Effective decay length

The variation of the observable effective decay lengths is limited from below and above. The lower limit is the period for the surface perturbation distribution divided by 4tt the upper limit is one-half of the water correlation length. 

NaCI concentration (M) Effective decay length (nm) Debye length (nm)... 

The interactions between bare mica surfaces in 10 and 10 M KNO solutions were determined at pH = 3.5. In both cases an exponential type relation F(D) = 0-lcD was indicated, with decay lengths 1/k = 1.4 nm and 8 nm for the two salt concentrations, respectively, but with an effective surface potential tp = 40 mV, considerably lower than its value at the higher pH used in the PEO experiments (figure 6a, curve (a)). The lower value of p is probably the result of a lower net degre of ionization of the mica surface in the presence of the large H1" concentration (the low pH was used to ensure full ionization and polyelectrolyte). 

The effective sampling depth or penetration depth (dp) is representative of the characteristic decay length and represents the distance at which the intensity of the evanescent field has decayed to 1/e with respect to the maximum (at the interface), as defined by ... 

Figure 24 Gibbsean segregation effects illustrated by ratio of profile decay length with an oxygen leak to that without an oxygen leak plotted versus oxide heat of formation. The substrate was silicon, and the primary ion was Ar+. (From Ref. 81.)...

In order to explain this behavior, one may note that, as the particle size decreases, the potential well becomes less deep, whereas the ratio of the decay length of the potential and the particle size increases. Consequently, there are two opposing effects (1) the collisions become less effective because of the increase in the probability of escape of the particles... 

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... 

For the case of purely attractive forces (such as Lon-don-van der Waals forces) the length Sjr over which they act is a useful characteristic. An attractive force which acts over a distance which is much less than Sc will not contribute substantially to the overall rate. When repulsive forces (such as the electrostatic double-layer forces) are also present, they may effectively prevent particles from arriving at the collector, even when they act only over a very short distance. For this reason the decay length alone cannot characterize the relative importance of the joint effect of attractive and repulsive farces. Useful characteristics of their combined effect may be obtained by considering the total potential energy of interaction between the particle and the collector. 

A discussion regarding the molecular polarizability is provided in the Appendix. In the present paper, we will use for the molecular polarizability expression A.7, which provides a lower bound for y, in the absence of saturation effects. When eq A.7 is inserted into eq 15, the decay length acquires the simple form (C). = 0 for k > 1)... 

While the hydration force was associated with the structuring of water in the vicinity of a lyophilic surface [12], there is no consensus about its microscopic origin. This incertitude is probably due to the apparent contradictory experimental results for phospholipid bilayers, the hydration force is apparently independent of the electrolyte concentration and has a decay length of about 2 A [11], while for mica surfaces the hydration is strongly dependent not only on the electrolyte concentration, but also on the nature of the cation (cation-specific effects) [17] and has a decay length of about 10 A. 

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-... 

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