Pair Of Colloids Research Articles

Strong-coupling effective-field theory for asymmetrically charged plates with counterions only.

We are interested in rationalizing the phenomenon of like-charge attraction between charged bodies, such as a pair of colloids, in the strong coupling regime. The two colloids are modelled as uniformly charged parallel plates, neutralized by mobile counterions. In an earlier work [Palaia etal., J. Phys. Chem. B 126, 3143 (2022)1520-610610.1021/acs.jpcb.2c00028], we developed an effective-field theory for symmetric plates, stemming from the ground-state description that holds at infinite couplings. Here, we generalize the approach to the asymmetric case, where the plates bear charges of the same sign, but of different values. In the symmetric situation, the mobile ions, which are localized in the vicinity of the two plates, share equally between both of them. Here, the sharing is nontrivial, depending both on the coupling parameter and the distance between the plates. We thus introduce a counterion occupation parameter that is determined variationally to ensure minimum of the free energy. The analytical results for the pressure as a function of the plate-plate distance d agree well with our Monte Carlo data, in a large interval of strong and intermediate coupling constants Ξ. We show in particular that within this description there exists a range of large distances at which the attractive pressure features a 1/d^{2} behavior.

Study of the precipitation trend of asphaltenes and waxes in crude oil using computational chemistry and statistical thermodynamics methods

Asphaltenes aggregation and waxes in petroleum were simulated considering five molecular structures containing functional groups: asphaltenes, resins, and non-polar hydrocarbons in a heavy oil crude. The properties of molecules were calculated using the density functional theory. The van der Waals constants associated with the pairwise interactions and the Hamaker constants for the dispersed phase (formed by asphaltenes and waxes) and the dispersion medium (created by non-polar hydrocarbons) were estimated. Sparse pass size as a function of its composition is calculated using Qyle groups and the Young–Laplace equation. We also assessed the potential colloidal pair corresponding to the interactions between the asphaltene and resin aggregates for different dispersion media, the attractive energies between the asphaltene molecules (−60 10–20 J ≈ ) are more than twice as high as the attractive energies concerning the rest of the molecules present ( × -30–10] 10–20 ≈ × J). It is predicted that attraction energy between the aggregates decreases with the increase of the presence of resin in the dispersed phase, This is explained by the fact that the increase in the concentration n of resin can lead to a decrease in the relative size d of the aggregates by up to 90 % (for n = 0.1, d = 0.1 and for n = 0.9, d = 0.1). This decrease in aggregate size is manifested in a theoretically calculated effective viscosity reduction of up to 50 %.

Direction-dependent dynamics of colloidal particle pairs and the Stokes-Einstein relation in quasi-two-dimensional fluids

Hydrodynamic interactions are important for diverse fluids, especially those with low Reynolds number such as microbial and particle-laden suspensions, and proteins diffusing in membranes. Unfortunately, while far-field (asymptotic) hydrodynamic interactions are fully understood in two- and three-dimensions, near-field interactions are not, and thus our understanding of motions in dense fluid suspensions is still lacking. In this contribution, we experimentally explore the hydrodynamic correlations between particles in quasi-two-dimensional colloidal fluids in the near-field. Surprisingly, the measured displacement and relaxation of particle pairs in the body frame exhibit direction-dependent dynamics that can be connected quantitatively to the measured near-field hydrodynamic interactions. These findings, in turn, suggest a mechanism for how and when hydrodynamics can lead to a breakdown of the ubiquitous Stokes-Einstein relation (SER). We observe this breakdown, and we show that the direction-dependent breakdown of the SER is ameliorated along directions where hydrodynamic correlations are smallest. In total, the work uncovers significant ramifications of near-field hydrodynamics on transport and dynamic restructuring of fluids in two-dimensions.

Coupling effect of solvent–colloid interaction on diffusivity and viscosity of colloidal hard-sphere suspensions: Statistical mechanical free-volume approach

Apart from describing the transport behaviors to a reliable accuracy, it remains as yet far from satisfactory to comprehend the explicit role of the solvent–colloid interaction on the diffusivity and viscosity of colloidal hard-sphere suspensions. Here, we exploit the free volume effect on the diffusivity and viscosity by means of statistical mechanics, which enables to express them in terms of the solvent–solvent, colloid–colloid, and solvent–colloid pair correlation functions as a function of the colloidal concentration. The agreement between the theory and experiment is found to be very good over the entire colloidal volume fraction ϕ investigated by experiment, i.e., up to ϕ∼0.60. The present theory predicts a crossover in the solvent effect on the diffusivity: Above ϕc=0.38, the solvent–colloid interaction enhances the diffusivity of the colloidal particles suspended therein, whereas below ϕc, it serves as a diffusion barrier against the particles.

Quantitative surface free energy with micro-colloid probe pairs.

Measurement of the surface free energy (SFE) of a material allows the prediction of its adhesion properties. Materials can have microscale or sub-microscale surface inhomogeneities, engineered or random, which affect the surface macroscopic behaviour. However, quantitative characterization of the SFE at such length scales remains challenging in view of the variety of instruments and techniques available, the poor knowledge of critical variables and parameters during measurements and the need for appropriate contact models to derive the SFE from the measurements. Failure to characterize adhesion correctly may result in defective components or lengthy process optimization costing billions to industry. Conversely, for planar and homogeneous surfaces, contact angle (CA) measurements are standardized and allow for calculating the SFE using for example the Owen-Wendt model, relying only on the properties of the probing liquids. As such, we assessed and report here a method to correlate quantitative measurements of force-distance curves made with an atomic force microscope (AFM) and with silica and polystyrene (PS) colloidal probe pairs, with quantitative CA measurements and CA-derived SFE values. We measured five surfaces (mica, highly oriented pyrolytic graphite, thermally grown silica on silicon, silicon, and silicon with a super-hydrophobic coating), ranging from hydrophilic to super-hydrophobic, and found an excellent classification of the AFM measurements when these are represented by a set of principal components (PCs), and when both silica and PS colloidal probes are considered together. A regression of the PCs onto the CA measurements allows recovery of the SFE at the length scale of the colloidal probes, which is here ca. 1 micron. We found that once the PC-regression model is built, test sets of only ten AFM force-distance curves are sufficient to predict the local SFE with the calibrated silica and PS colloidal probes.

Active responsive colloids coupled to different thermostats.

We introduce a model of active responsive colloids (ARCs) in which an internal degree of freedom (DoF) of a single colloidal particle is "activated" by coupling it to a different thermostat than for the translational DoFs. As for the responsive internal DoF, we consider specifically the size (diameter) of the spherical particles, which is confined by a harmonic parent potential being either entropic or energetic in nature. The ARCs interact via a repulsive Hertzian pair potential, appropriate to model hydrogels or elastic colloids, and are studied for various densities using Brownian dynamics simulations. We tune the internal activity in the nonequilibrium steady state by scanning through a wide range of internal temperatures, both smaller ("colder") and larger ("hotter") than the translational temperature. The results show a rich and intriguing behavior for the emergent property distributions, colloidal pair structure, and the diffusive translational dynamics controlled by the internal activity, substantially depending on whether the internal DoF moves in an entropic or energetic potential. We discuss theoretical thermal limits and phenomenological models which can explain some of the nonequilibrium trends qualitatively. Our study indicates that particle dynamical polydispersity as well as the structure and dynamics of dense macromolecular suspensions can be vastly tuned by internal activity in terms of internal "hot" or "cold" fluctuating states.

Electrostatic pair-interaction of nearby metal or metal-coated colloids at fluid interfaces.

In this paper, we theoretically study the electrostatic interaction between a pair of identical colloids with constant surface potentials sitting in close vicinity next to each other at the fluid interface. By employing a simplified yet reasonable model system, the problem is solved within the framework of classical density functional theory and linearized as well as nonlinear Poisson-Boltzmann (PB) theory. Apart from providing a sound theoretical framework generally applicable to any such problem, our novel findings, all of which contradict common beliefs, include the following: first, quantitative and qualitative differences between the interactions obtained within the linear and the nonlinear PB theories; second, the importance of the electrostatic interaction between the omnipresent three-phase contact lines in interfacial systems; and, third, the occurrence of an attractive electrostatic interaction between a pair of identical metal colloids. The unusual attraction we report largely stems from an attractive line interaction, which although scales linearly with the size of the particle can compete with the surface interactions and can be strong enough to alter the nature of the total electrostatic interaction. Our results should find applications in metal or metal-coated particle-stabilized emulsions where densely packed particle arrays are not only frequently observed but also sometimes required.

Translational and rotational dynamics of colloidal particles interacting through reacting linkers

Much work has studied effective interactions between micron-sized particles carrying linkers forming reversible, interparticle linkages. These studies allowed understanding the equilibrium properties of colloids interacting through ligand-receptor interactions. Nevertheless, understanding the kinetics of multivalent interactions remains an open problem. Here, we study how molecular details of the linkers, such as the reaction rates at which interparticle linkages form or break, affect the relative dynamics of pairs of cross-linked colloids. Using a simulation method tracking single binding and unbinding events between complementary linkers, we rationalize recent experiments and prove that particles' interfaces can move across each other while being cross-linked. We clarify how, starting from diffusing colloids, the dynamics become arrested when increasing the number of interparticle linkages or decreasing the reaction rates. Before getting arrested, particles diffuse through rolling motion. The ability to detect rolling motion will be useful to shed new light on host-pathogen interactions.

Stability of binary colloidal crystals immersed in a cholesteric liquid crystal.

In this paper, we model a number of both closed-packed and non-closed-packed crystals inside a cholesteric liquid crystal (LC) with different pitch values and nematic LC through the Landau-de Gennes free-energy method. We used binary boundary conditions (normal and planar anchoring) applied on the surface of colloids as we are interested in investigating the stability of binary crystals. The results indicate that body-centered-cubic (BCC) crystals have a lower-energy lattice defect structure than the diamond crystal, and the most energetically favorable BCC lattice can be formed in a cholesteric liquid crystal with a pitch value commensurate with the lattice spacing. Furthermore, it is shown that a pair of binary colloids can be self-assemble into a stable face-centered-cubic lattice structure inside a nematic LC, as it has the lowest energy comparing to diamond and BCC crystals.

Interactions, topology and photonic properties of liquid crystal colloids and dispersions

Liquid crystal-based colloids demonstrate new type of colloidal interaction between the particles, which is of elastic origin, has very long range and is extremely strong, with pair-binding elastic potential exceeding several thousands of kBT. This gives rise to novel and strong colloidal assembly mechanisms, which can be used to assemble 2D and 3D colloidal crystals. This mini-review discusses colloidal pair interaction mechanisms and topological aspects of colloidal interaction. Topological defects, which are responsible for elastic forces between colloidal particles show an amazing diversity of different structures, including colloidal entanglement, knotting and linking of particles. An introduction is given to dispersions of liquid crystal droplets in an immiscible fluid, which represent a new class of photonic micro-devices, including micro-lasers, micro-fibers and optical micro-cavities made of tuneable liquid crystals.

Effects of organic matter coatings on the mobility of goethite colloids in model sand and undisturbed soil

SummaryThe mobility of goethite (OMCG) colloids coated with organic matter was studied in goethite‐coated quartz sand and in undisturbed subsoil rich in natural coatings of iron oxide. Classic Derjaguin–Landau–Verwey–Overbeek (DLVO) interactions and DLVO extended by Lewis acid–base parameters (XDLVO) were estimated between colloids and goethite‐coated sand from zeta potentials and sessile drop contact angles. The OMCG colloids were retained completely in goethite‐coated sand, whereas preconditioning of the solid matrix with dissolved organic matter (DOM) enabled subsequent colloid transport. Zeta potential values showed that goethite‐coated sand was modified strongly by DOM preconditioning. The DLVO and XDLVO interactions were estimated for the pairs of OMCG colloids and for (i) quartz, (ii) goethite and (iii) organic matter‐coated goethite. Both DLVO approaches were able to predict general trends of colloid breakthrough. An exception was the XDLVO interaction for combination (iii), which showed short‐distance (<1.3 nm) repulsive interactions that were inconsistent with breakthrough behaviour. Analogous to OMCG colloid transport in the sand, DOM preconditioning was also the prerequisite for OMCG colloid transport in undisturbed subsoil. Total colloid breakthrough in the soil was less than in the sand, probably because of straining in pore throats and retention at air–water interfaces. We concluded that the DLVO and XDLVO approaches were in general capable of predicting trends of OMCG colloid mobility in goethite‐coated sand. We concluded further that the basic principles of OMCG colloid transport were transferrable from the simplified model system to the more complex natural system despite considerable differences in surface properties, pore structure and water content.Highlights How will organic matter (OM) coatings on the solid matrix affect mobility of iron oxide colloids? Effect of OM on mobility was assessed in simple model soil systems and in undisturbed soil. OM coatings modify properties of the solid matrix surface and are a prerequisite for colloid transport. Balances between OM transport, coating formation and decomposition control colloid mobility.

Topological defects in an unconfined nematic fluid induced by single and double spherical colloidal particles.

We present numerical solutions to the Landau-de Gennes free-energy model under the one-constant approximation for systems of single and double spherical colloidal particles immersed in an otherwise uniformly aligned nematic liquid crystal. A perfect homeotropic surface anchoring of liquid-crystal molecules on the spherical surface is considered. A large parameter space is carefully examined, including those in the free-energy model and those describing the dimer configurations and the background liquid-crystal orientation. The stability of the resulting liquid-crystal defects appearing in the neighborhood of the colloidal dimer pair is analyzed in light of the numerical results for their free energies. A number of scenarios are considered: a free dimer pair in a nematic fluid where the free-energy ground states are described in terms of a phase diagram, and a constrained dimer pair where the interparticle distance and the relative orientation of the distance vector to the nematic director can be manipulated. We pay particular attention to the nonsymmetric solutions, which yield several metastable defect states that can be observed in real systems. The high-precision numerical calculations are based on a spectral method, which is an enabling factor that allows us to compare the subtle difference in the free energies of different defect structures.

Ultrafast dynamics of ionic liquids in colloidal dispersion.

Ionic liquid (IL)-surfactant complexes have significance both in applications and fundamental research, but their underlying dynamics are not well understood. We apply polarization-controlled two-dimensional infrared spectroscopy (2D-IR) to study the dynamics of [BMIM][SCN]/surfactant/solvent model systems. We examine the effect of the choice of surfactants and solvent, and the IL-to-surfactant ratio (W-value), with a detailed analysis of the orientation and structural dynamics of each system. Different surfactants create very different environments for the entrapped ILs, ranging from a semi-static micro-environment to a fluxional environment that evolves even faster than the bulk IL. The oil-phase also clearly affects the microscopic dynamics. The anisotropy decay for entrapped ILs completes within 10 ps, which is similar to free thiocyanate ion in water, while a significant reorientation-induced spectral diffusion (RISD) effect is observed. The entrapped ionic liquid are highly dynamic for all W-values, and no core-shell structure is observed. We hypothesize that, instead of an ionic liquid-reverse micelle (IL-RM), the microscopic structure of this system is small colloidal dispersions or pairs of IL and surfactants. A detailed analysis of the polarization-controlled 2D-IR spectra of AOT system reveals a potential ion-exchange mechanism.

Magnetically actuated and controlled colloidal sphere-pair swimmer

Magnetically actuated swimming of microscopic objects has been attracting attention partly due to its promising applications in the bio-medical field and partly due to interesting physics of swimming in general. While colloidal particles that are free to move in fluid can be an attractive swimming system due it its simplicity and ability to assemble in situ, stability of their dynamics and the possibility of stable swimming behavior in periodically varying magnetic fields has not been considered. Dynamic behavior of two magnetically interacting colloidal particles subjected to rotating magnetic field of switching frequency is analyzed here and is shown to result in stable swimming without any stabilizing feedback. A new mechanism of swimming that relies only on rotations of the particles themselves and of the particle pair axis is found to dominate the swimming dynamics of the colloidal particle pair. Simulation results and analytical arguments demonstrate that this swimming strategy compares favorably to dragging the particles with an external magnetic force when colloidal particle sizes are reduced.

Critical Casimir interactions and colloidal self-assembly in near-critical solvents.

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly.

Poisson-Boltzmann study of the effective electrostatic interaction between colloids at an electrolyte interface

The effective electrostatic interaction between a pair of colloids, both of them located close to each other at an electrolyte interface, is studied by employing the full, nonlinear Poisson-Boltzmann (PB) theory within classical density functional theory. Using a simplified yet appropriate model, all contributions to the effective interaction are obtained exactly, albeit numerically. The comparison between our results and those obtained within linearized PB theory reveals that the latter overestimates these contributions significantly at short inter-particle separations. Whereas the surface contributions to the linear and the nonlinear PB results differ only quantitatively, the line contributions show qualitative differences at short separations. Moreover, a dependence of the line contribution on the solvation properties of the two adjacent fluids is found, which is absent within the linear theory. Our results are expected to enrich the understanding of effective interfacial interactions between colloids.

Modified Mason number for charged paramagnetic colloidal suspensions.

The dynamics of magnetorheological fluids have typically been described by the Mason number, a governing parameter defined as the ratio between viscous and magnetic forces in the fluid. For most experimental suspensions of magnetic particles, surface forces, such as steric and electrostatic interactions, can significantly influence the dynamics. Here we propose a theory of a modified Mason number that accounts for surface forces and show that this modified Mason number is a function of interparticle distance. We demonstrate that this modified Mason number is accurate in describing the dynamics of a rotating pair of paramagnetic colloids of identical or mismatched sizes in either high or low salt solutions. The modified Mason number is confirmed to be pseudoconstant for particle pairs and particle chains undergoing a stable-metastable transition during rotation. The interparticle distance term can be calculated using theory or can be measured experimentally. This modified Mason number is more applicable to magnetorheological systems where surface forces are not negligible.

Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions.

The self-assembly of nanoparticles can enable the generation of composites with predesigned properties, but reproducing the structural diversity of atomic and molecular crystals remains a challenge. We combined anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. The orientations of the nanocrystals, as well as the crystallographic axes of the ensuing triclinic colloidal crystals, are coupled to the uniform alignment direction of the nematic host, which can be readily controlled on large scales. We examine colloidal pair and many-body interactions and show how triclinic crystals with orientational ordering of the semiconductor nanorods emerge from competing long-range elastic and electrostatic forces.

Positioning colloids at the surfaces of cholesteric liquid crystal droplets.

We report on the internal configurations of aqueous dispersions of droplets of cholesteric liquid crystals (LCs; 5-50 μm-in-diameter; comprised of 4-cyano-4'-pentylbiphenyl and 4-(1-methylheptyloxycarbonyl)phenyl-4-hexyloxybenzoate) and their influence on the positioning of surface-adsorbed colloids (0.2 or 1 μm-in-diameter polystyrene (PS)). When N = 2D/P was less than 4, where D is the droplet diameter and P is the cholesteric pitch, the droplets adopted a twisted bipolar structure (TBS) and colloids were observed to assume positions at either the poles or equator of the droplets. A statistical analysis of the distribution of locations of the colloids revealed a potential well of depth 2.7 kBT near the equator, a conclusion that was supported by computer simulations performed via the minimization of the Landau-de Gennes free energy (well depth of 7 kBT from simulation). In contrast, for N > 4, a majority of the droplets exhibited a radial spherical structure (RSS) characterized by a pair of closely spaced surface defects (angle of separation with respect to the center of the droplet θ < 5°) connected by a disclination winding to/from the droplet center, which led to the positioning of pairs of colloids with well-defined spacing at these surface defects. The separation of the pairs of surface-adsorbed colloids was colloid size-dependent, ranging from 1.11 ± 0.04 μm for 1 μm-in-diameter colloids to 1.7 ± 0.2 μm for 200 nm-in-diameter colloids. We also observed long-lived metastable configurations in which the two surface point defects were separated by much larger distances (corresponding to populations with angles of θ = 20 ± 10° and 85 ± 10° with respect to the center), and observed these pairs of defects to also position pairs of colloids. A third configuration, the diametrical spherical structure (DSS) was also observed. Consistent with the predictions of computer simulations, we found experimentally that the DSS is indeed composed of disconnected defect rings positioned along the diameter of the droplet. Overall, these results reveal that the rich palette of defects exhibited by confined cholesteric LC systems (equilibrium and metastable) provide the basis of a versatile class of templates that enable the surface positioning of colloids in ways that are not possible with achiral LC droplets.

Coarse-grained treatment of the self-assembly of colloids suspended in a nematic host phase.

The complex interplay of molecular scale effects, nonlinearities in the orientational field and long-range elastic forces makes liquid-crystal physics very challenging. A consistent way to extract information from the microscopic, molecular scale up to the meso- and macroscopic scale is still missing. Here, we develop a hybrid procedure that bridges this gap by combining extensive Monte Carlo (MC) simulations, a local Landau-de Gennes theory, classical density functional theory, and finite-size scaling theory. As a test case to demonstrate the power and validity of our novel approach we study the effective interaction among colloids with Boojum defect topology immersed in a nematic liquid crystal. In particular, at sufficiently small separations colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about 30°. Using the effective potential in coarse-grained two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.