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