Rotational Diffusion Constants Research Articles

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel–Fulcher–Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Burst-by-Burst Measurement of Rotational Diffusion at Nanosecond Resolution Reveals Hot-Brownian Motion and Single-Chain Binding.

We record dark-field scattering bursts of individual gold nanorods, 52 × 15 nm2 in average size, freely diffusing in water suspension. We deduce their Brownian rotational diffusion constant from autocorrelation functions on a single-event basis. Due to spectral selection by the plasmonic resonance with the excitation laser, the distribution of rotational diffusion constants is much narrower than expected from the size distribution measured by TEM. As rotational diffusion depends on particle hydrodynamic volume, viscosity, and temperature, it can sense those parameters at the single-particle level. We demonstrate measurements of hot Brownian rotational diffusion of nanorods in temperature and viscosity gradients caused by plasmonic heating. Further, we monitor hydrodynamic volumes of gold nanorods upon addition of very low concentrations of the water-soluble polymer PVA, which binds to the particles, leading to measurable changes in their diffusion constant corresponding to binding of one to a few polymer coils. We propose this analysis technique for very low concentrations of biomolecules in solution.

Chirality reversing active Brownian motion in two dimensions

We study the dynamics of a chirality reversing active Brownian particle (ABP), which models the chirality reversing active motion common in many microorganisms and microswimmers. We show that, for such a motion, the presence of the two time-scales set by the chirality reversing rate γ and rotational diffusion constant gives rise to four dynamical regimes, namely, (I) , (II) , (III) and (IV) , each showing different behavior. The short-time regime (I) is characterized by a strongly anisotropic and non-Gaussian position distribution, which crosses over to a diffusive Gaussian behavior in the long-time regime (IV) via an intermediate regime (II) or (III), depending on the relative strength of γ and . In regime (II), the chirality reversing active Brownian motion reduces to that of an ordinary ABP, with an effective rotation diffusion coefficient which depends on the angular velocity. Finally, we find that, the regime (III) is characterized by an effective chiral active Brownian motion.

Relating the Induced Free Charge Density Gradient in a Room-Temperature Ionic Liquid to Molecular-Scale Organization.

We report on dilution-dependent changes in the local environments of chromophores incorporated into room-temperature ionic liquid (RTIL)-molecular solvent binary systems where the ionic liquid cation and molecular solvent possess the same alkyl chain length. We have used the RTIL 1-decyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (DMPyrr+TFSI-) and the molecular solvent 1-decanol. Perylene was used as a non-polar probe, and cresyl violet (CV+) was used as a polar probe chromophore. We observe that in both regions there is a change in the chromophore local environments with increasing 1-decanol content. The changes in the nonpolar regions of the binary RTIL-molecular solvent system occur at a lower 1-decanol concentration than changes in the polar regions. Both chromophores reorient as oblate rotors in this binary system, allowing detailed information on the relative values of the Cartesian components of the rotational diffusion constants to be extracted from the experimental data. The induced free charge density gradient, ρf, known to exist in RTILs, persists to high 1-decanol content (1-decanol mole fraction of 0.75), with the structural details of the gradient being reflected in depth-dependent changes in the Cartesian components of the rotational diffusion constants of CV+. This is the first time that changes in molecular organization have been correlated with ρf.

Polarization effects on intermolecular vibrational energy transfer analyzed by 2DIR spectroscopy

AbstractIn the present work, we analyze the influence of the polarization effects taking place during the course of a 2DIR spectroscopy experiment performed on a molecular system undergoing an intermolecular vibrational energy transfer process. When both donor and acceptor molecules participating in the vibrational energy transfer are embedded in a host solvent, they face rotational diffusion that strongly distorts the resulting 2DIR spectra. It could be expected that the difference between rotational diffusion constants will be of particular interest. For this purpose, the polarization effects are discussed according to the different orderings of the laser‐molecule interactions. Next, we study the distortions of the spectra as a function of the rotational diffusion constants of the individual molecules. The knowledge of these polarization effects is relevant to the interpretation of the spectra. Finally, the conclusions reached in this work for a vibrational energy transfer are valid for any other type of third‐order optical process performed on the same molecular system.

Resetting-mediated navigation of an active Brownian searcher in a homogeneous topography.

Designing navigation strategies for search-time optimization remains of interest in various interdisciplinary branches in science. Herein, we focus on active Brownian walkers in noisy and confined environments, which are mediated by one such autonomous strategy, namely stochastic resetting. As such, resetting stops the motion and compels the walkers to restart from the initial configuration intermittently. The resetting clock is operated externally without any influence from the searchers. In particular, the resetting coordinates are either quenched (fixed) or annealed (fluctuating) over the entire topography. Although the strategy relies upon simple governing laws of motion, it shows a significant ramification for the search-time statistics, in contrast to the search process conducted by the underlying reset-free dynamics. Using extensive numerical simulations, we show that the resetting-driven protocols enhance the performance of these active searchers. This, however, depends robustly on the inherent search-time fluctuations, measured by the coefficient of variation of the underlying reset-free process. We also explore the effects of different boundaries and rotational diffusion constants on the search-time fluctuations in the presence of resetting. Notably, for the annealed condition, resetting is always found to expedite the search process. These features, as well as their applicability to more general optimization problems from queuing systems, computer science and randomized numerical algorithms, to active living systems such as enzyme turnover and backtracking recovery of RNA polymerases in gene expression, make resetting-based strategies universally promising.

Persistence of an active asymmetric rigid Brownian particle in two dimensions.

We have studied the persistence probability p(t) of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability of a stochastic variable that has not changed its signin a given fixed time interval. We have investigated two cases: (1) diffusion of a free active particle and (2) that of a harmonically trapped particle. In our earlier work, by Ghosh et al. [J. Chem. Phys. 152, 174901 (2020)], we had shown that p(t) can be used to determine the translational and rotational diffusion constant of an asymmetrically shaped particle. The method has the advantage that the measurement of the rotational motion of the anisotropic particle is not required. In this paper, we extend the study to an active anisotropic particle and show how the persistence probability of an anisotropic particle is modified in the presence of a propulsion velocity. Furthermore, we validate our analytical expression against the measured persistence probability from the numerical simulations of single particle Langevin dynamics and test whether the method proposed in our earlier work can help distinguish between active and passive anisotropic particles.

Microscopic diffusion coefficients of dumbbell- and spherocylinder-shaped colloids and their application in simulations of crowded monolayers.

We explore the diffusion properties of colloidal particles with dumbbell and spherocylinder shapes using a hydrodynamic bead-shell approach and additional Brownian dynamics (BD) simulations. By applying the bead-shell method, we determine empirical formulas for the microscopic diffusion coefficients. A comparison of these formulas and established experimental and theoretical results shows remarkable agreement. For example, the maximum relative discrepancy found for dumbbells is less than 5%. As an application example of the empirical formulas, we perform two-dimensional (2D) BD simulations based on a single dumbbell or spherocylinder in a suspension of spheres and calculate the resulting effective long-time diffusion coefficients. The performed BD simulations can be compared to quasi-2D systems such as colloids confined at the interface of two fluids. We find that the effective diffusion coefficient of translation mostly depends on the sphere area fraction ϕ, while the effective diffusion coefficient of rotation is influenced by the aspect ratio and ϕ. Furthermore, the effective rotational diffusion constant seems to depend on the particle shape with the corresponding implementation of the interactions. In the resolution limit of our methods, the shape-dependent differences of the microscopic diffusion coefficients and the long-time diffusion constant of translation are negligible in the first approximation. The determined empirical formulas for the microscopic diffusion coefficients add to the knowledge of the diffusion of anisotropic particles, and they can be used in countless future studies.

Diffusive dynamics of elongated particles in active colloidal suspensions of motile algae

Swimming microorganisms can influence the diffusion of passive particles. The effect of this swimmer-particle interaction depends on different properties, such as the hydrodynamic field of the swimmer and the relative sizes of microorganisms and particles. We investigated an enhancement of the diffusion of silica doublets in a suspension of microalgae Chlamydomonas reinhardtii in a flat capillary. Depending on the concentration of microswimmers, the translational and rotational diffusion constants increase by several orders of magnitude in the presence of the swimming algae. For low concentrations of algae, the doublets exhibit Brownian motion in a fluctuating flow field generated by multiple swimmers. One can observe strong, diffusive transport caused by occasional large displacements. At high swimmer concentration, the algae form dense clusters, where the rotational motion of the doublets shows a subdiffusive behaviour while the translational motion remains diffusive.

Cellulose Nanocrystals as a Model Substance for Rigid Rod Particle Suspension Rheology

A cellulose nanocrystal (CNC) sample with an average particle length and width of 170 and 7.8 nm, respectively, that was prepared from chemical pulp via sulfuric acid hydrolysis procedures was used as the test sample for a basic rheological study on rigid rod particle suspensions. The dynamic viscoelastic (VE) behavior of the CNC suspensions dispersed into a highly viscous aqueous sucrose solution at 60 wt % was examined over a range of concentrations (ν) in a semidilute regime at several temperatures. The obtained VE spectra were smoothly superposed onto master curves at a standard temperature of 25 °C using shift factors identical to those of the medium aqueous sucrose solution. The fundamental VE parameters, such as the zero-shear viscosity, the high frequency limiting viscosity, the average relaxation time (τw), and the reciprocal of the steady-state compliance (Je–1), were precisely determined from the master curves as functions of ν. The average rotational diffusion constant of the CNC particles dispersed into suspensions at a dilute condition, Dr0, was also determined at 25 °C using depolarized dynamic light scattering techniques. The relationship τw0 = (6Dr0)−1 was confirmed in the dilute regime, and τw ∝ ν2(6Dr0)−1 was observed in the semidilute regime as predicted by the Doi–Edwards (D–E) theory. Another relationship Je–1 = (3/5)νkBT, where kBT is the product of the Boltzmann constant and the absolute temperature, was also reasonably confirmed in the semidilute regime until the concentration approached the liquid crystal phase transition boundary, as also predicted by the D–E theory. Consequently, the CNC sample behaves as ideal model particles for the detailed study of rigid rod particle suspensions.

Increased stability of nitroxide radicals in ionic liquids: more than a viscosity effect.

Radical stability has been subject to continuous research due to its importance in polymerization as well as in all-organic batteries. Recently, the SOMO-HOMO conversion was identified as the main factor in controlling the stability of distonic radicals, for which the negative charge resides on the same molecule. Based on this finding, the idea of ionic liquids stabilizing radicals was hypothesized in this study. A series of ionic liquids were tested in EPR measurements of the 3-carboxy-2,2,5,5-tetramethyl-pyrroline-1-oxyl. Unusually high rotational diffusion constants (τR), 4 times larger compared to conventional media such as dichloromethane (DCM), were recorded at room temperature. This finding could only be explained by a strong interaction existing between the radical and ionic liquid ions, which was confirmed with quantum chemical calculations, with interaction energies falling between -17.1 kJ mol-1 for tetramethylphosphonium tetrafluoroborate and -85.6 kJ mol-1 for 1,3-dimethylimidazolium triflate. Elevated temperature measurements performed at 80 °C reduced the viscosity of the ionic liquids to that of DCM, while the τR values remained relatively high, thus further confirming that the rotational hindrance occurred due to radical-ionic liquid interactions. The calculated interaction energies between the radical and ionic liquids ions were also found to correlate well with experimental rotational diffusion constants, thus offering us a valuable tool in tailoring ionic liquids for enhanced stability of nitroxide radicals. The findings of this study showcase the ability of ionic liquids to reduce reactivity of nitroxides without the need for any chemical modification of the radical.

Diffusion-Limited Cluster Aggregation: Impact of Rotational Diffusion

Diffusion-limited cluster aggregation (DLCA) is a well established model for the formation of highly porous low-density non-equilibrium structures. One of the main conclusions of the previous studies considering this model is that the rotational diffusion of aggregating clusters does not change their structure characterized by a universal fractal dimension of $d_f=1.7-1.8$. In contradiction to this assumption, we demonstrate that the rotation movement of clusters significantly changes the structure of forming aggregates. The fractal dimension of rotating clusters is lower than the one found in the standard DLCA model and decreases with the increasing ratio of rotational and translational diffusion constants $D_r/D_t$, which offers a possibility to tune the structures of the aggregates below the conventional DLCA fractal dimension limit.

Orientational dynamics of a heated Janus particle.

Using large scale molecular dynamics simulations, we study the orientational dynamics of a heated Janus particle which exhibits self-propulsion. The asymmetry in the microscopic interaction of the colloid with the solvent is implemented by choosing different wetting parameters for the two halves of the sphere. This choice leads to a different microscopic Kapitza resistance across the solid-fluid boundary of the two halves of the sphere, and consequently a gradient in temperature is created across the poles of the sphere. It is this self-created temperature gradient which leads to a self-propulsion along the direction of the symmetry axis. In this article, we look at the orientational dynamics of such a system, as well as the subsequent enhancement of the translational diffusivity of the heated Janus colloid at late times. The orientational correlation of the symmetry axis is measured from the simulation and provides a direct access to the rotational diffusion constant. The heating leads to an increase in the rotational diffusivity of the colloid. We quantify this increase in rotational diffusion D r against the temperature difference δT ≡ T(R, 0) - T(R, π) across the poles of the Janus sphere as well as the average surface temperature difference ΔT ≡ T(R) - T(∞) from the ambient fluid. Since the rotational diffusion is determined by the complete flow field in the solvent, we illustrate that comparing D r against δT is misleading and is better quantified when compared against ΔT. The later quantification results in a data collapse for different choices of the microscopic interaction. The average propulsion velocity is also measured for different choices of the wetting parameter. The directionality of self-propulsion changes depending on the microscopic interaction. We show that whenever the attractive interaction of the colloid with the solvent is switched off, the phoretic mobility changes sign. Furthermore, the propulsion velocity is zero for heating below a certain threshold value. This is also corroborated by the probability distribution of the angle between the displacement vector Δr(t) ≡ r(t) - r(0) and the symmetry axis. Finally, we combine the measured propulsion velocity and the rotational diffusion time τ r = 1/2D r to estimate the enhancement in the long time diffusion coefficient of the particle.

Determination of the Anisotropic Rotational Diffusion Constant of Microcrystals Dispersed in Liquid Medium.

Microcrystals of ErBa2Cu4O8 suspended in a liquid medium were triaxially aligned by a frequency-modulated magnetic field and allowed a free rotational relaxation after the magnetic field was turned off. In situ X-ray diffraction measurements of the suspension were performed during relaxation, and the temporal change of the orientation fluctuation was monitored via broadening of the diffraction spots. The rotational diffusion constants were determined using the plot of the orientation fluctuation versus the elapsed time of rotational relaxation. The diffusion constants thus determined were in close agreement with those evaluated by the Stokes law but showed slight anisotropy, indicating that the microcrystals studied had shape anisotropy. The present method can provide a useful means for experimentally determining rotational diffusion constants of microcrystals suspended in viscous media. This paper shows that, due to the combination of the initial triaxial alignment and the subsequent monitoring of the relaxation process by means of X-ray diffraction, the diffusion constants along arbitrary crystallographic axes are determined separately.

Nonlinear response theory for Markov processes. III. Stochastic models for dipole reorientations

The nonlinear response of molecular systems undergoing Markovian stochastic reorientations is calculated up to fifth order in the amplitude of the external field. Time-dependent perturbation theory is used to compute the relevant response functions as in earlier treatments (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012), Phys. Rev. E{\bf 96}, 022150 (2017)). Here, we consider the reorientational motion of isolated molecules and extend the existing calculations for the model of isotropic rotational diffusion to the model of anisotropic rotational diffusion and to the model of rotational random jumps. Depending on the values of some model parameters, we observe a hump in the modulus of the nonlinear susceptibility for either of these models. Interestingly, for the model of rotational random jumps, the appearance of this hump depends on the way the coupling to the external field is modelled in the master equation approach. If the model of anisotropic rotational diffusion is considered, the orientation of the diffusion tensor relative to the molecular dipole moment and additionally the amount of anisotropy in the rotational diffusion constants determine the detailed shape of the nonlinear response. In this case, the height of the observed hump is found to increase with increasing 'diffusional anisotropy'. We discuss our results in relation to the features observed experimentally in supercooled liquids.

Observation of the linewidth broadening of single spins in diamond nanoparticles in aqueous fluid and its relation to the rotational Brownian motion

Capturing the fast rotational motion of single nanoparticles has been hindered owing to the difficulty of acquiring directional information under the optical diffraction limit. Here, we report the linewidth broadening of the electron spin resonance of single nitrogen vacancy (NV) centers that matches the rotational diffusion constant of the host nanodiamonds. When nanodiamonds are gradually detached from the substrates that they were fixed to, their optically detected spin resonance peaks are broadened by 1.8 MHz, which corresponds to the rotational diffusion constant of nanoparticles with a diameter of 11.4 nm from the Einstein–Smoluchowski relation.

Rate constants for proteins binding to substrates with multiple binding sites using a generalized forward flux sampling expression.

To predict the response of a biochemical system, knowledge of the intrinsic and effective rate constants of proteins is crucial. The experimentally accessible effective rate constant for association can be decomposed in a diffusion-limited rate at which proteins come into contact and an intrinsic association rate at which the proteins in contact truly bind. Reversely, when dissociating, bound proteins first separate into a contact pair with an intrinsic dissociation rate, before moving away by diffusion. While microscopic expressions exist that enable the calculation of the intrinsic and effective rate constants by conducting a single rare event simulation of the protein dissociation reaction, these expressions are only valid when the substrate has just one binding site. If the substrate has multiple binding sites, a bound enzyme can, besides dissociating into the bulk, also hop to another binding site. Calculating transition rate constants between multiple states with forward flux sampling requires a generalized rate expression. We present this expression here and use it to derive explicit expressions for all intrinsic and effective rate constants involving binding to multiple states, including rebinding. We illustrate our approach by computing the intrinsic and effective association, dissociation, and hopping rate constants for a system in which a patchy particle model enzyme binds to a substrate with two binding sites. We find that these rate constants increase as a function of the rotational diffusion constant of the particles. The hopping rate constant decreases as a function of the distance between the binding sites. Finally, we find that blocking one of the binding sites enhances both association and dissociation rate constants. Our approach and results are important for understanding and modeling association reactions in enzyme-substrate systems and other patchy particle systems and open the way for large multiscale simulations of such systems.

Inferring the Chemotactic Strategy of P. putida and E. coli Using Modified Kramers-Moyal Coefficients.

Many bacteria perform a run-and-tumble random walk to explore their surrounding and to perform chemotaxis. In this article we present a novel method to infer the relevant parameters of bacterial motion from experimental trajectories including the tumbling events. We introduce a stochastic model for the orientation angle, where a shot-noise process initiates tumbles, and analytically calculate conditional moments, reminiscent of Kramers-Moyal coefficients. Matching them with the moments calculated from experimental trajectories of the bacteria E. coli and Pseudomonas putida, we are able to infer their respective tumble rates, the rotational diffusion constants, and the distributions of tumble angles in good agreement with results from conventional tumble recognizers. We also define a novel tumble recognizer, which explicitly quantifies the error in recognizing tumbles. In the presence of a chemical gradient we condition the moments on the bacterial direction of motion and thereby explore the chemotaxis strategy. For both bacteria we recover and quantify the classical chemotactic strategy, where the tumble rate is smallest along the chemical gradient. In addition, for E. coli we detect some cells, which bias their mean tumble angle towards smaller values. Our findings are supported by a scaling analysis of appropriate ratios of conditional moments, which are directly calculated from experimental data.

Sum Frequency Generation Spectroscopy and Molecular Dynamics Simulations Reveal a Rotationally Fluid Adsorption State of α-Pinene on Silica

A rotationally fluid state of α-pinene at fused silica/vapor interfaces is revealed by computational and experimental vibrational sum frequency generation (SFG) studies. We report the first assignment of the vibrational modes in the notoriously congested C–H stretching region of α-pinene and identify its bridge methylene group on the four-membered ring (“βCH2”) as the origin of its dominant spectral feature. We find that the spectra are perfused with Fermi resonances that need to be accounted for explicitly in the computation of vibrational spectra of strained hydrocarbons such as α-pinene. The preferred orientations of α-pinene are consistent with optimization of van der Waals contacts with the silica surface that results in a bimodal distribution of highly fluxional orientations in which the βCH2 group points “towards” or “away from” the surface. Classical molecular dynamics simulations further provide rotational diffusion constants of 49 ± 1 ps and 2580 ± 60 ps, which are attributed to two broad types ...

Analysis of the dynamics of water confined in hydrated calcium silica(C-S-H) based on the quasi-elastic neutron scattering spectra

Cement is a widely used construction material in the world. Calcium-silicate-hydrate (C-S-H) is the main component of aged cement (concrete). The quality and durability of concrete are strongly affected by the dynamics of water confined in it. Dynamics of the confined water can be studied experimentally by the quasi-elastic neutron scattering (QENS). In this paper, the jump-diffusion and rotation-diffusion model (JRM) is used to fit the QENS spectra of C-S-H paste samples at different measured temperatures for the whole scattering vector Q-range from 0.3 to 1.7 -1. Five important parameters are extracted to describe the dynamics of water confined in C-S-H samples: the index of immobile water C, the rotational diffusion constant Dr, the mean square displacement (MSD) u2 , the self-diffusion coefficient Dt, and the average residence time between jumps 0. Here, all the C-S-H samples, each with a 30% weight ratio of water to cement, are measured at temperatures ranging from 230 to 280 K. The fitted parameters can quantitatively describe the dynamics of water confined on different scales of C-S-H gel pores. The results show that the QENS spectra are fitted very well not only for small Q (Q 1 -1) but also for large Q (Q 1 -1). The obtained rotational diffusion constant is Q dependent. Thus the contribution of the water molecule rotation to a QENS spectrum increases with the value of Q increasing. The mean square displacement (MSD) u2 decreases with the increase of Q, which can be used to distinguish the confined water, ultra-confined water, and bound water contained in C-S-H samples. When Q is small, the fitted Dt and 0 vary with the measured temperature. Dt has a maximum value at 230 K and 0 has a peak at 240 K. These indicate that the dynamics of the confined water shows different behaviors at 230 K and 240 K. There are crossover or critical phenomena for water confined in C-S-H sample at low temperature.