Soft-core Models Research Articles

Correlations in Hard- and Soft-Core Generic Polymer Models

Generic polymer models capturing the chain connectivity and the non-bonded excluded-volume interactions between polymer segments can be classified into hard- and soft-core models depending on their non-bonded pair potential. Here we compared the correlation effects on the structural and thermodynamic properties of the hard- and soft-core models given by the polymer reference interaction site model (PRISM) theory, and found different behaviors of the soft-core models at large invariant degree of polymerization (IDP) depending on how IDP is varied. We also proposed an efficient numerical approach, which enables us to accurately solve the PRISM theory for chain lengths as large as 106.

Low-lying bound and resonance states in Λ61Ca and ΛΛ62Ca

In this paper, the energy, and wavefunctions of the low-lying bound and resonance states of [Formula: see text]Ca and [Formula: see text]Ca are studied. For [Formula: see text]Ca we adopted [Formula: see text]Ca two-body cluster model while for [Formula: see text]Ca we adopted [Formula: see text]Ca three-body cluster model. Two models of potentials, namely SH: Hulthén type and WS: Woods–Saxon type potentials, each having a spin-orbit coupling term is chosen for the [Formula: see text]-nucleus pair while three-range Gaussian (TRG) Nijmegen hardcore and softcore potential models are chosen for [Formula: see text] pair. The resulting few-body (two- and three-body) Schrödinger equations are solved numerically to get the bound state energies and wavefunctions. For the three-body calculation, we used hyperspherical coordinates. The formalism of supersymmetric quantum mechanics is applied to construct a one-parameter family of isospectral potential to investigate the resonance states of the [Formula: see text]Ca ([Formula: see text]Ca) core-[Formula: see text] two-body system. To study the effect of replacement of the outer core valence nucleon(s) of [Formula: see text]Ca by [Formula: see text] hyperon(s), two- and three-body cluster model calculations for the bound states of [Formula: see text]Ca and [Formula: see text]Ca are also carried out using the same set of two-body potentials, as used for [Formula: see text]Ca and [Formula: see text]Ca respectively. And a clear enhancement in the one- and two-[Formula: see text] separation energies and a shrinking of the overall size of the nucleus is indicated. The computed results are compared with some of those found in the literature.

Simulation of surfactant adsorption at liquid-liquid interface: What we may expect from soft-core models?

The present work attempts to systematically explore the surfactant sorption at liquid-liquid interfaces with coarse-grained models targeting thermodynamic properties of reference liquid solutions. We employ dissipative particle dynamics with soft-core forcefield tested against experimental data on micellization of surfactants in water, and the previous results are reproduced in this work. We consider three different nonionic surfactants: hexaethylene glycol monododecyl ether (C12E6), 2-[4-(2,4,4-trimethylpentan-2-yl)phenoxy]ethanol) known as Triton X-100 (TX-100), and two alkyl glucoside surfactants (CnG1) with n-alkane tail fragments and a saccharide hydrophilic head at decane-water and toluene-water interfaces. For TX-100, we composed a model based on the literature forcefield and found good agreement with the experimental critical micelle concentrations (CMCs). The head-head interactions are of different origins for different surfactant groups: entropic repulsion between ethylene oxide chains of C12E6 and TX-100, and more chemically specific and complex interactions between the maltose heads of alkyl glucosides. We interpret our results with the Redlich-Peterson equation of monolayer adsorption in order to relate the adsorption to the bulk concentration of the surfactant and the interfacial tension. The densities of the adsorbed monolayer at CMC mostly agree with the experimental data, and a reasonable agreement was obtained for the interfacial tension at CMC. At the same time, we found significant discrepancies between the simulated and experimental adsorption isotherms. We explain them by the oversimplified forcefield: when the parameters are fitted to the free energies of bulk solutions, they may not correctly reproduce the interfacial free energies.

Mobility of Polymer Melts in a Regular Array of Carbon Nanotubes

In polymer nanocomposites, mechanical properties essentially depend on the alignment of nanoparticles and polymers. In this work, we investigate an entangled polymer melt in a confinement computationally, in order to get an insight into the mobility behavior of the polymer chains. The confinement consists of nanotubes, arranged in a hexagonal array. We use dissipative particle dynamics, a fast, soft-core simulation method, and reintroduce entanglement dynamics via slip-springs. We observe a distinct influence of the confinement as diffusion is increased in the direction parallel to the nanotubes. Furthermore, we observe that an orientation of the polymers parallel to the nanotubes and chains are compressed in the direction orthogonal to their primitive path. The diffusion parallel to the nanotubes increases further as we increase the nanotube volume fraction in our systems. Moreover, we investigate the slip-spring distribution in the proximity of the nanotube surfaces of our fast and simple slip-spring model, which we find to coincide with results reported for more sophisticated and expensive methods. Our DPD model shows potential applicability to a wide range of polymer nanocomposites while preserving reptation behavior, which is typically lost due to the use of soft-core models.

Knotting behaviour of polymer chains in the melt state for soft-core models with and without slip-springs

We analyse the knotting behaviour of linear polymer melts in two types of soft-core models, namely dissipative-particle dynamics and hybrid-particle-field models, as well as their variants with slip-springs which are added to recover entangled polymer dynamics. The probability to form knots is found drastically higher in the hybrid-particle-field model compared to its parent hard-core molecular dynamics model. By comparing the knottedness in dissipative-particle dynamics and hybrid-particle-field models with and without slip-springs, we find the impact of slip-springs on the knotting properties to be negligible. As a dynamic property, we measure the characteristic time of knot formation and destruction, and find it to be (i) of the same order as single-monomer motion and (ii) independent of the chain length in all soft-core models. Knots are therefore formed and destroyed predominantly by the unphysical chain crossing. This work demonstrates that the addition of slip-springs does not alter the knotting behaviour, and it provides a general understanding of knotted structures in these two soft-core models of polymer melts.

Fine Grained Tensor Network Methods.

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2D tensor networks-such as corner transfer matrix renormalization schemes-which are more involved on complex lattice structures. We prove the validity of our approach by numerically computing the ground-state properties of the ferromagnetic spin-1 transverse-field Ising model on the 2D triangular and 3D stacked triangular lattice, as well as of the hardcore and softcore Bose-Hubbard models on the triangular lattice. Our results are benchmarked against those obtained with other techniques, such as perturbative continuous unitary transformations and graph projected entangled pair states, showing excellent agreement and also improved performance in several regimes.

Explanation of main tunneling mechanism in electrical conductivity of polymer/carbon nanotubes nanocomposites by interphase percolation

In this paper, the tunneling effect as the main mechanism for charge transferring in polymer/carbon nanotubes (CNT) nanocomposites (PCNT) is correlated with interphase percolation. Soft-core and hard-core models express the percolation threshold based on a previous report. Furthermore, the tunneling effect is related to the interphase layer around the nanoparticles and the excluded volume and percolation threshold are defined for this case. The calculations of all models are compared to the experimentally measured percolation threshold in some samples. The predictions of soft-core and hard-core approaches deviate from the low percolation threshold in PCNT. It is found that the model assuming the interphase as tunneling distance can properly describe the low level of percolation threshold in PCNT. Based on this model, the effects of main parameters on the percolation threshold and the electrical conductivity of PCNT are described. The predictions demonstrate that the thin and long CNT together with the thick interphase show positive impacts on the percolation threshold and conductivity.

Effect of a core-softened O–O interatomic interaction on the shock compression of fused silica

Isotropic soft-core potentials have attracted considerable attention due to their ability to reproduce thermodynamic, dynamic, and structural anomalies observed in tetrahedral network-forming compounds such as water and silica. The aim of the present work is to assess the relevance of effective core-softening pertinent to the oxygen-oxygen interaction in silica to the thermodynamics and phase change mechanisms that occur in shock compressed fused silica. We utilize the MD simulation method with a recently published numerical interatomic potential derived from an ab initio MD simulation of liquid silica via force-matching. The resulting potential indicates an effective shoulder-like core-softening of the oxygen-oxygen repulsion. To better understand the role of the core-softening we analyze two derivative force-matching potentials in which the soft-core is replaced with a repulsive core either in the three-body potential term or in all the potential terms. Our analysis is further augmented by a comparison with several popular empirical models for silica that lack an explicit core-softening. The first outstanding feature of shock compressed glass reproduced with the soft-core models but not with the other models is that the shock compression values at pressures above 20 GPa are larger than those observed under hydrostatic compression (an anomalous shock Hugoniot densification). Our calculations indicate the occurrence of a phase transformation along the shock Hugoniot that we link to the O–O repulsion core-softening. The phase transformation is associated with a Hugoniot temperature reversal similar to that observed experimentally. With the soft-core models, the phase change is an isostructural transformation between amorphous polymorphs with no associated melting event. We further examine the nature of the structural transformation by comparing it to the Hugoniot calculations for stishovite. For stishovite, the Hugoniot exhibits temperature reversal and associated phase transformation, which is a transition to a disordered phase (liquid or dense amorphous), regardless of whether or not the model accounts for core-softening. The onset pressures of the transformation predicted by different models show a wide scatter within 60-110 GPa; for potentials without core-softening, the onset pressure is much higher than 110 GPa. Our results show that the core-softening of the interaction in the oxygen subsystem of silica is the key mechanism for the structural transformation and thermodynamics in shock compressed silica. These results may provide an important contribution to a unified picture of anomalous response to shock compression observed in other network-forming oxides and single-component systems with core-softening of effective interactions.

Nucleation simulation using a model of hard/soft discs

In this paper we present a computer study of the quantum dot (QD) nucleation probability with three possible models of particle interaction; Soft Core (SC), Hard Core (HC) and Hard Core/Soft Shell (HCSS) model. Computer analysis of the nucleation probability is performed on a 500 by 500 lattice with 2000 simulations per event. If a matrix is assumed to represent an SiO2 substrate in which a pure Si quantum dot can grow, it is demonstrated that nucleation centers are more easily distinguished and initially more likely to form in the SC and HCSS models rather than in the HC model. If particles are allowed to move, nucleation centers can appear even in the HC model independent of a preexisting local density. A low probability of nucleation in the HC model and a high probability of nucleation in the SC model are evident from the system entropy curve. The probability of nucleation, therefore, depends on the local density change, percolation probability and system entropy. Low probability of nucleation in the HC model is in accordance with a lower probability of percolating clusters forming in a given model.

Linear Basis Function Approach to Efficient Alchemical Free Energy Calculations. 1. Removal of Uncharged Atomic Sites.

We present a general approach to transform between molecular potential functions during free energy calculations using a variance minimized linear basis functional form. This approach splits the potential energy function into a sum of pairs of basis functions, which depend on coordinates, and 'alchemical' switches, which depend only on the coupling variable. The power of this approach is that, first, the calculation of the coupling parameter dependent terms is removed from inner loop force calculation routines, second, the flexibility in specifying basis functions and alchemical switches allows users to choose transformation pathways that maximize statistical efficiency, and third, it is possible to predict entirely in postprocessing, without any additional energy evaluations, the thermodynamic properties along any alchemical path with moderate overlap from an initial simulation that uses the same basis functions. This allows construction of optimized, minimum variance alchemical switches from a single simulation with fixed basis functions and trial alchemical switching functions. We describe how to construct these linear basis potentials for real molecular systems of different sizes and shapes, considering particularly the problems of eliminating singularities and minimizing variance of particle removal in dense fluids. The statistical error in free energy calculations using the optimized basis functions is lower than standard soft core models, and approach the minimum variance possible over all pair potentials. We recommend an optimized set of basis functions and alchemical switches for standard molecular free energy calculations.

Gutzwiller study of phase diagrams of extended Bose—Hubbard models

Hard-core and soft-core extended Bose-Hubbard models with fixed boson densities are studied by using the Gutzwiller variational wave function. The phase diagram of the softcore model strongly depends on its transfer integral. Specifically, a supersolid phase can be the ground state even below half-filling for a large transfer integral. The density difference between nearest-neighbor sites, which is an order parameter of the supersolid phase, strongly depends on the boson density, especially for a small transfer integral.

Fast off-lattice Monte Carlo simulations of soft-core spherocylinders: Isotropic-nematic transition and comparisons with virial expansion

We proposed a novel anisotropic soft-core potential for spherocylinders that takes into account the degree of overlap between two spherocylinders, thus superior to other soft-core spherocylinder models depending only on the minimum distance between two line segments representing spherocylinders, for example, that used by Vink and Schilling [Phys. Rev. E 71, 051716 (2005)]. Using Monte Carlo simulations in an isothermal-isobaric ensemble with replica exchange at different pressures and multiple histogram re-weighting technique, we studied the isotropic-nematic transition of both models, which recover the standard model of hard spherocylinders for liquid crystals as the repulsion strength ε → ∞, and compared simulation results with virial expansion predictions. We found that isotropic-nematic transition still occurs at high enough densities even for small ε, and that virial expansion predictions become more accurate with increasing aspect ratio of spherocylinders and should be exact in the limit of infinitely large aspect ratio.

Quasi-exactly solvable relativistic soft-core Coulomb models

By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein–Gordon and Dirac equations with the family of soft-core Coulomb potentials Vq(r)=−Z/(rq+βq)1/q, Z>0, β>0, q≥1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations.

Probing ???? Potential

We determined scattering length and effective range of ¥E¥E scattering for the ¥E¥E relative energy (M¥E¥E-2M¥E) from ¥E¥E threshold to 30 MeV/c2. Phase shift of the ¥E¥E wave function which described by scattering length and effective range was determined by fitting the ¥E¥E mass spectrum. The obtained scattering length -0.10+0.37-1.56 i¾ 0.04, and effective range 13.90 +14.35-9.13 i¾ 10.53 fm is the most consistent with the values predicted by using a series of the Nijmegen soft core models NSC97's. However the predicted values by using the Nijmegen hard core model ND (G-matrix), the extended soft core model ESC00, and the Kyoto-Niigata FSS are out of three standard deviations from the determined scattering parameters. Further, we determine ¥E¥E potential by fitting the ¥E¥E invariant mass spectrum using numerically solved ¥E¥E wave function with two-Gaussian shaped potential well. The ¥E¥E scattering parameters derived from the wave function are found to be scattering length -0.09, and effective range 29.34 fm with a maximum phase shift of 2.4 deg.

EXTRACTION OF ΛΛ SCATTERING LENGTH

We determine ΛΛ scattering parameters from a ΛΛ invariant mass spectrum that was obtained by 12 C (K-, K+ΛΛ) reaction at the KEK Proton Synchrotron. In the framework of Watson's procedure, the obtained scattering length [Formula: see text] and effective range [Formula: see text] are most consistent with the values predicted by using the Nijmegen soft core models (NSC97's). However, the predicted values by using the Nijmegen hard-core ND ( G -matrix) and the extended soft-core (ESC00) models are out of two standard deviations from the determined scattering parameters.

Reliability of soft-core approximations in theoretical studies of molecules in intense laser fields

The popular approach of softening the Coulomb singularity in models with reduced dimensionality leads to uncontrollable discrepancies with numerical results obtained using exact potentials. This is demonstrated for ionization and dissociation probabilities as well as for high-order harmonic generation spectra even of the simple hydrogen molecular ion in aligned geometry. Soft-core models perform better in full dimensions, thereby losing one of their advantages, namely the gain in computation time that is achieved by going to reduced dimensionality. However, the much simpler numerical implementation of soft-core potentials carries over to full dimensions. Moreover, a generalization of the soft-core potential given in previous work [M. Lein, P. P. Corso, J. P. Marangos, and P. L. Knight, Phys. Rev. A 67, 023819 (2003)] is proposed, leading to a tremendous improvement toward the exact results, which is very promising for future calculations without cylindrical symmetry.

Counterintuitive ground states in soft-core models

It is well known that statistical mechanics systems exhibit subtle behavior in high dimensions. In this paper, we show that certain natural soft-core models, such as the Gaussian core model, have unexpectedly complex ground states even in relatively low dimensions. Specifically, we disprove a conjecture of Torquato and Stillinger, who predicted that dilute ground states of the Gaussian core model in dimensions 2 through 8 would be Bravais lattices. We show that in dimensions 5 and 7, there are in fact lower-energy non-Bravais lattices. (The nearest three-dimensional analog is the hexagonal close-packing, but it has higher energy than the face-centered cubic lattice.) We believe these phenomena are in fact quite widespread, and we relate them to decorrelation in high dimensions.

Frustration and anomalous behavior in the Bell-Lavis model of liquid water

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.

An investigation of soft-core potentials for the simulation of mesogenic molecules and molecules composed of rigid and flexible segments

The phase behaviour of three soft core spherocylinder models is investigated with a view to producing an effective potential for use in coarse-grained simulations of liquid crystal phases and polymers composed of rigid and flexible segments. Provided potentials are not made too soft, two of the soft core models are found to work well in terms of successfully reproducing mesophases and in providing considerable improvements in computational speed over other commonly used coarse-grained models. In Monte Carlo simulations a soft-core spherocylinder model in which a cut and shifted Lennard–Jones potential is truncated with a linear tangential potential is found to be particularly effective; while for molecular dynamics a better model is provided by a DPD-like quadratic potential. Here, computational speed-ups of 20 – 30 × are seen in equilibration times in comparison to the well-known soft repulsive spherocylinder (SRS) model. The quadratic potential is used in an additional set of coarse-grained simulations of a liquid crystal with a flexible chain, which exhibits spontaneous formation of a nematic phase. The use of different types of interaction sites is also illustrated by the simulation of a spherocylinder with two “tails” formed from spheres. Here, varying the hardness of the sphere-spherocylinder interaction potential allows the formation of a smectic-A phase which exhibits microphase separation.

Modeling percolation in high-aspect-ratio fiber systems. I. Soft-core versus hard-core models

Numerical and analytical studies of the onset of percolation in high-aspect-ratio fiber fiber systems such as nanotube reinforced polymers available in the literature have consistently modeled fibers as penetrable, straight, capped cylinders, also referred to as spherocylinders. In reality, however, fibers of very high-aspect ratio embedded in a polymer do not come into direct physical contact with each other, let alone exhibit any degree of penetrability. Further, embedded fibers of very high-aspect ratio are often actually wavy, rather than straight. In this two-part paper we address these critical differences between known physical systems, and the presently used spherocylinder percolation model. In Paper I we evaluate the effect of allowing penetration of the model fibers on simulation results by comparing the soft-core and the hard-core approaches to modeling percolation onset. We use Monte Carlo simulations to investigate the relationship between percolation threshold and excluded volume for both modeling approaches. Our results show that the generally accepted inverse proportionality between percolation threshold and excluded volume holds for both models. We further demonstrate that the error introduced by allowing the fibers to intersect is non-negligible, and is a function of both aspect ratio and tunneling distance. Thus while the results of both the soft-core model and hard-core assumptions can be matched to select experimental results, the hard-core model is more appropriate for modeling percolation in nanotubes-reinforced composites. The hard-core model can also potentially be used as a tool in calculating the tunneling distance in composite materials, given the fiber morphology and experimentally derived electrical percolation threshold. In Paper II we investigate the effect of the waviness of the fibers on the onset of percolation in fiber reinforced composites.