Rotational diffusion collective

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

The time that characterizes the rotational diffusion of the macromolecule as a whole (x j and the mobility of the main chains (x J and of the side branches (Tside) are collected in the following equation J 1 1... 

The analysis of the dynamics and dielectric relaxation is made by means of the collective dipole time-correlation function (t) = (M(/).M(0)> /( M(0) 2), from which one can obtain the far-infrared spectrum by a Fourier-Laplace transformation and the main dielectric relaxation time by fitting < >(/) by exponential or multi-exponentials in the long-time rotational-diffusion regime. Results for (t) and the corresponding frequency-dependent absorption coefficient, A" = ilf < >(/) cos (cot)dt are shown in Figure 16-6 for several simulated states. The main spectra capture essentially the microwave region whereas the insert shows the far-infrared spectral region. 

Gotlib, Yu. Ya., Svetlov, Yu. E. The theory of vibrational and rotational diffusive processes in diains of rotators and polymer chains. In collected articles Mekhanizmy relaksatsionnykh yavlenii v tverdykh telakh (Mechanisms of relaxation phenomena in solids), Moscow Nauka 1972 (pp- 215-219)... 

Among nonisotopic techniques, fluorescence (both intrinsic and extrinsic) offers a convenient mode of detection, and the sensitivity of some fluorescent labels is comparable to that of radiolabeled iodine. Recent innovations include the use of polarized light for excitation, such that the degree of polarization of the emission as well as its intensity can provide information about the concentration and size-related behavior (e.g., rotational diffusion) of the fluorescent-labeled molecule. One disadvantage of steady-state fluorescence techniques is that many analytical samples either autofluoresce or quench the fluorescence of the substance of interest. A recent development that circumvents this problem utilizes long-lived fluorophores such as the lanthanide metal ions as labels. Detection is time resolved and data are collected after the decay of spurious or otherwise unwanted fluorescence, i.e., after 100-200 psec. 

The alternative NMR approach that has provided information on microemuisions is relaxation. However, on the whole, relaxation has been less informative than anticipated from earlier studies of micellar solutions and has provided little unique information on microemulsion structure, although in the case of droplet structures it is probably the most reliable way of deducing any changes in droplet size and shape, particularly for concentrated systems. The reason for this is that NMR relaxation probes the rotational diffusion of droplets, which is relatively insensitive to interdroplet interactions. This is in contrast to, for example, translational collective and self-diffusion and viscosity which depend strongly on interactions. Furthermore, NMR relaxation is a useful technique for characterizing the local properties of the surfactant film. 

To make the significance of the NMR technique as an experimental tool in surfactant science more apparent, it is important to compare the strengths and the weaknesses of the NMR relaxation technique in relation to other experimental techniques. In comparison with other experimental techniques to study, for example, microemulsion droplet size, the NMR relaxation technique has two major advantages, both of which are associated with the fact that it is reorientational motions that are measured. One is that the relaxation rate, i.e., R2, is sensitive to small variations in micellar size. For example, in the case of a sphere, the rotational correlation time is proportional to the cube of the radius. This can be compared with the translational self-diffusion coefficient, which varies linearly with the radius. The second, and perhaps the most important, advantage is the fact that the rotational diffusion of particles in solution is essentially independent of interparticle interactions (electrostatic and hydrodynamic). This is in contrast to most other techniques available to study surfactant systems or colloidal systems in general, such as viscosity, collective and self-diffusion, and scattered light intensity. A weakness of the NMR relaxation approach to aggregate size determinations, compared with form factor determinations, would be the difficulties in absolute calibration, since the transformation from information on dynamics to information on structure must be performed by means of a motional model. 

Now we proceed to study into more detail librational interaction-induced motions. Relaxation processes will be more suc-cintly treated in section up, since they are adressed in greater detail elsewhere in this course. In our last section we will touch on some coherent features of the rotational diffusion arising from strong dipolar interactions. No attempt is done to speculate on manifestations of the walk process since it seems unlikely that dipolar spectroscopy will ever be a convenient tool to detect slow currents as long as we dont know how the collective characters of slow motions could be isolated from the total absorption pattern. 

The complex dynamics of liquid crystals is characterized by a superposition of local and collective motions, comprising internal isomerization, overall rotational diffusion (rotation of the molecule about the long axis and reorientation of this axis) and translational diffusion, and collective order fluctuations. Different NMR techniques are designed to follow these motions and to differentiate the various motional modes on the basis of their timescale. 

To summarize, there is a sizable and self-consistent body of data indicating that rotational and translational mobility of molecules inside swollen gel-type CFPs are interrelated and controlled mainly by viscosity. Accordingly, T, self-diffusion and diffusion coefficients bear the same information (at least for comparative purposes) concerning diffusion rates within swollen gel phases. However, the measurement of r is by far the most simple (it requires only the collection of a single spectrum). For this reason, only r values have been used so far in the interpretation of diffusion phenomena in swollen heterogeneous metal catalysts supported on CFPs [81,82]. 

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