Translational Self-diffusion Coefficients Research Articles

NMR investigation of multi-scale dynamics in ionic liquids containing Li+ and La3+: From vehicular to hopping transport mechanism

The dynamics in mixtures of ionic liquid and monoatomic cations has been studied at different time scales ranging from the nanosecond up to the second. The mixtures were composed of cholinium bis(trifluoromethanesulfonyl)imide ([Chol][TFSI]) and LiTFSI, with LiTFSI mole fraction, ▪, spanning from 0 to 0.5 (saturated solution), and [Chol][TFSI] and ▪ from 0 to 0.12. The translational self-diffusion coefficients of ▪, ▪ and ▪ have been measured, along with NMR their relaxation times at various magnetic fields, in order to decipher the intertwined dynamics between the ions, and to reveal how the local dynamics impact the long range translational diffusion. When the concentrations of lithium and lanthanum are increased in the liquid, the long range dynamics of all the ions drop. In the case of LiTFSI, the self-diffusion coefficient of lithium becomes higher than the one of TFSI at high concentration, revealing a change in lithium transport mechanisms. The NMR relaxation data confirm this change, showing a clearer transition at ▪. It is interpreted as a change from a vehicular transport mechanism of the lithium below ▪ to a hopping mechanism above. A similar crossover seems to occur in the lanthanum solutions. This phenomenon seems correlated to the departure of the hydroxyl group of the organic cation from the lithium solvation shell.

Designer pair statistics of disordered many-particle systems with novel properties.

The knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing database of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform, and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperatures that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve many-particle systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics.

Molecular simulations of transport properties of polar hydrofluoroethers: Force field development, fractional Stokes-Einstein and free volume relations

Hydrofluoroethers (HFEs) having simultaneously hydrocarbon (HC) and fluorocarbon (FC) moieties connected through ether oxygen are polar chain molecules with dielectric properties, which makes them a good heat transfer medium, e.g., for cooling of electronics or magnetic devices. In this work, we report, validate, and test high level-ab initio derived force fields and we use partial charges fitted to the electrostatic potential surface (EPS) to reproduce the dipole moments. Computer simulations were performed over a wide range of temperatures and densities to calculate the transport coefficients in the condensed-phase and comparisons were made against available experimental data for five selected molecules; namely HFE-7000, HFE-7100, HFE −7200, HFE −7300, and HFE −7500. Furthermore, structural properties and enthalpy of vaporization were obtained from molecular simulations. Cohen and Turnbull formula for the translational self-diffusion coefficient was tested in the free-volume cast, which itself was correlated against the isothermal compressibility, which can explain the phenomenon of transport properties in liquids, D∝exp-γ/Vf/V∗. The fractional Stokes-Einstein relation was also tested to scale the self-diffusion coefficient vs viscosity in the form of (DT−1) ∝ (1/η)s, with s ranging between ≈ 0.89 and 0.92 for the five molecules in the reduced density range of ρσ3 = 0.56 to 0.75. Finally, the non-equilibrium molecular dynamics (NEMD) simulations of thermal conductivity was found to outperform the equilibrium Green-Kubo approach, but both with comparable accuracy.

PH-Induced Biophysical Perspectives of Binding of Surface-Active Ionic Liquid [BMIM][OSU] with HSA and Dynamics of the Formed Complex.

The influence of pH on the human serum albumin (HSA) interaction with ionic liquid (IL)1-butyl 3-methylimidazolium octyl sulfate ([BMIM][OSU]) at its sub-micellar concentration of 5 mM (well below CMC ∼31 mM at 25 °C) in aqueous solution has been monitored employing different methods, viz., circular dichroism (CD), fluorescence, electrokinetic determination of the zeta potential (ZP), nuclear magnetic resonance (NMR), small-angle neutron scattering (SANS), and molecular docking (MD). CD analysis indicated a noticeable reduction of the α-helical content of HSA by IL at pH 3. A significant interaction of the anionic part of IL with HSA was evident from the 1H chemical shifts and saturation transfer difference (STD) NMR. A strong binding between IL and HSA was observed at pH 3 relative to pH 5, revealing the importance of electrostatic and hydrophobic interactions assessed from global binding affinities and molecular correlation times derived from STD NMR and a combined selective/nonselective spin-relaxation analysis, respectively. ZP data supported the electrostatic interaction between HSA and the anionic part of IL. The nature of IL self-diffusion with HSA was assessed from the translational self-diffusion coefficients by pulse field gradient NMR. SANS results revealed the formation of prolate ellipsoidal geometry of the IL-HSA complex. MD identified the preferential binding sites of IL to the tryptophan centers on HSA. The association of IL with HSA was supported by fluorescence measurements, in addition to the structural changes that occurred in the protein by the interaction with IL. The anionic part of IL contributed a major interaction with HSA at the pH levels of study (3, 5, 8, and 11.4); at pH > 8 (effectively 11.4), the protein also interacted weakly with the cationic component of IL.

Self-Diffusion in Confined Water: A Comparison between the Dynamics of Supercooled Water in Hydrophobic Carbon Nanotubes and Hydrophilic Porous Silica.

Confined liquids are model systems for the study of the metastable supercooled state, especially for bulk water, in which the onset of crystallization below 230 K hinders the application of experimental techniques. Nevertheless, in addition to suppressing crystallization, confinement at the nanoscale drastically alters the properties of water. Evidently, the behavior of confined water depends critically on the nature of the confining environment and the interactions of confined water molecules with the confining matrix. A comparative study of the dynamics of water under hydrophobic and hydrophilic confinement could therefore help to clarify the underlying interactions. As we demonstrate in this work using a few representative results from the relevant literature, the accurate assessment of the translational mobility of water molecules, especially in the supercooled state, can unmistakably distinguish between the hydrophilic and hydrophobic nature of the confining environments. Among the numerous experimental methods currently available, we selected nuclear magnetic resonance (NMR) in a field gradient, which directly measures the macroscopic translational self-diffusion coefficient, and quasi-elastic neutron scattering (QENS), which can determine the microscopic translational dynamics of the water molecules. Dielectric relaxation, which probes the re-orientational degrees of freedom, are also discussed.

Molecular interactions of ionic liquids with SiO2 surfaces determined from colloid probe atomic force microscopy.

Ionic liquids (ILs) interact strongly with many different types of solid surfaces in a wide range of applications, e.g. lubrication, energy storage and conversion, etc. However, due to the nearly immeasurable large number of potential ILs available, identifying the appropriate ILs for specific solid interfaces with desirable properties is a challenge. Theoretical studies are highly useful for effective development of design and applications of these complex molecular systems. However, obtaining reliable force field models and interaction parameters is highly demanding. In this work, we apply a new methodology by deriving the interaction parameters directly from the experimental data, determined by colloid probe atomic force microscopy (CP-AFM). The reliability of the derived interaction parameters is tested by performing molecular dynamics simulations to calculate translational self-diffusion coefficients and comparing them with those obtained from NMR diffusometry.

Molecular size and shape effects: Rotational diffusion and the Stokes-Einstein-Debye relation

Formulation of rotational diffusion coefficient and the Stokes-Einstein-Debye (SED) relation is presented for diatomic molecular liquids by molecular dynamics simulation with two-center Lennard-Jones (2CLJ) potentials. Shear viscosity ηsv and rotational diffusion coefficient Dr are expressed as a function of molecular mass and number density N/V, or moment of inertia, packing fraction, temperature T, interaction energy, and molecular elongation l∗ ≡ l/σ, where N is the number of molecules included in the system volume V, l the bond length in the diatomic molecules, and σ the size parameter used in the LJ potentials. The packing fraction and elongation are the variables expressing molecular size and shape, respectively. These results produce directly a molecular-basis SED relation as Drηsv/T ∝ vm∗1/3l∗−3(N/V), where vm∗ is the dimensionless molecular volume expressed as an analytical function only of elongation l∗. That is, this SED equation depends not on the size but on the shape. This is highly contrasted with the original SED relation based on the size, which suggests overall reconsideration of the relation on a molecular scale. The shape term accounts for a paradox that more spherical molecules such as N2 deviate more strongly from the original SED equation based on a spherical particle. In addition, the SED relation without the size is consistent with the Stokes-Einstein relation for both the Lennard-Jones and 2CLJ liquids expressed as Dηsv/T ∝ (N/V)1/3, where D is the translational self-diffusion coefficient.

On the validity of the Stokes–Einstein relation for various water force fields

The translational self-diffusion coefficient and the shear viscosity of water are related by the fractional Stokes–Einstein relation. We report extensive novel molecular dynamics simulations for the self-diffusion coefficient and the shear viscosity of water. The SPC/E and TIP4P/2005 water models are used in the temperature range 220–560 K and at 1 or 1,000 bar. We compute the fractional exponents t, and s that correspond to the two forms of the fractional Stokes–Einstein relation and respectively. We analyse other available experimental and numerical simulation data. In the current analysis two temperature ranges are considered (above or below 274 K) and in both cases deviations from the Stokes–Einstein relation are observed with different values for the fractional exponents obtained for each temperature range. For temperatures above 274 K, both water models perform comparably, while for temperatures below 274 K TIP4P/2005 outperforms SPC/E. This is a direct result of the ability of TIP4P/2005 to predict water densities more accurately and thus predict more accurately the water self-diffusion coefficient and the shear viscosity.

Extraction of Reliable Molecular Information from Diffusion NMR Spectroscopy: Hydrodynamic Volume or Molecular Mass?

Measuring accurate translational self-diffusion coefficients (Dt ) by NMR techniques with modern spectrometers has become rather routine. In contrast, the derivation of reliable molecular information therefrom still remains a nontrivial task. In this paper, two established approaches to estimating molecular size in terms of hydrodynamic volume (VH ) or molecular weight (M) are compared. Ad hoc designed experiments allowed the critical aspects of their application to be explored by translating relatively complex theoretical principles into practical take-home messages. For instance, comparing the Dt values of three isosteric Cp2 MCl2 complexes (Cp=cyclopentadienyl, M=Ti, Zr, Hf), having significantly different molecular mass, provided an empirical demonstration that VH is the critical molecular property affecting Dt . This central concept served to clarify the assumptions behind the derivation of Dt =ƒ(M) power laws from the Stokes-Einstein equation. Some pitfalls in establishing log (Dt ) versus log (M) linear correlations for a set of species have been highlighted by further investigations of selected examples. The effectiveness of the Stokes-Einstein equation itself in describing the aggregation or polymerization of differently shaped species has been explored by comparing, for example, a ball-shaped silsesquioxane cage with its cigar-like dimeric form, or styrene with polystyrene macromolecules.

Diffusion microrheology of ferrofluids

We provide a statistical mechanics approach to study the linear microrheology of thermally equilibrated and homogeneous ferrofluids. Theexpressions for the elastic and loss moduli depend on the bulk microstructure of the magnetic fluid determined by the structure factor of thesuspension of magnetic particles. The comparison of the predicted microrheology with computer simulations confirms that as a function ofrelaxation frequency of thermal fluctuations of the particle concentration both theory and simulations have the same trends. At very shortfrequencies the viscous modulus relates to the translational and rotational self-diffusion coefficients of a ferro-particle.

Translational diffusion across a free-standing smectic film above the bulk smectic-A-isotropic transition temperature.

Calculations of translational self-diffusion coefficient in free-standing smectic films during a series of layer-thinning transitions as the temperature is raised above the bulk smectic-A-isotropic transition have been carried out. A molecular model based upon the random walk theory is applied for calculating the translational diffusion coefficient (TDC) D_{∥} across the smectic film both in the bulk of the film, as well as in the vicinity of the bounding surfaces. Calculations of D_{∥} require the set of the orientational and translational order parameters (OPs) which have been obtained by using the extended McMillan approach with anisotropic forces. The effect of E on the orientational and translational OPs, as well as on the TDC of smectic films has been investigated. A reasonable agreement between the theoretically predicted and the experimentally obtained data on the TDC in the bulk of the partially fluorinated H10F5MOPP film has been obtained. We also found, in agreement with the experimentally observed behavior of D_{∥}(N)(N=25,13,11,10), that the translational diffusion coefficient in the bulk of the film gradually increases as the film thickness N is decreased.

The twist-bend nematic phase: translational self-diffusion and biaxiality studied by 1H nuclear magnetic resonance diffusometry

ABSTRACTRecently, there has been a surge of interest in mesogens exhibiting the twist-bend nematic (NTB) phase that is shown to be chiral even though formed by effectively achiral molecules. Although it now seems to be clear that the NTB phase in the bulk is formed by degenerate domains having opposite handedness, the presence of a supramolecular heliconical structure proposed in the Dozov model has been contradicted by the Hoffmann et al. model in which the heliconical arrangement is replaced by a polar nematic phase. The evidence in support of this is that the quadrupolar splitting tensor measured in various experiments is uniaxial and not biaxial as expected for the twist-bend nematic structure. In this debate, among other evidence, the molecular translational diffusion, and its magnitude with respect to that in the nematic phase above the NTB phase, has also been invoked to eliminate or to confirm one model or the other. We attempt to resolve this issue by reporting the first measurements of the translational self-diffusion coefficients in the nematic and twist-bend nematic phases formed 1″,7″-bis-4-(4′-cyanobiphenyl-4′-yl) heptane (CB7CB). Such measurements certainly appear to resolve the differences between the two models in favour of that for the classic twist-bend nematic phase.

A physically constrained classical description of the homogeneous nucleation of ice in water.

Liquid water can persist in a supercooled state to below 238 K in the Earth's atmosphere, a temperature range where homogeneous nucleation becomes increasingly probable. However, the rate of homogeneous ice nucleation in supercooled water is poorly constrained, in part, because supercooled water eludes experimental scrutiny in the region of the homogeneous nucleation regime where it can exist only fleetingly. Here we present a new parameterization of the rate of homogeneous ice nucleation based on classical nucleation theory. In our approach, we constrain the key terms in classical theory, i.e., the diffusion activation energy and the ice-liquid interfacial energy, with physically consistent parameterizations of the pertinent quantities. The diffusion activation energy is related to the translational self-diffusion coefficient of water for which we assess a range of descriptions and conclude that the most physically consistent fit is provided by a power law. The other key term is the interfacial energy between the ice embryo and supercooled water whose temperature dependence we constrain using the Turnbull correlation, which relates the interfacial energy to the difference in enthalpy between the solid and liquid phases. The only adjustable parameter in our model is the absolute value of the interfacial energy at one reference temperature. That value is determined by fitting this classical model to a selection of laboratory homogeneous ice nucleation data sets between 233.6 K and 238.5 K. On extrapolation to temperatures below 233 K, into a range not accessible to standard techniques, we predict that the homogeneous nucleation rate peaks between about 227 and 231 K at a maximum nucleation rate many orders of magnitude lower than previous parameterizations suggest. This extrapolation to temperatures below 233 K is consistent with the most recent measurement of the ice nucleation rate in micrometer-sized droplets at temperatures of 227-232 K on very short time scales using an X-ray laser technique. In summary, we present a new physically constrained parameterization for homogeneous ice nucleation which is consistent with the latest literature nucleation data and our physical understanding of the properties of supercooled water.

The effect of hydrogen bonding propensity and enantiomeric composition on the dynamics of supercooled ketoprofen - dielectric, rheological and NMR studies.

The aim of this work is to analyze in detail the effect of small hydrogen bonding (HB) structures and enantiomeric composition on the dynamics of glass-forming liquid ketoprofen. For that purpose dielectric relaxation, rheological and NMR studies were performed. Investigated samples are racemic ketoprofen, a single enantiomer of ketoprofen and a racemic ketoprofen methyl ester with no tendency to form HB dimers. The combination of complementary experimental techniques enables us to show that macroscopic viscosity η and α-relaxation time τα have nearly the same temperature dependencies, whereas the relation between the viscosity (or molecular reorientation) and the translational self-diffusion coefficient violates Stokes-Einstein law already at high temperature. Additionally, based on dielectric relaxation studies performed on increased pressure we were able to identify similarities and key differences in the supercooled liquid dynamics of investigated materials affected by their tendency to form intermolecular hydrogen bonds. This includes the effect of pressure on the glass transition temperature Tg, changes in the fragility parameter m and activation volume ΔV, the role of thermal energy and density fluctuations in governing the viscous liquid dynamics (Ev/Ep ratio). Finally, we have also demonstrated that the dynamic behaviour of a single enantiomer and the racemic mixture of the same compound are very much alike. Nevertheless, some slight differences were observed, particularly in the τα(T) dependencies measured in the vicinity of glass transition both at ambient and elevated pressure.

Interrelationship between Number of Mobile Protons, Diffusion Coefficient, and AC Conductivity in Superprotonic Conductors, CsHSO4 and Rb3H(SeO4)2

Using quasielastic neutron scattering (QENS), we investigated the proton dynamics for two superprotonic conductors, CsHSO4 and Rb3H(SeO4)2. To evaluate the self-diffusion coefficients and the number of mobile protons on both superprotonic and normal phases, we focused on proton dynamics not only in the phase above Tc, but also in the phase below Tc. In Rb3H(SeO4)2, the self-diffusion of protons was observed even below the Tc phase. In contrast to popular belief, no large changes in the self-diffusion coefficients were observed across Tc. Nevertheless, the increase in the number of mobile protons across Tc was about 14.5 times, which was estimated from the integrated intensity of QENS spectra, and this change could not account for the increased magnitude of proton conductivity, which is about 500 times. As a large translational self-diffusion coefficient has not been reported in previous works by QENS experiments, there are still unknown factors that contribute to the Nernst–Einstein relation that need to ...

Viscosity, relaxation time, and dynamics within a model asphalt of larger molecules.

The dynamics properties of a new "next generation" model asphalt system that represents SHRP AAA-1 asphalt using larger molecules than past models is studied using molecular simulation. The system contains 72 molecules distributed over 12 molecule types that range from nonpolar branched alkanes to polar resins and asphaltenes. Molecular weights range from 290 to 890 g/mol. All-atom molecular dynamics simulations conducted at six temperatures from 298.15 to 533.15 K provide a wealth of correlation data. The modified Kohlrausch-Williams-Watts equation was regressed to reorientation time correlation functions and extrapolated to calculate average rotational relaxation times for individual molecules. The rotational relaxation rate of molecules decreased significantly with increasing size and decreasing temperature. Translational self-diffusion coefficients followed an Arrhenius dependence. Similar activation energies of ∼42 kJ/mol were found for all 12 molecules in the model system, while diffusion prefactors spanned an order of magnitude. Viscosities calculated directly at 533.15 K and estimated at lower temperatures using the Debye-Stokes-Einstein relationship were consistent with experimental data for asphalts. The product of diffusion coefficient and rotational relaxation time showed only small changes with temperature above 358.15 K, indicating rotation and translation that couple self-consistently with viscosity. At lower temperatures, rotation slowed more than diffusion.

Combined Measurement of Translational and Rotational Diffusion in Quaternary Acyclic Ammonium and Cyclic Pyrrolidinium Ionic Liquids

The translational self-diffusion coefficients (D(T)) for a series of tetra-alkyl acyclic ammonium and cyclic pyrrolidinium ionic liquids (ILs) were measured using (1)H pulse field gradient (PFG) NMR spectroscopy over various temperatures. These NMR diffusion results were combined with previously measured rotational diffusion coefficients (D(R)) obtained from (14)N NMR relaxation measurements for the same ILs (Alam, T. M.; et al. J. Phys. Chem. A 2011, 115, 4307- 4316). The D(T)/D(R) ratio was then used to estimate the effective hydrodynamic radius and corresponding volumes without the need to directly measure the viscosities of the ILs. The generality, validity, and performance of using this D(T)/D(R) ratio is discussed and compared to the effective hydrodynamic volumes obtained using classic D(T)/viscosity and D(R)/viscosity relationships. The temperature variation observed for the molecular volumes obtained using the D(T)/D(R) ratio is argued to be a signature for the breakdown or decoupling of the Stokes-Einstein and Stoke-Einstein-Debye relationships in these neat IL systems, consistent with recent molecular dynamic simulations.

Proline induced disruption of the structure and dynamics of water

We use quasi-elastic neutron scattering spectroscopy to study the diffusive motion of water molecules at ambient temperature as a function of the solute molar fraction of the amino acid, proline. We validate molecular dynamics simulations against experimental quasielastic neutron scattering data and then use the simulations to reveal, and understand, a strong dependence of the translational self-diffusion coefficient of water on the distance to the amino acid molecule. An analysis based on the juxtaposition of water molecules in the simulation shows that the rigidity of proline imposes itself on the local water structure, which disrupts the hydrogen-bond network of water leading to an increase in the mean lifetime of hydrogen bonds. The net effect is some distortion of the proline molecule and a slowing down of the water mobility.

Stable glasses of indomethacin and α,α,β-tris-naphthylbenzene transform into ordinary supercooled liquids

Secondary ion mass spectrometry has been used to characterize translational motion in vapor-deposited glasses of indomethacin (IMC) and α,α,β-tris-naphthylbenzene (TNB). Vapor deposition onto substrates at ∼0.99 T(g) produced ordinary glasses that evolve according to fickian diffusion during annealing. The resulting self-diffusion coefficients for the supercooled liquids are in good agreement with previous reports. Deposition onto substrates at 0.85 T(g) produced highly stable glasses that transform with a propagating front mechanism. In contrast to previous reports, the liquid produced by this transformation has the same translational mobility as the ordinary supercooled liquid; we associate this result with lower impurity levels in the current samples. The front velocities for both TNB and IMC stable glasses are very similar functions of the translational self-diffusion coefficients of the supercooled liquids, consistent with view that the growth front velocity is controlled by mobility in the liquid adjacent to the stable glass.

Conformational dynamics of sub-micron sized wormlike polyelectrolyte polymer in flow fields

Conformational dynamics of a single chain of wormlike polyelectrolyte xanthan polymer has been investigated in the external flow fields by employing a well-suited coarse-grained Brownian dynamics simulation. This goes beyond other simulations, which do not consider the hydrodynamic interaction between pairs of beads in polyelectrolyte polysaccharide and the long-range electrostatic screening effect. Conformational properties, such as the radius of gyration and the static structure factor, were unchanged with the flow strength parameter (i.e., Weissenberg number) in the uniform flow. However, influences by flow strength as well as flow type were evident in both simple shear and extensional-like flows with non-zero velocity gradients in flow regimes, commonly exhibiting a sigmoidal transition in the radius of gyration. Transition to a higher plateau, and independence of long-range electrostatic screening on chain conformation, can be encountered earlier with increasing flow strength, as a special feature of a polyelectrolyte in extensional-like flow. The translational self-diffusion coefficient increases when increasing either the flow strength or the electrostatic screening effect in uniform and simple shear flows. Scaling behavior of the static structure factor is quite well-correlated with respect to each flow field, where the Flory-Edwards exponent (ν) decreases with higher values of flow strength and flow type parameters, but for lower screening effect. Present results on the mesoscopic scale devoted to the bulk space can readily serve as the basis for further scrutiny of the behavior of wormlike polyelectrolytes within various flow fields in confined spaces. Open image in new window