Rotational characteristic time

Figure 7 (a) Arrhenius plot of the residence time Xq for different levels of hydration of water at the surface of H20-hydrated d-CPC protein (empty symbols) contained in hydrated Vycor (solid symbols) as compared with bulk water (empty circles) [49]. (b) Arrhenius plot of the hindered rotations characteristic time, x,. This time can be associated with the hydrogen bond lifetime [69]. 

The sign ambiguity is related with the direction of propagation of the deformation. The rotational characteristic time tq is... 

This is obvious for the simplest case of nondeformable anisotropic particles. Even if such particles do not change the form, i.e. they are rigid, a new in principle effect in comparison to spherical particles, is their turn upon the flow of dispersion. For suspensions of anisodiametrical particles we can introduce a new characteristic time parameter Dr-1, equal to an inverse value of the coefficient of rotational diffusion and, correspondingly, a dimensionless parameter C = yDr 1. The value of Dr is expressed via the ratio of semiaxes of ellipsoid to the viscosity of a dispersion medium. 

A possible approach to interpretation of a low-frequency region of the G ( ) dependence of filled polymers is to compare it with a specific relaxation mechanism, which appears due to the presence of a filler in the melt. We have already spoken about two possible mechanisms — the first, associated with adsorption phenomena on a filler s surface and the second, determined by the possibility of rotational diffusion of anisodiametrical particles with characteristic time D 1. But even if these effects are not taken into account, the presence of a filler can be related with the appearance of a new characteristic time, Xf, common for any systems. It is expressed in the following way... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

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

E.g. tryptophane residues of proteins excite at 290-295 mn but they emit photons somewhere between 310 and 350 mn. The missing energy is deposited in the tryptophane molecular enviromuent in the form of vibrational states. While the excitation process is complete in pico-seconds, the relaxation back to the initial state may take nano-seconds. While this period may appear very short, it is actually an extremely relevant time scale for proteins. Due to the inherent thermal energy, proteins move in their (aqueous) solution, they display both translational and rotational diffusion, and for both of these the characteristic time scale is nano-seconds for normal proteins. Thus we may excite the protein at time 0 and recollect some photons some nano seconds later. With the invention of lasers, as well as of very fast detectors, it is completely feasible to follow the protein relax back to its ground state with sub-nano second resolution. The relaxation process may be a simple exponential decay, although tryptophane of reasons we will not dwell on here display a multi-exponential decay. 

X3 process. The sample loses its alignment due to rotation but due to quantization of energy the molecules will be aligned after a characteristic time over and over again. The time dependence of the third order polarisability has been described by Mukamel and is given below ... 

At T = 77 K in MTHF, the kinetics of fluorescence decay of P-L-Q with a bridge containing one bicyclo[2.2.2]octyl is of a non-exponential character. This effect can be explained by the coexistence in the frozen solution of several rotational conformations of the P-L-Q molecule (rotation of the porphyrin fragment around the a bond in its meso position is meant here). The characteristic time of the fluorescence decay for the predominant portion of the P-L-Q particles at 77 K, r 1.1 x 10 1°s, virtually coincides with the value of r = l/k(e1 at 298 K, i.e. the rate of tunneling from P to Q is independent of temperature. The exponential character of the fluorescence decay curve at 298 K indicates that, at this temperature, the rate of rotation exceeds k(e1. ... 

Interest in thermotropic liquid crystals has focussed mainly on macroscopic properties studies relating these properties to the microscopic molecular order are new. Lyotropic liquid crystals, e.g. lipid-water systems, however, are better known from a microscopic point of view. We detail the descriptions of chain flexibility that were obtained from recent DMR experiments on deuterated soap molecules. Models were developed, and most chain deformations appear to result from intramolecular isomeric rotations that are compatible with intermodular steric hindrance. The characteristic times of chain motions can be estimated from earlier proton resonance experiments. There is a possibility of collective motions in the bilayer. The biological relevance of these findings is considered briefly. Recent similar DMR studies of thermotropic liquid crystals also suggest some molecular flexibility. 

Power spectra of the autocorrelation functions of the linear and angular velocities parallel and perpendicular to the C3 symmetrical axes have also been examined by Neusy et al. (32). In the rotator phase, there is good agreement with the Raman data (36). The calculated characteristic time (r4) for reorientation of the C3 axes from one [111] direction to another and also the reorientation time (r3) for rotation of molecules around the C3 axes were similar... 

An essential requirement is that the characteristic time, T2, for the decay of the macroscopic polarisation must be much longer than the time taken for the polarising radiation pulse to dissipate. This requirement is readily satisfied the pin-diode S2 is held closed until the pulsed radiation has dissipated, and is then opened to capture the coherent radiation emitted by the polarised gas, due to one or more rotational transitions producing spontaneous emission. If all is well, the emission is detected against a near-zero radiation background. 

The in-plane rotational correlation time (rinterfacial characteristics. In abulk solution, the rotational correlation time (r) of a fluorophore is expressed as... 

---