Rotational Diffusion Research Articles

Retraction Note: Effect of micro-viscosity on the rotational diffusion: pulsed laser-based time-resolved single-molecule study

Retraction Note: Effect of micro-viscosity on the rotational diffusion: pulsed laser-based time-resolved single-molecule study

Chemically reactive and aging macromolecular mixtures. II. Phase separation and coarsening.

In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a gel-like state. In the present work, we formulate a thermodynamically consistent kinetic framework to study the interplay between phase separation, chemical reaction, and aging in spatially inhomogeneous macromolecular mixtures. A numerical algorithm is also proposed to simulate domain growth from collisions of liquid and gel domains via passive Brownian motion in both two and three spatial dimensions. Our results show that the coarsening behavior is significantly influenced by the degree of gelation and Brownian motion. The presence of a gel phase inside condensates strongly limits the diffusive transport processes, and Brownian motion coalescence controls the coarsening process in systems with high area/volume fractions of gel-like condensates, leading to the formation of interconnected domains with atypical domain growth rates controlled by size-dependent translational and rotational diffusivities.

19F NMR relaxation of buried tryptophan side chains suggest anisotropic rotational diffusion of the protein RfaH.

The recent application of 19F NMR in the study of biomolecular structure and dynamics has made it a potentially attractive probe to complement traditional 15N/13C labelled probes for backbone and sidechain dynamics, albeit with some complications. The utility of 15N relaxation rates of rigid backbone amide groups to determine the rotational diffusion tensor of proteins is well established. Here we show that the measured 19F relaxation rates of two buried and possibly immobile 19F labelled tryptophan sidechains for the multidomain protein RfaH, in its closed conformation, are in reasonable agreement with the calculated values, only when anisotropic rotational diffusion of the protein is considered. While the sparsity of 19F relaxation data from a limited number of probes precludes the experimental determination of the rotational diffusion tensor here, these results demonstrate the influence of rotational diffusion anisotropy of proteins on 19F NMR relaxation of rigid tryptophan sidechains, while adding to the expanding literature of 19F NMR relaxation data sets in biomolecules.

Chiral active systems near a substrate: Emergent damping length controlled by fluid friction

Chiral active fluids show the emergence of a turbulent behaviour characterised by multiple dynamic vortices whose maximum size varies for each experimental system, depending on conditions not yet identified. We propose and develop an approach to model the effect of friction close to a surface in a particle based hydrodynamic simulation method in two dimensions, in which the friction coefficient can be related to the system parameters and to the emergence of a damping length. This length is system dependent, limits the size of the emergent vortices, and influences other relevant system properties such as the actuated velocity, rotational diffusion, or the cutoff of the energy spectra. Comparison of simulation and experimental results of a large ensemble of rotating colloids sedimented on a surface shows a good agreement, which demonstrates the predictive capabilities of the approach, which can be applied to a wider class of quasi-two-dimensional systems with friction.

Two-species model for nonlinear flow of wormlike micelle solutions. Part II: Experiment

Applications often expose wormlike micelle solutions to a very wide range of shear and temperature conditions. The two-species model presented in Part I [Salipante et al., J. Rheol. 68 (2024)] describes the nonlinear rheology over a wide range of shear rates. Here, we compare the model predictions to measurements using a combination of microcapillary and rotational rheology to measure the viscosity of surfactant solutions across seven decades of shear rate and five decades of viscosity. The effect of temperature is studied between 20 and 60 °C for different surfactant concentrations. Model parameters are determined from both small-amplitude shear measurements and fitting to the nonlinear data. Under shear stress, the model predicts due to hindered combination kinetics that the average micelle length decreases from several micrometers to a few hundred nanometers. At sufficiently high stress, the micelle shear rheology exhibits a transition from entangled wormlike behavior to a dilute rod rheology in agreement with the model. Transient stress-growth measurements exhibit a large overshoot, which is rather well predicted by the model with hindered combination rate. Microcapillary flow birefringence also is adequately predicted by the model, confirming the accuracy of its predicted micelle lengths and exhibiting a marked change in stress-optic response at the transition between entangled polymers and dilute rods. The relaxation of retardance after flow cessation follows model predictions that include micelle-micelle interactions, which are sensitive to the rotational diffusivity and length. These methods can be applied broadly to explore relationships between composition and performance.

Impact of Surface Chemistry and Particle Size on Inertial Cavitation Driven Transport of Silica Nanoparticles and Microparticles

AbstractThis study investigated the high‐intensity focused ultrasound (HIFU)‐mediated propulsion of mesoporous silica nanoparticles (MSNs) and microspheres (MSMs). Nanoparticles are heavily sought as vehicles for drug delivery, but their transport through tissue is often restricted. Here, MSNs and MSMs are hydrophobically modified and coated with phospholipids to facilitate inertial cavitation to promote propulsion under HIFU. Modified nanoparticles show significantly enhanced cavitation and propulsion, achieving a maximum displacement of 250 µm (≈2500 body length) and speed of ≈1600 µm s−1 (16 000 body length s−1), compared to unmodified nanoparticles (2 µm, 20 body length, 60 µm s−1, 600 body length). In contrast, microparticles demonstrate comparable cavitation responses. Modified microparticles reached a maximum speed of 4000 µm s−1 (800 body length s−1) and displacement of 230 µm (46 body length), and unmodified microparticles achieved 2000 µm s−1 (400 body length s−1) and 75 µm (15 body length). In all HIFU‐responsive samples, displacement and speed decreased with successive pulses, implying that particles fatigue with continued pulsing. Analyses of particle trajectories and rotational diffusion times suggest that cavitation occurs uniformly on particle surfaces rather than at specific sites. These principles are important for the design of future drug‐delivery vehicles capable of ultrasound‐triggered motion.

Ion Association and Hydration of Some Heavy-Metal Nitrate Salts in Aqueous Solution.

Aqueous solutions of four heavy-metal nitrate salts (AgNO3, TlNO3, Cd(NO3)2 and Pb(NO3)2) have been studied at 25 °C using broadband dielectric relaxation spectroscopy (DRS) at frequencies 0.27 ≤ ν/GHz ≤ 115 over the approximate concentration range 0.2 ≲ c/mol L-1 ≲ 2.0 (0.08 ≲ c/mol L-1 ≲ 0.4 for the less-soluble TlNO3). The spectra for AgNO3, TlNO3, and Pb(NO3)2 were best described by assuming the presence of three relaxation processes. These consisted of one solute-related Debye mode centered at ∼2 GHz and two higher-frequency solvent-related modes: one an intense Cole-Cole mode centered at ∼18 GHz and the other a small-amplitude Debye mode at ∼500 GHz. These modes can be assigned, respectively, to the rotational diffusion of contact ion pairs (CIPs), the cooperative relaxation of solvent water molecules, and its preceding fast H-bond flip. For Cd(NO3)2 solutions an additional solute-related Debye mode of small-amplitude, centered at ∼0.5 GHz, was required to adequately fit the spectra. This mode was consistent with the presence of small amounts of solvent-shared ion pairs. Detailed analysis of the solvent modes indicated that all the cations are strongly solvated with, at infinite dilution, effective total hydration numbers (Zt0 values) of irrotationally bound water molecules of ∼5 for both Ag+ and Tl+, ∼10 for Pb2+, and ∼20 for Cd2+. These results clearly indicate the presence of a partial second hydration shell for Pb2+(aq) and an almost complete second shell for Cd2+(aq). However, the hydration numbers decline considerably with increasing solute concentration due to ion-ion interactions. Association constants for the formation of contact ion pairs indicated weak complexation that varies in the order: Tl+ < Ag+ < Pb2+ < Cd2+, consistent with the charge/radius ratios of the cations and their Gibbs energies of hydration. Where comparisons were possible the present constants mostly agreed well with the rather uncertain literature values.

Slow Conformational Exchange between Partially Folded and Near-Native States of Ubiquitin: Evidence for a Multistate Folding Model.

The mechanism by which small proteins fold, i.e., via intermediates or via a two-state mechanism, is a subject of intense investigation. Intermediate states in the folding pathways of these proteins are sparsely populated due to transient lifetimes under normal conditions rendering them transparent to a majority of the biophysical methods employed for structural, thermodynamic, and kinetic characterization, which attributes are essential for understanding the cooperative folding/unfolding of such proteins. Dynamic NMR spectroscopy has enabled the characterization of folding intermediates of ubiquitin that exist in equilibrium under conditions of low pH and denaturants. At low pH, an unlocked state defined as N' is in fast exchange with an invisible state, U″, as observed by CEST NMR. Addition of urea to ubiquitin at pH 2 creates two new states F' and U', which are in slow exchange (kF'→U' = 0.14 and kU'→F' = 0.28 s-1) as indicated by longitudinal ZZ-magnetization exchange spectroscopy. High-resolution solution NMR structures of F' show it to be in an "unlocked" conformation with measurable changes in rotational diffusion, translational diffusion, and rotational correlational times. U' is characterized by the presence of just the highly conserved N-terminal β1-β2 hairpin. The folding of ubiquitin is cooperative and is nucleated by the formation of an N-terminal β-hairpin followed by significant hydrophobic collapse of the protein core resulting in the formation of bulk of the secondary structural elements stabilized by extensive tertiary contacts. U' and F' may thus be described as early and late folding intermediates in the ubiquitin folding pathway.

Molecular-Scale Interactions in the Choline Chloride-Ethylene Glycol Deep Eutectic Solvent System: The Importance of Chromophore Charge in Mediating Rotational Dynamics.

We report on the rotational diffusion dynamics of three chromophores (disodium fluorescein, oxazine 725, and perylene) in a series of choline chloride-ethylene glycol (ChCl:EG) deep eutectic solvent (DES) systems. We observe behavior independent of DES bulk viscosity for the cationic and neutral probes and behavior that is consistent with stick-limit interactions for the modified Debye-Stokes-Einstein model for the anionic probe. This finding indicates that the anionic species is integral to the interactions between DES constituent species that are responsible for local organization, consistent with previous MD simulations that showed higher interaction energies associated with both the hydrogen bond donor (EG) and hydrogen bond acceptor (Ch+) interactions with Cl- in ChCl:EG mixtures. The reorientation data reported here also indicate a region around 15 mol % ChCl where the stoichiometric relationship between the species gives rise to changes in the details of intermolecular interactions.

Aggregation-disaggregation regulated fluorescence resonance energy transfer of perovskite nanocrystals for the detection of ascorbic acid

Fluorescence resonance energy transfer (FRET) from fluorescent nanoparticles to small molecules is an attractive approach for bioanalysis. It remains challenging to reversibly regulate the FRET, let alone use reversible FRET to detect ions or molecules. Here we demonstrate an aggregation/disaggregation strategy for reversible regulation of FRET based on metal–ligand coordination chemistry and redox reactions. An amino-functionalized red fluorescent (∼668 nm) perovskite nanocrystals (PNCs) was prepared as the energy donor. Fe3+ can coordinate with the amino groups on PNCs, resulting in the aggregation of PNCs and enhanced absorption from 600 to 700 nm on the surface of PNCs. Aggregation can reduce the distance between PNCs and Fe3+–amino complexes, as well as restrict rotational and translational diffusion of PNCs or Fe3+–amino complexes, consequently enhancing the FRET between PNCs and Fe3+–amino complexes. Interestingly, reductive ascorbic acid can reduce Fe3+ to Fe2+ in the complexes, leading to a weakening of absorption at 668 nm and dispersion of PNCs, resulting in the disappearance of the FRET process involved in PNCs. Based on the FRET switch, we have realized consecutive quantitative analysis of Fe3+ and ascorbic acid in real samples. We expect that reversible FRET process can be regulated by aggregation-disaggregation instructed by coordination and redox reactions, and that the regulation strategy could significantly expand the application scope of PNCs in fluorescence detection.

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.

Active string fluids and gels formed by dipolar active Brownian particles in 3D.

Self-propelled particles possessing permanent magnetic dipole moments occur naturally in magnetotactic bacteria and can be built into man-made systems such as active colloids or micro-robots. Yet, the interplay between self-propulsion and anisotropic dipole-dipole interactions on dynamic self-assembly in three dimensions (3D) remains poorly understood. We conduct Brownian dynamics simulations of active dipolar particles in 3D, focusing on the low-density regime, where dipolar hard spheres tend to form chain-like aggregates and percolated networks with increasing dipolar coupling strength. We find that strong active forces override dipolar attractions, effectively inhibiting chain-like aggregation and network formation. Conversely, activating particles with low to moderate forces results in a fluid composed of active chains and rings. At strong dipolar coupling strengths, this active fluid transitions into an active gel, consisting of a percolated network of active chains. Although the overall structure of the active gel remains interconnected, the network experiences more frequent configurational rearrangements due to the reduced bond lifetime of active dipolar particles. Consequently, particles exhibit enhanced translational and rotational diffusion within the active fluid of strings and active gels compared to their passive counterparts. We quantify the influence of activity on aggregate topology as they transition from branched structures to unconnected chains and rings. Our findings are summarized in a state diagram, delineating the impact of dipolar coupling strength and active force magnitude on the system.

Ballistic to diffusive transition for swimmers in a periodic vortex array.

We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of sectionin phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of sectionsurrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.

Diffusion of proteins in crowded solutions studied by docking-based modeling.

The diffusion of proteins is significantly affected by macromolecular crowding. Molecular simulations accounting for protein interactions at atomic resolution are useful for characterizing the diffusion patterns in crowded environments. We present a comprehensive analysis of protein diffusion under different crowding conditions based on our recent docking-based approach simulating an intracellular crowded environment by sampling the intermolecular energy landscape using the Markov Chain Monte Carlo protocol. The procedure was extensively benchmarked, and the results are in very good agreement with the available experimental and theoretical data. The translational and rotational diffusion rates were determined for different types of proteins under crowding conditions in a broad range of concentrations. A protein system representing most abundant protein types in the E. coli cytoplasm was simulated, as well as large systems of other proteins of varying sizes in heterogeneous and self-crowding solutions. Dynamics of individual proteins was analyzed as a function of concentration and different diffusion rates in homogeneous and heterogeneous crowding. Smaller proteins diffused faster in heterogeneous crowding of larger molecules, compared to their diffusion in the self-crowded solution. Larger proteins displayed the opposite behavior, diffusing faster in the self-crowded solution. The results show the predictive power of our structure-based simulation approach for long timescales of cell-size systems at atomic resolution.

A novel RNA sensor based on dynamics of oligonucleotide-functionalized Janus particles driven by rotational diffusion

PCR tests are used to diagnose infections caused by high-risk viruses and infectious bacteria, including novel coronaviruses. However, the current methods are problematic because of their long testing time and operational complexity. In this study, we focused on rotational Brownian motion that changes microscopically. We developed a new biosensor that is specific, quick, and facile for detecting target DNA/RNA by photographing the rotational Brownian motion of oligonucleotide probe-modified Janus particles under a microscope and analyzing the diffusivity, which is the degree of motion. The Stokes–Einstein–Debye relationship shows the rotational diffusivity of the particles is inversely proportional to the particle size cubed. For Janus particles, which emit fluorescence on only half of their surface, the rotational diffusivity corresponds to the correlation time, which is the correlation intensity per elapsed time of the flashing signal obtained from the rotational Brownian motion of the particles. In the presence of the target RNA, Janus particles captured the RNA, leading to the formation of Janus particle-RNA complexes and an increase in particle volume, which increased the correlation time. The correlation time of the Janus particle-target RNA complexes increased with increasing target RNA concentrations.

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.

Free volume theory of self-diffusion in zeolites: Molecular simulation and experiment

Neutron scattering and molecular dynamics are used to unravel the microscopic mechanisms that govern methane diffusion in MFI zeolite (silicalite-1). First, using neutron scattering for silicalite-1 loaded with different methane amounts, we analyze the experimental dynamic structure factor S(q,ω) in terms of molecular rotations and translations. While the rotational diffusion is found to be nearly independent of the zeolite loading, the translational diffusivity drastically decreases with the adsorbed amount. To gain insights into the diffusion mechanisms, trajectories obtained using molecular dynamics simulations are analyzed by determining mean square displacements 〈Δr2(t)〉 and incoherent scattering functions F(q,t). We also determine how anisotropy affects diffusion by considering independently the x, y and z directions. While the activation energy for diffusion is found to be weakly dependent on methane loading, the self-diffusivity decreases as the loading increases. Both the experimental and molecular simulation results suggest that steric repulsion between confined molecules – which increases as the loading increases – drastically affects diffusion. Using a free volume theory, we provide a simple formalism to predict consistently diffusion in the internal porous network of MFI zeolite. To demonstrate the applicability of this simple yet robust framework, we show that the free volume theory accurately captures diffusion in each direction of space but also when the size of the adsorbate molecule is arbitrarily increased.

A Four-Dimensional No-Equilibrium Chaotic System with Multi-Scroll Chaotic Hidden Attractors and its Application in Image Encryption

Abstract In recent years, constructing hidden attractors with multi-scroll has become a key discussion point in the research and application fields of chaos science. In this paper, with the existing four-dimensional (4D) chaotic system as the base, a new four-dimensional chaotic system featuring significant characteristics of multi-scroll hidden attractors is constructed by adding a nonlinear function. Comprehensive studies including theoretical analyses and numerical simulations have been carried out on the dynamic properties of the new chaotic system, and all the results show that this system exhibits extremely complex chaotic behaviours and excellent unpredictability, which has great value in image encryption. Therefore, an image encryption scheme based on the new chaotic system is proposed, which cleverly integrates the new scrambling algorithm based on parity coordinate transformation and the new rotational diffusion algorithm. And the effectiveness of this encryption algorithm has been thoroughly analyzed and tested. The results based on the experiments show that this encryption algorithm exhibits significant advantages in performance, which can greatly enhance the security of images during encryption and transmission.

Gate-Switchable Molecular Diffusion on a Graphene Field-Effect Transistor.

Controlling the surface diffusion of particles on 2D devices creates opportunities for advancing microscopic processes such as nanoassembly, thin-film growth, and catalysis. Here, we demonstrate the ability to control the diffusion of F4TCNQ molecules at the surface of clean graphene field-effect transistors (FETs) via electrostatic gating. Tuning the back-gate voltage (VG) of a graphene FET switches molecular adsorbates between negative and neutral charge states, leading to dramatic changes in their diffusion properties. Scanning tunneling microscopy measurements reveal that the diffusivity of neutral molecules decreases rapidly with a decreasing VG and involves rotational diffusion processes. The molecular diffusivity of negatively charged molecules, on the other hand, remains nearly constant over a wide range of applied VG values and is dominated by purely translational processes. First-principles density functional theory calculations confirm that the energy landscapes experienced by neutral vs charged molecules lead to diffusion behavior consistent with experiment. Gate-tunability of the diffusion barrier for F4TCNQ molecules on graphene enables graphene FETs to act as diffusion switches.