ABSTRACT
The total constant Aii, governing the interaction between two bodies of material i, at short distances, in vacuo, in van der Waals-London (dispersion) interactions (which is alluded to as the Hamaker constant), is expressed as:
ii= π β2q [II-5] where qi is the number of atoms per unit volume and β the constant in London’s equation for the interaction between two atoms i, and β = 3/4 α2hv (see eq. [II-4]):
Hamaker (1937a) fi rst calculated the dispersion (van der Waals-London) interaction energy for larger bodies by a pair-wise summation of the properties of the individual molecules (assuming these properties to be additive, and non-retarded). Using this (“macroscopic”) approximation, the total attractive dispersion energy for two semiinfi nite fl at parallel bodies (of material i), separated by a distance , in air or in vacuo, becomes (for greater than a few atomic diameters):
For two materials 1 and 2, singly or together embedded or immersed in medium 3, the combining rules are respectively described by:
and:
Given the applicability of eq. [II-8], eqs. [II-10] and [II-11] can also be expressed as (Visser, 1972):
and:
It is clear that A131 (eq. [II-10]) always is positive (or zero), however, equally clearly, A132 can assume negative values, i.e., when:
and when:
(see Visser, 1972). These conditions (eqs. [II-12A] and [II-12B]) result in repulsive Lifshitz-van
der Waals forces (van Oss, Omenyi and Neumann, 1979; Neumann, Omenyi and van Oss, 1979). It should be clear that these conditions are by no means rare or exceptional. Hamaker already indicated the possibility of such repulsive (dispersion) forces (1937a), which possibility was reiterated by Derjaguin in 1954. The precise conditions under which a repulsion could be expected to occur were fi rst given by Visser (1972, 1976). All of these considerations initially only applied to van der Waals-London interactions, utilizing Hamaker constant combining rules. However, as shown in Chapter III, the surface thermodynamic approach for obtaining eqs. [II10] and [II-11] is essentially the same as Hamaker’s approach (1937a), as long as eq. [II-9] is valid. This validity, however, remains strictly limited to Lifshitz-van der Waals (LW) interactions, see below.
