W. Richard Bowen and Nidal Hilal 4

40 2. MEASUREMENT OF PARTICLE ANd SURFACE INTERACTIONS
2.3.1.2 Retardation of van der Waals Forces
As the distance between interacting atoms increases, the time for the
electric field of one atom to interact increases, and for a large enough distance
will become comparable with the time over which the dipole itself
fluctuates, leading to fluctuations in the interacting dipoles becoming out
of step. This can lead to the interaction becoming less favourable, causing
the strength of the interaction to decrease with the inverse seventh
power of the separation distance rather than to the inverse sixth power
[2, 14]. Because of this mechanism, it is only the London dispersion interactions
that are affected by these retardation affects and not the Debye or
Keesom interactions.
2.3.1.3 Calculation of Hamaker Constants
Looking at Table 2.1, it can be seen that if the Hamaker constant is
known, it is possible to calculate the interaction energy between surfaces,
provided that particle radii and distances of separation are available. The
Hamaker constant though is not an easily obtained value.
Lifshitz theory [11] can be used to calculate the Hamaker constant,
but the calculations require complete knowledge of the dielectric spectra
over the entire frequency range for all of the individual materials comprising
the system. This type of data is not available for most substances,
so another method is required for which data is more widely available.
Ninham and Parsegian [15] considered the construction of the dielectric
spectra for all frequencies and concluded that not all parts of the
frequency range are equally important. They found that the ultraviolet
absorption regime is the most important of all the contributions to the
frequency sum. Hough and White [16] also emphasised the importance
of the ultraviolet absorption peak. To obtain the parameters for the UV
peak, refractive index data measured over a range of wavelengths, �,
usually in the visible part of the spectrum, can be used. The following
equation was then constructed [16]:
2 2 ω
no ( ω) � 1 � ( no ( ω)
� 1)
� C
2
ω
2
UV
UV
(2.11)
π
where ω�
λ
2 c , no(�) is the refractive index at a given frequency and c is
the speed of light in a vacuum.
2
2
Thus, if a graph of ( no � 1)
is plotted versus ( no �1) �2 , a straight line
2
of slope 1/ωUV
and intercept CUV will be obtained. This method of analysis
is called the ‘Cauchy Plot’.