Chemistry Reference
In-Depth Information
The theory of the Taylor dispersion technique is well described in the literature
[11-20], and so the authors only indicate some relevant points concerning this method
on the experimental determination of binary and ternary diffusion coef¿ cients (Figure
2).
It is based on the dispersion of small amounts of solution injected into laminar
carrier streams of solvent or solution of different composition, À owing through a long
capillary tube. The length of the TeÀ on dispersion tube used in the present study was
measured directly by stretching the tube in a large hall and using two high quality the-
odolytes and appropriate mirrors to accurately focus on the tube ends. This technique
gave a tube length of 3.2799 (
0.0001) ×10
4
mm, in agreement with less precise
control measurements using a good quality measuring tape. The radius of the tube,
0.5570 (
±
0.0003) mm, was calculated from the tube volume obtained by accurately
weighing (resolution 0.1 mg) the tube when empty and when ¿ lled with distilled water
of known density. At the start of each run, a 6-port TeÀ on injection valve (Rheodyne,
model 5020) was used to introduce 0.063 ml of solution into the laminar carrier stream
of slightly different composition. A À ow rate of 0.17 ml min
-1
was maintained by a
metering pump (Gilson model Minipuls 3) to give retention times of about 1.1
× 10
4
s. The dispersion tube and the injection valve were kept at 298.15K and 310.15K (
±
±
0.01K) in an air thermostat.
Dispersion of the injected samples has been monitored using a differential refrac-
tometer (Waters model 2410) at the outlet of the dispersion tube. Detector voltages,
V
(
t
), were measured at accurately 5 s intervals with a digital voltmeter (Agilent 34401
A) with an IEEE interface.
Binary diffusion coef¿ cients have been evaluated by ¿ tting the dispersion Equa-
tion (8)
V
(
t
) =
V
0
+
V
1
t
+
V
max
(
t
R
/
t
)
1/2
exp
[
- 12
D
(
t
-
t
R
)
2
/
r
2
t
]
(8)
to the detector voltages, where
r
is the internal radius of our Teflon dispersion tube.
The additional fitting parameters were the mean sample retention time
t
R
, peak height
V
max
, baseline voltage
V
0
, and baseline slope
V
1
. Gravitational instabilities and unwant-
ed convection are negligible because the carrier is confined to narrow bore capillary
tubing.
Extensions of the Taylor technique have been used to measure ternary mutual dif-
fusion coef¿ cients (
D
ik
) for multicomponent solutions. These
D
ik
coef¿ cients, de¿ ned
by Equations (3) and (4), were evaluated by ¿ tting the ternary dispersion equation
(Equation 9) to two or more replicate pairs of peaks for each carrier stream.
⎡
2
2
⎤
⎛
12
Dt t
(
−
)
⎞
⎛
12
D t t
(
−
)
⎞
()
(
)
1/ 2
(9)
Vt
=+ +
V Vt
V
t t
/
W
exp
−
1
R
+−
(1
W
) exp
−
2
R
⎢
⎥
⎜
⎟
⎜
⎟
0
1
ax
R
1
1
⎝
rt
2
⎠
⎝
rt
2
⎠
⎣
⎦
Two pairs of refractive index profiles,
D
1
and
D
2
, are the eigenvalues of the matrix of
the ternary
D
i
k
co
ef
ficien
t
s. I
n
these experiments, small volumes of ǻV of solution,
o
f
com
p
osition
and
are injected into carrier solutions of composition
c
c
+
Δ
c
c
+
Δ
c
1
1
2
2
and
c
, at time t = 0.
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