Paramagnetic Relaxation in Dilute Potassium Ferricyanide

Rannestad, Andreas; Wagner, Peter E.

doi:10.1103/physrev.131.1953

Cited by 33 publications

(10 citation statements)

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“…44,48,49,52,53,56 The temperature dependence shows a direct, an Orbach–Aminov, and a Raman process. The Orbach–Aminov coefficient depends on the square of the concentration of the paramagnetic ion, but the Raman coefficient is independent of concentration.…”

Section: Resultsmentioning

confidence: 98%

“…The values of b for individual OX063 and Finland trityl samples vary as much as four orders of magnitude over 4–100 K. The temperature dependence of every sample can be fit over its entire temperature range by three spin–lattice relaxation terms well-known from studies of materials for masers and polarized targets: 44,48,49,52,53,56 a direct process, an Orbach–Aminov process and a Raman process.

b = A_{dir} v \coth \frac{h v}{k T} + \frac{A_{Orb}}{({normale}^{\frac{Θ_{Orb}}{T}} - 1)} + A_{Ram} {(\frac{T}{Θ_{normalD}})}^{9} I_{8} (\frac{T}{Θ_{D}})

where A dir , A Orb and A Ram are the coefficients of the direct, Orbach–Aminov and Raman processes, respectively; Θ Orb is the Orbach temperature corresponding to the excited state energy specific for OX063 or Finland trityl; Θ D is the Debye temperature of the solvent; and I 8 () is the 8th transport integral, see for example.…”

Section: Resultsmentioning

confidence: 99%

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Electron spin dynamics and spin–lattice relaxation of trityl radicals in frozen solutions

Chen

Maryasov

Rogozhnikova

et al. 2016

Phys. Chem. Chem. Phys.

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Electron spin–lattice relaxation of two trityl radicals, d24-OX063 and Finland trityl, were studied under conditions relevant to their use in dissolution dynamic nuclear polarization (DNP). The dependence of relaxation kinetics on temperature up to 100 K and on concentration up to 60 mM was obtained at X- and W-bands (0.35 and 3.5 Tesla, respectively). The relaxation is quite similar at both bands and for both trityl radicals. At concentrations typical for DNP, relaxation is mediated by excitation transfer and spin-diffusion to fast-relaxing centers identified as triads of trityl radicals that spontaneously form in the frozen samples. These centers relax by an Orbach–Aminov mechanism and determine the relaxation, saturation and electron spin dynamics during DNP.

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Section: Resultsmentioning

confidence: 98%

b = A_{dir} v \coth \frac{h v}{k T} + \frac{A_{Orb}}{({normale}^{\frac{Θ_{Orb}}{T}} - 1)} + A_{Ram} {(\frac{T}{Θ_{normalD}})}^{9} I_{8} (\frac{T}{Θ_{D}})

Section: Resultsmentioning

confidence: 99%

Electron spin dynamics and spin–lattice relaxation of trityl radicals in frozen solutions

Chen

Maryasov

Rogozhnikova

et al. 2016

Phys. Chem. Chem. Phys.

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“…Stapleton and co-workers 12 " 14 have found that in the temperature range between about 4 and 20 K the electron-spin relaxation rate (1/7^) of low-spin ferric iron in a number of heme and iron-sulfur proteins is dominated by a two-phonon (Raman) process with a temperature dependence that deviates significantly from the T 9 power law expected 15,16 and found experimentally 17,18 in ordinary three-dimensional solids. For a Debye temperature much higher than the temperature of interest and for vibrations distributed uniformly over the molecule, 19 the contribution of the Raman process can be shown to be given by the integral 1 _ r 00 a> 4 [g(a>)] 2 exp(/?coMr)…”

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Low-frequency modes in proteins: Use of the effective-medium approximation to interpret the fractal dimension observed in electron-spin relaxation measurements

Elber

Karplus

1986

Phys. Rev. Lett.

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A method based on the effective-medium approximation is developed for calculations of the low-frequency density of vibrational states, g(a)), in proteins. The calculated values of the fractal exponent y [g(oj) ~-w y ] are anomalously low (0 < y < 1) in accord with estimates from measurements of the electron-spin relaxation time in low-spin ferric proteins. The essential element leading to the low y value is the limited cross-chain connectivity in proteins, rather than the geometric arrangement of the polypeptide chain.

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“…Thus Pace et al (1960) and Feng and Bloembergen (1963) have verified 3+ the inverse temperature dependence for the 8=3/2 Cr ion in Al 2 o 3 at low temperatures, while , Rannestad and Wagner (1963), and Scott and Jeffries (1962) have observed the changeover with temperature from the single phonon process to the highly temperature dependent Raman mechanism, for S=l/2 ions of both the iron and rare earth groups. Davids and Wagner (1964) were able to verify that for an S•l/2 ion such as Fe 3 was decided to re-examine the implications in the resulta of Van Vleck's theory of spin-phonon interaction when applied to multi-level systems, particularly in the light of the more general treatment by Mattuck and Strandberg (1960).…”

Section: Introductionmentioning

confidence: 99%

FIELD DEPENDENCE OF SPIN-LATTICE RELAXATION TIMES OF Cr³⁺

Rumin¹

1966

Can. J. Phys.

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ABSTRACT.The changes in spin-lattice relaxation time with the magnitude and orientation of the de magnetic field, frequency, and temperatut'e have been calculated from simplified expressions for the spin-phonon transition probabilities of an S c 3/2 ion.The relaxation times for INTRODUCTION.II. THEORY OF SPIN-LATTICE RELAXATION.III.1. 2.The Interaction Hamiltonian.Spin-Phonon Transition Probabilities for the Direct Process.THE MEASUREMENT OF SPIN-LATTICE RELAXATION TIMES.1. 2.3.Relaxation Times in a S=~ Spin System.Pulse Saturation Measurements on a S)~ System. PROCEDURE. 1.Experimental. 2.Calculations.VIII. RESULTS AND DISCUSSION. 1.Cr 3 + in K 3 Co(CN) 6 .IX.x. .Cr 3 + in A 1 2 0 3 • 3.Cr 3 + in RbAl(S0 4 ) 2 .12H 2 0. 4.The Slopes in the Logarithmic Plots of T 1 versus 1/Z. 5.Calculations for Steady-State Saturation Conditions. CONCLUSIONS.BIBLIOGRAPHY. INTRODUCTIONWhen the thermal-equilibrium energy distribution of a group of paramagnetic ions, whose paramagnetism is due to a net magnetic dipole moment associated with their spins, is in sorne way disturbed, the subsequent return to equilibrium is said to take place through spin-lattice relaxation if it occurs as the result of the exchange of energy-conserving quanta between the spins and the thermal spectrum of the host lattice. by Mattuck and Strandberg (1960), the spin-lattice interaction of paramagnetic ions in crystals is understood to occur through the thermal modulation of the crystalline electric field. The theory predicts that at very low temperatures, T, the spin-lattice transition probability, wij' between spin states i and j will be determined by a direct, one-phonon process with wij varying as T, while at higher temperatures a two-phonon, Raman mechanism will dominate with wij varying as T 7 or T 9 .In the case of a two-level system the return to equilibrium of the population of levels 1 and 2 is characterized by a spin-lattice relaxation time T 1 where T 1 = l/2w 12 • No such simple relationship exists in the case of multi-level systems but an effective spin-lattice relaxation time TR is still used to describe the return to equilibrium of the population of a pair of levels, even though this generally involves all the *Woonton (1961) furnishes an excellent bibliography related to theoretical and experimental work on spin-lattice relaxation.-2-other spin levels as well.Much of the early theoretica1 and experimental work was centred on the ions of the 3d iron group.The measured values of TR often did not agree well with the theory, and exp1anationsfor some of the inconsistencies were proposed by Bloembergen et al (1959), who considered the role played by cross-relaxation, and by , Van Vleck (1961), and , who extended the concept of crossrelaxation to excited states.Several effects predicted by the theory of spin-lattice relaxation have been verified experimentally. Thus Pace et al (1960) and Feng and Bloembergen (1963) have verified 3+ the inverse temperature dependence for the 8=3/2 Cr ion in Al 2 o 3 at low temperatures, while , Rannestad and...

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Paramagnetic Relaxation in Dilute Potassium Ferricyanide

Cited by 33 publications

References 20 publications

Electron spin dynamics and spin–lattice relaxation of trityl radicals in frozen solutions

Electron spin dynamics and spin–lattice relaxation of trityl radicals in frozen solutions

Low-frequency modes in proteins: Use of the effective-medium approximation to interpret the fractal dimension observed in electron-spin relaxation measurements

FIELD DEPENDENCE OF SPIN-LATTICE RELAXATION TIMES OF Cr³⁺

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Paramagnetic Relaxation in Dilute Potassium Ferricyanide

Cited by 33 publications

References 20 publications

Electron spin dynamics and spin–lattice relaxation of trityl radicals in frozen solutions

Electron spin dynamics and spin–lattice relaxation of trityl radicals in frozen solutions

Low-frequency modes in proteins: Use of the effective-medium approximation to interpret the fractal dimension observed in electron-spin relaxation measurements

FIELD DEPENDENCE OF SPIN-LATTICE RELAXATION TIMES OF Cr3+

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FIELD DEPENDENCE OF SPIN-LATTICE RELAXATION TIMES OF Cr³⁺