Orientational relaxation time

The results obtained allow one to follow the collapse of a static contour and its further narrowing by collisions. The limiting cases are the simplest to describe. In particular, from (6.45) it can be easily obtained that as 1/tj - 0 

Each term of this sum corresponds to a static contour of the corresponding branch, except the Q-branch, which by virtue of (6.29) is a -function. In the opposite limiting case (as 1 /xj — oo) 

Substituting this expansion into (6.45) and taking into account that 

59) describes a collapsed spectrum, narrowing with increase of 1/tj. This is the Rocard formula derived in Chapter 2 by means of perturbation theory. 

During transition from one limiting case to the other the change of shape is most significant in the central part of the spectrum. The Q-branch is much narrower than other ones observed in the IR spectrum and it broadens initially, as described in Section 2 of the present chapter. 

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This ratio of orientational relaxation times is sometimes used to identify the situation corresponding to perturbation theory [85]. 

Let us demonstrate that the tendency to narrowing never manifests itself before the whole spectrum collapses, i.e. that the broadening of its central part is monotonic until Eq. (6.13) becomes valid. Let us consider quantity x j, denoting the orientational relaxation time at ( = 2. If rovibrational interaction is taken into account when calculating Kf(t) it is necessary to make the definition of xg/ given in Chapter 2 more precise. Collapse of the Q-branch rotational structure at T = I/ojqXj 1 shifts the centre of the whole spectrum to frequency cog. It must be eliminated by the definition... 

As can be seen, the difference in behaviour of orientational relaxation times Te,2 in models of weak and strong collisions is manifested more strongly than in the case of isotropic scattering. Relation (6.26) is... 

Inequality (6.67) is the softest criterion of perturbation theory. Its physical meaning is straightforward the reorientation angle (2.30) should be small. Otherwise, a complete circle may be accomplished during the correlation time of angular momentum and the rotation may be considered to be quasi-free. Diffusional theory should not be extended to this situation. When it was nevertheless done [268], the results turned out to be qualitatively incorrect orientational relaxation time 19,2 remained finite for xj —> 00. In reality t0j2 tends to infinity in this limit [27, 269]. 

Limiting ourselves to derivation of the Hubbard relation in the simplest case ( = 1 (for t = 2 see Appendix 9), we write out the definition of orientational relaxation time... 

From the foregoing it will be clear that whenever entanglements and long chain branching are both present the dynamics in a polymer melt are highly co-operative. The orientational relaxation time of chain segments is exponentially dependent on both the contour distance to the nearest effective free end and on the effective entanglement density of its enviroiunent at all previous timescales. 

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.

The proper choice of a solvent for a particular application depends on several factors, among which its physical properties are of prime importance. The solvent should first of all be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapour pressure, and their temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity also need to be considered. Electrical, optical and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant too. Furthermore, molecular characteristics, such as the size, surface area and volume, as well as orientational relaxation times have appreciable bearing on the applicability of a solvent or on the interpretation of solvent effects. These properties are discussed and presented in this Chapter. 

Table 3.10 Orientational relaxation times and ultrasound absorption characteristic of solvents...

The situation of a freely-draining macromolecule without excluded-volume effects and internal viscosity, when zv = 2, and the above eigenvalues reduce to (1.17), is especially simple. In this case, equation (2.29) describes Rouse modes, and it is convenient to use the largest orientation relaxation time... 

Here, D and E are the parameters of zero field splitting (ZES) defined by Eqs. (10-14a) - (10-14c) and Tj s the orientation relaxation time of the axial second-rank tensor [5]. 

By using nonlinear least squares fitting, the orientation relaxation time (to,), fluorescence lifetime (r/), and the initial value of anisotropy (r(0)) were obtained. The typical results of the fitting to the time dependence of polarized fluorescence of I in n-nexane is shown in Fig. 1. In order to confirm the validity of the data analysis, the fluorescence lifetime was also measured with the magic angle arrangement. 

The orientation relaxation time of I in ethanol was found to be very close to that predicted for slip boundary condition. Important point of our results is that the rotational diffusion in ethanol is faster than that expected for the stick boundary condition. Our results may suggest that the strong hydrogen bonding between the solvent molecules allows the solute to rotate more freely within the solvent cage than in other polar solvents. 

In the above, X is the chain stretch, which is greater than unity when the flow is fast enough (i.e., y T, > 1) that the retraction process is not complete, and the chain s primitive path therefore becomes stretched. This magnifies the stress, as shown by the multiplier X in the equation for the stress tensor a, Eq. (3-78d). The tensor Q is defined as Q/5, where Q is defined by Eq. (3-70). Convective constraint release is responsible for the last terms in Eqns. (A3-29a) and (A3-29c) these cause the orientation relaxation time r to be shorter than the reptation time Zti and reduce the chain stretch X. Derive the predicted dependence of the dimensionless shear stress On/G and the first normal stress difference M/G on the dimensionless shear rate y for rd/r, = 50 and compare your results with those plotted in Fig. 3-35. 

The dynamics of molecular motion in simple (i.e., nonviscous) liquids have long been of interest in their own right and because of their importance in mediating liquid state chemical reactions. Collective orientational relaxation times, which measure the return of partially aligned liquids to their isotropic equilibrium states and are usually in the 5-100-ps range, have been determined in many fluids from Rayleigh linewidths or optical Kerr... 

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