing the quadrupole resonance at low-temperature on samples that have been cooled in different ways with slow cooling, the phase transition may take place and the low-temperature phase resonance is observed, while fast cooling freezes the sample in its high-temperature phase. Two crystalline forms have been identified in acetonitrile 26) and some other compounds 2). 

Fio. 11. Paramagnetic resonance absorption derivatives of (a) 1.2 wt %, (b) 3.6 wt %, and (c) 5.8 wt % reduced chromia-alumina samples at 77°K. Dashed lines separate jS-, S-, and y-phase resonances. A very weak y-phase type resonance appears in each sample (120). 

The 8-phase chromium resonance in chromia-alumina has been observed by several workers. It is dependent upon the alumina support since it does not appear in samples of chromia-silica, although it is observed in the case of chromia-silica-alumina. The isolated Cr + ions could conceivably be situated either in the bulk of the support, or on its surface. There is some evidence that both situations prevail. Nuclear magnetic resonance studies to be discussed presently (121) indicate that for impregnated chromia-alumina catalysts calcined at 500 the majority of these ions are on the surface. However, when such catalysts are heated above 600°, the 8 phase is greatly enhanced because of diffusion of chromium ions from the -phase into interior sites in the alumina lattice. The same situation arises with coprecipitated chromia-alumina catalysts (34). The S-phase resonance intensity of coprecipitated chromia-alumina was found to increase with calcination temperature, indicating an increasing three-dimensional dispersion of Cr + ions. In general, the S-phase resonance dominates the ESR spectra of chromia-alumina catalysts at low chromium concentrations, and therefore it... 

During a study of the ESR spectra of coprecipitated chromia-alumina, Poole et cU. (34) observed a j3-phase resonance which appeared (see Fig. 14) to be a superposition of a narrow (l Hpj, 300 to 750... 

QBR resonator before deposition (Inset zoom on the QBR after deposition of a 2 pm droplet], (b] Evaporation curves of droplets with volumes ranging between 0.15 and 15 fl in an vs. t representation (inset phase resonance curves before deposition [red] and during the evaporation process after deposition]. 

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