Repulsive Pair Potential Research Articles

A colloidal model for the equilibrium assembly and liquid-liquid phase separation of the reflectin A1 protein

Reflectin is an intrinsically disordered protein known for its ability to modulate the biophotonic camouflage of cephalopods based on its assembly-induced osmotic properties. Its reversible self-assembly into discrete, size-controlled clusters and condensed droplets are known to depend sensitively on the net protein charge, making reflectin stimuli-responsive to pH, phosphorylation, and electric fields. Despite considerable efforts to characterize this behavior, the detailed physical mechanisms of reflectin’s assembly are not yet fully understood. Here, we pursue a coarse-grained molecular understanding of reflectin assembly using a combination of experiments and simulations. We hypothesize that reflectin assembly and phase behavior can be explained from a remarkably simple colloidal model whereby individual protein monomers effectively interact via a short-range attractive and long-range repulsive (SA-LR) pair potential. We parameterize a coarse-grained SA-LR interaction potential for reflectin A1 from small-angle x-ray scattering measurements, and then extend it to a range of pH values using Gouy-Chapman theory to model monomer-monomer electrostatic interactions. The pH-dependent SA-LR interaction is then used in molecular dynamics simulations of reflectin assembly, which successfully capture a number of qualitative features of reflectin, including pH-dependent formation of discrete-sized nanoclusters and liquid-liquid phase separation at high pH, resulting in a putative phase diagram for reflectin. Importantly, we find that at low pH size-controlled reflectin clusters are equilibrium assemblies, which dynamically exchange protein monomers to maintain an equilibrium size distribution. These findings provide a mechanistic understanding of the equilibrium assembly of reflectin, and suggest that colloidal-scale models capture key driving forces and interactions to explain thermodynamic aspects of native reflectin behavior. Furthermore, the success of SA-LR interactions presented in this study demonstrates the potential of a colloidal interpretation of interactions and phenomena in a range of intrinsically disordered proteins.

Interacting many-particle systems in the random Kac–Luttinger model and proof of Bose–Einstein condensation

Following a model originally considered by Kac and Luttinger, we study interacting many-particle systems in a random background. The background consists of hard spherical obstacles with fixed radius and that are distributed via a Poisson point process with constant intensity on Rd, 2≤d∈N. Interactions among the (bosonic) particles are described through repulsive pair potentials of mean-field type. As a main result, we prove (complete) Bose–Einstein condensation (BEC) in the thermodynamic limit and into the minimizer of a Hartree-type functional, in probability or with probability almost one depending on the strength of the interaction. As an important ingredient, we use very recent results obtained by Alain-Sol Sznitman regarding the spectral gap of the Dirichlet Laplacian in a Poissonian cloud of hard spherical obstacles in large boxes. To the best of our knowledge, our paper provides the first proof of BEC for systems of interacting particles in the Kac–Luttinger model, or in fact for some higher-dimensional interacting random continuum model.

Direct measurement of repulsive and attractive pair potentials using pairs of optical traps

We present a technique for measuring the interactions between pairs of colloidal particles in two optical traps. This method is particularly suitable for measuring strongly attractive potentials, an otherwise challenging task. The interaction energy is calculated from the distribution of inter-particle separations by accounting for the contribution from the optical traps with arbitrary trap profiles. The method is simple to implement and applicable to different types of pair potentials and optical trapping geometries. We apply the method to measure dipolar pair interactions in experiments with paramagnetic colloids in external magnetic fields. We obtain consistent and accurate results in all regimes, from strongly attractive to repulsive potentials. By means of computer simulations, we demonstrate that the proposed method can be successfully applied to systems with complex pair interactions characterized by multiple attractive and repulsive regimes, which are ubiquitous in soft and biological matter.

Structural transition, orientational order, and anomalous specific heat in a two-dimensional dimer crystal of core-softened particles.

Systems featuring hard-core-soft-shell repulsive pair potentials can form ordered phases, where particles organize themselves in aggregates with nontrivial geometries. The dimer crystal formed by one such potential, namely, the hard-core plus generalized exponential model of order 4, has been recently investigated, revealing a low-temperature structural phase transition, with the onset of nematic ordering of the dimers. In the present work, we aim to characterize this phase transition via a mean-field theory, by which a detailed analysis of the low-temperature properties of the system is carried out under quadrupole approximation. We determine the transition temperature and identify its order parameter, highlighting the link between the structural transition and the nematic ordering of the system. The first-order character of the transition is established and supported by the Landau expansion of the free energy in powers of the order parameter. The theory is subsequently generalized to take into account lattice vibrations and dimer length fluctuations. Finally, we provide an explanation for the anomalous behavior displayed by the specific heat in the vanishing-temperature limit, which is also supported by Monte Carlo simulations.

Colloidal Stability of PFSA-Ionomer Dispersions Part II: Determination of Suspension pH Using Single-Ion Potential Energies.

Perfluorosulfonic acid (PFSA) ionomers serve a vital role in the performance and stability of fuel-cell catalyst layers. These properties, in turn, depend on the colloidal processing of precursor inks. To understand the colloidal structure of fuel-cell catalyst layers, we explore the aggregation of PFSA ionomers dissolved in water/alcohol solutions and relate the predicted aggregation to experimental measurements of solution pH. Not all side chains contribute to measured pH because of burying inside particle aggregates. To account for the measured degree of dissociation, a new description is developed for how PFSA aggregates interact with each other. The developed single-counterion electrostatic repulsive pair potential from Part I is incorporated into the Smoluchowski collision-based kinetics of interacting aggregates with buried side chains. We demonstrate that the surrounding solvent mixture affects the degree of aggregation as well as the pH of the system primarily through the solution dielectric permittivity, which drives the strength of the interparticle repulsive energies. Successful pH prediction of Nafion ionomer dispersions in water/n-propanol solutions validates the numerical calculations. Nafion-dispersion pH measurements serve as a surrogate for Nafion particle-size distributions. The model and framework can be leveraged to explore different ink formulations.

Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances

Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances

On the analyticity of the pressure for a non-ideal gas with high density boundary conditions

We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.

Analyticity for Classical Gasses via Recursion

We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor $$e^2$$ over the classical cluster expansion approach and a factor e over the known limit of cluster expansion convergence. The criterion is based on a contractive property of a recursive computation of the density of a point process. The key ingredients in our proofs include an integral identity for the density of a Gibbs point process and an adaptation of the algorithmic correlation decay method from theoretical computer science. We also deduce from our results an improved bound for analyticity of the pressure as a function of the density.

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.

Statistical correlations in quantum systems with explicit three-body interactions

Higher-order and pairwise statistical correlations are quantified via mutual information, in quantum systems consisting of three pairwise interacting oscillators, that are subjected to a three-body Gaussian type potential. Variational wave functions are used for these calculations. The correlation measures are calculated in both position and momentum space, to examine their dependence on the coupling strength and width of the three-body potential. Results are presented for both positive and negative three-body potentials, and attractive and repulsive two-body ones. Extremal points are observed when the pair and higher-order measures are examined as a function of the coupling strength for positive three-body potentials. This illustrates that the magnitudes of these statistical correlations can be adjusted with the strength of the three-body potential. Higher-order mutual information is positive-valued in momentum space and negative-valued in position space, in systems with attractive pair and positive three-body potentials. The interpretation is that synergistic interactions among the three particles are dominant in momentum space while the redundant (pairwise) ones prevail in position space. These behaviours are reversed in systems with repulsive pair potentials and negative three-body ones. The demeanour of the correlation measures with respect to the width of the Gaussian potential is also examined. The extremal points that are present as a function of the coupling strength, are more pronounced for broader potentials, while they disappear for narrower potentials. The positions of these extremal points move to smaller coupling strengths, as the potential narrows. Trends in the one-, two-, and three-variable Shannon entropies in these systems are also discussed.

The EXP pair-potential system. IV. Isotherms, isochores, and isomorphs in the two crystalline phases.

This paper studies numerically the solid phase of a system of particles interacting by the exponentially repulsive pair potential, which is a face-centered cubic (fcc) crystal at low densities and a body-centered cubic (bcc) crystal at higher densities [U. R. Pedersen et al., J. Chem. Phys. 150, 174501 (2019)]. Structure is studied via the pair-distribution function and dynamics via the velocity autocorrelation function and the phonon density of states. These quantities are evaluated along isotherms, isochores, and three isomorphs in both crystal phases. Isomorphs are traced out by integrating the density-temperature relation characterizing configurational adiabats, starting from state points in the middle of the fcc-bcc coexistence region. Good isomorph invariance of structure and dynamics is seen in both crystal phases, which is notable in view of the large density variations studied. This is consistent with the fact that the virial potential-energy correlation coefficient is close to unity in the entire fcc phase and in most of the bcc phase (basically below the re-entrant density). Our findings confirm that the isomorph theory, developed and primarily studied for liquids, applies equally well for solids.

Sequential phase transitions and transient structured fluctuations in two-dimensional systems with a high-density Kagome lattice phase.

We report studies of (i) the isothermal density dependent sequences of phases in two-dimensional systems of particles with repulsive pair potentials devised by Truskett [J. Chem. Phys. 145, 054901 (2016)] and Torquato [Phys. Rev. E 88, 042309 (2013)] to support a high-density Kagome lattice phase and (ii) transient structured fluctuations close to a transition to a Kagome lattice. The commonalities in the sequences of phases in these systems and other 2D systems suggest the existence of a universal mechanism driving all to favor similar packing arrangements as the density is increased, but the simulations also show that the only such general rule proposed, namely, the Süto theorem, is not a necessary condition for the support of multiple distinct lattice structures by a particular pair potential. The transient fluctuations in the liquid close to the liquid-to-Kagome phase transition have Kagome symmetry, whereas deeper in the liquid phase, the fluctuations have hexagonal symmetry. When the transition is string-to-Kagome phase, the transient structured fluctuations in the string phase have both six-fold and other than six-fold symmetries. The path of the string-to-Kagome transition in the Truskett system involves intermediate honeycomb configurations that subsequently buckle to form a Kagome lattice. The path of the string-to-Kagome transition in the Torquato system suggests that the Kagome phase is formed by coiled strings merging together; increasing density generates a Kagome phase with imperfections such as 8-particle rings.

The Asymptotics of Eigenfunctions of the Absolutely Continuous Spectrum. The Scattering Problem of Three One-Dimensional Quantum Particles

In the paper the asymptotic structure of eigenfunctions of the absolutely continuous spectrum of the scattering problem is described. The case of three one-dimensional quantum particles interacting by repulsive pair potentials with a compact support is considered.

Towards a simplified description of thermoelectric materials: accuracy of approximate density functional theory for phonon dispersions

We calculate the phonon-dispersion relations of several two-dimensional materials and diamond using the density-functional based tight-binding approach (DFTB). Our goal is to verify if this numerically efficient method provides sufficiently accurate phonon frequencies and group velocities to compute reliable thermoelectric properties. To this end, the results are compared to available DFT results and experimental data. To quantify the accuracy for a given band, a descriptor is introduced that summarizes contributions to the lattice conductivity that are available already in the harmonic approximation. We find that the DFTB predictions depend strongly on the employed repulsive pair-potentials, which are an important prerequisite of this method. For carbon-based materials, accurate pair-potentials are identified and lead to errors of the descriptor that are of the same order as differences between different local and semi-local DFT approaches.

Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations

The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, Di, and rotational diffusion coefficient, Dr, are reported as a function of m and ρ or volume fraction, ξ. The mDi data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m3Dr against ρ at low densities but as ∼m6Dr at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and Di scale approximately as m and m-1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented.

The EXP pair-potential system. III. Thermodynamic phase diagram.

This paper determines the thermodynamic phase diagram of the EXP system of particles interacting by the purely repulsive exponential pair potential. The solid phase is face-centered cubic (fcc) at low densities and pressures. At higher densities and pressures, the solid phase is body-centered cubic (bcc) with a re-entrant liquid phase at the highest pressures simulated. The investigation first identifies the phase diagram at zero temperature at which the following four crystal structures are considered: fcc, bcc, hexagonal close packed, and cubic diamond. There is a T = 0 phase transition at pressure 2.651 × 10-3 with the thermodynamically stable structure being fcc below and bcc above this pressure. The densities of the two crystal structures at the phase transition are 1.7469 × 10-2 (fcc) and 1.7471 × 10-2 (bcc). At finite temperatures, the fcc-bcc, fcc-liquid, and bcc-liquid coexistence lines are determined by numerical integration of the Clausius-Clapeyron equation and validated by interface-pinning simulations at selected state points. The bcc-fcc phase transition is a weak first-order transition. The liquid-fcc-bcc triple point, which is determined by the interface-pinning method, has temperature 5.9 × 10-5 and pressure 2.5 × 10-6; the triple-point densities are 1.556 × 10-3 (liquid), 1.583 × 10-3 (bcc), and 1.587 × 10-3 (fcc).

The EXP pair-potential system. I. Fluid phase isotherms, isochores, and quasiuniversality.

It was recently shown that the exponentially repulsive EXP pair potential defines a system of particles in terms of which simple liquids' quasiuniversality may be explained [A. K. Bacher et al., Nat. Commun. 5, 5424 (2014); J. C. Dyre, J. Phys.: Condens. Matter 28, 323001 (2016)]. This paper and its companion [A. K. Bacher et al., J. Chem. Phys. 149, 114502 (2018)] present a detailed simulation study of the EXP system. Here we study how structure monitored by the radial distribution function and dynamics monitored by the mean-square displacement as a function of time evolve along the system's isotherms and isochores. The focus is on the gas and liquid phases, which are distinguished pragmatically by the absence or presence of a minimum in the radial distribution function above its first maximum. A constant-potential-energy (NVU)-based proof of quasiuniversality is presented, and quasiuniversality is illustrated by showing that the structure of the Lennard-Jones system at four state points is well approximated by those of EXP pair-potential systems with the same reduced diffusion constant. Paper II studies the EXP system's isomorphs, focusing also on the gas and liquid phases.

Tight-Binding Approximation-Enhanced Global Optimization

Solving and predicting atomic structures from first-principles methodologies is limited by the computational cost of exploring the search space, even when relatively inexpensive density functionals are used. Here, we present an efficient approach where the search is performed using density functional tight-binding, with an automatic adaptive parametrization scheme for the repulsive pair potentials. We successfully apply the method to the genetic algorithm optimization of bulk carbon, titanium dioxide, palladium oxide, and calcium hydroxide, and we assess the stability of the unknown crystal structure of palladium hydroxide.

Structure and stability of charged colloid-nanoparticle mixtures.

Physical properties of colloidal materials can be modified by addition of nanoparticles. Within a model of like-charged mixtures of particles governed by effective electrostatic interactions, we explore the influence of charged nanoparticles on the structure and thermodynamic phase stability of charge-stabilized colloidal suspensions. Focusing on salt-free mixtures of particles of high size and charge asymmetry, interacting via repulsive Yukawa effective pair potentials, we perform molecular dynamics simulations and compute radial distribution functions and static structure factors. Analysis of these structural properties indicates that increasing the charge and concentration of nanoparticles progressively weakens correlations between charged colloids. We show that addition of charged nanoparticles to a suspension of like-charged colloids can induce a colloidal crystal to melt and can facilitate aggregation of a fluid suspension due to attractive van der Waals interactions. We attribute the destabilizing influence of charged nanoparticles to enhanced screening of electrostatic interactions, which weakens repulsion between charged colloids. This interpretation is consistent with recent predictions of an effective interaction theory of charged colloid-nanoparticle mixtures.

Novel Pyrochlorelike Crystal with a Photonic Band Gap Self-Assembled Using Colloids with a Simple Interaction Potential.

Using computer simulations, we investigate the phase behavior of a system of particles interacting with a remarkably simple repulsive square-shoulder pair potential and report the formation of a novel (and stable) pyrochlorelike crystal phase. The lattice structure of the pyrochlorelike phase formed in our simulations possesses two inherent length scales corresponding to the inter- and intratetrahedral neighbors. We show that it can be used to fabricate a photonic crystal which displays complete photonic band gaps in both the direct and inverted dielectric structures.