Rotational Diffusion Model Research Articles

Role of Exchange Cations and Layer Charge on the Dynamics of Confined Water.

Describing the dynamic behavior of water confined in clay minerals is a fascinating challenge and crucial in many research areas, ranging from materials science and geotechnical engineering to environmental sustainability. Water is the most abundant resource on Earth, and the high reactivity of naturally occurring hydrous clay minerals used since prehistoric times for a variety of applications means that water-clay interaction is a ubiquitous phenomenon in nature. We have attempted to experimentally distinguish the rotational dynamics and translational diffusion of two distinct populations of interlayer water, confined and ultraconfined, in the sodium (Na) forms of two smectite clay minerals, montmorillonite (Mt) and hectorite (Ht). Samples hydrated at a pseudo one-layer hydration (1LH) state under ambient conditions were studied with quasi-elastic neutron scattering (QENS) between 150 and 300 K. Using a simplified revised jump-diffusion and rotation-diffusion model (srJRM), we observed that while interlayer water near the ditrigonal cavity in Ht forms strong H-bonds to both adjacent surface O and structural OH, H-bonding of other more prevalent interlayer water with the surface O is weaker compared to Mt, inducing a higher temperature for dynamical changes of confined water. Given the lower layer charge and faster dynamics observed for Ht compared to Mt, we consider this strong evidence confirming the influence of the interlayer cation and surfaces on confined water dynamics.

Rotational diffusion of shape-switching particles dissolved in biaxial liquid crystals

ABSTRACT The interpretation of many experimental or computational studies on the orientational dynamics of molecules dissolved in liquid crystals relies on assuming some stochastic model for their time evolution. The Rotational Diffusion model is typically employed for this purpose, representing the molecules being monitored as rigid particles. However, this is not a realistic assumption for many molecules or nanoparticles in solution, and we have previously proposed a model to describe the rotational diffusion of a shape-changing particle dissolved in uniaxial fluids. Here, we extend the model allowing the host medium to be of biaxial symmetry, and we apply the theory to a simple example case, as well as exploring its general features.

Inertial rotational diffusion and magnetic relaxation of the spin system in a strong magnetic field

Analytical expressions for the longitudinal and transverse correlation functions pertaining to inertial magnetic relaxation are obtained by expanding the deterministic magnetization trajectories into a Fourier series and averaging the result over all possible initial conditions applying the stationary Boltzmann distribution function. The longitudinal and transverse components of the magnetic susceptibility tensor are calculated for a system of noninteracting macrospins in a strong uniform external field using Bloch's phenomenological approach, which postulates the exponential evolution of the spin system towards equilibrium, and the Lorentz model of rotational diffusion of the magnetization vector. It is shown that the strength of the external field and the magnitude of the inertia parameters noticeably affect the shape of the susceptibility in the THz (nutation resonance) spectrum region. It is also demonstrated that the simple analytical Lorentz-type expression describes the main features of the complex susceptibility in the ferromagnetic resonance and nutation resonance regions.

Solid-state NMR spectroscopy uncovers internal dynamics of antiviral compounds.

In this study we analyzed the internal dynamics of antiviral compounds such as amantadine and rimantadine and the model compound hexamethylbenzene (HMB) using solid-state 2H NMR spectroscopy. Amantadine and rimantadine have been successfully used to treat influenza and dyskinesia, and their antiviral activity can be characterized using structural and dynamical information from solid-state 2H NMR relaxation. The relaxation data collected for a range of temperatures can be fit using analytical models for the internal dynamics of these compounds to yield physical parameters such as activation energies and diffusion constants that quantify the different modes of motion. Here, we performed quadrupolar-echo and relaxation experiments on powdered samples of deuterated amantadine, rimantadine, and HMB for temperatures between −150⁰C and 60⁰C. HMB displayed two rotational modes about its internal symmetry axes with vastly different timescales. Quadrupolar-echo spectra showed that rimantadine exhibits methyl rotation about its 3-fold axis with no rotation about the C-C axis linked to the cage, while amantadine undergoes slow rotation about the cage axis. The order parameters calculated from the residual quadrupolar couplings for all three compounds were large (>0.8), indicating restricted off-axial dynamics. Spin-lattice (T1Z) and quadrupolar-order relaxation times (T1Q) were calculated for different orientations within the polycrystalline samples. The temperature and angular dependences of these relaxation times were fit using three models: anisotropic rotational diffusion [1,2], axial diffusion, and discrete jumps, among which the anisotropic rotational diffusion model displayed universal applicability. Application of NMR relaxometry to these drugs within the membrane channel will further enable us to understand their activity and the effect of the lipid environment on their structural dynamics.

Anomalous diffusion, gigahertz, and terahertz spectroscopy of aliphatic ketones.

The experimental results of the complex dielectric permittivity of aliphatic ketones in dilute solutions of inert solvent cyclohexane in the gigahertz (GHz) and terahertz (THz) frequencies of the electromagnetic spectrum are examined in terms of the theory of inertial anomalous diffusion of polar molecules, considered as an assembly of molecules with interacting dipolar groups, in polar liquids. The theory is based on the generalization of the Debye rotational diffusion model of dielectric relaxation of polar molecules. The model comprises two interacting dipolar groups-one lighter and the other heavier; each has a finite moment of inertia and each experiences a finite friction with an extensive range of damping or drag coefficient and the dipole moment ratio of the two groups. The lighter group refers to the reference molecule, whereas the heavier group simulates the neighboring molecules, and the two groups interact with each other via the dipole-dipole interaction potential. The resulting approximate expression contains terms in both the Rocard form and the Сole-Сole form. The experimental data on aliphatic ketones are shown to fit extremely well with the theory, and parameters of the fit offer physical significance. An agreement of the plot of the experimental data on dielectric loss versus frequency to the formulas derived from the model offers a mathematical basis of the semiempirical equations used in the literature to fit the experimental data. Experimental results of the dielectric loss of neat polar liquid acetone in GHz and THz, as an example, are shown to fit the theory; however, the interaction potential parameter compared to its dilute solution counterpart is significantly increased, reflecting the increase in the dipole-dipole interaction energy.

Microscopic diffusion in cationic vesicles across different phases

Understanding the phase behavior and microscopic diffusion mechanism of cationic vesicles is crucial for controlled-release kinetics in gene/DNA transfection. Here, we report our findings on the structure, phase behavior, and microscopic dynamics of a vesicle based on a cationic double-chained surfactant, dihexadecyldimethylammonium bromide (DHDAB), which is a promising candidate for a nonviral gene/DNA carrier. Small-angle neutron-scattering measurements reveal that DHDAB aggregates are in the form of unilamellar vesicles. Calorimetric studies show a strong thermal hysteresis in the heating and cooling cycles following different pathways. Two first-order transitions are observed at 303 and 318 K in the heating cycle. Fourier transform infrared spectroscopy reveals that the first transition (at 303 K) is associated with a polymorphic (solid-solid) transition from coagel to an intermediate crystalline (IC) phase, and subsequently the second transition (at 318 K) is an order-disorder transition from IC to the fluid phase. Interestingly, it is found that in the cooling cycle, the fluid phase directly transforms back into the coagel phase without passing through the IC phase. This is also confirmed by an elastic fixed window scan (EFWS) using incoherent neutron scattering. The phase behavior of DHDAB is in strong contrast to that of its longer-chain counterpart, dioctadecyldimethylammonium bromide (DODAB), where the intermediate gel phase was observed during the cooling cycle. Moreover, no polymorphic transition was observed in the heating cycle of DODAB, in which the coagel phase directly converts to the fluid phase. These sharply contrasting phase behaviors for DHDAB and DODAB suggest the strong dependence of membrane phase behavior to the alkyl chain length. EFWS measurements reveal that the phase transitions observed in the DHDAB membrane are associated with strong changes in the DHDAB dynamics. The changes in conformational entropy of DHDAB molecules estimated from EFWS confirm that the coagel-fluid and IC-fluid phase transitions are accompanied by strong changes in the conformations of the alkyl chains. The microscopic dynamics of DHDAB molecules in each of these phases is investigated by employing quasielastic neutron-scattering (QENS). In the ordered phases (coagel and IC), only localized internal dynamics of the DHDAB is observed in the QENS spectra. However, in the fluid phase, the presence of a long-range lateral diffusion is detected in addition to the localized internal dynamics of the alkyl chain. The lateral motion is found to follow Fickian diffusion. The internal dynamics of DHDAB depends on the phase state of the bilayer. In the ordered phase, the internal dynamics is described by a fractional uniaxial rotational diffusion model. However, in the fluid phase, where alkyl tails are disordered with significant gauche defects, the internal dynamics is described using localized translation within confined spheres. This study highlights the rich phase behavior of the DHDAB membrane and the surfactant dynamics across these phases.

Quasielastic neutron scattering reveals the temperature dependent rotational dynamics of densely grafted oleic acid.

We study the dynamics of pure oleic acid and grafted oleic acid synthesized by decomposing iron oleate into oleic acid grafted iron oxide nanoparticles. Our quasielastic neutron scattering study shows that oleic acid dominantly performs translational diffusion at room temperature. On the other hand, in nanocomposites, constraints imposed by grafting and crowding of neighboring chains restrict the grafted oleic acid to uniaxial rotation. Interestingly, it also manifests mobility in grafted oleic acid below the crystallization temperature of pure oleic acid. The data from grafted oleic acid could be effectively described using a uniaxial rotational diffusion model with an additional elastic scattering contribution. This kind of elastic scattering arises due to the restricted bond mobility and increases with decreasing temperature. The radius of rotation obtained from the fitted data agrees very well with the geometry of the molecule and grafting density. These results open possibilities of research on the confined surfactant systems, which could be analyzed using the approach described here.

Water dynamics in C–S–H and M-S-H cement pastes: A revised jump-diffusion and rotation-diffusion model

The Quasi-Elastic Neutron Scattering (QENS) spectra from four cement pastes are re-analyzed by a new revised jump-diffusion and rotation-diffusion model (rJRM). From the QENS fit, it can be seen that the rJRM is an improved model to fit QENS spectra within the whole detected neutron energy transfer and scattering vector. By the rJRM fitting, the structure parameters extracted from QENS spectra show that both the additives aluminum-silicate nanotubes (ASN) and carboxyl group functionalized ASN (ASN-COOH) can improve magnesium-silicate-hydrate (M-S-H) toward calcium-silicate-hydrate (C–S–H) direction in mechanical properties, but the improvement is weakened with decreasing temperatures. The extracted dynamical parameters show that there is a dynamic anomaly near 230 K in not only translational but also rotational diffusion of water confined in all the investigated samples. The anomaly in rotational diffusion is new compared with those results obtained by the QENS fit using other models.

Optimization of image writer modes for optically rewritable electronic paper

ABSTRACT Time-limited exposure of electrode-free optically rewritable electronic paper is essential for applications, but performance characteristics can be modest. In this study we investigate whether image writer mode can improve kinetics of the photosensitive layer order parameter, which is described by the rotational diffusion model. The model that we developed allows adjusting the transmittance spectra of polarisers. We have found that fairly uniform transmittance spectra of polarisers enable to obtain competitive contrast ratio of 8:1 within 10 s of exposure. In comparison with the long-time exposure, the reflectance coefficient reduces by 24%. Computer-simulated image is consistent with the experimental observations.

Optically Rewritable Liquid Crystal Displays: Characteristics and Performance

Recent achievements in the photoalignment technique for fabrication of optically rewritable electronic paper with high performance characteristics are surveyed with emphasis on temporal constraints on the exposure process. The possibility of creating electrode-free electronic paper has very important practical aspects. However, many existing studies do not include sufficient analysis on how to achieve acceptable reflective characteristics within short exposure time. In order to achieve this goal, we have applied the rotational diffusion model. We find that the parameters of the diffusion model can be adjusted to get acceptable light-reflecting characteristics within 10 s of exposure. In comparison with the long-time exposure, the reflectance coefficient reduces by 24%. The route to material improvements for optimized e-paper device is discussed.

Assessment of Analytical Orientation Prediction Models for Suspensions Containing Fibers and Spheres

Analytical orientation models like the Folgar Tucker (FT) model are widely applied to predict the orientation of suspended non-spherical particles. The accuracy of these models depends on empirical model parameters. In this work, we assess how well analytical orientation models can predict the orientation of suspensions not only consisting of fibers but also of an additional second particle type in the shape of disks, which are varied in size and filling fraction. We mainly focus on the FT model, and we also compare its accuracy to more complex models like Reduced-Strain Closure model (RSC), Moldflow Rotational Diffusion model (MRD), and Anisotropic Rotary Diffusion model (ARD). In our work, we address the following questions. First, can the FT model predict the orientation of suspensions despite the additional particle phase affecting the rotation of the fibers? Second, is it possible to formulate an expression for the sole Folgar Tucker model parameter that is based on the suspension composition? Third, is there an advantage to choose more complex orientation prediction models that require the adjustment of additional model parameters?

Temperature-dependent dynamics of endohedral fullerene Sc2@C80(CH2Ph) studied by EPR spectroscopy.

Endohedral fullerenes are promising materials for the quantum information and quantum processing due to the unique properties of the electron-nuclear spin system well isolated from the environment inside the fullerene cage. The endofullerene Sc2@C80(CH2Ph) features a strong hyperfine interaction between one electron spin 1/2 localized at the Sc2 dimer and two equivalent 45Sc nuclear spins 7/2, which yields 64 well resolved EPR transitions. We report a comprehensive analysis of the temperature dependence of the EPR spectrum of Sc2@C80(CH2Ph) dissolved in d-toluene measured in a wide temperature range above and below the melting point. The nature of the electron spin coherence phase memory is investigated. The properties of all resonance lines in a liquid phase were treated within the model of the free rotational diffusion. Both, analytical expressions and numerical examination provide an excellent agreement between the experimental and simulated spectra. A detailed study of the experimental data confirms the assumption of the independent motions of the fullerene cage and the Sc2 core. The data obtained show three regimes of molecular motion detected at different temperatures: the free rotation of both the fullerene cage and its bi-metal core, the motion of the core in the frozen fullerene cage, and, finally, a state with a fixed structure of both parts of the metallofullerene molecules. The data analysis reveals a significant nuclear quadrupole interaction playing an important role for the mixing of the different nuclear spin multiplets.

Anomalous diffusion of molecules with rotating polar groups: The joint role played by inertia and dipole coupling in microwave and far-infrared absorption.

Budó's generalization [A. Budó, J. Chem. Phys. 17, 686 (1949)10.1063/1.1747370] of the Debye rotational diffusion model of dielectric relaxation of polar molecules to an assembly with internal interacting polar groups is extended to inertial anomalous diffusion. Thus, the theory can be applied both in the GHz and the THz regions, accounting for anomalous behavior as well as the necessary return to optical transparency at very high frequencies. The linking of both dispersion regions in a single model including anomalous effects is accomplished via a fractional Fokker-Planck equation in phase space based on the continuous time random walk ansatz. The latter is written via the Langevin equations for the stochastic dynamics of pairs of interacting heavy polar groups embedded in the frame of reference of a particular molecule or molecular dimer rotating about a space-fixed axis. The fractional Fokker-Planck equation is then converted to a three-term matrix differential recurrence equation for the statistical moments. This is solved in the frequency domain for the linear dielectric response using matrix continued fractions. Thus, one has the complex susceptibility χ(ω) for extensive ranges of damping, group dipole moment ratio, and friction. The susceptibility, as inferred from the small oscillation limit, inherently comprises a low frequency (GHz) band with width depending on the anomalous parameter and a far-infrared (THz) or Poley peak of resonant character with a comblike structure of harmonic peaks. This behavior is due to the double transcendental nature of the after-effect function.

Reorientational dynamics of molecules in liquid methane: A molecular dynamics simulation study

Rotational motion of molecules in liquids plays an important role in determining the liquids' Nuclear Magnetic Resonance (NMR) spin-relaxation properties. The traditional theory of NMR spin relaxation assumes that the reorientational dynamics of molecules in liquids can be described by a continuous-time rotational-diffusion random walk with a single rotational-diffusion coefficient. However, recent experimental and theoretical studies have demonstrated that the simple rotational-diffusion model does not fully capture the rotational dynamics of molecules in liquids: for example, the reorientation of molecules in liquid water occurs through a combination of continuous-time rotational diffusion and discrete, large angular jumps resulting from collective rearrangements of the hydrogen-bond network of water.In order to obtain further insights into the origin of large angular jumps in the rotational motion of liquid water, we studied the rotational dynamics of methane - an apolar, non‑hydrogen-bonding liquid with a spherically symmetric molecule. The reorientational propagator and the ensemble-averaged Legendre polynomial reorientational functions of liquid methane were analysed using molecular dynamics simulations. On the femtosecond timescale, the reorientational motion of methane molecules was found to be characterised by free-rotation gas-like Gaussian decay of the reorientational Legendre polynomials, a result consistent with the available experimental data for liquid methane. On the long timescale (picoseconds) the decay of the reorientational Legendre polynomials was exponential, suggestive of a Debye-like continuous-time rotational diffusion behaviour. However, the ratios of the exponential time constants for different orders of the Legendre polynomials failed to match the rotational-diffusion model. We discuss the implications of these findings for the understanding of rotational motion of molecules in hydrogen-bonding and non‑hydrogen-bonding liquids.

Effects of Hydrogen Bonding on the Rotational Dynamics of Water-Like Molecules in Liquids: Insights from Molecular Dynamics Simulations

Rotational motion of molecules plays an important role in determining NMR spin relaxation properties of liquids. The textbook theory of NMR spin relaxation predominantly uses the assumption that the reorientational dynamics of molecules is described by a continuous time rotational diffusion random walk with a single rotational diffusion coefficient. Previously we and others have shown that reorientation of water molecules on the timescales of picoseconds is not consistent with the Debye rotational-diffusion model. In particular, multiple timescales of molecular reorientation were observed in liquid water. This was attributed to the hydrogen bonding network in water and the consequent presence of collective rearrangements of the molecular network. In order to better understand the origins of the complex reorientational behaviour of water molecules, we carried out molecular dynamics (MD) simulations of a liquid that has a similar molecular geometry to water but does not form hydrogen bonds: hydrogen sulfide. These simulations were carried out at T=208K and p=1 atm (~5K below the boiling point). Ensemble-averaged Legendre polynomial functions of hydrogen sulfide exhibited a Gaussian decay on the sub-picosecond timescale but, unlike water, did not exhibit oscillatory behaviour. We attribute these differences to hydrogen sulfide’s absence of hydrogen bonding.

Translational and Rotational Diffusion in Liquid Water at Very High Pressure: A Simulation Study.

Translational and rotational diffusion coefficients of liquid water have been computed from molecular dynamics simulation with a recent polarizable potential at 298, 400, and 550 K at very high pressure. At 298 K, the model reproduces the initial increase and the occurrence of a maximum for the translational and rotational diffusion coefficients when the pressure increases. At 400 and 550 K, translational and rotational diffusion coefficients are found to monotonically decrease when pressure increases in the gigapascal range, with the translational coefficient decreasing faster than the rotational one. At 400 K, such an evolution of the rotational diffusion coefficient contrasts with quasielastic neutron scattering results predicting a near independence of the rotational diffusion with a pressure increase above ≃0.5 GPa. An interpretation is proposed to explain this discrepancy. The pressure dependence of the translation-rotation coupling is analyzed. The anisotropy of rotational diffusion is investigated by computing the rotational diffusion tensor in a molecular system of axes and the reorientational correlation times of rank 1 and rank 2 of the inertia axes and of the OH bond vector. Deviation of the simulation data with respect to the predictions of the isotropic Debye model of rotational diffusion are quantified and can be used to estimate experimental rotational diffusion coefficients from experimental reorientational correlation times.

Cluster Formation by Mobile Molecular Communication Systems

This paper considers mobile molecular communication systems where mobile bio-nanomachines release signaling molecules to form a cluster of bio-nanomachines. This paper examines how the sensitivity of bio-nanomachines to detect signaling molecules impacts on cluster formation. When the sensitivity is high, each bio-nanomachine reacts to signaling molecules that it releases. When the sensitivity is low, a bio-nanomachine reacts to signaling molecules only when a group of bio-nanomachines collectively releases signaling molecules. We extend a rotational diffusion model to describe the mobility of bio-nanomachines by considering the sensitivity of bio-nanomachines to detect signaling molecules. We also develop measures to characterize formed clusters. Simulation experiment results are shown to demonstrate how the sensitivity of bio-nanomachine to detect signaling molecules impacts the number of clusters formed, the mean cluster size, the mean cluster diameter, and the mean nearest neighbor distance between clusters.

Spin Probe Determination of Molecular Orientation Distribution and Rotational Mobility in Liquid Crystals: Model-Free Approach.

A model-free approach for simulation of EPR spectra of nitroxide spin probes in liquid-crystalline materials was suggested and used to obtain parameters of molecular orientation and rotational mobility. The developed method is based on experimental recording and numerical simulation of the angular dependence of EPR spectra, which is shown to be much more informative in comparison with a single EPR spectrum. Quantitative spectral simulations considering both local orientational ordering and distribution of local directors in the sample were used for discrimination of models of rotational mobility and orientational alignment. The method was applied for detailed quantitative characterization of axial, orthorhombic, and low-symmetry non-orthorhombic molecular orientation distributions. It is shown that the ordinarily used model of rotational diffusion in a mean-field potential is suitable for the description of molecular mobility and orientational ordering only for relatively low sample temperatures and low-mobility probe molecules with large sizes. In cases of high molecular mobility, the more realistic jump mechanism of molecular moves can be approximately described as quasi-librations. For ordered liquid crystals it was found that mostly the order parameters up to rank 12-14 are essential and easily determined. When well-aligned materials are described, the order parameters up to 18th rank or even higher become meaningful. Both molecular and sample biaxiality is analyzed and quantitatively characterized. The local molecular ordering and sample orientational alignment are quantitatively characterized separately.

Spurious violation of the Stokes\u2013Einstein\u2013Debye relation in supercooled water

The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the {boldsymbol{ell }}-th degree Legendre polynomials {{boldsymbol{tau }}}_{{boldsymbol{ell }}}, and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, {{boldsymbol{tau }}}_{{boldsymbol{ell }}}kBT/η and Dt{{boldsymbol{tau }}}_{{boldsymbol{ell }}}, where Dt is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values are decoupled with η/T, but are coupled with the translational diffusion constant Dt. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.

A revised jump-diffusion and rotation-diffusion model

Quasi-elastic neutron scattering (QENS) has many applications that are directly related to the development of high-performance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model (rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate (MSH) sample are fitted well for the Q range from 0.3 Å−1 to 1.9 Å−1 and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water (or bound water) C and the confining radius of mobile water a0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence time τ0, the rotational diffusion coefficient Dr, and the mean squared displacement (MSD) . The rJRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.