Self-diffusion coefficients experiments

Holz, M Lucas, O Muller, C, NMR in the Presence of an Electric Current, Simultaneous Measurements of Ionic Mobilities, Transference Numbers, and Self-Diffusion Coefficients Using an NMR Pulsed-Gradient Experiment, Journal of Magnetic Resonance 58, 294, 1984. Hooper, HH Baker, JP Blanch, HW Prausnitz, JM, Swelling Equilibria for Positively Ionized Polyacrylamide Hydrogels, Macromolecules 23, 1096, 1990. 

An important technical development of the PFG and STD experiments was introduced at the beginning of the 1990s the Diffusion Ordered Spectroscopy, that is DOSY.69 70 It provides a convenient way of displaying the molecular self-diffusion information in a bi-dimensional array, with the NMR spectrum in one dimension and the self-diffusion coefficient in the other. While the chemical-shift information is obtained by Fast Fourier Transformation (FFT) of the time domain data, the diffusion information is obtained by an Inverse Laplace Transformation (ILT) of the signal decay data. The goal of DOSY experiment is to separate species spectroscopically (not physically) present in a mixture of compounds for this reason, DOSY is also known as "NMR chromatography."... 

These experiments suggest that as the long time self-diffusion coefficient approaches zero the relaxation time becomes infinite, suggesting an elastic structure. In an important study of the diffusion coefficients for a wide range of concentrations, Ottewill and Williams14 showed that it does indeed reduce toward zero as the hard sphere transition is approached. This is shown in Figure 5.6, where the ratio of the long time diffusion coefficient to the diffusion coefficient in the dilute limit is plotted as a function of concentration. 

Therefore we expect Df, identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient D KRg 1) as the salt concentration is increased. The above result for KRg 1 limit is analogous to the Nernst-Hartley equation reported in Ref. 33. The theory described here accounts for stmctural correlations inside poly electrolyte chains. 

At low Q the experiments measure the collective diffusion coefficient D. of concentration fluctuations. Due to the repulsive interaction the effective diffusion increases 1/S(Q). Well beyond the interaction peak at high Q, where S(Q)=1, the measured diffusion tends to become equal to the self-diffusion D. A hydrodynamics factor H(Q) describes the additional effects on D ff=DaH(Q)/S Q) due to hydrodynamics interactions (see e.g. [342]). Variations of D(Q)S(Q) with Q (Fig. 6.28) may be attributed to the modulation with H(Q) displaying a peak, where S(Q) also has its maximum. For the transport in a crowded solution inside a cell the self-diffusion coefficient is the relevant parameter. It is strongly... 

While D issuing from these experiments is not strictly the diffusion coefficient of water per se, but rather that of H throughout the ensemble of environments in the hydration microstructure, these authors rationalized that it could in fact be identified with D at both high and low water contents. It should be appreciated that self-diffusion coefficients measured in this way reflect fundamental hopping events on a molecular scale. 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

Figure 4.4-2 Pulse-echo sequence in an NMR experiment for the measurement of self-diffusion coefficients.

Experiments snch as the one illnstrated in Fignre 4.38 not only give us self-diffusion coefficients for certain snbstances, bnt as the temperatnre of the experiment is varied, they give us the temperature dependence of the process and a measurement of the activation energy barrier to diffnsion. Diffusion in solid systems, then, can be modeled as an activated process that is, an Arrhenius-type relationship can be written in which an activation energy, Ea, and temperatnre dependence are incorporated, along with a preexponential factor. Do, sometimes called ht frequency factor ... 

Conclusion the self-diffusion coefficient DA cannot be determined solely by tracer experiments (mean square tracer displacement). Either information from non-equi-... 

To dearly distinguish between these two modes of solvent penetration of the gel, we immersed poly(acrylamide-co-sodium methacrylate) gels swollen with water and equilibrated with either pH 4.0 HQ or pH 9.2 NaOH solution into limited volumes of solutions of 10 wt % deuterium oxide (DzO) in water at the same pHs. By measuring the decline in density of the solution with time using a densitometer, we extracted the diffusion coefficient of D20 into the gel using a least squares curve fit of the exact solution for this diffusion problem to the data [121,149]. The curve fit in each case was excellent, and the diffusion coefficients obtained were 2.3 x 10 5cm2/s into the ionized pH 9.2 gel and 2.4 x 10 5 cm2/s into the nonionized pH 4.0 gel. These compare favorably with the self diffusion coefficient of D20, which is 2.6 x 10 5 cm2/s, since the presence of the polymer can be expected to reduce the diffusion coefficient about 10% in these cases [150], In short, these experiments show that individual solvent molecules can rapidly redistribute between the solution and the gel by a Fickian diffusion process with diffusion coefficients slightly less than in the free solution. 

Field gradient NMR has been employed to determine the self-diffusion coefficient of a Pluronic triblock, and the hydrodynamic radius has been compared to DLS measurements on the same system (Almgren et al. 1992). NMR was found to give a somewhat lower value for the hydrodynamic radius than DLS. However, at infinite dilution the values obtained from the two techniques are the same. A similar observation has been made for eye I o - PB027P H 0,44 in aqueous solution (Yu et al. 1996c). Tin s effect has been attributed (Almgren et al. 1995) to the difference in dynamic averaging for the DLS and NMR experiments. In DLS,... 

The dramatic increase of water density at a charged surface was observed by Toney et al. in their in situ X-ray scattering experiments, which has not yet been confirmed by simulation results.58,70 In another MD simulation work, Kiselev et al. found that selfdiffusion coefficient strongly decreases with increasing electric field.27 However, no difference between the self-diffusion coefficients for motion parallel and perpendicular to the external field was observed. 

Diffusions NMR spectroscopy (e.g. PGSE = Pulsed Gradient Spin Echo STE = Stimulated Echo DOSY = Diffusion Ordered Spectroscopy) is a straightforward and accurate method for determination of the self-diffusion coefficient of a molecule. Its principal use in dendrimer chemistry is for size determination of dissolved dendrimers since the self-diffusion coefficient is directly correlated with the hydrodynamic radius of the molecule via the Stokes-Einstein equation [24]. Although one-dimensional and multidimensional diffusion NMR experiments can thus make an important contribution to structural characterisation of dendrimers, they have been used comparatively rarely until recently [25, 26]. 

As discussed in Section 12.4 the PFGE experiment allows the measurement of the Xe self-diffusion coefficient in arbitrary materials. 

As schematically shown in Figure 12.5 the self-diffusion coefficient D can be determined from the PFGE experiment for different values of A. For normal diffusion, for which Fick s law holds 1, D is independent of A and the average square distance the diffusing particles cover during the diffusion time A is directly proportional to A (Einstein relationship) ... 

The Kirkendall effect arises from the different values of the self-diffusion coefficients of the components of a substitutional solid solution, determined by Matano s method. Matano s interface is defined by the condition that as much of the diffusing atoms have migrated away from the one side as have entered the other. If DA = DB, its position coincides with the initial interface between phases A and B. If I)A f DB, it displaces into the side of a faster diffusant (see Fig. 1.22c). Note that KirkendalFs discovery only relates to disordered phases. It was indeed a discovery since at that time most reseachers considered the relation l)A = DB to hold for any solid solution of substitutional type. KirkendalFs experiments showed that in fact this is not always the case. 

When applying this relationship, one must be aware of (z) all diffusion mechanisms operative in a non-growing compound, (zz) the concentration of vacancies of a given component in this compound and (zzz) the value of its self-diffusion coefficient associated with the vacancy mechanism. In view of the lack of specially planned experiments aimed at obtaining all necessary data for the same compound, including reaction- and self-diffusion coefficients of its components, at present only calculations based on the results compiled from several works are possible. 

While the clathrate model is attractive, it is not correct to assume that the water is organized in some long-lived structure the observation that the self-diffusion coefficient for co-sphere water is larger than that for the solute rules this out. However, the rotational correlation time is shorter for ethanol and t-butyl alcohol in water (in the clathrate cage ) than in the pure liquid (Goldammer and Hertz, 1970 Goldammer and Zeidler, 1969). Nmr experiments show that in water the solvent dipole moments point away from the apolar groups (Hertz and Radle, 1973). 

Self-Diffusion Coefficients of Ions and Solvent Water (Dj in a 2.2 molal Ltl Solution Obtained from MD Simulation and Experiments at 305... 

Results of Self-Diffusion Experiments. Self-diffusion coefficient studies with fused salts really began to gather momentum after radioisotopes became... 

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