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′ijkχ′ijk, imaginary χ″ijkχ″ijk parts of complex high frequency orientational susceptibility χijk* 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 xj's 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 Bergmann's 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 xj's 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 Fröhlich's equation as well as graphical plots of χ′ijk/χ0ijk−wjkχ′ijk/χ0ijk−wjk and χ″ijk/χ0ijk−wjkχ″ijk/χ0ijk−wjk curve at wjk→0wjk→0. c1 and c2 are positive for Fröhlich's method whereas most of the c2's are negative for graphical method. The dipole moments μ2 and μ1 for all the systems are calculated from slopes β   of χ′ijk−wjkχ′ijk−wjk curve at wjk→0wjk→0 and compared with the measured μ’s due to τ  ’s from ratio of slopes of χ″ijk−wjkχ″ijk−wjk and χ′ijk−wjkχ′ijk−wjk curves at wjk→0wjk→0 as well as χ″ijk−χ′ijkχ″ijk−χ′ijk linear curves and reported μ’s due to Higasi's most probable τ. The reported and measured τ’s and μ  ’s agree with the most probable τ0=τ1τ2 and μ1's of the eight system like τ2's and μ2's 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 μtheo's 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 Eyring's 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.