Supporting Information
A simple method for assessment and minimization of errors in
determination of electrophoretic or electroosmotic mobilities and
velocities associated with the axial electric field distortion
Paweł Nowak, Michał Woźniakiewicz*, Paweł Kościelniak
Jagiellonian University in Kraków, Faculty of Chemistry, Department of Analytical Chemistry,
Kraków, Poland
Abstract
It is commonly accepted that the modern capillary electrophoresis instruments equipped
with efficient cooling system enable accurate determination of electrophoretic or
electroosmotic mobilities. It is also often assumed that velocity of migration in a given
buffer is constant throughout the capillary length. It is simultaneously neglected that the
non-cooled parts of capillary produce extensive Joule heating leading to an axial electric
field distortion, which contributes to a difference between the effective and nominal
electric field potentials and between velocities in the cooled and non-cooled parts of
capillary. This simplification introduces systematic errors, which so far were however not
investigated experimentally. There was also no method proposed for their elimination. We
show a simple and fast method allowing for estimation and elimination of these errors
that is based on combination of a long-end and short-end injections. We use it to study
the effects caused by variation of temperature, electric field, capillary length, and pH.
Corresponding Author:
*Michał Woźniakiewicz, PhD, Jagiellonian University in Kraków, Faculty of Chemistry,
Department of Analytical Chemistry, Kraków, Poland, Ingardena St. 3, 30-060 Kraków, Poland,
michal.wozniakiewicz@uj.edu.pl, tel./fax: +48 12 663 20 84
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1. Velocities in the cooled and non-cooled sections
From the plots presenting relationship between average velocity and contribution of the noncooled section one can calculate local velocities in the thermostated and unthermostated
capillary parts. The values obtained using different separation voltages and 59.0 cm long
capillary have been depicted in Fig.S-1.
Fig.S-1.The calculated values of local electrophoretic (A), electroosmotic (B) or total/apparent (C)
velocities in the cooledor non-cooled (C/NC) capillary sections, referring to variable temperature of coolant
and separation potential. Owing to the calculation method used to obtain these data, which is based on
linear model fitted to only two independent experimental points, these values should be used rather for
qualitative comparison than for quantitative analysis.
Generally, a steep increase of the velocity in the cooled region is observed with growing
temperature and separation voltage. The velocities in the non-cooled region, interestingly,
behave in a quite specific manner. Electroosmotic velocities grow linearly with temperature,
however not so steep as in the cooled region. The absolute values of electrophoretic velocities,
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in turn, grow only subtly or even decrease with temperature, as it is noted for 25 and 30 kV
voltages, yielding yet greater nonuniformity of axial velocity throughout the capillary. It is
noticeable that at higher temperature the change of electrophoretic velocity between two
capillary parts is really pronounced, even 5-fold difference is noted. It implies that difference in
the local electric field potentials can be similarly significant, yet greater than 1.5-fold difference
noted by Krylov’s group at low temperature [1]. The sum of electrophoretic and electroosmotic
velocities, i.e. total velocity, resembles the behavior of electroosmotic component due to its
leading contribution. All these values, however, should be used rather for indication of trends
than for quantitative description. It results from the calculation method, based on an approximate
linear model.
At this point an interesting question emerges, whether different values of electroosmotic velocity
in the cooled and non-cooled parts indicate that the bulk solution migrates with different velocity
in the same capillary vessel of the same diameter? One should be aware that the mass
conservation low is always fulfilled, so that any changes in axial velocity would be adequately
compensated by changes of pressure [2,3], but such phenomenon cannot be confirmed now.
Remarkably, radial gradients of temperature, pressure and velocity contribute to laminar flow
profile of bulk solution, and they may also have a bearing on the measured migration times of
EOF marker. The other issue is accuracy of our method of velocity determination, especially due
to the fact that the model is built only on two independent measurements, and that some
variations of electroosmosis could also take place in time of separation. Deeper insight into
these phenomena seems to be very interesting, and this will be one of the aims of our future
work.
To confront differences in velocities in the cooled and non-cooled sections with differences in
temperature reached in each part, we have employed a simplified universal method for
predicting electrolyte temperatures (SUMET) proposed by Krylov’s group [4]. On this basis the
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differences in temperature have been estimated at four separation voltages, depicted in
Table S-1.
Table S-1. The predicted relation between separation voltage and difference of temperature between the
cooled and non-cooled capillary parts at nominal temperature of coolant amounting 20 ̊C.
Separation
Temperature
voltage (kV)
difference ( ̊C)
12.5
6.3
20.0
12.5
25.0
17.9
30.0
23.3
It is seen that the differences are quite significant, up to 23.3 ̊C for separation voltage of 30 kV
and temperature of coolant of 20 ̊C. One may assume that they will be yet greater at higher
temperature of coolant due to the abovementionedauto-thermal effect.
2. Effect of capillary length
Separation voltage has been decreased proportionally to capillary length, to keep the value of
the nominal electric field potential unchanged. Fig.S-2 shows the results obtained for two distinct
potentials. One can see that each capillary length has its own characteristics of the generated
errors. The errors differ in magnitude for distinct capillaries despite keeping the same potential,
but also in some temperature ranges, differ in sign. It is also interesting that the shape of plots is
however somehow similar between distinct capillaries of the same potential values. In general, it
implies that in the shorter capillary the velocities reached in the cooled region can be lower than
in the non-cooled region, what was not observed for the longer capillary. This may be caused by
the more significant role of viscosity-related effect comparing to field distortion-related effect in
the shorter capillary. The relation between velocities can be however reversed at specific
temperature values, as it is also seen on the charts (intersection with x axis). Another interesting
observation is that the relative errors can decrease with increase in nominal temperature of
coolant, although the absolute errors still grow in such case (not shown). Further elucidation of
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these outcomes is not the current purpose, but seems to be fairly promising to enable a deeper
understanding of these phenomena.
Fig.S-2. Presentation of the predicted relative errors of electrophoretic (left) or electroosmotic (right)
mobilities as a function of nominal temperature in relation to two distinct total capillary lengths. Two
different nominal voltage-to-length ratios (electric field potentials) have been chosen and kept unchanged
for the long and short capillaries.
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3. Supplementary results
Table S-2. The values of current, power, and power per length measured for the minimal and maximal
separation voltages applied during experiments: 12.5 and 30.0 kV, in relation to temperature, for 59.0 cm
total capillary length.
Current (µA)
Temperature
( ̊C)
20
30
40
50
60
Power (W)
Power / length
(W/m)
12.5 kV
30.0 kV
12.5 kV
30.0 kV
12.5 kV
30.0 kV
35.4
42.8
50.5
58.5
66.4
97.0
120.7
144.0
168.8
190.7
0.44
0.54
0.63
0.73
0.83
2.91
3.62
4.32
5.06
5.72
0.75
0.91
1.07
1.24
1.41
4.93
6.14
7.32
8.58
9.70
Table S-3. The values of CV in percentages (coefficient of variation) calculated for migration times of EOF
marker (DMSO) and 10-hydroxywarfarin (W10) from 3 repetitions, performed using separation voltage of
30 kV.
20
30
40
50
60
long-end
short-end
injection
injection
DMSO
W10
DMSO
W10
2.1
2.2
1.7
3.3
1.9
4.2
1.5
4.4
1.6
4.6
1.3
4.5
1.2
3.4
2.6
2.9
8.4
10.4
3.1
5.2
References
[1] Evenhuis, C. J., Musheev, M. U., Krylov, S. N., Anal. Chem. 2010, 82, 8398–8401.
[2] Xuan, X., Li, D., Electrophoresis 2005, 26, 166–175.
[3] Xuan, X., Li, D., J. Chromatogr. A 2005, 1064, 227–237.
[4] Evenhuis, C. J., Musheev, M. U., Krylov, S. N., Anal. Chem. 2011, 83, 1808–1814.
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