Chemistry Reference
In-Depth Information
surface can be derived by combining Equation (6) with the adsorption isotherm
for the protein molecule (Equation (3)), or the respective expression for the
distribution of protein molecules over states (Equation (5)), which in the case
of diffusion-controlled adsorption serve as the boundary conditions for
Equation (6).
When the adsorption takes place on a spherical surface (drop or bubble), the
interfacial curvature can be approximately taken into account for sub-surface
concentrations c(0,t) far from equilibrium. This is done by introducing an
additional term into Equation (6), allowing for radial diffusion to the surface:
2
3
p
Z
p
r
D
p
p
t
0
t
c
0
D
r
4
5
c 0
;
t
t
0
G
ðÞ¼
2
c
0
ð
Þ
d
t
:
ð
7
Þ
0
Here, r is the radius of curvature, and the + and
signs refer to the diffusion
in the drop or in the solution around the bubble, respectively.
The corresponding equations for the separate contributions to the time-
evolution behaviour of the adsorption of protein and surfactant in a mixture
have the following forms:
2
3
p
Z
t
p
r
D
P
p
p
t
0
t
c
0P
D
P
r
4
5
c
P
0
;
t
t
0
G
P
ðÞ¼
2
c
0P
ð
Þ
d
t
;
ð
8
Þ
0
2
3
p
Z
t
p
r
D
S
p
p
t
0
t
c
0S
D
S
r
4
5
c
S
0
;
t
t
0
G
S
ðÞ¼
2
c
0S
ð
Þ
d
t
;
ð
9
Þ
0
where D
P
and D
S
are the diffusion coefficients of protein and surfactant,
respectively, and c
0P
and c
0S
are the corresponding bulk concentrations.
14.3 Materials and Methods
Lysozyme from chicken egg-white (Sigma, L-6876, 14.3 kDa, pI
11) was
used without further purification. All protein solutions were prepared in 10 mM
sodium phosphate buffer (pH
¼
7.0) from appropriate stock solutions of
Na
2
HPO
4
and NaH
2
PO
4
. The solutions were prepared with Millipore water.
The surface tension of the buffer solution at 211C was 72.7 mN m
1
. Mixed
protein + surfactant solutions were prepared keeping the concentration of the
protein constant and varying the surfactant concentration. The surfactant was
sodium dodecyl sulfate (SDS) with a critical micelle concentration of 8
10
3
mol L
1
.
The dynamic surface tension of pure and mixed protein solutions at short
adsorption times was measured using the maximum bubble pressure tensio-
meter BPA-1P (Sinterface Technologies, Germany). This technique is based on
B
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