Rotational Diffusion Coefficients Research Articles

Impacts of Small SBA-15 Mesopores on Translation and Rotational Diffusion of Benzyl Alcohol.

Small SBA-15 pores can enhance the catalytic activity of gold catalysts in the selective oxidation of benzyl alcohol reaction. The goal of this work is to probe the impact of SBA-15 pores on the translational and rotational diffusion of the reactive species (e.g., benzyl alcohol). Herein, we demonstrate the use of nuclear magnetic resonance-based diffusion-ordered spectroscopy (DOSY) and T1 relaxation techniques to measure the translational and rotational diffusion coefficients of liquid benzyl alcohol molecules in three distinct environments: bulk, pore, and near-surface. The DOSY and T1 relaxation techniques render the routine diffusion measurements for liquid molecules confined in small pores possible. Furthermore, we measure the translational and rotational diffusion coefficients of benzyl alcohol molecules in the bulk, pore, and near-surface environments at varying temperatures. These measurements are then correlated via the Arrhenius equation to determine the activation energy associated with their translational (Et) and rotational (Er) diffusion. A higher activation energy suggests a more difficult diffusion process, while a lower activation energy implies a facile diffusion process. Our findings demonstrate that the ranking of Et follows the order of bulk (difficult) > near-surface > pore (easy), whereas the ranking of Er follows the order of pore (difficult) > bulk > near-surface (easy). This result suggests that the small SBA-15 pores can facilitate the translational diffusion but hinder the rotational diffusion of benzyl alcohol molecules.

Size dependence of transport coefficients of thin and long asphaltene molecules as determined using a mode-coupling theory approach

Rotational diffusion coefficients (Dr) and viscosities (η) of rigid rod molecules consisting of N beads were first revisited for the situation at low density. Starting from this, the transport coefficients at high density condition were expressed in terms of different density pair correlation functions, such as intermolecular radial distribution function and structure factor. This was attained using a mode-coupling theory approach to approximate the intermolecular force–force correlation function, and thus the friction coefficient. As these density pair correlation functions are dependent on N, they determine how “entangled” the rigid rod molecules are, and therefore reproducing the crossover in the log –log plot of transport coefficients with N. It was found that there are crossovers in transport coefficients from Dr∼N−2.3 and η∼N2.3 at low N to Dr∼N−6.5 and η∼N6.5 at high N. The strength of N dependence is mainly determined by the competition between available free space and the compressibility of the system.

Tagged particle behavior in a harmonic chain of direction-reversing active Brownian particles

Abstract We study the tagged particle dynamics in a harmonic chain of direction-reversing active Brownian particles, with the spring constant k, rotation diffusion coefficient D R , and directional reversal rate γ. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. For well-separated time-scales, k − 1 , D R − 1 and γ −1, the strength of the spring constant k relative to D R and γ gives rise to different coupling limits, and for each coupling limit there are short, intermediate, and long-time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth t ν , where the value of the exponent ν depends on the specific regime. For a quenched initial orientation, the exponent ν crosses over from 3 to 1 / 2 , via intermediate values 5 / 2 or 1, depending on the specific coupling limits. However, for the annealed initial orientation, ν crosses over from 2 to 1 / 2 via an intermediate value 3 / 2 or 1 for the strong coupling limit and the weak coupling limit, respectively. An additional time-scale t N = N 2 / k emerges for a system with a finite number of oscillators N. We show that the behavior of the tagged particle variance across tN can be expressed in terms of a crossover scaling function, which we find exactly. Moreover, we study the velocity autocorrelation. Finally, we characterize the stationary state behavior of the separation between two consecutive particles by calculating the corresponding spatio-temporal correlation function.

Single-particle rotational sensing for analyzing the neutralization activity of antiviral antibodies

Due to the pathogen-specific targeting, neutralization capabilities, and enduring efficacy, neutralizing antibodies (NAs) have received widespread attentions as a critical immunotherapeutic strategy against infectious viruses. However, because of the high variability and complexity of pathogens, rapid determination of neutralization activity of antiviral antibodies remains a challenge. Here, we report a new method, named as out-of-plane polarization imaging based single-particle rotational sensing, for rapid analysis of neutralization activity of antiviral antibody against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Using the spike protein functionalized gold nanorods (AuNRs) and angiotensin-converting enzyme 2 (ACE2) coated gold nanoparticles (AuNPs) as the rotational sensors and chaperone probes, we demonstrated the single-particle rotational sensing strategy for the measurement of rotational diffusion coefficient of the chaperone-bound rotational sensors caused by the specific spike protein-ACE2 interactions. This enables us to measure the neutralizing activity of neutralizing antibody from the analysis of dose-dependent changes in rotational diffusion coefficient (Dr) of the rotational sensors upon the treatment of SARS-CoV-2 antibody. With this technique, we achieved the quantitative determination of neutralization activity of a commercially available SARS-CoV-2 antibody (IC50, 294.1 ng/mL) with satisfying accuracy and anti-interference ability. This simple and robust method holds the potential for rapid and accurate evaluation of neutralization activity against different pathogenic viruses.

In situ pulmonary mucus hydration assay using rotational and translational diffusion of gold nanorods with polarization-sensitive optical coherence tomography.

Assessing the nanostructure of polymer solutions and biofluids is broadly useful for understanding drug delivery and disease progression and for monitoring therapy. Our objective is to quantify bronchial mucus solids concentration (wt. %) during hypertonic saline (HTS) treatment in vitro via nanostructurally constrained diffusion of gold nanorods (GNRs) monitored by polarization-sensitive optical coherence tomography (PS-OCT). Using PS-OCT, we quantified GNR translational () and rotational () diffusion coefficients within polyethylene oxide solutions (0 to 3wt. %) and human bronchial epithelial cell (hBEC) mucus (0 to 6.4wt. %). Interpolation of and data is used to develop an assay to quantify mucus concentration. The assay is demonstrated on the mucus layer of an air-liquid interface hBEC culture during HTS treatment. In polymer solutions and mucus, and monotonically decrease with increasing concentration. is more sensitive than to changes above 1.5wt. % of mucus and exhibits less intrasample variability. Mucus on HTS-treated hBEC cultures exhibits dynamic mixing from cilia. A region of hard-packed mucus is revealed by measurements. The extended dynamic range afforded by simultaneous measurement of and of GNRs using PS-OCT enables resolving concentration of the bronchial mucus layer over a range from healthy to disease in depth and time during HTS treatment in vitro.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Measuring nanoparticles shape by structured illumination

Exploiting the size and shape of nanoparticles is critical for engineering the optical and mechanical properties of nanoparticle systems that are ubiquitous in everyday life. However, accurate determination of nanoparticle morphology usually requires elaborated methods such as XRD or TEM, which are not suitable for non-invasive and rapid control. Dynamic light scattering on the other hand, relies on the motion of nanoparticles and mixes different rotational and translational diffusion coefficients to infer synthetic information about the shape in terms of effective hydrodynamic characteristics. Here, we introduce a new scattering approach for measuring shape. We demonstrate analytically, numerically, and experimentally that the contrast of low-intensity fluctuations arising from the scattering of classically entangled optical fields allows determining the polarimetric anisotropy of nanoparticles. By leveraging the active variation of illumination structuring, we control the non-Gaussian statistics of the measured fluctuations, which, in turn, provides means to improve the measurement sensitivity. This technique offers practical opportunities for applications ranging from molecular chemistry to drug delivery to nanostructures synthesis where the real-time, quantitative assessment of nanoparticles shapes is indispensable.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity v 0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of v 0 polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Dynamics of anisotropic colloidal systems: What to choose, DLS, DDM or XPCS?

Investigation of the dynamics of colloids in bulk can be hindered by issues such as multiple scattering and sample opacity. These challenges are exacerbated when dealing with inorganic materials. In this study, we employed a model system of Akaganeite colloidal rods to assess three leading dynamics measurement techniques: 3D-(depolarized) dynamic light scattering (3D-(D)DLS), polarized-differential dynamic microscopy (P-DDM), and x-ray photon correlation spectroscopy (XPCS). Our analysis revealed that the translational and rotational diffusion coefficients captured by these methods show a remarkable alignment. Additionally, by examining the q-ranges and maximum volume fractions for each approach, we offer insights into the best technique for investigating the dynamics of anisotropic systems at the colloidal scale.

Rotational and translational diffusion of biomolecules in complex liquids and HeLa cells.

Diffusive motion accompanies many physical and biological processes. The Stokes-Sutherland-Einstein relation for the translational diffusion coefficient, DT, agrees with experiments done in simple fluids but fails for complex fluids. Moreover, the interdependence between DT and rotational diffusion coefficient, DR, also deviates in complex fluids from the classical relation of DT/DR = 4r2/3 known in simple fluids. Makuch et al. Soft Matter, 2020, 16, 114-124 presented a generalization of the classical translational and rotational diffusion theory for complex fluids. In this work, we empirically verify this model based on simultaneous translational and rotational diffusion measurements. We use fluorescently stained cowpea chlorotic mottle virus (CCMV) particles as monodisperse probes and aqueous polyethylene glycol (PEG) solutions as a model complex fluid. The theory and experimental data obtained from fluorescence correlation spectroscopy (FCS) measurements agreed. Finally, we used the same model and analyzed the diffusion of Yo-Pro-1 stained large ribosomal subunits (LSU) in the cytoplasm and nucleus of living HeLa cells.

Experimental study of confined diffusion of rough and smooth ellipsoidal colloids

The study of diffusion in complex confined environments has received great attention in the field of condensed matter physics. The emergence of colloidal systems provides an excellent experimental model system for quantitatively studying the confined diffusion of microscopic particles. When colloidal particles change from spherical to ellipsoidal shape, the system presents anisotropic diffusion dynamics. Recent studies have found that rough surfaces, another important physical parameter of colloids, can lead to unusual rotational dynamics in spherical colloidal systems. However, due to the lack of a suitable experimental system, little is known about the effect of rough surfaces on the confined diffusion of ellipsoidal colloidal particles. In this work, rough colloidal spheres, rough colloidal ellipsoids, and smooth colloidal ellipsoids are prepared, and then monolayer colloidal samples are prepared to study the confined diffusions of these two types of ellipsoids in dense packing of the rough sphere colloids. By calculating the mean square displacement, intermediate self-scattering function, and orientation correlation function of the ellipsoids, we quantitatively characterize the diffusion dynamics of rough and smooth ellipsoids in varying concentrations of rough spheres. The results indicate that the translational diffusion and rotational diffusion of rough ellipsoids and smooth ellipsoids slow down as the concentration of rough spheres increases. This is due to the confinement of the ellipsoid by the surrounding spheres. At low stacking fractions of spheres, smooth and rough ellipsoids show similar translational diffusion and rotational diffusion. However, as the stacking fraction of spheres increases, there is a significant difference in advection diffusion between rough ellipsoids and smooth ellipsoids. The advection diffusion of rough ellipsoids is significantly slower than that of smooth ellipsoids. This is because the rough surface strongly inhibits rotation, meaning that the rotational diffusion of the rough ellipsoids is significantly slower than that of the smooth ellipsoids. By extracting the diffusion coefficients for translation and rotation from the ellipsoid's long-time mean-square displacements, we find that at <i>ϕ</i> = 0.60 and 0.65, the diffusion coefficients of rough ellipsoids are smaller than those of smooth ellipsoids. The translational diffusion coefficient of the rough ellipsoids is notably smaller than that of the smooth ellipsoids. However, the rotation diffusion coefficient of the rough ellipsoids is not significantly different from that of the smooth ellipsoids. This suggests that the rough surface mainly affect translational diffusion, strongly suppressing the translational diffusion of the ellipsoids. By calculating the displacement probability distribution for ellipsoidal motion, we find that at <i>ϕ</i> = 0.65, the translational displacements of rough ellipsoids have a relatively narrow distribution. This suggests that the translational motion of particles is suppressed by the rough surface. However, the distributions of rotation displacement for smooth ellipsoids and rough ellipsoids are very similar, indicating that the rough surface has less influence on particle rotation. At <i>ϕ</i> = 0.74, the rough surface suppresses both the translation and the rotation of the ellipsoid, resulting in a narrower displacement distribution than in the case of smooth ellipsoid. These findings suggest that rough surfaces significantly impede ellipsoidal diffusion, leading the translational and rotational motions not to occur simultaneously. This study provides an in-depth understanding of the role of rough surfaces of colloidal particles in confined diffusion, as well as an experimental basis for explaining the diffusion laws of rough materials.

First coarse grain then scale: How to estimate diffusion coefficients of confined molecules.

An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.

Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides a Fast but Still Accurate Treatment of Hydrodynamic Interactions in Brownian Dynamics Simulations of Biological Macromolecules.

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HIs). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here, we explore the use of an alternative way to accelerate the calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA-RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA-RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast, approximate way of including HIs in BD simulations of intermediate-scale systems.

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.

Solutions of rods and spheres: Predictions for the diffusion coefficient

The systems considered here are mixtures of neutral rods and spheres in solution, for which I aim to describe the rods’ diffusion coefficient. Several situations are studied according to the partial volume fractions and relative sizes between the two types of colloids. Using scaling analyses, I either obtain the translational or the rotational diffusion coefficient. Some of my predictions are compared with available experimental and numerical data, showing good agreement. The relevance of this work is to provide models that capture the main features concerning the diffusion of rods in mixed colloidal solutions and make contact with a much more intricate problem of diffusion in crowded media, such as the interior of the cytoplasm.

Swirling transition with social interactions: Analyzed by a sixth-order Landau-type model (a)

Swirling groups of animals or bacteria are a common phenomenon in nature. It is thought that this collective organization occurs in the vicinity of a continuous transition between dynamic states to ensure robust group cohesion while allowing for high sensitivity to outside stimuli like predators. Here, we present Brownian dynamics simulations of active particles with social interactions which can form stable swirls. We observe a transition between swarming and swirling states and analyze these using a sixth-order Landau-type model. Our results suggest that the transition is weakly discontinuous. However, by lowering the rotational diffusion coefficient, it becomes continuous.

Learning run-and-tumble chemotaxis with support vector machines

To navigate in spatial fields of sensory cues, bacterial cells employ gradient sensing by temporal comparison for run-and-tumble chemotaxis. Sensing and motility noise imply trade-off choices between precision and accuracy. To gain insight into these trade-offs, we learn optimal chemotactic decision filters using supervised machine learning, applying support vector machines to a biologically motivated training dataset. We discuss how the optimal filter depends on the level of sensing and motility noise, and derive an empirical power law for the optimal measurement time with as a function of the rotational diffusion coefficient D rot characterizing motility noise. A weak amount of motility noise slightly increases chemotactic performance.

Effect of curvature on the diffusion of colloidal bananas.

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods-also known as colloidal bananas-as a function of their opening angle α. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from 0^{∘} (straight rods) to nearly 360^{∘}(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when α>180^{∘}. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Pressure-Gradient Counterwork of Dual-Fuel Driven Nanocarriers in Abnormal Interstitial Fluids for Enhancing Drug Delivery Efficiency.

The abnormal pressure in tumor tissue is a significant limitation on the drug delivery efficiency of tumor therapy. This work reports a gradient-driven nanomotor as drug nanocarrier with the pressure-counterworking function. The dual-fuel nanomotors are formed by co-electrospinning of the photosensitive polymers with calcium peroxide (CaO2 ) and catalase (CAT), followed by ultraviolet (UV) irradiation and bovine serum albumin (BSA) incubation. The UV-responsive cleavage nanomotors can effectively release O2 molecules at the fractures as a driving force to increase the delivery speed and escape the phagocytosis of macrophage system in normal tissues. Furthermore, CAT catalyzes H2 O2 produced by CaO2 and the tumor interstitial fluids to provide stronger power for the nanomotors. Additionally, according to the analysis of directional motions of the nanomotors, the functional relationship between the rotational diffusion coefficient (DR ) and the physiological viscosity is constructed. The dual-fuel nanocarriers enable up to 13.25% of the injected dose (ID)/per gram tissue and significantly improve the penetration in deep tumor. It is of vital importance to design and obtain the adaptive pressure-gradient counterworking nanomotors, which can effectively improve the drug delivery efficiency in vitro and in vivo.

Desorption of a Flexible Polymer with Activity from a Homogeneous Attractive Surface

The interfacial behavior of a flexible polymer with activity, which is named active Brownian polymer (ABPO), is studied by Langevin dynamics simulations. On the dependence of the adsorption strength and activity characterized by the Péclet number (Pe), the polymer displays two typical states on the surface: adsorption and desorption states. We find that the diffusion behavior of ABPO that is parallel to the surface yields the “active Rouse model” and the activity causes the adsorption–desorption transition at a certain adsorption strength. Particular attention is given to how the desorption time, τdes, changes with the activity. At intermediate activity, τdes displays an exponential decay with the inverse of the effective temperature, Teff ∝1 + Pe2/18, which is reminiscent of the mechanism of thermal activation. At higher activity, due to easily overcoming the attractive energy barrier, τdes ∝Pe–1 is found. At lower activity, a power-law dependence of τdes on the diffusion coefficient perpendicular to the surface (D⊥) is observed (τdes ∼D⊥–1.28). Further, we observed a non-monotonic dependence of desorption time on the rotation diffusion coefficient DR of the monomer and found that τdes exists on a scaling relation with the chain length N, τdes ∼ Nϕ, and the scaling exponent ϕ decreases with the increase of activity. Our results highlight that the activity can be used to regulate the polymer adsorption and desorption behavior.