are in Table 12.2. It is seen that the values tend to increase with molar mass
for a homologous series and are higher for a crystalline than for a liquid
material (compare solid paraffin withn-hexadecane). The values across
water tend to be about an order of magnitude smaller than those across air.
For most food systems, the values for solids or liquids in liquids are of order
kBT. For air–water–air the Hamaker constant is about 10 times larger.
Values for proteins in water are not well known; the result for BSA in Table
12.2 refers to protein crystals. In practice, proteins are often swollen, i.e.,
contain water, and the Hamaker constant across water will then be
(markedly) smaller.
Some Complications. As mentioned in Section 3.1, the London
dispersion forces generally constitute the most important part of the van der
Waals attraction. These forces are due to mutually induced dipoles. Since
the dipoles fluctuate very fast, and because the electromagnetic wave
involved in establishing the attraction travels at finite speed, a dipole in one
particle and its induced counterpart in the other particle will be out of phase
if the distance between them is large. Thisretardationbecomes appreciable
forhvalues larger than about 5 nm. To be sure, this only applies to the
dispersion forces, and not to those dependent on a permanent dipole.
However, the latter forces become screened by any electrolyte present
between the two particles. Altogether, the Hamaker constant tends to
decrease in magnitude with increasinghvalue. To give an example for water,
calculated by Lifshits theory, at 1 nm the effective value ofAwould be 38,
and at 5 nm 31? 10 ^21 J. Nonetheless, van der Waals attraction can be
appreciable at relatively large distances (say, up to 100 nm).
Another significant point is the influence of anadsorbed substanceon
the effective value ofA. For not very small particles (R 4 h)only some of the
molecules in each particle contribute to the van der Waals interaction. In the
insert in Figure 12.1, the ‘‘active part’’ is indicated by hatching; it roughly
concerns layers with a thickness equal to the separation distance h.
Assuming adsorption layers to have a thickness of, say, 2 nm, it will be clear
that for smallh(say, 5 nm) the value ofAis largely determined by the
adsorbate rather than by the material of the particles. In passing, the
magnitude ofhtends to be uncertain for particles onto which a surfactant is
adsorbed, especially if the latter is a polymer.
Applications. Despite these complications, the Hamaker–de Boer–
Lifshits theory is very useful. It is commonly applied in virtually all theories
on colloidal interaction. If no other colloidal interaction forces act, it can be
used directly. A case in point in foods is triglyceride crystals in triglyceride
oil (Hamaker constant of order 0.5kBT). Here no other substantial forces