Computational confirmation of scaling predictions for equilibrium polymers

We report the results of extensive Dynamic Monte Carlo simulations of systems of self-assembled Equilibrium Polymers without rings in good solvent. Confirming recent theoretical predictions, the mean-chain length is found to scale as \Lav = \Lstar (\phi/\phistar)^\alpha \propto \phi^\alpha \exp(\delta E) with exponents $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = [1+(\gamma-1)/(\nu d -1)]/2 \approx 0.60, \delta_s=1/2$ in the dilute and semi-dilute limits respectively. The average size of the micelles, as measured by the end-to-end distance and the radius of gyration, follows a very similar crossover scaling to that of conventional quenched polymer chains. In the semi-dilute regime, the chain size distribution is found to be exponential, crossing over to a Schultz-Zimm type distribution in the dilute limit. The very large size of our simulations (which involve mean chain lengths up to 5000, even at high polymer densities) allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma = 1.165 \pm 0.01$.Comment: 6 pages, 4 figures, LATE

Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed $v$ that is an explicit function or functional of the density $\rho$. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.Comment: 32 pages, 6 figure

Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature

We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of these arises because the supersaturation is greatest far from the meniscus, creating inversion of the density which can lead to fluid motion; although isothermal, this is somewhat like the Benard problem (a single-phase fluid heated from below). The other is the intrinsic diffusive instability which results either in nucleation or in spinodal decomposition at large supersaturations. Experimental results on a simple binary mixture show interesting oscillations in heat capacity and optical properties for a wide range of ramp parameters. We argue that these oscillations arise under conditions where both nonlinearities are important

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form

Phase ordering of two-dimensional symmetric binary fluids: a droplet scaling state

The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains itself, throughout the viscous hydrodynamic regime, by a `coalescence-induced coalescence' mechanism. Scaling is recovered (with length scale $l \sim t$, as in $d=3$). The crossover to the inertial hydrodynamic regime is delayed even longer than in $d=3$; on entering it, full symmetry is finally restored and we find $l\sim t^{2/3}$, regardless of the initial state.Comment: 4 pages, three figures include

Dynamical Monte Carlo Study of Equilibrium Polymers : Static Properties

We report results of extensive Dynamical Monte Carlo investigations on self-assembled Equilibrium Polymers (EP) without loops in good solvent. (This is thought to provide a good model of giant surfactant micelles.) Using a novel algorithm we are able to describe efficiently both static and dynamic properties of systems in which the mean chain length \Lav is effectively comparable to that of laboratory experiments (up to 5000 monomers, even at high polymer densities). We sample up to scission energies of $E/k_BT=15$ over nearly three orders of magnitude in monomer density $\phi$, and present a detailed crossover study ranging from swollen EP chains in the dilute regime up to dense molten systems. Confirming recent theoretical predictions, the mean-chain length is found to scale as \Lav \propto \phi^\alpha \exp(\delta E) where the exponents approach $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = 1/2 [1+(\gamma-1)/(\nu d -1)] \approx 0.6, \delta_s=1/2$ in the dilute and semidilute limits respectively. The chain length distribution is qualitatively well described in the dilute limit by the Schulz-Zimm distribution \cN(s)\approx s^{\gamma-1} \exp(-s) where the scaling variable is s=\gamma L/\Lav. The very large size of these simulations allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma \approx 1.165 \pm 0.01$. ....... Finite-size effects are discussed in detail.Comment: 15 pages, 14 figures, LATE

Osmotic Pressure of Solutions Containing Flexible Polymers Subject to an Annealed Molecular Weight Distribution

The osmotic pressure $P$ in equilibrium polymers (EP) in good solvent is investigated by means of a three dimensional off-lattice Monte Carlo simulation. Our results compare well with real space renormalisation group theory and the osmotic compressibility K \propto \phi \upd \phi/\upd P from recent light scattering study of systems of long worm-like micelles. We confirm the scaling predictions for EP based on traditional physics of quenched monodisperse polymers in the dilute and semidilute limit. Specifically, we find $P\propto \phi^{2.3}$ and, hence, $K \propto \phi^{-0.3}$ in the semidilute regime --- in agreement with both theory and experiment. At higher concentrations where the semidilute blobs become too small and hard-core interactions and packing effects become dominant, a much stronger increase % \log(P/\phi)\approx \log(\Nav^2/\phi) \propto \phi is evidenced and, consequently, the compressibility decreases much more rapidly with $\phi$ than predicted from semidilute polymer theory, but again in agreement with experiment.Comment: 7 pages, 4 figures, LATE

Nonequilibrium dynamics of mixtures of active and passive colloidal particles

We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial dimensions. By a stability analysis of the field theory, we obtain equations for the spinodal that describes the onset of a motility-induced instability leading to cluster formation in such mixtures. The prediction for the spinodal is found to be in good agreement with particle-resolved computer simulations. Furthermore, we show that in active-passive mixtures the spinodal instability can be of two different types. One type is associated with a stationary bifurcation and occurs also in one-component active systems, whereas the other type is associated with a Hopf bifurcation and can occur only in active-passive mixtures. Remarkably, the Hopf bifurcation leads to moving clusters. This explains recent results from simulations of active-passive particle mixtures, where moving clusters and interfaces that are not seen in the corresponding one-component systems have been observed.Comment: 17 pages, 3 figure