Electron transverse relaxation time

The application of a 90° detection pulse will cause the resonator through which it is applied to respond by ringing , and it will not be possible to detect an FID until the ringing response has decayed to below the signal level. Thus, the advantages of pulsed EPR can only be realised if the electronic transverse relaxation time T2 of the sample is longer than the resonator dead time which, in general, is inversely proportional to the measurement frequency. This places limits on the combinations of sample type, size and EPR freqnency that can benefit from the use of pulsed EPR. 

Recapitulating, the SBM theory is based on two fundamental assumptions. The first one is that the electron relaxation (which is a motion in the electron spin space) is uncorrelated with molecular reorientation (which is a spatial motion infiuencing the dipole coupling). The second assumption is that the electron spin system is dominated hy the electronic Zeeman interaction. Other interactions lead to relaxation, which can be described in terms of the longitudinal and transverse relaxation times Tie and T g. This point will be elaborated on later. In this sense, one can call the modified Solomon Bloembergen equations a Zeeman-limit theory. The validity of both the above assumptions is questionable in many cases of practical importance. 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

Another important parameter that influences the inner sphere relaxivity of the Gd(III)-based contrast agents is the electronic relaxation time. Both the longitudinal and transverse electron spin relaxation times contribute to the overall correlation times xa for the dipolar interaction and are usually interpreted in terms of a transient zero-field splitting (ZFS) interaction (22). The pertinent equations [Eqs. (6) and (7)] that describe the magnetic field dependence of 1/Tie and 1/T2e have been proposed by Bloembergen and Morgan and... 

Here T2 is transverse relaxation time of an electron spin. The EPR absorption lineshape is related to free induction decay G(t) through the Fourier transformation [16]. After averaging over all angles between the surface and the external magnetic field H the following equation was obtained for D = 2 systems [138] ... 

Nitroxide relaxation times include (1) the electron spin lattice or longitudinal relaxation time, Tj (2) the electron spin-spin or transverse relaxation time, T2 (3) the... 

BSisoB + Aiso)//i. The width of the lines in this fast tumbling case is defined by (nT2), where T2 is the transversal relaxation time of the electron spin. For nitroxide radicals and magnetic field values of about 0.3 T this is valid for rotational correlation times faster than 10 ps. 

The long transverse relaxation times could be exploited to determine experimentally the difEision constant D of the charge carriers [36], [34]. For this measurement, Hahn sequences and other electron-spin-echo experiments were carried out in applied magnetic fields Bo, with a constant magnetic field gradient G superposed parallel to Bo. When the spins difiuse within the time interval 2r, i.e. the time between the first 90° pulse and the echo afier the 180° pulse at time r, they arrive at locations where the coherence of the spin precession is destroyed owing to the field gradient This leads to an additional decay of the echo amplitude A(r) ... 

Here, yj is the nuclear gyromagnetic ratio, g is the electron g-factor, is the Bohr magneton, rodH is the electron spin-proton distance, and a>i and a>s are the nuclear and electron Larmor frequencies, respectively (co = yB, where B is the magnetic field). The correlation times, Zd, are defined as 1/zd — 1/tr + 1/Te + 1/i m ( = 1,2), where iR is the rotational correlation time, and Pie and T2e are the longitudinal and transverse electron spin relaxation times of Gd +. 

A further resolution advantage arises in the ENDOR spectra since the line width is limited by the longitudinal relaxation time Tie of the electron spins or the transverse relaxation time T2n of nuclear spins, rather than by the transverse relaxation time T2e of the electron spins. Since in solids or soft matter T2 > 72, ENDOR lines are usually narrower than ESR lines. 

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

T,f = longitudinal relaxation time of free state T e = electron spin relaxation time Ti = transverse relaxation time Lb = transverse relaxation time in paramagnetic complex (bound state)... 

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