tension downward as well as an upward buoyancy due to displaced water. The resulting force F
is monitored and related to the surface tension yas shown in Equation 2-2:
F = p,~g/wf + 27(t +w) cos p ghutl (2-2)
where p, and ps correspond to the densities of the Wilhelmy plate and the subphase, respectively,
g corresponds to the gravitational constant, t (thickness), w (width), and I (length) are the
dimensions of the Wilhelmy plate, B is the contact angle made by the subphase onto the plate (6
= 0 for a completely wetted plate, cos8= 1), and h corresponds to the plate height immersed into
the subphase. When measuring the change in F (AF) for a stationary plate after formation of an
adsorbed Langmuir monolayer, assuming that t is negligible compared to w, the equation can be
reduced to:
AF = 2wA7 (2-3)
and therefore, the surface pressure riis directly related to the change in force and the width of the
plate:
x = (2-4)
2w
With the Wilhelmy plate technique, the sensitivity can be as low as 5x10-3 mN/m. Nevertheless,
since very small amounts of impurities can affect surface pressure measurements, the water
subphase consists of Millipore filtered water with resistivities greater than 18.2 MGZ.cm.
Moreover, the trough needs to be carefully cleaned for instance with ethanol before forming a
Langmuir monolayer and rinsed several times with Millipore filtered water. Contamination with
impurities coming from the air can also be minimized by covering the trough or by carrying out
the experiments in a clean room. The subphase temperature can also be regulated with a
circulating water bath.