Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

Abstract

The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a t −3/2 long time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations. PACS. 76.60.Lz Spin echoes and 83.10.Mj Molecular dynamics, Brownian dynamics and 33.20.-t Molecular spectra

Molecular velocity auto-correlations in glycerol/water mixtures studied by NMR MGSE method

“…The part of curved surface is clearly visible in the contour plot of the second derivative of ( ) of the mixture with 5 vol% of glycerol content in Fig.3, which shows how ⟨Δ 2 ⟩ occurs at high modulation frequencies and disappears with increasing echo-time at > 40 ms, when the trajectories of spins become long enough to span the whole extend of heterogeneity and to average off the diffusion diversity into ⟨Δ 2 ⟩ = 0, what is also seen in Figs.2 and 6. Similar diversity was observed in the MGSE measurements of VAS in water, ethanol and toluene with the explanation of the molecular self-diffusion in the vortexes of hydrodynamic fluctuations [69].…”

“…from which ( ) and thus ( ) can be extracted with considerable difficulty by changing Δ and if they are in the range of VAF correlation time . At the present state of the art, the MFG coil induction limits the width and the shape of the MFG pulses to above 1 ms, which is close to or slightly above values of in some liquids [69]. Thus, neglecting the dependence of the echo decay on and Δ according to Eq.6, when measuring the self-diffusion in water by PGSE method, gives an apparent self-diffusion coefficients that may differ from one another [49,35,81] and also deviate from those obtained from the theory and the simulations of molecular dynamics and water binary mixtures [41,23].…”

“…Instead of constant value along the echo time, , anticipated for the mono-exponential decays, discrepancies occur that cause the 3D plots to show a curved surface at short intervals and of higher frequencies. In the case of simple liquids [69], we interpreted similar curved surface by the molecular diffusion diversity due to the motion in the vortexes of hydrodynamic fluctuations. Namely, during initial interval after the spin excitation, when the trajectories of the molecules are still short, the spins may observe local inhomogeneity caused by the distribution of internal MFG in the porous medium [69] or motional diversity due to fluxes or hydrodynamic oscillation in liquids [66].…”

“…Theories [38,78,26,37] and simulations [2,3,77] predict a long-time asymptote of the VAF as the −3∕2 -long time tail in liquids. Recent studies by the NMR modulated gradient spin-echo (MGSE) method [69] have shown a deviation from this asymptotic properties in simple liquids such as water, ethanol and glycerol due to inter-molecular interactions. In these measurements the unusual heterogeneity of molecular motion is observed, when the measurement interval is very short, which one cannot describe by a simple diffusion coefficient.…”

Magnetic resonance measurements of cellular and sub-cellular membrane structures in live and fixed neural tissue

“…Low-cost, portable, bench-top, single-sided NMR devices with greater than 10 T/m static gradients (45) can probe submicron structures (46) that ordinarily cannot be resolved from larger microscale structures using state-of-the-art pulsed gradient MR systems with lower maximum gradient strengths (47). Displacement encoding within a static gradient field occurs by using radiofrequency (RF) pulses (8,9) to switch the "effective gradient" (11), allowing for diffusion encoding times as short as 100 µs (48). This permits resolution of submicron structures that can contain rapidly exchanging water pools (46).…”