arXiv subjects

J. Ravi Prakash

Publications and source records attributed to J. Ravi Prakash.

46 records · Page 3Linked to original sources

arXiv2010

Collapse dynamics of copolymers in a poor solvent: Influence of hydrodynamic interactions and chain sequence

We investigate the dynamics of the collapse of a single copolymer chain, when the solvent quality is suddenly quenched from good to poor. We employ Brownian dynamics simulations of a bead-spring chain model and incorporate fluctuating hydrodynamic interactions via the Rotne-Prager-Yamakawa tensor. Various copolymer architectures are studied within the framework of a two-letter HP model, where monomers of type H (hydrophobic) attract each other, while all interactions involving P (polar or hydrophilic) monomers are purely repulsive. The hydrodynamic interactions are found to assist the collapse. Furthermore, the chain sequence has a strong influence on the kinetics and on the compactness and energy of the final state. The dynamics is typically characterised by initial rapid cluster formation, followed by coalescence and final rearrangement to form the compact globule. The coalescence stage takes most of the collapse time, and its duration is particularly sensitive to the details of the architecture. Long blocks of type P are identified as the main bottlenecks to find the globular state rapidly.

cond-mat.soft↗

arXiv2009

Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics

We present a comparative study of two computer simulation methods to obtain static and dynamic properties of dilute polymer solutions. The first approach is a recently established hybrid algorithm based upon dissipative coupling between Molecular Dynamics and lattice Boltzmann (LB), while the second is standard Brownian Dynamics (BD) with fluctuating hydrodynamic interactions. Applying these methods to the same physical system (a single polymer chain in a good solvent in thermal equilibrium) allows us to draw a detailed and quantitative comparison in terms of both accuracy and efficiency. It is found that the static conformations of the LB model are distorted when the box length L is too small compared to the chain size. Furthermore, some dynamic properties of the LB model are subject to an $L^{-1}$ finite size effect, while the BD model directly reproduces the asymptotic $L \to \infty$ behavior. Apart from these finite size effects, it is also found that in order to obtain the correct dynamic properties for the LB simulations, it is crucial to properly thermalize all the kinetic modes. Only in this case, the results are in excellent agreement with each other, as expected. Moreover, Brownian Dynamics is found to be much more efficient than lattice Boltzmann as long as the degree of polymerization is not excessively large.

cond-mat.soft↗

arXiv2007

Coil-Stretch Transition and the Break Down of Continuum Models

The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules traveling along the centerline in the wake of the cylinder. With increasing Wi, the coil-stretch transition leads to an unbounded growth in the stress maximum in the cylinder wake. Finite element computations for a FENE-P fluid reveal that, although polymer molecules undergo a coil-stretch transition in the cylinder wake, the mean extension of the molecules saturates to a value close to the fully extended length, leading to bounded stresses with increasing Wi. The existence of a coil-stretch transition has been deduced by examining the behavior of ultra-dilute Oldroyd-B and FENE-P fluids. In this case, the solution along the centerline in the cylinder wake can be obtained exactly since the velocity field is uncoupled from the stress and conformation tensor fields. Estimation of the number of finite elements required to achieve convergence reveals the in-feasibility of obtaining solutions for the Oldroyd-B model for Wi > 1.

cond-mat.soft↗

arXiv2006

Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This "FENE-PG" force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely-extensible bead-spring chains with hydrodynamic interactions. The closed set of ODE's governing the evolution of the second-moments of the configurational probability distribution in the approximate models are used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynamics simulations. In particular, predictions of coil-stretch hysteresis are in quantitative agreement with simulations' results. Additional simplifying diagonalization-of-normal-modes assumptions are found to lead to considerable savings in computation time, without significant loss in accuracy.

cond-mat.soft↗

arXiv2005

The origin of dynamic scaling in dilute polymer solutions

The hydrodynamic radius of a polymer chain, obtained using Brownian dynamics simulations of the continuum Edwards model, is found to obey a crossover in the excluded volume parameter z, which is significantly different from that observed for the radius of gyration. It is shown that this difference arises from contributions due to dynamic correlations to the diffusivity, which are ignored in the commonly used definition of hydrodynamic radius based on the Kirkwood expression. The swelling of the hydrodynamic radius from the theta-state, obtained from simulations, shows remarkable agreement with experimental measurements.

cond-mat.soft↗

arXiv2004

Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow

The role of solvent quality in determining the universal material properties of dilute polymer solutions undergoing steady simple shear flow is examined. A bead-spring chain representation of the polymer molecule is used, and the influence of solvent molecules on polymer conformations is modelled by a narrow Gaussian excluded volume potential that acts pair-wise between the beads of the chain. Brownian dynamics simulations data, acquired for chains of finite length, and extrapolated to the limit of infinite chain length, are shown to be model independent. This feature of the narrow Gaussian potential, which leads to results identical to a $δ$-function repulsive potential, enables the prediction of both universal crossover scaling functions and asymptotic behavior in the excluded volume limit. Universal viscometric functions, obtained by this procedure, are found to exhibit increased shear thinning with increasing solvent quality. In the excluded volume limit, they are found to obey power law scaling with the characteristic shear rate $β$, in close agreement with previously obtained renormalization group results. The presence of excluded volume interactions is also shown to lead to a weakening of the alignment of the polymer chain with the flow direction.

cond-mat.soft↗

arXiv2003

Equilibrium swelling and universal ratios in dilute polymer solutions: Exact Brownian dynamics simulations for a delta function excluded volume potential

A narrow Gaussian excluded volume potential, which tends to a delta-function repulsive potential in the limit of a width parameter d* going to zero, has been used to examine the universal consequences of excluded volume interactions on the equilibrium and linear viscoelastic properties of dilute polymer solutions. Brownian dynamics simulations data, acquired for chains of finite length, has been extrapolated to the limit of infinite chain length to obtain model independent predictions. The success of the method in predicting well known aspects of static solution properties suggests that it can be used as a systematic means by which the influence of solvent quality on both equilibrium and non-equilibrium properties can be studied.

cond-mat.soft↗

arXiv1999

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected.

cond-mat.soft↗

arXiv1998

Viscometric Functions for a Dilute Solution of Polymers in a Good Solvent

A dilute polymer solution is modeled as a suspension of non-interacting Hookean dumbbells and the effect of excluded volume is taken into account by incorporating a narrow Gaussian repulsive potential between the beads of each dumbbell. The narrow Gaussian potential is a means of regularising a delta-function potential---it tends to the delta-function potential in the limit of the width parameter going to zero. Exact predictions of viscometric functions in simple shear flow are obtained with the help of a retarded motion expansion and by Brownian dynamics simulations. It is shown that for relatively small non-zero values of the width parameter, the presence of excluded volume causes a swelling of the dumbbell at equilibrium, and shear thinning in simple shear flow. On the other hand, a delta function excluded volume potential does not lead to either swelling or to shear thinning. Approximate viscometric functions, obtained by assuming that the bead-connector vector is described by a Gaussian non-equilibrium distribution function, are found to be accurate above a threshold value of the width parameter, for a given value of the strength of excluded volume interaction. A first order perturbation expansion reveals that the Gaussian approximation is exact to first order in the strength of excluded volume interaction. The predictions of an alternative quadratic excluded volume potential suggested earlier by Fixman (J. Chem. Phys., 1966, 45, 785; 793) are also compared with those of the narrow Gaussian potential.

cond-mat.stat-mech↗

arXiv1998

The Kinetic Theory of Dilute Solutions of Flexible Polymers: Hydrodynamic Interaction

The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer solutions, is discussed. In particular, recent advances in the treatment of hydrodynamic interaction are reviewed, and the successive refinements which have ultimately led to the prediction of universal viscometric functions in theta solvents are highlighted.

cond-mat.stat-mech↗