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protonation of Ca(C18)2. The calcium is also complexed
with chelant to some extent. The other molecules formed
from Ca(C18)2 are stearic acid and stearate anion. At higher
pH, even though the calcium is complexed effectively, the
dissolution of Ca(C18)2 is still considered very low since
the stearate anion has limited solubility, and at the tem-
perature of study (25 °C), it cannot form micelles alone to
increase its solubility.
above the CMC, the effective pKa is that in micellar form.
At the pH = pKa, half of the surfactant is in cationic form
and half in zwitterionic form. At pH below the pKa, the
cationic form dominates, and at pH above the pKa, the
zwitterionic form dominates. In addition to protonation of
the stearate and the DDAO, the effectiveness of com-
plexation of Na2EDTA varies with pH as previously dis-
cussed, with higher pH being more effective.
In explaining the pH effects on Ca(C18)2 dissolution,
three effects dominate as pH decreases; the protonated
nonionic stearic acid/anionic stearate anion ratio increases;
the cationic DDAO/zwitterionic DDAO ratio increases;
and complexation of calcium by Na2EDTA decreases. The
effect of micellar composition on the effective pKa of the
stearate is probably a secondary effect in explaining trends.
Charge repulsion of the head groups when anionic stearate
is incorporated into an SDS micelle would inhibit co-
micellization of stearate with SDS, so the increase in sol-
ubility of Ca(C18)2 at pH below 5 in a chelant-free SDS
solution is due to a higher fraction of the fatty acid being in
nonionic, protonated form. The highest synergism in mixed
micellization is for a cationic/anionic surfactant mixture
[14], explaining why the highest solubility in a chelant-free
surfactant system is DDAO at low pH where it is below its
pKa and primarily in cationic form, co-micellizing with
anionic stearate and (less synergistically) with protonated
stearic acid. The synergism between a zwitterionic and an
anionic surfactant is between that of an anionic/anionic and
a cationic/anionic surfactant mixture [14], explaining why
the solubility of Ca(C18)2 at high pH (where the DDAO is
primarily zwitterionic) is greater than that for SDS, but less
than that of DDAO at low pH in the absence of chelant.
Table 1 shows the ionic form of possible formed soap
components and of micellar DDAO at low, intermediate,
and high pH.
Surfactant Only Systems
In the absence of additives, the CMC of SDS is
6.7 9 10-3 M [10]. Extrapolating from reported CMC
values with added electrolyte [11, 12] to pure surfactant
values, the DDAO at low pH where it is in cationic form
has a CMC of 7.0 9 10-3 M, and the DDAO at high pH
where it is in zwitterionic form has a CMC of
5.4 9 10-3 M. The dissolved calcium and stearate ions
will reduce the CMC values below these pure surfactant
values.
In this study, the SDS and DDAO are present at least an
order of magnitude above their CMC, so a high fraction
([93%) of these surfactants are present as micelles. As
shown in Figs. 1 and 2, in the absence of chelating agent,
both SDS and DDAO increased the solubility of Ca(C18)2
slightly, with DDAO causing higher solubility than SDS at
all pH levels. The SDS effect had little pH dependence
except at pH below 5 where solubility of Ca(C18)2
increased. The DDAO caused a monotonic increase in
solubility in Ca(C18)2 with decreasing pH, exhibiting an
order of magnitude greater solubility at pH of 4 compared
to SDS. At high pH (pH 7–11), the solubility of Ca(C18)2 in
DDAO is approximately five times higher than that in SDS.
The charge on the stearate/stearic acid molecule
becomes less negative (high fraction of protonated or
nonionic surfactant) as pH decreases as already discussed
with a pKa around 4.5. The effective pKa can alter upon
incorporation of the stearate into mixed micelles depending
on the charge of the co-surfactant, increasing when co-
micellizing with an anionic surfactant like SDS [13].
The DDAO is an amphoteric surfactant, which can exist
in the form of a cationic or a zwitterionic surfactant
depending on the solution pH as shown by the protonation
reaction:
At low pH, the main soap scum component that forms
mixed micelles with the added soluble surfactant is non-
ionic stearic acid. The formation of mixed micelles is
expected to be most effective in either cationic (DDAO at
low pH) or anionic surfactant micelles since cationic/non-
ionic or anionic/nonionic surfactant synergism is present.
At intermediate pH, stearic acid and stearate anion form
mixed micelles with added surfactant. The DDAO is
composed of both cationic and zwitterionic surfactants.
The formation of mixed micelles when DDAO is used can
be enhanced due to the mixed cationic (DDAO) and
anionic (stearate) surfactants. However, the solubility of
Ca(C18)2 is lower than at low pH because stearate solubility
is so low in equilibrium with Ca(C18)2 when no calcium is
complexed. Also, less protonated stearic acid is formed
than at low pH.
The pKa of DDAO monomer is reported at about 5 [12],
but the effective pKa can be much higher in micelle form,
even higher when co-micellized with an anionic surfactant
[12]. Since 0.1 M DDAO is about two orders of magnitude
At high pH, the soap scum mostly remains as an
undissolved solid precipitate since the solubility of soap
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