Analysis of electron spin echoes by spectral representation of the stochastic Liouville equationa)

  • Schwartz L
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Abstract

Motional effects can easily be incorporated into calculated spin echo decay envelopes by idealizing the effects of the pulses and by using the stochastic Liouville equation (SLE) to govern the time dependence of the density matrix between pulses. The spectral representation of the 90 degrees - [tau] -180 degrees - [tau] envelope is: [Sigma] l,mal,mexp(-( [Lambda] l+ [Lambda] *m) [tau] ), where [Lambda] l is the lth eigenvalue of the SLE matrix, and al,m are products of relevant components of eigenvectors. The long time (large [tau] ) phase memory time Tminfinity is equal to (Re [Lambda] 1)-1, where [Lambda] l is the smallest eigenvalue. For an axially symmetric g-tensor case in the slow motional region, Tminfinity / [tau] R approximately=3 mod F [tau] R mod -12/, 2 mod F [tau] R mod -13/, and 1, for Brownian, free, and jump diffusion models, respectively, with F identical to 2 [beta] eH0(g/sub ///-gperpendicular to )/3h(cross) and [tau] R the rotational correlation time. Analogous results hold for nitroxides having nuclear hyperfine tensors. The echo results are compared with simple methods of measuring [tau] R from CW spectra. The overall shape of the echo envelopes in the slow motional region is exp(-bF2 [tau] 3/ [tau] R) for very short times and exp(-2 [tau] /Tminfinity ) for the longer times. Carr-Purcell (CP) sequences suppress the initial exponential in [tau] 3 and increase the phase memory times as a function of decreasing [tau] . Detailed analysis of CP sequences can provide information on motional model. The analysis of motional averaging of nuclear modulation effects by this method is also given and it is pointed out that this approach may be useful in studying very slow motions. Despite the simplicity of the methods, the authors are able to approximately fit experimental data from the Tempone/glycerol-water system in both fast and slow motional regions. [Journal Article; U.S. Copyright Clearance Center Code: 0021-9606/82/235410-16$ 02.10; 30 Refs]

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Authors

  • Leslie J. Schwartz

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