Biomedical Engineering Reference
In-Depth Information
dσ = -Г dµ = -ГRTdlnC
(1)
where dσ, Г, dµ, R, T, and C are the change in the surface tension in the solution, the
adsorption density of the surfactant, the change in the chemical potential of the surfactant,
universal gas constant, absolute temperature, and the concentration of the surfactant in
aqueous solution, respectively. Since the concentrations of the surfactant solutions are dilute
the activity is replaced by concentration. Eq. (1) can be written as
Г = -1/RT(dσ/dlnC)
(2)
Maximum adsorption density is calculated by limiting the concentration in the above
equation to CMC of the surfactant. Hence Eq. (2) can be expressed as
Г
max
= -1/(2.303RT) limit
C→CMC
(dσ/dlogC)
T
(3)
The minimum area per molecule (A
min
) in Å
2
can be calculated from
A
max
= 10
20
/N
A
Г
max
(4)
where N
A
is the Avogadro number. The values of Г
max
and A
min
are given in Table 1. The
standard free energy of adsorption is obtained from
ΔG
ad
o
= ΔG
m
- (П
cmc
/Г
max
)
(5)
where ΔG
m
is the standard free energy change of micellization
ΔG
m
o
= RTdlnC
cmc
(6)
and П
cmc
= σ
water
- σ
cmc
the values are given in Table 1.
Table 1. CMC and area per minimum from surface tension data at 25
O
C
Г
max
× 10
6
(mol m
-2
)
Sample
CMC
mM
П
cmc
(mN/m)
A
min
(Å
2
)
-ΔG
m
(kJ mol
-1
)
-ΔG
ad
(kJ mol
-1
)
MR
30.2
30.8
3.00
55.4
8.67
18.9
MR+LYS
64.6
35.5
0.94
117.0
6.79
44.5
CTAB*
0.90
37.0
2.90
57.0
27.8
40.0
SDS*
8.5
36.5
2.60
63.0
22.1
35.2
*taken from [Dash, Misra, 2011] for the temperature 30
O
C.
Comparative analysis of obtained parameters for MR with those for typical surfactants
(CTAB and SDS) [Dash, Misra, 2011] shows that some of them are close to each other, for
example, Г
max
and A
min
. At the same time, it is evident that MR is less surface active due to
less negative values of such parameters as П
cmc
, ΔG
m
and ΔG
ad
. Its micelle is less stable.
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