Diffusion paradox

The above experimental results largely relate to spectroscopic techniques, which do not give direct information about the spatial scale of the molecular motions. The size of the spatial heterogeneities is estimated by indirect methods such as sensitivity of the dynamics to the probe size or from the differences between translational and rotational diffusion coefficients (rotation-translation paradox). It might be expected that the additional spatial information provided by neutron scattering could help to discriminate between the two scenarios proposed. 

On the other hand, when the membrane is saturated, transport still occurs. This transport must be due to a hydraulic-pressure gradient because oversaturated activities are nonphysical. In addition, Buechi and Scherer found that only a hydraulic model can explain the experimentally observed sharp drying front in the membrane. Overall, both types of macroscopic models describe part of the transport that is occurring, but the correct model is some kind of superposition between them. - The two types of models are seen as operating fully at the limits of water concentration and must somehow be averaged between those limits. As mentioned, the hydraulic-diffusive models try to do this, but from a nonphysical and inconsistent standpoint that ignores Schroeder s paradox and its effects on the transport properties. 

CMP processes also leave a metallic contamination typically in the 10"-10 at/cm range. These contaminants arise from the outcropping metals, the slurries, and the mechanical environment of the polishers. In front-end applications (STI), these levels are prohibited because they are not compatible with the following hot processes. In the case of back-end steps, these parasitic metals must be removed as well, even if this seems more paradoxical with the use of metallization steps. Indeed a large amount of charges at the interconnection level or the presence of mobile ions such as sodium or potassium can induce disturbances during the electrical information transfer. Furthermore, a superficial conductive metallic contamination can generate shorts between two adjacent lines by percolation conduction mechanism. And last but not least, fast diffusers such as copper can reach... 

As just mentioned, there are a large number of unsolved problems in membrane biophysics, including the questions of local anisotropic diffusion, hysteresis, protein-lipid phase separations, the role of fluctuations in membrane fusion, and the mathematical problems of diffusion in two dimensions Stokes paradox). 

There are many sources of this paradoxical situation, in which a theoretical understanding lags far behind experiment in such a practically relevant area as electro-diffusion. There was a period of intense qualitative development in this area in the 1920s until the early 1950s when the modern classics of chemical physics developed the theory of electrolytic conductance and related phenomena [11]—[13]. These works were mainly concerned with the mean field approach to microscopic mechanisms determining such properties of electrolyte solutions as ion diffusivity, dielectric susceptibility, etc. in particular, they were concerned with the effects of an externally applied stationary and alternating electric field upon the above properties... 

In order to understand the above questions/paradoxes, a mode coupling theoretical (MCT) analysis of time-dependent diffusion for two-dimensional systems has been performed. The study is motivated by the success of the MCT in describing the diffusion in 3-D systems. The main concern in this study is to extend the MCT for 2-D systems and study the diffusion in a Lennard-Jones fluid. An attempt has also been made to answer the anomaly in the computer simulation studies. 

Porstendorfer Mercer (1979) did similar experiments with 220Rn-laden air at 106 to 109 Bq m-3. Their diffusion tube had a central electrode and deposition was measured with and without an electrical field. Collection on the charged electrode was more efficient in moist than in very dry air (relative humidity, RH < 2%). In moist air, D was 6.8 x 10-6 m2 s 1 irrespective of whether the 212Pb was partially or wholly neutralised before deposition. In very dry air and low 220Rn concentrations, D was 4.7 x 10-6, and it was concluded that the charged component had D equal to 2.4 x 10-6 m2 s 1. Paradoxically, this would correspond to k = 1 x 10 4 m2 V-1 s 1, the mobility found by Jonassen Hayes (1972) for 222Rn decay products in moist air. In all Porstendorfer Mercer s experiments, the ageing time was very short. 

MacLeod, Christine (1991). The Paradoxes of Patenting Invention and its Diffusion in 18th and 19th Century Britain, France, and North America. Technology and Culture, 32 885-911. 

Motter, A.E., Zhou, C and Kurths,). Network synchronization, diffusion, and the paradox of heterogeneity. Phys Rev E Stat Nonlin Soft Matter Phys 2005,71 016116. 

In the Au/Al203/NiAl(100) system, hemispherical particles occur even at low coverage,7 unlike the situation with titania size distribution was narrow, and particles were stable to 600 K, implying low mobility of adsorbed atoms. Paradoxically, on alumina large particles migrate and coalesce faster than small ones, presumably because the metal-support interaction is weaker but with Au/FeO the diffusivity of atoms is higher due to a lower concentration of surface defects. 

To be sure, Clausius and Maxwell had given, much earlier, a kinetic interpretation of viscosity, heat conduction, and diffusion. They, however, confined themselves to stationary processes, and hence the paradox we are discussing did not arise. 

On a molecular scale there is no sharp boundary between hydrodynamically stagnant and movable solvent molecules. As discussed In sec. 2.2, the, say tangential, diffusion coefficient of water near many surfaces may be somewhat lower than in bulk, but it is not zero. The very existence of ionic conduction In the layer(s) adjacent to surfaces also points to non-zero mobility. Yet, phenomenologically such layers behave as immobilized. This looks like a paradox, but the phenomenon is encountered in other places as well. For Instance, a few percent of gelatin added to water may hydrodynamically immobilize the liquid completely, without markedly impairing ionic conduction or self-diffusion of dissolved ions. Macroscopic immobilization of a fluid is not in conflict with mobility on a molecular sceile. 

---