Low-frequency velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo

In addition to the fast correlation for local stochastic motion, the molecu lar velocity correlation function in a fluid enclosed within the pore bound aries features a slow long time-tail decay. Here we present its study by th e NMR modulated gradient spin-echo method (MGSE) [1] on a system of water t rapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo atten uation proportional to a value of the molecular velocity correlation spectr um at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency molecular dynamic s in fluids. In our experiment, it enables to extract the low frequency cor relation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay o f the spectrum), which can be interpreted as a molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated fr om the solution of the Langevin equation for restricted diffusion (which ex hibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories a nd simulation, which predict slow negative long time tail of molecular velo city correlation dynamics in confined fluids, the obtained velocity correla tion spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of th e recently developed approach to the spin echo in porous media, that uses t he spin phase average with the cumulant expansion to Set the attenuation as a discord of spin spatial coherence [4]. (C) 2001 Elsevier Science Inc. Al l rights reserved.