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.Comment: 27 pages, 17 figure

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.Comment: 12 pages inclusive of 10 PostScript (*.eps) figures, uses svjour, psfrag and graphicx. Submitted for publication to Euro. Phys. J.

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.Comment: 25 pages, 13 figures, Submitted to Macromolecule

Optimisation of a Brownian dynamics algorithm for semidilute polymer solutions

Simulating the static and dynamic properties of semidilute polymer solutions with Brownian dynamics (BD) requires the computation of a large system of polymer chains coupled to one another through excluded-volume and hydrodynamic interactions. In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique. By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we develop a BD algorithm in which the computational cost scales as O(N^{1.8}), where N is the number of monomers in the simulation box. We show that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that \theta-solutions can be simulated by switching off excluded-volume interactions. A comparison of the predictions of the radius of gyration, the end-to-end vector, and the self-diffusion coefficient by BD, at a range of concentrations, with the hybrid Lattice Boltzmann/Molecular Dynamics (LB/MD) method shows excellent agreement between the two methods. In contrast to the situation for dilute solutions, the LB/MD method is shown to be significantly more computationally efficient than the current implementation of BD for simulating semidilute solutions. We argue however that further optimisations should be possible.Comment: 17 pages, 8 figures, revised version to appear in Physical Review E (2012