The primary purpose of simultaneous recording of conductivity and temperature as a function of time, was to obtain an additional indication besides T(t)-curves for phase transitions during cooling and heating of a sample (see Chaps. 3.4.2 and 6). After consideration of few precautions the recorded conductivity can, though at reduced accuracy, also be used for analysis of the temperature dependence of the specific conductivity.
In contrast to the cell constants of conductivity cells used for stationary conductivity measurements, the cell constants of the G(t)-T(t)-measuring cells are temperature dependent (see also Chap. 3.4.1.2). Several approaches were examined for analysis of this temperature dependence. A quadratic fit of the measurement data as shown in Figure 5-13 for the cell constants of three measuring cells calculated from conductivities and specific conductivities of three blends of the system EMIOTf/MPII yields sufficient accurate results and can be easily performed.
280 290 300 310 320
0.3 0.4 0.5 0.6 0.7 0.8
B / cm-1
T / K
Figure 5-13: Cell constants of G(t)-T(t)-measuring cells determined with blends of the system EMIOTf/MPII as a function of temperature and corresponding quadratic fits; (▬▬) 20 mol% MPII, (▬▲▬) 40 mol% MPII, (▬▼▬) 60 mol% MPII.
Analysis of the recorded conductivity with the calculated cell constants yields specific conductivities that are typically in good agreement with specific conductivities obtained by stationary conductivity measurements. In Figure 5-14 specific conductivities of
≈ 0.05 mol L-1 I2 in mixtures of EMIOTf/MPII are compared. The conductivities are calculated from G(t)-T(t)-measurement data and according to the VFT-equation (Eq. (5.1)) from conductivity data obtained from stationary measurements respectively. Deviations are only obtained at high temperatures which is mainly based on interfering signals for G(t)-T(t)-measurements. The main disadvantage of this method is that at least three values for specific conductivities of the sample, distributed over a broad temperature range, are necessary to obtain accurate cell constants.
220 240 260 280 300 320 340
0
Figure 5-14: Specific conductivities of ≈ 0.05 mol L-1 I2 in mixtures of EMIOTf/MPII calculated from conductivity data from dynamic conductivity measurements (▬) as a function of temperature at varying MPII concentrations and corresponding fits according to the VFT-equation (Eq. (5.1)) calculated from conductivity data obtained by stationary conductivity measurements;
(▬▬) 10 mol% MPII, (▬ ▬) 20 mol% MPII, (▬▲▬) 40 mol% MPII, (▬U▬) 50 mol% MPII, (▬▼▬) 60 mol% MPII, (▬V▬) 80 mol% MPII, (▬¡▬) 100 mol% MPII.
If the temperature coefficient of the applied glass is disregarded, the temperature dependence of the cell constant is primarily based on the fill level (hl) that is inversely proportional to the density (ρ):
2
where ms is the mass of the sample and rc the medial radius of the cell. The cell constants analysed in Figure 5-13 with regard to their temperature dependence are also inversely
proportional to the density of the sample. In Figure 5-15 the results from analysis of this relation according to linear and quadratic fits are shown for three blends of the system EMIOTf/MPII. With the proportional factor and the mass of the sample, the cell constant can be directly calculated from the density of the sample according to Eq. (5.3).
0.67 0.68 0.69 0.70 0.71 0.72
0.3 0.4 0.5 0.6 0.7 0.8
B / cm-1
ρ-1 / L kg-1
Figure 5-15: Cell constants of G(t)-T(t)-measuring cells determined with blends of the system EMIOTf/MPII as a function of density and corresponding linear (▬) and quadratic (▬) fits;
() 20 mol% MPII, (▲) 40 mol% MPII, (▼) 60 mol% MPII.
Thus, after determination of the proportional factor of the cell constant by calibration, the specific conductivity can be directly calculated from the recorded conductivity and the density of the sample and vice versa. Calculation of densities from conductivity data can be of special interest for highly viscous ILs due to viscosity induced errors for common vibrating tube densitometry [161]. As discussed in Chap. 3.4.1.2 the cell constant may be altered by crystallising samples and during cleaning of the cell. Therefore, it is necessary to regularly calibrate the cell to obtain sufficient accurate results.
5.3 Summary and Appraisal of Results
Specific conductivities of eleven ILs were determined in a temperature range between 5 °C and 50 °C, for the ILs BMPlFAP, BMPlOTf, and Me3SDCA for the first time. Analysis of the conductivity for several EMI and BMPl based ILs showed a strong influence of the anion and its varying size, basicity, and tendency to formation of hydrogen bridge bonds.
The impact of the alkyl chain length in the 1-alkyl-3-methylimidazolium-cation on the conductivity was examined as well. A growing chain length causes increasing van der Waals interactions, increasing ion radii and consequently decreasing ion mobilities.
Additionally, the density decreases and consequently the charge carrier concentration.
These factors cause a strong decrease of conductivity. The planarity and aromaticity of the cation has additional influence on the conductivity, i.e.: the conductivity increases with increasing planarity and aromaticity of the cation.
Evaluation of the fragility, based on the determined specific conductivities, yielded similar results as analysis of viscosity data from literature. The values for the strength D calculated from VFT-parameters are in the fragile range for all examined ILs. Thus, they show a strong non-Arrhenius behaviour and the validity of analysis of the temperature dependence of conductivity according to the VFT-equation is confirmed. The slight variations of D with varying anions at fixed cations and vice versa were addressed in terms of varying ionic interactions and coordination numbers. They generally match the assumptions discussed above. The strength D increases with increasing alkyl chain length in the cation due to increasing van der Waals interactions. By variation of the anion the magnitude of Coulombic interactions increases in the order DCA < BF4 < NTf2 < OTf resulting in increasing strength as well.
Evaluation of conductivity data with respect to fragility is based on the assumption that conductivity variations with temperature depend exclusively on viscosity changes. Despite this approximation, it is a useful method for classification of ILs since conductivities are often more accurate than viscosities determined with common rheometer devices and can be obtained much faster than highly accurate viscosities determined with an Ubbelhode viscometer.
The conductivities of the electrolyte mixtures are generally in the same order as are the conductivities of the applied solvent ILs. Analysis of the temperature dependence of the specific conductivities according to the VFT-equation yields accurate results in contrast to analysis of the temperature dependence of I3¯-diffusion coefficients. All examined systems
showed continuously increasing conductivities with decreasing MPII concentration.
Analysis of the measurement data according to a third grade polynomial yielded sufficient results for accurate interpolation of conductivities of MPII concentrations within the examined mixing range.
Specific conductivities obtained from conductivity data recorded with G(t)-T(t)-measuring cells showed good agreement with those calculated by the VFT-equation from specific conductivities obtained from stationary conductivity measurements. The temperature dependence of the cell constants was analysed and two possibilities for processing of conductivity data from continuous conductivity measurements were shown. The more time-consuming but also more reliable method is a separate determination of the specific conductivity of the sample for at least three different temperatures and calibration of the cell for each specific measurement. The other possibility is a temperature dependent calibration of the cell to obtain the proportional factor that correlates the cell constant and the reciprocal value of the density. Thus, after determination of this proportional factor, the specific conductivity can be directly calculated from the recorded conductivity and the density of the sample and vice versa. For this method regular calibration of the cell is necessary to obtain sufficient accurate results.
6 Determination of Phase Transition Points in Pure Ionic Liquids and their Binary Mixtures
In the following chapters the results from simultaneous T(t)- and-G(t) measurements (Chap. 3.4) in pure ILs and blends of ILs are summarised and discussed. The obtained (l)-(s)-phase transition points are crucial factors for application of electrolytes, since they determine the lower limit of the operating range of these electrolytes.
The accuracy of phase transition points of organic solvents and their binary mixtures determined by evaluation of T(t)-measurements along with the reliability of the measurement technique has been extensively discussed in Refs. [103,107,108]. The accuracy of the conductivity data obtained by simultaneous T(t)- and G(t)-measurements was analysed in Chap. 5.2. Analysis of the accuracy and comparison of phase transition points of ILs determined by evaluation of T(t)-curves and G(t)-curves follows in Chap. 6.1.
The results of examination of potential DSSC-electrolytes with the verified measurement techniques are summarised in Chap. 6.2.