A mobility evaluation method through an accurate measurement, combining simulation of Least-Square Error Method (LSEM), is reported. The results reveal better accuracy of strong electrolytes with a higher concentration of 10-3 M. The evaluated mobility (μ) decreases with increase in concentration and strongly correlated the results of the conventional calculation from the interpolation method (Table)[1]. The calculated parameter of effective restoring force (k) increases with increase both in the frequency and concentration. Results are verified from Newton Equation, which can be widely developed on the ionic movement analysis.
EXPERIMENT
Figure 1(a) shows the device and system including a function generator (AFG-3252) and a lock-in amplifier (SR-830). Fig. 1(b) shows the standard deviation (SD) versus frequency of NaCl solutions from 10-4 to 10-3 M. With a higher concentration, the SD of NaCl solutions becomes smaller[2]. Fig. 1(c) is our device photo. The device contains a precision cut square reservoir on the resin surface. Au/Ge/Ni alloy and Auelectrodes were evaporated on both sidewalls. The system was finally enclosed in a shielding box to ensure the system grounded properly. For clearer understanding the fundamental electrolytic properties, eight reagent grade electrolytes were prepared because of their univalent, simple, and spherical structures (NaCl, KCl, NaBr, KBr, HCl, HBr, NaOH, and KOH).
MODEL DERIVATION
In our mathematical model, the mass of cation and anion are m1 and m2 respectively. E=V/d is electric field. Ionic behavior can be described as Newton's differential equation (Eq. (1)(2)), where S is relative displacement, k is effective restoring force parameter. The corresponding footnotes of each parameter is 1 and 2, respectively. The AC conductivity (σ(ω)), dielectric constant (ε') and dielectric loss (ε") can be derived as Eq.(3) and (4). The optimal μ and kcan be solved numerically from LSEM of six unknown parameters and eight equations.
RESULTS AND DISCUSSION
Figure 2(a) shows the the frequency dispersion of σ(ω) of NaCl solutions from 10-4 to 10-3 M, computed from ten measurements. All experiments in this paper are under 100 mVp-p bias and room temperature (298 K). Results reveal better accuracy of the proposed experiments. Fig. 2(b) shows the stable conductivity (σ) and bulk resistance (Rb) versus NaCl concentration at f=1 kHz, where Rb is calculated through the Nyquist plots[3]. In concentrated electrolytes, the charge increases and Rb decreases. The σ(ω) of NaCl increases with increase in frequency[4] with fixed concentration because ions cannot pass through the electrodes region, hence face highest resistivity. At higher frequencies, rapid periodic reversal of electric field makes ions difficult to diffuse, leading to mobility improvement. With a given frequency, all σ(ω) are also increased with increase in concentrations, which results in more effective charges and σ(ω) increases. In concentrated cases, the frequency- independent region in σ(ω) clearly occurs at higher frequencies. Fig.3 (a) shows the frequency dispersion of σ(ω) for different electrolytes of 10-3 M. All σ(ω) also increases with increase in frequency. In addition, σ(ω) of acids is much higher than neutral and basic electrolytes which can be ascribed to proton transfer[5]. Fig. 3(b) shows the frequency-independent region of σ and Rb. Fig. 4(a) shows frequency dispersion of dielectric constant (ε’) for different electrolytes under 10-3 M. Strong dispersion relation of ε’ at low frequencies, and saturates at higher frequencies. It can be explained as ions not only accumulating at the interface but also aligning themselves along the electric field. As frequency is increased, ions cannot follow rapid inversion in electric field and hence diminish their contribution to the polarization. Due to extra assistance of proton transfer, larger ε’ exists in acids compared to other electrolytes. Fig. 4(b) shows the frequency dispersion of dielectric loss (ε’’). As shown in figure, ε’’ increases up to a specific frequency after which it decreases. All electrolytes appear relaxation frequency at each peak value, which presents the relaxation of total polarization. The relaxation frequency of acids occurs at a higher frequency which is also attributed to the proton transfer, which enhances the conduction as well as the lower resistance.
Figure 5(a) shows the frequency dispersion of μ from eight electrolytes under 10-3 M. The initial μ value is small, then increases with increase in frequency, finally saturates at higher frequencies. Fig. 5(b) shows the frequency dispersion of k under 10-3 M. The initial k is also small, then increases with increase in frequency, and finally saturates at higher frequencies. Fig. 6(a) and Fig. 6(b) shows the stable value (at f=1kHz) calculated from LSEM of μ and k. With the concentration increases, the mobility decreases but k increases, which is reasonable in physical explanation.