3.3.1 Measurement Setup
3.3.1.1 Thermostat Assembly
Temperature control was ensured by using the thermostat assembly which is described in detail in Refs. [60,61]. The thermostat consists of a thermal insulated bath of about 60 L silicone oil (Baysilon M5®, Bayer) in which a mechanical stirrer, a heat exchanger, a source of heat, a platinum resistance thermometer, and the measuring cell are immersed.
Via the heat exchanger a cryostat (HM 90W, Holzwarth & Co.), which acts as cold bath, is coupled to the thermostat. A thorough mixing of the bath is ensured by a mechanical stirrer. The temperature is controlled by a PID controller joined to an a.c. bridge which is connected to the platinum resistance thermometer. The error voltage of the bridge is used for temperature measurement and, via the PID controller, for controlling heating power of the heating source as well. [61] With this assembly a temperature stability of ± 2 mK was achieved. The temperature of the thermostat bath and simultaneous measurement temperature was determined by an ASL F-250 MkII thermometer (Automatic Systems Laboratories, Milton Keynes). The lower limit of the working range at about -60 °C is set by the insufficient cooling power of the cryostat, the upper limit at about 50 °C by the flammability of ethanol, which is used a cooling liquid.
3.3.1.2 Conductivity Cells
The used conductivity cells are already described in Ref. [134]. The conductivity cells consist of a two-electrode arrangement and feature a small sample volume of only 2-3 mL, which is very important for investigation of expensive electrolytes such as ILs. Due to the cell geometry the cell constants are independent of the fill level and due to the small temperature coefficient of the used Pyrex®-glass, they are assumed to be temperature independent [61,133]. The cell constants are listed in Table 3-3, an example of the conductivity cells is shown in Figure 3-12. The cells were filled and sealed gas tight in a glove-box under Ar-atmosphere. For fast and easy measurements, a mounting was used that fits in the top cover of the thermostat bath and can hold up to 10 conductivity cells.
Figure 3-12: Conductivity cell for conductivity measurements.
3.3.1.3 Conductivity Bridge
The exact design of the used conductivity bridge is described by Wachter et al. [60]. The conductivity bridge is made up of a symmetrical Wheatstone-bridge with a Wagner earth, a resistance decade and a sine generator, which feds the measuring bridge with alternating voltage and enables measurements in a frequency range from 30 Hz to 10 kHz. The measuring cell represents a branch of the Wheatstone-bridge. The electrical equivalent circuit of the measuring cell consists of a series connection of the ohmic resistance of the electrolyte RE and the double-layer capacity at the phase boundary Cd. Opposed to it is the reference impedance which is, due to practical reasons, made up of parallel connection of the resistance decade and a capacitor. The balancing conditions are fulfilled, if:
( )
2E 1
E d
R R
ωR C −
= + (3.28)
( )
21
d E d
C C
ωR C −
= + (3.29)
where R is the resistance and C the capacity of the balanced measuring bridge. (ωRECd)-2 becomes negligibly small and therefore R to RE, by platinisation of the electrodes due to the enlarged electrode surface and Cd respectively. Actually a slight frequency dependence of RE in ω-1 was found.
3.3.2 Calibration of Conductivity Cells
Since some measuring cells needed extensive repairs, a calibration of these measuring cells was necessary. Instead of using internal references, a direct calibration via aqueous KCl-solutions was performed as no reliable reference cell with a cell constant of similar magnitude was available.
The diluted aqueous KCl-solutions of known concentrations were made by adding weighed KCl (Merck, supra pure) under nitrogen into tri-distilled, gas-free weighed water. The used scale (AE240 range I d = 0.01 mg, II d = 0.1 mg, Mettler) has an accuracy of ± 0.01 mg.
The equivalent conductivity Λ25KCl°C of KCl can be calculated according to a conductivity equation given by Barthel et al. [133]:
1 2 3 2
149.873 95.01c 38.48 logc c 183.1c 176.4c
Λ = − + + − (3.30)
where c is the concentration in mol L-1. The electrolyte resistance RE is obtained by extrapolation of the frequency dependent resistance values Rν to infinite frequencies, as explained in Chap. 3.3.3. To get the exact electrolyte resistance RKCl, RE is corrected by subtraction of the supply line resistance, which was determined to be 0.3 Ω for all measuring cells. The cell constants B were calculated with the determined resistance
H O2
R of the applied water according to Eq. (3.31).
2
1 1 1
KCl H O
B c
R R
⎛ ⎞−
= Λ ⎜⎜⎝ − ⎟⎟⎠ (3.31)
Every cell was calibrated with three 0.01 M KCl-solutions at 25 °C. The cell constants for each measuring cell show maximum errors which are based on errors of KCl concentration and temperature regulation and inaccuracies during extrapolation of the frequency dependent Rν values as well. The extent of these specific errors can only be estimated;
therefore a rigorous calculation of errors is not feasible. The calculated mean values of the cell constants are listed in Table 3-3 along with the corresponding maximum errors and relative errors which were obtained by deviations of the results of the three measurements.
Table 3-3: Cell constants of the conductivity cells and the corresponding maximum and relative errors.
Cell B [cm-1] ΔB [cm-1] ΔB100
B [%]
2 38.45 0.13 0.3
3 48.13 0.15 0.3
4 57.9 0.2 0.4
5 62.63 0.14 0.2
6 91.0 0.2 0.2
7 47.33 0.14 0.3
8 52.5 0.2 0.4
The determined errors are much larger than the errors that were originally determined for these cells by Carl [134]. These may be due to inappropriate storing and handling of the cells in the past and insufficient platinisation of the electrodes which resulted in stronger frequency dependence as well. The cell constants are assumed to be temperature independent according to results of previous studies [61,133].
3.3.3 Data Editing and Evaluation
As explained in Chap. 3.3.1.3, due to the applied parallel connection of the reference impedance, a dependency of Rν in ω-2 was expected. Instead of that, a dependency of Rν in ω-1 was found. Therefore the frequency dependent Rν values were analysed according to Eq. (3.32) and extrapolated to infinite frequencies to get the real electrolyte resistance RE
from the interception with the y-axis.
1
Rν =RE +bν− (3.32)
The obtained value for RE was corrected by the sum of the supply line resistances. From the determined RE values the specific conductivities κ were calculated with the previously determined cell constants B according to the following equation:
E
B
κ = R (3.33)
Due to their magnitude and their impact on the determined specific conductivities, the relative errors of the cell constants are also assumed to be the relative errors of the specific conductivities. Other specific errors, such as inaccuracies during extrapolation of the frequency dependent Rν values and errors of temperature regulation, can only be estimated and are assumed to be negligible. In general, purities of the examined ILs are much lower compared to organic solvents and inorganic salts which can be obtained with very high purities. Therefore the required measuring accuracies for examination of ILs are also lower. The applied measurement setup is consequently appropriate.