An approximate theoretical calculation of the spin-lattice relaxation times in fluids near—but above—the critical point

Abstract

We present a theory to calculate, first, the correlation function of the physical quantity (angular momentum for spin-rotation interaction, second order spherical harmonics for the dipolar interaction), involved in magnetic spin-lattice relaxation and then the relaxation times. The time behaviour of the physical quantity h(t) is described by a generalized Langevin equation whose memory function, K(t), is assumed to be proportional to the density fluctuation correlation function, N(t). The time-independent proportionality function, α, is obtained by assuming that the relaxation time τ _h (for h(t) to reach local equilibrium) is equal to the correlation time, τ _n , of the density fluctuations. The density fluctuation correlation function is calculated by using the classical hydrodynamics form of the structure factor S(q, ω) [1, 2]. The definition chosen for N(t) forces us to consider only temperatures above the critical temperature, since we do not know the particle density of the liquid below the critical temperature.

The α-dependence of the memory function, the total effect correlation function and the normalized power spectrum is presented. Once the choice of α is made (α is temperature dependent), the main result of the theory is to give a minimum, above the critical temperature, for the spin-lattice relaxation times. The variation law (ΔT ∝ ω^1/2) of the shift, ΔT, in the temperature of the minimum from the critical temperature with respect to the frequency, found experimentally by Krynicki et al. [2], is verified. But while this result is consistent with experimental T ₁ measurements for CHCl₃, it is not with those for HCl (and H₂S): for dipolar and spin-rotation interaction we found a similar temperature dependence.