Anisotropic rotational motion

Time Resolved Fluorescence Depolarization. In Equation 3, it is assumed that the polarization decays to zero as a single exponential function, which is equivalent to assuming that the molecular shape is spherical with isotropic rotational motion. Multiexponential decays arise from anisotropic rotational motion, which might indicate a nonspherical molecule, a molecule rotating in a nonuniform environment, a fluorophore bound to tbe molecule in a manner that binders its motion, or a mixture of fluorophores with different rotational rates. 

Carbon-13 NMR has been used to study anisotropic rotational motion in liquids, as have combinations of techniques. Gillen and Griffiths (1972) have obtained the two reorientational relaxation times for benzene (a symmetric top) by combining reorientation relaxation times obtained from Raman band shapes and deuterium spin-lattice NMR relaxation times. The most extensive series of measurements probing anisotropic molecular reorientations have been made by Pecora and co-workers (Alms et al., (1973a, b)), who combined Carbon-13 spin lattice relaxation times with those obtained from depolarized Rayleigh spectra. 

The present design of our MAS probe is clearly amenable to variable temperature operation. Hence, one can study site exchange processes as a function of temperature and possibly separate rotational motion from translational motion of the molecule on the surface. Anisotropic rotational motion can be studied by nmr, e.g. deuterated pyridine and n-butyl amine. The ease of the experiment suggested that nmr with enriched samples would be equally as straightforward. In the near future, the Al, Ag, Rh nmr spectroscopy of the surface acceptor can also be studied. 

Freed et al. [3] evaluated the relaxation rate of polymer chains by the analysis of the anisotropic spectra of nitroxide spin labels. The main triplet spectrum was due to hyperfine coupling caused by the nitrogen nucleus. It narrowed with an increase in mobility of the radicals because of motional averaging of the anisotropic hyperfine interaction. The rotational correlation time of nitroxide spin labels can be estimated using the procedure of Freed et al. by taking into account the anisotropic rotational motion. The ESR line width, AHmsi of the spectrum can be expressed as follows ... 

Definitive proof of the structure of porphine in the solid state awaits a variable-temperature crystallographic (X-ray or neutron diffraction) study the analysis of the anisotropic displacement factors (ADP) should disclose any rotational motion or its absence as well as determine the positions of the inner hydrogens. A search in the September 1998 version of the Cambridge Structural Database [CSD (91MI187)] showed that the only structures of porphine (codename PORPIN) were obtained in 1965 and 1972. 

Another example comes from the work of Johnson, et a/.18 These workers studied spin labels dissolved in lipid bilayer dispersions of dipalmitoylphos-phatidylcholine and cholesterol (9 1 by weight) in the hope that anisotropic rotational diffusion of the spin label would mimic the motion of the bilayer components. In addition to 5-DS, which is sensitive to rotational motion about the NO bond, they used the steroidal nitroxide 8, which tends to rotate about an axis perpendicular to the N-O bond. ESR measurements were carried out at both 9 and 35 GHz and at temperatures ranging from 30 to 30 °C. Rather different results were obtained with the two spin labels, largely as a result of the different axes of rotation. Because the rotation rates were very slow, ESR spectra appeared as powder patterns rather than isotropic spectra and special methods were needed to extract the motional data. 

While the assumption of an isotropic rotational motion is reasonable for low molecular weight chelates, macromolecules have anisotropic rotation involving internal motions. In the Lipari-Szabo approach, two kinds of motion are assumed to affect relaxation a rapid, local motion, which lies in the extreme narrowing limit and a slower, global motion (86,87). Provided they are statistically independent and the global motion is isotropic, the reduced spectral density function can be written as ... 

Equations (8.25) to (8.28) are no longer valid in the case of hindered rotations occurring in anisotropic media such as lipid bilayers and liquid crystals. In these media, the rotational motions of the probe are hindered and the emission anisotropy does not decay to zero but to a steady value rc0 (see Chapter 5). For isotropic rotations (rod-like probe), assuming a single correlation time, the emission anisotropy can be written in the following form ... 

It is convenient to consider a model of an anisotropic recombination region the reflecting recombination sphere (white sphere) with black reaction spots on its surface [77, 78], The measure of the reaction anisotropy here is the geometrical steric factor Q which is a ratio of a black spot square to a total surface square. Such a model could be actual for reactions of complex biologically active molecules and tunnelling recombination when the donor electron has an asymmetric (e.g., p-like) wavefunction. Note the non-trivial result that at small Q, due to the partial averaging of the reaction anisotropy by rotational motion arising due to numerous repeated contacts of reactants before the reaction, the reaction rate is K() oc J 1/2 rather than the intuitive estimate Kq oc Q. 

Eq. (3.21) discussed in Section 3.3.2 is only valid if the motion of the molecules under study has no preferential orientation, i.e. is not anisotropic. Strictly speaking, this applies only for approximately spherical bodies such as adamantane. Even an ellipsoidal molecule like trans-decalin performs anisotropic motion in solution it will preferentially undergo rotation and translation such that it displaces as few as possible of the other molecules present. This anisotropic rotation during translation is described by the three diagonal components Rlt R2, and R3 of the rotational diffusion tensor. If the principal axes of this tensor coincide with those of the moment of inertia - as can frequently be assumed in practice - then Rl, R2, and R3 indicate the speed at which the molecule rotates about its three principal axes. 

The connection between anisotropic molecular motion and nuclear relaxation was derived by Woessner as early as 1962 [161]. Accordingly, the dipole-dipole relaxation time of a carbon nucleus is a function of the diagonal components R, R2, and R3 of the rotational diffusion tensor and the cosines X, p, and v of the angles assumed by the C —H bonds relative to the principal axes of this tensor ... 

Differing 7j values for CH3, CH2, and CH carbon nuclei within a molecule can arise not only by methyl rotation or anisotropic molecular motion, but also from the segmental mobility of partial structures, even when the dipolar mechanism predominates. Thus the spin-lattice relaxation times of methylene carbon atoms in long alkane chains pass through a minimum at the middle of the chain. In the presence of heavy nonassociating... 

V02+ substituted PCA (V02+ substituted for Gd3+,Mn2+, etc.) BPCA rotational motion, including specifics of anisotropic rotation (TR(XjyjZ)).Also details of BPCA-protein interactions. 

On the other hand, when rotational motion is slow, or when the symmetry of the complex is less than cubic, as in Mn2+ complexes with macromolecules, Au)Xr is often greater than one, the anisotropic interactions are incompletely averaged and EPR spectra similar to those for randomly oriented solid samples are observed. In these cases the spectra depend upon the angular relationships between the magnetic field vector and the crystal field axis of the ion. Moreover, when the symmetry of the manganese ion complexes deviate greatly from cubic, the EPR spectra depend upon the sharing of spectral intensity between the normal and forbidden (AMS = + 1, Amp = + 1) transitions. 

The pump pulse in time-resolved pump-probe absorption spectroscopy is often linearly polarized, so photoexcitation generally creates an anisotropic distribution of excited molecules. In essence, the polarized light photoselects those molecules whose transition moments are nominally aligned with respect to the pump polarization vector (12,13). If the anisotropy generated by the pump pulse is probed on a time scale that is fast compared to the rotational motion of the probed transition, the measured anisotropy can be used to determine the angle between the pumped and probed transitions. Therefore, time-resolved polarized absorption spectroscopy can be used to acquire information related to molecular structure and structural dynamics. 

An important reference point is the rotational correlation time of the protein molecule itself, denoted tc, (also the notation xm is used) corresponding to the time required for the molecule to rotate one radian (Scheme 1). The rotational motion/ diffusion of the molecule can be isotropic or anisotropic and depends on the size and shape of the molecule as well as on solvent viscosity. Thus, in aqueous... 

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