Long-range Repulsive Interactions Research Articles

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties.

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

Self-assembly of colloids with competing interactions confined in spheres.

At low temperatures, colloidal particles with short-range attractive and long-range repulsive interactions can form various periodic microphases in bulk. In this paper, we investigate the self-assembly behaviour of colloids with competing interactions under spherical confinement by conducting molecular dynamics simulations. We find that the cluster, mixture, cylindrical, perforated lamellar and lamellar structures can be obtained, but the details of the ordered structures are different from those in bulk systems. Interestingly, the system tends to form more perforated structures when confined in smaller spheres. The mechanism behind this phenomenon is driven by the relationship between the energy of the ordered structures and the bending of the confinement wall, which is different from the mechanism in copolymer systems.

Molecular Dynamics Analysis of Lithium-Ion Transport Properties in All-Solid-State Lithium-Ion Battery

Lithium-ion batteries have been widely used in electronic products since their commercialization, but the use of liquid electrolytes carries safety risks of electrolyte volatilization, leakage, and corrosion. Meanwhile, solid-state electrolytes have the advantage of high safety performance compared with liquid electrolytes. Therefore, all-solid-state Lithium-ion batteries has become a new research topic. LiNi x Co y Mn z O2 (NCM, x+y+z =1) material have been used as a representative ternary compound cathode material in Lithium-ion batteries. However, understanding the influencing conditions during the transport of Lithium ions in NCM materials is incomplete and difficult to observe experimentally. Therefore, our goal is to understand the factors influencing Lithium-ion transport properties. In this work, molecular dynamics (MD) simulations of NCM materials were used to analyze the transport properties of Lithium-ion.According to Wei's study, we created three patterns for transition metal alignment for LiNi0. 33Co0. 33Mn0. 33O2(NCM333). Then, MD simulations were performed for the three types of NCM333. The Lithium-ion transport properties are considered in different Lithium-ion content rate (100%, 88%, 77%, 66%, 55%, 44%, 33%, and 22%) which represent different state of charge (SOC). The occupied positions of Lithium-ion in the initial NCM structure were randomly constructed for different percentages of Lithium-ion content. According to Zhu's research, we used the Morse potential energy in the LAMMPS as the basis and added the corresponding Coulomb force and long-range repulsive interaction force. In the end, the potential model based on Morse-type interaction, Coulomb interaction and a long-range repulsive interaction were used. The size of the simulation box was 34.74 Å×29.72 Å×28.54 Å. The total number of atoms was 3456. The temperature of the system during the MD simulation was set at 300 K, the timestep was set at 1.0 fs, and the sampling interval for trajectories was 500 steps. To relax the system, a 0.5 ns NPT process was first applied. After 10 ns of NVT process was performed, the size of the simulation box at the final equilibrated state was compared with that of 100% Lithium-ion content. The results showed that the simulation box volume variation was less than 2% in all calculated Lithium-ion content. Radial distribution function (RDF) analysis was also performed using the same conditions, and the results were consistent with Lee's study. These two analyses confirmed the integrity of the structural NCM in the simulation.The mean-squared displacement (MSD) analysis was performed on the NCM333 material throughout the trajectories in the 10 ns NVT process. From the MSD data, all three patterns of NCM333 have very minimal Lithium-ion mean square displacement at 100% Lithium-ion content, and the values of Lithium-ion mean square displacement for each pattern were very close to each other, which was not only consistent with the structural properties of NCM333, but also with the Lee's study. In the simulation of Pattern 1 with different Lithium-ion contents, it can be seen that there was a more significant migration of lithium ions compared to 100% Lithium-ion content, which was also reflected in the mean square displacement data. The mean square displacement data at 88% Lithium-ion content was significantly smaller than those at 55% Lithium-ion content, but all rang of the mean square displacement data were much larger than those at 100% Lithium-ion content. Because at 100% Lithium-ion content, there was no vacancy around the Lithium-ion, so only vibrations occured. When the Lithium-ion content is less than 100%, vacancies appear, so the Lithium-ion occur in vibration and diffusion.The Lithium-ion diffusion coefficient was obtained by linear fitting the MSD data in the region of 2.5ns-5ns. The figure shows the Lithium-ion diffusion coefficients (DLi) of the NCM333 material for different Lithium-ion contents. As shown in the figure, the experimental value is 3.3x10-11cm2/s and the theoretical value of the Wei's study is 5x10-9cm2/s when the Lithium-ion content of NCM333 was 33%. Also the calculated value was approximately one hundredth times larger than the experimental, consistent with the Wei's study. The diffusion coefficient maximum peak exists around 50% Lithium-ion content, which was inconsistent with our prediction. Our predictions suggest that as the Lithium-ion content decreases, more vacancies will occur and therefore the DLi should increase. Further refinement and improvements will be considered to confirm these phenomena. Figure 1

Complexes of photosensitive surfactant and fluorescent dye for light-induced manipulation of colloids

Light-driven diffusioosmosis is a membrane-free method for manipulating colloidal ensembles at solid–liquid interfaces based on photo-sensitive molecules inducing fluid flows along solid surfaces. In this study, we present our findings on porous colloids settled at a solid wall in an aqueous solution comprising a photo-sensitive azobenzene-containing cationic surfactant and a cyanine-based dye, capable of ionically binding to each other. The surfactant acts as an activation agent for diffusioosmotic flow. When exposed to modulated light, it undergoes photo-isomerization from a hydrophobic trans-state to a more hydrophilic cis-state, creating a concentration gradient near the irradiated area of the wall. The resulting osmotic pressure gradient sets the flow in motion. Porous colloids actively participate in flow generation by readily incorporating the surfactant molecules in the trans-state and releasing them in the cis-state, creating a constant source of diffusioosmotic flow. Under UV illumination, an excess of cis-isomers near the porous colloids elicits long-range repulsive interactions, tenfold the diameter of a particle. The dye acts as a sensor for the surfactant filling or emptying the pores of the colloids. It forms a complex with the trans-isomer and diffuses into the pores, where photoisomerization to cis-state destroys the complex and causes both the dye and the surfactant to leave the pores, altering the luminescence brightness within the colloids. We demonstrated that the presence of the dye affects cis-trans isomer ratios of the surfactant at photo-stationary states, thereby influencing the process of diffusioosmosis. This process enables the manipulation of colloidal particles and remote control of the interaction potential between them, facilitating the formation of well-ordered surface aggregates.

Charge-driven liquid-crystalline behavior of ligand-functionalized nanorods in apolar solvent.

Concentrated colloidal suspensions of nanorods often exhibit liquid-crystalline (LC) behavior. The transition to a nematic LC phase, with long-range orientational order of the particles, is usually well-captured by Onsager's theory for hard rods, at least qualitatively. The theory shows how the volume fraction at the transition decreases with increasing aspect ratio of the rods. It also explains that the long-range electrostatic repulsive interaction occurring between rods stabilized by their surface charge can significantly increase their effective diameter, resulting in a decrease in the volume fraction at the transition, as compared to sterically stabilized rods. Here, we report on a system of ligand-stabilized LaPO4 nanorods, of aspect ratio ≈11, dispersed in apolar medium exhibiting the counter-intuitive observation that the onset of nematic self-assembly occurs at an extremely low volume fraction of ≈0.25%, which is lower than observed (≈3%) with the same particles when charged-stabilized in polar solvent. Furthermore, the nanorod volume fraction at the transition increases with increasing concentration of ligands, in a similar way as in polar media where increasing the ionic strength leads to surface charge screening. This peculiar system was investigated by dynamic light scattering, Fourier-transform infrared spectroscopy, zetametry, electron microscopy, polarized light microscopy, photoluminescence measurements, and X-ray scattering. Based on these experimental data, we formulate several tentative scenarios that might explain this unexpected phase behavior. However, at this stage, its full understanding remains a pending theoretical challenge. Nevertheless, this study shows that dispersing anisotropic nanoparticles in an apolar solvent may sometimes lead to spontaneous ordering events that defy our intuitive ideas about colloidal systems.

Aza-Favorsky reaction with regioisomeric C- and N-linked 1,4-bis(imino)benzenes: Synthetic and reactivity dissimilarities

Structurally analogous C- and N-linked 1,4-bis(imino)-functionalized benzenes react with acetylenes in the KOBut/ DMSO superbase system to give the corresponding bis-(propargylamino)-containing derivatives in 62–82% yields (C-linking) or 38–42% yields (N-linking). In the latter case, with phenylacetylene, the yields of mono- and bisadducts were 32 and 38%, respectively. The observed dissimilarities between both bisimine chemotypes in the reactivity and synthetic outcomes imply the long-range adverse repulsive interaction between nitrogen anionic center and the second nitrogen atom in the N-linked 1,4-bis(imino) benzenes.

Orientational Melting in a Mesoscopic System of Charged Particles.

A mesoscopic system of a few particles can undergo changes of configuration that resemble phase transitions but with a nonuniversal behavior. A notable example is orientational melting, in which localized particles with long-range repulsive interactions forming a two-dimensional crystal become delocalized in common closed trajectories. Here we report the observation of orientational melting occurring in a two-dimensional crystal of up to 15 ions. We measure density-density correlations to quantitatively characterize the occurrence of melting, and use a MonteCarlo simulation to extract the angular kinetic energy of the ions. By adding a pinning impurity, we demonstrate the nonuniversality of orientational melting and create novel configurations in which localized and delocalized particles coexist. Our system realizes an experimental testbed for studying changes of configurations in two-dimensional mesoscopic systems, and our results pave the way for the study of quantum phenomena in ensembles of delocalized ions.

Abnormally soft acoustic phonons in the Mg3Sb2 allomerisms

Softening modes in phonon dispersion are often indications of intriguing physical phenomena such as phase transition and exotic thermal conductance. The promising thermoelectric material Mg3Sb2 and its allomerisms including CaZn2Sb2, SrZn2Sb2, etc. are investigated for phonon dispersion variation in this study using density functional theory (DFT) calculations. Two different soft transverse acoustic (TA) modes are present in Mg3Sb2, one at the A point along the out-of-plane direction and the other at the in-plane M point with a lower frequency. In contrast, the in-plane TA modes of CaZn2Sb2 and SrZn2Sb2 exhibit much higher in energy, but they both have extremely soft TA modes at the A point instead. Here, we construct an oscillator model based on the projected interatomic force constant tensor along vibrational directions. Our results suggest that the disappearing shear interaction of the near-neighbor bond, tilted Mg–Sb plays a large role in the abnormally soft in-plane TA mode in Mg3Sb2. In contrast, the covalent vertical Zn–Sb bonds in CaZn2Sb2 and SrZn2Sb2 have also negligible shear interactions. In all cases, the “missing” nearest-neighbor interaction, combined with the weak next-neighbor interaction and repulsive long-range interaction result in the observed low-energy TA modes. Soft acoustic phonon is associated with lower thermal conductivity frequently. In general, we expect such in-depth analyses on the origin of these abnormally soft phonon modes in the Mg3Sb2 allomerisms would provide insights into seeking high-performance thermoelectric materials in the rich family of the Zintl phase compounds.

Photosensitive Spherical Polymer Brushes: Light-Triggered Process of Particle Repulsion

We report on a light-triggered process at which repulsive interactions between microparticles with a polyelectrolyte (PE) brush coating can be remotely controlled. The spherical polyelectrolyte brushes are loaded with photosensitive azobenzene containing surfactant which can undergo reversible photo-isomerization from trans to cis state. The surfactant hydrophilicity is altered by illumination with light of an appropriate wavelength, at which a dynamic exchange of the more surface-active trans isomer in comparison to the more water soluble cis isomer with the PE brush generates a concentration gradient of the cis isomers near a solid surface where the particle is sedimented. In this way, each spherical brush produces its local lateral diffusioosmotic flow pointing outside in a radial direction resulting in mutual long-range repulsive interactions. We demonstrate that a PE layer has a higher tendency to absorb surfactant in comparison to plain silica particles, yielding a larger flow strength. This correlation holds true up to a critical intensity, where the dynamic exchange is adsorption limited with respect to trans isomers and especially pronounced for the PE-coated particles.

Normal mode oscillations of anharmonically trapped nonlocal nonlinear kerr media

Normal mode oscillations of anharmonically confined, one-dimensional, nonlocal nonlinear kerr media with repulsive long-range interaction are investigated analytically and numerically. Variational approximation is used to analytically determine the center of mass and breathing (width) modes. Frequency shifts caused by quartic distortion of the exciting potential are shown to be amplified by the long-range repulsive interaction. Beating structure and higher harmonic modes are also revealed.

Modified Thirring model beyond the excluded-volume approximation

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a modified version of the Thirring model for self-gravitating systems with attractive and repulsive long-range interactions in which particles are treated as hard spheres in dimension d = 1, 2, 3. Equilibrium states of the model are studied under completely open conditions, in the unconstrained ensemble, by means of both Monte Carlo simulations and analytical methods and are compared with the corresponding states at fixed number of particles, in the isothermal-isobaric ensemble. Our theoretical description is performed for an arbitrary local equation of state, which allows us to examine the system beyond the excluded-volume approximation. The simulations confirm the theoretical prediction of the possible occurrence of first-order phase transitions in the unconstrained ensemble. This work contributes to the understanding of long-range interacting systems exchanging heat, work and matter with the environment.

Biomolecular Complexation on the "Wrong Side": A Case Study of the Influence of Salts and Sugars on the Interactions between Bovine Serum Albumin and Sodium Polystyrene Sulfonate.

In the protein purification, drug delivery, food industry, and biotechnological applications involving protein–polyelectrolyte complexation, proper selection of co-solutes and solution conditions plays a crucial role. The onset of (bio)macromolecular complexation occurs even on the so-called “wrong side” of the protein isoionic point where both the protein and the polyelectrolyte are net like-charged. To gain mechanistic insights into the modulatory role of salts (NaCl, NaBr, and NaI) and sugars (sucrose and sucralose) in protein–polyelectrolyte complexation under such conditions, interaction between bovine serum albumin (BSA) and sodium polystyrene sulfonate (NaPSS) at pH = 8.0 was studied by a combination of isothermal titration calorimetry, fluorescence spectroscopy, circular dichroism, and thermodynamic modeling. The BSA–NaPSS complexation proceeds by two binding processes (first, formation of intrapolymer complexes and then formation of interpolymer complexes), both driven by favorable electrostatic interactions between the negatively charged sulfonic groups (−SO3–) of NaPSS and positively charged patches on the BSA surface. Two such positive patches were identified, each responsible for one of the two binding processes. The presence of salts screened both short-range attractive and long-range repulsive electrostatic interactions between both macromolecules, resulting in a nonmonotonic dependence of the binding affinity on the total ionic strength for both binding processes. In addition, distinct anion-specific effects were observed (NaCl < NaBr < NaI). The effect of sugars was less pronounced: sucrose had no effect on the complexation, but its chlorinated analogue, sucralose, promoted it slightly due to the screening of long-range repulsive electrostatic interactions between BSA and NaPSS. Although short-range non-electrostatic interactions are frequently mentioned in the literature in relation to BSA or NaPSS, we found that the main driving force of complexation on the “wrong side” are electrostatic interactions.

Application of a Simple Short-Range Attraction and Long-Range Repulsion Colloidal Model toward Predicting the Viscosity of Protein Solutions.

Some hard-sphere colloidal models have been criticized for inaccurately predicting the solution viscosity of complex biological molecules like proteins. Competing short-range attractions and long-range repulsions, also known as short-range attraction and long-range repulsion (SALR) interactions, have been thought to affect the microstructure of a protein solution at low to moderate ionic strength. However, such interactions have been implicated primarily in causing phase transition, protein gelation, or reversible cluster formation, and their effect on protein solution viscosity change is not fully understood. In this work, we show the application of a hard-sphere colloidal model with SALR interactions toward predicting the viscosity of dilute to semi-dilute protein solutions. The comparison is performed for a globular-shaped albumin and Y-shaped therapeutic monoclonal antibody that are not explained by previous colloidal models. The model predictions show that it is the coupling between attractions and repulsions that gives rise to the observed experimental trends in solution viscosity as a function of pH, concentration, and ionic strength. The parameters of the model are obtained from measurements of the second virial coefficient and net surface charge/zeta-potential, without additional fitting of the viscosity.

Phase Separation in Systems of Interacting Active Brownian Particles

The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive interactions between particles and their associated macroscopic models, which are formally obtained using different coarse-graining methods. The macroscopic limits are integro-differential equations for the density in phase space (positions and orientations) of the particles and may include nonlinearities in both the diffusive and advective components. In contrast to passive particles, systems of active particles can undergo phase separation without any attractive interactions, a mechanism known as motility-induced phase separation (MIPS). We explore the onset of such a transition for each model in the parameter space of occupied volume fraction and P\'eclet number via a linear stability analysis and numerical simulations at both the microscopic and macroscopic levels. We establish that one of the models, namely the mean-field model which assumes long-range repulsive interactions, cannot explain the emergence of MIPS. In contrast, MIPS is observed for the remaining three models that assume short-range interactions that localize the interaction terms in space.

Repulsive Interactions of Eco-corona-Covered Microplastic Particles Quantitatively Follow Modeling of Polymer Brushes.

The environmental fate and toxicity of microplastic particles are dominated by their surface properties. In the environment, an adsorbed layer of biomolecules and natural organic matter forms the so-called eco-corona. A quantitative description of how this eco-corona changes the particles' colloidal interactions is still missing. Here, we demonstrate with colloidal probe-atomic force microscopy that eco-corona formation on microplastic particles introduces a compressible film on the surface, which changes the mechanical behavior. We measure single particle-particle interactions and find a pronounced increase of long-range repulsive interactions upon eco-corona formation. These force-separation characteristics follow the Alexander-de Gennes (AdG) polymer brush model under certain conditions. We further compare the obtained fitting parameters to known systems like polyelectrolyte multilayers and propose these as model systems for the eco-corona. Our results show that concepts of fundamental polymer physics, like the AdG model, also help in understanding more complex systems like biomolecules adsorbed to surfaces, i.e., the eco-corona.

Dual nature of magnetic nanoparticle dispersions enables control over short-range attraction and long-range repulsion interactions

Competition between attractive and repulsive interactions drives the formation of complex phases in colloidal suspensions. A major experimental challenge lies in decoupling independent roles of attractive and repulsive forces in governing the equilibrium morphology and long-range spatial distribution of assemblies. Here, we uncover the ‘dual nature’ of magnetic nanoparticle dispersions, particulate and continuous, enabling control of the short-range attraction and long-range repulsion (SALR) between suspended microparticles. We show that non-magnetic microparticles suspended in an aqueous magnetic nanoparticle dispersion simultaneously experience a short-range depletion attraction due to the particulate nature of the fluid in competition with an in situ tunable long-range magnetic dipolar repulsion attributed to the continuous nature of the fluid. The study presents an experimental platform for achieving in situ control over SALR between colloids leading to the formation of reconfigurable structures of unusual morphologies, which are not obtained using external fields or depletion interactions alone.

Revisiting Anderson-Higgs mechanism: application of Lieb-Schultz-Mattis theorem

We consider an electron model of superconductivity on a three-dimensional lattice where there are on-site attractive Hubbard interaction and long-range repulsive Coulomb interaction. It is claimed that fully gapped s-wave superconductivity within this model, if present, exhibits spontaneous translation symmetry breaking possibly related to a charge order. Our discussions are based on an application of the Lieb-Schultz-Mattis theorem under some physical assumptions. The inconsistency between the proposed supersolid and experiments can impose some constraints on a reasonable choice of a theoretical model.

Steric Interaction of Polyglycerol-Functionalized Detonation Nanodiamonds.

Detonation nanodiamonds have found numerous potential applications in a diverse array of fields such as biomedical imaging and drug delivery. Here, we systematically characterized non-functionalized and polyglycerol-functionalized detonation nanodiamond particles (DNPs) dispersed in aqueous suspensions at different ionic strengths (∼1.0 × 10-7 to 1.0 × 10-2 M) via dynamic light scattering and cryogenic transmission electron microscopy. For these colloidal suspensions, the total potential energies of interactions between a pair of DNPs were theoretically calculated using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory plus the fitting of the Boltzmann distribution to the interparticle spacing distribution of the colloidal DNPs. These investigations revealed that the non-functionalized DNPs are dispersed in aqueous media through the long-range (>10 nm) and weak (<7 kBT) electrical double-layer repulsive interaction, while the driving force on dispersion of polyglycerol-functionalized DNPs is mostly derived from the short-range (<2 nm) and strong (∼55 kBT) steric repulsive potential barrier generated by the polyglycerol. Moreover, our results show that the truly monodispersed and individually dispersed DNP colloids, forming no aggregates in aqueous suspensions, are available by both functionalizing DNPs by polyglycerol and increasing ionic strength of suspending media to ≳1.0 × 10-2 M.

Structural and Dynamical Behaviour of Colloids with Competing Interactions Confined in Slit Pores.

Systems with short-range attractive and long-range repulsive interactions can form periodic modulated phases at low temperatures, such as cluster-crystal, hexagonal, lamellar and bicontinuous gyroid phases. These periodic microphases should be stable regardless of the physical origin of the interactions. However, they have not yet been experimentally observed in colloidal systems, where, in principle, the interactions can be tuned by modifying the colloidal solution. Our goal is to investigate whether the formation of some of these periodic microphases can be promoted by confinement in narrow slit pores. By performing simulations of a simple model with competing interactions, we find that both the cluster-crystal and lamellar phases can be stable up to higher temperatures than in the bulk system, whereas the hexagonal phase is destabilised at temperatures somewhat lower than in bulk. Besides, we observed that the internal ordering of the lamellar phase can be modified by changing the pore width. Interestingly, for sufficiently wide pores to host three lamellae, there is a range of temperatures for which the two lamellae close to the walls are internally ordered, whereas the one at the centre of the pore remains internally disordered. We also find that particle diffusion under confinement exhibits a complex dependence with the pore width and with the density, obtaining larger and smaller values of the diffusion coefficient than in the corresponding bulk system.

Metal–Organic Superlattices Induced by Long-Range Repulsive Interactions on a Metal Surface

Chains of Na atoms and dicyanovinyl-quinquethiophene (DCV5T-Me2) molecules with ionic bonds form a superlattice on Au(111). Through a detailed analysis of the interchain distances obtained from scanning tunneling microscopy images at various molecular coverages, we found that the chain arrangement substantially deviates from a random distribution of noninteracting chains. Instead, the distribution of chain spacings provides evidence for the existence of an interchain long-range repulsive potential. Furthermore, the experimental results can be modeled by a repulsive potential with a 1/d distance dependence, characteristic of Coulomb interactions. Density functional theory calculations of free-standing molecular chains reveal a charge depletion at the periphery of the chains, which is attributed to the intrinsic polar property of the molecule and is responsible for the long-range repulsion.