Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9703193

A Wigner-Seitz model of charged lamellar colloidal dispersions

Emmanuel Trizac·Jean-Pierre Hansen
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Emmanuel Trizac, Jean-Pierre Hansen. 1997-03-21. A Wigner-Seitz model of charged lamellar colloidal dispersions. https://doi.org/10.1103/physreve.56.3137

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Slow Dynamics and the Geometry of Jammed Packings

Saddle points in the energy landscape of granular packings dominate the discrete steepest descent dynamics and ultimately determine the path that an out of mechanical equilibrium packing will follow and the resulting stable minimum that it will find. The saddle points that ultimately determine the resulting minima tend to be low-index saddle points. For models with an analytic energy landscape, such as the $p$-spin model, the steepest descent minimization path is affected by higher-index saddle points, which pull the system towards saddle points of decreasing index before arriving at the minima. Here, we examine the steepest descent minimization path of granular packings and compare them to the $p$-spin model. We show that the granular packing steepest descent minimization paths act like their smooth energy landscape counterparts and get attracted by saddle points. The index versus time curves for all models follow a shifted, stretched exponential. We further show that the shape parameter for the granular packings is unchanged when the energy landscape is modified to become analytic (Gaussian potential in a harmonic well) or non-local (Mari-Krzakala-Kurchan). The $p$-spin, on the other hand, has a significantly larger shape parameter. The reason is not due to the dimensionality, packing fraction, nonanalyticity, or the locality of the Hamiltonian of the models. The exact reason for the discrepancy in the shape parameter is \st{still} an unsolved mystery.

cond-mat.soft↗
arXiv2026

A Phase-Field Study of Desiccation Crack Pattern Maturation under Drying-Wetting Cycles

The characteristic intersection angle of the desiccation crack relaxes from near \ang{90} toward \ang{120} under repeated drying--wetting cycles. However, the theoretical understanding of this relaxation is insufficient, especially the modeling of the drying--wetting cycles. Here we introduce a phase-field model of desiccation fracture, extending the model proposed in previous studies by adding crack healing and a scar effect left by past cracks. By repeating drying--wetting cycles in a finite element simulation, we find that the angle distribution develops a growing peak near \ang{120} as the cycle number increases, consistent with experiments. The standard deviation of the intersection angle from \ang{120} relaxes exponentially with a characteristic time of about 2.85 cycles. These results are consistent with experiments, except that the characteristic time is slightly smaller than the experimental value. Crack energy dominates the total energy and also relaxes exponentially with nearly the same characteristic cycle as the angle relaxation. This decay is driven mainly by a shortening of the effective crack length rather than a change in effective fracture toughness.

cond-mat.soft↗
arXiv2026

Kinetics of ferritin crystal formation and melting in acoustically levitated droplets

Understanding protein crystallization pathways is essential for controlling crystallization in structural biology, materials science, and pharmaceutical applications. Classical nucleation theory does not fully capture crystallization processes for several proteins, including ferritin. Here, we combine acoustic levitation with small- and wide-angle X-ray scattering (SAXS and WAXS) to monitor ferritin crystallization in evaporating aqueous polyethylene glycol (PEG) solutions. Acoustic levitation rapidly drives the droplets through a broad range of protein and polymer concentrations, enabling time-resolved measurements of crystallization during evaporation. The scattering data show that ferritin crystals form during evaporation and subsequently lose their crystalline order upon further dehydration. Varying the PEG molecular weight switches between distinct crystallization pathways: one dominated by attractive protein-protein interactions and another dominated by repulsive interactions and excluded-volume effects. Furthermore, we find that lower molecular weight PEG (1000 g/mol) suppresses the dehydration-induced loss of crystalline order observed for higher molecular weight PEG (6000 g/mol), providing a simple strategy for improving protein crystal stability.

cond-mat.soft↗