W. Richard Bowen and Nidal Hilal 4

70 2. MEASUREMENT OF PARTICLE ANd SURFACE INTERACTIONS
2.5 EFFECt oF RouGHnESS on MEASuREd AdHESIon
And SuRFACE FoRCES
The continuum theories outlined above, such as the JKR and DMT
theories, assume that perfectly smooth surfaces come into contact [2].
Unfortunately, the degree of roughness of particles and surfaces is quite
variable, and often, except for when studying molecularly smooth surfaces,
some account may be needed to be taken of roughness. The presence
of asperities on surfaces coming into contact serves, in most cases,
to effectively decrease the contact area. There are a number of models
that have been developed to account for the effect of surface roughness
on measured adhesion when trying to infer various properties of interactions
from adhesion forces. These generally use some measure of roughness,
such as the root mean square (rms) roughness of the surface, or
values for mean asperity size to account for the reduced contact areas
due to the presence of surface asperities [158–165]. As well as serving
to keep the two surfaces separated, the angle at which asperities on the
particle surfaces approach each other may also affect the effective contact
area and thus the measured adhesion [166]. Rabinovich et al. [162] determined
that surface roughness values as small as 1.6 nm rms were significant
and could reduce adhesion values by as much as fivefold from that
expected.
In addition, rough particles make determination of the radius of probe
particles, and hence normalisation by particle size, difficult. Larson and
colleagues [167] determined an effective probe radius when performing
measurements between TiO 2 colloids and crystal surfaces by fitting force
data to an electrical double layer model, with surface potential values
determined independently. This allowed calculation of an effective probe
radius that was used to normalise all subsequent force measurements.
AbbREVIAtIonS And SyMbolS
a Effective hard sphere particle radius in solution m
ac Contact radius m
ai Particle radius of molecule i M
a VW van der Waals gas constant N m 4 mol �2
A131 Effective Hamaker constant in medium 3 J
AH Hamaker constant (in vacuum or in medium) J
bVW van der Waals gas constant m3 mol�1 c Velocity of light in a vacuum (2.998 � 108 ) m s�1