Range decay length

As already noted in the Introduction, such a behavior can be attributed to two contrary effects. For small particles, i.e., particle sizes in the transition and free molecular range, the potential well is not deep whereas the decay length of the potential is greater than the particle size. Therefore, the collisions may be less effective because of the shallow potential well (i.e., the sticking probability may be less than unity), whereas the rate of collisions between the particles may increase because of the increase in the effective collision cross section caused by the increased... 

In a number of experiments,1 the measured repulsive force between two mica plates was greater than that predicted on the basis of the Poisson-Boltzmann equation, when the distance between them was below about 40 A. This higher repulsive force arises only for sufficiently large ionic strengths and has a decay length in the range of 3-10 A. In contrast, the repulsive force between two parallel phospholipid bylayers falls off with a decay length between... 

When the surfaces were not rigid, as in the case of lipid bilayers, the oscillations of the force were smoothed out and the interactions became monotonic. The short-range repulsion between neutral7 or weakly charged8 bilayers, often called hydration force, was exhaustively investigated experimentally and was found to have an exponential decay, with a decay length between 1.5 and 3 A, while the preexponential factor varied by more than an order of magnitude. 

We will use in the calculations l = 2.76 A (which corresponds to the distance between molecules in the structure ofice I, as compared to about 2.9 Afor molecules in water), and e = 80. For the local dielectric constant, we will assume e" = 1, which constitutes a lower bound. In a perfect tetrahedral coordination, the average distance between two successive water layers is A = (4/3)1, and the decay length of the hydration interaction calculated using eq 37 is X = 2.96 A. It should be noted that the latter value is in the range determined experimentally for the hydration force between phospholipid bilayers.4 Lower values ofX can be obtained for higher e". For the distance between the center of the ion pair and the interface (located at the boundary of the first organized water layer), the value A = 1.0 A was selected. 

It is well-known that free films of water stabilized by surfactants can exist as somewhat thicker primary films, or common black films, and thinner secondary films, or Newton black films. The thickness of the former decreases sharply upon addition of electrolyte, and for this reason its stability was attributed to the balance between the electrostatic double-layer repulsion and the van der Waals attraction. A decrease in its stability leads either to film rupture or to an abrupt thinning to a Newton black film, which consists of two surfactant monolayers separated by a very thin layer ofwater. The thickness of the Newton black film is almost independent of the concentration of electrolyte this suggests that another repulsive force than the double layer is involved in its stability. This repulsion is the result of the structuring of water in the vicinity of the surface. Extensive experimental measurements of the separation distance between neutral lipid bilayers in water as a function of applied pressure1 indicated that the hydration force has an exponential behavior, with a decay length between 1.5 and 3 A, and a preexponential factor that varies in a rather large range. 

The various qualitative behaviors of the hydration force in different systems (either oscillatory [12] or monotonic [10], with various decay lengths (2—3 A [10] or about 10 A [13]), either independent of electrolyte concentration [10] or exhibiting strong specific ion effects [14]) appear to point out toward the existence of a number of different microscopic origins for the short range repulsions between surfaces immersed in water, in excess to those accounted by the DLVO theory. On the other hand, there are some striking similarities between the hydration forces in different systems. For example, the Molecular Dy-... 

Later an exceptionally long-range attractive force between mica surfaces made hydrophobic by LB deposition of a monolayer of dimethyldioctadecyl-ammonium bromide (DODAB) was measured by Christenson and Claesson [82], It was shown to be an exponentially decaying force with a decay-length of 12-13 nm in the distance range 20-80 nm. This force was noted to be up to 100 times stronger than the expected van der Waals attraction (Fig. 5). 

Figure 8.11 Decay lengths of an evanescent wave as a function ofy at t 650 nm. The range of the decay length is changed from 153 to 205 nm.

---