Lattice Monte Carlo Study Research Articles

Spatial Organization of Slit-Confined Melts of Ring Polymers with Nonconserved Topology: A Lattice Monte Carlo Study.

We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we explore the influence of confinement on single-chain conformations and interchain interactions. We demonstrate that confinement makes chains globally larger and more elongated while enhancing both contacts and knottedness propensities. As for multichain properties, we show that ring-ring contacts decrease with the confinement, yet neighboring rings overlap more as confinement grows. These aspects are accompanied by a marked decrease in the links formed between pairs of neighboring rings. In connection with the quantitative relation between links and entanglements in polymer melts recently established by us [Ubertini M. A.; Rosa A.Macromolecules2023, 56, 3354-3362], we propose that confinement can be used to set polymer networks that act softer under mechanical stress and suggest a viable experimental setup to validate our results.

Pairing enhanced by local orbital fluctuations in a model for monolayer FeSe

The pairing mechanism in different classes of correlated materials, including iron based superconductors, is still under debate. For FeSe monolayers, uniform nematic fluctuations have been shown in a lattice Monte Carlo study to play a potentially important role. Here, using dynamical mean field theory calculations for the same model system, we obtain a similar phase diagram and provide an alternative interpretation of the superconductivity in terms of local orbital fluctuations and phase rigidity. Our study clarifies the relation between the superconducting order parameter, superfluid stiffness and orbital fluctuations, and provides a link between the spin/orbital freezing theory of unconventional superconductivity and theoretical works considering the role of nematic fluctuations.

Lattice Monte Carlo study of orientational order in a confined system of biaxial particles: Effect of an external electric field.

In this work we have used lattice Monte Carlo to determine the orientational order of a system of biaxial particles confined between two walls inducing perfect order and subjected to an electric field perpendicular to the walls. The particles are set to interact with their nearest neighbors through a biaxial version of the Lebwohl-Lasher potential. A particular set of values for the molecular reduced polarizabilities defining the potential used was considered; the Metropolis sampling algorithm was used in the Monte Carlo simulations. The relevant order parameters were determined in the middle plane of the sample and for some cases across the whole thickness of the sample. We have determined the temperature-electric field phase diagram for this system and found, as expected, five different system configurations corresponding to three different mesophases. At low temperatures and low fields the system finds itself in an undistorted biaxial phase. On increasing the field at low temperatures, a Freedericksz transition takes place and the secondary directors reorient towards the field while the primary director stays undistorted and parallel to the walls. On increasing the field further, a second Freedericksz transition occurs and the primary director orients also towards the field direction. The orientational order measured at the field strengths tested is not affected by the field. On increasing the temperature, a transition to a uniaxial phase occurs and within the range of this phase a field increase leads also to a Freedericksz transition where the main director reorients towards the field. At higher temperature a transition to a disordered phase is found. We have performed finite size scaling analysis for the Freedericksz critical fields and found that they scale with the distance L between the walls as L^{-1} as expected from continuum theory. From these fields we have also determined the temperature dependence of two elastic constant ratios. Critical exponents and critical temperatures for the order parameter and the correlation length for the biaxial-uniaxial phase transition and the uniaxial to disordered phase transition were also determined by finite size scaling and are discussed.

A kinetic lattice Monte Carlo study of post-irradiation annealing of model reactor pressure vessel steels

Significant embrittlement in reactor pressure vessel (RPV) steels can be caused by the formation of nanometer-scale Mn–Ni–Si precipitates (MNSPs) and annealing is a promising technique for reducing embrittlement. To achieve better understanding of the evolution of these precipitates at the atomic scale, a kinetic lattice Monte Carlo (KLMC) model, parameterized using CALPHAD and recent atom probe tomography (APT) data, is used to simulate post-irradiation annealing of MNSPs. The model predicts MNSP volume fractions, number densities and sizes that agree well with the experimental observations. The model also predicts that the initial structure of the precipitates may be B2 bcc phases with one sublattice occupied by Ni and the other sublattice occupied by Mn and Si, as well as shows a modest temperature dependence of the MNSP composition. The results show that the simple approach can be used to model MNSP evolution and supports that these precipitates are stable thermodynamic phases.

Energetic ion-induced modification of embedded Au nanoparticles size: a three-dimensional kinetic lattice Monte Carlo study

Nanometer-sized noble metallic particles embedded in dielectric matrices are of wide interest. To exploit their plasmonic properties, efforts have been made to vary their size and shape by various methods during or after fabrication. Energetic ion irradiation has been found to be very useful in this objective. In the present work, we have studied the effect of inter-particle separation using atomistic simulations to gain a better understanding of the pathway in the modification of size of nanoparticles which are smaller than the ion track size in the matrix. It is found that the size of nanoparticles can be varied depending on the initial inter-particle separation and the temperature in the spike generated by the passed energetic ion. The results agree with the model proposed by our group, based on inter-particle separation, to explain experimental results on the swift heavy ion-induced modification of the size of embedded nanoparticles.

Lattice Monte Carlo study of pre-conformal dynamics in strongly flavoured QCD in the light of the chiral phase transition at finite temperature

We study the thermal phase transition in colour SU(Nc=3) Quantum Chromodynamics (QCD) with a variable number of fermions in the fundamental representation by using lattice Monte Carlo simulations. We collect the (pseudo) critical couplings βLc for Nf=(0,4,6, and 8), and we investigate the pre-conformal dynamics associated with the infra-red fixed point in terms of the Nf dependence of the transition temperature. We propose three independent estimates of the number of flavour Nf⁎ where the conformal phase would emerge, which give consistent results within the largish errors. We consider lines of fixed Nt in the space of (Nf, bare lattice coupling), and locate the vanishing of the step-scaling function for Nf⁎∼11.1±1.6. We define a typical interaction strength gTc at the scale of critical temperature Tc and we find that gTc meets the zero temperature critical couplings estimated by the two-loop Schwinger–Dyson equation or the IRFP coupling in the four-loop beta-function at Nf⁎∼12.5±1.6. Further, we study the Nf dependences of Tc/M where M is a UV Nf independent reference scale determined by utilising the coupling at the scale of the lattice spacing. Then, Tc/M turns out to be a decreasing function of Nf and the vanishing Tc/M indicates the emergence of the conformal window at Nf⁎∼10.4±1.2.

Activity coefficient of monomer in different aggregates of a surfactant solution: a Lattice Monte Carlo Study

In this paper, canonical lattice Monte Carlo simulation technique is used to derive cluster size distribution of a surfactant solution, by which activity coefficient of a monomer in solution and in the micellar phase is estimated. To do this, correlation of cluster concentration with the aggregation number is needed. The multiple equilibrium method is used to relate cluster size distribution to the activity coefficient. The introduced idea is not only applicable to the lattice model techniques, but also to any method that can produce cluster size distribution. The method can be used as a reference to test activity coefficient data of lattice-based equations of state. Results show that the activity coefficients of monomers in micellar aggregates are much greater than unity, in accordance with the experimental results.

Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study

The low-energy theory of graphene exhibits spontaneous chiral symmetry breaking due to pairing of quasiparticles and holes, corresponding to a semimetal-insulator transition at strong Coulomb coupling. We report a Lattice Monte Carlo study of the critical exponents of this transition as a function of the number of Dirac flavors $N_f^{}$, finding $\delta = 1.25 \pm 0.05$ for $N_f^{} = 0$, $\delta = 2.26 \pm 0.06$ for $N_f^{} = 2$ and $\delta = 2.62 \pm 0.11$ for $N_f^{} = 4$, with $\gamma \simeq 1$ throughout. We compare our results with recent analytical work for graphene and closely related systems, and discuss scenarios for the fate of the chiral transition at finite temperature and carrier density, an issue of relevance for upcoming experiments with suspended graphene samples.

Some physics of the two-dimensional [formula omitted] supersymmetric Yang–Mills theory: Lattice Monte Carlo study

We illustrate some physical application of a lattice formulation of the two-dimensional N=(2,2) supersymmetric SU(2) Yang–Mills theory with a (small) supersymmetry breaking scalar mass. Two aspects, power-like behavior of certain correlation functions (which implies the absence of the mass gap) and the static potential V(R) between probe charges in the fundamental representation, are considered. For the latter, for R≲1/g, we observe a linear confining potential with a finite string tension. This confining behavior appears distinct from a theoretical conjecture that a probe charge in the fundamental representation is screened in two-dimensional gauge theory with an adjoint massless fermion, although the static potential for R≳1/g has to be systematically explored to conclude real asymptotic behavior in large distance.

Nucleation of fluids confined between parallel walls: A lattice Monte Carlo study

Nucleation phenomena in lattice gas models of simple and chain molecules confined in slitlike pores are studied using Monte Carlo methods. Finite-size scaling is used to investigate the nature of phase transitions accompanying the formation of layers at the pore walls. It is demonstrated that nucleation leads to the symmetry breaking and the formation of nuclei at one wall only.

Adsorption and Morphology Transition of Surfactants on Hydrophobic Surfaces: A Lattice Monte Carlo Study

In this work, we first show that there are only five independent interchange parameters in the surfactant-solvent-interface system in Larson's model, and then adsorption and morphology transition of surfactants on hydrophobic surfaces are studied by extensive lattice Monte Carlo simulations. In our simulations, we found that there exist six adsorbed morphologies: (1) premature admicelle, (2) hemisphere, (3) hemisphere-hemicylinder mixture, (4) wormlike hemicylinder, (5) perforated monolayer, and (6) monolayer. The surface morphologies and the amount of adsorption on hydrophobic surfaces are found to be affected obviously by two interchange parameters. One is the attractive interaction between tail groups and surface (chiTS), and the other is the solubility of head groups in bulk (chiHW). Phase diagrams in chiHW versus chiTS planes for surfactants with different hydrophobicities (chiTW) and for surfactants with different molecular structures are determined in this work, from which the transitions of surface morphologies and adsorption behaviors are discussed.

Polymer-centered theory in comparison with surfactant-centered theory: A lattice Monte Carlo study

Lattice Monte Carlo simulation is used to study micellization of both pure and surfactant-polymer mixture, with an emphasis on cluster size distribution. The amphiphile molecule is of the type H(4)T(4) where the H (head) monomers like the solvent molecules and the T (tail) monomers are solvophobic. To compare polymer- and surfactant-centered theories, copolymers with the structure of (H(4)T(4))(5) are used instead of homopolymers. Since above copolymer molecules have the structural unit like the structure of surfactant molecules, it is possible to study the competition between the binding of surfactant molecules to the copolymer and the micellization in a copolymer-free solution. Results show that, first, surfactant molecules bind to the copolymer molecules, and not until copolymers are saturated do micelles form. Furthermore, it is shown that for the model used in this paper, the polymer-centered theory is more appropriate than the surfactant-centered theory, and finally the cooperative nature of cluster formation on copolymers is also discussed.

Wetting behavior of associating binary mixtures at attractive walls: A lattice Monte Carlo study

The lattice gas model is used to study the effects of molecular association on the wettability of surfaces with attractive walls by binary symmetric associating mixtures. The model assumes that the adsorbate particles occupy a regular cubic lattice of sites and that the interactions between adsorbate particles involve only the first nearest neighbors. The energies of interaction between the pairs of like particles are the same, while the only interaction between a pair of unlike particles is due to association. Only the formation of dimers is allowed and the energy of association is finite. The particles are subject to the surface, van der Waals-like potential, assumed to be the same for both components. The model is studied with the help of the Monte Carlo simulation method in the grand canonical ensemble. Only the ground state properties are treated analytically. It is demonstrated that, in general, molecular association hinders wetting. In particular, in the systems with nonzero wetting temperature, the increase of the association energy leads to the increase of the wetting temperature and for sufficiently high energy of association the mixture does not wet the surface at all. When the system is expected to exhibit complete wetting at the ground state, the film formed by strongly associating mixtures wets the surface only at sufficiently low temperatures, below the dewetting temperature. It is demonstrated that the dewetting temperature increases with the strength of the surface potential as well as with the increase of the association energy.

A lattice model Monte Carlo study of coil-to-globule and other conformational transitions of polymer, amphiphile, and solvent

A model of polymer-amphiphile-solvent systems on a cubic lattice is used to investigate the phase diagram of such systems. The polymer is treated within the canonical ensemble (T,V,N) and the amphiphile and solvent are treated within the grand canonical ensemble (T,V,μ). Using a range of Monte Carlo moves the phase diagram of polymer-amphiphile-solvent mixtures, as a function of solvent quality (parametrized by χ) and relative chemical potential, μ, is studied for the dilute polymer limit. The effect of increasing the polymer chain length, N, on the critical aggregation concentration (CAC), and the type of polymer-amphiphile complex formed above the CAC are also examined. For some parameters, it is found that the polymer and amphiphile form a polymer-micelle complex at low amphiphile concentrations, and that the polymer coil-to-globule transition point increases with increasing amphiphile concentration. The resulting collapsed globule has a solvent core and is surrounded by a layer of amphiphile. These results are in good qualitative agreement with experimental results for the poly(N-isopropylacrylamide) (PNIPAM)/sodium dodecyl sulfate (SDS) system. At higher amphiphile concentrations, the polymer and amphiphile form several layered structures depending on the strength of the three-body amphiphilic interactions, l. Finally, the effect of the polymer chain length, N, and the strength of the three-body amphiphilic interactions, l, on the stability of the polymer-amphiphile structures is investigated.

Monte Carlo study of vacancy-mediated impurity diffusion in silicon

We present a kinetic lattice Monte Carlo study of the behavior of a dopant flux driven by a vacancy gradient, associated with the diffusion of substitutional impurities via a vacancy mechanism in silicon. Recent ab initio results are used for a quantitative description of the impurity-vacancy interaction. We find a dopant flux smaller than, but in the same direction as, that predicted by the pair diffusion model, with the deviation greatest at high temperatures.

A lattice Monte Carlo study of inverse symmetry breaking in a two-scalar model in three dimensions

We carry a Monte Carlo study of the coupled two-scalar λf12f22 model in three dimensions. We find no trace of inverse symmetry breaking in the region of negative λ's for which the one-loop effective potential predicts this phenomenon. Moreover, for λ's negative enough, but still in the stability region for the potential, one of the transitions turns out to be of first order, both for zero and finite temperature.

Statics and dynamics of homopolymer adsorption and desorption: A Monte Carlo study

We present results from an extensive lattice Monte Carlo study of the adsorption and desorption of homopolymer chains from semidilute solution onto a solid/liquid interface. We have studied in detail the growth, equilibrium structure and dynamics, and rinsing of layers of homopolymers adsorbed from solution. For solution concentrations at or near the overlap threshold we directly verify the self-similar structure of the adsorbed layer first predicted by de Gennes. This scaling result is confirmed without our having to make any assumptions or inferences as required in experiments. By following the flight of the individual chains, we obtain a detailed description of their structure and dynamics, including direct proof that the adsorbed chains form two broad categories: a tightly bound category with a long characteristic time of exchange with the solution, and a loosely bound category with a very short characteristic time of exchange. We study the differing conformations of these two subpopulations, as well as the kinetics of chain exchange between the adsorbed phases and the bulk solution. Finally, we examine the active displacement of the self-similar adsorbed layer by a solution of different chains. We describe different regimes of desorption, characterized by exponential and faster than exponential decays of the adsorbed layer.

A lattice Monte Carlo study of the hot electroweak phase transition

We study the finite temperature electroweak phase transition with lattice perturbation theory and Monte Carlo techniques. Dimensional reduction is used to approximate the full four-dimensional SU(2)+fundamental doublet Higgs theory by an efftive three-dimensional SU(2)+ adjoint Higgs+fundamental Higgs theory with coefficients depending on temperature via screening masses and mass counterterms. Fermions contribute to the effective theory only via the N F and m top dependence of the coefficients. For sufficiently small lattices ( N 3 < 30 3 for m H = 35 GeV) the study of the one-loop lattice effective potential shows the existence of the second order phase transition even for the small Higgs masses. At the same time, a clear signal of a first order phase transition is seen on the lattice simulations with a transition temperature close to but less than the value determined from the perturbative calculations. This indicates that the dynamics of the first order electroweak phase transition depends strongly on non-perturbative effects and is not exclusively related to the so-called ø 3 term in the effective potential.

A lattice Monte Carlo study of long chain conformations at solid–polymer melt interfaces

In this paper we present a comprehensive lattice Monte Carlo study of long chain conformations at solid–polymer melt interfaces. Segmental scale interfacial features, like the bond orientational distribution were found to be independent of surface–segment energetics, and statistically identical with Helfand’s predictions for the full-occupancy, infinite chain length limit. Conformational statistics of chains longer than 5–6 statistical segments followed the predictions of the Scheutjens–Fleer theory and the same power laws as a single ideal chain at the critical value of the surface–segment adsorption free-energy. Our simulations tested the predictions of random walk next to a ‘‘reflective’’ surface statistics for the spatial variations of chain dimensions and chain center of mass density. It was found that these statistics furnish the correct long chain limit, independently of surface–segment energetics. The random walk next to a ‘‘reflective’’ boundary predictions for the ‘‘adsorbed’’ amount and the distributions of tail, loop, and train number, as well as tail and loop size were in quantitative agreement with the simulation data. The correspondence between random walks and real (or simulated) chains required the knowledge of a single, microscopic parameter, the number of chemical segments per statistical segment, a∞. This quantity was very close to the average length of adsorbed sequences (trains), in the long chain limit. Our simulations tested thoroughly and established firmly the validity of ‘‘reflective’’ boundary statistics in the melt. The inevitability of these statistics has broad implications on ‘‘desorption’’ kinetics, chain mobility, and chain relaxation, which are currently under study.

Monte Carlo studies of polymer network formation

We are presenting a lattice Monte Carlo study of the formation of polymer networks using the bond fluctuating method. Starting from a pure polymer melt (chain length N=50, density Φ=0.3) and two component polymer mixtures (A:B=1:1), we get simple two component or interpenetrated polymer networks. The time evolution of the building process, the static structure factor, and the topology of the network are presented in dependence of the cross-link density.