Non-additivity of pair interactions in charged colloids

Anisotropic remixing of a phase separated binary colloidal system with particles of different sizes in an external modulation

We explore the phase behavior of a binary colloidal system under external spatially periodic modulation. We perform Monte Carlo simulations on a binary mixture of big and small repulsive Lennard-Jones particles with a diameter ratio of 2:1. We characterize structure by isotropic and anisotropic pair correlation functions, cluster size distribution, bond angle distribution, order parameter, and specific heat. We observe the demixing of the species in the absence of external modulation. However, the mixing of the species gets enhanced with increasing potential strength along with the alignment of the particles transverse to the modulation. The de-mixing order parameter shows discontinuity with increasing modulation strength, characterizing a first order phase transition. The peak in specific heat increases linearly with the size of the system. We also look into the dynamical behavior of the system via computing Mean Square Displacement (MSD) along both parallel and perpendicular directions to the modulation. We observe a decrease in the diffusion coefficient for both types of particles as we increase the strength of the modulation.

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

Tunability of Interactions between the Core and Shell in Rattle-Type Particles Studied with Liquid-Cell Electron Microscopy

Yolk-shell or rattle-type particles consist of a core particle that is free to move inside a thin shell. A stable core with a fully accessible surface is of interest in fields such as catalysis and sensing. However, the stability of a charged nanoparticle core within the cavity of a charged thin shell remains largely unexplored. Liquid-cell (scanning) transmission electron microscopy is an ideal technique to probe the core-shell interactions at nanometer spatial resolution. Here, we show by means of calculations and experiments that these interactions are highly tunable. We found that in dilute solutions adding a monovalent salt led to stronger confinement of the core to the middle of the geometry. In deionized water, the Debye length κ-1 becomes comparable to the shell radius Rshell, leading to a less steep electric potential gradient and a reduced core-shell interaction, which can be detrimental to the stability of nanorattles. For a salt concentration range of 0.5-250 mM, the repulsion was relatively long-ranged due to the concave geometry of the shell. At salt concentrations of 100 and 250 mM, the core was found to move almost exclusively near the shell wall, which can be due to hydrodynamics, a secondary minimum in the interaction potential, or a combination of both. The possibility of imaging nanoparticles inside shells at high spatial resolution with liquid-cell electron microscopy makes rattle particles a powerful experimental model system to learn about nanoparticle interactions. Additionally, our results highlight the possibilities for manipulating the interactions between core and shell that could be used in future applications.

Electrical Excitation Decay Time in Chains of Nanoscale Non-Point Dipoles

On the basis of a previously developed model of disperse systems containing non-point dipole particles self-assembled into chains inside a liquid substrate, the decay time of electrical excitations induced in dipoles by an external field is investigated. It was shown that when the external field is completely turned off (from 10-6 V / m to 106 V / m levels) at biologically significant low frequencies (for example, 13 Hz), the decay time of the excitations of nanoscale dipoles nonlinearly depends on the chain length. It was found that the decay time of excitations increases sharply (by four to five orders of magnitude), with an increase in the chain length more than 19-20 dipoles.

The extent of counterion dissociation at the interface of cationic diblock copolymer nanoparticles in non-polar solvents

HYPOTHESIS

Diblock copolymer nanoparticles prepared in non-polar solvents that are sterically stabilized but possess ionic functionality from the inclusion of cationic comonomers in the stabilizer shell are known to exhibit complex electrokinetic behavior (Chem. Sci. 9 (2018) 922-934). For example, core-shell nanoparticles with cationic comonomers located solely within the shell layer have lower magnitude electrophoretic mobilities than nanoparticles containing the same cationic comonomers located within the core, whereas nanoparticles prepared using a minor fraction of steric stabilizer chains containing cationic comonomer repeat units have comparable electrophoretic mobilities to nanoparticles prepared with this cationic comonomer solely located within the core. We hypothesize that these observations can be explained in terms of the strength of the Coulombic interaction between counterions and the nanoparticle interface.

EXPERIMENTS

The highly-fluorinated anionic counterion associated with these cationic nanoparticles is studied by ¹⁹F nuclear magnetic resonance (NMR) spectroscopy in n-dodecane. This revealed only one type of ¹⁹F environment for a soluble macromolecular cation (the oil-soluble steric stabilizer chains used to prepare the nanoparticles), whereas two distinct environments were observed for the sterically-stabilized cationic nanoparticles. Both ¹⁹F diffusion NMR and ¹⁹F-¹³C heteronuclear single quantum correlation (HSQC) measurements support the existence of two environments for this counterion.

FINDINGS

The existence of two distinct ¹⁹F environments for the highly-fluorinated anion associated with the sterically-stabilized nanoparticles demonstrates the presence of spectroscopically distinguishable populations of ion pairs and of fully dissociated free anions. ¹⁹F NMR spectra recorded for sterically-stabilized nanoparticles with a fully ionic shell (all stabilizer chains containing the cationic comonomer) and those with a partly ionic shell (10% of stabilizer chains containing the cationic comonomer) reveal a higher proportion of dissociated anions in the partly ionic case. This suggests a stronger Coulombic interaction between counterions and the cationic interface when the shell is fully ionic, which accounts for the observed reduction in the magnitude of the electrophoretic mobility.

Electrolytic conductivity of ionic polymers in a nonpolar solvent

The electrolytic conductivity of two electrolytes as solutions in the nonpolar solvent, n -dodecane, as a function of concentration has been studied. One was a small molecule electrolyte (tetraalkyl cation and a highly fluorinated tetraphenylborate anion), and the other was a macromolecular electrolyte (cation-containing poly(alkyl methacrylate) chain with the same anion). Two series of the macromolecular cation were prepared: one with entirely cation-containing molecules and the other with a small proportion (10%) cation-containing and the rest nonionic. The conductivity data were qualitatively similar for all systems, which formed both single ions and triple ions. The data from the two series of macromolecular electrolytes were particularly informative to understand some recent and counterintuitive electrokinetic data for particles that were stabilized by these polymers. Reducing the proportion of cationic chains in the stabilizer of the particles was found to increase their electrophoretic mobility. In the conductivity data in this study, reducing the proportion of cationic chains in solution was found to increase the magnitude of the single-ion equilibrium constant and suppress the formation of triple ions. These data should support the development of models to understand these electrokinetic results.

Experimental Evidence for Algebraic Double-Layer Forces

According to conventional wisdom, electric double-layer forces normally decay exponentially with separation distance. Here, we present experimental evidence of algebraically decaying double-layer interactions. We show that algebraic interactions arise in both strongly overlapping as well as counterion-only regimes, albeit the evidence is less clear for the former regime. In both of these cases, the disjoining pressure profile assumes an inverse square distance dependence. At small separation distances, another algebraic regime is recovered. In this regime, the pressure decays as the inverse of separation distance.

Influence of Softness on the Stability of Binary Colloidal Crystals

Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB₄ phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.

Surfactant mediated particle aggregation in nonpolar solvents

The aggregation behavior of particles in nonpolar media is studied with time-resolved light scattering.

Failure of Debye-Hückel Screening in Low-Charge Colloidal Suspensions

Derjaguin–Landau–Verwey–Overbeek (DLVO) theory remains the cornerstone of colloid stability. Electrostatic interactions dominate van der Waals attractions at large colloid-colloid separations h, unless strongly screened. Under these conditions, the potential U ( h ) between charged colloids is expected to be exponentially screened, U ( h ) ∼ exp ( − κ h ) / h , with κ − 1 = λ D where λ D is the classical Debye-Hückel screening length. By measuring the force between individual charged particles at dilute electrolyte concentrations (<mM) using optical tweezers, we tested experimentally the prediction κ − 1 = λ D in a nonpolar solvent. At low salt concentrations, we found close agreement between the directly-measured decay length κ − 1 and Debye-Hückel predictions. However, above a critical electrolyte concentration (≈450 μ M), we obtained significant discrepancies between measured and predicted screening lengths, with κ − 1 ≫ λ D . In marked contrast to expectations, we found that the measured screening length κ − 1 appears to grow as the ionic strength of the solution is increased. The origin of this discrepancy is discussed and the importance of considering the surface is highlighted.

Complex electric double layers in charged topological colloids

Charged surfaces in contact with liquids containing ions are accompanied in equilibrium by an electric double layer consisting of a layer of electric charge on the surface that is screened by a diffuse ion cloud in the bulk fluid. This screening cloud determines not only the interactions between charged colloidal particles or polyelectrolytes and their self-assembly into ordered structures, but it is also pivotal in understanding energy storage devices, such as electrochemical cells and supercapacitors. However, little is known to what spatial complexity the electric double layers can be designed. Here, we show that electric double layers of non-trivial topology and geometry -including tori, multi-tori and knots- can be realised in charged topological colloidal particles, using numerical modelling within a mean-field Poisson-Boltzmann theory. We show that the complexity of double layers -including geometry and topology- can be tuned by changing the Debye screening length of the medium, or by changing the shape and topology of the (colloidal) particle. More generally, this work is an attempt to introduce concepts of topology in the field of charged colloids, which could lead to novel exciting material design paradigms.

Quantifying the thickness of the electrical double layer neutralizing a planar electrode: the capacitive compactness

The spatial extension of the ionic cloud neutralizing a charged colloid or an electrode is usually characterized by the Debye length associated with the supporting charged fluid in the bulk. This spatial length arises naturally in the linear Poisson-Boltzmann theory of point charges, which is the cornerstone of the widely used Derjaguin-Landau-Verwey-Overbeek formalism describing the colloidal stability of electrified macroparticles. By definition, the Debye length is independent of important physical features of charged solutions such as the colloidal charge, electrostatic ion correlations, ionic excluded volume effects, or specific short-range interactions, just to mention a few. In order to include consistently these features to describe more accurately the thickness of the electrical double layer of an inhomogeneous charged fluid in planar geometry, we propose here the use of the capacitive compactness concept as a generalization of the compactness of the spherical electrical double layer around a small macroion (González-Tovar et al., J. Chem. Phys. 2004, 120, 9782). To exemplify the usefulness of the capacitive compactness to characterize strongly coupled charged fluids in external electric fields, we use integral equations theory and Monte Carlo simulations to analyze the electrical properties of a model molten salt near a planar electrode. In particular, we study the electrode's charge neutralization, and the maximum inversion of the net charge per unit area of the electrode-molten salt system as a function of the ionic concentration, and the electrode's charge. The behaviour of the associated capacitive compactness is interpreted in terms of the charge neutralization capacity of the highly correlated charged fluid, which evidences a shrinking/expansion of the electrical double layer at a microscopic level. The capacitive compactness and its first two derivatives are expressed in terms of experimentally measurable macroscopic properties such as the differential and integral capacity, the electrode's surface charge density, and the mean electrostatic potential at the electrode's surface.

Electrolyte-induced Instability of Colloidal Dispersions in Nonpolar Solvents

Dispersions of poly(methyl methacrylate) (PMMA) latexes were prepared in a low dielectric, nonpolar solvent (dodecane) both with and without the oil-soluble electrolyte, tetradodecylammonium-tetrakis(3,5-bis(trifluoromethyl)phenyl)borate. For dispersions with a high concentration of background electrolyte, the latexes become colloidally unstable and sediment in a short period of time (<1 h). This is completely reversible upon dilution. Instability of the dispersions is due to an apparent attraction between the colloids, directly observed using optical tweezers by bringing optically trapped particles into close proximity. Simple explanations generally used by colloid scientists to explain loss of stability (charge screening or stabilizer collapse) are insufficient to explain this observation. This unexpected interaction seems, therefore, to be a consequence of the materials that can be dispersed in low dielectric media and is expected to have ramifications for studying colloids in such solvents.