Physical Chemistry of Foods

than about 5 timesh, the result is

VvdW;p¼

A

12 ph^2

ð 12 : 2 Þ

where VvdW,p is expressed in J?m
^2. Also for some other geometries
equations have been derived.

Hamaker Constants. Calculation of the magnitude of the
Hamaker constant of a material proceeds by quantum mechanics, and we
will merely give results. For two bodies (particles) of the same material,
separated by vacuum, the Hamaker constant of this material can be inserted
in Eqs. (12.1) and (12.2). By convention, the Hamaker constant is calledA 11
for interaction between two bodies of material 1, etc. Table 12.1 illustrates
the relations in other cases. Eq. (12.3) is the most general one. If the material
of bodies 1 and 2 is the same, Eq. (12.4) results. Note that the Hamaker

TABLE12.1 Hamaker Constants (A) for Interaction Between Two Particles of

Materials 1 and 2, Separated by a Material 3

.GENERAL CASE:

A 12 ð 3 Þ¼A 12 
A 13 
A 23 þA 33 &ð

ffiffiffiffiffiffiffiffi

A 11

p

ffiffiffiffiffiffiffiffi

A 33

p

Þð

ffiffiffiffiffiffiffiffi

A 22

p

ffiffiffiffiffiffiffiffi

A 33

p

Þð 12 : 3 Þ

.IF 1¼2:

A 11 ð 3 Þ¼A 11 
 2 A 13 þA 33 &ð

ffiffiffiffiffiffiffiffi

A 11

p

ffiffiffiffiffiffiffiffi

A 33

p

Þ^2 ð 12 : 4 Þ

which impliesA 11 ð 3 Þ&A 33 ð 1 Þ

.IF 3¼VACUUM:

A 12 ð 3 Þ¼A 12 &

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

A 11 ?A 22

p

ð 12 : 5 Þ