Double relaxation phenomena of di-substituted benzenes and anilines in non-polar aprotic solvents under high frequency electric field

The derived linear equation (chi(oij) - chi(ij)')/chi(ij)' = omega(tau(1)+tau(2))chi(ij)"/chi(ij)' - omega(2)tau(1)tau(2) for different weight fractions w(j) of di-substituted benzenes and anilines (j) in aprotic and non-polar solvents (i) C6H6 and CCl4 under 9.945 GHz electric field are obtained from the available measured dielectric relative permittivities at 35 degreesC. The double relaxation times tau(1) and tau(2) of the flexible part and the whole molecule are estimated from the slope and intercept of the above equation. chi(ij)' and chi(ij)" are the real and imaginary parts of the high frequency complex orientational dielectric susceptibility chi(ij)* and chi(oij) is the low frequency dielectric susceptibility, which is real. They are, however, related with the measured relative permittivities. Values of tau(j) are calculated from the ratio of the individual slopes of the variations of chi(ij)" and chi(ij)' with w(j) at w(j) --> 0, assuming single Debye-like dispersion and compared with Murthy et al. [Indian J Phys, 63B (1989) 49 1] and Gopalakrishna [Trans Faraday Soc, 53 (1957) 767]. The weighted contributions c(1) and c(2) towards dielectric relaxations for tau(1) and tau(2) can, however, be obtained from Frohlich's theoretical formulations of chi(ij)'/chi(oij) and chi(ij)"/chi(oij) and compared with those from the experimentally measured values of and (chi(ij)"/chi(oij))(wj-->0). The latter measured values are employed to get symmetric distribution parameter gamma to yield symmetric relaxation time tau(s). The curve of (1/phi) log(cos 0) against 0 in degrees together with the values of (chi(ij)'/chi(oij))(wj-->0) and (chi(ij)"/chi(oij))(wj-->0) experimentally obtained, gives the asymmetric distribution parameter delta to get the characteristic relaxation time tau(es). All these findings ultimately establish the different types of relaxation behaviour for such complex molecules. The dipole moments mu(1) and mu(2) for the flexible part and the whole molecule are ascertained from tau(1) and tau(2) and the linear coefficients beta(1) of chi(ij)' versus w(j) and beta(2) of sigma(ij) versus w(j) curves respectively, where sigma(ij) is the hf conductivity. The values of p are finally compared with the reported it's and mu(theo)'s derived from available bond angles and bond moments of the substituted polar groups of di-substituted anilines to conclude that a part of the molecule is rotating while the whole molecular rotation occurs for di-substituted benzenes. The slight disagreement between measured values of mu and mu(theo) can, however, be interpreted by the inductive, mesomeric and electromeric effects of the polar groups of the parent molecules.