arXiv subjects

J. Ravi Prakash

Publications and source records attributed to J. Ravi Prakash.

At least 19 recordsLinked to original sources

arXiv2026

Linear Viscoelasticity of Semidilute Unentangled Flexible Polymer Solutions

The linear viscoelastic response of flexible polymer solutions in the dilute and semidilute unentangled regimes is investigated using Brownian dynamics simulations. The relaxation modulus and dynamic moduli are computed over a wide range of concentrations and chain discretizations for both $θ$ and good solvents. In the dilute limit, simulations recover Zimm-like behavior with solvent-quality-dependent power-law scaling in the intermediate time and frequency regimes, while in the semidilute unentangled regime a systematic crossover to Rouse-like dynamics is observed with increasing concentration due to screening of excluded-volume and hydrodynamic interactions. Comparison with experimental measurements shows excellent agreement for the storage modulus across both concentration regimes and for the loss modulus at low and intermediate frequencies, with deviations at high frequencies due to finite-chain discretization effects. Systematic accounting for these finite-chain length effects using successive fine-graining enables quantitative prediction of the loss modulus in the infinite-chain length limit.

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arXiv2026

Linking molecular timescales to linear viscoelastic response in dilute and semidilute unentangled wormlike micelle solutions

Unentangled wormlike micelle solutions relax stress through a dynamic interplay of reversible scission and intrachain relaxation involving a hierarchy of molecular timescales whose relationship to linear viscoelastic response remains incompletely resolved. A multiparticle mesoscopic Brownian dynamics framework has been developed in which persistent worms, represented by bead-spring chains with sticky ends, assemble to form wormlike micelles via reversible scission and fusion. Both linear and ring-like micelles are formed across the dilute and semidilute concentration regimes. Accurate predictions of dynamic properties are obtained through inclusion of hydrodynamic interactions using a RPY tensor. We identify and quantify characteristic timescales governing micellar dynamics, including bond lifetimes, self- and non-self-recombination times, breakage times of wormlike micelles of length $L$, relaxation times of various contributions to stress, and the longest relaxation time. The dependence of these timescales on sticker strength, concentration, micellar topology and hydrodynamic interactions is established. The presence of ring micelles is found to moderately prolong recombination and breakage processes, while hydrodynamic interactions are shown to affect some of the timescales by reducing sticker mobility. When appropriately scaled, the dependence on mean length of the non-self-recombination and micelle breakage times collapse onto master curves. Storage and loss moduli exhibit distinctive features in the intermediate-frequency regime that are absent in homopolymer solutions. A clear connection is made between micellar timescales and these signatures in the dynamic moduli at various characteristic frequencies, providing a direct link between microscopic dynamics and macroscopic rheology in unentangled wormlike micellar solutions, in dilute and semidilute concentration regimes.

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arXiv2025

Linear Viscoelasticity of Semiflexible Polymers with Hydrodynamic Interactions

The linear viscoelastic response of single semiflexible polymer chains in the infinite-dilution limit is studied using Brownian dynamics simulations of coarse-grained bead-spring chains. The springs obey the FENE-Fraenkel force law, a bending potential is used to capture chain stiffness and hydrodynamic interactions are included through the Rotne-Prager-Yamakawa tensor. By calculating the relaxation modulus following a step strain, we demonstrate that the bead-spring chain behaves like an inextensible semiflexible rod over a wide time window with an appropriate choice of spring stiffness and chain extensibility. In the absence of hydrodynamic interactions, our results agree with the existing theoretical predictions for the linear viscoelastic response of free-draining, inextensible, semiflexible rods in the limit of infinite dilution. It is shown that at intermediate times, the stress relaxation modulus exhibits power law behaviour, with the exponent ranging from $(-1/2)$ for flexible chains to $(-5/4)$ for highly rigid chains. At long times, rigid chains undergo orientational relaxation, while flexible chains exhibit Rouse relaxation. Hydrodynamic interactions are found to effect the behaviour at intermediate and long times, with the difference from free-draining behaviour increasing with increasing chain flexibility. Computations of the frequency dependence of loss and storage moduli are found to be in good agreement with experimental data for a wide variety of systems involving semiflexible polymers of varying stiffness across a broad frequency range.

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arXiv2025

Subdiffusion of sticky dendrimers in an associative polymer network

We investigate the static and dynamic properties of dendrimers diffusing through a network of linear associative polymers using coarse-grained Brownian dynamics simulations. Both dendrimers and network chains are modelled as bead-spring chain polymers, with hydrodynamic interactions incorporated for the accurate prediction of dynamic properties. Linear chains form a network via the associating groups distributed along their backbones, and the dendrimers interact attractively or repulsively with the network, enabling a direct comparison of sticky and non-sticky behaviour of dendrimers. Structural analysis reveals that while non-sticky dendrimers shrink with increasing network concentration, similar to linear polymer behaviour, sticky dendrimers exhibit stretching at low concentrations due to binding interactions. Dendrimer dynamics are largely insensitive to network architecture but are strongly influenced by the strength of dendrimer-network interactions. Increasing attraction to the network leads to subdiffusive motion and non-Gaussian displacement statistics, even when dendrimers are smaller than the average mesh size. The long-time diffusivity aligns with theoretical predictions for nanoparticle transport in polymer networks. Additionally, dendrimers deform the network locally, altering the mesh size distribution depending on their stickiness. These findings offer insight into the interplay between macromolecular architecture, binding interactions, and transport in polymeric environments.

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arXiv2025

A mesoscopic model for the rheology of dilute and semidilute solutions of wormlike micelles

The concept of a `persistent worm' is introduced, representing the smallest possible length of a wormlike micelle, and modelled by a bead-spring chain with sticky beads at the ends. Persistent worms are allowed to combine with each other at their sticky ends to form wormlike micelles with a distribution of lengths, and the semiflexibility of a wormlike micelle is captured with a bending potential between springs, both within and across persistent worms that stick to each other. Multi-particle Brownian dynamics simulations of such polydisperse and `polyflexible' wormlike micelles, with hydrodynamic interactions included and coupled with reversible scission/fusion of persistent worms, are used to investigate the static and dynamic properties of wormlike micellar solutions in the dilute and unentangled semidilute concentration regimes. The influence of the sticker energy and persistent worm concentration are examined and simulations are shown to validate theoretical mean-field predictions of the universal scaling with concentration of the chain length distribution of linear wormlike micelles, independent of the sticker energy. The presence of wormlike micelles that form rings is shown not to affect the static properties of linear wormlike micelles and mean-field predictions of ring length distributions are validated. Linear viscoelastic storage and loss moduli are computed and the unique features in the intermediate frequency regime compared to those of homopolymer solutions are highlighted. The inclusion of hydrodynamic interactions (HI) enables the distinction between Rouse and Zimm dynamics in wormlike micelle solutions to be elucidated. While the neglect of HI is justified in the case of entangled wormlike micelle solutions, here the concentration at which the onset of the screening of hydrodynamic interactions occurs is clearly identified.

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arXiv2024

Flow dichroism of DNA can be quantitatively predicted via coarse-grained molecular simulations

We demonstrate the use of multiscale polymer modelling to quantitatively predict DNA linear dichroism (LD) in shear flow. LD is the difference in absorption of light polarised along two perpendicular axes, and has long been applied to study biopolymer structure and drug-biopolymer interactions. As LD is orientation-dependent, the sample must be aligned in order to measure a signal. Shear flow via a Couette cell can generate the required orientation, however it is challenging to separate the LD due to changes in polymer conformation from specific interactions, e.g. drug-biopolymer. In this study, we have applied a combination of Brownian dynamics and equilibrium Monte Carlo simulations to accurately predict polymer alignment, and hence flow LD, at modest computational cost. As the optical and conformational contributions to the LD can be explicitly separated, our findings allow for enhanced quantitative interpretation of LD spectra through the use of an in-silico model to capture conformational changes. Our model requires no fitting and only five input parameters, the DNA contour length, persistence length, optical factor, solvent quality, and relaxation time, all of which have been well characterized in prior literature. The method is sufficiently general to apply to a wide range of biopolymers beyond DNA, and our findings could help guide the search for new pharmaceutical drug targets via flow LD.

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arXiv2024

Evanescent Gels: Competition Between Sticker Dynamics and Single Chain Relaxation

Solutions of polymer chains are modelled using non-equilibrium Brownian dynamics simulations, with physically associative beads which form reversible crosslinks to establish a system-spanning physical gel network. Rheological properties such as the zero-shear-rate viscosity and relaxation modulus are investigated systematically as functions of polymer concentration and the binding energy between associative sites. It is shown that a system-spanning network can form regardless of binding energy at sufficiently high concentration. However, the contribution to the stress sustained by this physical network can decay faster than other relaxation processes, even single chain relaxations. If the polymer relaxation time scales overlap with short-lived associations, the mechanical response of a gel becomes ``evanescent'', decaying before it can be rheologically observed, even though the network is instantaneously mechanically rigid. In our simulations, the concentration of elastically active chains and the dynamic modulii are computed independently. This makes it possible to combine structural and rheological information to identify the concentration at which the sol-gel transition occurs as a function of binding energy. Further, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines if the gel is in the evanescent regime.

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arXiv2024

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.

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arXiv2022

Dilute polymer solutions under shear flow: comprehensive qualitative analysis using a bead-spring chain model with a FENE-Fraenkel spring

Although the non-equilibrium behaviour of polymer solutions is generally well understood, particularly in extensional flow, there remain several unanswered questions for dilute solutions in simple shear flow, and full quantitative agreement with experiments has not been achieved. For example, experimental viscosity data exhibit qualitative differences in shear-thinning exponents, shear rate for onset of shear-thinning and high-shear Newtonian plateaus depending on polymer semiflexibility, contour length and solvent quality. While polymer models are able to incorporate all of these effects through various spring force laws, bending potentials, excluded volume (EV) potentials, and hydrodynamic interaction (HI), the inclusion of each piece of physics has not been systematically matched to experimentally observed behaviour. Furthermore, attempts to develop multiscale models (in the sense of representing an arbitrarily small or large polymer chain) which can make quantitative predictions are hindered by the lack of ability to fully match the results of bead-rod models, often used to represent a polymer chain at the Kuhn step level, with bead-spring models, which take into account the entropic elasticity.In light of these difficulties, this work aims to develop a general model based on the so-called FENE-Fraenkel spring, originally formulated by Larson and coworkers [J. Chem. Phys. 124 (2006), 10.1063/1.2161210], which can span the range from rigid rod to traditional entropic spring, as well as include a bending potential, EV and HI. As we show, this model can reproduce, and smoothly move between, a wide range of previously observed polymer solution rheology in shear flow.

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arXiv2022

Shear viscosity for finitely extensible chains with fluctuating internal friction and hydrodynamic interactions

An exact solution of coarse-grained polymer models with fluctuating internal friction and hydrodynamic interactions has not been proposed so far due to a one-to-all coupling between the connector vector velocities that precludes the formulation of the governing stochastic differential equations. A methodology for the removal of this coupling is presented, and the governing stochastic differential equations, obtained by attaching a kinetic interpretation to the Fokker-Planck equation for the system, are integrated numerically using Brownian dynamics simulations. The proposed computational route eliminates the calculation of the divergence of the diffusion tensor which appears in models with internal friction, and is about an order of magnitude faster than the recursion-based algorithm for the decoupling of connector-vector velocities previously developed [J. Rheol., 65, 903 (2021)] for the solution of freely draining models with internal friction. The effects of the interplay of various combinations of finite extensibility, internal friction and hydrodynamic interactions on the steady-shear-viscosity is examined. While finite extensibility leads solely to shear-thinning, both internal friction and hydrodynamic interactions result in shear-thinning followed by shear-thickening. The shear-thickening induced by internal friction effects are more pronounced than that due to hydrodynamic interactions.

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arXiv2022

Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains

Chromatin is known to be organized into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction strength parameters from experimentally known contact maps and use them to predict chromatin organization and dynamics. Taking two domains on the human chromosome as examples, we investigate its 3D organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Considering different cell types, we quantify changes in interaction strengths and chromatin shape fluctuations in different epigenetic states. Perturbing the interaction strengths systematically, we further investigate how epigenetic-like changes can alter the spatio-temporal nature of the domains. Our results show that heterogeneous weak interactions are crucial in determining the organization of the domains. Computing effective stiffness and relaxation times, we investigate how perturbations in interactions affect the solid-like and liquid-like nature of chromatin domains. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops.

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arXiv2022

Universality of dilute solutions of ring polymers in the thermal crossover region between $θ$ and athermal solvents

Due to their unique topology of having no chain ends, dilute solutions of ring polymers exhibit behaviour distinct from their linear chain counterparts. The universality of their static and dynamic properties, as a function of solvent quality $z$ in the thermal crossover regime between $θ$ and athermal solvents, is studied here using Brownian dynamics simulations. The universal ratio $U_{\text{RD}}$ of the radius of gyration $R_g$ to the hydrodynamic radius $R_H$ is determined, and a comparative study of the swelling ratio $α_g$ of the radius of gyration, the swelling ratio $α_H$ of the hydrodynamic radius, and the swelling ratio $α_X$ of the mean polymer stretch $X$ along the $x$-axis, for linear and ring polymers, is carried out. The ratio $U_{\text{RD}}$ for dilute ring polymer solutions is found to converge asymptotically to a constant value as $z \to \infty$, which is a major difference from the behaviour of solutions of linear chains, where no such asymptotic limit exists. Additionally, the ratio of the mean stretch along the $x$-axis to the hydrodynamic radius, $(X/R_H)$, is found to be independent of $z$ for polymeric rings, unlike in the case for linear polymers. These results indicate a fundamental difference in the scaling of static and dynamic properties of rings and linear chains in the thermal crossover regime.

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arXiv2021

Universal scaling and characterisation of gelation in associative polymer solutions

A Brownian dynamics algorithm is used to describe the static behaviour of associative polymer solutions. Predictions for the fractions of stickers bound by intra-chain and inter-chain association, as a function of system parameters, such as the number of stickers, the number of monomers between stickers, the solvent quality, and concentration are obtained. A systematic comparison with the scaling relations predicted by the mean-field theory of Dobrynin (Macromolecules, 37, 3881, 2004) is carried out. Different regimes of scaling behaviour are identified depending on the monomer concentration, the density of stickers on a chain, and the solvent quality for backbone monomers. Simulation results validate the predictions of the mean-field theory across a wide range of parameter values in all the scaling regimes. The value of the des Cloizeaux exponent proposed by Dobrynin for sticky polymer solutions, is shown to lead to a collapse of simulation data for all the scaling relations considered here. Three different signatures for the characterisation of gelation are identified, with each leading to a different value of the concentration at the sol-gel transition. The modified Flory-Stockmayer expression is found to be validated by simulations for all three gelation signatures. Simulation results confirm the prediction of scaling theory for the gelation line that separates sol and gel phases, when the modified Flory-Stockmayer expression is used. Phase separation is found to occur with increasing concentration for systems in which the backbone monomers are under theta-solvent conditions, and is shown to coincide with a breakdown in the predictions of scaling theory.

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arXiv2021

How important are fluctuations in the treatment of internal friction in polymers?

The Rouse model with internal friction (RIF), a widely used theoretical framework to interpret the effects of internal friction on conformational transitions in biomolecules, is shown to be an approximate treatment that is based on preaveraging internal friction. By comparison with Brownian dynamics simulations of an exact coarse-grained model that incorporates fluctuations in internal friction, the accuracy of the preaveraged model predictions is examined both at and away from equilibrium. While the two models predict intrachain autocorrelations that approach each other for long enough chain segments, they differ in their predictions for shorter segments. Furthermore, the two models differ qualitatively in their predictions for the chain extension and viscosity in shear flow, which is taken to represent a prototypical out-of-equilibrium condition.

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arXiv2021

Rouse model with fluctuating internal friction

A coarse-grained bead-spring-dashpot chain model with the dashpots representing the presence of internal friction, is solved exactly numerically, for the case of chains with more than two beads. Using a decoupling procedure to remove the explicit coupling of a bead's velocity with that of its nearest neighbors, the governing set of stochastic differential equations are solved with Brownian dynamics simulations to obtain material functions in oscillatory and steady simple shear flow. Simulation results for the real and imaginary components of the complex viscosity have been compared with the results of previously derived semi-analytical approximations, and the difference in the predictions are seen to diminish with an increase in the number of beads in the chain. The inclusion of internal friction results in a non-monotonous variation of the viscosity with shear rate, with the occurrence of continuous shear-thickening following an initial shear-thinning regime. The onset of shear-thickening in the first normal stress coefficient is pushed to lower shear rates with an increase in the internal friction parameter.

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arXiv2020

Viscometric Functions and Rheo-optical Properties of Dilute Polymer Solutions: Comparison of FENE-Fraenkel Dumbbells with Rodlike Models

Rigid macromolecules or polymer chains with persistence length on the order of the contour length (or greater) have traditionally been modelled as rods or very stiff springs. The FENE-Fraenkel-spring dumbbell, which is finitely extensible about a non-zero natural length with tunable harmonic stiffness, is one such model which has previously been shown to reproduce bead-rod behaviour in the absence of hydrodynamic interactions. The force law for the FENE-Fraenkel spring reduces to the Hookean or FENE spring force law for appropriately chosen values of the spring parameters. It is consequently possible to explore the crossover region between the limits of bead-spring and bead-rod behaviour by varying the parameters suitably. In this study, using a semi-implicit predictor-corrector Brownian dynamics algorithm, the FENE-Fraenkel spring is shown to imitate a rod with hydrodynamic interactions when spring stiffness, extensibility and simulation timestep are chosen carefully. By relaxing the spring stiffness and extensibility, the FENE-Fraenkel spring can also reproduce spring-like behaviour, such as a crossover from $-1/3$ to $-2/3$ power-law scaling in the viscosity with shear rate, and a change from positive to negative second normal stress difference. Furthermore, comparisons with experimental data on the viscosity and linear dichroism of high aspect ratio, rigid macromolecules shows that the extensibility and stiffness of the FENE-Fraenkel spring allows for equal or improved accuracy in modelling inflexible molecules compared to rodlike models.

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arXiv2020

Computing 3D chromatin configurations from contact probability maps by Inverse Brownian Dynamics

The three-dimensional organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state - accessibility and the amount of gene expression - of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In the present work, a novel Inverse Brownian Dynamics (IBD) method based on a coarse grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

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arXiv2020

Wet and dry internal friction can be measured with the Jarzynski equality

The existence of two types of internal friction wet and dry is revisited, and a simple protocol is proposed for distinguishing between the two types and extracting the appropriate internal friction coefficient. The scheme requires repeatedly stretching a polymer molecule, and measuring the average work dissipated in the process by applying the Jarzynski equality. The internal friction coefficient is then estimated from the average dissipated work in the extrapolated limit of zero solvent viscosity. The validity of the protocol is established through analytical calculations on a one-dimensional free-draining Hookean spring-dashpot model for a polymer, and Brownian dynamics simulations of: (a) a single-mode nonlinear spring-dashpot model for a polymer, and (b) a finitely extensible bead-spring chain with cohesive intra-chain interactions, both of which incorporate fluctuating hydrodynamic interactions. Well-established single-molecule manipulation techniques, such as optical tweezer-based pulling, can be used to implement the suggested protocol experimentally.

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