Double relaxation phenomena of associated binary polar liquid mixture in non-polar solvent under high frequency electric field

Double relaxation times τ2 and τ1 due to whole molecular rotation and the flexible parts of the binary polar liquid mixture (jk) 3-bromoaniline and 1-propanol dissolved in non-polar solvent (i) benzene were estimated in terms of measured real χ ′ i j k , imaginary χ ″ i j k parts of complex high frequency orientational susceptibility χ i j k * and χ0ijk which is real at 20, 30, 40 and 47 °C experimental temperatures for 0.0, 0.25, 0.50,0.75 and 1.00 mole fractions xjʹs of 1-propanol under 9.1 GHz electric field. The slopes ω(τ2 + τ1) and intercepts ω2τ2τ1 of the analytical straight line equations used to estimate τ2 and τ1 were derived from Bergmannʹs equation [U. Saha, S.K. Sit, R.C. Basak, S. Acharyya, J. Phys. D: Appl. Phys. 27 (1994) 596] based on two Debye type dispersion model of binary polar mixture. The systems 3-bromoaniline in C6H6 and 1-propanol in C6H6 show τ2 and τ1 only at 47 °C temperature like 3-bromoaniline + 1-propanol in C6H6 at 20 and 47 °C temperatures for 0.25 and 0.50 mole fractions xjʹs of 1-propanol. The binary polar mixture for xj = 0.75 of 1-propanol is an exception exhibiting double relaxation times at all the experimental temperatures. The relative contributions c1 and c2 due to τ1 and τ2 for eight non-rigid systems were calculated from Fröhlichʹs equation as well as graphical plots of χ ′ i j k / χ 0 i j k − w j k and χ ″ i j k / χ 0 i j k − w j k curve at w j k → 0 . c1 and c2 are positive for Fröhlichʹs method whereas most of the c2ʹs are negative for graphical method. The dipole moments μ2 and μ1 for all the systems are calculated from slopes β of χ ′ i j k − w j k curve at w j k → 0 and compared with the measured μ’s due to τ’s from ratio of slopes of χ ″ i j k − w j k and χ ′ i j k − w j k curves at w j k → 0 as well as χ ″ i j k − χ ′ i j k linear curves and reported μ’s due to Higasiʹs most probable τ. The reported and measured τ’s and μ’s agree with the most probable τ 0 = τ 1 τ 2 and μ1ʹs of the eight system like τ2ʹs and μ2ʹs of the rest twelve systems. This indicates that double relaxation phenomena yield average τ and μ for binary polar mixture under GHz electric field. The associational behavior of the polar molecules are inferred from the theoretical dipole moments μtheoʹs in terms of bond angles and bond moments of the substituent polar groups to exhibit solute–solute or solute–solvent molecular association arising out of inductive, mesomeric and electromeric effects of polar groups in them. The associative natures are ascertained from convex or concave shape of τjk or μjk–xj curves and μjk–T curves respectively under different state of molecular environment. The thermodynamic energy parameters are calculated from Eyringʹs rate theory to know the molecular dynamics of the systems in order to establish the fact that the binary polar mixture obeys the Debye–Smyth relaxation mechanism.