Translational self-diffusion relaxation

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. 

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. 

Fenchenko studied free induction decays and transverse relaxation in entangled polymer melts. He considered both the effects of the dipolar interactions between spins in different polymer chains and within an isolated segment along s single chain. Sebastiao and co-workers presented a unifying model for molecular dynamics and NMR relaxation for chiral and non-chiral nematic liquid crystals. The model included molecular rotations/ reorientations, translational self-diffusion as well as collective motions. For the chiral nematic phase, an additional relaxation mechanism was proposed, associated with rotations induced by translational diffusion along the helical axis. The model was applied to interpret experimental data, to which we return below. 

This chapter concludes by pointing out that relaxation of multispin proton systems played a major role in the early days of NMR relaxation measurements on liquid crystals [5.34]. In particular, the detection of director fluctuations [5.35] by means of its characteristic frequency dependence in proton Ti [5.36-5.39] started intensive NMR research on liquid crystals. Since there are many inequivalent proton species in a liquid crystalline molecule, it is impossible to distinguish various atomic sites from a broad proton lineshape, which is a result of strong dipolar couplings. Moreover, translation self-diffusion also modulates the intermolecular dipole-dipole interactions and contributes to proton relaxation in liquid crystals [5.40, 5.41]. Partially deuterated liquid crystals may be used to reduce the number of inequivalent proton species. Proton spin relaxation studies remain as a possible method of probing intermolecular interactions or translational motions in liquid crystals. 

Variable frequency proton Ti studies were first used to detect the characteristic dependence of Ti due to director fluctuations [6.20] in liquid crystals. It was recognized soon after that besides the director fluctuations, relaxation mechanisms, which are effective in normal liquids such as translational self-diffusion and molecular reorientation [6.24], also contribute to the proton spin relaxation in liquid crystals. Though the frequency dependences of these latter mechanisms are different from the relaxation, the precise nature of proton Ti frequency dispersion studied over a limited frequency range using commercial NMR spectrometers often may not be unambiguously identified. Furthermore, because of a large number of particles involved in collective motions, the motional spectrum has much of its intensities in the low-frequency domain far from the conventional Larmor frequencies. The suppression of director fluctuations in the MHz region due... 

Director fluctuations are however not the only spin-lattice relaxation mechanism in nematics. Translational self-diffusion of nematic molecules modulates the inter-molecular nuclear dipole-dipole interactions and induces - as first emphasized by Vilfan, Blinc and Doane [36], another contribution... 

Translational self-diffusion. Whereas in bulk nematics, translational self-diffusion modulates only the dipolar interactions between protons on different molecules (i.e. intermolecular interactions), in microdroplets it also modulates intra-molecular dipolar interactions because the director field in a confined geometry is non-uniform. This new relaxation mechanism is called translational diffusion induced rotation (TDIR). Since intramolecular dipolar interactions are generally stronger than intermolecular interactions, translational selfdiffusion represents a much more effective relaxation mechanism in micro-droplets than in bulk nematics. TDIR is also effective at much lower frequencies than diffusion induced modulation of inter-molecular... 

Here r is the distance from the cylinder axis and is the coherence length. The distance that the molecule migrates in the iso-tropic phase during a NMR measurement VD/(5v is in the above case of the order of the cylinder diameter R and the motional averaging by translational self-diffusion must be taken into account. The diffusion coefficient in the surface layer was estimated as Dg 10 ° cm s" and is much smaller than the bulk value. The time a molecule resides at the surface is then t IqID = QT s. In the fast exchange regime the effective spin-spin relaxation rate can be expressed as... 

The only microscopic feature suU remembered by the system when described by Eq. (4.3) is that of the H-bond dynamics as simulated by the variable if. As mentioned in the introduction, the integrations in time appearing on the right-hand side of Eq. (4.3) are made legitimate by the fact that the correlation functions dielectric relaxation and self-diffusion processes. Henceforth we shall neglect the third term on the right-hand side of Eq. (4.3) concerning rototranslational phenomena. This assumption allows us to obtain two independent equations for rotation and translation, respectively. 

C. Analysis of Molecular Translations and Rotations by Combined H NMR Relaxation and NMR Self-Diffusion Studies... 

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. Andrec et al. used a Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data. Sturz and Dolle examined the reorientational motion of toluene in neat liquid by using relaxation measurements. The relaxation rates were analyzed by rotational diffusion models. Chen et al measured self-diffusion coefficients for fluid hydrogen and fluid deuterium at pressures up to 200 MPa and in the temperature range 171-372 K by the spin echo method. The diffusion coefficients D were described by the rough sphere (RHS) model invoking the rotation translational coupling parameter A = 1. 

Figure 5.13 shows the dependence on pressure, for various temperatures, of the rotational and translational molecular mobility for trifluoromethane. Rotational mobility is characterized by the deuteron spin-lattice relaxation time, Tj, and translational mobility is characterized by the self-diffusion coefficient. In all nonpolar liquids, and also in most polar liquids, changes in temperature and pressure have a stronger influence upon the translational mobility than upon the rotational mobility. 

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