Oscillatory force profiles

At high surfactant concentrations, the force curves become rather complex, often displaying an oscillatory force profile (85, 86, 168-175). The measured interactions now reflect how the organization of the self-assembly structures of the surfactants changes as the gap between the surfaces is varied. The oscillatory forces may occur due to the presence of micelles or due to the systematic removal of lamellae in bilayer structured fluids. Furthermore, attractive forces associated with... 

At relatively low polymer adsorption levels, oscillatory force profiles similar to those observed for micellar solutions are also seen in polyelectrolyte-containing systems. As with micellar structuring, these oscillations originate from an inhomogenous density distribution of polymer (or polymer/surfactant complexes) within the film. Furthermore, the characteristic length-scale of the oscillatory forces indicate that this structuring is controlled by electrostatic interactions. To date, no complete theory describing this phenomenon exists ... 

Similar oscillatory force profiles were also seen in SFA measurements between mica surfaces in liquid organic alkanes (Fig. 1.6). The periodicity of the force minima was 0.4-0.5 nm and did not change with an increase in the length of the alkyl chains, indicating that the alkyl chains had a tendency to orient parallel to the mica surface. 

Subsequent SFA force measurements were taken between mica surfaces coated in a variety of surfactant monolayers in symmetric and asymmetric organic liquids. These measurements showed oscillatory force profiles between molecularly smooth polar and nonpolar surfaces in symmetric liquids only, indicating that the oscillatory forces in these cases were due to geometric packing of the molecules on the approach of the surfaces a summary of these results is shown in Fig. 1.7. 

Owing to the oscillatory force profile caused by the hydration layers, there is more than one stable tip position for the tip-sample distance regulation, as indicated by the dotted line in Fig. 18.8a. Consequently, the tip jumps between these feedback positions during the imaging, as shown in Fig. 18.8b. In the image, the tip was scanned from the lowest terrace (Terrace 1) corresponding to... 

It is straightforward to show that the desired steady-state (i.e., the origin) is unstable. A robust tracking control law can be constructed to stabilize the CSTR under forced oscillatory operation. That is, we can derive a controller to track an oscillatory temperature profile (say, yr t) = a- - sin(47rt)), which can be generated by the exosystem (3) where... 

As we have seen in Section 6.6.1 such confined liquids may behave quite differently from the bulk lubricant. Near the surfaces, the formation of layered structures can lead to an oscillatory density profile (see Fig. 6.12). When these layered structures start to overlap, the confined liquid may undergo a phase transition to a crystalline or glassy state, as observed in surface force apparatus experiments [471,497-500], This is correlated with a strong increase in viscosity. Shearing of such solidified films, may lead to stick-slip motions. When a critical shear strength is exceeded, the film liquefies. The system relaxes by relative movement of the surfaces and the lubricant solidifies again. 

An example of the effective force (derivative of the pair potential with respect to the separation) experienced by the two approaching macroions is shown in Fig. 3b. The oscillatory decay part of the force profile reflects in an effective way the impact of the discrete nature of the solvent on interparticle forces. The... 

Although quantitative thin-film force measurements of polymer/surfactant-containing systems are relatively new, quite fascinating behaviour has already been found. In particular, the strongly interacting synergistic adsorption system (e.g. Case II) containing an anionic polyelectrolyte and a cationic surfactant has been extensively studied. This system has revealed both oscillatory force versus distance profiles, and interfacial gel formation within individual films. 

Figure 1.2 The origin of the oscillatory force. The pressure between two surfaces depends on the density of the liquid molecules in the confined film. The pressure reaches a maximum for [ordered] films with a discrete number of molecular layers, leading to repulsive peaks in the pressure/force profile. For intermediate distances the liquid is in a disordered and low-density state, causing a negative pressure and attractive force between the surfaces. [Figure adapted from Israelachvili. ]...

According to Eq. 1.1, the density or ordering ofthe boundary layer at the solid wall governs the oscillatory force between two approaching surfaces. Therefore any factors that influence this ordering will in turn influence the force profile. These factors include not only the properties of the intervening medium but also the chemical and physical properties ofthe surface itself, as discussed next. 

The A/ curve shows an oscillatory profile with two peaks separated by 0.25 nm. This distance corresponds to the diameter of a water molecule, which suggests that the oscillatory force is caused by the hydration layers formed on a DPPC bilayer. 

I) The density profile Pf z] has a rapidly damped oscillatory behaviour. Usually the number of oscillations is less than that found with the force apparatus, fig. 2.3. Simulations with much larger numbers of molecules are needed to further analyze this difference. 

The oscillatory behaviour of surface relaxation — inward for Af/12, outward for A 23 — seems to be fairly universal (Fu et al., 1984 Landman et al., 1980 Jiang et al., 1986). It is found not only experimentally and in fully self-consistent calculations, but also in simplified calculations a la Heine-Finnis. If a frozen charge density is used, for example a step density or the Lang -Kohn jellium surface profile, and the ions are relaxed to positions of zero force, oscillatory relaxations are found (Landman et al., 1980). This shows that it is not a consequence of the Fricdel oscillations in the surface charge density. 

The beach profile (Figure 2.9) is the product of the oscillatory onshore and offshore motions of its constituent materials affected by the waves and the wave-induced currents. Granular particles on the seabed can be dislodged and suspended in the water column by a combination of drag and lift forces. These forces on the particles are exerted by bott-tom shear stresses developed by either the wave velocity exceeding a threshold value or the occurrence of turbulence. Once the particles are in the water column, they are kept in suspension longer than in subaerially wind-blown conditions because of a combination... 

The hydration force on a lipid membrane has been investigated by various methods due to its importance in the biological processes. However, the force measurements by surface force apparatus (SFA) and the osmotic pressure method showed no oscillatory profiles. 

Thus, it was questioned if there were any intrinsic hydration layers on a lipid membrane. The oscillatory profile observed in the A/ versus distance curve obtained by FM-AFM revealed the existence of the hydration layer on a DPPC bilayer (Fig. 18.8a). In FM-AFM, the force is measured with a tip having a nanometer-scale cross section, while the force measured by SFA and the osmotic pressure method is averaged over a micrometer-scale area. Such global averaging may smear out the local distance dependence, showing the oscillatory profile. The result clearly showed the importance of having local spatial resolution in the investigations on interfacial phenomena. 

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