Chemistry Reference
In-Depth Information
layer:
25
þ
a
P
Y
P
:
P
o
0
Þ
Y
P
1
o
0
o
RT
¼
ln 1
Y
P
ð
ð
1
Þ
Here, P is the surface pressure, R the gas constant, T the temperature, and a
P
the intermolecular interaction parameter.
When a protein molecule with m ionized groups is interacting with an ionic
surfactant, Coulombic interactions occur and complexes will be formed. The
formation of such complexes is determined by the average activity of ions
participating in the reaction, (c
P
m
c
S
)
1/(1 1 m)
, assuming the average activity
coefficient to be equal to 1. Other complexes, such as between protein and buffer
ions, can also be formed, but these are less surface-active and therefore their
contribution to the surface pressure can be neglected. The respective equation of
state of the surface layer, consisting of proteins and ionic surfactants, is
þ
a
PS
Y
PS
þ
a
S
Y
S
P
o
0
Þ þ
Y
PS
1
o
0
o
RT
¼
ln 1
Y
PS
Y
S
ð
þ
2a
SPS
Y
PS
Y
S
:
ð
2
Þ
The subscript PS refers to the protein
surfactant complex and the subscript S
refers to the surfactant. The adsorption isotherms for the protein
surfactant
complex in state 1 and the surfactant not bound to the protein are
b
PS
c
P
c
S
1
=
1
þ
m
ð
Þ
¼
b
PS
c
m
=
1
þ
m
ð
Þ
c
1
=
1
þ
m
ð
Þ
P
S
h
Y
PS
2a
SPS
Y
S
i
;
o
G
1
1
Y
PS
Y
S
Þ
o
1
=
o
exp
2a
PS
o
1
¼
ð
3
Þ
o
ð
Y
S
1
Y
PS
Y
S
Þ
1
=
2
¼
b
S
c
S
c
C
ð
Þ
exp
2a
S
Y
S
2a
SPS
Y
PS
½
;
ð
4
Þ
ð
where we have
o
¼
(
P
i
¼
1
G
i
)/G (the subscript PS is here omitted for the sake of
simplicity), and Y
PS
¼
o
G. The q
u
antity c
C
is the surfactant counter-ion
concentration, so that we have (c
S
c
C
)
2
¼
c
S
in the absence of inorganic salt. The
quantity a
SPS
is the intermolecular interaction parameter describing the inter-
action of free surfactant with the protein
surfactant complex.
The distribution of protein adsorption over the states is given by an expres-
sion which follows from Equation (3) when written for any arbitrary jth state of
the complex:
o
j
o
1
o
ð
Þ
o
j
o
1
ð
1
Y
PS
Y
S
Þ
exp 2a
PS
Y
PS
o
G
j
¼
G
:
ð
5
Þ
h
i
P
n
o
i
o
1
o
ð
o
i
o
1
Þ
ð
1
Y
PS
Y
S
Þ
exp 2a
PS
Y
PS
o
i
¼
1
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