Probe rotational diffusion

Phillies, et a/. (69) present results confirming Streletzky and Phillies s(64) prior interpretation that HPC solutions have a dominant, concentration-independent characteristic dynamic length scale, namely the radius of a polymer chain, which for this species is i 50 nm. In particular (i) There are distinct small-probe and large-probe phenomenologies, with the division between small and large probes being about 50 nm, the same at all polymer concentrations, (ii) For small probes, the relative amplitude of the sharp and broad modes depends markedly on scattering vector q with a crossover near q 70 nm. (iii) The mean relaxation rate of the small-probe broad mode increases markedly near 50 nm. (iv) The probe intermedi- 

Koenderink, et al. examined the motion of perfluorinated hydrocarbon spheres through xanthan solutions(72). Depolarized QELSS spectra were measured at a series of angles and fitted to second-order cumulant expansions. The spheres had radius 92.5 nm the xanthan molecular weight was 4 MDa. Koenderink, et al. measured solution viscosity, shear thinning, storage and loss moduli, translational and rotational diffusion coefficients Dp and Dr of the probes, and probe sedimentation coefficient s, and made an extensive and systematic comparison 

Jamil and Russo studied translational and rotational diffusion of poly-tetrafluoroethylene latex in aqueous sodium polystyrenesulfonate (NaPSS)(75). Spectra were single exponentials Dp and Dr were extracted from the dependence of the spectral linewidths. Addition of NaCl causes the probes to aggregate further addition of NaPSS reverses the salt-induced probe aggregation, even though it appears that NaPSS does not bind to the latex particles. The Dr tracks the changes in viscosity of the solution attendant on addition of polymer, in the sense that rjDr is independent of polymer concentration, other parameters being fixed. However, at fixed c, qDr does decrease as the salt concentration is increased. 

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Comparison may be made with literature data on solution viscosities. The probe diffusion coefficient does not simply track the solution viscosity instead. Dpi] typically increases markedly with increasing polymer concentration and molecular weight. The probe rotational diffusion coefficient, for which there are Umited sets of experiments, either has the same concentration dependence as the viscosity or, in other systems, has a concentration dependence that is significantly weaker than the concentration dependence of the viscosity or the probe translational diffusion coefficient. 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

Fluorescence polarization 1) steady state 2) time-resolved emission anisotropy rotational diffusion of the whole probe simple technique but Perrin s Law often not valid sophisticated technique but very powerful also provides order parameters... 

R. M. Levy and R. P. Sheridan, Combined effect of restricted rotational diffusion plus jumps on nuclear magnetic resonance and fluorescence probes of aromatic ring motions in proteins, Biophys. J. 41, 217-221 (1983). 

The above experimental results largely relate to spectroscopic techniques, which do not give direct information about the spatial scale of the molecular motions. The size of the spatial heterogeneities is estimated by indirect methods such as sensitivity of the dynamics to the probe size or from the differences between translational and rotational diffusion coefficients (rotation-translation paradox). It might be expected that the additional spatial information provided by neutron scattering could help to discriminate between the two scenarios proposed. 

One can employ linearly polarized light to excite selectively those fluorophores that are in a particular orientation. The difference between excitation and emitted light polarization changes whenever fluorophores rotate during the period of time between excitation and emission. The magnitude of depolarization can be measured, and one can therefore deduce the fluorophore s rotational relaxation kinetics. Extrinsic fluorescence probes are especially useful here, because the proper choice of their fluorescence lifetime will greatly improve the measurement of rotational relaxation rates. One can also determine the freedom of motion of the probe relative to the rotational diffusion properties of the macromolecule to which it is attached. When held rigidly by the macromolecule, the depolarization of a probe s fluorescence is dominated by the the motion of the macromolecule. 

Fig. 3. (a-c) Time resolved changes of the O-H stretching absorption of OH/OH dimers as measured with spectrally integrated probe pulses centered at Epr and corrected for rotational diffusion (symbols, pump pulses centered at Ep=2950 cm"1). The solid lines represent numerical fits based on exponential kinetic components with time constants of 200 fs, 1 ps and 15 ps. Inset of Fig. (c) Time evolution up to a 70 ps delay time, (d-f) Oscillatory component of the signals in Figs, (a-c) and Fourier transforms (insets). 

In conclusion, a typical time of 300 fs has been found for the excited-state intramolecular double proton transfer in TAB and DAC. The proton transfer dynamics is not influenced by aggregation. In addition, a vibronic cooling time of 20 ps has been measured for the probe molecules in the molecular and stacked configurations. Finally, aggregation is found to almost completely hamper the rotational diffusion motions of the molecules during the fluorescence state lifetime of 4 ns. 

Reticulum ATPase [105,106], Owing to the long-lived nature of the triplet state, Eosin derivatives are suitable to study protein dynamics in the microsecond-millisecond range. Rotational correlation times are obtained by monitoring the time-dependent anisotropy of the probe s phosphorescence [107-112] and/or the recovery of the ground state absorption [113— 118] or fluorescence [119-122], The decay of the anisotropy allows determination of the mobility of the protein chain that cover the binding site and the rotational diffusion of the protein, the latter being a function of the size and shape of the protein, the viscosity of the medium, and the temperature. 

Bagchi and co-workers [47-50] have explored the role of translational diffusion in the dynamics of solvation by employing a Smoluchowski-Vlasov equation (see also Calef and Wolyness [37] and Nichols and Calef [42]). A significant contribution to polarization relaxation is observed in certain cases. It is found that the Onsager inverted snowball model is correct only when the rotational diffusion mechanism of solvation dominates the polarization relaxation. The Onsager model significantly breaks down when there is an important translational contribution to the polarization relaxation [47-50]. In fact, translational effects can rapidly accelerate solvation near the probe. In certain cases, the predicted behavior can actually approach the uniform continuum result that rs = t,. 

From an experimental point of view, if we want to establish whether a loss of anisotropy is due to rotational diffusion or to energy transfer, we must probe very short times when molecular motions are inhibited. This is precisely what we did by observing fluorescence anisotropy on the sub-picosecond time-... 

This electro-optical effect, commonly observed as transient changes in optical birefringence of a solution following application, removal, or reversal of a biasing electric field E(t), has been used extensively as a probe of dynamics of blopolymer solutions, notably by O Konski, and is a valuable tool because it gives information different in form, but related to, results from conventional dielectric relaxation measurements. The state of the subject to 1975 has been comprehensively presented in two review volumes edited by O Konski (25). The discussion here is confined to an outline of a response theory treatment, to be published in more detail elsewhere, of the quadratic effect. The results are more general than earlier ones obtained from rotational diffusion models and should be a useful basis for further theoretical and experimental developments. 

Electron spin resonance (ESR) studies of radical probe species also suggest complexity. Evans et al. [250] study the temperature dependence of IL viscosity and the diffusion of probe molecules in a series of dissimilar IL solvents. The results indicate that, at least over the temperature range studied, the activation energy for viscous flow of the liquid correlates well with the activation energies for both translational and rotational diffusion, indicative of Stoke-Einstein and Debye-Stokes-Einstein diffusion, respectively. Where exceptions to these trends are noted, they appear to be associated with structural inhomogeneity in the solvent. However, Strehmel and co-workers [251] take a different approach, and use ESR to study the behavior of spin probes in a homologous series of ILs. In these studies, comparisons of viscosity and probe dynamics across different (but structurally similar) ILs do not lead to a Stokes-Einstein correlation between viscosity and solute diffusion. Since the capacities for specific interactions are... 

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