Measurement of Van der Waals Forces

An electric field due to dipoles emanating from a material in a salt solution will be screened according to the Gouy-Chapman theory in an exponential decay fashion typical for the electric double layer (see Chapter 4). The decay length will be given by the Debye length ko (Eq. (4.8)). For the interaction between two parallel surfaces over a gap of width x filled with electrolyte solution, the field from surface 1 will have decayed to exp —x/ k-c) when it has reached the other surface. The dielectric response of surface 2 will be shielded the same way. This will lead to damping of the interaction that we can describe by a simple correction factor 

V (x) is the van der Waals interaction without screening. For a 0.1 M NaCl solution, the Debye length is k = 0.95 nm. For a distance between the surfaces of 2 nm, the Keesom and Debye interaction will be reduced to less than 8% of the unscreened interaction. The screening of the static contributions by ions is especially relevant for biological systems, where the interactions may be dominated by the Keesom and Debye interactions and physiological solutions typically contain more than 0.1 M salt. For systems where the London dispersion forces are dominating, screening will have a minor effect. 

For the interaction of lipid bilayers across a layer of water, a Hamaker constant of 7.5 X 10 J is calculated. A value of only 3 x 10 J was measured. One reason is probably a reduction of the Keesom and Debye by the presence of ions [88]. 

Even when taking into account that van der Waals forces for macroscopic objects fall slower than the fast decay law for single molecules, the direct measurement of van der Waals forces is demanding with respect to precise distance control and 

With the advent of the surface forces apparatus (SFA, see Section 3.1) that employs molecularly smooth mica surfaces, Tabor and Winterton [30] were the 

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It is extremely difficult to measure the Hamaker constant directly, although this has been the object of considerable research efforts. Direct evaluation, however, is complicated either by experimental difficulties or by uncertainties in the values of other variables that affect the observations. The direct measurement of van der Waals forces has been undertaken by literally measuring the force between macroscopic bodies as a function of their separation. The distances, of course, must be very small, so optical interference methods may be used to evaluate the separation. The force has been measured from the displacement of a sensitive spring (or from capacitance-type measurements). 

Israelachvili, J. N., Intermodular and Surface Forces, 2d ed., Academic Press, New York, 1991. (Graduate and undergraduate levels. An excellent source for the relation between molecular-level van der Waals interactions and macroscopic properties and phenomena such as surface tension, cohesive energies of materials, adhesion, and wetting. Also discusses direct measurement of van der Waals forces using the surface force apparatus.)... 

The 1954 Lifshitz result immediately enjoyed two kinds of success. When the materials were given the properties of gases, all the earlier Keesom-Debye-London-Casimir results readily emerged. Better, the new formulation was able to explain Derjaguin and Abrikosova s19 first successful force-balance measurements of van der Waals forces between a quartz plate and a quartz lens. The numbers checked out. 

A different approach yielding values of work of adhesion involves sensitive measurements of detachment force and contact radius when two surfaces are carefully moved towards and apart from another. The instrument is known as surface force apparatus (SFA) and was first developed by Tabor and Winterton " for direct measurement of van der Waals forces between molecularly smooth surfaces. Further improvements were carried on by Israelachvih and Tabor. ... 

A monolayer of adsorbed molecules is sufficient to mask the surface forces emanating from contacting substrates. Direct measurement of van der Waals forces (1), adhesion measurements in high vacuum (2) and contact angle measurements (3) illustrate this point. A much thicker layer is required to prevent mechanical interaction between the contacting surfaces. In the case of a sphere on a flat the film thickness must be rather greater than the diameter of the circular contact region (4) in order to supress the interaction of the substrates. 

Mutter J L and Bechhoefer J 1994 Measurement and manipulation of van der Waals forces in atomic-force microscopy J. Vac. Sc/. Technol. B 12 2251... 

One of the most important things to bear in mind in studying van der Waals forces is that this topic has ramifications that extend far beyond our discussion here. Van der Waals interactions, for example, contribute to the nonideality of gases and, closer to home, gas adsorption. We also see how these forces are related to surface tension, thereby connecting this material with the contents of Chapter 6 (see Vignette X below). These connections also imply that certain macroscopic properties and measurements can be used to determine the strength of van der Waals forces between macroscopic objects. We elaborate on these ideas through illustrative examples in this chapter. 

We have already seen from Example 10.1 that van der Waals forces play a major role in the heat of vaporization of liquids, and it is not surprising, in view of our discussion in Section 10.2 about colloid stability, that they also play a significant part in (or at least influence) a number of macroscopic phenomena such as adhesion, cohesion, self-assembly of surfactants, conformation of biological macromolecules, and formation of biological cells. We see below in this chapter (Section 10.7) some additional examples of the relation between van der Waals forces and macroscopic properties of materials and investigate how, as a consequence, measurements of macroscopic properties could be used to determine the Hamaker constant, a material property that represents the strength of van der Waals attraction (or repulsion see Section 10.8b) between macroscopic bodies. In this section, we present one illustration of the macroscopic implications of van der Waals forces in thermodynamics, namely, the relation between the interaction forces discussed in the previous section and the van der Waals equation of state. In particular, our objective is to relate the molecular van der Waals parameter (e.g., 0n in Equation (33)) to the parameter a that appears in the van der Waals equation of state ... 

It is evident from Figure 10.7 that the measurements are consistent with both unretarded and retarded attractive forces at appropriate separation distances. It has also been possible to verify directly the functional dependence on radii for the attraction between dissimilar spheres (see Table 10.4), to determine the retardation of van der Waals forces (see Table 10.1), and to evaluate the Hamaker constant for several solids, including quartz. Values in the range of 6 10 20 to 7 10 20 J have been found for quartz by this method. This is remarkably close to the value listed in Table 10.5 for Si02. 

FIG. 10.7 Direct measurements of van der Waals dispersion forces. The measurements correspond to the force between two flat (mica) surfaces separated by a distance d. The line shown is the theoretical expression for unretarded van der Waals force. The figure shows that the unretarded expression describes the measurements sufficiently accurately for d about 6.5 nm or less. (Redrawn with permission of J. N. Israelachvili and G. E. Adams, J. Chem. Soc., Faraday Trans. 1, 78, 975 (1978).)... 

That s the worst. Several kinds of measurements reassure us that the Lifshitz strategy of converting spectra into forces works reliably enough to capture the key features of van der Waals forces. 

One still hears the archaic designation "Hamaker constant" for Anam = AAm/Bm(D from the time when people did not recognize that the coefficient could itself vary with separation l. In modern usage this spatially varying coefficient, evaluated at zero separation, remains a popular and useful measure of the strength of van der Waals forces. 

Interactions between crossed cylinders of mica in air, uncoated or coated with fatty acid monolayers, are described in J. N. Israelachvili and D. Tabor, "The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm," Proc. R. Soc. London Ser. A, 331, 19-38 (1972). An excellent review of this and related work is given in J. N. Israelachvili and D. Tabor, Van der Waals Forces Theory and Experiment, Vol. 7 of Progress in Surface and Membrane Science Series (Academic Press, New York and London, 1973). Later reconciliation of theory and experiment required taking note of cylinder radius L. R. White, J. N. Israelachvili, and B. W. Ninham, "Dispersion interaction of crossed mica cylinders A reanalysis of the Israelachvili-Tabor experiments," J. Chem. Soc. Faraday Trans. 1, 72, 2526-36 (1976). 

For measurements between crossed mica cylinders coated with phospholipid bilayers in water, see J. Marra andj. Israelachvili, "Direct measurements of forces between phosphatidylcholine and phosphatidylethanolamine bilayers in aqueous electrolyte solutions," Biochemistry, 24, 4608-18 (1985). Interpretation in terms of expressions for layered structures and the connection to direct measurements between bilayers in water is given in V. A. Parsegian, "Reconciliation of van der Waals force measurements between phosphatidylcholine bilayers in water and between bilayer-coated mica surfaces," Langmuir, 9, 3625-8 (1993). The bilayer-bilayer interactions are reported in E. A. Evans and M. Metcalfe, "Free energy potential for aggregation of giant, neutral lipid bilayer vesicles by van der Waals attraction," Biophys. J., 46, 423-6 (1984). 

V. A. Parsegian, "Reconciliation of van der Waals force measurements between phosphatidylcholine bilayer in water and between bilayer-coated mica surfaces," Langmuir, 9, 3625-8 (1993). 

Since the first report by Ducker et al. on the direct measurement of colloidal forces using AFM [43], a number of investigations have been carried out to measure attractive van der Waals forces, electrostatic forces (double-layer forces) [44], hydrophobic forces [45-50], intermolecular forces between ligands and receptors [51,52], such as the avidin-biotin complex... 

Shear-Sensitive Systems. In addition to hydrodynamic effects and simple viscous behavior, the act of pigmentation creates a certain amount of complex behavior (13). If the particles are fine. Brownian movement (14-17) and rotational diffusion (14. 18. 19) are among the phenomena that cause dispersed systems to display complex rheology. The role of van der Waals forces in inducing flocculation (20) and the countervailing role of two electroviscous effects (17. 21. 22) in imparting stability, particularly in aqueous systems, have been noted. Steric repulsions appear to be the responsible factor in nonaqueous systems (23. 24). The adsorbed layer can be quite large (25-28). as detected by diffusion and density measurements of filled systems or by viscometry and normal stress differences (29). 

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