arXiv subjects

E. Trizac

Publications and source records attributed to E. Trizac.

90 records · Page 5Linked to original sources

arXiv2004

Theory of orientational ordering in colloidal molecular crystals

Freezing of charged colloids on square or triangular two-dimensional periodic substrates has been recently shown to realize a rich variety of orientational orders. We propose a theoretical framework to analyze the corresponding structures. A fundamental ingredient is that a non spherical charged object in an electrolyte creates a screened electrostatic potential that is anisotropic at any distance. Our approach is in excellent agreement with the known experimental and numerical results, and explains in simple terms the reentrant orientational melting observed in these so called colloidal molecular crystals. We also investigate the case of a rectangular periodic substrate and predict an unusual phase transition between orientationnaly ordered states, as the aspect ratio of the unit cell is changed.

cond-mat.stat-mech↗

arXiv2003

Correlations in Ballistic Processes

We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the reaction-controlled limit when particles undergo mostly elastic collisions and therefore are always near equilibrium, the correlations are accounted analytically. For ballistic aggregation, for instance, the density decays as $n\sim t^{-ξ}$ with $ξ=2d/(d+3)$ in the reaction-controlled limit in $d$ dimensions, in contrast with well-known mean-field prediction $ξ=2d/(d+2)$.

cond-mat.stat-mech↗

arXiv2003

Alexander's prescription for colloidal charge renormalization

The interactions between charged colloidal particles in an electrolyte may be described by usual Debye-Hückel theory provided the source of the electric field is suitably renormalized. For spherical colloids, we reconsider and simplify the treatment of the popular proposal put forward by Alexander {\it et al.} [J. Chem. Phys. {\bf 80}, 5776 (1984)], which has proven efficient in predicting renormalized quantities (charge and salt content). We give explicit formulae for the effective charge and describe the most efficient way to apply Alexander's et al. renormalization prescription in practice. Particular attention is paid to the definition of the relevant screening length, an issue that appears confused in the literature.

cond-mat.soft↗

arXiv2003

Effective charge versus bare charge for colloids in the infinite dilution limit

We propose an analytical approximation for the dependence of the effective charge on the bare charge for spherical and cylindrical macro-ions as a function of the size of the colloid and salt content, for the situation of a unique colloid immersed in a sea of electrolyte (where the definition of an effective charge is non ambiguous). Our approach is based on the Poisson-Boltzmann (PB) mean-field theory. Mathematically speaking, our estimate is asymptotically exact in the limit $κa\gg 1$, where $a$ is the radius of the colloid and $κ$ the inverse screening length. In practice, a careful comparison with effective charges parameters obtained by numerically solving the full non-linear PB theory proves that it is good down to $κa\sim 1$. This is precisely the limit appropriate to treat colloidal suspensions. A particular emphasis is put on the range of parameters suitable to describe both single and double strand DNA molecules under physiological conditions.

cond-mat.soft↗

arXiv2002

A molecular dynamics "Maxwell Demon" experiment for granular mixtures

We report a series of molecular dynamics simulations and investigate the possibility to separate a granular mixture of inelastic hard spheres by vigorously shaking it in a box made of two connected compartments. As its one-component counterpart, the system exhibits a ``left-right'' symmetry breaking entirely due to the inelasticity of grain-grain collisions, and triggered by increasing the number of particles. In the compartment where the density of grains is larger, we observe a partial segregation with a predominance of heavy particles. However, this compartment still has a higher density of light particles than the other one, which is light-rich. The density, granular temperature and anisotropic pressure profiles are monitored. We also discuss how to construct a relevant order parameter for this transition and show that the resulting bifurcation diagram is dominated by large fluctuations.

cond-mat.stat-mech↗

arXiv2002

Effective interactions and phase behaviour for a model clay suspension in an electrolyte

Since the early observation of nematic phases of disc-like clay colloids by Langmuir in 1938, the phase behaviour of such systems has resisted theoretical understanding. The main reason is that there is no satisfactory generalization for charged discs of the isotropic DLVO potential describing the effective interactions between a pair of spherical colloids in an electrolyte. In this contribution, we show how to construct such a pair potential, incorporating approximately both the non-linear effects of counter-ion condensation (charge renormalization) and the anisotropy of the charged platelets. The consequences on the phase behaviour of Laponite dispersions (thin discs of 30 nm diameter and 1 nm thickness) are discussed, and investigation into the mesostructure via Monte Carlo simulations are presented.

cond-mat.soft↗

arXiv2002

Lack of energy equipartition in homogeneous heated binary granular mixtures

We consider the problem of determining the granular temperatures of the components of a homogeneous binary heated mixture of inelastic hard spheres, in the framework of Enskog kinetic theory. Equations are derived for the temperatures of each species and their ratio, which is different from unity, as may be expected since the system is out of equilibrium. We focus on the particular heating mechanism where the inelastic energy loss is compensated by an injection through a random external force (``stochastic thermostat''). The influence of various parameters and their possible experimental relevance is discussed.

cond-mat.stat-mech↗

arXiv2001

On the velocity distributions of the one-dimensional inelastic gas

We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are investigated, and special emphasis is paid to the small inelasticity limit. The results are obtained from analytical arguments applied to the Boltzmann equation along with three complementary numerical techniques (Molecular Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of integro-differential kinetic equations). For the freely cooling fluid, we investigate in detail the scaling properties of the bimodal velocity distribution emerging close to elasticity and calculate the scaling function associated with the distribution function. In the heated steady state, we find that, depending on the inelasticity, the distribution function may display two different stretched exponential tails at large velocities. The inelasticity dependence of the crossover velocity is determined and it is found that the extremely high velocity tail may not be observable at ``experimentally relevant'' inelasticities.

cond-mat.stat-mech↗

arXiv2001

Randomly Driven Granular Fluids: collisional statistics and short scale structure

We present a molecular dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short distance correlations in the non-equilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e. factorization of the two-particle distribution function, $f^{(2)}(x_1,x_2) \simeq χf^(1)(x_1) f^{(1)}(x_2)$ in a product of single particle ones, where $x_i = \{{\bf r}_i, {\bf v}_i \}$ with $i=1,2$ and $χ$ represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space $\{x_1,x_2\}$, where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle- and noise-induced recollisions magnifies the departure from mean field behavior. The implications of this breakdown in several physical quantities are explored.

cond-mat.stat-mech↗

arXiv2001

Reply to: Comment on `Long-range electrostatic interactions between like-charged colloids: steric and confinement effects'

In his Comment (cond-mat/0104060) to [Phys. Rev. E 60, 6530 (1999)], Mateescu shows that while the effective interactions remain repulsive when the specific size of the micro-ions is taken into account via a Modified Poisson-Boltzmann equation, a similar conclusion cannot be reached for the situation of complete lateral confinement. This point is correct but has already been considered in a more general study [Phys. Rev. E 62, R1465 (2000), where repulsion is generically obtained]; moreover, we argue that it illustrates the irrelevancy of the notion of pair potential in completely confined configurations, as shown on a simple example.

cond-mat.stat-mech↗

arXiv2000

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised.

cond-mat.stat-mech↗

arXiv2000

Effective interactions between like-charged macromolecules

We investigate, within a local density functional theory formalism, the interactions between like-charged polyions immersed in a confined electrolyte. We obtain a simple condition for a repulsive effective pair potential, that can be related to the thermodynamic stability criterion of the uncharged counterpart of microscopic species constituting the electrolyte. Under the same condition, the phenomenon of charge inversion (over-charging), where the polyion bare charge is over-screened by its electric double layer, is shown to be impossible. These results hold beyond standard mean-field theories (such as Poisson-Boltzmann or Modified Poisson-Boltzmann approaches).

cond-mat.soft↗

arXiv2000

Screened electrostatic interactions between clay platelets

An effective pair potential for systems of uniformly charged lamellar colloids in the presence of an electrolytic solution of microscopic co- and counterions is derived. The charge distribution on the discs is expressed as a collection of multipole moments, and the tensors which determine the interactions between these multipoles are derived from a screened Coulomb potential. Unlike previous studies of such systems, the interaction energy may now be expressed for discs at arbitrary mutual orientation. The potential is shown to be exactly equivalent to the use of linearized Poisson-Boltzmann theory.

cond-mat.soft↗

arXiv1999

Non-Linear Poisson-Boltzmann Theory of a Wigner-Seitz Model for Swollen Clays

Swollen stacks of finite-size disc-like Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its centre, together with an overall charge-neutral distribution of microscopic co and counterions, within a primitive model description. The non-linear Poisson-Boltzmann (PB) equation for the electrostatic potential profile is solved numerically within a highly efficient Green's function formulation. Previous predictions of linearised Poisson-Boltzmann (LPB) theory are confirmed at a qualitative level, but large quantitative differences between PB and LPB theories are found at physically relevant values of the charge carried by the platelets. A hybrid theory treating edge effect at the linearised level yields good potential profiles. The force between two coaxial platelets, calculated within PB theory, is an order of magnitude smaller than predicted by LPB theory

cond-mat.soft↗

arXiv1999

Long-range electrostatic interactions between like-charged colloids: steric and confinement effects

Within the framework of a Modified Poisson-Boltzmann theory accounting for steric effects of microions, we prove analytically that the effective pair interactions between like-charge colloids immersed in a confined electrolyte are repulsive. Our approach encompasses and extends previously known results to the case of complete confinement, and further incorporates the finite size of the microions which is absent in the standard Poisson-Boltzmann theory.

cond-mat.soft↗

arXiv1999

Finite-size corrections to the free energy of crystalline solids

We analyse the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading ($\ln N/N$) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit ($N\to\infty$), we estimate the free energy of a defect free crystal of particles interacting through an $r^{-12}$-potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at $ρσ^{3}$=1.0409, the excess free energy of a defect-free hard-sphere crystal is $5.91889(4)kT$ per particle. This, however, is not the free energy of an equilibrium hard-sphere crystal. The presence of an finite concentration of vacancies results in a reduction of the free energy that is some two orders of magnitude larger than the present error estimate.

cond-mat.stat-mech↗

arXiv1998

Randomly Driven Granular Fluids: large scale structure

The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long range correlations, which behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We calculate the corresponding structure factors over the whole range of wave numbers, and find good agreement with two-dimensional molecular dynamics simulations. It is also shown by means of a mode coupling calculation, how the mean field values for the steady state temperature and collision frequency, as obtained from the Enskog-Boltzmann equation, are renormalized by long wavelength hydrodynamic fluctuations.

cond-mat.stat-mech↗

arXiv1998

Non-linear Poisson-Boltzmann Theory for Swollen Clays

The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient, robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in fair agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.

cond-mat.soft↗