constant of themediumbetween the two bodies concerned is also involved in
the interaction energy. If, moreover, the materials 1 and 3 are similar in
composition and density,A11(3)tends to be small. If there is no material 3,
but vacuum,A 33 equals zero; for most gases, including air, it is negligible.
We then need Eq. (12.5).
The equations in Table 12.1 also give expressions after the&sign that
are based on theBerthelot principle, which states thatA 12 ¼ðA 11 ?A 22 Þ^0 :^5 ;
see Eq. (12.5). The relation is not fully correct, but it serves to illustrate some
important points. The first is that the Hamaker constant is always positive if
the particles are of the same material [Eq. (12.4)]; this implies that the
interaction energy is always negative, i.e., the force between the bodies is
always attractive. Secondly, the Hamaker constant will remain the same if
the materials of the particles and of the fluid between them are interchanged.
In other words, the attraction between two water drops across air will be
equal to the attraction between two air bubbles (of the same radius) in
water. If the three materials are all different, Eq. (12.3) shows thatAcan be
negative, i.e., the interactioncanbe repulsive. This has been experimentally
confirmed, for instance for films of some organic liquids between glass and
air [A 22 in Eq. (12.3) then equals zero, whileA 11 >A 33 ; cf. Table 12.2].
Currently, the more elaborate and precise Lifshits theory for the
calculation of Hamaker constants is applied rather than the Hamaker–de
Boer theory; it yields values that agree well with experiment. Some results
TABLE12.2 Values of the Hamaker Constant of
Various Materials Across Vacuum (A 11 ) and Across
Water (A11(3)), in 10^21 JMaterial A 11 A11(3)
Water 37 —
Ethanol 42
n-Pentane 38 3.4
n-Decane 48 4.6
n-Hexadecane 52 5.4
Solid paraffin 71
Solid stearic acid 50 * 3
Polystyrene 65 9
Glass * 90 * 13
Bovine serum albumin * 5
Biological cells * 1
(Division by 4.05 givesArelative tokBTat room
temperature.) For the most part calculated by Lifshits theory.