Translational Correlation Times Research Articles

Diffusion of Water Molecules on the Surface of Silica Nanoparticles─Insights from Nuclear Magnetic Resonance Relaxometry.

1H spin-lattice nuclear magnetic resonance (NMR) relaxation experiments have been performed for water dispersions of functionalized silica nanoparticles of diameters of 25 and 45 nm. The experiments have been performed in a broad frequency range spanning 3 orders of magnitude, from 10 kHz to 10 MHz, versus temperature, from 313 to 263 K. On the basis of the data, two-dimensional translation diffusion (diffusion close to the nanoparticle surface within a layer of the order of a few diameters of water molecules) has been revealed. The translational correlation times as well as the residence life times on the nanoparticle surface have been determined. It has turned out that the residence lifetime is temperature-independent and is on the order of 5 × 10-6 s for the smaller nanoparticles and by about a factor of 3 longer for the larger ones. The translational correlation time for the case of 25 nm nanoparticles is also temperature-independent and yields about 6 × 10-7 s, while for the dispersion of the larger nanoparticles, the correlation times changed from about 8 × 10-7 s at 313 K to about 1.2 × 10-6 s at 263 K. In addition to the quantitative characterization of the two-dimensional translation diffusion, correlation times associated with bound water molecules have been determined. The studies have also given insights into the population of the bound and diffusing water on the surface water fractions.

Relationship between Translational and Rotational Dynamics of Alkyltriethylammonium-Based Ionic Liquids.

1H spin-lattice relaxation experiments have been performed for a series of ionic liquids including bis(trifluoromethanesulfonyl)imide anion and cations of a varying alkyl chain length: triethylhexylammonium, triethyloctylammonium, decyltriethylammonium, dodecyltriethylammonium, triethyltetradecylammonium, and hexadecyltriethylammonium. The relaxation studies were carried out in abroad frequency range covering three orders of magnitude, from 10 kHz to 10 MHz, versus temperature. On the basis of a thorough, quantitative analysis of this reach data set, parameters characterizing the relative, cation-cation, translation diffusion (relative diffusion coefficients and translational correlation times), and rotational motion of the cation (rotational correlation times) were determined. Relationships between these quantities and their dependence on the alkyl chain length were discussed in comparison to analogous properties of molecular liquids. It was shown, among other findings, that the ratio between the translational and rotational correlation times is smaller than for molecular liquids and considerably dependent on temperature. Moreover, a comparison of relative and self-diffusion coefficients indicate correlated translational dynamics of the cations.

Translational and rotational diffusion of three glass forming alcohols by 1H field cycling NMR relaxometry

1H field-cycling NMR relaxometry was applied to investigate the dynamics of the three glass forming alcohols 2-phenylbutan-1-ol (BEP), 2-(trifluoromethyl)phenetyl alcohol (2TFMP), and 4-(trifluoromethyl)phenetyl alcohol (4TFMP), all having a phenyl ring as substituent. 1H longitudinal relaxation rates, R1, were measured at Larmor frequencies (ν) from 0.01 to 35 MHz in the liquid phase of the three alcohols between 213 and 313 K. Data analysis was performed using master curves built on the basis of the frequency temperature superposition principle exploiting the NMR susceptibility representation. Longitudinal relaxation was considered to arise from two dynamic processes, i.e. translational diffusion and molecular rotations. For the first process a force-free hard-sphere model was used, whereas the phenomenological Davidson-Cole function was employed to model the second motional process. The analysis allowed translational and rotational correlation times to be determined over a wide time scale (10−11 - 10−3 s). The ratio between the two correlation times indicated the formation of hydrogen bonded networks for all alcohols, while their trends with temperature suggested that BEP forms stronger hydrogen bonds. The resulting self-diffusion coefficients were in agreement with the values independently determined from the slope of R1vs ν1/2 at low frequencies.

Self-diffusion micromechanism in Nafion studied by 2H NMR relaxation dispersion.

Field Cycling (FC) 2H nuclear magnetic resonance (NMR) relaxometry was applied to study dynamics in Nafion NR 212 in the temperature range from 300 K to 190 K and water content of λ = 8.2. The sensitive time window of FC was extended up to eight decades using the temperature-frequency superposition principle and master curve. The rotational correlation times obtained from 2H FC NMR coincide with translational correlation times gained from static field 2H NMR diffusometry in the temperature range applied. This fact means that a long-range mass transport in Nafion is coupled to molecular rotations. It is assumed that confined water in Nafion has more ordered oxygen sublattices as compared with bulk water, on a short range is similar to ice. We discuss the possible role of D and L defects, typical for the ordered ice structure and using this concept to describe the processes of self-diffusion of confined water in Nafion, as well as the similarity of temperature and humidity dependence of self-diffusion and proton conductivity.

Motional Dynamics of Halogen-Bonded Complexes Probed by Low-Field NMR Relaxometry and Overhauser Dynamic Nuclear Polarization.

Halogen bonding is a subject of considerable interest owing to wide-ranging chemical, materials and biological applications. The motional dynamics of halogen-bonded complexes play a pivotal role in comprehending the nature of the halogen-bonding interaction. However, not many attempts appear to have been made to shed light on the dynamical characteristics of halogen-bonded species. For the first time, we demonstrate here that the combination of low-field NMR relaxometry and Overhauser dynamic nuclear polarization (ODNP) makes it possible to obtain a cogent picture of the motional dynamics of halogen-bonded species. We discuss here the advantages of this combined approach. Low-field relaxometry allows us to infer the hydrodynamic radius and rotational correlation time, whereas ODNP probes the molecular translational correlation times (involving the substrate as well as the organic radical) with high sensitivity at low field.

Nuclear magnetic relaxation and diffusion study of the ionic liquids 1-ethyl- and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide confined in porous glass.

The molecular dynamics of the room-temperature ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (Bmim Tf2N) confined in porous glass is studied by nuclear magnetic resonance (NMR) relaxometry and diffusometry and is compared with the bulk dynamics over a wide temperature range. The molecular reorientation processes for anions and cations alike are found to be significantly affected by the presence of the glass interface at high temperatures. In this respect, the ionic liquid behaves similarly to polar liquids where proton NMR relaxation is governed by reorientations mediated by translational displacements (RMTDs). This process becomes less significant towards lower temperatures when the characteristic translational correlation times of the ions approach a timescale comparable with those of the RMTD process, and the relaxation dispersions in bulk and in confinement become similar below a temperature corresponding to about 1.2Tg , a value where the onset of dynamic heterogeneity has been observed before. The self-diffusion coefficient, on the other hand, is found to be strongly reduced than the bulk within the accessible temperature range of 248K and above and is significantly slower than expected from the tortuosity effect, suggesting that ion-surface interactions affect the macroscopic properties.

Towards Overhauser DNP in supercritical CO2

Overhauser Dynamic Nuclear Polarization (ODNP) is a well known technique to improve NMR sensitivity in the liquid state, where the large polarization of an electron spin is transferred to a nucleus of interest by cross-relaxation. The efficiency of the Overhauser mechanism for dipolar interactions depends critically on fast local translational dynamics at the timescale of the inverse electron Larmor frequency. The maximum polarization enhancement that can be achieved for 1H at high magnetic fields benefits from a low viscosity solvent. In this paper we investigate the option to use supercritical CO2 as a solvent for Overhauser DNP. We have investigated the diffusion constants and longitudinal nuclear relaxation rates of toluene in high pressure CO2. The change in 1H T1 by addition of TEMPO radical was analyzed to determine the Overhauser cross-relaxation in such a mixture, and is compared with calculations based on the Force Free Hard Sphere (FFHS) model. By analyzing the relaxation data within this model we find translational correlation times in the range of 2–4ps, depending on temperature, pressure and toluene concentration. Such short correlation times may be instrumental for future Overhauser DNP applications at high magnetic fields, as are commonly used in NMR. Preliminary DNP experiments have been performed at 3.4T on high pressure superheated water and model systems such as toluene in high pressure CO2.

Dynamics of the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulphonyl)imide studied by nuclear magnetic resonance dispersion and diffusion.

The dynamics of the imidazolium based room temperature ionic liquid Bmim Tf2N was investigated by means of nuclear magnetic resonance relaxation dispersion (NMRD) and nuclear magnetic resonance pulsed field gradient (NMR-PFG) diffusion experiments on the bulk liquid in a wide range of temperatures. Relaxation and diffusion properties were determined for anions and cations individually, giving evidence of heterogeneities in the dynamics of the ionic liquid. The relevant NMR relaxation mechanisms are the inter- and intramolecular dipolar interactions between the molecular ions reflecting the molecular translational and rotational diffusion. Rotational and translational correlation times could be obtained and showed different dependences on temperature. The experimental diffusion values follow the Vogel-Fulcher-Tammann (VFT) relation above a transition temperature Tc∼ 1.26 Tg, below which a deviation was observed. Differential scanning calorimetry experiments show a transition at the same temperature.

The transport and conductivity properties of the ionic liquid EMIMTCM

The ionic liquid 1-ethyl-3-methylimidazolium tricyanomethanide (EMIMTCM) is a very interesting, yet so far poorly studied, ionic liquid which has a low viscosity, high conductivity, and acceptable electrochemical stability for use as an electrolyte. In this study the self-diffusion coefficients, spin–lattice relaxation times, and spin–spin relaxation times of EMIMTCM were measured over the temperature range 263 to 343K. To gain insight into the origin of the physical properties of EMIMTCM, the temperature dependence of the measured cation diffusion coefficient was compared with two structurally related EMIM-based ionic liquids which differed only in the choice of anion: 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)amide (EMIMFSA) and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulphonyl)amine (EMIMTFSA). The experimentally determined diffusion coefficient, conductivity, and viscosity values were analysed using the Stokes–Einstein–Sutherland, Stokes–Einstein–Debye and Vogel–Fulcher–Tamman equations, respectively. The correlation time (τcation) of the cations were calculated from the relaxation data using the Bloembergen–Purcell–Pound equation. The overall isotropic molecular reorientational correlation time, τc, and translational correlation time, τD, of the cations were calculated from the viscosity and translational diffusion coefficients, respectively. The results of this study provide information on reorientational and translational motions of EMIMTCM and the correlation times were found to be in the following order τD>τc>τcation and EMIMTCM diffused faster than EMIMTFSA and EMIMFSA, due to the smaller size of the TCM anion and its lower viscosity.

Translational Dynamics of Water at the Phospholipid Interface

The residual water-proton magnetic relaxation dispersion profile obtained from suspensions of phospholipid vesicles in deuterium oxide was found to be a logarithmic function of the proton Larmor frequency at high magnetic field strengths, and independent of Larmor frequency at low magnetic field strengths. The residual proton relaxation is caused by dipole-dipole coupling between the residual water proton in otherwise deuterated water and the phospholipid protons. The logarithmic dependence on magnetic field strength is the signature of water-proton diffusive exploration on the interface that is approximately two-dimensionally constrained. Application of relaxation theory for two-dimensional diffusion to the spin-lattice relaxation data yields a translational correlation time of approximately 70 ps for water diffusing in the interface of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) vesicles.

Probing Structure and Dynamics of Bulk and Confined Crude Oils by Multiscale NMR Spectroscopy, Diffusometry, and Relaxometry

We propose using a set of noninvasive multiscale NMR techniques for probing the structure and dynamics of bulk and confined crude oils with and without asphaltene. High-field 1D (1)H and (13)C NMR spectroscopies evidence the proton species and the amount of asphaltene and give an average chain length for the hydrocarbon aliphatic chains. Two-dimensional (1)H diffusion-ordered NMR spectroscopy (DOSY) spectra allow us to identify two populations of hydrocarbons characterized by two distributions of translational diffusion coefficients in the presence of asphaltene and a single one without asphaltene. A detailed analysis of the distributions of longitudinal, T1, relaxation times measured at different magnetic fields is proposed in terms of highly skewed bimodal (or monomodal) log-normal distributions, confirming the two environments in the presence of asphaltene and a single one without asphaltene. We show that these distributions are similar to the gas and gel permeation chromatography distributions, thus showing a connection of the hydrocarbon dynamics with their chain lengths. The remarkable observed features of the nuclear magnetic relaxation dispersion (NMRD) profiles of <1/T1> for bulk and confined crude oils with and without asphaltene are interpreted with an original relaxation model of intermittent surface dynamics of proton species at the proximity of asphaltene nanoaggregates and bulk dynamics in between clusters of these nanoaggregates. This allows us to probe the 2D translational diffusion correlation time and the time of residence of hydrocarbons in the proximity of the asphaltene nanoaggregates. Provided that the diffusion of the hydrocarbons close to the asphaltene nanoaggregates is three times smaller than the bulk diffusion, as the DOSY experiments show, this time of residence gives an average radius of exploration for the 2D hydrocarbon diffusion, r2D ≈ 3.9 nm, of the same order of magnitude as the aggregate sizes found by J. Eyssautier with SAXS and SANS in asphaltene solutions and by O. C. Mullins with the observation of gravitational gradients of asphaltenes in oilfield reservoirs.

The magnetic field dependence of water T1 in tissues

The magnetic field dependence of the composite (1)H(2)O nuclear magnetic resonance signal T(1) was measured for excised samples of rat liver, muscle, and kidney over the field range from 0.7 to 7 T (35-300 MHz) with a nuclear magnetic resonance spectrometer using sample-shuttle methods. Based on extensive measurements on simpler component systems, the magnetic field dependence of T(1) of all tissues studied are readily fitted at Larmor frequencies above 1 MHz with a simple relaxation equation consisting of three contributions: a power law, A*ω(-0.60) related to the interaction of water with long-lived-protein binding sites, a logarithmic term B*τ(d) *log(1+1/(ωτ(d))(2)) related to water diffusion at macromolecular interfacial regions, and a constant term associated with the high frequency limit of water-spin-lattice relaxation. The parameters A and B include the concentration and surface area dependences respectively. The logarithmic diffusion term becomes significant at high magnetic fields and is consistent with rapid translational dynamics at macromolecular surfaces. The data are fitted well with translational correlation times of approximately 15 ps for human brain white matter, but with a B value three times larger than gray matter tissues. This analysis suggests that the water-surface translational correlation time is approximately three times longer than in gray matter.

Comparison of Various Correlation Times in Polymer Melts by Molecular Dynamics Simulation

This investigation presents data from prolonged molecular dynamics simulations of dense monodisperse polymer melts of linear polymer chains of length between N = 3 and N = 255. Hear N is number of chain coarse-grained segments. The study aim is to observe the crossover from Rouse-like dynamics for short chains to reptation-like dynamics for long chains and its influence on various translational and orientational correlation times. To address the problem, we calculate a variety of different quantities: standard mean-square displacement of inner monomer and of the chain mass centre, autocorrelation function of chain end-to-end vector, orientational autocorrelation functions of segment and chain end-to-end vector. The last two functions define NMR relaxation in polymer melts. The chain length dependences of all large-scale correlation times reveals clear crossover from non-entangled to entangled dynamics near NC ≈ 35. Additional primitive path analysis of the same data gives statistically consistent entanglement value NE ≈ 14, i.e., the longest chain investigated is well entangled and displays explicit motional anisotropy. The full data assembly explains qualitatively strong dependence of NMR transverse relaxation time for Rouse-like regime and weak one in reptation regime.

Paramagnetic Contributions to Nuclear Spin-Lattice Relaxation in Proteins

Paramagnetic contributions to spin-lattice relaxation rate constants are very useful in providing long-range distance constraints for structural determinations by NMR and also for controlling image contrast in clinical MRI protocols. When a radical with a long electron-spin-relaxation time is bound to a protein, the paramagnetic contribution to the water-proton-spin-lattice-relaxation rate is larger than predicted by usual theory. We show that this excess nuclear spin relaxation efficiency results from long-lived-bound water molecules for which the electron-nuclear coupling is correlated with the long rotational correlation time of the protein. Because the correlation time is so long compared with the relative translational correlation times, even distant water molecules make significant contributions and increase the relaxation efficiency of the paramagnetic center. If the rotational motion of the protein is stopped, as in a solid protein, a protein gel, or a tissue, the paramagnetic contributions to relaxation are both qualitatively and quantitatively changed from the solution limit. The spin-lattice relaxation for different paramagnetic systems may be understood in terms of the intrinsic dynamics of the protein and the spin dynamics of the paramagnetic center, which depends on the identity and magnetic characteristics of the paramagnetic center. These different effects are important for applications to magnetic imaging and structure determination by solid state NMR.

Probing the hydration water diffusion of macromolecular surfaces and interfaces

We probe the translational dynamics of the hydration water surrounding the macromolecular surfaces of selected polyelectrolytes, lipid vesicles and intrinsically disordered proteins with site specificity in aqueous solutions. These measurements are made possible by the recent development of a new instrumental and methodological approach based on Overhauser dynamic nuclear polarization (DNP)-enhanced nuclear magnetic resonance (NMR) spectroscopy. This technique selectively amplifies 1H NMR signals of hydration water around a spin label that is attached to a molecular site of interest. The selective 1H NMR amplification within molecular length scales of a spin label is achieved by utilizing short-distance range (∼r−3) magnetic dipolar interactions between the 1H spin of water and the electron spin of a nitroxide radical-based label. Key features include the fact that only minute quantities (<10 μl) and dilute (⩾100 μM) sample concentrations are needed. There is no size limit on the macromolecule or molecular assembly to be analyzed. Hydration water with translational correlation times between 10 and 800 ps is measured within ∼10 Å distance of the spin label, encompassing the typical thickness of a hydration layer with three water molecules across. The hydration water moving within this time scale has significant implications, as this is what is modulated whenever macromolecules or molecular assemblies undergo interactions, binding or conformational changes. We demonstrate, with the examples of polymer complexation, protein aggregation and lipid–polymer interaction, that the measurements of interfacial hydration dynamics can sensitively and site specifically probe macromolecular interactions.

Dynamics in an Idealized Ionic Liquid Model

An idealized four-site ionic liquid model having characteristics approximating those of 1-butyl-3-methylimidazolium hexafluorophosphate ([Im(41)][PF(6)]) is introduced as a low-cost alternative to existing all-atom models for purposes of simulating solute-based dynamics over nanosecond and longer time scales. The structural and energetic properties of the model are in reasonable agreement with those of [Im(41)][PF(6)] and similar ionic liquids, but the dynamics are unrealistically slow. A temperature shift of approximately 100 K is required to produce agreement between the viscosity and diffusion coefficients of the model and experimental values. Several aspects of the ion dynamics such as subdiffusive translational motions, non-Gaussian van Hove distributions, and jumplike displacements in both positions and orientations, are similar to behavior observed in supercooled liquids. Translational diffusion coefficients and rotational correlation times show roughly the proportionalities to viscosity expected from hydrodynamic models, and slip hydrodynamic calculations provide reasonable accuracy in some cases. But anomalously high rotational diffusion coefficients which decouple from viscosity at low temperature are also observed. These anomalies are explained in terms of the prevalence of 180 degrees rotational jumps coupled to the presence of marked heterogeneity in rotational motions, especially about one molecular axis. Comparisons between the dynamics observed in the ionic liquid (IL) model and a neutral mixture (NM) counterpart help to explain the origins of the distinctive dynamics in ionic liquids compared to conventional solvents. The requirement for balancing electrostatic interactions in the IL leads to uniform and interleaved distributions of cations and anions resembling a distorted ionic lattice, similar to the structure of molten NaCl. The resistance to reorganizing this structure is what leads to the slow dynamics of ionic liquids. The coupling among large collections of ions is presumably responsible for the similarity of ionic liquids to supercooled conventional liquids.

Dimensionality of Diffusive Exploration at the Protein Interface in Solution

The dynamics of water are critically important to the energies of interaction between proteins and substrates and determine the efficiency of transport at the interface. The magnetic field dependence of the nuclear spin-lattice relaxation rate constant 1/T(1) of water protons provides a direct characterization of water diffusional dynamics at the protein interface. We find that the surface-average translational correlation time is 30-40 ps and the magnetic field dependence of the water proton 1/T(1) is characteristic of two-dimensional diffusion of water in the protein interfacial region. The reduced dimensionality substantially increases the intermolecular re-encounter probability and the efficiency of the surface exploration by the small molecule, water in this case. We propose a comprehensive theory of the translational effects of a small diffusing particle confined in the vicinity of a spherical macromolecule as a function of the relative size of the two particles. We show that the change in the apparent dimensionality of the diffusive exploration is a general result of the small diffusing particle encountering a much larger particle that presents a diffusion barrier. Examination of the effects of the size of the confinement relative to the macromolecule size reveals that the reduced dimensionality characterizing the small-molecule diffusion persists to remarkably small radius ratios. The experimental results on several different proteins in solution support the proposed theoretical model, which may be generalized to other small-particle-large-body systems like vesicles and micelles.

Superparamagnetic iron oxide nanoparticles – Proton Nuclear Magnetic Resonance Dispersion curves

Superparamagnetic nanoparticles are widely used as contrast agents for magnetic resonance imaging. We present the Proton Nuclear Magnetic Resonance Dispersion curves for colloidal suspension of iron oxide nanoparticles used as contrast agents. The systems studied are composed of iron oxide nanoparticles of two different sizes, 80–150 nm dextran coated and 300–400 nm silicon coated. Previous studies show that the longitudinal relaxation time dispersion as a function of the proton Larmor frequency is not easily obtained for the aqueous colloidal suspension of 300–400 nm diameter nanoparticles. We obtained this system longitudinal relaxation time dispersion over a broad range of magnetic fields in a viscous medium. A theoretical model that accounts for the relaxation rate of water protons under the influence of such colloidal superparamagnetic nanoparticles was fitted to the experimental data of both systems. The fit allows access to characteristic parameters of superparamagnetic nanoparticles such as the Neel relaxation time, the nanoparticle radius, particle's magnetic moment and translational correlation time, important parameters for the contrast agent efficiency.

Physicochemical studies on hydrophobic PEO‐PPO‐PEO triblock copolymer micelles in SDS micellar environment

AbstractThe shape, size, aggregation, hydration, and correlation times of water insoluble PEO‐PPO‐PEO triblock copolymer micelles with sodium dodecylsulfate (SDS) micelles were investigated using transport studies and dynamic light scattering technique. From the conductance of micellar solutions of the polymer in 25 mM SDS and 5 mM NaCl, the hydration of polymer micelles were determined using the principle of obstruction of electrolyte migration by the polymer. The asymmetry of the micellar particles of polymer and polymer‐SDS mixed micellar systems in 5 mM NaCl and their average axial ratios were calculated using intrinsic viscosity and hydration data obeying Simha–Einstein equation. Hydration number and micellar sizes were variable with temperature. The shape of the polymer micelles has been ellipsoidal rather than spherical. The micellar volume, hydrodynamic radius, radius of gyration, diffusional coefficients as well as translational, rotational and effective correlation times have been calculated from the absolute values of the axes. The partial molal volume of polymer micelles has also been determined and its comparison with the molar volume of pure polymer suggested a volume contraction due to immobilization of the water phase by the hydrophilic head groups of the polymer. The thermodynamic activation parameters for viscous flow favor a more ordered water structure around polymer micelles at higher temperatures. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2410–2420, 2007

Dynamics of surface water in ZrO2 studied by quasielastic neutron scattering

A quasielastic neutron scattering experiment has revealed the dynamics of surface water in a high surface area zirconium oxide in the temperature range of 300-360 K. The characteristic times of the rotational (picoseconds) and translational (tens of picoseconds) components of diffusion motion are well separated. The rotational correlation time shows an Arrhenius-type behavior with an activation energy of 4.48 kJ/mol, which is lower compared to bulk water. The rotational diffusion at room temperature is slower by about a factor of 2 compared to bulk water, whereas the translational diffusion slows down by a factor of 40. In contrast to bulk water, the translational correlation time exhibits an Arrhenius-type temperature dependence with an activation energy of 11.38 kJ/mol. Comparison of different models for jump diffusion processes suggests that water molecules perform two-dimensional jumps at a well-defined, almost temperature-independent distance of 4.21-4.32 A. Such a large jump distance indicates a low molecular density of the layer of diffusing molecules. We argue that undissociated water molecules on an average form two hydrations layers on top of the surface layer of hydroxyl groups, and all the layers have similar molecular density. Quasielastic neutron scattering experiment assesses the dynamics of the outermost hydration layer, whereas slower motion of the water molecules in the inner hydration layer contributes to the elastic signal.