Alexander's Prescription for Colloidal Charge Renormalization

Trizac, Emmanuel; Bocquet, Lydéric; Aubouy, Miguel; Grünberg, H. H. von

doi:10.1021/la027056m

Cited by 136 publications

(202 citation statements)

References 61 publications

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“…These parameters are estimated as in Ref. [25][26][27], accounting for modest charge renormalization, and they agree with the dispersion's experimentally determined equation of state [15,28].…”

supporting

confidence: 65%

“…Our particles interact instead through soft potentials. Assuming an effective Yukawa potential [25][26][27], the pair potential of two average-sized particles reaches about 3 kT at a volume fraction of 20%, corresponding to a surface separation (for bcc) of 8 nm. In this state, overlap of the particles themselves is still a rare occurrence, determined by the frequency of very large particles.…”

mentioning

confidence: 99%

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Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

Cabane

Artzner

et al. 2016

Phys. Rev. Lett.

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We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB 2 , liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and it suggests routes for designing self-assembling colloidal crystals from the bottom up.

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supporting

confidence: 65%

mentioning

confidence: 99%

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

Cabane

Artzner

et al. 2016

Phys. Rev. Lett.

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“…The DLVO theory is a linearized theory and therefore neglects nonlinear screening effects [19,18] which give rise to effective many-body forces [20][21][22][23][24]. Nonlinear effects can at least partially be accounted for by charge renormalization which is conveniently calculated in a spherical Poisson-Boltzmann cell model [25]. The cell approach was recently generalized towards binary mixtures by Torres et al [26].…”

Section: Introductionmentioning

confidence: 99%

Nonadditivity in the effective interactions of binary charged colloidal suspensions

Allahyarov

Löwen

2009

J. Phys.: Condens. Matter

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Based on primitive model computer simulations with explicit microions, we calculate the effective interactions in a binary mixture of charged colloids with species A and B for different size and charge ratios. An optimal pairwise interaction is obtained by fitting the many-body effective forces. This interaction is close to a Yukawa (or Derjaguin-Landau-Verwey-Overbeek (DLVO)) pair potential but the AB cross-interaction is different from the geometric mean of the two direct AA and BB interactions. As a function of charge asymmetry, the corresponding nonadditivity parameter is first positive, then significantly negative and is then positive again. We finally show that an inclusion of nonadditivity within an optimal effective Yukawa model gives better predictions for the fluid pair structure than DLVO theory.

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“…To compute Z and ψ(r = a) self-consistently, we calculate the full electrostatic potential ψ(r) in a charge-neutral, spherical Wigner-Seitz cell [37][38][39] with radius R = aφ −1/3 , containing a spherical colloidal particle centered at the origin. On the colloid surface we impose Gauss's law, βe ∂ψ(r) ∂r | r=a = −Zλ B /a 2 .…”

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confidence: 99%

Crystallization and reentrant melting of charged colloids in nonpolar solvents

Kanai

Boon

et al. 2015

Phys. Rev. E

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We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse micelles. At low AOT concentrations, the charged particles crystallize into body-centered-cubic (bcc) or face-centered-cubic (fcc) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved reentrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the reentrant melting and the data collapse. Colloidal particles can spontaneously form structures that exhibit long-range ordered states, making them a fascinating system for fundamental studies of crystal phase behavior [1][2][3][4]. The majority of studies focus on colloids which model the hard-sphere interaction, a strong repulsion that prevents particles from overlapping, whose range is restricted to contact [5]. Hard-sphere crystallization is driven through purely entropic effects, and the phase behavior is well studied [5][6][7][8][9]. Typically, the colloids used for these studies are stericallystabilized polymeric particles in nonaqueous solvents, which can match both the density ρ and refractive index n of the particles, enabling confocal microscopy to be used for these investigations. Even earlier studies focused on charged particles, where crystallization is driven by strong long-range repulsive interactions arising from Coulombic charges on the particles [1,[10][11][12][13][14][15][16][17][18][19][20][21][22]. These studies were performed on particles in aqueous solvents, which makes charge effects much easier to induce, but precludes index matching, limiting the use of optical techniques except at very low densities. Instead, x-ray scattering studies [23] showed a fascinating phase behavior of Wigner crystals, including a body-centered-cubic (bcc) phase at low concentration, and a solid-solid transition to a face-centered-cubic (fcc) phase at higher densities [15][16][17][18]24,25]. It is also possible to induce charge on particles in nonaqueous solvents through the addition of charge control agents [21,[26][27][28]. However, in this case, there is strong coupling between the charge on the particle surface and the ions in solution. Charge-induced crystallization should still be expected, although new behavior may also occur as a consequence of this coupling. Nevertheless, these systems have never been investigated experimentally, and the range of potential behavior has not yet been explored.In this Rapid Communication, we investigate the crystallization behavior of colloidal particles in nonpolar solvents. By adding aerosol-OT (AOT) reverse micelles, we both charge the particles and add ions to the solution. As AOT concentration increases from zero, the system undergoes a first transition from fluid to a charge-stabilized bcc Wigner crystal, and * Corresponding author: plu@fas.harvard.edu then a second solid-sol...

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Alexander's Prescription for Colloidal Charge Renormalization

Cited by 136 publications

References 61 publications

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

Nonadditivity in the effective interactions of binary charged colloidal suspensions

Crystallization and reentrant melting of charged colloids in nonpolar solvents

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