Complexation between oppositely charged polyelectrolytes: beyond the Random Phase Approximation

We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectrolyte mixture that includes both complexation and incompatibility.Comment: 18 pages, 4 figures. Submitted to EPJ-

Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia

Cells or bacteria carrying cilia on their surface show many striking features : alignment of cilia in an array, two-phase asymmetric beating for each cilium, coordination between cilia and existence of metachronal waves with a constant phase difference between two adjacent cilia. We give simple theoretical arguments based on hydrodynamic coupling and an internal mechanism of the cilium derived from the behavior of a collection of molecular motors, to account qualitatively for these cooperative features. Hydrodynamic interactions can lead to the alignment of an array of cilia. We study the effect of a transverse external flow and obtain a two-phase asymmetrical beating, faster along the flow and slower against the flow, proceeding around an average curved position. We show that an aligned array of cilia is able to spontaneously break the left-right symmetry and to create a global average flow. Metachronism arises as a local minimum of the beating threshold and leads to a rather constant flow

Solid like friction of a polymer chain

We propose a simple friction model for isolated polymer chains on a solid substrate. The chains are pulled at constant velocity by one end, the other end can be trapped on the solid substrate on localised sites. We focus on the energy dissipation due to the traps. This simple model leads to non trivial friction laws, depending on the velocity and the distance between traps. Some refinements of the model such as the effect of thermal fluctuation are also reported.Comment: 16 pages, 4 eps figures, accepted for publuication in Eur. Phys. J. E New version of 20/07/2000 minor modifications to figure

Phase separation and nucleation in mixtures of particles with different temperatures

Differences in activities in colloidal particles are sufficient to drive phase separation between active and passive (or less active) particles, even if they have only excluded volume interactions. In this paper, we study the phase separation kinetics and propose a theory of phase separation of colloidal mixtures in the diffusive limit. Our model considers a mixture of diffusing particles coupled to different thermostats, it thus has a non-equilibrium nature due to the temperature differences. However, we show that indeed the system recovers an effective equilibrium thermodynamics in the dilute limit. We obtain phase diagrams showing the asymmetry in concentrations due to activity differences. By using a more general approach, we show the equivalence of phase separation kinetics with the well known Cahn-Hilliard theory. On the other hand, higher order expansions in concentration indicate the emergence of non-equilibrium effects leading to a breakdown of the equilibrium analogy. We lay out the general theory in terms of accessible parameters which we demonstrate by several applications. In this simple formalism, we capture a positive surface tension for hard spheres}, and interesting scaling laws for interfacial properties, droplet growth dynamics, and phase segregation conditions. \rev{Several of our results are in agreement with existing numerical simulations while we also propose testable predictions.Comment: Published version, 19 pages (main text+appendix), 4 figure

Bistability, oscillations and bidirectional motion of ensemble of hydrodynamically-coupled molecular motors

We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motors displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean--field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynamic coupling as well as on system size. We quantify the phase diagram for the different phases that characterize the collective motion of hydrodynamically coupled motors and show that sustained oscillations can be reached for biologically relevant parameters, hence demonstrating the relevance of hydrodynamic interactions in intracellular transport

Charge Distribution on Annealed Polyelectrolytes

We investigate the equilibrium charge distribution along a single annealed polyelectrolyte chain under different conditions. The coupling between the conformation of the chain and the local charge distribution is described for various solvent qualities and salt concentration. In salt free solution, we find a slight charge depletion in the central part of the chain: the charges accumulate at the ends. The effect is less important if salt is added to the solution since the charge inhomogeneity is localized close to the chain ends over a distance of order of the Debye length. In the case of poor solvent conditions we find a different charging of beads and strings in the framework of the necklace model. This inhomogeneity leads to a charge instability and a first order transition between spherical globules and elongated chains.Comment: 20 pages, 4 figure

Motion of an Adhesive Gel in a Swelling Gradient: a Mechanism for Cell Locomotion

Motivated by the motion of nematode sperm cells, we present a model for the motion of an adhesive gel on a solid substrate. The gel polymerizes at the leading edge and depolymerizes at the rear. The motion results from a competition between a self-generated swelling gradient and the adhesion on the substrate. The resulting stress provokes the rupture of the adhesion points and allows for the motion. The model predicts an unusual force-velocity relation which depends in significant ways on the point of application of the force.Comment: 4 pages, 1 figur

Compression of finite size polymer brushes

We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $\xi\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a disk), the lateral extension $u_S$ of the border chains follows the scaling law $u_S = \xi \phi (S/\xi)$. The scaling function $\phi (x)$ is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small $x$, $\phi (x)$ decays as a power law in agreement with simple arguments. The effective line tension and the variation with compression height of the force applied on the brush are also calculated.Comment: 6 pages, 7 figures, submitted to PCC