Probe rotational time correlation functions

Thus, the combined SE and the DSE equations predict that the product Dtxc = (A Tc)sedse should equal 2r /9. Measurements of probe translational diffusion and rotational diffusion made in glass-formers have found that the product Dtr can be much larger than this value, revealing a breakdown of the Stokes-Einstein (SE) relation and the Debye-Stokes-Einstein (DSE) relation. There is an enhancement of probe translational diffusion in comparison with rotational diffusion. The time dependence of the probe rotational time correlation functions tit) is well-described by the KWW function,... 

We discuss the rotational dynamics of water molecules in terms of the time correlation functions, Ciit) = (P [cos 0 (it)]) (/ = 1, 2), where Pi is the /th Legendre polynomial, cos 0 (it) = U (0) U (it), u [, Is a unit vector along the water dipole (HOH bisector), and U2 is a unit vector along an OH bond. Infrared spectroscopy probes Ci(it), and deuterium NMR probes According to the Debye model (Brownian rotational motion), both... 

This ansatz can be rationalized by some theoretical considerations [325,326]. It is also supported by the experimental data at very low concentrations of the component A where the study is reduced to the dynamics of the probe A in host B. Each probe molecule experiences the same environment, which eliminates the complications from concentration fluctuations. We have mentioned in Section III, paragraph 4, that the probe rotational correlation function indeed has the Kohlrausch form. The differential between the probe rotational time xA and the host a-relaxation time xaB is gauged by their ratio, xA/xaB. As expected, the slower the host B compared with the probe A, the larger the coupling parameter, nA = (1 — pA), obtained from the stretch exponent (3A of the measured probe correlation function. The experimental data are shown in Fig. 52. For more details, see Ref. 172. 

Computer simulation studies have explored translational and rotational dynamics in micellar solutions and shown that both translational and rotational dynamics in the hydration layer of micelles (Stem layer) are significantly slower than that in the bulk. The dipole-dipole time correlation function (which measures the rotational dynamics) shows the appearance of a long-time tail of the time constant in the 100 ps range or above. The dependence of the rotational dynamics on the probe location has also been investigated and it was found that the dynamics becomes faster as the probe moves away from the surface [7]. 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

Sample preparation was given elsewhere [2]. Femtosecond fluorescence upconversion and picosecond time-correlated single-photon-counting set-ups were employed for the measurement of the fluorescence transients. The system response (FWHM) of the femtosecond fluorescence up-conversion and time-correlated single-photon-counting setups are 280 fs and 16 ps, respectively [3] The measured transients were fitted to multiexponential functions convoluted with the system response function. After deconvolution the time resolution was 100 fs. In the upconversion experiments, excitation was at 350 nm, the transients were measured from 420 nm upto 680 nm. Experiments were performed under magic angle conditions (to remove the fluorescence intensity effects of rotational motions of the probed molecules), as well as under polarization conditions in order to obtain the time evolution of the fluorescence anisotropy. 

Most experimental techniques do not probe reorientational motions directly but measure the time-dependence of properties which themselves are sensitive to orientation. Thus in far infrared and Raman spectroscopy one measures dipole or polarizability fluctuations with respect to particular normal modes of vibration. Although the interpretation can be complicated, in cases where the fluctuations arise predominantly from rotational motions of localized groups correlation functions of the first and second Legendre polynomials, C t) and 2(1) respectively, can be retrieved from the data. 

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. 

The 2,2,6,6-tetramethylpiperidinoxyl radical (TEMPO) was first prepared in 1960 by Lebedev and Kazarnovskii by oxidation of its piperidine precursor.18 The steric hindrance of the NO bond in TEMPO makes it a highly stable radical species, resistant to air and moisture. Paramagnetic TEMPO radicals can be employed as powerful spin probes for elucidating the structure and dynamics of both synthetic and biopolymers (e.g., proteins and DNA) by ESR spectroscopy.19 Unlike solid-phase 1H-NMR where magic angle spinning is required in order to reduce the anisotropic effects in the solid-phase environment, solid-phase ESR spectroscopy can be conducted without specialized equipment. Thus, we conducted comparative ESR studies of various polymers with persistent radical labels, and we also determined rotational correlation times as a function of... 

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