Self diffusivity, concentration dependence

A rapid increase in diffusivity in the saturation region is therefore to be expected, as illustrated in Figure 7 (17). Although the corrected diffusivity (Dq) is, in principle, concentration dependent, the concentration dependence of this quantity is generally much weaker than that of the thermodynamic correction factor d ap d a q). The assumption of a constant corrected diffusivity is therefore an acceptable approximation for many systems. More detailed analysis shows that the corrected diffusivity is closely related to the self-diffusivity or tracer diffusivity, and at low sorbate concentrations these quantities become identical. 

Rymden, R. Stilbs, P. (1985b). Concentration and molecular weight dependence of counterion self-diffusion in aqueous poly(acrylic acid) solutions. Journal of Physical Chemistry, 89, 3502-5. 

NMR Self-Diffusion of Desmopressin. The NMR-diffusion technique (3,10) offers a convenient way to measure the translational self-diffusion coefficient of molecules in solution and in isotropic liquid crystalline phases. The technique is nonperturbing, in that it does not require the addition of foreign probe molecules or the creation of a concentration-gradient in the sample it is direct in that it does not involve any model dependent assumptions. Obstruction by objects much smaller than the molecular root-mean-square displacement during A (approx 1 pm), lead to a reduced apparent diffusion coefficient in equation (1) (10). Thus, the NMR-diffusion technique offers a fruitful way to study molecular interactions in liquids (11) and the phase structure of liquid crystalline phases (11,12). 

To date, D coefficients of carbohydrates established with the PFGSE approactf - " have been undertaken to (1) validate the theoretical self-diffusion coefficients calculated from MD trajectories, (2) demonstrate the complexation of lanthanide cations by sugars,(3) probe the geometry of a molecular capsule formed by electrostatic interactions between oppositely charged P-cyclodextrins, (4) study the influence of concentration and temperature dependence on the hydrodynamic properties of disaccharides, and (5) discriminate between extended and folded conformations of nucleotide-sugars. ... 

Self-difFusion coefficients were measured with the NMR spin-echo method and mutual diffusion coefficients by digital image holography. As can be seen from Figure 4.4-3, the diffusion coefficients show the whole bandwidth of diffusion coefficient values, from 10 m s on the methanol-rich side, down to 10 on the [BMIM][PFg]-rich side. The concentration dependence of the diffusion coefficients on the methanol-rich side is extreme, and shows that special care and attention should be paid in the dimensioning of chemical processes with ionic Hquids. 

Because field-gradient spin-echo measurements of D depend on no driving force such as a concentration, temperature, or velocity gradient, etc., they reflect Brownian motion of the molecules in the laboratory reference frame, and are usually referred to as self-diffusion. These attributes are further discussed in Sections 2 and 3. 

Callaghan and Pinder48,49 used the PGSE method in a detailed examination of the diffusion of linear polystyrene molecules dissolved in CC14. They applied standard dilute hydrodynamic theory to self-diffusion (as distinct from mutual diffusion) and identified the lowest-order concentration dependence of D with the coefficient kF, writing... 

The primary difference between D and D is a thermodynamic factor involving the concentration dependence of the activity coefficient of component 1. The thermodynamic factor arises because mass diffusion has a chemical potential gradient as a driving force, but the diffusivity is measured proportional to a concentration gradient and is thus influenced by the nonideality of the solution. This effect is absent in self-diffusion. 

In a typical tracer self-diffusion experiment, the tracer concentration probability, p, depends upon position, whereas the total interstitial concentration probability, p, does not. 

Although there has not been much theoretical work other than a quantitative study by Hynes et al [58], there are some computer simulation studies of the mass dependence of diffusion which provide valuable insight to this problem (see Refs. 96-105). Alder et al. [96, 97] have studied the mass dependence of a solute diffusion at an infinite solute dilution in binary isotopic hard-sphere mixtures. The mass effect and its influence on the concentration dependence of the self-diffusion coefficient in a binary isotopic Lennard-Jones mixture up to solute-solvent mass ratio 5 was studied by Ebbsjo et al. [98]. Later on, Bearman and Jolly [99, 100] studied the mass dependence of diffusion in binary mixtures by varying the solute-solvent mass ratio from 1 to 16, and recently Kerl and Willeke [101] have reported a study for binary and ternary isotopic mixtures. Also, by varying the size of the tagged molecule the mass dependence of diffusion for a binary Lennard-Jones mixture has been studied by Ould-Kaddour and Barrat by performing MD simulations [102]. There have also been some experimental studies of mass diffusion [106-109]. 

The self-diffusion of the individual components is strongly affected by the formation of micelles in the solution. This applies to the surfactant, the counterion, the water, and to solubilized molecules. As illustrated in Fig. 2.11 for sodium dodecyl sulfate, surfactant and counterion diffusion are very weakly dependent on concentration below the CMC while a marked decrease in the micellar region is observed for the surfactant and a less marked one for the counterion37. Water diffusion shows a stronger concentration dependence below the CMC than above it. Self-diffusion studies using radioactive tracers have been performed to obtain information on CMC, on counterion binding, on hydration and on intermicellar interactions and shape changes. 

Counterion binding is not a well defined quantity, with various experimental techniques weighing the ion distribution slightly differently. Thermodynamic methods (e.g. ion activities or osmotic coefficients) monitor the free counterion concentration, transport methods (e.g. ion self diffusion or conductivity) the counterions diffusing with the micelle, and spectroscopic methods (e.g. NMR) the counterions in close contact with the micelle surface. Measurement of the effect of Na+ counterions on the symmetric S-O stretching modes would also be expected to be highly dependent on the distance of the counterion from the micelle surface (similar to the NMR method). 

Theoretical formulas show that the self-diffusivity of interstitial metal atoms decreases with an increase in the concentration of included hydrogen, which blocks free interstitial sites. A calculation of the coefficient of self-diffusion in the QCA is presented in Fig. 8.14. To calculate concentration dependences of the self-diffusivity, authors used eHh = 0-6 kcal/mol [217]. The curves are normalized to a self-diffusivity of 2.9 x 1CT3 sm/sec at 0H = 0 [218]. As can be seen, the character of curves 1-3 and 5 substantially depends on the value of an = hh/shh, which reflects the difference between... 

However, the diffusivity also depends on the concentration of defects, which is also thermally activated according to (1.2). Hence, the self-diffusion coefficient D is described as... 

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