Oscillatory force

While evidence for hydration forces date back to early work on clays [1], the understanding of these solvent-induced forces was revolutionized by Horn and Israelachvili using the modem surface force apparatus. Here, for the first time, one had a direct measurement of the oscillatory forces between crossed mica cylinders immersed in a solvent, octamethylcyclotetrasiloxane (OMCTS) [67]. 

In many materials, the relaxations between the layers oscillate. For example, if the first-to-second layer spacing is reduced by a few percent, the second-to-third layer spacing would be increased, but by a smaller amount, as illustrated in figure Al,7,31b). These oscillatory relaxations have been measured with FEED [4, 5] and ion scattering [6, 7] to extend to at least the fifth atomic layer into the material. The oscillatory nature of the relaxations results from oscillations in the electron density perpendicular to the surface, which are called Eriedel oscillations [8]. The Eriedel oscillations arise from Eenni-Dirac statistics and impart oscillatory forces to the ion cores. 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

An oscillatory force which decays exponentially with surface separation ... 

There are other forces that come into play when the thickness of the liquid fihn is in the nanometer range and the size of the molecule is no longer negligible. Short-range oscillatory forces arise then because the liquid molecules feel the presence of the walls of the substrate and are forced to form a layered structure near the interface. These forces are also called structural or solvation forces [6]. 

The surface forces apparatus (SEA) can measure the interaction forces between two surfaces through a liquid [10,11]. The SEA consists of two curved, molecularly smooth mica surfaces made from sheets with a thickness of a few micrometers. These sheets are glued to quartz cylindrical lenses ( 10-mm radius of curvature) and mounted with then-axes perpendicular to each other. The distance is measured by a Fabry-Perot optical technique using multiple beam interference fringes. The distance resolution is 1-2 A and the force sensitivity is about 10 nN. With the SEA many fundamental interactions between surfaces in aqueous solutions and nonaqueous liquids have been identified and quantified. These include the van der Waals and electrostatic double-layer forces, oscillatory forces, repulsive hydration forces, attractive hydrophobic forces, steric interactions involving polymeric systems, and capillary and adhesion forces. Although cleaved mica is the most commonly used substrate material in the SEA, it can also be coated with thin films of materials with different chemical and physical properties [12]. 

Recently the wall-PRISM theory has been used to investigate the forces between hydrophobic surfaces immersed in polyelectrolyte solutions [98], Polyelectrolyte solutions display strong peaks at low wavevectors in the static structure factor, which is a manifestation of liquid-like order on long lengths-cales. Consequently, the force between surfaces confining polyelectrolyte solutions is an oscillatory function of their separation. The wall-PRISM theory predicts oscillatory forces in salt-free solutions with a period of oscillation that scales with concentration as p 1/3 and p 1/2 in dilute and semidilute solutions, respectively. This behavior is explained in terms of liquid-like ordering in the bulk solution which results in liquid-like layering when the solution is confined between surfaces. In the presence of added salt the theory predicts the possibility of a predominantly attractive force under some conditions. These predictions are in accord with available experiments [99,100]. 

Note that the radial and vertical components are out of phase, and that the coefficient multiplying r is only half that multiplying z. Thus, the effect of the ac field is to exert an oscillatory force on the particle with an effective field strength in the vertical direction that is twice the radial field strength. As a result of the larger field strength in the z-direction, the onset of instability is governed by the z-component of the equation of motion, so we need examine only that component. 

Note 3 A material specimen which behaves as a Voigt-Kelvin solid under forced oscillation , with a mass added at the point of application of the applied oscillatory force... 

So-called solvation/structural forces, or (in water) hydration forces, arise in the gap between a pair of particles or surfaces when solvent (water) molecules become ordered by the proximity of the surfaces. When such ordering occurs, there is a breakdown in the classical continuum theories of the van der Waals and electrostatic double-layer forces, with the consequence that the monotonic forces they conventionally predict are replaced (or accompanied) by exponentially decaying oscillatory forces with a periodicity roughly equal to the size of the confined species (Min et al, 2008). In practice, these confined species may be of widely variable structural and chemical types — ranging in size from small solvent molecules (like water) up to macromolecules and nanoparticles. 

The direct measurement of the interaction force between two mica surfaces1 indicated a large repulsion at relatively short distances, which could not be accounted for by the DLVO theory. This force was associated with the structuring of water in the vicinity of the surface.2 Theoretical work and computer simulations8-5 indicated that, in the vicinity of a planar surface, the density of the liquid oscillates with the distance, with a periodicity of the order of molecular size. This reveals that, near the surface, the liquid is ordered in quasi-discrete layers. When two plan ar surfaces approach each other at sufficiently short distances, the molecules of the liquid reorder in discrete layers, generating an oscillatory force.6... 

Recently, Chu et al. [41,42] and Chu and Wasan [43] have made simulation and MSA studies of the structure and forces in thin films and colloidal dispersions. They include the effect of polydispersity. They also find oscillatory forces. 

If the solution between two surfaces contains surfactants that form highly charged micelles, a different effect occurs. Theory, confirmed by measurement [49-51], shows that the Debye length is then to be calculated as if the micelles and their "boimd" coimter-ions are simply ignored. The doublelayer force is here much longer ranged than it would be on the basis of standard theory. These forces are sometimes called "depletion" forces. The mechanism is the same as that for the oscillatory forces discussed in section 3.5.1. 

These results support the assumption that the oscillatory forces are caused by electrostatic repulsion between the layered polyelectrolytes. On the other hand the c 1/3 dependency indicates that the step size is determined by the geometry but not by electrostatics. It is assumed that the concentration of free counterions around the PEI is quite low and that the step size Ah is ... 

Oscillatory structural forces appear in two cases (1) in thin films of pme solvent between two smooth solid surfaces (2) in thin liquid films containing colloidal particles (including macromolecules and surfactant micelles). In the first case, the oscillatory forces are called the solvation... 

Fig. 8 Design of an interfacial stress rheometer. Here a magnetized rod is subjected to an oscillatory force generated by the Helmholtz coils. The motion of the rod is detected using a microscope and photodiode array. Differences between the applied force and resulting phase and magnitude of the displacement give information on the viscoelastic properties of the monolayer. Both the storage modulus G and the loss modulus G" can be determined [2,21] (reproduced with permission from the American Chemical Society)...

Thin liquid films made from the mixed solutions below CAC exhibit a stratification phenomenon, with a stratum thickness corresponding to the mesh size of the polymeric network, i.e. the distance between overlap points of two polymer chains. The oscillatory forces are particular to polyelectrolytes and disappear when the electrostatic forces are screened with salt. The study of freely suspended films gives new useful insights into the structure of semidilute polymer solutions which are presently the object of numerous speculations. 

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