Brownian Dynamics Simulations Research Articles

Elastic particle model for coil-stretch transition of dilute polymers in an elongational flow

The phenomenon of the ‘coil-stretch’ (C-S) transition, wherein a long-chain polymer initially in a coiled state undergoes a sudden configuration change to become fully stretched under steady elongational flows, has been widely recognized. This transition can display intricate hysteresis behaviours under specific critical conditions, giving rise to unique rheological characteristics in dilute polymer solutions. Historically, microscopic stochastic models and Brownian dynamics simulations have shed light on the underlying mechanisms of the transition by uncovering bistable configurations of polymer chains. Following the initial work by Cerf (J. Chem. Phys., vol. 20, 1952, pp. 395–402), we introduce a continuum model in this study to investigate the C-S transition in a constant uniaxial elongational flow. Our approach involves approximating the unfolding process of the polymer chain as an axisymmetric deformation of an elastic particle. We make the assumption that the particle possesses uniform material properties, which can be represented by a nonlinear, strain-hardening constitutive equation to replicate the finite extensibility of the polymer chain. Subsequently, we analytically solve for the steady-state deformation using a polarization method. By employing this reduced model, we effectively capture the C-S transition and establish its specific correlations with material and geometric properties. The hysteresis phenomena can be comprehended through a force-balance analysis, which involves comparing the externally applied viscous forces with the intrinsic elastic responsive forces. We demonstrate that our model, while simple, unveils rich elastohydrodynamics of the C-S transition.

Mechanism of DNA origami folding elucidated by mesoscopic simulations

Many experimental and computational efforts have sought to understand DNA origami folding, but the time and length scales of this process pose significant challenges. Here, we present a mesoscopic model that uses a switchable force field to capture the behavior of single- and double-stranded DNA motifs and transitions between them, allowing us to simulate the folding of DNA origami up to several kilobases in size. Brownian dynamics simulations of small structures reveal a hierarchical folding process involving zipping into a partially folded precursor followed by crystallization into the final structure. We elucidate the effects of various design choices on folding order and kinetics. Larger structures are found to exhibit heterogeneous staple incorporation kinetics and frequent trapping in metastable states, as opposed to more accessible structures which exhibit first-order kinetics and virtually defect-free folding. This model opens an avenue to better understand and design DNA nanostructures for improved yield and folding performance.

Magneto-Permeability Effect in Ferrofluid Flow Through Porous Media Studied via Multiparticle Collision Dynamics

AbstractAs more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles’ magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.

Exploring Mechanisms of Lipid Nanoparticle-Mucus Interactions in Healthy and Cystic Fibrosis Conditions.

Mucus forms the first defense line of human lungs, and as such hampers the efficient delivery of therapeutics to the underlying epithelium. This holds particularly true for genetic cargo such as CRISPR-based gene editing tools which cannot readily surmount the mucosal barrier. While lipid nanoparticles (LNPs) emerged as versatile non-viral gene delivery systems that could help overcome the delivery challenge, many knowledge gaps remain, especially for diseased states such as cystic fibrosis (CF). This study provides fundamental insights into Cas9 mRNA or ribonucleoprotein-loaded LNP-mucus interactions in healthy and diseased states by assessing the impact of the genetic cargo, mucin sialylation, mucin concentration, ionic strength, pH, and polyethylene glycol (PEG) concentration and nature on LNP diffusivity leveraging experimental approaches and Brownian dynamics simulations. Taken together, this study identifies key mucus and LNP characteristics that are critical to enabling a rational LNP design for transmucosal delivery. This article is protected by copyright. All rights reserved.

On the Brownian motion of a colloid trapped in optical tweezers: Experiments and simulations

The trapping potential induced by the interaction of a highly focused laser light with a spherical dielectric particle can be accurately approximated by a parabolic potential. In this work, we revisit experimental and numerical methodologies used to characterize the Brownian motion of a colloidal particle under the influence of a simple harmonic potential produced by optical tweezers. A classic Brownian dynamics simulation is used to model the experimental results, focusing on statistical properties that can be measured by direct visualization of the system using videomicroscopy. This work represents a useful insight into the underlying physics behind the optical tweezers technique, also giving guidelines regarding programming protocols and experimental analysis methodologies, that may be of help for students working with such techniques, as well as for professors teaching undergraduate advanced optics courses.

Effects of chain resolution on the configurational and rheological predictions of dilute polymer solutions in flow fields with hydrodynamic interactions

In a recent study, the resolution of a polymer chain model was shown to significantly affect rheological predictions from Brownian dynamics (BD) simulations [Kumar and Dalal, “Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow,” J. Non-Newtonian Fluid Mech. 315, 105017 (2023)], even in the absence of hydrodynamic interactions (HI) and excluded volume. In this study, we investigate the effects of chain resolution in the presence of HI. Toward this, we perform BD simulations of a long polymer chain, with the discretization level varying from a single Kuhn step (bead–rod model) to several tens of Kuhn-steps (bead–spring model). The chain models were subjected to flow fields of uniaxial extension (purely stretching) and steady shear (equal rates of stretching and rotation). Broadly, our results indicate an amplification of the differences observed between the differently resolved bead–rod and bead–spring models, in the presence of HI. Interestingly, all rheological predictions qualitatively fall in two groups for extensional flow, with the predictions from the bead–spring model with HI being close to those of the bead–rod model without HI. This indicates significantly reduced sensitivity of coarser bead–spring models to HI, relative to the one resolved to a single Kuhn step. However, in shear flow, the bead–spring rheological predictions fall between those of the bead–rod model with and without HI, forming a third group. This is linked to the presence of stretched and coiled states in the ensemble for shear flow. HI effects are large for the coiled states and weak for the stretched states, thereby yielding predictions that are intermediate between those for no HI and dominant HI. Thus, quite surprisingly, the quality of predictions of the bead–spring models is strongly affected by the physics of the flow field, irrespective of the parameterization.

Chiral active particles are sensitive reporters to environmental geometry

Chiral active particles (CAPs) are self-propelling particles that break time-reversal symmetry by orbiting or spinning, leading to intriguing behaviors. Here, we examined the dynamics of CAPs moving in 2D lattices of disk obstacles through active Brownian dynamics simulations and granular experiments with grass seeds. We find that the effective diffusivity of the CAPs is sensitive to the structure of the obstacle lattice, a feature absent in achiral active particles. We further studied the transport of CAPs in obstacle arrays under an external field and found a reentrant directional locking effect, which can be used to sort CAPs with different activities. Finally, we demonstrated that parallelogram lattices of obstacles without mirror symmetry can separate clockwise and counter-clockwise CAPs. The mechanisms of the above three novel phenomena are qualitatively explained. As such, our work provides a basis for designing chirality-based tools for single-cell diagnosis and separation, and active particle-based environmental sensors.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution.

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Design of a Brownian ratchet based on repetitive aggregation and dispersion of stimuli-responsive molecules.

We propose a Brownian ratchet for the unidirectional transport of stimuli-responsive molecules confined in a series of asymmetric geometries. It relies on repetitive cycles of aggregation and dispersion, which cause significant changes in molecular distribution within the confining geometry and enable the Brownian motion of the molecules to be ratcheted in a specific direction. To demonstrate the feasibility of the proposed Brownian ratchet, we conducted Brownian dynamics simulations where stimuli-responsive molecules were repeatedly aggregated and dispersed in a series of truncated conical tubes by altering intermolecular interactions. These simulations demonstrated the unidirectional transport of the molecules, indicating the efficacy of the proposed Brownian ratchet. Furthermore, we found that it becomes more effective with higher concentrations of molecules. This study suggests that, through the deliberate control of molecular assembly and disassembly by stimuli-responsive intermolecular interactions, it is possible to achieve directional and controlled molecular transport in various nanoscale applications.

Revealing the sub-organelle structure and rheological properties of the Escherichia coli nucleoid by live-cell single-particle tracking and Brownian dynamics simulation

Revealing the sub-organelle structure and rheological properties of the Escherichia coli nucleoid by live-cell single-particle tracking and Brownian dynamics simulation

Motility-induced phase separation of soft active Brownian particles

Motility-induced phase separation (MIPS) is the hallmark of non-equilibrium phase transition in active matter. Here, by means of Brownian dynamics simulations, we determine the phase behavior and the critical point for phase separation induced by motility of a two-dimensional system of soft active Brownian particles, whose interaction is modeled by the generalized purely repulsive Weeks–Chandler–Andersen potential. We refer to this model as soft active Brownian particles. We determine and analyze the influence of particle softness on the MIPS and show that the liquid–gas coexistence region is wider, the softer the interparticle interactions becomes. Moreover, the critical value of the self-propulsion velocity at which diluted and dense phases start to coexist also increases; as a consequence, the softer the particle interaction is, the bigger self-propulsion velocities are needed in order to observe a MIPS.

Brownian dynamics simulations of bottlebrush polymers in dilute solution under simple shear and uniaxial extensional flows.

We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.

External field-driven property localization in liquids of responsive macromolecules.

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.

Elucidation of the trapping characteristics of magnetic disk-like particles in a Hagen-Poiseuille flow via Brownian dynamics simulations (usage of multi-magnetic poles)

In the present study, we elucidate the behaviour of a suspension composed of magnetic disk-like particles that flow in a Hagen-Poiseuille flow in a gradient magnetic field and the trapping characteristics of the magnetic particles. To this end, we utilise multiple pairs of magnetic poles located outside the cylindrical system. Brownian dynamics simulations were performed in order to clarify the dependence of these characteristics on a variety of factors. It is seen that an increase in the magnetic field strength improves the trapping characteristics of disk-like particles if the influence of an applied magnetic field is sufficiently more dominant than that of a flow field and that of the magnetic particle-particle interaction. In the case of a strong magnetic particle-particle interaction, thin chain-like clusters are formed from an anchored particle trapped around a magnetic pole. If the two poles are sufficiently close to each other, an arch-type cluster is formed between them. We expect that this arch-type cluster may give rise to good trapping performance even in the presence of a strong flow field if the formation arises at a sufficiently large separation distance between the pair of magnetic poles. Highlights We have performed Brownian dynamics simulations for a magnetic disk-like particle suspension in a Hagen-Poiseuille flow. If the magnetic particle-particle interaction is sufficiently more dominant than the flow field, thin chain-like clusters are formed from an anchored particle. As the pole separation distance decreases, an arch-type configuration tends to be formed along the surface of the wall. This arch-type cluster that is formed between the pair of magnetic poles may be expected to improve the trapping characteristics depending on the pole separation distance.

Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers.

The static and dynamic properties of dendrimers in semidilute solutions of linear chains of comparable size are investigated using Brownian dynamics simulations. The radius of gyration and diffusivity of a wide variety of low generation dendrimers and linear chains in solution follow universal scaling laws independent of their topology. Analysis of the shape functions and internal density of dendrimers shows that they are more spherical than linear chains and have a dense core. At intermediate times, dendrimers become subdiffusive, with an exponent higher than that previously reported for nanoparticles in semidilute polymer solutions. The long-time diffusivity of dendrimers does not follow theoretical predictions for nanoparticles. We propose a new scaling law for the long-time diffusion coefficients of dendrimers which accounts for the fact that, unlike nanoparticles, dendrimers shrink with an increase in background solution concentration. Analysis of the properties of a special case of a higher functionality dendrimer shows a transition from polymer-like to nanoparticle-like behaviour.

Dilute gel networks vs. clumpy gels in colloidal systems with a competition between repulsive and attractive interactions.

Using Brownian dynamics simulations we study gel-forming colloidal systems. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We apply reduction algorithms and observe that dilute networks and dense gels differ in the way structural properties like the thickness of strands emerge. We also analyze the percolation behavior and find that two different regimes of percolation exist which might be responsible for structural differences. In dilute networks we confirm that solidity is mainly a consequence of pentagonal bipyramids forming in the network. In dense gels, tetrahedral structures also influence solidity.

Numerical study of the effect of particle size dispersion on order within colloidal assemblies

The formation of colloidal crystals is of interest in many fields, especially because of their optical properties. These properties are dictated by the colloidal arrangement. It is known that introducing particles with different sizes can change the structure of crystals and thus their resultant optical properties. To better understand how specific arrangements of particles can be obtained, a detailed understanding of the formation mechanisms is needed. The influence of particle size distribution on the formation of colloidal crystals is studied by means of Brownian dynamics simulations performed with different types of interaction potentials. Crystal formation is first analyzed in systems containing homogeneous particles, then in systems with a size distribution.It is shown that the interaction potential has a strong influence on the colloidal arrangement. For homogeneous particles, the width of the potential well affects the aggregate shape: a larger width leads to more elongated structures. When a size distribution is introduced, aggregation becomes more difficult since the number of isolated colloids increases, and aggregates become disordered regardless of the interaction potentials. Depending on the interaction potential, differences in the aggregates are observed. These differences are rationalized in terms of the specific features of the different potentials.

Brownian dynamics simulation on the parallel superposition rheology of a colloidal gel

Parallel superposition rheology has been explored using Brownian dynamics simulations on a model colloidal gel by imposing a small amplitude probing oscillation parallel to the main shear flow. This study aims to investigate the constituting principles behind the material functions in parallel superposition rheometry (PSR) and to elucidate the principles behind the structure responses. The viscoelastic spectra under frequency sweeps show that in a high-frequency region, each curve can be superimposed onto a single master curve using horizontal shift factors equal to viscosity which is a reminiscence of time-shear rate superposition in orthogonal superposition rheometry. This corresponds to the region where a parallel superposition analysis can be adequately performed as the shear rate controls the viscoelastic spectra of the gel independently from probing perturbation. On the other hand, in the low-frequency region, this principle breaks down and even negative storage modulus is observed due to the strong flow coupling effect, which is also found in experiments. By introducing the spatial moduli, it is found that the negative modulus originates from the attractive potential region. In the flow conditions where negative modulus occurs, the shear force is strong enough to break down every surface bond between the particles. In this state, the increase in structural factor in response to the rise in the shear rate dominates particle stress, even within the attractive potential region. This arises because the isolated particles have more opportunities to interact with other particles as the shear rate of the imposed perturbation increases. This structural response, influenced by the attractive potential, results in a negative storage modulus and a positive loss modulus after performing Fourier transformation. This paper, for the first time by a simulation approach, demonstrates the essential characteristics of the material functions obtained using PSR. Also, this study is expected to enhance our understanding on the flowing materials and suggest a criterion for the reliable application of superposition rheology using a viscoelastic master curve.

Sampling Efficiency of Transverse Forces in Dense Liquids.

Sampling the Boltzmann distribution using forces that violate detailed balance can be faster than with the equilibrium evolution, but the acceleration depends on the nature of the nonequilibrium drive and the physical situation. Here, we study the efficiency of forces transverse to energy gradients in dense liquids through a combination of techniques: Brownian dynamics simulations, exact infinite-dimensional calculation, and a mode-coupling approximation. We find that the sampling speedup varies nonmonotonically with temperature, and decreases as the system becomes more glassy. We characterize the interplay between the distance to equilibrium and the efficiency of transverse forces by means of odd transport coefficients.

Brownian-molecular dynamic correspondence in two-dimensional hard-disk fluids

It has been both experimentally and theoretically observed that the structural and dynamical properties of glass-forming fluids can be scaled and described within the dynamic universality class of hard spheres. One of the key predictions of this universality is the long-time dynamic equivalence between Brownian and Molecular dynamics systems governed by the same kind of interaction potential. However, the application and extent of this principle has not been validated for two-dimensional systems. To this end, we employ Brownian and Molecular Dynamics simulations to validate this principle in the two-dimensional case, analysing the long-time properties of systems made up of monodisperse hard disks. By introducing a suitable density-dependent scaling factor, we successfully extend the principle of dynamic equivalence to two dimensions. This dynamic correspondence will facilitate the interpretation of long-time molecular dynamic properties in the context of colloidal dynamics. For instance, this correspondence will allow us to establish the extension of the colloidal freezing criterion to the molecular case.