Chemistry Reference
In-Depth Information
trough. Deviations from the equilibrium surface concentrations are at a
maximum at the centre of the circular wave field where wave amplitudes
are at a maximum. Excursions from the equilibrium surfactant coverage
(0.288 Pg cm
-2
) for crests or troughs converge toward the equilibrium con-
centration at large distances from the centre of the tank. This behaviour is
expected since the standing circular capillary wave field in the experiment
exhibits a maximum amplitude at the centre. Wave amplitudes decreased
as one moved outward from the centre. Images recorded when the centre is
a trough, rather than a crest, exhibit the opposite trend from that presented
in Table 1. The surfactant concentration was less than the equilibrium
value in the centre, and then alternating positive/negative excursions from
the equilibrium value. Consequently, the SHG imaging technique pre-
sented here is measuring surfactant concentrations that are consistent with
a compression and dilation of the monolayer in the peaks and troughs, re-
spectively.
Table 1.
Surfactant surface concentration (Pg cm
-2
) and 95 % confidence limits
for the image in Figure 1
Surfactant Concentration
>Pg cm
-2
@
Crest (Centre)
0.338 r 0.197
Trough 1
0.282 r 0.051
Crest 2
0.322 r 0.073
Trough 2
0.218 r 0.046
While these results are intriguing, we need to address the large con-
fidence limits for the measurements obtained at the tank centre. There are
two primary reasons for this large confidence limit. The first is that there
are very few pixels to average over for the centre crest or trough (in com-
parison to other crests or troughs). With the optical system aligned to col-
lect signal from regions of zero wave slope only, the image of the central
crest (or trough) has the fewest number of pixels available for averaging.
We included as many pixels as possible in the averaging process for the
central portion of the wave field. This may have included pixels in the im-
age not necessarily corresponding to exactly a slope of zero, and which
were not necessarily focused in the image plane. This was compounded by
the fact that there are small deviations or irregularities in the diameter of
the tank resulting from manufacturing and paraffin coating of the inner
walls. These diameter deviations are small. Nevertheless, they affect the
waves resulting in an approximation, albeit a good approximation, to a true
standing wave with slight distortions. The wave field is generated at the
