Dielectric Relaxation Behavior of Amide and Phenol Mixtures in C₆H₆ Under Microwave Field

Abstract

Susceptibility (χ_ijk) and conductivity (σ_ijk) measurement techniques are used to determine the dielectric relaxation behavior of N,N-dimethylformamide (DMF) (j) and N,N-dimethylacetamide (DMA) (j) with phenol (k) dissolved in C₆H₆ (i) under S-Band, C-Band, X-Band and Ku-Band microwave fields at different temperatures (25, 30 and 35 °C) using Debye’s dielectric model. The possibility of relaxation times (τ₂ and τ₁) for inter and intra molecular rotation are predicted from measured data of $\chi_{ijk}$$\left( { = \varepsilon_{ijk}^{\prime} - \varepsilon_\infty{ijk} } \right)$, $\chi_{ijk}^{\prime\prime}$ (= $\varepsilon_{ijk}^{\prime\prime}$) and $\chi_{0ijk}$(= $\varepsilon_{0ijk}$ − $\varepsilon_\infty{ijk}$) applying slope and intercept of linear plots of $\frac{{\upchi }_{0ijk-}{\upchi }_{ijk}^{\prime}}{{\upchi }_{ijk}^{\prime}}$ against $\left(\frac{{\upchi }_{ijk}^{\prime\prime}}{{\upchi }_{ijk}^{\prime}}\right)$, which confirm mono relaxation behavior τ₂ only for eight polar mixtures. The τ values are calculated from $\chi_{ijk}^{\prime}$ and $\chi_{ijk}^{\prime\prime}$ parts of complex susceptibility $\chi_{ijk}^{\ast}$ with variation of weight fraction (w_jk) of solutes as and the linear slope of the imaginary against real parts of the complex susceptibility data. Similarly, relaxation times, τ, are also estimated from the ratio of slopes of imaginary $\sigma_{ijk}^{\prime\prime} = \left( {\omega \in_{0} \in_{ijk}^{\prime} } \right)$ and real $\sigma_{ijk}^{\prime} = \left( {\omega \in_{0} \in_{ijk}^{\prime\prime} } \right)$ parts of the complex conductivity $\sigma_{ijk}^{\ast}$, as well as the linear slope of imaginary against real parts of the complex conductivity data. The τ values from both measurements are compared. The dipole moments $\mu_{ijk}$ values are estimated from both measurement techniques by applying Debye’s model of polar–non-polar liquid mixture under S-Band (3.8 GHz), C-Band (7.2 GHz), X-Band (10.5 GHz) and Ku-Band (17.6 GHz) microwave fields at 25, 30 and 35 °C. Various molecular associations are determined in terms of relaxation time τ and dipole moment µ to estimate different molecular interactions among polar molecules or polar–non-polar molecules. Thermodynamic energy parameters are also calculated using Eyring’s rate theory to predict molecular dynamics or nature of molecular environment surrounding the polar molecules DMF, DMA or phenol (p-cresol, p-chlorophenol, 2,4 dichlorophenol and p-nitrophenol). The existence of the Debye relaxation mechanism in all the systems under observation is validated by the estimated Debye factor from both of the measurement methods. The values of $\gamma ={\Delta H}_{\tau }/{\Delta H}_{\eta }$ indicates that most of the molecules behave as solid phase rotors. A new simple microwave sensor is proposed, designed from measured penetration depths at different temperatures under microwave field.