Separation Between Surfaces

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

The dimension of machine elements has been reduced continuously in recent years with the advance of micromachining technology, and the separation between surfaces in rela-... 

FIG. 13.8 Plot of ne, versus d, the minimum separation between surfaces, for two spheres of equal radius (100 nm). Curves are drawn for different values of k with constant values of A (2 10 19 J) and p0 (25.7 mV). (Redrawn with permission from E. J. W. Verwey and J. Th. G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam, Netherlands, 1948.)... 

The surface force apparatus (SFA) has been used extensively over the past 30 years to measure the force directly as a function of separation between surfaces in liquids and vapors. If the force-measuring spring is replaced with a mechanically more rigid support, the two opposing surfaces become an ideal model pore for the study of confinement effects on phase behavior [16], A detailed review can be found in reference ]. Briefly, the shift of the melting temperature AT can be related to the size h of the condensate measured with SFA according to... 

Experiments regarding the force between mica surfaces revealed that the traditional DLVO theory provides good agreement at large separations but fails at low separations and high electrolyte concentrations.13 For some electrolytes, even at relatively low ionic strengths (10 3 M) there is an additional strong repulsion at low separations between surfaces. 

In the denominator of Eq. (1) is included the distance of separation of the surfaces from each other d raised to a power n. Since the van der Waals attraction is an inverse function of distance of separation d, the closer the molecules are together, the greater the force of attraction. This effect is accentuated even more by the power n to which d is raised n also decreases as the distance of separation becomes less. From a distance d of about 800 A separation between surfaces, n gradually decreases from 3 to 2 at about 80 A separation (Brisco and Tabor, 1972). 

Although the separation between surface and bulk reduction is not always straightforward, the hydrogen consumption quantities were determined for temperatures lower than 900-950 K. They are given in Table 3. From them, it is possible to calculate the ceria surface areas of each catalyst, provided that some hypothesis are done on the mean oxidation state of the precious metal before starting the TPR experiment. In this study, the calculations were made with two different hypothesis hypothesis 1) the metals are under the Rh + and Pt + states, h3T)Othesis which was found valid for the fresh systems [9] and hypothesis 2)... 

TTHE MOST IMPORTANT FORCES ACTING BETWEEN MEMBRANE SURFACES are van der Waals, electrostatic, and hydration. The first two forces are explained by the Deijaguin-Landau-Verwey-Overbeek (DLVO) theory (I) the existence of the hydration force was anticipated before it was measured (2). The van der Waals force is always attractive and displays a power law distance dependence, whereas the electrostatic and hydration forces are repulsive and exponentially decay with distance. The electrostatic force describes the interaction between charged membrane surfaces when the separation between surfaces is above 10 molecular solvent diameters. The hydration force acts between charged and uncharged membrane surfaces and at distances below 10 molecular solvent diameters its value dominates the values of van der Waals and electrostatic forces (3). The term hydration reflects the belief that the force is due to the structure of water between the surfaces. Electrostatic and hydration forces are similar in some respects both are exponential and repulsive and their theoretical description involves coupling electrostatic concepts and ideas borrowed from statistical mechanics. Although the nature of the electrostatic force is solidly established, this is not the case for the hydration force. To illustrate the role the electrostatic... 

There are basically two possible scenarios for the behavioxir of this prenematic mean field force when the separation between surfaces is reduced, and both depend on the degree of the surface-induced nematic order. For low surface-induced order, the magnitude of the attractive force just increases when approaching the isotropic-nematic phase transition from above. On the other hand, if a surface induces a high degree of LC orientation, the prenematic phase can spontaneously transform into the nematic phase, when the separation is decreased below a certain value. This is the nematic capillary condensation, that is discussed further on in this Chapter. 

Whereas the first experiments on structmral forces in liquid crystals were performed using a Surface Force Apparatus (SFA, discussed later on in part 3 of this chapter), a temperature controlled AFM was used later [4] to measure the forces between the AFM probe and the surface, mediated by a liquid crystal in between. Compared to other methods, using an AFM for measuring surface forces has some advantages and also some drawbacks. The most important advantage is, that the temperature of the sample can be controlled in a simple way to better than 0.01 K. Furthermore, the sample is not in direct contact with large mechanical parts like in the case of a SFA, and only a small amount of liquid crystal is needed for the experiment. The drawback of the AFM is, that the separation between surfaces is not measured directly... 

Degradation of stored polymeric composites should be minimised, especially in poor environments. Protection of materials and manufactured units should be provided, with separation between surfaces to avoid direct contact or frictional damage. Wrapping, packaging and crates may be used as separators. 

The charge separation between surface and the ions in the Stem and diffuse layer generates an electric field which is described by an electric potential i/r. The potential i/ o on the surface is finite and has the same sign as the surface charge. Within the diffuse layer, the electric potential decays exponentially from the diffuse layer potential to zero in the free solvent (i/rCoo) = 0, Fig. 3.3). 

Near the surface, AG is dominated by the Coulomb energy profile and, therefore, it is approximately equal to the difference of the electrostatic potentials at the proton positions before and after the transfer. This difference depends strongly on the distance of the proton from the surface. Values of AG were found in the range of 0.5 eV. This value decreases, however, to the activation energy of proton transport in bulk water when the proton-surface separation exceeds 3 A (the thickness of one monolayer of water). Moreover, the electrostatic activation energy is a function of the separation between surface charges, which lies in the range of 7 to 15 A. 

As evaporation occurs and solid surfaces are brought together, repulsive forces arising from electrostatic repulsion, hydration forces, and solvent structure resist contraction of the gel. The pore liquid will diffuse or flow from the swollen interior of the gel toward the exterior to allow the surfaces to move further apart. The disjoining forces thus produce an osmotic flow. Since these forces become important when the separation between surfaces is small, they are most likely to be important near the end of drying, when the pore diameter may approach 2 nm. 

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