Langevin Dynamics Simulations Research Articles

Langevin dynamics simulation and collision frequency modification in population balance model of nanoparticle coagulation during simultaneous agglomeration and sintering

Coagulation of nanoparticles from the free-molecular to the transition regime under a high-temperature environment is investigated by coupling Langevin Dynamics (LD) model with agglomeration and finite-rate sintering. The effect of temperature on the evolution of particle size and structure is investigated, variations in agglomeration-sintering dynamics are obtained. The fractal dimension of agglomerates at different temperatures can be expressed as a function of the ratio between the characteristic collision time and sintering time. The overall collision frequency (β) is enhanced by the polydispersity and fractal properties of agglomerates compared to the monodisperse collision kernel functions. Finally, the classic function of β is modified based on the LD simulations and used in a one-dimensional population balance equation, which reproduces a better prediction of the evolution of particle size distribution during particle coagulation with agglomeration and sintering.

Effects of inertia on conformation and dynamics of tangentially driven active filaments.

Active filamentlike systems propelling along their backbone exist across scales ranging from motor-driven biofilaments to worms and robotic chains. In macroscopic active filaments such as a chain of robots, in contrast to their microscopic counterparts, inertial effects on their motion cannot be ignored. Nonetheless, the consequences of the interplay between inertia and flexibility on the shape and dynamics of active filaments remain unexplored. Here we examine inertial effects on a flexible tangentially driven active polymer model pertinent to the above examples and we determine the conditions under which inertia becomes important. Performing Langevin dynamics simulations of active polymers with underdamped and overdamped dynamics for a wide range of contour lengths and activities, we uncover striking inertial effects on conformation and dynamics for high levels of activities. Inertial collisions increase the persistence length of active polymers and remarkably alter their scaling behavior. In stark contrast to passive polymers, inertia leaves its fingerprint at long times by an enhanced diffusion of the center of mass. We rationalize inertia-induced enhanced dynamics by analytical calculations of center-of-mass velocity correlations, applicable to any active polymer model, which reveal significant contributions from active force fluctuations convoluted by inertial relaxation.

Mechanical fatigue testing in silico: Dynamic evolution of material properties of nanoscale biological particles

Biological particles have evolved to possess mechanical characteristics necessary to carry out their functions. We developed a computational approach to "fatigue testing in silico", in which constant-amplitude cyclic loading is applied to a particle to explore its mechanobiology. We used this approach to describe dynamic evolution of nanomaterial properties and low-cycle fatigue in the thin spherical encapsulin shell, thick spherical Cowpea Chlorotic Mottle Virus (CCMV) capsid, and thick cylindrical microtubule (MT) fragment over 20 cycles of deformation. Changing structures and force-deformation curves enabled us to describe their damage-dependent biomechanics (strength, deformability, stiffness), thermodynamics (released and dissipated energies, enthalpy, and entropy) and material properties (toughness). Thick CCMV and MT particles experience material fatigue due to slow recovery and damage accumulation over 3-5 loading cycles; thin encapsulin shells show little fatigue due to rapid remodeling and limited damage. The results obtained challenge the existing paradigm: damage in biological particles is partially reversible owing to particle's partial recovery; fatigue crack may or may not grow with each loading cycle and may heal; and particles adapt to deformation amplitude and frequency to minimize the energy dissipated. Using crack size to quantitate damage is problematic as several cracks might form simultaneously in a particle. Dynamic evolution of strength, deformability, and stiffness, can be predicted by analyzing the cycle number (N) dependent damage, [Formula: see text] , where α is a power law and Nf is fatigue life. Fatigue testing in silico can now be used to explore damage-induced changes in the material properties of other biological particles. STATEMENT OF SIGNIFICANCE: Biological particles possess mechanical characteristics necessary to perform their functions. We developed "fatigue testing in silico" approach, which employes Langevin Dynamics simulations of constant-amplitude cyclic loading of nanoscale biological particles, to explore dynamic evolution of the mechanical, energetic, and material properties of the thin and thick spherical particles of encapsulin and Cowpea Chlorotic Mottle Virus, and the microtubule filament fragment. Our study of damage growth and fatigue development challenge the existing paradigm. Damage in biological particles is partially reversible as fatigue crack might heal with each loading cycle. Particles adapt to deformation amplitude and frequency to minimize energy dissipation. The evolution of strength, deformability, and stiffness, can be accurately predicted by analyzing the damage growth in particle structure.

Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity.

Cell membranes phase separate into ordered and disordered domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in and domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into and domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

Impact of flexibility on the aggregation of polymeric macromolecules.

Dependence of the dimerization probability and the aggregation behavior of polymeric macromolecules on their flexibility is studied using Langevin dynamics simulations. It is found that the dimerization probability is a non-monotonic function of the polymers persistence length. For a given value of inter-polymer attraction strength, semiflexible polymers have lower dimerization probability relative to flexible and rigid polymers of the same length. The threshold temperature of the formation of aggregates in a many-polymer system and its dependence on the polymers persistence length is also investigated. The simulation results of two- and many-polymer systems are in good agreement and show how the amount of flexibility affects the dimerization and the aggregation behaviors of polymeric macromolecules.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization.

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Nonequilibrium diffusion of active particles bound to a semiflexible polymer network: Simulations and fractional Langevin equation.

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question concerns quantitatively explaining how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semiflexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays superdiffusive and subdiffusive athermal motion with a time-dependent anomalous exponent α. In such viscoelastic feedback, the active particle always exhibits superdiffusion with α = 3/2 at times shorter than the self-propulsion time (τA). At times greater than τA, the subdiffusive motion emerges with α bounded between 1/2 and 3/4. Remarkably, active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high Pe limit, athermal fluctuation in the stiff filament eventually leads to α = 1/2, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semiflexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe (Pe∗) and crossover times (τ∗ and τ†) above which active viscoelastic dynamics emerge on timescales of τ∗≲ t ≲ τ†. Our study may provide theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments.

Fabrication parameters affecting the structural color of colloidal films: A combined numerical investigation

Colloidal assembly formed by drying of suspensions is expected to be applied to optical materials using their structural color resulting from the microstructure. We combine two numerical simulation techniques to investigate how the fabrication conditions of the self-assembled colloidal films affect their structural color. We first perform Langevin dynamics simulations to form colloidal films with various microstructures depending on the several fabrication parameters and then perform the finite-difference time-domain simulations of electromagnetic field analysis to calculate the structural color intensity of the obtained microstructures. To improve the structural color intensity, we show that the surface tension of the solvent should be sufficiently large so that capillary interactions exceed the interparticle adhesion by van der Waals force and furthermore that under this condition the smaller drying rate is favorable. This study suggests a guideline to design the fabrication process of colloidal films generating structural color.

Target searches of interacting Brownian particles in dilute systems.

We study the target searches of interacting Brownian particles in a finite domain, focusing on the effect of interparticle interactions on the search time. We derive the integral equationfor the mean first-passage time and acquire its solution as a series expansion in the orders of the Mayer function. We analytically obtain the leading order correction to the search time for dilute systems, which are most relevant to target search problems and prove a universal relation given by the particle density and the second virial coefficient. Finally, we validate our theoretical prediction by Langevin dynamics simulations for the various types of the interaction potential.

Modelling nanoparticle agglomeration in the transition regime: A comparison between detailed Langevin Dynamics and population balance calculations

The prediction of nanoparticle agglomeration using population balance modelling is a difficult endeavour as continuously growing clusters undergo different collision regimes and exhibit complex, fractal-like structures. A key model parameter in this context is the collision kernel which governs the agglomeration dynamics within the particle population. In this work, we exploit a recently developed model for Brownian coagulation to solve the population balance equation for an initially monodisperse system of spherical nanoparticles in a quiescent gas. Since the model was originally developed for the limiting cases of ballistic and diffusive agglomeration, we incorporate a suitable interpolation scheme to extend the kernel expression to the more general transition regime.The results obtained from population balance calculations are validated by means of detailed Langevin Dynamics simulations where agglomerates and their individual trajectories are resolved. A comparison of agglomeration dynamics and evolving size distributions reveals strong agreement between the two approaches which corroborates the accuracy of the collision kernel model. In contrast, conventional models for the kernel are not able to reproduce the results from detailed Langevin Dynamics simulations as they noticeably underpredict the width of the agglomerate size distribution.Analysis of the agglomerates’ morphology distribution further reveals that fractal dimensions of clusters are normally distributed and can be characterized by a size-dependent mean value and standard deviation. We find, however, that the specifics of the morphology distribution do not need to be included in the kernel as omission causes only minor changes with respect to the collision dynamics. Using a size-dependent averaged fractal dimension is sufficient within PBE calculations.

Controlling the drying characteristics of suspensions via colloidal interactions: Particle-scale modeling

During drying of colloidal suspensions, evaporation of the suspending liquid drives the formation of concentrated particle layers beneath the receding free surface. The particle layers can lower the drying rate especially when the suspensions contain small nanoparticles. We investigate how such drying characteristics are affected by interactions between particles by use of Langevin dynamics simulations, for which we develop an analytical model to evaluate the decreasing drying rate from the permeation resistance of the formed particle layers. Considering aqueous suspensions where the particles interact through DLVO potentials, we show that there is an ionic strength where the drying rate is the most lowered and that the decrease in the drying rate is remarkably suppressed when the particles aggregate at sufficiently high ionic strength. This behavior reflects the structure of particle layers varied by the interactions. Our result provides an example how to control the drying characteristics by suspension composition.

Translocation of an active polymer into a two dimensional circular nano-container

Translocation dynamics of an active semi-flexible polymer through a nano-pore into a rigid two dimensional circular nano-container has been studied by using Langevin dynamics simulations. The results show that the force exponent β, for regime of small nano-container radius, i.e. , where R g is the gyration radius of the passive semi-flexible polymer in two dimensional free space, is , while for large values of the asymptotic value of the force exponent is . The force exponent is defined by the scaling form of the average translocation time , where F sp is the self-propelling force. Moreover, using the definition of the turning number (number of net turns of the polymer configuration) for the polymer inside the cavity, it has been found that at the end of translocation process for small value of R and in the strong force limit the polymer configuration is more regular than the case in which the value of R is large or the force is weak.

Force-induced melting of DNA hairpin: Unfolding pathways and phase diagrams.

Using the exact enumeration technique, we have studied the force-induced melting of a DNA hairpin on the face centered cubic lattice for two different sequences which differ in terms of loop closing base pairs. The melting profiles obtained from the exact enumeration technique is consistent with the Gaussian network model and Langevin dynamics simulations. Probability distribution analysis based on the exact density of states revealed the microscopic details of the opening of the hairpin. We showed the existence of intermediate states near the melting temperature. We further showed that different ensembles used to model single-molecule force spectroscopy setups may give different force-temperature diagrams. We delineate the possible reasons for the observed discrepancies.

Lane formation in 3D driven pair-ion plasmas: II Non-Parallel External Forcing

In Part 1 of the companion paper, we have investigated lane formation dynamics of driven three-dimensional (3-D) pair-ion plasmas (PIP) in the presence of parallel external forcing using extensive Langevin dynamics (LD) simulation. In continuation of the work, in this Part 2, we investigate lane formation dynamics in the presence of non-parallel external forcing, and the effect of both constant and time varying forces are studied. In our model, positively charged PIP particles are pushed into the field direction by an external force $\boldsymbol{F}_{A} = E_A\cos \omega _At$ while the negatively charged PIP particles are pulled by an external force $\boldsymbol{F}_{B} = E_B\cos \omega _Bt$ in a direction perpendicular to the external force $\boldsymbol{F}_{A}$ . We show that in the case of non-parallel forces, the lanes are observed with an orientation (characterised by angle of inclination $\theta$ ) tilted in the direction of the force difference vector ( $\boldsymbol{F}_{A} - \boldsymbol{F}_{B}$ ). The instantaneous lane order parameter, order parameter with gradient of angle of inclination ( $\phi (\theta )$ ) and distribution function of $\Delta \theta$ have been implemented to characterise the phase transition. A spontaneous formation and breaking of lanes are observed when under the influence of time-varying forces. The effect is further investigated for three different situations: first, when $\omega _A \neq 0$ and $\omega _B = 0$ ; second, when $\omega _A = \omega _B \neq 0$ ; and third, for $\omega _A \neq \omega _B \neq 0$ . Our study reveals that for the first case, a periodic oscillation of angle of inclination is observed. If oscillating forces of the same frequency are applied, the oscillation in angle of inclination disappears, and spontaneous formation and breaking of lanes is observed. However, in the presence of forces with different frequencies, flipping of lane inclination between the positive and negative domain of $\theta$ is observed. Further, some aspects of the lane formation dynamics of a PIP system is also studied in the presence of an external magnetic field where the lane formation dynamics is found to be accelerated.

Diffusion of knots in nanochannel-confined DNA molecules.

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.

Combining Langevin dynamics and CFD-PBM model to predict TiO2 nanoparticle evolution during aerosol synthesis

The computational fluid dynamics coupled with the population balance model (CFD-PBM) based on the monodisperse model is widely used for the design of aerosol synthesis nanoparticles. Due to the monodisperse assumption, it is insufficient to accurately describe the particle polydispersity and morphology during particle evolution in the reactor. To solve these limitations, we employed the mesoscale Langevin dynamics (LD) simulation for particle coagulation and combined it with CFD-PBM to investigate the particle evolution in a tubular aerosol reactor. Particle coagulation is simulated by LD simulations, which is split into two separate stages including the pure coalescence stage at high temperatures and the subsequent pure agglomeration stage at low temperatures. The evolution function of morphology (Df) and the in-real-time coagulation rate (β) are derived from LD and then applied for the PBM calculation. CFD-PBM model estimates the primary and agglomerate nanoparticle diameters in a tubular aerosol reactor within 90% and 75% accuracy, respectively, compared to the experimental measurements in the literature. By this LD-combined CFD-PBM model, the evolution of particle morphology along the axis can also be evaluated.

Lane formation in 3D driven pair-ion plasmas: I Parallel External Forcing

Lane formation dynamics of driven three-dimensional pair-ion plasmas (PIP) is investigated. Extensive Langevin dynamics simulation is performed to study the influence of an external electric field on the behaviour of the PIP system. In our model, one half of the particles are pushed into the field direction by an external force $\boldsymbol {F}_{A}$ while the other half are pulled into the opposite direction by an external force $\boldsymbol {F}_{B}$ . We show that if $\boldsymbol {F}_{A}$ and $\boldsymbol {F}_{B}$ are parallel, the system undergoes a non-equilibrium phase transition from a disordered state to a lane formation state parallel to the field direction with increasing field strength. The lanes are formed by the same kind of particles moving collectively with the field. The lane order parameter has been implemented to detect phase transition. Further, we show the lane formation in the presence of a time-varying external electric field. In particular, the effect of parallel forces are investigated. Unlike the previously reported two-dimensional case (Sarma, et al., Phys. Plasmas, vol. 27, 2020, p. 012106; Baruah, et al., J. Plasma Phys., vol. 87, issue 2, 2021, p. 905870202), for the time-varying electric field case, spontaneous formation and the breaking of lanes are not observed for all values of applied frequencies; however, the orderness varies and spontaneous formation and breaking of lanes is observed for values close to a critical frequency $\omega _c$ . Further, some aspects of the lane formation dynamics of a PIP system are also studied in the presence of an external magnetic field, which reveals that the presence of an external magnetic field accelerates the lane formation process and introduces a drift of the lanes in a direction perpendicular to both electric and magnetic fields.

Dissipative solitary waves in a two-dimensional complex plasma: Amorphous versus crystalline.

The propagation of a dissipative soliton was experimentally studied in a two-dimensional binary complex plasma. The crystallization was suppressed in the center of the particle suspension where two types of particles were mixed. The motions of individual particles were recorded using video microscopy, and the macroscopic properties of the solitons were measured in the amorphous binary mixture in the center and in the plasma crystal in the periphery. Although the overall shape and parameters of solitons propagating in amorphous and crystalline regions were quite similar, their velocity structures at small scales as well as the velocity distributions were profoundly distinct. Moreover, the local structure rearranged drastically in and behind the soliton, which was not observed in the plasma crystal. Langevin dynamics simulations were performed, and the results agreed with the experimental observations.

The effects of the shape of a capsid on the ejection rate of a single polymer chain through a nanopore.

The shape of a viral capsid affects the equilibrium conformation of DNA inside the capsid: the equilibrium DNA conformation inside a spherical capsid is a concentric spool while the equilibrium conformation inside an elongated capsid is a twisted toroid. The conformation of DNA, jammed inside the capsid due to high internal pressure, influences the ejection kinetics of the DNA from the capsid. Therefore, one would expect that the DNA ejection kinetics would be subject to the shape of the viral capsid. The effects of the capsid shape on the ejection, however, remain elusive partly due to a plethora of viral capsid shapes. In this work, we perform Langevin dynamics simulations for the ejection of a polymer chain from three different types of viral capsids: (1) spherical, (2) cubic, and (3) cuboid capsids. We find that the ejection rate of the polymer chain from the spherical capsid is much faster than that from either cubic or cuboid capsids. The polymer chain in the spherical capsid may undergo collective rotational relaxation more readily such that the polymer chain becomes more mobile inside the spherical capsid, which enhances the ejection kinetics. On the other hand, a threading motion is dominant inside cubic and cuboid capsids. We also find that the effects of the collective rotational motion become more significant for a more rigid chain inside a capsid.

Theoretical upper bound of multiplexing in biological sensory receptors

Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.