Self-diffusion small molecules

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. 

Brown, W Stilbs, P Lindstrom, T, Self-Diffusion of Small Molecules in Cellulose Gels using FT-Pulsed Field Gradient NMR, Journal of Applied Polymer Science 29, 823,1984. Brownstein, KR Tarr, CE, Importance of Classical Diffusion in NMR Studies of Water in Biological Cells, Physical Review A 19, 2446, 1979. 

When it comes to the equilibration of water concentration gradients, the relevant transport coefficient is the chemical diffusion coefficient, Dwp. This parameter is related to the self-diffusion coefficient by the thermodynamic factor (see above) if the elementary transport mechanism is assumed to be the same. The hydration isotherm (see Figure 8) directly provides the driving force for chemical water diffusion. Under fuel-cell conditions, i.e., high degrees of hydration, the concentration of water in the membrane may change with only a small variation of the chemical potential of water. In the two-phase region (i.e., water contents of >14 water molecules... 

The jamming effect, i.e., the slowing down of the longitudinal diffusion of a polymer chain by the head-on collision with other chains, can be treated by a model similar to that proposed by Cohen and Turnbull [112] for self diffusion of small molecules in a fluid. This model assumes that if at least one surrounding polymer chain exists within the critical hole ahead of a test chain, both collide, and this prevents the test chain from diffusing longitudinally. With this assumption, we express the longitudinal diffusion coefficient Dp of the test chain as... 

Next, it will be helpful to anticipate a description of experimental procedures and consider the magnitude of measured diffusion coefficients. The self-diffusion coefficients for ordinary liquids with small molecules are of the order of magnitude 10 9 m2 s for colloidal substances, they are typically of the order 10"11 m2 s l. In the next section, we see that for spherical particles the diffusion coefficient is inversely proportional to the radius of the sphere. Therefore, every increase by a factor of 10 in size decreases the diffusion coefficient by the same factor. Qualitatively, this same inverse relationship applies to nonspherical particles as well. Once again, we see that diffusion decreases in importance with increasing particle size, precisely those conditions for which sedimentation increases in importance. For larger particles, for which D is very small, the diffusion coefficient also becomes harder to measure. For... 

In polymers, the field-gradient spin-echo methods of measuring self-diffusion have been useful in three more or less distinct areas, the diffusion of polymers in their own melt and in concentrated solutions, in dilute and semidilute solutions, and the diffusion of penetrants and diluents in polymer hosts. A fourth category, the diffusion of bulky or flexible molecules in polymer hosts, is useful for subject matter not closely associated with the first and third category. It should be noted that the work reviewed here represents only a small fraction of the diffusion studies in polymers, including those using other NMR methods. 

The diffusion of small molecules in rubbers is of both theoretical and practical importance. The theories of diffusion based on consideration of free volume can be tested by measurement of self-diffusion using methods such as pulsed field gradient NMR. Selfdiffusion of small molecules must be understood for applications of rubbers as seals in contact with solvents, and for example for diffusion of plasticisers and other small molecules. 

Functional properties and stability of rubbery materials Chapters 1, 3, 4, 7, 12 and 13, give examples of applications of spectroscopic techniques for the characterisation of thermal stability and degradation, kinetics of thermal decomposition, ageing, oxidation and weathering, self-diffusion of small molecules in rubbery materials, adhesion of rubbers to metals, fluid adsorption and swelling. 

Self-Diffusivity Self-diffusivity is denoted by DA A and is the measure of mobility of a species in itself for instance, using a small concentration of molecules tagged with a radioactive isotope so they can be detected. Tagged and untagged molecules presumably do not have significantly different properties. Hence, the solution is ideal, and there are practically no gradients to force or "drive diffusion. This kind of diffusion is presumed to be purely statistical in nature. 

Local motions which occur in macromolecular systems can be probed from the diffusion process of small molecules in concentrated polymeric solutions. The translational diffusion is detected from NMR over a time scale which may vary from about 1 to 100 ms. Such a time interval corresponds to a very large number of elementary collisions and a long random path consequently, details about mechanisms of molecular jump are not disclosed from this NMR approach. However, the dynamical behaviour of small solvent molecules, immersed in a polymer melt and observed over a long time interval, permits the determination of characteristic parameters of the diffusion process. Applying the Langevin s equation, the self-diffusion coefficient Ds is defined as... 

Since the pioneering work of Stejskal, the pulse field gradient method is currently used to characterize the diffusion process of small molecules or of macromolecules in dilute or semi-dilute solutions [18-20]. In this Chapter, the NMR approach is illustrated from the self-diffiision of ( dohexane molecules through polybutadiene. Variations of the Ds self-diffusion coefficient of cyclohexane in polybutadiene have been reported as a temperature function considering several concentrations [21]. 

Examples of Ihe deterniinalioii of self-diffusion coefficients in solids are Ihe diffusion of hydrogen ions and water molecules (labelled with T and O, respectively) in alums, of Cl (labelled with Cl) in AgCl, and of 1 (labelled with l) in Agl. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radio-tracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. 

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