Jean-Pierre Hansen

A rescaled MSA structure factor for dilute charged colloidal dispersions

The structure of a dispersion of charged colloidal particles interacting through a screened Coulomb potential is well described at moderate to high densities by calculating the correlations in the mean spherical approximation (MSA). In this paper we extend the validity of the MSA calculation to arbitrarily low densities, using a physical rescaling argument which preserves the analytic form of the MSA solution. Our results are in excellent agreement with other numerical calculations and with experimental low-density light scattering data. The method may be viewed as a generalization of Gillans prescription for one component plasmas to systems interacting through a Yukawa potential. An advantage of the present prescription is that it allows a smooth transition from strong to weak coupling, and it implies no functional relation between the experimentally independent parameters.

Self‐consistent integral equations for fluid pair distribution functions: Another attempt

We propose a new mixed integral equation for the pair distribution function of classical fluids, which interpolates continuously between the soft core mean spherical closure at short distances, and the hypernetted chain closure at large distances. Thermodynamic consistency between the virial and compressibility equations of state is achieved by varying a single parameter in a suitably chosen switching function. The new integral equation generalizes a recent suggestion by Rogers and Young to the case of realistic pair potentials containing an attractive part. When compared to available computer simulation data, the new equation is found to yield excellent results for the thermodynamics and pair structure of a wide variety of potential models (including atomic and ionic fluids and mixtures) over an extensive range of temperatures and densities. The equation can also be used to invert structural data to extract effective pair potentials, with reasonable success.

Accurate Effective Pair Potentials for Polymer Solutions

Dilute or semidilute solutions of nonintersecting self-avoiding walk (SAW) polymer chains are mapped onto a fluid of “soft” particles interacting via an effective pair potential between their centers of mass. This mapping is achieved by inverting the pair distribution function of the centers of mass of the original polymer chains, using integral equation techniques from the theory of simple fluids. The resulting effective pair potential is finite at all distances, has a range of the order of the radius of gyration, and turns out to be only moderately concentration-dependent. The dependence of the effective potential on polymer length is analyzed in an effort to extract the scaling limit. The effective potential is used to derive the osmotic equation of state, which is compared to simulation data for the full SAW segment model, and to the predictions of renormalization group calculations. A similar inversion procedure is used to derive an effective wall–polymer potential from the center of mass density pro...

Electric-field-controlled water and ion permeation of a hydrophobic nanopore.

The permeation of hydrophobic, cylindrical nanopores by water molecules and ions is investigated under equilibrium and out-of-equilibrium conditions by extensive molecular-dynamics simulations. Neglecting the chemical structure of the confining pore surface, we focus on the effects of pore radius and electric field on permeation. The simulations confirm the intermittent filling of the pore by water, reported earlier under equilibrium conditions for pore radii larger than a critical radius R(c). Below this radius, water can still permeate the pore under the action of a strong electric field generated by an ion concentration imbalance at both ends of the pore embedded in a structureless membrane. The water driven into the channel undergoes considerable electrostriction characterized by a mean density up to twice the bulk density and by a dramatic drop in dielectric permittivity which can be traced back to a considerable distortion of the hydrogen-bond network inside the pore. The free-energy barrier to ion permeation is estimated by a variant of umbrella sampling for Na(+), K(+), Ca(2+), and Cl(-) ions, and correlates well with known solvation free energies in bulk water. Starting from an initial imbalance in ion concentration, equilibrium is gradually restored by successive ion passages through the water-filled pore. At each passage the electric field across the pore drops, reducing the initial electrostriction, until the pore, of radius less than R(c), closes to water and hence to ion transport, thus providing a possible mechanism for voltage-dependent gating of hydrophobic pores.

Influence of Polymer-Excluded Volume on the Phase-Behavior of Colloid-Polymer Mixtures

We determine the depletion-induced phase-behavior of hard-sphere colloids and interacting polymers by large-scale Monte Carlo simulations using very accurate coarse-graining techniques. A comparison with standard Asakura-Oosawa model theories and simulations shows that including excluded-volume interactions between polymers leads to qualitative differences in the phase diagrams. These effects become increasingly important for larger relative polymer size. Our simulation results agree quantitatively with recent experiments.

Molecular dynamics study of binary soft‐sphere mixtures: Jump motions of atoms in the glassy state

Three very long runs of constant temperature molecular dynamics (MD) simulations, extending over typically 2×105 time steps, have been carried out for a state just above the glass transition of equimolar soft‐sphere mixtures, with 500 atoms interacting through vαβ(r) =e(σαβ /r)12, where σαβ =(σα +σβ )/2, and α,β (species indices)=1, 2. The ratio of diameters σ2/σ1 was chosen to be 1.2. Jump‐type atomic motions are clearly found to occur in the glassy states. A coordinated (strongly correlated) jump motion was observed, where a cluster of several atoms dynamically linked at nearest‐neighbor distances jump at successive close times. These simulations demonstrate that the characteristic time scale of structural relaxation becomes very long near the glass transition, and calculated mean square displacements exhibit complicated behaviors. Thermodynamic quantities, however, such as the mean pressure, energy, and pair distribution functions, appear to behave normaly, with no significant observable relaxations fo...

A Monte Carlo study of the classical two-dimensional one-component plasma

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The “exact” simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a couplingγ= e2/kBT−140.

Nonlinear counterion screening in colloidal suspensions

A new ‘‘ab initio’’ method is presented which is designed to simulate highly asymmetric systems of charged particles such as micellar solutions and charge‐stabilized colloidal suspensions. The hybrid description considers the macroion degrees of freedom explicitly, while the microscopic counterions are treated within the framework of density functional theory. The counterion density profile is treated as a dynamical variable which is coupled to the macroion positions; the corresponding equation of motions are derived from a Lagrangian which contains a fictitious kinetic energy term associated with the inhomogeneous counterion density, with a fictitious mass chosen so that the counterions stay as close as possible to the surface of lowest free energy (adiabatic condition). The discontinuous behavior of the counterion density profile at the macroion surfaces is suppressed by the use of a classical pseudopotential scheme without spoiling the rapid variation of the counterion density profile outside the macro...

Electric field-controlled water permeation coupled to ion transport through a nanopore

We report molecular dynamics simulations of a generic hydrophobic nanopore connecting two reservoirs which are initially at different Na(+) concentrations, as in a biological cell. The nanopore is impermeable to water under equilibrium conditions, but the strong electric field caused by the ionic concentration gradient drives water molecules in. The density and structure of water in the pore are highly field dependent. In a typical simulation run, we observe a succession of cation passages through the pore, characterized by approximately bulk mobility. These ion passages reduce the electric field, until the pore empties of water and closes to further ion transport, thus providing a possible mechanism for biological ion channel gating.

Polymer induced depletion potentials in polymer-colloid mixtures

The depletion interactions between two colloidal plates or between two colloidal spheres, induced by interacting polymers in a good solvent, are calculated theoretically and by computer simulations. A simple analytical theory is shown to be quantitatively accurate for the case of two plates. A related depletion potential is derived for two spheres; it also agrees very well with direct computer simulations. Theories based on ideal polymers show important deviations with increasing polymer concentration: They overestimate the range of the depletion potential between two plates or two spheres at all densities, with the largest relative change occurring in the dilute regime. They underestimate the well depth at contact for the case of two plates, but overestimate it for two spheres. Depletion potentials are also calculated using a coarse graining approach which represents the polymers as “soft colloids;” good agreement is found in the dilute regime. Finally, the effect of the polymers on colloid–colloid osmot...