Solution translational diffusion

It is important to note that diffusion is not a universally defined term. In foods, the processes of self-diffusion of the polymer matrix molecules, selfdiffusion of solutes, translational diffusion of solutes, and diffusion of moisture and other liquids have not been well discerned among theorists. All of these diffusion or mobility-based processes may occur in foods and pharmaceuticals. Yet recent theories do not clearly and consistently address which of these processes are of significance to chemical reactions, and how changes in water content or a as well as T or Tg affect each of these types of diffusion. 

Diffusion-ordered NMR spectroscopy (DOSY) is a powerful tool for structural studies of molecular aggregates in solution. Translational diffusion coefficients (D) determined by DOSY correlate directly with the sizes and dimensions of aggregates. The diffusion coefficients of 18 and a 1 1 mixture of 18 and 19 at a low concentration in chloroform-(ij are 4.09 x 10and 2.57 x 10 ° m S", respectively. The ratio of D1S.19/D19 of 0.63 was reasonably close to the theoretical range of 0.59 to 0.60 expected for a linear trimer. These results confirmed the formation of oligomeric assemblies even at low concentrations. 

We have applied FCS to the measurement of local temperature in a small area in solution under laser trapping conditions. The translational diffusion coefficient of a solute molecule is dependent on the temperature of the solution. The diffusion coefficient determined by FCS can provide the temperature in the small area. This method needs no contact of the solution and the extremely dilute concentration of dye does not disturb the sample. In addition, the FCS optical set-up allows spatial resolution less than 400 nm in a plane orthogonal to the optical axis. In the following, we will present the experimental set-up, principle of the measurement, and one of the applications of this method to the quantitative evaluation of temperature elevation accompanying optical tweezers. 

For example, in the case of PS and applying the Smoluchowski equation [333], it is possible to estimate the precipitation time, fpr, of globules of radius R and translation diffusion coefficient D in solutions of polymer concentration cp (the number of chains per unit volume) [334]. Assuming a standard diffusion-limited aggregation process, two globules merge every time they collide in the course of Brownian motion. Thus, one can write Eq. 2 ... 

Reactions described earlier were not limited by rotational diffusion of reactants. It is evident that such bimolecular reactions can occur that are limited not by translational diffusion but by the rate of reactant orientation before forming the TS. We discussed the reactions of sterically hindered phenoxyl recombination in viscous liquids (see Chapter 15). We studied the reaction of the type radical + molecule, which are not limited by translational diffusion in a solution but are limited by the rate of reactant orientation in the polymer matrix [28]. This is the reaction of stable nitroxyl radical addition to the double bond of methylenequinone. 

The motions of a molecular system, for example a solution, occur on many time scales. There are very fast electronic motions, the basic mechanism in chemical reactions then, the nuclear motions, vibrations, librations, rotations, and translations (diffusion). In the Bom-Oppenheimer spirit, one can consider the electronic motion as separated from the nuclear motions, thus one can talk of micro-deformations to be treated quantum mechani-... 

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 review aims to highlight some recent studies that involve liquid crystals and show the utility of newer pulse NMR techniques in LC. They may involve solutes dissolved in ordered phases and their applications, or may involve the molecular ordering, rotational and/or translational diffusion of solvent molecules. Deuterium NMR spectroscopy has demonstrated many advantages over other nuclei like H and 13C, but the need to specifically deuteriate mesogens is sometimes a major drawback. 13C NMR spectroscopy seems to be useful since non-enriched samples can often be used. However, the use of 13C NMR in semi-solids like LC often requires more sophisticated NMR techniques and instrumentation. There are indeed many uncharted... 

Fig. 8.1. Stokes and free volume translational diffusion processes. Black circles solute molecules. White circles solvent molecules.

Hydrodynamic properties, such as the translational diffusion coefficient, or the shear viscosity, are very useful in the conformational study of chain molecules, and are routinely employed to characterize different types of polymers [15,20, 21]. One can consider the translational friction coefficient, fi, related to a transport property, the translational diffusion coefficient, D, through the Einstein equation, applicable for infinitely dilute solutions ... 

But p decreases with salt concentration with an apparent exponent of k which changes from 0 at low salt concentration to — at high salt concentrations. The N-independence of p arises from a cancellation between hydrodynamic interaction and electrostatic coupling between the polyelectrolyte and other ions in the solution. It is to be noted that the self-translational diffusion coefficient D is proportional to as in the Zimm model with full... 

For small chains in solution the translational diffusion significantly contributes to the overall decay of Schain(Q>0- Therefore precise knowledge of the centre of mass diffusion is essential. Combing dynamic light scattering (DLS) and NSE revealed effective collective diffusion coefficients. Measurements at different concentrations showed that up to a polymer volume fraction of 10% no concentration dependence could be detected. All data are well below the overlap volume fraction of (p =0.23. Since no -dependence was seen, the data may be directly compared with the Zimm prediction [6] for dilute solutions ... 

Figure 5.8 presents typical spectra taken on both polymer solutions at 300 K (a) and 378 K (b). The PDMS data are represented by open symbols, while the PIB data are shown by full symbols. Let us first look at the data at 378 K. At Q=0.04 A"i (QR =0.S) we are in the regime of translational diffusion, where the contributions of the intrachain modes amount to only 1%. There the spectra from both polymers are identical. Since both polymers are characterized by equal chain dimensions, the equality of the translational diffusion coefficients implies that the draining properties are also equal. In going to larger Q-values, gradually the spectra from the PlB-solutions commences to decay at later times. This effect increases with increasing Q and is maximal at Q=0.4 A" (see Fig. 5.8a). 

Monteiro, C. Herve du Penhoat, C. Translational Diffusion of Dilute Aqueous Solutions of Sugars as Probed by NMR and Hydrodynamic Theory. J. Phys. Chan. A 2001, 105, 9827-9833. 

To explain the Green function method for the formulation of Dx, D and D, of the fuzzy cylinder [19], we first consider the transverse diffusion process of a test fuzzy cylinder in the solution. As in the case of rodlike polymers [107], we imagine two hypothetical planes which are perpendicular to the axis of the cylinder and touch the bases of the cylinder (see Fig. 15a). The two planes move and rotate as the cylinder moves longitudinally and rotationally. Thus, we can consider the motion of the cylinder to be restricted to transverse diffusion inside the laminar region between the two planes. When some other fuzzy cylinders enter this laminar region, they may hinder the transverse diffusion of the test cylinder. When the test fuzzy cylinder and the portions of such other cylinders are projected onto one of the hypothetical planes, the transverse diffusion process of the test cylinder appears as a two-dimensional translational diffusion of a circle (the projection of the test cylinder) hindered by ribbon-like obstacles (cf. Fig. 15a). 

Fig. 16a, b. Computer simulation results for rodlike polymers in solution a the translational diffusion coefficients [122,123] b the rotational diffusion coefficient [119,122,123]... 

In the detection of the autocorrelation functions in self-beat spectroscopy, solution polydispersity can lead to a non-exponential form. If we assume that there are no contributions to the autocorrelation function except those from translational diffusion for the different types of molecules, we can consider two simple cases a continuous distribution of solute particle sizes and several distinct components in a solution. We shall approach the two cases by determining their effect on the observed correlation function. 

Considerable progress has been made in going beyond the simple Debye continuum model. Non-Debye relaxation solvents have been considered. Solvents with nonuniform dielectric properties, and translational diffusion have been analyzed. This is discussed in Section II. Furthermore, models which mimic microscopic solute/solvent structure (such as the linearized mean spherical approximation), but still allow for analytical evaluation have been extensively explored [38, 41-43], Finally, detailed molecular dynamics calculations have been made on the solvation of water [57, 58, 71]. 

In dynamic light scattering (DLS), or photon correlation spectroscopy, temporal fluctuations of the intensity of scattered light are measured and this is related to the dynamics of the solution. In dilute micellar solutions, DLS provides the z-average of the translational diffusion coefficient. The hydrodynamic radius, Rh, of the scattering particles can then be obtained from the Stokes-Einstein equation (eqn 1.2).The intensity fraction as a function of apparent hydrodynamic radius is shown for a triblock solution in Fig. 3.4. The peak with the smaller value of apparent hydrodynamic radius, RH.aPP corresponds to molecules and that at large / Hs,Pp to micelles. 

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