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Solution of non-linear differential problem with application to selected geotechnical problems

100%
Milewska A., Milewska A.
Archives of Civil Engineering
|
2011
|
issue 2
2
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Non-classical operational calculus applied to certain linear discrete time-system

58%
Mieloszyk E., Milewska A., Magulska M.
Bulletin of the Polish Academy of Sciences: Technical Sciences
|
2006
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vol. 54
|
issue 4
3
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NMR Relaxation and ESR Lineshape of Anisotropically Rotating Paramagnetic Molecules

51%
Kubica A., Milewska A., Noinska M., Earle K., Kruk D.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2
527-532
EN
The role of anisotropic rotation for electron spin resonance lineshape and nuclear magnetic relaxation dispersion profiles for paramagnetic molecules with electron spin quantum number S ≥ 1 is discussed. The ESR spectra and nuclear magnetic relaxation dispersion profiles are calculated by means of an approach based on the stochastic Liouville equation and referred to in the literature as "Swedish slow motion theory". This description is valid for arbitrary motional conditions and interaction strengths. Molecular tumbling influences the ESR spectra by modulating zero field splitting interactions. The nuclear spin relaxation is affected by the rotational motion in a twofold way: via the electron spin dynamics and as a direct source of modulations of the electron-nuclear dipole-dipole interactions. For coinciding principal axes systems of the permanent (residual, static) zero field splitting and rotational tensors the ESR lineshape is not affected by rotational anisotropy. Rotational anisotropy is important for nuclear relaxation as it is influenced by molecular rotation not only via the electron spin dynamics, but also directly by modulations of the electron spin-nuclear spin dipole-dipole interaction (when the dipole-dipole and zero field splitting frames do not coincide). The anisotropy effects depend strongly on the relative orientation of the dipole-dipole and permanent zero field splitting axes. Nevertheless, a different scenario is also possible. When the diffusion axis coincides with the dipole-dipole axis (but not with the principal axis system of the permanent zero field splitting), the nuclear spin relaxation as well as the ESR lineshape, become sensitive to the rotational anisotropy. The possible dependence of the ESR lineshape and nuclear spin relaxation on the rotational anisotropy should be carefully considered when attempting a joint analysis of ESR and nuclear magnetic relaxation dispersion results for paramagnetic molecules.
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