Dielectric Analysis on Aqueous Solutions by a High-Precision Double-Logarithmic-Derivative Method for Relaxation Frequency Calculation

In this paper, cooling dielectric spectra of NaCl and KCl aqueous solutions with different concentrations from 10°C to -60°C were first measured and the corresponding crystallization and dielectric relaxation behavior were analyzed. Subsequently, by establishing a high-precision double-logarithmic-derivative method, dielectric relaxation frequencies contained in dielectric spectra were accurately calculated. Furthermore, with the help of this proposed method, the relaxation polarization time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\tau}$</tex> and the activation energy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{E}_{\mathbf{a}}$</tex> of water molecules in composite ice formed by low-temperature aqueous solutions with different concentrations were calculated and analyzed. The results indicate that the accuracy of relaxation frequency identification reaches 2.10-4.67 times that of classical methods. As the concentration ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\beta}$</tex> increases, the relaxation time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\tau}$</tex> of water molecules in composite ice formed by low-temperature solution rapidly decreases and the activation energy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{E}_{\mathbf{a}}$</tex> significantly increases when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{0} &lt; \boldsymbol{\beta}\leq \boldsymbol{0.5}$</tex>. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\beta}\geq \boldsymbol{1}, \boldsymbol{\tau}$</tex> slowly increases and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{E}_{\mathbf{a}}$</tex> gradually decreases. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{E}_{\mathbf{a}}-\boldsymbol{\beta}$</tex> curves of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{NaCl}$</tex> composite ice and KCl composite ice show maximum values at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{\beta}_{\mathbf{NaCl}}=\boldsymbol{0.56}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta_{\text{KCl}}=0.62$</tex>, respectively.