Impedance Spectroscopy of Binary Mixtures of Dimethyl Silicone Fluid and Methyl Iso Butyl Ketone

A precision LCR metre was used to measure the parallel resistance (RP) and parallel capacitance (CP) of a capacitive cell filled with samples of binary mixes of methyl isobutyl ketone (MIBK) and dimethyl silicone fluid (DMSF), over the frequency range of 100 Hz to 2 MHz, at a temperature of 303.15 K. Using RP and CP, complex impedance Z*(ω) was computed. A four-element equivalent circuit model was used to fit the complex impedance data. The fitting provided the values of various circuit elements representing various electrical processes occurring in the capacitive measurement cell under the influence of an applied ac field. The Bode plot presentation of the complex impedance data confirmed the values of various circuit elements determined using the fitting process. Complex impedance formalism supports the observation of the electronic double-layer capacitance (EDLC) phenomena and ionic conduction relaxation phenomena.


Introduction
A versatile technique for simultaneous electrical and dielectric property estimation of materials [1] is known as complex impedance spectroscopy (CIS) [1].The dielectric and electric behavior of single crystal, polycrystalline, amorphous ceramic materials [1-5] and other materials has extensively been characterized using such a powerful approach [1][2][3][4][5][6].Contribution of the overall electrical characteristics in the frequency domain caused by electrode reactions at the electrode/sample contact [2] and ion movement through the materials [2] have also been evaluated and separated by this technique [2][3].
Previously, we published the results of the study of complex permittivity spectra for binary combinations of MIBK and DMSF at 303.15 K temperature over the 100 Hz to 2 MHz frequency range [7].To gain information about the electrical processes occurring in the same system, under the influence of the applied ac field of frequency ranging from 100 Hz to 2 MHz at 303.15 K temperature, CIS study was carried out and the results are reported here [8].

Experimental Details
ACS Chemicals Pvt. Ltd. (India) provided the MIBK (AR Grade) [6][7], whereas, DMSF (With 350 Centistokes Viscosity) was purchased from Narayan Co-operation Pvt.Ltd [6][7].No purification process was performed in our laboratory before utilization for the measurements.The binary liquid solutions of sixteen weight fractions of MIBK and DMSF were prepared using a digital analytical balance meter with an accuracy of ± 0.0001 g [6][7].Using an Agilent E-4980 precision LCR meter, parallel resistance (RP) and parallel capacitance (CP) of a capacitive cell filled with the liquid samples were measured in the range of 100 Hz to 2 MHz at 303.15 K [6][7].The design of sample container (capacitive cell) was created in our lab and was fabricated by a local manufacturer [6][7].The information regarding the sample holder is provided in reference [6][7].Frequency-dependent values of the parallel capacitance (Cp) and parallel resistance (Rp) were used to calculate complex impedance (Z* (ω)) using the equation [9]: Where ω = 2πf, CP = Capacitance with the Sample, Rp= Parallel Resistance with the Sample, CERROR= C0-CTh, CTh= Theoretical Capacitance, and C0 = Capacitance without the Sample.

Results and Discussion
Figures 1(A) and (B) show the spectra of the real and imaginary parts of Z * (ω), for samples of different concentrations.It can be observed that Z′ (ω) rapidly drops for the concentration range 0.593 ≤ XA ≤ 1.000 with frequency in the whole frequency range.Additionally, it is noted that for the concentration range 0.000 ≤ XA ≤ 0.548, it is steady up to 10 4 Hz and rapidly drops after 10 4 Hz.Z′′ (ω) spectra for the MIBK and up to XA ≤ 0.769 exhibit maxima at a frequency higher than 10 3 Hz.With an increase in the concentration of DMSF in MIBK, the peak of the spectra shifts towards lower frequency regime.From the inset of Figure 1(B), it can be seen that the scaling of the impedance spectra works, perfectly well only in the frequency region where the electrode polarization effects are absent in the dielectric spectrum; however, for the lower frequencies, the scaling does not work [6,10].Experimentally obtained Z*(ω) data of the studied systems were fitted to the electric circuit model, shown in the inset of Figure 2, which consists of two resistors and capacitors.Figure 2 shows the graph Z " (ω) versus Z ' (ω) for three representative concentrations, namely 0.000, 0.240 and 0.492.As can be seen from this figure that the experimental data are perfectly overlapping the fitted data for all the concentrations.Values of the resistor (R2) and capacitors (C1 and C2) for all the concentrations, obtained by the fitting procedure, are tabulated in Table 1.The geometric time constant is calculated using τg = R2C1 [6,11].The value of τg is compared with the ionic conductivity relaxation time (τσ) [12].Both the values of τg and τσ are matching with each other.It can be observed from Table 1 that C1 and R2 increase and decrease, respectively, as the concentration of MIBK in DMSF decreases [6].Capacitor C2 represents the electronic double-layer capacitance (EDLC) [6].Capacitor (C2) values, changes from the order of μF to nF as DMSF concentration in MIBK rises [6].The resistor (R1), represents the external circuit's resistance, which is minimal at very high frequencies [6].

Conclusions
The present study examined the frequency and concentration dependence of Z * (ω) for the combination of two compounds, DMSF and MIBK, in liquid form, in the lower frequency regime 100 Hz to 2 MHz at the constant single temperature 303.15 K.The maxima is observed in the imaginary part of Z * (ω), and it can be concluded from the result that the maxima shifts towards the lower frequency regime as the amount of DMSF increases in MIBK.The scaling of the impedance spectra works perfectly well, only in the frequency region, where the electrode polarization effects are absent in the dielectric spectrum.However, for the lower frequencies, the scaling does not work.Derived data of Z * (ω) were fitted to the four element RC -circuit model, consisting of two capacitors and two resistors.Each of the four elements of the equivalent circuit are associated with the electrical process taking place in the capacitive cell filled with the bulk sample formed by mixtures of DMSF and MIBK.Three of the four fitting parameters (C1, C2 and R2) of the equivalent circuit are found to vary systematically with concentration of DMSF in MIBK.Very small and nearly concentration independent value of the fourth element R1 of the circuit, represents equivalent external resistance of the capacitive cell.Bode plot presentation of Z * (ω) data also provided nearly same values of the capacitive and resistive elements of the equivalent circuit.

Figure 2 .
Figure 2. Representative Plots of Experimental Data Points of Z " (ω) versus Z ' (ω), for XA = 0.000, 0.240 and 0.492.Solid curves are obtained by fitting experimental data points to the four element equivalent circuit shown in the inset.