Crystallization and reentrant melting of charged colloids in nonpolar solvents

Charge regulation of nanoparticles in the presence of multivalent electrolytes

We explore the charge regulation (CR) of spherical nanoparticles immersed in an asymmetric electrolyte of a specified pH. Using a recently developed reactive canonical Monte Carlo (MC) simulation method, titration isotherms are obtained for suspensions containing monovalent, divalent, and trivalent coions. A theory based on the modified Poisson-Boltzmann approximation, which incorporates the electrostatic ion solvation free energy and discrete surface charge effects, is used to compare with the simulation results. A remarkably good agreement is found without any fitting parameters, both for the ion distributions and titration curves, suggesting that ionic correlations between coions and hydronium ions at the nanoparticle surface play only a minor role in determining the association equilibrium between hydroniums and the functional sites on the nanoparticle surface. On the other hand, if suspension contains multivalent counterions, we observe a large deviation between theory and simulations, showing that the electrostatic correlations between counterions and hydronium ions at the nanoparticle surface are very significant and must be properly taken into account to correctly describe CR for such solutions.

Colloidal Crystals of Charged-Polymer-Brush-Decorated Hybrid Particles in Low-Polarity Solvents

Colloidal crystals are self-assembled systems that are suitable as models for studying crystallization; they are also attractive as nanostructures with a periodic arrangement of materials that have different refractive indices. Here, we present a method of constructing colloidal crystals in an organic solvent using charged-polymer-brush-decorated core-shell-type hybrid particles synthesized by surface-initiated living radical polymerization. The core-shell-type hybrid particles consisted of a silica particle core surrounded by a shell of polymer brushes obtained by the polymerization of methyl methacrylate and a small amount of a cationic monomer, [2-(methacryloyloxy)ethyl]trimethylammonium chloride. When the core-shell-type hybrid particles were dispersed in a low-polarity solvent with a dielectric constant of ∼11, colloidal crystals formed when the particle volume fraction exceeded a certain threshold, and remarkably, the interparticle distance in the colloidal crystal reached more than several micrometers under certain colloidal crystallization conditions. The colloidal crystallization behavior depended upon the surface charge density of the hybrid particles, ionic strength of the suspension, and dielectric constant of the solvent. The proposed method to construct colloidal crystals using electrostatic interactions between charged polymer brushes will promote the development of systems exhibiting particle self-assembly.

Aggregation behavior of nanoparticles: Revisiting the phase diagram of colloids

Surface functionalization of metal nanoparticles (NPs), e.g., using peptides and proteins, has recently attracted a considerable attention in the field of design of therapeutics and diagnostics. The possibility of diverse functionalization allows them to selectively interact with proteins, while the metal core ensures solubility, making them tunable therapeutic agents against diseases due to mis-folding or aggregation. On the other hand, their action is limited by possible self-aggregation, which could be, however, prevented based on the full understanding of their phase diagram as a function of the environmental variables (temperature, ionic strength of the solution, concentration) and intrinsic characteristics (size, charge, amount, and type of functional groups). A common modeling strategy to study the phase behavior is to represent the NPs as spheres interacting via effective potentials implicitly accounting for the solvation effects. Their size put the NPs into the class of colloids, albeit with particularly complex interactions including both attractive and repulsive features, and a consequently complex phase diagram. In this work, we review the studies exploring the phases of these systems starting from those with only attractive or repulsive interactions, displaying a simpler disperse-clustered-aggregated transitions. The phase diagram is here interpreted focusing on the universal aspects, i.e., those dependent on the general feature of the potentials, and available data are organized in a parametric phase diagram. We then consider the potentials with competing attractive short range well and average-long-range repulsive tail, better representing the NPs. Through the proper combination of the attractive only and repulsive only potentials, we are able to interpret the appearance of novel phases, characterized by aggregates with different structural characteristics. We identify the essential parameters that stabilize the disperse phase potentially useful to optimize NP therapeutic activity and indicate how to tune the phase behavior by changing environmental conditions or the NP chemical–physical properties.

Revealing thermally-activated nucleation pathways of diffusionless solid-to-solid transition

Solid-to-solid transitions usually occur via athermal nucleation pathways on pre-existing defects due to immense strain energy. However, the extent to which athermal nucleation persists under low strain energy comparable to the interface energy, and whether thermally-activated nucleation is still possible are mostly unknown. To address these questions, the microscopic observation of the transformation dynamics is a prerequisite. Using a charged colloidal system that allows the triggering of an fcc-to-bcc transition while enabling in-situ single-particle-level observation, we experimentally find both athermal and thermally-activated pathways controlled by the softness of the parent crystal. In particular, we reveal three new transition pathways: ingrain homogeneous nucleation driven by spontaneous dislocation generation, heterogeneous nucleation assisted by premelting grain boundaries, and wall-assisted growth. Our findings reveal the physical principles behind the system-dependent pathway selection and shed light on the control of solid-to-solid transitions through the parent phase's softness and defect landscape.

Point defects in crystals of charged colloids

Charged colloidal particles-on both the nano and micron scales-have been instrumental in enhancing our understanding of both atomic and colloidal crystals. These systems can be straightforwardly realized in the lab and tuned to self-assemble into body-centered-cubic (BCC) and face-centered-cubic (FCC) crystals. While these crystals will always exhibit a finite number of point defects, including vacancies and interstitials-which can dramatically impact their material properties-their existence is usually ignored in scientific studies. Here, we use computer simulations and free-energy calculations to characterize vacancies and interstitials in FCC and BCC crystals of point-Yukawa particles. We show that, in the BCC phase, defects are surprisingly more common than in the FCC phase, and the interstitials manifest as so-called crowdions: an exotic one-dimensional defect proposed to exist in atomic BCC crystals. Our results open the door to directly observe these elusive defects in the lab.

Stiffness of the interface between a colloidal body-centered cubic crystal and its liquid

Equilibrium interfaces were established between body-centered cubic (BCC) crystals and their liquid using charged colloidal particles in an electric bottle. By measuring a time series of interfacial positions and computing the average power spectrum, their interfacial stiffness was determined according to the capillary fluctuation method. For the (100) and the (114) interfaces, the stiffnesses were 0.15 and 0.18 [Formula: see text] (σ: particle diameter), respectively, and were isotropic in the plane of the interface. For comparison, similar charged colloids were used to create an interface between a face-centered cubic (FCC) crystal and its liquid. Its stiffness was significantly larger: 0.26 [Formula: see text] This result gives experimental support to the explanations offered for the preferential nucleation of BCC over FCC in metallic alloys.

Colloids in rotating electric and magnetic fields: designing tunable interactions with spatial field hodographs

Opening a way to designing tunable interactions between colloidal particles in rotating electric and magnetic fields provides rich opportunities both for fundamental studies of phase transitions and engineering of soft materials. Spatial hodographs, showing the distribution of the field magnitude and orientation, allow the adjustment of interactions and can be an extremely potent tool for prospective experiments, but remain unstudied systematically. Here, we calculate the tunable interactions between spherical particles in rhodonea, conical, cylindrical, and ellipsoidal field hodographs, as the most experimentally important cases. We discovered that spatial hodographs are reduced to each other, providing a plethora of interactions, e.g., repulsive, attractive, barrier-like, and double-scale repulsive ones. Complementing the "magic" conical angle, the "magic" compression and ellipticity of cylindrical and ellipsoidal hodographs are introduced. In the "magic" hodographs, the interactions become spatially isotropic and attain dispersion-force-like asymptotic (the same for pairwise and many-body energies), being attractive or repulsive, if the particle permittivity is larger or smaller than that of the solvent. With the diagrammatic method and numerical calculations, we obtained physically meaningful fits to the many-body tunable potentials for silica (iron oxide) particles in deionised water in the rotating electric (magnetic) fields. Our results provide essential guidance for future experiments and simulations of colloidal liquids, crystals, gels, and glasses, important for a broad range of problems in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Direct observation of crystallization and melting with colloids

We study the kinetics of crystal growth and melting of two types of colloidal crystals: body-centered cubic (BCC) crystals and face-centered cubic (FCC) crystals. A dielectrophoretic "electric bottle" confines colloids, enabling precise control of the motion of the interface. We track the particle motion, and by introducing a structural order parameter, we measure the jump frequencies of particles to and from the crystal and determine from these the free-energy difference between the phases and the interface mobility. We find that the interface is rough in both BCC and FCC cases. Moreover, the jump frequencies correspond to those expected from the random walk of the particles, which translates to collision-limited growth in metallic systems. The mobility of the BCC interface is greater than that of the FCC interface. In addition, contrary to the prediction of some early computer simulations, we show that there is no significant asymmetry between the mobilities for crystallization and melting.

Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations

Glasses are among the most widely used of everyday materials, yet the process by which a liquid's viscosity increases by 14 decades to become a glass remains unclear, as often contradictory theories provide equally good descriptions of the available data. Knowledge of emergent lengthscales and higher-order structure could help resolve this, but this requires time-resolved measurements of dense particle coordinates-previously only obtained over a limited time interval. Here we present an experimental study of a model colloidal system over a dynamic window significantly larger than previous measurements, revealing structural ordering more strongly linked to dynamics than previously found. Furthermore we find that immobile regions and domains of local structure grow concurrently with density, and that these regions have low configurational entropy. We thus show that local structure plays an important role at deep supercooling, consistent with a thermodynamic interpretation of the glass transition rather than a principally dynamic description.

Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids

The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.

Charge regulation of nonpolar colloids

Individual colloids often carry a charge as a result of the dissociation (or adsorption) of weakly-ionized surface groups. The magnitude depends on the precise chemical environment surrounding a particle, which in a concentrated dispersion is a function of the colloid packing fraction η. Theoretical studies have suggested that the effective charge Z_eff in regulated systems could, in general, decrease with increasing η. We test this hypothesis for nonpolar dispersions by determining Z_eff(η) over a wide range of packing fractions (10^-5 ≤ η ≤ 0.3) using a combination of small-angle X-ray scattering and electrophoretic mobility measurements. All dispersions remain entirely in the fluid phase regime. We find a complex dependence of the particle charge as a function of the packing fraction, with Z_eff initially decreasing at low concentrations before finally increasing at high η. We attribute the non-monotonic density dependence to a crossover from concentration-independent screening at low η, to a high packing fraction regime in which counterions outnumber salt ions and electrostatic screening becomes η-dependent. The efficiency of charge stabilization at high concentrations may explain the unusually high stability of concentrated nanoparticle dispersions which has been reported.

Charging Poly(methyl Methacrylate) Latexes in Nonpolar Solvents: Effect of Particle Concentration

The electrophoresis of a well-established model system of charged colloids in nonpolar solvents has been studied as a function of particle volume fraction at constant surfactant concentration. Dispersions of poly(12-hydroxystearic acid)-stabilized poly(methyl methacrylate) (PMMA) latexes in dodecane were prepared with added Aerosol OT surfactant as the charging agent. The electrophoretic mobility (μ) of the PMMA latexes is found to decrease with particle concentration. The particles are charged by a small molecule charging agent (AOT) at finite concentration, and this makes the origin of this decrease in μ unclear. There are two suggested explanations. The decrease could either be due to the reservoir of available surfactant being exhausted at high particle concentrations or the interactions between the charged particles at high particle number concentrations. Contrast-variation small-angle neutron scattering measurements of PMMA latexes and deuterated AOT-d₃₄ surfactant in latex core contrast-matched solvent were used to study the former, and electrokinetic modeling was used to study the latter. As the same amount of AOT-d₃₄ is found to be incorporated with the latexes at all volume fractions, the solvodynamic and electrical interactions between particles are determined to be the explanation for the decrease in mobility. These measurements show that, for small latexes, there are interactions between the charged particles at all accessible particle volume fractions and that it is necessary to account for this to accurately determine the electrokinetic ζ potential.

Crystallization, Reentrant Melting, and Resolubilization of Virus Nanoparticles

Crystallization is a fundamental and ubiquitous process that is well understood in the case of atoms or small molecules, but its outcome is still hard to predict in the case of nanoparticles or macromolecular complexes. Controlling the organization of virus nanoparticles into a variety of 3D supramolecular architectures is often done by multivalent ions and is of great interest for biomedical applications such as drug or gene delivery and biosensing, as well as for bionanomaterials and catalysis. In this paper, we show that slow dialysis, over several hours, of wild-type Simian Virus 40 (wt SV40) nanoparticle solution against salt solutions containing MgCl₂, with or without added NaCl, results in wt SV40 nanoparticles arranged in a body cubic center crystal structure with Im3m space group, as a thermodynamic product, in coexistence with soluble wt SV40 nanoparticles. The nanoparticle crystals formed above a critical MgCl₂ concentrations. Reentrant melting and resolubilization of the virus nanoparticles took place when the MgCl₂ concentrations passed a second threshold. Using synchrotron solution X-ray scattering we determined the structures and the mass fraction of the soluble and crystal phases as a function of MgCl₂ and NaCl concentrations. A thermodynamic model, which balances the chemical potentials of the Mg²⁺ ions in each of the possible states, explains our observations. The model reveals the mechanism of both the crystallization and the reentrant melting and resolubilization and shows that counterion entropy is the main driving force for both processes.

Doping colloidal bcc crystals - interstitial solids and meta-stable clusters

The addition of a small amount of dopant impurities to crystals is a common method to tune the properties of materials. Usually the doping grade is restricted by the low solubility of the dopants; increasing the doping concentration beyond this solubility limit leads to supersaturated solutions in which dopant clusters dominate the material properties, often leading to deterioration of strength and performance. Descriptions of doped solids often assume that thermal excitations of the on average perfect matrix are small. However, especially for bcc crystals close to their melting point it has recently become clear that the effects of thermal disorder are strong. Here we study the doping of weak bcc crystals of charged colloids via Brownian dynamics simulations. We find a complex phase diagram upon varying the dopant concentration. At low dopant concentrations we find an interstitial solid solution. As we increase the amount of dopants a complex meta-stable liquid-in-solid cluster phase emerges. Ultimately this phase becomes meta-stable with respect to macroscopic crystal-crystal coexistence. These results illustrate the complex behaviour that emerges when thermal excitations of the matrix drive impure crystals to a weak state.

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

At the triple point of a repulsive screened Coulomb system, a fcc crystal, a bcc crystal, and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single-particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.

Direct Observation of Entropic Stabilization of bcc Crystals Near Melting

Crystals with low latent heat are predicted to melt from an entropically stabilized body-centered cubic symmetry. At this weakly first-order transition, strongly correlated fluctuations are expected to emerge, which could change the nature of the transition. Here we show how large fluctuations stabilize bcc crystals formed from charged colloids, giving rise to strongly power-law correlated heterogeneous dynamics. Moreover, we find that significant nonaffine particle displacements lead to a vanishing of the nonaffine shear modulus at the transition. We interpret these observations by reformulating the Born-Huang theory to account for nonaffinity, illustrating a scenario of ordered solids reaching a state where classical lattice dynamics fail.

Anomalous dynamics of interstitial dopants in soft crystals

The dynamics of interstitial dopants govern the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically stabilized body-centered cubic (BCC) crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localized and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: (i) The instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and (ii) elastic interactions cause strong dopant-dopant interactions even at low doping fractions. These results illustrate how describing nonclassical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopant-dopant interactions into account.

Photo-Crosslinkable Colloids: From Fluid Structure and Dynamics of Spheres to Suspensions of Ellipsoids

Recently-developed photo-crosslinkable PMMA (polymethylmethacrylate) colloidal spheres are a highly promising system for fundamental studies in colloidal physics and may have a wide range of future technological applications. We synthesize these colloids and characterize their size distribution. Their swelling in a density- and index- matching organic solvent system is demonstrated and we employ dynamic light scattering (DLS), as also the recently-developed confocal differential dynamic microscopy (ConDDM), to characterize the structure and the dynamics of a fluid bulk suspension of such colloids at different particle densities, detecting significant particle charging effects. We stretch these photo-crosslinkable spheres into ellipsoids. The fact that the ellipsoids are cross-linked allows them to be fluorescently stained, permitting a dense suspension of ellipsoids, a simple model of fluid matter, to be imaged by direct confocal microscopy.

Tuning Colloid-Interface Interactions by Salt Partitioning

We show that the interaction of an oil-dispersed colloidal particle with an oil-water interface is highly tunable from attractive to repulsive, either by varying the sign of the colloidal charge via charge regulation or by varying the difference in hydrophilicity between the dissolved cations and anions. In addition, we investigate the yet unexplored interplay between the self-regulated colloidal surface charge distribution with the planar double layer across the oil-water interface and the spherical one around the colloid. Our findings explain recent experiments and have direct relevance for tunable Pickering emulsions.

Alternating strings and clusters in suspensions of charged colloids

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.

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

A thermodynamically equilibrated fluid of hard spheroids is a simple model of liquid matter. In this model, the coupling between the rotational degrees of freedom of the constituent particles and their translations may be switched off by a continuous deformation of a spheroid of aspect ratio t into a sphere (t=1). We demonstrate, by experiments, theory, and computer simulations, that dramatic nonanalytic changes in structure and thermodynamics of the fluids take place, as the coupling between rotations and translations is made to vanish. This nonanalyticity, reminiscent of a second-order liquid-liquid phase transition, is not a trivial consequence of the shape of an individual particle. Rather, free volume considerations relate the observed transition to a similar nonanalyticity at t=1 in structural properties of jammed granular ellipsoids. This observation suggests a deep connection to exist between the physics of jamming and the thermodynamics of simple fluids.

Density-induced reentrant melting of colloidal Wigner crystals

By using projections of the colloid–ion mixture to a system of (soft) repulsive spheres and the one-component plasma, we explain the experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density.

Celebrating Soft Matter's 10th Anniversary: Influencing the charge of poly(methyl methacrylate) latexes in nonpolar solvents

Sterically-stabilized poly(methyl methacrylate) (PMMA) latexes dispersed in nonpolar solvents are a classic, well-studied system in colloid science. This is because they can easily be synthesized with a narrow size distribution and because they interact essentially as hard spheres. These PMMA latexes can be charged using several methods (by adding surfactants, incorporating ionizable groups, or dispersing in autoionizable solvents), and due to the low relative permittivity of the solvents (εr ≈ 2 for alkanes to εr ≈ 8 for halogenated solvents), the charges have long-range interactions. The number of studies of these PMMA particles as charged species has increased over the past ten years, after few studies immediately following their discovery. A large number of variations in both the physical and chemical properties of the system (size, concentration, surfactant type, or solvent, as a few examples) have been studied by many groups. By considering the literature on these particles as a whole, it is possible to determine the variables that have an effect on the charge of particles. An understanding of the process of charge formation will add to understanding how to control charge in nonaqueous solvents as well as make it possible to develop improved technologically relevant applications for charged polymer nanoparticles.

Precise colloids with tunable interactions for confocal microscopy

Model colloidal systems studied with confocal microscopy have led to numerous insights into the physics of condensed matter. Though confocal microscopy is an extremely powerful tool, it requires a careful choice and preparation of the colloid. Uncontrolled or unknown variations in the size, density, and composition of the individual particles and interactions between particles, often influenced by the synthetic route taken to form them, lead to difficulties in interpreting the behavior of the dispersion. Here we describe the straightforward synthesis of copolymer particles which can be refractive index- and density-matched simultaneously to a non-plasticizing mixture of high dielectric solvents. The interactions between particles are accurately tuned by surface grafting of polymer brushes using Atom Transfer Radical Polymerization (ATRP), from hard-sphere-like to long-ranged electrostatic repulsion or mixed charge attraction. We also modify the buoyant density of the particles by altering the copolymer ratio while maintaining their refractive index match to the suspending solution resulting in well controlled sedimentation. The tunability of the inter-particle interactions, the low volatility of the solvents, and the capacity to simultaneously match both the refractive index and density of the particles to the fluid opens up new possibilities for exploring the physics of colloidal systems.

Effective charges and virial pressure of concentrated macroion solutions

The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.