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Jean-Pierre Hansen

Publications and source records attributed to Jean-Pierre Hansen.

At least 19 recordsLinked to original sources
arXiv2018

Casimir force in dense confined electrolytes

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an alternative mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface-surface interaction.

cond-mat.soft↗
arXiv2011

Ultrasoft primitive model of polyionic solutions: structure, aggregation, and dynamics

We introduce an ultrasoft core model of interpenetrating polycations and polyanions with continuous Gaussian charge distributions, to investigate polyelectrolyte aggregation in dilute and semi-dilute, salt-free solutions. The model is studied by a combination of approximate theories (random phase approximation and hypernetted chain theory) and numerical simulations. The calculated pair structure, thermodynamics, phase diagram and polyion dynamics of the symmetric version of the model (the "ultrasoft restricted primitive model" or UPRM) differ from the corresponding properties of the widely studied "restricted primitive model" (RPM) where ions have hard cores. At sufficiently low temperatures and densities, oppositely charged polyions form weakly interacting, polarizable neutral pairs. The clustering probabilities, dielectric behavior and electrical conductivity point to a line of sharp conductor-insulator transitions in the density-temperature plane. At very low temperatures the conductor-insulator transition line terminates near the top of a first order coexistence curve separating a high-density, liquid phase from a low-density, vapor phase. The simulation data hint at a tricritical behavior, reminiscent of that observed of the two-dimensional Coulomb Gas, which contrasts with the Ising criticality of its three-dimensional counterpart, the RPM.

cond-mat.soft↗
arXiv2011

Clustering, conductor-insulator transition and phase separation of an ultrasoft model of electrolytes

We investigate the clustering and phase separation of a model of ultrasoft, oppositely charged macroions by a combination of Monte Carlo and Molecular Dynamics simulations. Static and dynamic diagnostics, including the dielectric permittivity and the electric conductivity of the model, show that ion pairing induces a sharp conductor-insulator transition at low temperatures and densities, which impacts the separation into dilute and concentrated phases below a critical temperature. Preliminary evidence is presented for a possible tricritical nature of the phase diagram of the model.

cond-mat.soft↗
arXiv2007

The transition from highly to fully stretched polymer brushes in good solvent

The stretching of brushes of long polymers grafted to a planar surface is investigated byMonte Carlo simulations in the limit of very high grafting densities, as achieved in recent experiments. The monomer density profiles are shown to deviate considerably from the parabolic limiting form predicted by self-consistent field theory. A rapid transition is observed from parabolic to fully stretched polymers, characterized by a dramatic change in the end-monomer height distribution and by a clear cross-over in the slope of the brush height versus scaled grafting density.

cond-mat.soft↗
arXiv2007

A multi-blob representation of semi-dilute polymer solutions

A coarse-grained multi-blob description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and non-bonded blobs. The number of blobs is chosen such that the blob density does not exceed their overlap threshold, allowing polymer concentrations to be explored deep into the semi-dilute regime. This quantitative multi-blob description is shown to preserve known scaling laws of polymer solutions and provides accurate estimates of amplitudes, while leading to orders of magnitude increase of simulation efficiency and allowing analytic calculations of structural and thermodynamic properties.

cond-mat.soft↗
arXiv2007

Reversible gelation and dynamical arrest of dipolar colloids

We use molecular dynamics simulations of a simple model to show that dispersions of slightly elongated colloidal particles with long-range dipolar interactions, like ferrofluids, can form a physical (reversible) gel at low volume fractions. On cooling, the particles first self-assemble into a transient percolating network of cross-linked chains, which, at much lower temperatures, then undergoes a kinetic transition to a dynamically arrested state with broken ergodicity. This transition from a transient to a frozen gel is characterised by dynamical signatures reminiscent of jamming in much denser dispersions.

cond-mat.soft↗
arXiv2006

Multi-scale coarse-graining of diblock copolymer self-assembly: from monomers to ordered micelles

Starting from a microscopic lattice model, we investigate clustering, micellization and micelle ordering in semi-dilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse graining strategy, whereby the AB copolymers are mapped onto ``ultrasoft'' dumbells with monomer-averaged effective interactions between the centres of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n of roughly 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.

cond-mat.soft↗
arXiv2006

Dielectric response of a polar fluid trapped in a spherical nanocavity

We present extensive Molecular Dynamics simulation results for the structure, static and dynamical response of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii $R=2.5$, 3, and 4 nm embedded in a dielectric continuum of permittivity $ε' \geq 1$. The polarisation of the external medium by the charge distribution inside the cavity is accounted for by appropriate image charges. We focus on the influence of the external permittivity $ε'$ on the static and dynamic properties of the confined fluid. The density profile and local orientational order parameter of the dipoles turn out to be remarkably insensitive to $ε'$. Permittivity profiles $ε(r)$ inside the spherical cavity are calculated from a generalised Kirkwood formula. These profiles oscillate in phase with the density profiles and go to a ``bulk'' value $ε_b$ away from the confining surface; $ε_b$ is only weakly dependent on $ε'$, except for $ε' = 1$ (vacuum), and is strongly reduced compared to the permittivity of a uniform (bulk) fluid under comparable thermodynamic conditions. The dynamic relaxation of the total dipole moment of the sample is found to be strongly dependent on $ε'$, and to exhibit oscillatory behaviour when $ε'=1$; the relaxation is an order of magnitude faster than in the bulk. The complex frequency-dependent permittivity $ε(ω)$ is sensitive to $ε'$ at low frequencies, and the zero frequency limit $ε(ω=0)$ is systematically lower than the ``bulk'' value $ε_b$ of the static primitivity.

cond-mat.soft↗
arXiv2005

Solving the Fokker-Planck kinetic equation on a lattice

We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar to the Lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized Hermite-Gauss procedure is used to construct a discretized kinetic equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations. The stability of the algorithm with respect to the finite time-step $Δt$ is characterized by the eigenvalues of the collision matrix. A heuristic second-order algorithm in $Δt$ is applied to investigate the time evolution of the distribution function of simple model systems, and compared to known analytical solutions. Preliminary investigations of sedimenting Brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the Lattice-Fokker-Planck algorithm to simulate non-trivial situations. Interactions between Brownian particles may be accounted for by adding a standard BGK collision operator to the discretized Fokker-Planck kernel.

cond-mat.stat-mech↗
arXiv2005

Phase separation of a model binary polymer solution in an external field

The phase separation of a simple binary mixture of incompatible linear polymers in solution is investigated using an extension of the sedimentation equilibrium method, whereby the osmotic pressure of the mixture is extracted from the density profiles of the inhomogeneous mixture in a gravitational field. In Monte-Carlo simulations the field can be tuned to induce significant inhomogeneity, while keeping the density profiles sufficiently smooth for the macroscopic condition of hydrostatic equilibrium to remain applicable. The method is applied here for a simplified model of ideal, but mutually avoiding polymers, which readily phase separate at relatively low densities. The Monte-Carlo data are interpreted with the help of an approximate bulk phase diagram calculated from a simple, second order virial coefficient theory. By deriving effective potentials between polymer centres of mass, the binary mixture of polymers is coarse-grained to a ``soft colloid'' picture reminiscent of the Widom-Rowlinson model for incompatible atomic mixtures. This approach significantly speeds up the simulations, and accurately reproduces the behaviour of the full monomer resolved model.

cond-mat.soft↗
arXiv2004

Structure and equation of state of interaction site models for disc-shaped lamellar colloids

We apply RISM (Reference Interaction Site Model) and PRISM (polymer-RISM) theories to calculate the site-site pair structure and the osmotic equation of state of suspensions of circular or hexagonal platelets (lamellar colloids) over a range of ratios of the particle diameter over thickness. Despite the neglect of edge effects, the simpler PRISM theory yields results in good agreement with the more elaborate RISM calculations, provided the correct form factor, characterizing the intramolecular structure of the platelets, is used. The RISM equation of state is sensitive to the number of sites used to model the platelets, but saturates when the hard spheres, associated with the interaction sites, nearly touch; the limiting equation of state agrees reasonably well with available simulation data for all densities up to the isotropic-nematic transition. When properly scaled with the second virial coefficient, the equations of state of platelets with different aspect ratios nearly collapse on a single master curve.

cond-mat.soft↗
arXiv2004

Kinetic models of ion transport through a nanopore

Kinetic equations for the stationary state distribution function of ions moving through narrow pores are solved for a number of one-dimensional models of single ion transport. Ions move through pores of length $L$, under the action of a constant external field and of a concentration gradient. The interaction of single ions with the confining pore surface and with water molecules inside the pore are modelled by a Fokker-Planck term in the kinetic equation, or by uncorrelated collisions with thermalizing centres distributed along the pore. The temporary binding of ions to polar residues lining the pore is modelled by stopping traps or energy barriers. Analytic expressions for the stationary ion current through the pore are derived for several versions of the model, as functions of key physical parameters. In all cases, saturation of the current at high fields is predicted. Such simple models, for which results are analytic, may prove useful in the study of the current/voltage relations of ion channels through membranes.

cond-mat.soft↗
arXiv2003

Phase separation of a multiple occupancy lattice gas

A binary lattice gas model that allows for multiple occupancy of lattice sites, inspired by recent coarse-grained descriptions of solutions of interacting polymers, is investigated by combining the steepest descent approximation with an exploration of the multidimensional energy landscape, and by Gibbs ensemble Monte Carlo simulations. The one-component version of the model, involving on site and nearest neighbour interactions, is shown to exhibit microphase separation into two sub-lattices with different mean occupation numbers. The symmetric two-component version of the multiple occupancy lattice gas is shown to exhibit a demixing transition into two phases above a critical mean occupation number.

cond-mat.soft↗
arXiv2003

Onsager model for a variable dielectric permittivity near an interface

Using a generalisation of an Onsager type approach, we are able to predict a dielectric permittivity profile of an inhomogeneous dipolar fluid in the presence of a dielectric interface. The reaction and cavity fields are calculated semi-analytically using bispherical coordinates. An asymptotic expression for the local permittivity is derived as a function of distance from the interface.

cond-mat.soft↗
arXiv2002

Intermittent permeation of cylindrical nanopores by water

Molecular Dynamics simulations of water molecules in nanometre sized cylindrical channels connecting two reservoirs show that the permeation of water is very sensitive to the channel radius and to electric polarization of the embedding material. At threshold, the permeation is {\emph{intermittent}} on a nanosecond timescale, and strongly enhanced by the presence of an ion inside the channel, providing a possible mechanism for gating. Confined water remains surprisingly fluid and bulk-like. Its behaviour differs strikingly from that of a reference Lennard-Jones fluid, which tends to contract into a highly layered structure inside the channel.

cond-mat.soft↗
arXiv2000

The plasma-insulator transition of spin-polarized Hydrogen

A mixed classical-quantum density functional theory is used to calculate pair correlations and the free energy of a spin-polarized Hydrogen plasma. A transition to an atomic insulator phase is estimated to occur around r_s=2.5 at T=10^4K, and a pressure $P\approx0.5Mbar$. Spin polarization is imposed to prevent the formation of H_2 molecules.

cond-mat.stat-mech↗
arXiv1997

A Wigner-Seitz model of charged lamellar colloidal dispersions

A concentrated suspension of lamellar colloidal particles (e. g. clay) is modelled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within Poisson-Boltzmann theory, with appropriate boundary conditions on the surface of the WS cell, supposed to account for the confinement effect of neighbouring platelets. Expressions are obtained for the free energy, osmotic and disjoining pressures and the capacitance in terms of the local electrostatic potential and the co- and counterion density profiles. Explicit solutions of the linearized Poisson-Boltzmann (LPB) equation are obtained for circular and square platelets placed at the centre of a cylindrical or parallelepipedic cell. The resulting free energy is found to go through a minimum as a function of the aspect ratio of the cell, for any given volume (determined by the macroscopic concentration of platelets), platelet surface charge and salt concentration. The optimum aspect ratio is found to be nearly independent of the two latter physical parameters. The osmotic and disjoining pressures are found to coincide at the free energy minimum, while the total quadrupole moment of the electric double-layer formed by the platelet and the surrounding co- and counterions vanishes simultaneously. The osmotic equation-of-state is calculated for a variety of physical conditions. The limit of vanishing platelet concentration is considered in some detail, and the force acting between two coaxial platelets is calculated in that limit as a function of their separation.

cond-mat.soft↗