Atomic clock schemes

This chapter is organized as follows. First, the need for still further enhancement in the precision with which time is measured will be justified, and the concept of atomic clocks and their properties will be described in detail. Then, the properties required for such an atomic system suitable for time and frequency metrology will be developed as well as the conditions necessary to attain them, following schemes involving either ions or neutral atoms. For the utilization of ions in atomic clocks, the well-known technique of ion trapping is used. The next part of the discussion will be devoted, therefore, to both a panoramic view of the ion trap geometries used... 

All atomic clocks are based on the same servo-loop scheme (Figure 11.1). An internal atomic oscillator at cOai is used to lock an external or local atomic oscillator at frequency (Dq- The local oscillator is used to probe the atomic transition at (0, and... 

In this Section, we will describe briefly the most recent projects of atomic clocks involving/based on ion traps as described above. The first part concerns micro-wave clocks, while the one following will be dedicated to optical frequency clocks. Performances of atomic standards can be evaluated only by comparison (frequency beatings) with another devices. When a new atomic standard can be presumed to out-perform the norm, it can be evaluated only from the comparison with a second system, which must be build in a similar way. It is worth noting that performances of each scheme depend on the local oscillator a quartz (eventually, cryogenic) oscillator for the microwave range, and a laser for the optical one. 

The concept of this method is illustrated in Scheme 3.1, where the clock reaction (U R ) is the unimolecular radical rearrangement with a known rate constant ( r)- The rate constant for the H atom abstraction from RsSiH by a primary alkyl radical U can be obtained, provided that conditions are found in which the unrearranged radical U is partitioned between the two reaction channels, i.e., the reaction with RsSiH and the rearrangement to R. At the end of the reaction, the yields of unrearranged (UH) and rearranged (RH) products can be determined by GC or NMR analysis. Under pseudo-first-order conditions of silane concentration, the following relation holds UH/RH = (A H/A r)[R3SiH]. A number of reviews describe the radical clock approach in detail [3,4]. 

The first-order ft-scission of the ferf-butoxy radical is one of the oldest radical clock reactions and has been used for over 50 years for the measurement of the relative rates of hydrogen abstraction from organic compounds (AH) in solution (Scheme 10.14). At low conversions, when the concentration of AH has not appreciably changed, the ratio of the rate constants for hydrogen atom abstraction, kAH> and /3-scission, kp, can be determined simply by analysis for acetone and ferf-butyl alcohol formation in the reaction. This is most conveniently achieved by gas chromatography ... 

In 2008, Jin and Newcomb confirmed the findings on the activation of water as hydrogen atom donor by Cp2TiCl and, by using radical clocks, determined the rate constant for the H-atom transfer from the Ti(III) aqua-complex to secondary radicals (Scheme 31) [78]. 

Figure 3 shows the simple case of a clock reaction competing with hydrogen atom transfer from tin hydride. If one wished to determine, for example, the rate of addition of a primary alkyl radical to an activated alkene such as an acrylate, then the reaction could be run at low concentrations of tin hydride such that both the radical clock and its rearrangement product reacted predominantly with the alkene. The products of the acrylate addition reaction are deactivated with respect to addition to another acrylate molecule, and one could control concentrations such that these adducts reacted primarily with the tin hydride (Scheme 3). In this case, then, one would analyze for the acrylate addition products of the unrearranged and rearranged radicals.

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