Orientational decay times

The list of properties that can (and have been) used to gauge water models is quite long. In addition to those just mentioned, there are many thermodynamic properties such as heat capacity, surface tension, free energy, and temperature (or pressure) where the maximum density of water occurs for a specified pressure (or temperature) and various structures for ice. There are also dynamic properties such as viscosity, orientational decay times, and vibrational density of states that can be determined using simulations. 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

A small step rotational diffusion model has been used to describe molecular rotations (MR) of rigid molecules in the presence of a potential of mean torque.118 120,151 t0 calculate the orientation correlation functions, the rotational diffusion equation must be solved to give the conditional probability for the molecule in a certain orientation at time t given that it has a different orientation at t = 0, and the equilibrium probability for finding the molecule with a certain orientation. These orientation correlation functions were found as a sum of decaying exponentials.120 In the notation of Tarroni and Zannoni,123 the spectral denisities (m = 0, 1, 2) for a deuteron fixed on a reorienting symmetric top molecule are ... 

We simulated [38] the orientation TCF for sub-ensembles of molecules that have different OH stretch frequencies at t 0. We found that within 100 fs there was an initial drop that was frequency-dependent, with a larger amplitude of this drop for molecules on the blue side of the line. For times longer than about 1 ps the decay times for all frequencies were the same. We argued that since molecules on the red side of the line have stronger H bonds, they are less free to rotate than molecules on the blue side, leading to a smaller initial decay. For times... 

In Fig. 2. R is presented for a solution of 3 M NaCl in HD0 D20 at different temperatures. All signals show an overall non-exponential decay, but are close to a single exponential for delays >3 ps. After this delay time, the signals only represent the orientational dynamics of the HDO molecules in the first solvation shell of the Cl- ion, thanks to the difference in lifetimes of the O-H- -0 and the O-H- -Cl- vibrations. At 27 °C, the orientational relaxation time constant ror of these HDO molecules is 9.6 0.6 ps. which is quite long in comparison with the value of Tor of 2.6 ps of HDO molecules in a solution of HDO in D20 [12],... 

Fig. 3. Orientation relaxation times in sc CO2 obtained from anisotropy decay at 370 nm. Extrapolation to zero viscosity comes closest to the calculated free rotor time of the CH2I-radical.

In view of the effect of molecular mass on orientational phenomena the results of151) seem to be more explicable. In this work surprisingly low values for threshold voltage (U 8-40 V) and rise and decay times (x a 200 msec) were observed for an array of nematic polymers and copolymers. They are close to the corresponding values for low-molecular liquid crystals, which implies presumably that the polymers investigated were of low degrees of polymerization or had a very wide molecular mass distribution. 

From Eq. (3.1), the correlation time xc is defined as the time constant for which the correlation function exponentially decays to zero. At a time small compared with rc, exp(—t/xc) — 1 and we expect that essentially all spins maintain their original value. Therefore, most of the products will be A. At times long with respect to rc, we expect that all spins have changed their orientations many times, so that on the average half of the spins will result with the same Ms with respect to their original values, and the other half will have the other Ms value. Under these conditions, statistically half of the products will be A and half — A, and the summation over a large number n of spins will yield zero. 

Figure 1. Intensity profile of optical Kerr effect of NB at 25°C vs. time. The zero time is arbitrary and the peak transmission of the Kerr effect is about 10%. The rise time is 5.3 ps and the decay time is 15.2 ps. This decay time corresponds to a molecular orientation time of 30.4 ps (6).

Since the collective orientational correlation time depends on the structure of a liquid, it is plausible that the rate of structural evolution of the liquid is proportional to this quantity. Thus, at lower temperatures rcon is longer and therefore the structural fluctuations are slower. As a result, motional narrowing is less effective as the temperature is lowered. While less motional narrowing would normally lead to a slower decay in the time domain, in this case the spectral density goes down to zero frequency. Thus, motional narrowing can reduce the spectral density at low frequencies and thereby decrease the intermediate relaxation time. 

ISS data have been recorded in many pure and mixed molecular liquids [34,49, 75, 83, 83-85], In most cases, the data are not described precisely by Eq. (27). Rather, an additional decay component appears at intermediate times (decay times 500 fs). This has been interpreted [49, 84] in terms of higher order polarizability contributions to C (t) which represent translational motions, an interpretation supported by observations in CCI4 (whose single-molecule polarizability anisotropy vanishes by symmetry). This interpretation is not consistent with several molecular dynamics simulations of CSj [71, 86]. An alternative analysis has been presented [82] that incorporates theoretical results showing that even the single-molecule orientational correlation function C (t) should in fact show decay on the 0.5-ps time scale of cage fluctuations [87, 88]. 

The decay of the orientational correlation function is highly nonexponential and one needs at least four exponentials to fit it. The average orientational correlation time, t, is slower by about a factor of 20 than that of its bulk value. The orientational correlation function for the interfacial water molecules will, of course, decay in the very long time (of the order of tens of nanoseconds), either because of "evaporation" of the interfacial water molecules or rotation of the micelle. 

Another particularly interesting type of experiment gives information about the Co parent atom. At temperatures of < IK the Zeeman levels of Co I — 1) atoms in iron metal are not equally occupied as their separation is kT. Assuming that the spin-lattice relaxation times are longer than the total nuclear decay time, the preferential orientation of the nucleus... 

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