Surface energy magnitudes

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

Corn (C7), however, points out that adsorbed films or gas layers may exist between the particles and may alter the nature of the adhesive force. Corn also indicates that various investigators have derived a value of the order of 4na for Kw when adsorbed liquid films are involved. Bradley (Bll) has derived an identical expression where <7 is defined as the surface energy of the solid. All of these forms yield values of Kw of the same general magnitude. There are, however, other reports (Fuchs, F4, pp. 363, 373) that indicate adhesive forces between particles as much as two orders of magnitude smaller than these. 

As examples of the magnitude of variation in the free surface energies and the approximate constancy of the total surface energies the following data for benzene (Whittaker, Proc. Roy. 8oc. A, Lxxxi. 21,1900), mercury and carbon tetrachloride (Harkins and Koberts, J.A.G.B. XLiv. 656,1922) may be cited (see tables, p. 20). 

There exists as we have noted a separate phase at the interface between a liquid and a gas. The magnitude of the vapour-liquid interfacial energy is markedly dependent on the composition of the liquid and although experimental data are somewhat scanty, the surface energy is also affected by the nature of the gas in contact with it. It is to be anticipated that at the interface between two immiscible liquids a similar new interfacial phase will come into existence possessing a definite surface energy dependent on the composition of the two homogeneous liquid phases. 

Discuss with your neighbor how protein adsorption can still be spontaneous (AG < 0), even though some of these processes are endothermic (AH > 0). Look up values for the solid surface energies of the two substrates in Appendix 4 (you may have to select similar materials, but this is sufficient for these purposes). How do these enthalpies compare in magnitude to the respective surface energies ... 

Use values of modulus from Appendix 7, along with surface energy from Appendix 4, to estimate the following quantities. In both cases, take an interplanar distance of 10 cm as an order-of-magnitude estimate. 

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

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