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E Trizac

Publications and source records attributed to E Trizac.

9 recordsLinked to original sources
PubMed2004

The interplay between screening properties and colloid anisotropy: towards a reliable pair potential for disc-like charged particles.

The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour (relevant for colloidal interactions in dilute suspensions) is exactly that obtained within linearized PB theory, with the surface boundary condition of a uniform potential. The latter linear problem is solved by a new semi-analytical procedure and both the potential amplitude (quantified by an effective charge) and potential anisotropy coincide closely within PB and linearized PB, provided the disc bare charge is high enough. This anisotropy remains at all scales; it is encoded in a function that may vary over several orders of magnitude depending on the azimuthal angle under which the disc is seen. The results allow to construct a pair potential for discs interaction, that is strongly orientation dependent.

Aluminum Silicates↗
PubMed2003

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 approximately t(-xi) with xi=2d/(d+3) in the reaction-controlled limit in d dimensions, in contrast with the well-known mean-field prediction xi=2d/(d+2).

Journal Article↗
PubMed2003

Random inelasticity and velocity fluctuations in a driven granular gas.

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the "stochastic thermostat" model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high-velocity stretched-exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics.

Journal Article↗
PubMed2001

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 nonequilibrium 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)) approximately chif((1))(x(1))f((1))(x(2)) in a product of single-particle ones, where x(i)=[r(i),v(i)] with i=1,2 and chi 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.

Journal Article↗
PubMed2001

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

In his Comment to [Phys. Rev. E 60, 6530 (1999)], Mateescu shows that while the effective interactions remain repulsive when the specific size of the microions 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 in a simple example.

Comment↗
PubMed2000

Nonlinear poisson-boltzmann theory of a wigner-seitz model for swollen clays

Swollen stacks of finite-size disclike Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its center, together with an overall charge-neutral distribution of microscopic co and counterions, within a primitive model description. The nonlinear Poisson-Boltzmann (PB) equation for the electrostatic potential profile is solved numerically within a highly efficient Green's function formulation. Previous predictions of linearized 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 linearized 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.

Journal Article↗
PubMed2000

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, which 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).

Journal Article↗
PubMed1999

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.

Journal Article↗