Brownian Dynamics Simulations Research Articles

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.

Role of interaction range on the microstructure and dynamics of attractive colloidal systems.

Colloidal gelation phase diagram has been traditionally characterized using three key factors: particle volume fraction, strength of attraction, and range of attraction. While there's a rich body of literature on the role of attraction strength and particle volume fraction, majority of studies have been limited to short range interactions. Using Brownian dynamics simulations, we explored the effect that the range of attractions has on the microstructure and dynamics of both weakly and strongly attractive colloidal systems. Although gelation occurs significantly faster at high attraction strength, by an order of magnitude compared to low strength, we did not observe any clear trend in gelation-rate with respect to a change in the range of interaction. However, as the attraction range increases in both systems, the final structure undergoes a transition from a single connected network to a fluid of dense clusters. This results in a new gelation phase boundary for long range attractive colloids.

Phantom chain simulations for the fracture of star polymer networks with various strand densities.

Despite many attempts, the relationship between the fracture and structure of polymer networks is yet to be clarified. For this problem, a recent study on phantom chain simulations [Y. Masubuchi et al., Macromolecules, 2023, 56, 9359-9367.] has demonstrated that the fracture characteristics obtained for polymer networks with various node functionalities and conversion ratios lie on master curves if they are plotted against cycle rank, which is the number of closed loops in the network per network node. In this study, we extended the simulation to the effect of prepolymer concentration c on the relationships between the cycle rank and fracture characteristics within the concentration range of 1 ≲ c/c* ≲ 10, concerning the overlapping concentration c*. We created networks from sols of star-branched phantom bead-spring chains via an end-linking reaction between different chains through Brownian dynamics simulations upon varying the number of branching arms f from 1 to 8, and the conversion ratio φc from 0.6 to 0.95. For the resultant networks, the cycle rank ξ was consistent with the mean-field theory. The networks were uniaxially stretched with energy minimization until break to obtain modulus G, strain at break εb, stress at break σb, and work for fracture Wb. As reported earlier, εb data for various f and φc are located on a master curve if plotted against ξ. The other quantities also draw master curves as functions of ξ if normalized by the branch point density υbr. The master curves depend on c; as c increases, all the mechanical characteristics monotonically increase. If we plot σb/υbr and Wb/υbr against G/υbr, the data for various f and φc lie on master curves but depending on c. Consequently, the fracture characteristics are not solely described by the modulus.

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.

Diffusion, density, and defects on spheres.

We simulate and model diffusion of spherical colloids of radius, a, on spherical surfaces of radius, R, as a function of relative size and surface concentration. Using Brownian dynamics simulations, we quantify diffusion and microstructure at different concentrations ranging from single particles to dense crystalline states. Self-diffusion and structural metrics (pair distribution, local density, and topological charge) are indistinguishable between spheres and planes for all concentrations up to dense liquid states. For concentrations approaching and greater than the freezing transition, smaller spheres with higher curvature show increased diffusivities and nonuniform density/topological defect distributions, which differ qualitatively from planar surfaces. The total topological charge varies quadratically with sphere radius for dense liquid states and linearly with sphere radius for dense crystals with icosahedrally organized grain scars. Between the dense liquid and dense crystal states on spherical surfaces is a regime of fluctuating and interacting defect clusters. We show local density governs self-diffusion in dense liquids on flat and spherical surfaces via the pair distribution. In contrast, dynamic topological defects couple to finite diffusivities through freezing and in low density crystal states on spherical surfaces, where neither exist on flat surfaces.

Collective dynamics of active dumbbells near a circular obstacle.

In this article, we present the collective dynamics of active dumbbells in the presence of a static circular obstacle using Brownian dynamics simulation. The active dumbbells aggregate on the surface of a circular obstacle beyond a critical radius. The aggregation is non-uniform along the circumference, and the aggregate size increases with the activity (Pe) and the curvature radius (Ro). The dense aggregate of active dumbbells displays persistent rotational motion with a certain angular speed, which linearly increases with activity. Furthermore, we show a strong polar ordering of the active dumbbells within the aggregate. The polar ordering exhibits long-range correlation, with the correlation length corresponding to the aggregate size. Additionally, we show that the residence time of an active dumbbell on the obstacle surface increases rapidly with area fraction due to many-body interactions that lead to a slowdown of the rotational diffusion. This article further considers the dynamical behavior of a tracer particle in the solution of active dumbbells. Interestingly, the speed of the passive tracer particle displays a crossover from monotonically decreasing to increasing with the size of the tracer particle upon increasing the dumbbells' speed. Furthermore, the effective diffusion of the tracer particle displays non-monotonic behavior with the area fraction; the initial increase in diffusivity is followed by a decrease for a larger area fraction.

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.

Reconfigurable Assembly of Planar Colloidal Molecules via Chemical Reaction and Electric Polarization.

Colloidal molecules, ordered structures assembled from micro- and nanoparticles, serve as a valuable model for understanding the behavior of real molecules and for constructing materials with tunable properties. In this work, we introduce a universal strategy for assembling colloidal molecules consisting of a central active particle surrounded by several passive particles as ligands. During the assembly process, active particles attract the surrounding passive particles through phoresis and osmosis resulting from the chemical reactions on the surface of the active particles, while passive particles repel each other due to the electric polarization induced by an alternating current (AC) electric field. By carefully selecting particles of varying structures and sizes, we have assembled colloidal molecules of symmetric and asymmetric dimers, trimers, and multimers. Furthermore, the coordination number of these colloidal molecules can be regulated in real time and insitu by tuning the interaction forces between the constituent particles. Brownian dynamics simulations reproduced the formation of the colloidal molecules and validated that the self-assembly arises from chemically induced attraction and electrical dipolar repulsion. This strategy for reconfigurable colloidal assemblies poses the potential for designing adaptive micro-nanomachines.

Model predictive control of non-interacting active Brownian particles.

Active matter systems are strongly driven to assume non-equilibrium distributions owing to their self-propulsion, e.g., flocking and clustering. Controlling the active matter systems' spatiotemporal distributions offers exciting applications such as directed assembly, programmable materials, and microfluidic actuation. However, these applications involve environments with coupled dynamics and complex tasks, making intuitive control strategies insufficient. This necessitates the development of an automatic feedback control framework, where an algorithm determines appropriate actions based on the system's current state. In this work, we control the distribution of active Brownian particles by applying model predictive control (MPC), a model-based control algorithm that predicts future states and optimizes the control inputs to drive the system along a user-defined objective. The MPC model is based on the Smoluchowski equation with a self-propulsive convective term and an actuated spatiotemporal-varying external field that aligns particles with the applied direction, similar to a magnetic field. We apply the MPC framework to control a Brownian dynamics simulation of non-interacting active particles and illustrate the controller capabilities with two objectives: splitting and juggling sub-populations, and polar order flocking control.

Probing the modulation in facilitated diffusion guided by DNA-protein interactions in target search processes.

Many fundamental biophysical processes involving gene regulation and gene editing rely, at the molecular level, on an intricate methodology of searching and locating the precise target base pair sequence on the genome by specific binding proteins. A unique mechanism, known as 'facilitated diffusion', which is a combination of 1D sliding along with 3D movement, is considered to be the key step for such events. This also explains the relatively much shorter timescale of the target searching process, compared to other diffusion-controlled biophysical processes. In this work, we aim to probe the modulation of target search dynamics of a protein moiety by estimating the rate of the target search process, and the statistics of the search rounds and timescales accomplished by the 1D and 3D motions, based on first passage time (FPT) calculations. This is studied with its characteristics getting influenced by various given conditions such as, when the DNA is rigid or flexible, and when the target is placed at different locations on the DNA. The current theoretical framework includes a Brownian dynamics simulation setup adopting a straightforward coarse-grained model for a diffusing protein on DNA. Moreover, this theoretical analysis provides insights into the complex target search dynamics by highlighting the significance of the chain dynamics in the mechanistic details of the facilitated diffusion process.

Large bubble drives circular DNA melting.

We investigate the melting transition of non-supercoiled circular DNA of different lengths, employing Brownian dynamics simulations. In the absence of supercoiling, we find that melting of circular DNA is driven by a large bubble, which agrees with the previous predictions of circular DNA melting in the presence of supercoiling. By analyzing sector-wise changes in average base-pair distance, our study reveals that the melting behavior of circular DNA closely resembles that of linear DNA. Additionally, we find a marked difference in the thermal stability of circular DNA over linear DNA at very short length scales, an effect that diminishes as the length of circular DNA increases. The stability of smaller circular DNA is linked to the occurrence of transient small bubbles, characterized by a lower probability of growth.

Structure and dynamics in suspensions of magnetic platelets.

In this research, we employ Brownian dynamics simulations, density functional theory, and mean-field theory to explore the profound influence of shape anisotropy of magnetic nanoplatelets on suspension magnetic response. Each platelet is modelled as an oblate cylinder with a longitudinal point dipole, with an emphasis on strong dipolar interactions conducive to self-assembly. We investigate static structural and magnetic properties, characterising the system through pair distribution function, static structure factor, and cluster-size distribution. The findings demonstrate that shape-specific interactions and clustering lead to significant changes in reorientational relaxation times. Under zero field, distinctive modes in the dynamic magnetic susceptibility identify individual particles and particle clusters. In the presence of an applied field, the characteristic relaxation time of clusters increases, while that of single particles decreases. This research provides insights into the intricate interplay between shape anisotropy, clustering, and magnetic response in platelet suspensions, offering valuable perspectives for recent experimental observations.

DNA Barcodes Using a Dual Nanopore Device.

We report a novel method based on the current blockade (CB) characteristics obtained from a dual nanopore device that can determine DNA barcodes with near-perfect accuracy using a Brownian dynamics simulation strategy. The method supersedes our previously reported velocity correction algorithm (S. Seth and A. Bhattacharya, RSC Advances, 11:20781-20787, 2021), taking advantage of the better measurement of the time-of-flight (TOF) protocol offered by the dual nanopore setup. We demonstrate the efficacy of the method by comparing our simulation data from a coarse-grained model of a polymer chain consisting of 2048 excluded volume beads of diameter 𝜎 = 24bp using with those obtained from experimental CB data from a 48,500bp λ-phage DNA, providing a base pair resolution in simulation. The simulation time scale is compared to the experimental time scale by matching the simulated time-of-flight (TOF) velocity distributions with those obtained experimentally (Rand et al., ACS Nano, 16:5258-5273, 2022). We then use the evolving coordinates of the dsDNA and the molecular features to reconstruct the current blockade characteristics on the fly using a volumetric model based on the effective van der Waal radii of the species inside and in the immediate vicinity of the pore. Our BD simulation mimics the control-zoom-in-logic to understand the origin of the TOF distributions due to the relaxation of the out-of-equilibrium conformations followed by a reversal of the electric fields. The simulation algorithm is quite general and can be applied to differentiate DNA barcodes from different species.

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.

Tailoring the SnO2 Ink for Roll‐to‐Roll Manufacturing of Flexible Perovskite Solar Cells

Roll‐to‐roll (R2R) fabrication of high‐performance perovskite solar cells (PSCs) remains challenging for PSC commercialization. Herein, the R2R‐suitable electron transfer layer (ETL) SnO2 ink system for flexible PSCs is investigated. Water‐dispersed SnO2 inks, commonly used for flexible PSCs, form dewetting pinholes during R2R slot‐die coating owing to slower evaporation compared to spin coating. To prevent the dewetting of the pinhole, a low surface tension solvent (isopropyl alcohol, IPA) is added to the SnO2 ink. The IPA addition reduced surface tension, enhancing wetting behavior, but increased SnO2 nanoparticles (NPs) aggregation. Interestingly, the fabricated ETL films with highly aggregated SnO2 NPs are smooth, in contrast to the rough layers obtained via the spin‐coating process, owing to the high shear rate. Herein, NP aggregation and surface morphology are explored using Brownian dynamics simulations under shear conditions. Consequently, when the particles are agglomerated, the PSCs with slot‐die coating exhibit higher power conversion efficiency compared to ETL spin‐coated PSCs. Therefore, IPA addition to SnO2 ink is preferred for the R2R slot‐die process by improving the wetting properties and forming smooth films. In this study, a framework is provided for obtaining high‐quality films using the slot‐die coating of ETL and promotes the commercialization of PSCs.

Taylor dispersion in arbitrarily shaped axisymmetric channels

Advective dispersion of solutes in long thin axisymmetric channels is important to the analysis and design of a wide range of devices, including chemical separation systems and microfluidic chips. Despite extensive analysis of Taylor dispersion in various scenarios, most studies focus on long-term dispersion behaviour and cannot capture the transient evolution of the solute zone across the spatial variations in the channel. In the current study, we analyse the Taylor–Aris dispersion for arbitrarily shaped axisymmetric channels. We derive an expression for solute dynamics in terms of two coupled ordinary differential equations, which allow prediction of the time evolution of the mean location and axial (standard deviation) width of the solute zone as a function of the channel geometry. We compare and benchmark our predictions with Brownian dynamics simulations for a variety of cases, including linearly expanding/converging channels and periodic channels. We also present an analytical description of the physical regimes of transient positive versus negative axial growth of solute width. Finally, to further demonstrate the utility of the analysis, we demonstrate a method to engineer channel geometries to achieve desired solute width distributions over space and time. We apply the latter analysis to generate a geometry that results in a constant axial width and a second geometry that results in a sinusoidal axial variance in space.