Nonlinear Poisson-Boltzmann theory of a Wigner-Seitz model for swollen clays

Carvalho, Rimenys J.; Trizac, Emmanuel; Hansen, Jean‐Pierre

doi:10.1103/physreve.61.1634

Cited by 39 publications

(31 citation statements)

References 20 publications

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“…This is probably the way in which the Laponite solution makes the transition towards the colloidal glass state. The influence of these domains on the electrical conductivity of Laponite is related to the electrostatic interaction among the Laponite disks, which is a widely studied and not yet completely understood problem [28]. The physical origin of the large T ef f certainly lays in these complex interactions.…”

Section: Discussionmentioning

confidence: 99%

Experimental study of the fluctuation dissipation relation during an aging process

Bellon

Ciliberto

2002

Physica D: Nonlinear Phenomena

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The validity of fluctuation dissipation relations in an aging system is studied in a colloidal glass during the transition from a fluid-like to a solid-like state. The evolution of the rheological and electrical properties is analyzed in the range 1Hz − 40Hz. It is found that at the beginning of the transition the fluctuation dissipation relation is strongly violated in electrical measurements. The amplitude and the persistence time of this violation are decreasing functions of frequency. At the lowest frequencies of the measuring range it persists for times which are about 5% of the time needed to form the colloidal glass. This phenomenology is quite close to the recent theoretical predictions done for the violation of the fluctuation dissipation relation in glassy systems. In contrast in the rheological measurements no violation of the fluctuation dissipation relation is observed. The reasons of this large difference between the electrical and rheological measurements are discussed.

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Section: Discussionmentioning

confidence: 99%

Experimental study of the fluctuation dissipation relation during an aging process

Bellon

Ciliberto

2002

Physica D: Nonlinear Phenomena

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“…Phenomena involving the electrical double layer are common in systems in contact with the electrolyte solution, such as biological and artificial membranes [1], in liquid crystals [2], in clays [3], and solid electrolytes [4].…”

Section: Introductionmentioning

confidence: 99%

Thickness of electrical double layer. Effect of ion size

Bohinc¹,

Kralj‐Iglič²,

Iglič³

2001

Electrochimica Acta

247

157

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The thickness of a single flat electrical double layer is considered. The electrostatic mean field and the excluded volume effect are taken into account. A simple statistical mechanical approach is used, where the particles in the solution are distributed over a lattice with an adjustable lattice constant. Different sizes of ions are described by different values of the lattice constant. Two measures are introduced that describe an effective thickness of the electrical double layer: a distance where the density of the number of counterions drops to a chosen fraction of its maximal value, and a distance defining a region that contains a chosen fraction of the excess of the counterions. It is shown that the effective thickness of the electrical double layer increases with increasing counterion size and with decreasing bulk concentration of ions, whereas increasing the surface charge may cause either a decrease or an increase of the effective thickness. It is shown that the description of the effective thickness of the electrical double layer by the Debye length differs qualitatively from the description presented for low bulk concentrations of ions.

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“…The constants c k are a priori unknown and, in general, they must be determined from electroneutrality and ionic equilibrium or conservation constraints [19,23]. However, they are often taken as the bulk ionic concentrations n 0k , which is strictly only correct in an open system, but also an excellent approximation in a closed system when the dissolved salt concentration n 0 or the distance between charged surfaces are large enough (a statement which we will quantify below).…”

Section: The Poisson-boltzmann Equation In a Closed Systemmentioning

confidence: 98%

Effective Debye length in closed nanoscopic systems: A competition between two length scales

Tessier

Slater

2006

Electrophoresis

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The Poisson-Boltzmann equation (PBE) is widely employed in fields where the thermal motion of free ions is relevant, in particular in situations involving electrolytes in the vicinity of charged surfaces. The applications of this non-linear differential equation usually concern open systems (in osmotic equilibrium with an electrolyte reservoir, a semi-grand canonical ensemble), while solutions for closed systems (where the number of ions is fixed, a canonical ensemble) are either not appropriately distinguished from the former or are dismissed as a numerical calculation exercise. We consider herein the PBE for a confined, symmetric, univalent electrolyte and quantify how, in addition to the Debye length, its solution also depends on a second length scale, which embodies the contribution of ions by the surface (which may be significant in high surface-to-volume ratio micro- or nanofluidic capillaries). We thus establish that there are four distinct regimes for such systems, corresponding to the limits of the two parameters. We also show how the PBE in this case can be formulated in a familiar way by simply replacing the traditional Debye length by an effective Debye length, the value of which is obtained numerically from conservation conditions. But we also show that a simple expression for the value of the effective Debye length, obtained within a crude approximation, remains accurate even as the system size is reduced to nanoscopic dimensions, and well beyond the validity range typically associated with the solution of the PBE.

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Nonlinear Poisson-Boltzmann theory of a Wigner-Seitz model for swollen clays

Cited by 39 publications

References 20 publications

Experimental study of the fluctuation dissipation relation during an aging process

Experimental study of the fluctuation dissipation relation during an aging process

Thickness of electrical double layer. Effect of ion size

Effective Debye length in closed nanoscopic systems: A competition between two length scales

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