Stem layer, definition

Not all of the ions in the diffuse layer are necessarily mobile. Sometimes the distinction is made between the location of the tme interface, an intermediate interface called the Stem layer (5) where there are immobilized diffuse layer ions, and a surface of shear where the bulk fluid begins to move freely. The potential at the surface of shear is called the zeta potential. The only methods available to measure the zeta potential involve moving the surface relative to the bulk. Because the zeta potential is defined as the potential at the surface where the bulk fluid may move under shear, this is by definition the potential that is measured by these techniques (3). 

More pertinent for our purposes is the problem to what extent ionic double layers and the interfacial polarization are additive. In the absence of specific adsorption the problem is relatively minor the countercharge resides in the diffuse part, where solvent polarization is negligible (or neglected by definition) and the Interfacial polarization more or less coincides with the Stem layer, ignoring any contribution from the solid. To a first rough approximation the two potential drops are spatially separated and hence additive, so that... 

The applicability of continuum theories, such as the Poisson-Boltzmann model, in nanoscale is the most concerned issue in this field yet. Numerous conflicting results were reported in literature. We have done careful MD simulations of EOF and compared the ion distributions with the PB predictions rigorously to clarify the applicability of the continuum theory. To compare the descriptions from two different scales, above all, the observers have to be stand on the same base to avoid definition gaps. First, when presenting the MD results, the bin size should not be smaller than the solvent molecular diameter in comparison with the continuum theory otherwise, the MD results are not the macroscopic properties at the same level of the continuum. A second gap which departs the MD results from the PB predictions is the effect of the Stem layer. As well known, the PB equation describes only the ion distribution in diffusion (outer) layer of the electric double layer (EDL) [1]. In the continuum theory, the compact (iimer) layer of EDL is too thin (molecular scale) to be considered, and therefore, the PB equation almost governs the ion distribution in the whole domain. However, in nanofluidics the iimer layer which is also termed as Stem layer is comparable to the channel in size. The PB equation is not able to govern the ion behavior in the Stem layer in theory. Therefore, if one compares the MD... 

Note that it may be surprising that a chemical term is considered in Eq. (3), whereas we have supposed that no chemical reaction term was involved within the stagnant layer. As explained in Chapter 1, this stems from the fact that the effect of any chemical reaction within the diffusion layer depends on the relative magnitude of k5 /D versus unity. For usual laboratory conditions, 8 10 cm and D 5 x IC cm s and then 5 /D is of the order of 0.2 s. Thus, provided k is less than approximately 1 s it has no tangible effect on the concentration profiles of the species, whereas it has a definite effect in the bulk solution due to the long reaction times (usually longer or comparable to half an hour). In practice it is important to decide when the simplification in Eq. (2) or (3) applies to a given experimental situation. The discussion just presented affords a simple answer to the problem. Indeed, consider the electron transfer reaction in Eq. (5), possibly followed by a chemical step in Eq. (6). 

Apart from these four main techniques there are many other techniques but their applicability is often limited to some elements. MAS-NMR technique turns out to be very useful for determining if non zero nuclear spin elements are incorporated into the lattice because of its sensitivity to local environment symmetry. Also in favorable cases techniques as Mossbauer, diffuse reflectance UV-Vis and ESR spectroscopies are very helpful while high resolution electron micrographs and simulated imaging are of great interest (38) with in addition the possibility of specific chemical analysis at nanometer scale by EDX-STEM. At last XPS may be informative to determine if surface and bulk compositions are identical or not, although the technique by definition is only sensitive to the first top layers (1 to 2 nm) while zeolitic features concern the whole material. Some examples will be given below. 

Two topical issues may be mentioned. The first is the definition of the potentials that are measured by different techniques, say by AFM, electrokinetically and externally imposed, and their relationships [11], The second is of a more theoretical nature and concerns modeling of the nondiffuse part of the double layer. The classical approach is through Stem theory [2], which in most cases is adequate, although it requires two additional parameters. A more recent development is in terms of ion correlations, essentially an advanced statistical theory whereby all coulombic ion-ion and ion-surface interaction pairs are counted and statistically summed [2]. This is a step forward over the smeared-out models of Gouy and Stern. The issue here is that cases must be found where deviations from Gouy theory cannot be interpreted on the basis of the Stem model... 

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