Translational Diffusion Research Articles

New possibilities for the synthesis of high-molecular weight poly(2,5(6)-benzimidazole) and studies of its solutions in DMSO-based complex organic solvent

New possibilities for the synthesis of high-molecular weight poly(2,5(6)-benzimidazole) (ABPBI) based on a new monomer, 3,4-diaminobenzoic acid monophosphate, in polyphosphoric acid medium at high monomer concentration under stirring and on a Teflon® surface without stirring are investigated. New complex solvent for ABPBI is found. This solvent is based on dimethyl sulfoxide, methanol, and potassium hydroxide. For the first time, molecular weight values are obtained by dynamic light scattering and viscometry in complex solvent. In addition, Kuhn segment values are estimated. Maximal molecular mass MDη value reaches 94 kDa. The values of macromolecular equilibrium rigidity A are estimated as 4.4–5.7 nm according to translational diffusion coefficient and 3.3 nm according to intrinsic viscosity measurements.

Quasielastic Neutron Scattering and Molecular Dynamics Simulation Study on the Molecular Behaviour of Catechol in Zeolite Beta

The dynamics of catechol in zeolite Beta was studied using quesielastic neutron scattering (QENS) experiments and molecular dynamics simulations at 393 K, to understand the behaviour of phenolic monomers relevant in the catalytic conversion of lignin via metal nanoparticles supported on zeolites. Compared to previous work studying phenol, both methods observe that the presence of the second OH group in catechol can hinder mobility significantly, as explained by stronger hydrogen-bonding interactions between catechol and the Brønsted sites of the zeolite. The instrumental timescale of the QENS experiment allows us to probe rotational motion, and the catechol motions are best fit to an isotropic rotation model with a D^{rot} of 2.9 × 10^{10} s^{-1}. While this D^{rot} is within error of that measured for phenol, the fraction of molecules immobile on the instrumental timescale is found to be significantly higher for catechol. The MD simulations also exhibit this increased in ‘immobility’, showing that the long-range translational diffusion coefficients of catechol are lower than phenol by a factor of 7 in acidic zeolite Beta, and a factor of sim3 in the siliceous material, further illustrating the significance of Brønsted site H-bonding. Upon reproducing QENS observables from our simulations to probe rotational motions, a combination of two isotropic rotations was found to fit the MD-calculated EISF; one corresponds to the free rotation of catechol in the pore system of the zeolite, while the second rotation is used to approximate a restricted and rapid “rattling”, consistent with molecules anchored to the acid sites through their OH groups, the motion of which is too rapid to be observed by experiment.

Modeling the solid/liquid interfacial properties of methylimidazole confined in hydrophobic silica nanopores

Many chemical processes proceed in confined environments of silica nanopore, in which the confined reactants or guest adsorbates show drastically different properties from the bulk system. Therefore, the solid/liquid interfacial structure and dynamics of 1-methylimidazole (MeIm) confined in the hydrophobic silica nanopore passivated by methoxysilane groups (-Si(Me)3) were investigated using molecular dynamics (MD) simulations. The mass density of the confined MeIm is layering and pore-size independent, while the negligible layering structure for charge density is observed. The smaller pore size gives rise to a significantly slower reorientation dynamics and translational diffusion of MeIm. In 2.8 nm pore, the parallel diffusion coefficient of MeIm is nearly 10 times larger than the perpendicular one, and their difference becomes smaller with the increase in pore size. Hopefully the insights from this work are helpful to a better understanding of the effects of hydrophobic silica pore on the confined behaviors of liquids.

Enhanced Microscopic Dynamics of a Liver Lipid Membrane in the Presence of an Ionic Liquid.

Ionic liquids (ILs) are an important class of emerging compounds, owing to their widespread industrial applications in high-performance lubricants for food and cellulose processing, despite their toxicity to living organisms. It is believed that this toxicity is related to their actions on the cellular membrane. Hence, it is vital to understand the interaction of ILs with cell membranes. Here, we report on the effects of an imidazolium-based IL, 1-decyl-3-methylimidazolium tetrafluoroborate (DMIM[BF4]), on the microscopic dynamics of a membrane formed by liver extract lipid, using quasielastic neutron scattering (QENS). The presence of significant quasielastic broadening indicates that stochastic molecular motions of the lipids are active in the system. Two distinct molecular motions, (i) lateral motion of the lipid within the membrane leaflet and (ii) localized internal motions of the lipid, are found to contribute to the QENS broadening. While the lateral motion could be described assuming continuous diffusion, the internal motion is explained on the basis of localized translational diffusion. Incorporation of the IL into the liver lipid membrane is found to enhance the membrane dynamics by accelerating both lateral and internal motions of the lipids. This indicates that the IL induces disorder in the membrane and enhances the fluidity of lipids. This could be explained on the basis of its location in the lipid membrane. Results are compared with various other additives and we provide an indication of a possible correlation between the effects of guest molecules on the dynamics of the membrane and its location within the membrane.

Influence of Topology and Brønsted Acid Site Presence on Methanol Diffusion in Zeolites Beta and MFI

Detailed insight into molecular diffusion in zeolite frameworks is crucial for the analysis of the factors governing their catalytic performance in methanol-to-hydrocarbons (MTH) reactions. In this work, we present a molecular dynamics study of the diffusion of methanol in all-silica and acidic zeolite MFI and Beta frameworks over the range of temperatures 373–473 K. Owing to the difference in pore dimensions, methanol diffusion is more hindered in H-MFI, with diffusion coefficients that do not exceed 10 × 10−10 m2s−1. In comparison, H-Beta shows diffusivities that are one to two orders of magnitude larger. Consequently, the activation energy of translational diffusion can reach 16 kJ·mol−1 in H-MFI, depending on the molecular loading, against a value for H-Beta that remains between 6 and 8 kJ·mol−1. The analysis of the radial distribution functions and the residence time at the Brønsted acid sites shows a greater probability for methylation of the framework in the MFI structure compared to zeolite Beta, with the latter displaying a higher prevalence for methanol clustering. These results contribute to the understanding of the differences in catalytic performance of zeolites with varying micropore dimensions in MTH reactions.

Driving Forces of Protein Diffusion.

Diffusivity of a protein (a Brownian particle) is caused by random molecular collisions in the Stokes-Einstein picture. Alternatively, it can be viewed as driven by unbalanced stochastic forces acting from water on the protein. Molecular dynamics simulations of protein mutants carrying different charges are analyzed here in terms of the van der Waals (vdW) and electrostatic forces acting on the protein. They turn out to be remarkably strongly correlated and the total force is largely a compensation between vdW and electrostatic forces. Both vdW and electrostatic forces relax on the same time scale of 5-6 ns separated by 6 orders of magnitude from the relaxation time of the total force. Similar phenomenology applies to the dynamics and statistics of the fluctuating torque responsible for rotational diffusion. Standard linear theories of dielectric friction are grossly inapplicable to translational and rotational diffusion of proteins overestimating friction by many orders of magnitude.

Molecular Modeling to Estimate the Diffusion Coefficients of Drugs and Other Small Molecules.

Diffusion is a spontaneous process and one of the physicochemical phenomena responsible for molecular transport, the rate of which is governed mainly by the diffusion coefficient; however, few coefficients are available because the measurement of diffusion rates is not straightforward. The translational diffusion coefficient is related by the Stokes–Einstein equation to the approximate radius of the diffusing molecule. Therefore, the stable conformations of small molecules were first calculated by molecular modeling. A simple radius rs and an effective radius re were then proposed and estimated using the stable conformers with the van der Waals radii of atoms. The diffusion coefficients were finally calculated with the Stokes–Einstein equation. The results showed that, for the molecules with strong hydration ability, the diffusion coefficients are best given by re and for other compounds, rs provided the best coefficients, with a reasonably small deviation of ~0.3 × 10−6 cm2/s from the experimental data. This demonstrates the effectiveness of the theoretical estimation approach, suggesting that diffusion coefficients have potential use as an additional molecular property in drug screening.

Markovian exchange phenomena in magnetic resonance and the Lindblad equation

Nuclear Magnetic Resonance (NMR) experiments involve coherent and incoherent dynamics. Incoherent dynamics give rise to nuclear spin relaxation typically accounted for by a differential equation known as a quantum master equation. Out of the existing master equations the Lindblad equation is particularly important. A central theorem of open quantum theory states that a relaxation process represents a quantum Markovian process if and only if it can be described by a Lindblad master equation. This in turn raises serious questions regarding the compatibility of conventional NMR relaxation theory and one of the most fundamental results of open quantum theory. The NMR treatment of important Markovian relaxation mechanisms such as Brownian motion or chemical exchange events do in general not result in a master equation in Lindblad form and would therefore be at odds with the mathematically rigorous theory of open quantum systems. We explore this apparent conflict for two important chemical exchange phenomena and show that their conventional treatment may be recast into a suitable Lindblad equation. Similarities between spatial diffusion and multi-site exchange events allow us to extend our results to nuclear spin relaxation due to translational diffusion. As a result we are able to show that the NMR treatment of intramolecular exchange and translational diffusion represent valid quantum Markovian processes compatible with the rigorous definitions of open quantum theory.

Kinetic Langevin Description of Nanoparticle Diffusion

The paper deals with the study of the transport processes in dispersed media. The diffusion of the nanoparticles in gases and liquids are considered. In all cases the Langevin approach is used when the evolution of a dispersed particle is described by the stochastic equation. A solution for the autocorrelation function of the nanoparticle velocity is constructed and additional random force acting on it in addition to the usual Langevin force is analyzed. The model of the diffusion of the nanoparticles ensemble is developed. In the last section the diffusion of the carbon nanotubes in liquids is discussed. It is considered the translational and rotational diffusion of the carbon nanotubes

Examination of Interactions of Hexafluoro-2-propanol with Trp-Cage in Hexafluoro-2-propanol-Water by MD Simulations and Intermolecular Nuclear Overhauser Effects.

All-atom molecular dynamic simulations of the peptide Trp-cage in 30% hexafluoro-2-propanol- water (V/V) at 278 K have been carried out with the goal of exploring peptide hydrogen-solvent fluorine nuclear spin cross relaxation. Force field parameters for HFIP reported by Fioroni et al. along with the fluorine parameters of the TFE5 model reported by this lab were used. Water was represented by the TIP5P-Ew model. Peptide modeling used the AMBER99SB-ILDN force field. Translational diffusion coefficients of solution components at 278 K were predicted to within 35% of experimental values using these parameter sets. The simulations indicate that the solvent mixture is not homogeneous, with HFIP molecules clustered into aggregates as large as 53 fluoroalcohol molecules. The solvent environment of surface atoms of Trp-cage fluctuates between being HFIP-rich and more water-rich about every 10 ns. In accord with previous studies by other groups, the average concentration of HFIP near the surface of the peptide is significantly enhanced over the concentration of HFIP in the bulk solvent. In the simulations, ∼7% of the initial contacts between HFIP molecules and Trp-cage develop into peptide-fluoroalcohol interactions that persist for times as long as 8 ns. Most of the available experimental nuclear spin cross-relaxation rates (ΣHF) for hydrogens of the Trp-cage in 30% HFIP-water are reproduced from the MD trajectories to within uncertainties of the experimental data and the simulations. However, a few calculated ΣHF values for hydrogens of the Trp-cage do not agree with experiment. These tend to be situations where long-lived peptide-HFIP interactions are predicted. The disagreements between observed and calculated ΣHF in these instances signal defects in the modeling parameters and procedures that are presently unrecognized.

Revision of the calibration experiment in asymmetrical flow field-flow fractionation

Asymmetrical flow field-flow fractionation is a versatile chromatographic fractionation method. In combination with at least one detection technique it is used for size-based separation of colloids, biomolecules and polymers. Although often used as pure separation method, a well-elaborated theory is available that allows precise quantification of the translational diffusion coefficient D. Still, current literature suggests different ways to transform this theory into applicable experimental procedures and no “gold standard” for correct data processing exists. While some sources report a direct way to extract diffusion information from the fractogram, others suggest the necessity of an external calibration measurement to obtain the channel width w. In this work, we compare the different approaches and calibration algorithms based on original and literature data using our own open-source AF4 evaluation software. Based on the results, we conclude that available AF4 setups do not fulfill the requirements for absolute measurements of D. We show that the best way to conduct is to consider the area of the channel and D of the calibrant while neglecting the small peak which occurs in the void peak region.

Diffusion of skyrmions: the role of topology and anisotropy

We study the diffusive motion of metastable localized spin structures with various topological charges by combining atomistic spin model simulations with an extension to the Thiele equation taking into account translational and rotational degrees of freedom. The Brownian motion of skyrmions is shown to obey markedly different diffusion laws depending on their topological properties. We demonstrate that skyrmions with topological charges Q = −1 and Q = 0 exhibit anisotropic translational diffusion due to their non-circular shape. The coupling between rotational and translational Brownian motion, however, causes memory of the initial orientation to be lost on a timescale governed by the effective rotational diffusion coefficient, ultimately leading to isotropic diffusion in the long time limit.

Dynamics of Ionic Liquids in Confinement by Means of NMR Relaxometry-EMIM-FSI in a Silica Matrix as an Example.

1H and 19F spin–lattice relaxation studies for 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide in bulk and mesoporous MCM-41 silica matrix confinement were performed under varying temperatures in a broad range of magnetic fields, corresponding to 1H resonance frequency from 5Hz to 30MHz.A thorough analysis of the relaxation data revealed a three-dimensional translation diffusion of the ions in the bulk liquid and two-dimensional diffusion in the vicinity of the confining walls in the confinement. Parameters describing the translation dynamics were determined and compared. The rotational motion of both kinds of ions in the confinement was described by two correlation times that might be attributed to anisotropic reorientation of these species.

Residence and diffusion of a dynamically prototropic hydration probe in AOT reverse micelles

We investigated the hydration dynamics in the nanosized water pool of an Aerosol-OT (AOT) reverse micelle (RM) using a prototropic (proton-donating) fluorescent dye, N-methyl-7-hydroxyquinolinium (NM7HQ+), as the probe. NM7HQ+ is a photoacid, and the deprotonation of its excited-state cationic form (C*) gives rise to a neutral keto species (K*). In the present study, the residence sites of C* and K* in water pools of various sizes were determined by monitoring their time-resolved fluorescence anisotropy. Additionally, the evolutions of the C* and K* bands in the time-resolved fluorescence spectra were analyzed by fitting the spectra to the sum of two lognormal peak functions. The time-dependent spectral shifts of the species with different formal charges revealed the characteristic hydration behavior at the interface of the anionic AOT headgroups and the bound water region, as well as the rotational and translational diffusion of the probe within the RM.

Protein-Peptide Binding Energetics under Crowded Conditions.

Nearly all biological processes, including strictly regulated protein-protein interactions fundamental in cell signaling, occur inside living cells where the concentration of macromolecules can exceed 300 g/L. One such interaction is between a 7 kDa SH3 domain and a 25 kDa intrinsically disordered region of Son of Sevenless (SOS). Despite its key role in the mitogen-activated protein kinase signaling pathway of all eukaryotes, most biophysical characterizations of this complex are performed in dilute buffered solutions where cosolute concentrations rarely exceed 10 g/L. Here, we investigate the effects of proteins, sugars, and urea, at high g/L concentrations, on the kinetics and equilibrium thermodynamics of binding between SH3 and two SOS-derived peptides using 19F NMR lineshape analysis. We also analyze the temperature dependence, which enables quantification of the enthalpic and entropic contributions. The energetics of SH3-peptide binding in proteins differs from those in the small molecules we used as control cosolutes, demonstrating the importance of using proteins as physiologically relevant cosolutes. Although most of the protein cosolutes destabilize the SH3-peptide complexes, the effects are nongeneralizable and there are subtle differences, which are likely from weak nonspecific interactions between the test proteins and the protein crowders. We also quantify the effects of cosolutes on SH3 translational and rotational diffusion to rationalize the effects on association rate constants. The absence of a correlation between the SH3 diffusion data and the kinetic data in certain cosolutes suggests that the properties of the peptide in crowded conditions must be considered when interpreting energetic effects. These studies have implications for understanding protein-protein interactions in cells and show the importance of using physiologically relevant cosolutes for investigating macromolecular crowding effects.

Diffusion of Anisotropic Colloids in Periodic Arrays of Obstacles

Colloidal suspensions in confined geometries exhibit rich diffusion dynamics governed by particle shapes and particle-confinement interactions. Here, we propose a colloidal system, consisting of ellipsoids in periodic array of obstacles, to investigate the confined diffusion of anisotropic colloids. From the obstacle density-dependent diffusion, we discover a decoupling of translational and rotational diffusion in which only rotational motion is localized while translational motion remains diffusive. Moreover, by evaluating the probability distributions of displacements, we found Brownian but non-Gaussian diffusion behaviors with increasing the obstacle densities, which originates from the shape anisotropy of the colloid and the multiplicity of the local configurations of the ellipsoids with respect to the obstacle. Our results suggest that the shape anisotropy and spatial confinements play a vital role in the diffusion dynamics. It is important for understanding the transportations of anisotropic objects in complex environments.

Confinement Effects on Glass-Forming Aqueous Dimethyl Sulfoxide Solutions.

Combining broadband dielectric spectroscopy and nuclear magnetic resonance studies, we analyze the reorientation dynamics and the translational diffusion associated with the glassy slowdown of the eutectic aqueous dimethyl sulfoxide solution in nano-sized confinements, explicitly, in silica pores with different diameters and in ficoll and lysozyme matrices at different concentrations. We observe that both rotational and diffusive dynamics are slower and more heterogeneous in the confinements than in the bulk but the degree of these effects depends on the properties of the confinement and differs for the components of the solution. For the hard and the soft matrices, the slowdown and the heterogeneity become more prominent when the size of the confinement is reduced. In addition, the dynamics are more retarded for dimethyl sulfoxide than for water, implying specific guest-host interactions. Moreover, we find that the temperature dependence of the reorientation dynamics and of the translational diffusion differs in severe confinements, indicating a breakdown of the Stokes–Einstein–Debye relation. It is discussed to what extent these confinement effects can be rationalized in the framework of core-shell models, which assume bulk-like and slowed-down motions in central and interfacial confinement regions, respectively.

Nanoscale Relaxation in "Water-in-Salt" and "Water-in-Bisalt" Electrolytes.

"Water-in-salt" (WIS) and "water-in-bisalt" (WIBS) electrolytes have recently been developed for Li-ion batteries, combining the safety and environmental friendliness of aqueous electrolytes with a larger operating window made possible by a solid-electrolyte interphase. We report quasielastic neutron scattering (QENS) measurements on solutions of a WIS electrolyte at two concentrations, 13.9 and 21 m (molal) lithium bis(trifluoromethane)sulfonimide LiTFSI in H2O/D2O and a WIBS electrolyte at (21 m LiTFSI + 7 m lithium triflate (LiOTf)) in H2O/D2O. The data were Fourier transformed to obtain experimental intermediate scattering functions (ISFs) and compared with corresponding quantities obtained from molecular dynamics (MD) simulations. Both QENS and MD ISFs could be fitted well by a single stretched exponential function to obtain apparent translational diffusion coefficients for the water molecules. The QENS values agree well with the MD simulations for the 13.9 and 21 m solutions, but MD simulations predict a slower relaxation of water compared to QENS for the WIBS electrolyte. Comparison of the incoherent and coherent scattering reveals much faster water dynamics compared with structural relaxation of the ionic framework, consistent with the nanodomain picture where the lithium diffusion occurs through the tortuous water domain around the slower relaxing ionic matrix, leading to highly non-Gaussian water motion.

Low-Frequency (Gigahertz to Terahertz) Depolarized Raman Scattering Off n-Alkanes, Cycloalkanes, and Six-Membered Rings: A Physical Interpretation.

Molecular liquids have long been known to undergo various distinct intermolecular motions, from fast librations and cage-rattling oscillations to slow orientational and translational diffusion. However, their resultant gigahertz to terahertz spectra are far from simple, appearing as broad shapeless bands that span many orders of magnitude of frequency, making meaningful interpretation troublesome. Ad hoc spectral line shape fitting has become a notoriously fine art in the field; a unified approach to handling such spectra is long overdue. Here we apply ultrafast optical Kerr-effect (OKE) spectroscopy to study the intermolecular dynamics of room-temperature n-alkanes, cycloalkanes, and six-carbon rings, as well as liquid methane and propane. This work provides stress tests and converges upon an experimentally robust model across simple molecular series and range of temperatures, providing a blueprint for the interpretation of the dynamics of van der Waals liquids. This will enable the interpretation of low-frequency spectra of more complex liquids.

Thermodynamics, Dynamics, and Rheology of Fuel Surrogates: Application of the Time–Temperature Superposition Principle in Molecular Dynamics Simulations

All-atom molecular dynamics (MD) simulation is used to determine the thermodynamics and rheological properties of fuel surrogates, which are modeled as a mixture of n-hexadecane and methyl laurate. The volumetric properties of the studied systems, namely, density and coefficient of thermal expansion, show an excellent agreement with experiments. The temperature dependence of translational and rotational diffusion of the molecules follows an Arrhenius-type behavior, which is consistent with the temperature dependence of the zero shear viscosity obtained from nonequilibrium simulations. At high shear rates, the molecules align in the flow direction that gives rise to the shear-thinning behavior for these fuel surrogates. The time–temperature superposition (TTS) principle is then successfully applied to collapse the shear viscosity and translational/rotational motion data in all systems. The application of TTS on the dynamics data obtained in equilibrium, which are readily accessible in the all-atom MD simulations, allows one to reduce the time scale gap between experiments and simulations and predict the rheological response of complex fluids, especially mixtures of short alkanes and fatty acid esters, which are of interest in fuel surrogates.