Rotational relaxation time, related

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 [ ]... 

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

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 ... 

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. 

The origin of the n2 measured using the 10 ns pulses could be electronic or molecular rotation. These can be distinguished by measuring the ratio of the critical power for self-focusing for linear and circular polarised light. The observed ratio of 2.1 is consistent with a molecular rotation (11-13.161 and relates to the anisotropic polarisability of the molecule. The rotational relaxation time, calculated from the Debye formula (H), is about 0.5-2 ns, consistent with these results. 

The practical advantage of these relations is that, in MD simulations, single molecule properties like the self-diffusion coefficient and rotational relaxation times converge much faster than system properties due to additional averaging over the number of molecules in the ensemble. We applied eqs. 10 and 11 to our MD results using data at 800 K as a reference point in order to predict the viscosity over the entire temperature interval. In Fig. 7 we compare the predicted values with those obtained from simulation. It appears that in the temperature interval 600 K to 800 K predictions of Eq. (10) are more consistent with MD results than are the predictions of Eq. (11). This leads us to conclude that the viscosity temperature dependence in liquid HMX is more correlated... 

If we allow the molecules to rotate during the lifetime of excitation r the emission axis no longer bears the fixed relation with the electric vector of the incident beam and the degree of polarization is diminished. The extent of diminution, i.e., the depolarization, is therefore determined by tJq, where q is the rotational relaxation time of the whole fluorescing molecule. The degree of polarization p compared with that for the frozen system p0 can then be represented in the form... 

An important advantage of the depolarization technique is that it allows one to measure the molecular ordering, as well as the motional parameters. For this purpose, it is necessary to detect the time dependence of the anisotropy. In the presence of ordering constraints, the r value does not decay to zero, but to some limiting value foo r = (ro — roo)e / c - - poo. The rate of decay defines a rotational correlation time, and Poo is a direct measure of the order parameter through the following relation s = Poo/ o (29). The fluorescence depolarization method works well as long as fluorescence lifetimes, which are typically 10 s, are not too different from the rotation relaxation times to be measured. When the rotational correlation time... 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

It is clear that these equations are closely related to the phenomenological expression equation (7-28) except that the "molecular rotational relaxation time" ris now replaced by an effective relaxation time t where... 

We measured the temperature dependence of the absorption decay and obtained at temperatures above 30° C always a factor of 4 for the ratio between the two rotational correlation times (see equation 1, data not shown). This factor strongly suggests that at temperatures >30° Q where the liposome membrane is in the liquid cristalline state, the rotational difiusion of CF CF labelled in subunit m in fact may be regarded as restricted and uniaxial rotation about the bilayer membrane nomim according to the model of Saffinan and Delbriick (9V The rotational correlation time observed for uniaxial rotation of subimit in labelled CRCFj in the membrane was =200 20 ns at 30° C. This rotational relaxation time ror uniaxial anisotropic rotation of the labelled protein can be related to the size of the rotating unit (1,6,9) =(k.T)/(4.S. h-nO... 

ABSTRACT. The interaction of 2-p-toluidinylnaphthalene-6-sulfonate (TNS) with amylose and its related compounds in aqueous solution has been studied by both steady-state and transient fluorescence measurements. The fluorescence of TNS aqueous solution was enhanced by the addition of amylose, 3-limit dextrin, and amylopectin. The fluorescence decay of TNS bound to these polysaccharides were well described as a sum of two-exponential functions. This suggests that there are two different microenvironments at the binding sites. The fluorescence lifetime of major component for TNS-amylose system agreed with that of major component for TNS-y-cyclodextrin system. The mean rotational relaxation time of TNS bound to amylose is similar to that of the segmental motion of amylose chain. Based on these results, a configurational model for TNS-amylose complex has been proposed. 

It is important to realize that the relaxation times might depend on some factors that are properties of the atom or molecule itself and on others that are related to its environment. Thus rotational spectra of gases have linewidths (related to the rotational relaxation times) that depend on the mean times between coUisions for the molecules, which in turn depend on the gas pressure. In liquids, the collision lifetimes are much shorter, and so rotational energy is effectively non-quantized. On the other hand, if the probability of collisions is reduced, as in a molecular beam, we can increase the relaxation time, reduce linewidths, and so improve resolution. Of course, the relaxation time only defines a minimum width of spectral lines, which may be broadened by other experimental factors. 

Table 3.2 Reorientational rotation times in solution, compared with theoretical values for diffusion with slip or stick conditions. Experimental plots for solutes in various low-polar solvents (as in Figure 3.10) show that the rotational relaxation time r is linearly related to the viscosity (r = Zq +Ct], where Tq is small), and depends on no other solvent property. The table compares experimental values of C with values calculated (a) for slip conditions and (b) for stick conditions, the solute molecules being approximated to ellipsoids, with axial ratio a/b. Data from Ref. [16]. See text and Figure 3.11...

The difhision tensor for a nematic liquid is evidently a model-dependent quantity, and the numerical values obtained for its elements depend on the assumptions made in the calculation procedure. Actually the relation of Dy and Dx to rotational relaxation times is not obvious. In fact, the correlation functions determined from the NMR experiments correspond to a weighted sum of decaying exponentials of the type [10]... 

Now we refer to the analysis of a functional relationship between the times of orientational and rotational (angular momentum) relaxation that are rg/ and tj, respectively. To lowest order in Jf/, this relationship is given by the Hubbard relation (2.28). It is universal in the sense that it does not depend on the mechanisms of rotational relaxation. However, this relation does not hold when rg/ is calculated to higher order in Jf/. Corrections to the Hubbard relation are expressed in terms of higher correlation moments of co,(t) whose dependence on tj is specific for different mechanisms. Let us demonstrate this, taking the impact theory as an example. In principle it distinguishes correlated behaviour of the... 

It implies that relaxation times obey relation (3.47) even after gas condensation, although both 1/te and ydP become nonlinear in density. The contribution of the rotational broadening represented by the first component may be estimated to a rather high accuracy via the value of y found in (3.45). Subtrrcting it from the width observed, we obtain the dephasing contribution which is linear in T (see inset in Fig. 3.8). The... 

---