Relaxation time rotational

Another, purely experimental possibility to obtain a better estimate of the friction coefficient for rotational motion in chemical reactions consists of measuring rotational relaxation times of reactants and calculating it according to equation (A3,6,35) as y. =... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Figure A3.6.6. Viscosity dependence of rotational relaxation times of (ran.s -stilbene hr ethane (open circles) andn-octane (fiill circles) [89].

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

In this case one determines the spectral intensity solely in the centre, not over the whole frequency range. Therefore the analysis often refers not to the spectrum as a whole, but to relaxation times Tg,i or and their dependence on rotational relaxation time tj [85]. This dependence contains much information and can be easier to interpret. It enables one to determine when free rotation turns into rotational diffusion. 

It is taken into account that relaxation of different Cartesian components of a>Xl proceeds independently, and (coa,)=0. One can easily see that every cumulant in (Al.lb) when integrated yields the corresponding power of Ta i.e., of rotational relaxation time of the oc th component. Therefore,... 

Winter T. G., Hill G. L., Raff L. M. The temperature dependence of the rotational relaxation time in gases, 6th Intern. Congr. on Acoustics (Tokyo), J-4-2 (1968). 

Kistemaker P. G., de Vries A. E. Rotational relaxation times in nitrogen-noble-gas mixtures, Chem. Phys. 7, 371-82 (1975). 

Russel J. D., Bernstein R. B., Curtiss C. F. Transport properties of a gas of diatomic molecules. VI. Classical trajectory calculations of the rotational relaxation time of the Ar-N2 system, J. Chem. Phys. 57, 3304-7 (1972). 

T = the lifetime of the emitting fluorophore, and p = the rotational relaxation time of e molecule after excitation. 

The rotational relaxation time, p, is related to the molecular volume hy the equation ... 

The quantity riV/RT is equal to six times the rotational period. The rotational relaxation time, p, should he shorter than the fluorescence lifetime, t, for these equations to apply. It is possible to perform calculations for nonspherical molecules such as prolate and oblate ellipsoids of revolution, but in such cases, there are different rotational rates about the different principal axes. 

By the total internal reflection condition at the liquid-liquid interface, one can observe interfacial reaction in the evanescent layer, a very thin layer of a ca. 100 nm thickness. Fluorometry is an effective method for a sensitive detection of interfacial species and their dynamics [10]. Time-resolved laser spectrofluorometry is a powerful tool for the elucidation of rapid dynamic phenomena at the interface [11]. Time-resolved total reflection fluorometry can be used for the evaluation of rotational relaxation time and the viscosity of the interface [12]. Laser excitation can produce excited states of adsorbed compound. Thus, the triplet-triplet absorption of interfacial species was observed at the interface [13]. 

Rotational dynamics of a fluorescent dye adsorbed at the interface provides useful information concerning the rigidity of the microenvironment of liquid-liquid interfaee in terms of the interfacial viscosity. The rotational relaxation time of the rhodamine B dye was studied by time-resolved total internal reflection fluorescent anisotropy. In-plane... 

Surfactant Cone. (M) In-plane rotational relaxation time (ns) Interfacial viscosity (Pas)... 

A second approach with respect to anisotropic flavin (photo-)chemistry has been described by Trissl 18°) and Frehland and Trissl61). These authors anchored flavins in artificial lipid bilayers by means of C18-hydrocarbon chains at various positions of the chromophore. From fluorescence polarization analysis and model calculations they conclude, that the rotational relaxation time of the chromophore within the membrane is small compared to the fluorescence lifetime (about 2 ns74)). They further obtain the surprising result that the chromophore is localized within the water/lipid interface, with a tilt angle of about 30° (long axis of the chromophore against the normal of the membrane), irrespective of the position where the hydrocarbon chain is bound to the flavin nucleus. They estimate an upper limit of the microviscosity of the membrane of 1 Poise. 

The rotational relaxation time zK can be combined with time-dependent nuclear Overhauser effect (NOE) measurements to determine interproton... 

The results from fitting the anisotropy decay support the above conclusions. Wells and Lakowicz(200) resolved two exponential components in the anisotropy decay. They obtained ro = 0.11, t r = 0.3 ns, rj = 0.15, and t = 18.5 ns for the sample with no added Mg2+, and ro = 0.05, t R = 0.4 ns, r J = 0.17, and t"R = 17.4 ns for a sample with 10 mM Mg2+. Here r 0 and r o are the amplitudes of the fast and slow components. The longer rotational relaxation time corresponds to overall tumbling of the tRNA, although its amplitude is reduced by much more rapid local motions. The shorter relaxation time corresponds directly to a rapid local motion. Upon addition of Mg2+, the relative amplitude of die rapid local motion decreases, while that of the overall tumbling increases. This implies that the wyebutine base is held in a more rigid or constrained state, such as a 3 stack, in the presence of Mg2+. In that state, the amplitude of local angular motion is substantially diminished in comparison with that in the alternate state that prevails in the absence of Mg2+. As noted before, the exact nature of these conformation(s) is unresolved. 

C. D. Stubbs, W. M. Tsang, J. Belin, A. D. Smith, and S. M. Johnson, Incubation of exogenous fatty acids with lymphocytes. Changes in fatty add composition and effects on the rotational relaxation time of l,6-diphenyl-l,3,5-hexatriene, Biochemistry 19, 2756-2762 (1980). 

Consequently, this relaxation time is predicted to be nearly independent of the number of arms. Dielectric relaxation experiments for stars up to 18 arms by Boese et al. [95] show this behavior. The rotational relaxation time, however, can be considered similar to longest internal modes, i.e., it depends on the overall size and, assuming free draining... 

Characteristic time of the a-process Rotational relaxation time in the Allegra model Characteristic time of /1-relaxation... 

The internal rotational relaxation times of 1-pyrene carboxaldehyde in sulfonate systems may offer some indication of the extent of probe binding to the inverted micelle. In the absence of any background fluorescence interference to the time-dependent anisotropy decay profile, the internal rotational relaxation time should correlate with the strength of binding with the polar material in the polar core. However, spectral interference from the aromatic moieties of sulfonates is substantial, so that the values of internal rotational relaxation time can only be used for qualitative comparison. 

We have not measured fluorescence depolarization with fluorophors and our polymers, but such measurements have been made by others, particularly with proteins and, as you indicate, it is possible to determine rotational relaxation times for the macromolecule and thus to obtain some insight into its behavior in solution. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

Dielectric dispersion measurements also provide a means of determining rotational diffusion coefficients or mean rotational relaxation times of solute molecules. In principle, data for these hydrodynamic quantities can be used for a... 

Mean rotational relaxation time t extrapolated to infinite dilution allows computation of the rotational diffusion coefficient 0 and rotational friction coefficient f of an isolated macromolecule from the relations ... 

Fig. 36. Double logarithmic plots of mean rotational relaxation time versus weight-average molecular weight for PBLG in helicogenic solvents. Data in EDC (O) Wada (110), ( ) Erenrich and Scheraga (115) in m-cresol and EDC-m-cresol mixtures (3) Matsumoto...

Applequist and Mahr (114) proposed the use of Buckingham s equation (see the next subsection) for ellipsoids of revolution to calculate vacuum of rodlike molecules. They found for poly-L-tyrosine in quinoline that the values of 1/2 so computed from experiment varied linearly with molecular weight and yielded (4.94 0.014) D for fa. In this case, the molecular weights of the samples were indirectly estimated from the observed rotational relaxation times with the assumption of the relation for rigid rods. 

Fig. 41. Mean rotational relaxation time corrected for solvent viscosity and temperature, tT/ o, plotted against fN as a function of for PCBL in m-cresol in the helix-coil transition region (117). xTjt 0 is given in units erf sec deg/poise...

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