How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMR spin-echo diffusion attenuation functions. To exemplify the applicability of this approach, we employ a well-established two-region exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layer-dependent self-diffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the two-region exchange model in terms of SPT-observables and compare its predictions to that obtained using the exact transformation which we derived.Comment: v2: 14 pages, 6 figures, several enhancements, added references; v1: 7 pages, 3 figure

Freezing and melting transitions of liquids in mesopores with ink-bottle geometry

Freezing and melting behavior of nitrobenzene in mesoporous silicon with different pore size and with different porous structure have been studied using H-1 NMR cryoporometry. With the bulk phase surrounding the porous monoliths, in materials with uniform channel-like pores distinct pore-size-dependent freezing and melting transitions have been measured. These data were further used for the analysis of the fluid behavior in samples with modulated porous structure, namely linear pores with alternating cross-section. We have, in particular, considered two materials consisting of channel sections, which were separated by almost identical channel `necks' but notably differed in the respective channel diameters. In the smaller channel segments, the observed shift in the freezing temperature provides direct evidence of the relevance of a pore-blocking mechanism, i.e. of the retardation in the propagation of a solid front by the channel necks. In the channel segments with larger diameter, on the other hand, freezing is found to be initiated by homogeneous nucleation.DF

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter $S\simeq1$. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.Comment: 10 pages, 5 figure

History-dependent molecular dynamics in nanoporous host matrices

Ensembles of molecules confined to pore spaces with diameters of the order of a couple of molecular diameters reveal features which may notably deviate from their behaviour both in the bulk phase and under dominating host-guest interaction. We are going to demonstrate that under identical external conditions (temperature, pressure), different ensemble \"histories\" may give rise to dramatic differences in the states of these ensembles. PFG NMR diffusion measurements are introduced as a most sensitive tool for probing these differences

The role of string-like, supramolecular assemblies in reentrant supernematic liquid crystals

Using a combination of isothermal-isobaric Monte Carlo and microcanonical molecular dynamics we investigate the relation between structure and self-diffusion in various phases of a model liquid crystal using the Gay-Berne-Kihara potential. These molecules are confined to a mesoscopic slit-pore with atomically smooth substrate surfaces. As reported recently [see M. G. Mazza {\em et al.}, Phys. Rev. Lett. {\bf 105}, 227802 (2010)], a reentrant nematic (RN) phase may form at sufficiently high pressures/densities. This phase is characterized by a high degree of nematic order and a substantially enhanced self-diffusivity in the direction of the director $\hat{\bm{n}}$ which exceeds that of the lower-density nematic and an intermittent smectic A phase by about an order of magnitude. Here we demonstrate that the unique transport behavior in the RN phase may be linked to a confinement-induced packing effect which causes the formation of supramolecular, string-like conformations. The strings consist of several individual molecules that are capable of travelling in the direction of $\hat{\bm{n}}$ as individual "trains" consisting of chains of molecular "cars". Individual trains run in parallel and may pass each other at sufficiently high pressures.Comment: 24 page

Structural characterization of porous solids by simultaneously monitoring the low-temperature phase equilibria and diffusion of intrapore fluids using nuclear magnetic resonance

Nuclear magnetic resonance (NMR) provides a variety of tools for the structural characterization of porous solids. In this paper, we discuss a relatively novel approach called NMR cryodiffusometry, which is based on a simultaneous assessment of both the phase state of intraporous liquids at low temperatures, using NMR cryoporometry, and their transport properties, using NMR diffusometry. Choosing two model porous materials with ordered and disordered pore structures as the host systems, we discuss the methodological and fundamental aspects of the method. Thus, with the use of an intentionally micro-structured mesoporous silicon, we demonstrate how its structural features give rise to specific patterns in the effective molecular diffusivities measured upon progressive melting of a frozen liquid in the mesopores. We then present the results of a detailed study of the transport properties of the same liquid during both melting and freezing processes in Vycor porous glass, a material with a random pore structure.