Effective Pair Interactions Research Articles

A granular micromechanic-based model for Ultra High Performance Fiber-Reinforced Concrete (UHP FRC)

There is a growing interest in the application of UHP FRC (Ultra-High Performance Fiber-Reinforced Concrete) which has been under vigorous development since its inception over two decades ago. The advantages of these advanced materials is that they overcome the problems that plague conventional concrete, these include among others low residual strength and low tensile strength, poor crack control and resistance to crack propagation, which leads corrosion of the rebars and spalling. The aim of this paper is to provide a granular micromechanics-based model to describe the deformation behavior of UHP FRC material as it gives a robust method to link the micro-scale mechanisms with the macro-scale performance of materials with granular textures. In this model, the micro-scale is described by damage-elasto-plastic spring elements that represent the effective grain pair interactions decomposed into the so-called normal and tangential directions. Since the grain-pairs are variously oriented, the macro-scale response is obtained by integrating these interactions over the orientational space. Here we specialize the granular micromechanic model for UHP FRC by introducing a novel expression for the parameterized dissipation energy at the micro or the grain-pair scale. The newly introduced constitutive parameters are identified using experimental results for uniaxial extension and compression tests. The model is then applied to simulate the case of homogeneous compression, extension and shear to show the directional evolution of damage and plasticity and the consequent emergent anisotropy.

Computational investigation of the effects of polymer grafting on the effective interaction between silica nanoparticles in water.

Understanding and control of the effective interaction between nanoscale building blocks (colloids or nanoparticles) dispersed in a solvent is an important prerequisite for the development of bottom-up design strategies for soft functional materials. Here, we have employed all-atom molecular dynamics simulations to investigate the impact of polymer grafting on the solvent-mediated effective interaction between the silica nanoparticles (Si-NPs) in water, and in turn, on its bulk structural and thermodynamic properties. We found that the nature of the short grafting polymers [characterized by their interaction with water (hydrophobicity or hydrophilicity) and molecular weight] has a profound effect on the range and strength of the effective interaction between the Si-NPs. The hydrophobic polymer [such as polyethylene (PE)]-grafting of Si-NP gives rise to a more attractive interaction between the Si-NPs compared to the hydrophilic polymer [such as polyethylene glycol (PEG)] and non-grafted cases. This study further provides fundamental insights into the molecular origin of the observed behavior of the effective pair interactions between the grafted Si-NPs. For PE-grafted Si-NPs, the confined water (water inside the cavity formed by a pair of Si-NPs) undergoes a partial dewetting transition on approaching below a critical inter-particle separation leading to a stronger attractive interaction. Furthermore, we report that the effective attraction between the PE-grafted Si-NPs can be reliably controlled by changing the grafting PE density. We have also investigated the bulk structural and thermodynamic behavior of the coarse-grained Si-NP system where the particles interact via effective interaction in the absence of water. We believe that the insights gained from this work are important prerequisites for formulating rational bottom-up design strategies for functional materials where nano- (or, colloidal) particles are the building blocks.

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C60's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σα with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.

Solute-strengthening in metal alloys with short-range order

Recent surging interest in strengthening of High Entropy Alloys (HEAs) with possible chemical ordering motivates the development of new theory. Here, an existing theory for random alloys that accounts for solute-dislocation and solute–solute interactions is extended to include strengthening due to short-range order (SRO). Closed form expressions are presented for the yield strength and energy barrier of dislocation motion in alloys with SRO based on inputs of atomic misfit volumes, average lattice and elastic constants, the SRO parameters, and effective pair interactions between solutes. The theory shows both the long-established athermal strengthening effect of SRO as well as a notable effect of SRO on the misfit volume strengthening, which can increase or decrease strength. The generalized solute-strengthening theory is the most comprehensive to date that is applicable to macroscopically homogeneous single-phase alloys using inputs that can be measured, computed, or estimated.

Stress fluctuations and adiabatic speed of sound in liquids: a simple way to estimate it from ab initio simulations

One of the fundamental quantities in dynamics of the liquid state, the adiabatic speed of sound c_s, is extremely difficult to predict from computer simulations, especially in ab initio simulations. Here we derive an expression for the instantaneous correlator of fluctuations of longitudinal component of stress tensor, which contains c_s along with others quantities easy accessible via classical and ab initio computer simulations. We show that the proposed methodology works well in the case of Lennard-Jones and soft-sphere simple fluids, Kr–Ar liquid mixture in connection with simulations with effective pair interactions as well as for liquid Sb, fluid Hg and molten NaCl from ab initio simulations.

Interactions between γ-alumina surfaces in water and aqueous salt solutions

Particle agglomeration is relevant to numerous industrial applications and consumer products. The present work explores interactions between and agglomeration of gamma (γ)-alumina nanoparticles in pure water and dilute aqueous salt solutions. To characterize surface- and salt-specific effects, potential of mean force (PMF) profiles between γ-alumina surfaces ([110] and [100] facets) are extracted using classical molecular dynamics (MD) simulations. Supporting experiments are conducted using dynamic light scattering (DLS) to investigate agglomeration at the macroscale. The ion pairs considered are sodium chloride, ammonium acetate, barium nitrate, and barium acetate; sampling a broad range of the Hofmeister series. As particle surfaces approach contact, free-energy fluctuations of the PMF profiles reflect structural adjustments of the intervening aqueous phase. We extract values for the cohesive energy from the MD results, and parse the resultant effective pair interactions into van der Waals and electrostatic contributions. Molecular scale findings from simulations correlate with hydrodynamic radii of γ-alumina nanoparticles, obtained from DLS experiments. The results highlight the applicability of molecular simulations to identify the origins of macroscale observables.

Effective Interactions between Double-Stranded DNA Molecules in Aqueous Electrolyte Solutions: Effects of Molecular Architecture and Counterion Valency.

A computational investigation of the effects of molecular topology, namely, linear and circular, as well as counterion valency, on the ensuing pairwise effective interactions between DNA molecules in an unlinked state is presented. Umbrella sampling simulations have been performed through the introduction of bias potential along a reaction coordinate defined as the distance between the centers-of-mass of pairs of DNA molecules, and effective pair interaction potentials have been computed by employing the weighted histogram analysis method. An interesting comparison can be drawn between the different DNA topologies studied here, especially with regard to the contrasting effects of divalent counterions on the effective pair potentials: while DNA-DNA repulsion in short center-of-mass distances decreases significantly in the presence of divalent counterion-ions (as compared to monovalent ions) for linear DNA, the opposite effect occurs for the DNA minicircles. This can be attributed to the fact that linear DNA fragments can easily adopt relative orientations that minimize electrostatic and steric repulsions by rotating relative to one another and by exhibiting more pronounced bending due to the presence of free ends.

Theoretical study of interactions and structural and thermodynamical properties of nanopores within bilayer-membranes: Experimental inspiration

In this work, we consider a bilayer-membrane which is crossed by an assembly of (parallel) nanopores formed generally by peptide molecules. The deformations and thermal fluctuations of this bilayer-membrane give rise to repulsive effective pair-interactions between the parallel nanopores. Some recent experiment has revealed that the repulsive effective pair-potentials, as function of distance between adjacent nanopores, are of Born-Mayer type (soft-potential). Beside the repulsive forces, the nanopores mutually attract through the van der Waals forces. Our main goal is an extensive theoretical study of the structural and thermodynamical properties of the nanopores we consider as a dense gas system. When the bath temperature is fixed to some value (room temperature), the only remaining pertinent parameter of discussion is the nanopore-density, denoted as n, or equivalently, the peptide-molar-fraction, P/L. First, we propose a closer expression of the effective pair-potentials taking into account recent experimental measurements dealt with many lipid-bilayers (Gramicidin/DLPC, Gramicidin/C12EO5...). Second, we classify these effective pair-potentials in terms of the nanopore-density, and in particular, we show the existence of a typical nanopore-density, nc, below which the total pair-potential exhibits an energy-barrier which prevents the coagulation of the nanopores. When the nanopore-density reaches threshold, nc, the energy-barrier ceases to exist, and beyond this threshold, one assists to a complete coagulation of the nanopores. Third, we determine an exact theoretical expression of the structure factor of the nanopores, as a function of the wave-vector, within the framework of Random Phase Approximation, using a hard-disk model as a reference system. Finally, from the obtained structure factor, we extract the thermodynamical properties of the integrated nanopores, such as the virial pressure (state of equation), the isothermal compressibility and the chemical potential which are nanopore-density dependent.

Evolution of magnetic correlation in an inhomogeneous square lattice

We explore the magnetic properties of a two-dimensional Hubbard model on an inhomogeneous square lattice, which provides a platform for tuning the bandwidth of the flat band. In its limit, this inhomogeneous square lattice turns into a Lieb lattice, and it exhibits abundant properties due to the flat band structure at the Fermi level. By using the determinant quantum Monte Carlo simulation, we calculate the spin susceptibility, double occupancy, magnetization, spin structure factor, and effective pairing interaction of the system. It is found that the antiferromagnetic correlation is suppressed by the inhomogeneous strength and that the ferromagnetic correlation is enhanced. Both the antiferromagnetic correlation and ferromagnetic correlation are enhanced as the interaction increases. It is also found that the effective $d$-wave pairing interaction is suppressed by the increasing inhomogeneity. In addition, we also study the thermodynamic properties of the inhomogeneous square lattice, and the calculation of specific heat provides good support for our point. Our intensive numerical results provide a rich magnetic phase diagram over both the inhomogeneity and interaction.

On the Bardeen–Cooper–Schrieffer interaction in quantum graphs

We introduce a real-space version of the Bardeen–Cooper–Schrieffer interaction allowing the investigation of the non-trivial interplay between many-body physics and particles confinement on a quantum graph. When the two-body problem is considered, we find that the two-particle wavefunction is solution of an integro-differential Schrödinger equation. The solution of the two-body eigenproblem shows the presence of a two-particle bound state whose stability is enhanced in graphs with peculiar topology. We demonstrate that the enhancement effect is robust against many-body effects, which can be studied by means of the Richardson exact solution of the many-body problem. These findings suggest that the effective pairing interaction can be enhanced in quantum graphs with appropriate connectivity. Experimental evidences in Josephson junctions arrays are also discussed in connection with the microscopic mechanism described in the present work.

Pairing correlation of the three-band Hubbard model with the nearest attraction

To gain a deeper understanding of the high-temperature superconductivity in doped cuprates, the constrained-path quantum Monte Carlo method was used to explore the superconducting pairing correlation function and effective pairing interaction in the three-band Hubbard model. Our main observation was that in the low doping region, compared to other symmetries, [Formula: see text]-wave superconducting pairing dominates. The Coulomb interaction [Formula: see text] suppresses [Formula: see text]-wave pairing correlation, while the effective pairing interaction is both enhanced by the increasing [Formula: see text] and the nearest attraction. These results are used to understand the superconducting state in copper oxide high-temperature superconductors.

Asphaltene precipitation described with a Yukawa SAFT-VR/MSA equation of state

We combine the Statistical Associating Fluid Theory for Potentials of Variable Range (SAFT-VR) and the Mean Spherical Approximation (MSA) to develop an equation of state to model asphaltene precipitation in petroleum fluids including the measured asphaltene onset pressures (AOP’s) of a reservoir live oil. In this model, dispersive solvent–solvent and asphaltene–solvent interactions in reservoir fluid mixtures are represented by Yukawa potentials. The approach is based in the modeling of polar and ionic interactions via Yukawa potentials, as originally proposed by the Generalized Mean Spherical Approximation Theory, and also in recent studies in molecular simulation of charged fluids using non-Ewald effective pair interactions, as in the Wolf method.

Cluster variation method for investigation of multi-principal-element metallic alloys

We present atomic-scale investigations of the thermodynamic properties of quinary bcc-based multi-principal-element alloys (MPEAs) within {Al,Co,Cr,Fe,Mn,Mo,Ni}, by means of short-range pair energetics and the cluster variation method (CVM) in the irregular tetrahedron approximation. We focus on an essential couple of key-properties detrimental for potential applications of MPEAs, namely the trends to (i) long-range ordering (LRO) and (ii) phase separation (PS). While the CVM has been more commonly employed in a grand canonical frame controlled by chemical potentials (δμ), we propose an original δμ-driven CVM scheme which allows an easier exploration of wide composition spaces typical of MPEAs. This modified scheme yields a slice-by-slice analysis of this space, by means of pseudo-ternary isothermal sections, which demonstrates the ability of the CVM to lead, with moderate computational effort, to full phase diagrams of MPEAs. In particular, our CVM calculations provide elements to interpret recent unexpected experimental trends of AlCrFeMnMo. Comparison with earlier studies of the same MPEAs using the less accurate point-mean-field (PMF) approximation indicates that CVM and PMF have global agreement for LRO at higher temperatures, whereas CVM should definitely be preferred as soon as PS begins to occur. Both approaches, employed more systematically in future MPEA studies in conjunction with ab initio electron theory and dedicated experiments, may offer convenient tools to check the merits of, and even improve, the various sets of effective pair interactions nowadays increasingly available for atomic-scale simulations of MPEAs, thus helping to identify composition domains relevant to avoid trends (i) and (ii) and design more reliable MPEAs.

Shift of the superconducting dome induced by a conduction band of small occupancy: Enhanced d -wave pairing in the overdoped regime

Motivated by the presence of an extremely small electron pocket in the electronic band structure of infinite-layer nickelate superconductors, we systematically explore the superconducting (SC) properties of a two-dimensional Hubbard model influenced by an additional conduction band with small occupancy (dry Fermi sea). Our dynamic cluster quantum Monte Carlo calculations demonstrated the unusual impact of this additional dry metallic layer, which shifts the SC dome of the correlated Hubbard layer towards the overdoped regime, namely the $d$-wave SC can be enhanced (suppressed) in the overdoped (underdoped) regime. Simultaneously, the pseudogap crossover line shifts to the same higher doping regime as well. Our analysis revealed the interplay of the effective pairing interaction, pair-field susceptibility, and antiferromagnetic spin fluctuation in the underlying nonmonotonic physics. We postulate on the physical picture of the SC dome shift in terms of the Kondo-type electron-hole binding in the case of a dry additional conduction band. Our investigation provided valuable insights on tuning the SC properties via external dry bands.

Realizability of iso-g2 processes via effective pair interactions.

An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function g2(r) [or equivalently, structure factor S(k)] at some number density ρ can be achieved by many-body systems in d-dimensional Euclidean space. The Zhang-Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. To further test this conjecture, we study the realizability problem of the nonequilibrium iso-g2 process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which g2 remains invariant for a positive range of densities. Using a precise inverse algorithm that determines effective potentials that match hypothesized functional forms of g2(r) for all r and S(k) for all k, we show that the unit-step function g2, which is the zero-density limit of the hard-sphere potential, is remarkably realizable up to the packing fraction ϕ = 0.49 for d = 1. For d = 2 and 3, it is realizable up to the maximum "terminal" packing fraction ϕc = 1/2d, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through ϕc. For ϕ near but below ϕc, the large-r behaviors of the effective potentials are given exactly by the functional forms exp[ - κ(ϕ)r] for d = 1, r-1/2exp[ - κ(ϕ)r] for d = 2, and r-1exp[ - κ(ϕ)r] (Yukawa form) for d = 3, where κ-1(ϕ) is a screening length, and for ϕ = ϕc, the potentials at large r are given by the pure Coulomb forms in the respective dimensions as predicted by Torquato and Stillinger [Phys. Rev. E 68, 041113 (2003)]. We also find that the effective potential for the pair statistics of the 3D "ghost" random sequential addition at the maximum packing fraction ϕc = 1/8 is much shorter ranged than that for the 3D unit-step function g2 at ϕc; thus, it does not constrain the realizability of the unit-step function g2. Our inverse methodology yields effective potentials for realizable targets, and, as expected, it does not reach convergence for a target that is known to be non-realizable, despite the fact that it satisfies all known explicit necessary conditions. Our findings demonstrate that exploring the iso-g2 process via our inverse methodology is an effective and robust means to tackle the realizability problem and is expected to facilitate the design of novel nanoparticle systems with density-dependent effective potentials, including exotic hyperuniform states of matter.

Antiferromagnetic fluctuations and dominant dxy -wave pairing symmetry in nickelate-based superconductors

Motivated by recent experimental studies on superconductivity found in nickelate-based materials, we study the temperature dependence of the spin correlation and the superconducting pairing interaction within an effective two-band Hubbard model by the quantum Monte Carlo method. Based on parameters extracted from first-principles calculations, our intensive numerical results reveal that the pairing with a $d_{xy}$-wave symmetry firmly dominates over other pairings at low temperature, which is mainly determined by the Ni 3$d$ orbital. It is also found that the effective pairing interaction is enhanced as the on-site interaction increases, demonstrating that the superconductivity is driven by strong electron-electron correlation. Even though the $(\pi,\pi)$ antiferromagnetic correlation could be enhanced by electronic interaction, there is no evidence for long-range antiferromagnetic order exhibited in nickelate-based superconductors. Moreover, our results offer possible evidence that the pure electron correlation may not account for the charge density wave state observed in nickelates.

Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium.

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g_{2}(r) or corresponding structure factor S(k) in d-dimensional Euclidean space R^{d} is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)2470-004510.1103/PhysRevE.101.032124] conjectured that any realizable g_{2}(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g_{2}(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L_{2}-norm errors that are an order of magnitude smaller than that of previous methods. The results of our investigation lend further support to the Zhang-Torquato conjecture. Furthermore, our algorithm will enable one to probe systems with identical pair statistics but different higher-body statistics, which will shed light on the well-known degeneracy problem of statistical mechanics.

A study of thermodynamics of mixing for Al[formula omitted]Zn[formula omitted] liquid binary alloy

Thermodynamics of mixing, namely, the energy of mixing (ΔF), enthalpy of mixing (ΔQ) and entropy of mixing (ΔS) for Al1−xZnx liquid binary alloys are calculated theoretically by using the electronic theory of metals (ETM) along with the perturbative approach and the statistical mechanics at T=1000 K. The electron-ion and ion-ion effective pair interactions, vital for any microscopic study, are described by a local pseudopotential. The results of our calculations for energy of mixing, however, agree very well with the available experimental data. In the case of entropy of mixing and the enthalpy of mixing agreement with experimental data is found to be good. We offer a prescription to lessen the discrepancy between theory and experiment in the case of enthalpy of mixing and entropy of mixing, and this project will be undertaken as our future work.

Topological defect-propelled swimming of nematic colloids.

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation. Defect elongation is controlled by a rotating external magnetic field, allowing control over particle trajectories. The swimmers' translational motion relies on broken symmetries associated with lubrication forces between the colloid and the bounding surfaces, line tensions associated with the elongated defect, and anisotropic viscosities associated with the defect elongation adjacent to the colloid. The scattering or effective pair interaction of these swimmers is highly anisotropic, with polarization-dependent dimer stability and motion that depend strongly on entanglement and sharing of their extended defect structures. This research introduces transient, far-from-equilibrium topological defects as a class of virtual functional structures that generate modalities of motion and interaction.

Enhancing Tc in a composite superconductor/metal bilayer system: A dynamical cluster approximation study

It has been proposed that the superconducting transition temperature ${T}_{\text{c}}$ of an unconventional superconductor with a large pairing scale but strong phase fluctuations can be enhanced by coupling it to a metal. However, the general efficacy of this approach across different parameter regimes remains an open question. Using the dynamical cluster approximation, we study this question in a system composed of an attractive Hubbard layer in the intermediate coupling regime, where the magnitude of the attractive Coulomb interaction $|U|$ is slightly larger than the bandwidth $W$, hybridized with a noninteracting metallic layer. We find that while the superconducting transition becomes more mean-field-like with increasing interlayer hopping, the superconducting transition temperature ${T}_{\text{c}}$ exhibits a nonmonotonic dependence on the strength of the hybridization ${t}_{\ensuremath{\perp}}$. This behavior arises from a reduction of the effective pairing interaction in the correlated layer that outcompetes the growth in the intrinsic pair-field susceptibility induced by the coupling to the metallic layer. We find that the largest ${T}_{\text{c}}$ inferred here for the composite system is comparable to the maximum value currently estimated for the isolated negative-$U$ Hubbard model.