Retardation effects, range-dependence

Note first that in this older picture, for both the attractive (van der Waals) forces and for the repulsive double-layer forces, the water separating two surfaces is treated as a continuum (theme (i) again). Extensions of the theory within that restricted assumption are these van der Waals forces were presumed to be due solely to electronic correlations in the ultra-violet frequency range (dispersion forces). The later theory of Lifshitz [3-10] includes all frequencies, microwave, infra-red, ultra and far ultra-violet correlations accessible through dielectric data for the interacting materials. All many-body effects are included, as is the contribution of temperature-dependent forces (cooperative permanent dipole-dipole interactions) which are important or dominant in oil-water and biological systems. Further, the inclusion of so-called retardation effects, shows that different frequency responses lock in at different distances, already a clue to the specificity of interactions. The effects of different geometries of the particles, or multiple layered structures can all be taken care of in the complete theory [3-10]. 

Among the most important lessons learned from these studies is that exposures to toxicants can yield a wide spectrum of neurotoxic effects ranging from overt encephalopathy and severe mental retardation to subtle deficits in sensory, motor, and cognitive functions. These effects depend on the timing, magnitude, and duration of exposure and many other factors (Mendola et al., 2002). Multiple mechanisms, target molecules, biochemical pathways, and cellular processes may explain the assembly of effects attributable to exposures to these substances. 

At equilibrium conditions, at very low concentration, the elution volume of a macromolecule should be independent of the flow rate. However, with increasing molar mass in the UHMM range, in the absence of degradation, the elution volume strongly depends on the molar mass of the sample. This result does not depend on the concentration of the sample. This retardation effect occurs also at very low concentrations below the overlapping concentration c. The retardation of UHMM macromolecules has been studied by several workers it is a very complex effect and substantially stiU not well understood. The retardation effect is particularly meaningful in proximity to the exclusion limit of the columns and when the pore size approximately equals or is lower than the sizes of the macromolecules. A trivial conclusion is that for a successful fractionation of UHMM macromolecules without retardation effects, one must use SEC columns with ultralarge pore sizes. 

The value of the pH for optimum stability of silicic acid depends on what impurities are present in the solution. Traces of aluminum ions and to a lesser extent, iron, thorium, and beryllium ions tend to offset the effect of fluoride ion by forming complex fluorides and thus retard polymerization in this pH range. Depending on the purity of the solution, the pH of optimum stability may range from 1 to as high as 3-3.5. In silicic acid. solutions free from aluminum impurity, as little as 1 ppm of fluorine has a marked effect on the rate of polymerization in acid solution. 

In the range from 10 to 100 nm, retardation effects become relevant and the distance dependency changes to Ilvdw °c h [445]. 

Recently, measurements in the non-retarded range have been made, the most notable being those of Tabor and co-workers95 108, on the attraction between cleaved layers of mica stuck to two crossed cylinders. In addition to providing successful tests of the distance dependence of the van der Waals attraction, the effects of adsorbed monolayers have also been studied, again giving reasonable agreement with theoretical predictions. 

---