Diffusivity agreement between macroscopic

Fig. 25a, b. a. Collective diffusion coefficient D of a NIPA gel as determined by the kinetics of volume change, as a function of temperature. It diminishes at the critical point, b. collective diffusion coefficient as determined from the density fluctuations by use of photon correlation spectroscopy. The agreement between the results obtained from dynamics of microscopic fluctuations and from kinetics of macroscopic volume change is excellent considering the difficulty in the dynamic experiments... 

The techniques outlined above have been used to study diffusion in a wide range of zeolite systems. In general we find that there is reasonable agreement between the different macroscopic methods and also between the microscopic methods (QENS, and PFG NMR). However, although for several systems the macroscopic and microscopic measurements are also consistent, there are many systems for which we see significant discrepancies between the two classes of measurements. 

In principle, we can distinguish (for surfactant self-assemblies in general) between a microstructure in which either oil or water forms discrete domains (droplets, micelles) and one in which both form domains that extend over macroscopic distances (Fig. 7a). It appears that there are few techniques that can distinguish between the two principal cases uni- and bicontinuous. The first technique to prove bicontinuity was self-diffusion studies in which oil and water diffusion were monitored over macroscopic distances [35]. It appears that for most surfactant systems, microemulsions can be found where both oil and water diffusion are uninhibited and are only moderately reduced compared to the neat liquids. Quantitative agreement between experimental self-diffusion behavior and Scriven s suggestion of zero mean curvature surfactant monolayers has been demonstrated [36]. Independent experimental proof of bicontinuity has been obtained by cryo-electron microscopy, and neutron diffraction by contrast variation has demonstrated a low mean curvature surfactant film under balanced conditions. The bicontinuous microemulsion structure (Fig. 7b) has attracted considerable interest and has stimulated theoretical work strongly. 

Another reassuring result is the agreement between the D, values found by NMR or tracer techniques or determined at small momentum transfers by QNS on solids or liquids. From this well established macroscopic value, one can hope that preliminary QNS results obtained at higher Q values will be confirmed and extended. Indeed they are expected to lead either to the determination of characteristic jump-lengths and residence times in solids or to the finding of an abnormal proton diffusivity in solutions. This is a domain where QNS can bring a unique and important contribution to the understanding of the conduction mechanism. 

Tournassat et al. (2009) compared the BSM and TLM models with molecular dynamics simulations of a montmorillonite/water interface at the pore scale in 0.1 M NaCl. Simulation-derived values were compared with macroscopic model results obtained from the classical models. Although the Na concentration profile is well reproduced in the diffuse layer, anion exclusion is overestimated by the BSM and TLM theories under the experimental conditions employed the agreement between molecular dynamics simulated and modeled diffuse-layer composition is less accurate with TLM than with BSM. However, the potentials at the three planes of interest are accurately reproduced. It was also showed that molecular dynamics simulations can be used to constrain BSM parameters or, in combination with zeta potential measurements, TLM parameters, by providing suitable values for the capacitance parameters. 

Weber and Newman do the averaging by using a capillary framework. They assume that the two transport modes (diffusive for a vapor-equilibrated membrane and hydraulic for a liquid-equilibrated one) are assumed to occur in parallel and are switched between in a continuous fashion using the fraction of channels that are expanded by the liquid water. Their model is macroscopic but takes into account microscopic effects such as the channel-size distribution and the surface energy of the pores. Furthermore, they showed excellent agreement with experimental data from various sources and different operating conditions for values of the net water flux per proton flux through the membrane. 

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