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We study creep flow and yielding of particulate depletion gels under constant shear stress, combining data on different length and time scales. We characterise the breakage of meso-scale strands in the gel. Breakage events are distributed homogeneously in space, corresponding to macroscopically ductile flow. At the microscale, a spatio-temporal analysis of structural and mechanical metrics connects properties of strands before and after they fail, indicating that strand breakage is statistically predictable. Using results from different scales, we discuss the interplay between creeping and aging dynamics, and we demonstrate a viscosity bifurcation., Comment: 13 pages

We study an intriguing new type of self-assembled active colloidal polymer system in 3D. It is obtained from a suspension of Janus particles in an electric field that induces parallel dipoles in the particles as well as self-propulsion in the plane perpendicular to the field. At low packing fractions, in experiment, the particles self-assemble into 3D columns that are self-propelled in 2D. Explicit numerical simulations combining dipolar interactions and active self-propulsion find an activity dependent transition to a string phase by increasing dipole strength. We classify the collective dynamics of strings as a function of rotational and translational diffusion. Using an anisotropic version of the Rouse model of polymers with active driving, we analytically compute the strings' collective dynamics and centre of mass motion, which matches simulations and is consistent with experimental data. We also discover long range correlations of the fluctuations along the string contour that grow with the active persistence time, a purely active effect that disappears in the thermal limit., Comment: 6 pages, 4 figures

Active solids emerge from self-actuating components interacting with each other to form crystalline patterns. In equilibrium, commensurability underpins our understanding of nanoscale friction and particle-level dynamics of crystals. However, these concepts have yet to be imported into the realm of active matter. Here, we develop an experimental platform and a theoretical description for microscopic clusters composed of active particles confined and self-assembled into small crystals. In our experiments, these crystallites form upon circular confinement of active rollers, with a magic number of 61 rollers per well. Competition between solidity and self propulsion leads to self shearing and complex flow inversion behaviour, along with self sliding states and activity induced melting. We discover active stick slip dynamics, which periodically switch between a commensurate static state and an incommensurate self-sliding state characterised by a train of localised defects. We describe the steady state behaviour using a discretised model of active hydrodynamics. We then quantify the intermittent stick slip dynamics using a self-propelled extension of the Frenkel Kontorova (FK) model, a fundamental workhorse of slipping and flow in crystals. Our findings in a colloidal model system point to a wealth of phenomena in incommensurate active solids as design principles for both assembly and robotics down to the nanoscale.

We consider a suspension of non-interacting flat elastic particles in a Newtonian fluid. We model a flat shape as three beads, carried along by the flow according to Stokes' law, and connected by nonlinear springs, chosen such that the energy is quadratic in the area. In analogy with common dumbbell models involving two beads connected by linear springs, we solve the stochastic equations of motion exactly to compute the constitutive law for the stress tensor of a flat elastic particle suspension. A lower convected time derivative naturally arises as part of the constitutive law, but surprisingly the rheological response in strong extensional and strong contracting flows is similar to that of the classical Oldroyd-B model associated with dumbbell suspensions., Comment: 8 pages, 1 figure

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechano-chemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behaviour emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit., Comment: 5 pages, 4 figures

We consider a confined sheared active polar liquid crystal with a uniform orientation and study the effect of variations in the magnitude of polarization. Restricting our analysis to one-dimensional geometries, we demonstrate that with asymmetric boundary conditions, this system is characterized, macroscopically, by a linear shear stress vs. shear strain relationship that does not pass through the origin: At a zero strain rate, the fluid sustains a non-zero stress. Analytic solutions for the polarization, density, and velocity fields are derived for asymptotically large or small systems and are shown by comparison with precise numerical solutions to be good approximations for finite-size systems.

We characterise the steady states of a suspension of two-dimensional active brownian particles (ABPs). We calculate the steady-state probability distribution to lowest order in Peclet number. We show that macroscopic quantities can be calculated in analogous way to equilibrium systems using this probability distribution. We then derive expressions for the macroscopic pressure and position-orientation correlation functions. We check our results by direct comparison with extensive numerical simulations. A key finding is the importance of many-body effective interactions even at very low densities., Comment: Updated to fix typo in author last name. 5 pages, 2 figures

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two different self-propulsion mechanisms, active stresses and treadmilling polymerisation, and we investigate how the active drop motion is altered by these surface forces. We find a highly non-linear response to forces that we characterise using drop velocity, drop shape, and the traction between the drop and the substrate. Each self-propulsion mechanism gives rise to two main modes of motion: a long thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. In each case there is a sharp transition between parabolic, and long thin drops as a function of the applied forces and indications of drop break-up where large forces stretch the drop., Comment: 9 pages, 6 figures

We explore crystallisation and polymorph selection in active Brownian particles with numerical simulation. In agreement with previous work [Wysocki $\textit{et al.}$ $\textit{Europhys. Lett.}$, $\textbf{105}$ 48004 (2014)], we find that crystallisation is suppressed by activity and occurs at higher densities with increasing $P\'{e}clet$ number ($Pe$). While the nucleation rate decreases with increasing activity, the crystal growth rate increases due to the accelerated dynamics in the melt. As a result of this competition we observe the transition from a nucleation and growth regime at high $Pe$ to "spinodal nucleation" at low $Pe$. Unlike the case of passive hard spheres, where preference for FCC over HCP polymorphs is weak, activity causes the annealing of HCP stacking faults, thus strongly favouring the FCC symmetry at high $Pe$. When freezing occurs more slowly, in the nucleation and growth regime, this tendency is much reduced and we see a trend towards the passive case of little preference for either polymorph., Comment: 9 pages, 6 figures

Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless motion, (ii) the self-propulsion of active components at the substrate, which gives rise to crawling motion, and (iii) a net capillary force, possibly self-generated, and coupled to internal activity. We determine travelling-wave solutions to the lubrication equations as a function of a dimensionless activity parameter for each mode of motion. Numerical simulations are used to characterize the drop motion over a wide range of activity magnitudes, and explicit analytical solutions in excellent agreement with the simulations are derived in the weak-activity regime., Comment: to appear in Soft Matter (2020)

We report on a new mode of self-propulsion exhibited by compact drops of active liquids on a substrate which, remarkably, is tractionless, i.e., which imparts no mechanical stress locally on the surface. We show, both analytically and by numerical simulation, that the equations of motion for an active nematic drop possess a simple self-propelling solution, with no traction on the solid surface and in which the direction of motion is controlled by the winding of the nematic director field across the drop height. The physics underlying this mode of motion has the same origins as that giving rise to the zero viscosity observed in bacterial suspensions. This topologically protected tractionless self-propusion provides a robust physical mechanism for efficient cell migration in crowded environments like tissues.

Swimmers and self-propelled particles are physical models for the collective behaviour and motility of a wide variety of living systems, such as bacteria colonies, bird flocks and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behaviour. Here we study colloids in a DC electric field. Our quasi-two-dimensional system of electrically-driven particles exhibits a rich and exotic phase behaviour. At low field strengths, electrohydrodynamic flows lead to self-organisation into crystallites with hexagonal order. Upon self-propulsion of the particles due to Quincke rotation, we find an ordered phase of active matter in which the motile crystallites constantly change shape and collide with one another. At higher field strengths, this "dissolves" to an active gas. We parameterise a particulate simulation model which reproduces the experimentally observed phases and, at higher field strengths predicts an activity-driven demixing to band-like structures.

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe such systems. In these, the generalisation of a steady state is associated with a stationary probability density of micro-states and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of non-stationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples., Comment: 12+ pages, 2 figures

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar ordered phase appears because near-field lubrication rather than long-range hydrodnamics dominate the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions., Comment: 24 pages, 13 figures, European Physical Journal E (2018)

We consider the yielding under simple shear of a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. We recast this glassformer as an effective system of icosahedra [Pinney et al. J. Chem. Phys. 143 244507 (2015)]. Looking at the small-strain region of sheared simulations, we observe that shear rates affect the shear localisation behavior particularly at temperatures below the glass transition as defined with a fit to the Vogel-Fulcher-Tamman equation. At higher temperature, shear localisation starts immediately upon shearing for all shear rates. At lower temperatures, faster shear rates can result in a delayed start in shear localisation; which begins close to the yield stress. Building from a previous work which considered steady-state shear [Pinney et al. J. Chem. Phys. 143 244507 (2016)], we interpret the response to shear and the shear localisation in terms of a \emph{local} effective temperature with our system of icosahedra. We find that the effective temperatures of the regions undergoing shear localisation increase significantly with increasing strain (before reaching a steady state plateau)., Comment: 13 pages, accepted in Phys. Rev. E

We point out unconventional mechanical properties of confined active fluids, such as bacterial suspensions, under shear. Using a minimal model of an active liquid crystal with no free parameters, we predict the existence of a window of bacteria concentration for which a suspension of \textit{E.~Coli} effectively behaves, at steady-state, as a negative viscosity fluid and reach quantitative agreement with experimental measurements. Our theoretical analysis further shows that a negative apparent viscosity is due to a non-monotonic local velocity profile, and is associated with a non-monotonic stress vs. strain rate flow curve. This implies that fixed stress and fixed strain rate ensembles are not equivalent for active fluids., Comment: 5 pages, 4 figures

We theoretically study the self-propulsion of a thin (slender) colloid driven by asymmetric chemical reactions on its surface at vanishing Reynolds number. Using the method of matched asymptotic expansions, we obtain the colloid self-propulsion velocity as a function of its shape and surface physico-chemical properties. The mechanics of self-phoresis for rod-like swimmers has a richer spectrum of behaviours than spherical swimmers due to the presence of two small length scales, the slenderness of the rod and the width of the slip layer. This leads to subtleties in taking the limit of vanishing slenderness. As a result, even for very thin rods, the distribution of curvature along the surface of the swimmer, namely its shape, plays a surprising role in determining the efficiency of propulsion. We find that thin cylindrical self-phoretic swimmers with blunt ends move faster than thin prolate spheroid shaped swimmers with the same aspect ratio.

We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair, or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral cage. In turn, this has inspired synthetic biologists to design de novo protein cages. We use simple models, on multiple scales, to investigate the self-assembly of a spherical cage, focusing on the regularity of the packing of protein-like objects on the surface. Using building blocks, which are able to pack with icosahedral symmetry, we examine how stable these highly symmetric structures are to perturbations that may arise from the interplay between flexibility of the interacting blocks and entropic effects. We find that, in the presence of those perturbations, icosahedral packing is not the most stable arrangement for a wide range of parameters; rather disordered structures are found to be the most stable. Our results suggest that (i) many designed, or even natural, protein cages may not be regular in the presence of those perturbations, and (ii) that optimizing those flexibilities can be a possible design strategy to obtain regular synthetic cages with full control over their surface properties., Comment: 8 pages, 5 figures

We study the role of hydrodynamic interactions in the collective behaviour of collections of microscopic active particles suspended in a fluid. We introduce a novel calculational framework that allows us to separate the different contributions to their collective dynamics from hydrodynamic interactions on different length scales. Hence we are able to systematically show that lubrication forces when the particles are very close to each other play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that motility-induced phase separation is suppressed by near-field interactions, leading to open gel-like clusters rather than dense clusters. Interestingly, we find a globally polar ordered phase appears for neutral swimmers with no force dipole that is enhanced by near field lubrication forces in which the collision process rather than long-range interaction dominates the alignment mechanism., Comment: 7 pages, 4 figures

We present a detailed theoretical study which demonstrates that electrokinetic effects can also play a role in the motion of metallic-insulator spherical Janus particles. Essential to our analysis is the identification of the fact that the reaction rates depend on Pt- coating thickness and that the thickness of coating varies from pole to equator of the coated hemisphere. We find that their motion is due to a combination of neutral and ionic diffusiophoretic as well as electrophoretic effects whose interplay can be changed by varying the ionic properties of the fluid. This has great potential significance for optimising performance of designed synthetic swimmers.

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of particles organized into icosahedra under simple steady state shear. We recast this glassformer as an effective system of icosahedra [Pinney et al. J. Chem. Phys. 143 244507 (2015)]. From the observed population of icosahedra in each steady state, we obtain an effective temperature which is linearly dependent on the shear rate in the range considered. Upon shear banding, the system separates into a region of high shear rate and a region of low shear rate. The effective temperatures obtained in each case show that the low shear regions correspond to a significantly lower temperature than the high shear regions. Taking a weighted average of the effective temperature of these regions (weight determined by region size) yields an estimate of the effective temperature which compares well with an effective temperature based on the global mesocluster population of the whole system., Comment: accepted by J. Chehm. Phys

We study the effect of a nearby planar wall on the propulsion of a spherical phoretic micro-swimmer driven by reactions on its surface. An asymmetric coverage of catalysts on its surface which absorb reactants and generate products gives rise to an anisotropic interfacial flow that propels the swimmer. We analyse the near-wall dynamics of such a self-phoretic swimmer as a function of the asymmetric catalytic coverage of the surface. By an analysis of the fundamental singularities of the flow and concentration or electrostatic potential gradients generated we are able to obtain and rationalise a phase diagram of behaviours as a function of the characteristics of the swimmer surface. We find a variety of possible behaviours, from "bound states" where the swimmer remains near the wall to "scattering" or repulsive trajectories in which the swimmer ends far from the wall. The formation of some of the bound states is a purely wall-phoretic effect and cannot be obtained by simply mapping a phoretic swimmer to a hydrodynamic one.

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. Upon cooling these icosahedra organize into mesoclusters. We recast this glassformer as an effective system of icosahedra which we describe with a population dynamics model. This model we parameterize with data from the temperature regime accessible to molecular dynamics simulations. We then use the model to determine the population of icosahedra in mesoclusters at arbitrary temperature. Using simulation data to incorporate dynamics into the model we predict relaxation behavior at temperatures inaccessible to conventional approaches. Our model predicts super-Arrhenius dynamics whose relaxation time remains finite for non-zero temperature., Comment: 10 pages, 9 figures

We study the effect of a nearby planar wall on the propulsion of a phoretic Janus micro-swimmer driven by asymmetric reactions on its surface which absorb reactants and generate products. We show that the behaviour of these swimmers near a wall can be classified ${\bf based \ on \ whether}$ the swimmers are ${\bf mainly}$ absorbing or producing reaction solutes ${\bf and \ whether}$ their swimming directions are such that the inert or active face is at the front. We find that the wall-induced solute gradients always promote swimmer propulsion along the wall while the effect of hydrodynamics leads to re-orientation of the swimming direction away from the wall., Comment: 6 pages, 6 figures

We present a microscopic model of a disordered viscoelastic active solid, i.e. an active material whose long time behaviour is elastic as opposed to viscous. It is composed of filaments, passive crosslinks and molecular motors powered by stored chemical energy, e.g. actomyosin powered by ATP. Our model allows us to study the collective behaviour of contractile active elements and how their interaction with each other and the passive elastic elements determines the macroscopic mechanical properties of the active material. As a result of the (un)binding dynamics of the active elements, we find that this system provides a highly responsive material with a dynamic mechanical response strongly dependent on the amount of deformation., Comment: 5 pages, 2 figures, Published 7 July 2014

We simulate with hydrodynamics a suspension of active disks squirming through a Newtonian fluid. We explore numerically the full range of squirmer area fractions from dilute to close packed and show that "motility induced phase separation" (MIPS), which was recently proposed to arise generically in active matter, and which has been seen in simulations of active Brownian disks, is strongly suppressed by hydrodynamic interactions. We give an argument for why this should be the case and support it with counterpart simulations of active Brownian disks in a parameter regime that provides a closer counterpart to hydrodynamic suspensions than in previous studies., Comment: 10 pages, 7 figures; submitted for publication

We study analytically and numerically a generic continuum model of an isotropic active solid with internal stresses generated by non-equilibrium `active' mechano-chemical reactions. Our analysis shows that the gel can be tuned through three classes of dynamical states by increasing motor activity: a constant unstrained state of homogeneous density, a state where the local density exhibits sustained oscillations, and a steady-state which is spontaneously contracted, with a uniform mean density., Comment: 6 pages, 4 figures, EPL format

We analyze the behavior of a suspension of active polar particles under shear. In the absence of external forces, orientationally ordered active particles are known to exhibit a transition to a state of non-uniform polarization and spontaneous flow. Such a transition results from the interplay between elastic stresses, due to the liquid crystallinity of the suspension, and internal active stresses. In the presence of an external shear we find an extremely rich variety of phenomena, including an effective reduction (increase) in the apparent viscosity depending on the nature of the active stresses and the flow-alignment property of the particles, as well as more exotic behaviors such as a non-monotonic stress/strain-rate relation and yield stress for large activities., Comment: 10 pages, 10 figures

We study the dynamical properties of active polar liquid crystalline films. Like active nematic films, active polar films undergo a dynamical transitions to spontaneously flowing steady-states. Spontaneous flow in polar fluids is, however, always accompanied by strong concentration inhomogeneities or "banding" not seen in nematics. In addition, a spectacular property unique to polar active films is their ability to generate spontaneously oscillating and banded flows even at low activity. The oscillatory flows become increasingly complicated for strong polarity., Comment: 4 pages, 3 figures

The cytoskeleton provides eukaryotic cells with mechanical support and helps them perform their biological functions. It is a network of semiflexible polar protein filaments and many accessory proteins that bind to these filaments, regulate their assembly, link them to organelles and continuously remodel the network. Here we review recent theoretical work that aims to describe the cytoskeleton as a polar continuum driven out of equilibrium by internal chemical reactions. This work uses methods from soft condensed matter physics and has led to the formulation of a general framework for the description of the structure and rheology of active suspension of polar filaments and molecular motors., Comment: 30 pages, 5 figures. To appear in "Cell Motility", Peter Lenz, ed. (Springer, New York, 2007)

A simple model for the reaction-driven propulsion of a small device is proposed as a model for (part of) a molecular machine in aqueous media. Motion of the device is driven by an asymmetric distribution of reaction products. The propulsive velocity of the device is calculated as well as the scale of the velocity fluctuations. The effects of hydrodynamic flow as well as a number of different scenarios for the kinetics of the reaction are addressed.

Using a simple model, we study the fluctuating dynamics of inextensible, semiflexible polar filaments interacting with active and directed force generating centres such as molecular motors. Taking into account the fact that the activity occurs on time-scales comparable to the filament relaxation time, we obtain some unexpected differences between both the steady-state and dynamical behaviour of active as compared to passive filaments. For the statics, the filaments have a {novel} length-scale dependent rigidity. Dynamically, we find strongly enhanced anomalous diffusion., Comment: 5 pages, 3 figures

We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and entanglement. At low filament density the system develops a density instability, while at high filament density entanglement effects drive the instability of orientational fluctuations., Comment: 4pages, 2 eps figure, revtex4

The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length. It is also found that the onset of conformational instability is a re-entrant phenomenon as a function of polyelectrolyte length for the unscreened case, and the Debye length or salt concentration for the screened case. This may be relevant in understanding the experimentally observed re-entrant condensation of DNA., Comment: 8 pages, 4 figures

We introduce a simple geometric model for a double-stranded and double-helical polymer. We study the statistical mechanics of such polymers using both analytical techniques and simulation. Our model has a single energy-scale which determines both the bending and twisting rigidity of the polymer. The helix melts at a particular temperature T_c below which the chain has a helical structure and above which this structure is disordered. Under extension we find that for small forces, the behaviour is very similar to worm-like chain behaviour but becomes very different at higher forces., Comment: 4 pages, 6 figures

The statistical mechanics of a ribbon polymer made up of two semiflexible chains is studied using both analytical techniques and simulation. The system is found to have a crossover transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. The crossover happens when the persistence length of individual strands becomes comparable to the thickness of the ribbon. In the low temperature regime, the ribbon is observed to have a novel ``kink-rod'' structure with a mutual exclusion of twist and bend in contrast to smooth worm-like chain behaviour. This is due to its anisotropic rigidity and corresponds to an {\it infinitely} strong twist-bend coupling. The double-stranded polymer is also studied in a confined geometry. It is shown that when the polymer is restricted in a particular direction to a size less than the bare persistence length of the individual strands, it develops zigzag conformations which are indicated by an oscillatory tangent-tangent correlation function in the direction of confinement. Increasing the separation of the confining plates leads to a crossover to the free behaviour, which takes place at separations close to the bare persistence length. These results are expected to be relevant for experiments which involve complexation of two or more stiff or semiflexible polymers., Comment: 20 pages, 11 figures. PRE (in press)

The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length., Comment: 4 pages RevTex, 3 ps figures included using epsf, final version as appeared in PRL