Investigation of dielectric relaxation in tributyl phosphate from susceptibility and conductivity measurement under microwave field

Susceptibility (χij’s) and conductivity (σij’s) measurement techniques are proposed to determine dielectric behaviour in terms of relaxation time τ and dipole moment µ of tributyl phosphate (TBP, j) dissolved in various non-polar solvent (i) (p-xylene, cyclohexane and n-heptane) under S-band, C-band, X-band and Ku-band microwave field at different temperatures (25, 30 and 35°C) within Debye’s dielectric model. The possibility of double relaxation times (τ2 and τ1) for inter- and intra-molecular rotation of the polar molecule TBP is predicted from measured data of $${{\chi_{{{\text{ij}}}}^{{\prime}} }}$$ (= $${{\varepsilon_{{{\text{ij}}}}^{{{\prime}}} }}$$ −e∞ij), $${{\chi_{{{\text{ij}}}}^{{{\prime\prime}}} }}$$ (= $${{\varepsilon_{{{\text{ij}}}}^{{{\prime\prime}}} }}$$ ) and χ0ij (= e0ij – e∞ij) at different weight fractions wj’s of solute, applying slope and intercept of $$\frac{{\chi_{{0{\text{ij}} - }} \chi_{{{\text{ij}}}}^{{\prime}} }}{{\chi_{{{\text{ij}}}}^{{\prime}} }}$$ against $$\left( {\frac{{\chi_{{{\text{ij}}}}^{{{\prime\prime}}} }}{{\chi_{{{\text{ij}}}}^{{\prime}} }}} \right)$$ linear equation to confirm mono relaxation behaviour τ2 only. τ’s are measured from individual variation of real and imaginary parts of χij and σij with wj’s as well as linear relation of imaginary against real. The dipole moments µj’s are measured from both the measurement techniques under S-band (3.2 GHz), C-band (6.8 GHz), X-band (11.2 GHz) and Ku-band (16.5 GHz) microwave field at 25, 30 and 35°C temperatures. Various molecular associations are determined in terms of relaxation time τ and dipole moment µ in polar–non-polar liquid mixture. Thermodynamic energy parameters are also calculated from Eyring rate theory to predict molecular dynamics or nature of molecular environment surrounding the polar molecule TBP. Debye relaxation mechanism in all the systems under observation is validated by the estimated Debye factor from both the measurement methods. A new simple microwave sensor is proposed to design for determination of TBP concentration from measured penetration depth at different temperatures under microwave field.