Microscopic Relaxation Time Research Articles

Frequency dependence of the relative permittivity of polar substances

A study of the Brownian motion of a dipolar molecule surrounded by a dispersive dielectric medium has resulted in the following generalization of Onsager's equation ( - ∞)(2* + ∞)(2 + 1)/3(2* + 1) = (4πNμ2/3kTV)((∞ + 2)2/9)(1/(1+iωτμ')) where τμ' is a microscopic relaxation time which includes the effect of dipole-dipole coupling.

Theory of Higher-Order Effects in Fluids

A method is presented which, in principle, enables one to calculate higher-order coefficients for transport in fluids. To illustrate this theory the second-order terms in the pressure tensor which depend on the mass velocity are presented and evaluated approximately in terms of a microscopic relaxation time. Under certain approximations it is found that it is possible to sum the higher-order terms to every order.

Dielectric Relaxation of Polar Liquids

The statistical theory of the dielectric relaxation of polar liquids is developed using the fluctuation-dissipation approach to linear dissipative phenomena, and an expression is derived relating the complex dielectric constant to a time-dependent microscopic correlation function. It is found that a finite number of microscopic relaxation times leads to an equal number of macroscopic decay times, and, in the case of a single relaxation time τ0, the decay time is given by T0=[3ε0/(2ε0+ε∞)]τ0,ε0 being the static dielectric constant, and ε∞ being the high frequency dielectric constant. Relaxation times are also determined for systems having two decay times, and for systems characterized by the circular-arc and skewed-arc distribution functions.

The Application of Onsager's Theory to Dielectric Dispersion

It is shown that previous applications of Onsager's theory to dielectric dispersion have contained an incorrect assumption about the behaviour of the reaction field when the applied field is varying. An equation for the complex dielectric constant is derived, using Onsager's model and taking proper account of the reaction field. An approximate method of solving the equation is developed and it is shown that the equation approximates closely to the simple Debye equation - ∞ = (0 - ∞)/(1 + jωτ) the microscopic and macroscopic relaxation times being almost identical.