Time-Resolved Magnetic Field Effect

Since singlet-triplet mixing can be induced by the application of a static field, the spin dynamics can be investigated using the time-resolved magnetic field effect (TR MEE) on fluorescence. This method has been exploited to give measurements of spin-lattice relaxation times [8, 9]. It has been well documented in the literature that the experimentally observed fluorescence intensity I (t) can be expressed by the relation  

Here F(t)is the recombination rate of the ion pair, 9 is the fraction of spin-correlated pairs, which is assumed to be constant but can vary for different chemical systems and pss (t) is the time dependence of the singlet state population of the spin-correlated pair. The second term in Eq. (8.2) includes the contribution of the singlet component of the spin-uncorrelated pairs to the fluorescence intensity. Typically, the results of the TR MFE decay are presented as a ratio of the fluorescence intensity at an applied field (Ib ) and at zero field (7o), which becomes independent of the unknown function Fit). 

Molin and co-workers [9] have presented an analytical formulation for pssit) under the influence of spin relaxation, hyperflne modulation and mechanism at both high and zero field. The general form for the singlet probability in the presence ip ) and absence (p ) of an applied magnetic field take the form 

8 Correlation Between Spin Entanglement and the Spin Relaxation Time 

The TR MFE technique has been extensively used to measure the spin-lattice relaxation rates of radical ions in solutions, with a number of aromatic radical ions found to have a relaxation time in the order of 1 xs [ 13]. However, for cyclohexane and adamantane radical cations and their alkyl-substituted analogues [14-16] there is a surprising discrepancy in the relaxation times as shown in Table 8.2. The experimental values presented in Table 8.2 have been obtained by preparing a solution of the cycloalkane (c-RH) and hexafluorobenzene in n-hexane with typical concentrations of 0.01-0.1 and 0.01 M respectively. Upon irradiation of n-hexane with X-rays, the primary singlet correlated pairs are rapidly scavenged (within sub-nanoseconds) to produce the secondary c-RH+ and CeFg radical ion pair. 

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In order to calculate the time-resolved magnetic field effect, the simulation commenced by placing the cations and anions according to a particular distribution. 

In some systems, triplet BET can occur, as deduced from time-resolved optical spectroscopy, magnetic field effects, CIDNP, or optoacoustic calorimetry. Triplet BET is governed by energetic factors, which determine rates, and by the relative topologies of the potential surfaces of parent molecule, radical ions, and of accessible triplet or biradical states. Divergent topologies for different states may cause rearrangements. 

The radical anions of tram- and c/s-stilbene can be distinguished by ESR [503]. A radical ion pair has been observed by this method using trial-kylamines in acetonitrile [497], Electron back transfer (i.e., a reaction of the radical anion of frans-stilbene with the radical cation of the donor) opens a new pathway for intersystem crossing to the tram triplet state. Time-resolved resonance Raman spectroscopy of photoinduced electron transfer from amines to frans-stilbene has been reported [497,504], In the photooxidation of frans-stilbene the radical cation has been observed by flash photolysis using cyanoanthracenes [505-507], The radical cations of cis-and frans-stilbene were also produced by electron transfer from biphenyl to excited 9,10-dicyanoanthracene and subsequent electron transfer from stilbene to the radical cation of biphenyl [508]. External magnetic field effects... 

Many new physical methods were developed in response to needs of spin chemists. In particular, the time-resolved EPR (TREPR) ° and time-resolved NMR (CIDNP) techniques were found to be of unparalleled utility in terms of mechanistic understanding of radical chemistry. Theoretical work to explain CIDNP and CIDEP phenomena was able to link, for the first time, the spin physics of radical pairs to their diffusion, molecular tumbling, confinement (solvent cages versus supramo-lecular environments ), and the effects of externally applied magnetic fields. ... 

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