JeanPierre Hansen

University of Cambridge, Chemistry, Emeritus

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Papers by JeanPierre Hansen

Intermittent Permeation of Cylindrical Nanopores by Water

by Simone Melchiona and JeanPierre Hansen

Physical Review Letters, 2002

Molecular Dynamics simulations of water molecules in nanometre sized cylindrical channels connect... more 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 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.

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Solving the Fokker-Planck kinetic equation on a lattice

by Simone Melchiona and JeanPierre Hansen

Physical Review E, 2006

We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar t... more 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 ∆t is characterized by the eigenvalues of the collision matrix. A heuristic secondorder algorithm in ∆t 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.

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Mean-field theory of the phase diagram of ultrasoft, oppositely charged polyions in solution

The Journal of Chemical Physics, 2012

We investigate the phase separation of the "ultrasoft restricted primitive model" (URPM), a coars... more We investigate the phase separation of the "ultrasoft restricted primitive model" (URPM), a coarsegrained representation of oppositely charged, interpenetrating polyelectrolytes, within a mean-field description based on the "chemical picture." The latter distinguishes between free ions and dimers of oppositely charged ions (Bjerrum pairs) which are in chemical equilibrium governed by a law of mass action. Interactions between ions, and between ions and dimers are treated within linearized Poisson-Boltzmann theory, at four levels of approximation corresponding to increasingly refined descriptions of the interactions. The URPM is found to phase separate into a dilute phase of dimers, and a concentrated phase of mostly free (unpaired) ions below a critical temperature T c . The phase diagram differs, however, considerably from the predictions of recent simulations; T c is about three times higher, and the critical density is much lower than the corresponding simulation data G. Kahl, Soft Matter 7, 1690 (2011)]. Possible reasons for this unexpected failure of mean-field theory are discussed. The Kirkwood line, separating the regimes of monotonically decaying and damped oscillatory decay of the charge-charge correlation function at large distances is determined within the random phase approximation.

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