Biomedical Engineering Reference
In-Depth Information
Figure 14. Dependences of the critical micelle concentration, CMC, (closed symbols) and the residual
area per molecule,
a
, (open symbols) on the carbon number of the acyl or alkyl chain. The symbols (
z
,
{
), (
,
) and (
S
,
U
) indicate acyl ascorbates, acyl mannose and alkyl glucosides, respectively. The
CMC and
a
values for the acyl mannoses and alkyl glucosides were cited from the literature [42] and
[54], respectively.
w
logCMC
=
−
n
+
b
(8)
k
T
B
where
w
is the cohesive energy change per methylene group passing from the bulk of the
solution to the micelle,
k
B
is Boltzmann's constant, and
b
is a constant. The
w
values were
estimated to be 1.3 × 10
-21
, 2.0 × 10
-21
and 2.2 × 10
-21
J for acyl ascorbates, acyl mannoses
and alkyl glucosides, respectively. The
w
value for acyl ascorbates was much smaller than
those for the acyl mannoses and alkyl glucosides. The
a
values of
ca
. 0.40 nm
2
were
practically the same for the acyl mannoses and alkyl glucosides, while the
a
values of the acyl
ascorbates were
ca.
0.30 nm
2
, which was much smaller than those of acyl mannoses and alkyl
glucosides. Since acyl or alkyl derivatives would be oriented so as to stick their acyl or alkyl
residues into the air, the
a
value seemed to be exclusively determined by the hydrophilic
moiety. The molar volumes of mannose and glucose were 0.114 L/mol [55]. If the hexoses
are assumed to be spherical, the cross-sectional area is 0.40 nm
2
, which coincides with the
a
value evaluated from the surface tension measurement. The molar volume of ascorbic acid
was estimated to be 0.106 L/mol, from which the cross-sectional area was calculated to be
0.38 nm
2
under the assumption that the molecule was a sphere. The
a
value of 0.30 nm
2
was
much smaller than the cross-sectional area. Ascorbic acid has a γ-lactone ring, which is
smaller than the pyranose one of mannose or glucose. The γ-lactone ring might act as the
hydrophilic moiety of the acyl ascorbate. The surface tensions of decanoyl and lauroyl
ascorbates dissolved in distilled water were measured at various temperatures and pHs to
examine the temperature and pH dependences of the CMC values [31]. The temperature
dependence of the CMC was very weak for both the ascorbates. The
a
value was also
independent of the temperature, and was about 0.35 nm
2
. The effect of pH on the surface
tensions of decanoyl ascorbate solution at 30
o
C was examined. The CMC value was higher at
the higher pH. The p
K
a
value of ascorbic acid is 3.77 [56]. If we assume the p
K
a
value of
