The long time tail of molecular velocity correlation in a confined fluid: observation by modulated gradient spin-echo NMR

Abstract

In addition to the fast correlation for local stochastic motion the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time tail decay [1,2]. This article presents a study by the NMR modulated gradient spin-echo method (MGSE) [3] on a system of water trapped in the space between the closely packed polystyrene beads. The results prove that the obtained dependence of spin-echo attenuation on time, gradient strength and modulation frequency nicely corresponds to the recently developed NMR approach, which is able to describe the effects of arbitrarily shaped gradient pulse sequence on the spin-echo attenuation [4,5]. With an MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin-phase, giving the spin-echo attenuation proportional to a value of the velocity correlation spectrum at the modulation frequency. It enables to extract the low-frequency correlation spectrum of confined water molecules. The function exhibits a negative long time tail characteristic (a low-frequency decay of the spectrum), that can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay).