Crystallization and reentrant melting of charged colloids in nonpolar solvents

Abstract

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...

Anisotropic elasticity of experimental colloidal Wigner crystals

“…If we estimate an effective particle charge from the interaction strength, we find Z * ≈ √ U 0 0 ≈ 100e. This is a very rough order of magnitude estimate, but is consistent with the effective charges reported in a number of earlier studies [16,17,18].…”

“…Our a priori estimate of the screening length κ −1 was on the order of ≈ 0.8 -1µm, based on the added AOT concentration and the results of earlier conductivity measurements in particle-free AOT solutions [16,17]. We expect the addition of particles to decrease the screening length, as the additional counterions that dissociate from the particle surfaces contribute to the screening; indeed, we expect κ −1 to decrease further with increasing number density, which is not accounted for in the simple numerical model.…”

“…They furthermore enable the dissociation of the PHSA groups on the surface of the particles, with the dissociated proton entering a micelle core, so that the particles acquire a negative charge and the interparticle interaction becomes repulsive [16]. The 10mM concentration was chosen to generate an optimum balance between highly charged particles (at large [AOT]) and long screening lengths (at low [AOT]), in order to achieve large interparticle spacings; at this AOT concentration, we anticipate a charge-carrier concentration on the order of 4 nM, and a Debye screening length of κ −1 ≈ 0.8 -1µm [16,17,18].…”

Structural Transition in a Fluid of Spheroids: A Low-Density Vestige of Jamming

“…For higher aspect ratios, this procedure is insufficient and particle stabilization is achieved by introduction of the AOT (dioctyl sodium sulfosuccinate, Sigma-Aldrich 98%) micelles into the suspension. The AOT micelles charge the particles, but also screen long-range Coulomb repulsions [5,31], so that the interactions become quasihard at high AOT concentrations [32]. The coherent physical behavior observed in this work for the AOT-and the PHSA-stabilized particles, at different particle aspect ratios t and volume fractions ϕ, suggests that the chemical details of the stabilizing mechanism do not matter for our current purposes.…”

Triple Junction at the Triple Point Resolved on the Individual Particle Level

“…Furthermore, two neutral micelles can reversibly interact to yield two oppositely charged micelles; roughly one in 10 5 micelles acquires a single elementary charge in this way [55]. We use 20 mM dioctyl sodium sulfosuccinate (AOT), which is well above the estimated critical micelle concentration of about 1 mM [55][56][57], and yields reverse micelles with an essentially concentration-independent radius R m ≈ 1.5 nm [55,58]. At this AOT concentration the conductivity c ≈ 80 pS/cm, as measured using an immersion probe, and thus the number density of charged micelles, and hence ions, is estimated to be ρ m = 6πηR m c e 2 ≈ 10 19 m −3 (and the number density of all, that is charged and uncharged, micelles is higher by a factor of about 10 5 ).…”