Chemistry Reference
In-Depth Information
1
0.5
0
0.0001
0.001
0.01
[DDAB] / mol dm
-3
Figure 7 The fraction F of surviving bubbles after 1 h for 0.5 wt% colloidal silica +
DDAB at different surfactant concentrations
150
100
50
0
0
200
400
t
/ min
Figure 8 Typical bubble radius R versus time t for bubbles stabilized by 0.5 wt% colloidal
silica + 4
10
3
mol dm
3
DDAB
It is clear from the above that, above a certain concentration of silica, there is
an optimum ratio of surfactant to particle concentration that gives maximum
stability. This makes sense if there is a specific partial coverage of surfactant
required on the particles in order to give optimum surface hydrophobicity.
Some calculations were therefore carried out to estimate this coverage. The
adsorption isotherm for DDAB on silica was not directly determined, but the
maximum possible surface coverage was estimated assuming all of the DDAB
in the system adsorbs. For this calculation the specific surface area of the
5.5-nm colloidal silica was taken as 500 m
2
g
1
assuming spherical particles of
density 2.18
10
3
kg m
3
. The area per adsorbed DDAB molecule was taken
as the area per head group, i.e., 0.38 nm
2
.
14
As DDAB is not very soluble in the
aqueous phase, but adsorbs strongly to the silica particle surface, this calcu-
lation of the maximum possible coverage is expected to be a good estimate of
the actual coverage, provided the particles are not significantly aggregated, as
aggregation would reduce the actual surface area available for adsorption.
Table 1 shows values of maximum percentage coverage calculated for 5.5-nm
hydrophilic silica particles at different values of the surfactant concentration
[DDAB]. Table 2 gives the calculated values at different particle concentra-
tions. When the concentration of silica was fixed at 0.5 wt% (Table 1), and
comparing the calculated maximum percentage coverage with the [DDAB]
giving the most stable bubbles, the optimum surface coverage is 7%. But with
[DDAB] fixed at 10
3
mol dm
3
and the particle content varied (Table 2), the
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