Lennard-Jones Chains Research Articles

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules.

Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been shown to exist in molecular models with flexible bonds [Olsen, A. E. J. Chem. Phys. 2016, 145, 241103]. We here present three force-based methods to trace out pseudoisomorphs based on a single configuration and test them on the asymmetric dumbbell and 10-bead Lennard-Jones chain models with bonds modeled as harmonic springs. The three methods are based on requiring that particle forces, center-of-mass forces, and torques, respectively, are invariant in reduced units. For each of the two investigated models we identify a method that works well for tracing out pseudoisomorphs, but these methods are not the same. Overall, we find that the more internal degrees of freedom there are in the molecule studied, the less they appear to affect the gross dynamical behavior. Moreover, the "internal" degrees of freedom (including rotation) do not significantly affect the scaling behavior of the dynamical/transport coefficients provided some 'quenching' is performed.

A systematic analysis of the memory term in coarse-grained models: The case of the Markovian approximation

The systematic development of coarse-grained (CG) models via the Mori–Zwanzig projector operator formalism requires the explicit description of a deterministic drift term, a dissipative memory term and a random fluctuation term. The memory and fluctuating terms are related by the fluctuation–dissipation relation and are more challenging to sample and describe than the drift term due to complex dependence on space and time. This work proposes a rational basis for a Markovian data-driven approach to approximating the memory and fluctuating terms. We assumed a functional form for the memory kernel and under broad regularity hypothesis, we derived bounds for the error committed in replacing the original term with an approximation obtained by its asymptotic expansions. These error bounds depend on the characteristic time scale of the atomistic model, representing the decay of the autocorrelation function of the fluctuating force; and the characteristic time scale of the CG model, representing the decay of the autocorrelation function of the momenta of the beads. Using appropriate parameters to describe these time scales, we provide a quantitative meaning to the observation that the Markovian approximation improves as they separate. We then proceed to show how the leading-order term of such expansion can be identified with the Markovian approximation usually considered in the CG theory. We also show that, while the error of the approximation involving time can be controlled, the Markovian term usually considered in CG simulations may exhibit significant spatial variation. It follows that assuming a spatially constant memory term is an uncontrolled approximation which should be carefully checked. We complement our analysis with an application to the estimation of the memory in the CG model of a one-dimensional Lennard–Jones chain with different masses and interactions, showing that even for such a simple case, a non-negligible spatial dependence for the memory term exists.

Molecular dynamics simulations of droplet fusion reveals shear thinning

Recent experiments have shown that biomolecular condensates are viscoelastic rather than purely viscous. One possible consequence, from both experimental and theoretical studies [1, 2], is that condensates exhibit shear thickening or shear thinning, i.e., with effective viscosity higher or lower than the zero-shear viscosity. To gain deeper physical insight into the effects of viscoelasticity on condensate dynamics, here we carried out molecular dynamics simulations of droplet fusion. The droplets were formed from phase separation of Lennard-Jones particles or chains.

Bulk phase behavior and interfacial properties of binary mixtures of Lennard-Jones chains and solvent: a density functional theory study.

A Density Functional Theory study is performed to analyze both bulk and interfacial properties of solvent-polymer binary mixtures. The effects of increasing polymer chain length on the bulk phase diagram morphology and interfacial tension are presented and compared to the prior simulation results. Good agreement between simulation and Density Functional Theory is found, including its ability to reproduce the density inversion phenomenon for highly asymmetric solvent-polymer binary mixtures. The data on the interfacial tensions is used to compute contact angles of the mixture at a planar wall, with particular focus on the wetting transition. The dependence of the wetting temperature on the polymer chain length and the mixture composition is analyzed in detail.

Thermodynamic Scaling of the Shear Viscosity of Lennard-Jones Chains of Variable Rigidity

In this work, the thermodynamic scaling framework has been used to emphasize the limitations of fully flexible coarse grained molecular models to yield shear viscosity of real liquids. In particular, extensive molecular dynamics simulations have confirmed that, while being reasonable to describe the viscosity of short normal alkanes, the fully flexible Lennard-Jones and Mie chains force fields are inadequate to capture the density dependence of shear viscosity of medium to long alkanes. In addition, it is shown that such a weakness in terms of coarse grained molecular models can be readily quantified by using the thermodynamic scaling framework. As a simple alternative to these force fields, it is demonstrated that the insertion of a variable intramolecular rigidity in the Lennard-Jones chains model exhibits promising results to model medium to long chain-like real fluids from both thermodynamic and viscosity points of view.

Structure and Contact Angle in Sessile Droplets of Binary Mixtures of Lennard-Jones Chains: A Molecular Dynamics Study.

Molecular dynamics simulations were carried out to investigate cylindrical droplets consisting of binary mixtures of Lennard-Jones (LJ) fluids in contact with a solid substrate. The droplets are composed of mixtures of the monomeric LJ fluid plus linear-tangent chains of 2, 10, 20, and 30 segments per chain that interact through a harmonic potential and the spherically truncated and shifted potential Lennard-Jones. The solid surface was modeled as a semi-infinite platinum substrate with an FCC structure that interacts with the fluid by means of a LJ 9-3 potential. We place emphasis on the effect of mixing a monomeric LJ fluid with heavy components on the contact angle and on the droplet structure, especially in the liquid-solid region. The density profiles of the droplets reveal a strong discrete layering of the fluid in the vicinity of the solid-liquid interface. The layering is more pronounced at low temperatures and for mixtures of short chains (symmetric mixtures). The ordering of the fluid was much less intense for fluids of long chains (asymmetric mixtures), and some cases even show gas enrichment at the solid-liquid interface. Enrichment at the vapor-liquid interfaces and density inversion can also be observed. However, these effects are not as marked as in planar interfaces. The contact angle between the droplet and the substrate is calculated by fitting an ellipse to the vapor-liquid interface defined by the Gibbs dividing surface. In general, an increment in the concentration of the heavy component and a reduction of the temperature resulted in an increase of the contact angle, which in turn disfavored the wetting of the droplet.

Mechanisms for transient localization in a diatomic nonlinear chain

We investigate transient nonlinear localization, namely the self-excitation of energy bursts in an atomic lattice at finite temperature. As a basic model we consider the diatomic Lennard-Jones chain. Numerical simulations suggest that the effect originates from two different mechanisms. One is the thermal excitation of genuine discrete breathers with frequency in the phonon gap. The second is an effect of nonlinear coupling of fast, lighter particles with slow vibrations of the heavier ones. The quadratic term of the force generate an effective potential that can lead to transient grow of local energy on time scales the can be relatively long for small mass ratios. This heuristics is supported by a multiple-scale approximation based on the natural time-scale separation. For illustration, we consider a simplified single-particle model that allows for some insight of the localization dynamics.

Macromolecular regulators have matching effects on the phase equilibrium and interfacial tension of biomolecular condensates.

The interfacial tension of phase-separated biomolecular condensates affects their fusion and multiphase organization, and yet how this important property depends on the composition and interactions of the constituent macromolecules is poorly understood. Here we use molecular dynamics simulations to determine the interfacial tension and phase equilibrium of model condensate-forming systems. The model systems consist of binary mixtures of Lennard-Jones particles or chains of such particles. We refer to the two components as drivers and regulators; the former has stronger self-interactions and hence a higher critical temperature (Tc ) for phase separation. In previous work, we have shown that, depending on the relative strengths of driver-regulator and driver-driver interactions, regulators can either promote or suppress phase separation (i.e., increase or decrease Tc ). Here we find that the effects of regulators on Tc quantitatively match the effects on interfacial tension (γ). This important finding means that, when a condensate-forming system experiences a change in macromolecular composition or a change in intermolecular interactions (e.g., by mutation or posttranslational modification, or by variation in solvent conditions such as temperature, pH, or salt), the resulting change in Tc can be used to predict the change in γ and vice versa. We also report initial results showing that disparity in intermolecular interactions drives multiphase coexistence. These findings provide much needed guidance for understanding how biomolecular condensates mediate cellular functions.

Interfacial properties of binary mixtures of Lennard-Jones chains in planar interfaces by molecular dynamics simulation.

Binary mixtures of fully flexible linear tangent chains composed of bonded Lennard-Jones interaction sites (monomers) were studied using the molecular dynamics simulation in the NVT ensemble. Their interfacial properties were investigated in planar interfaces by direct simulation of an explicit liquid film in equilibrium with its vapor. A method for the calculation of long-range interactions in inhomogeneous fluids was implemented to take into account the potential truncation effects. Surface tension and the pressure tensor were calculated via the classical Irving-Kirkwood method; vapor pressure, orthobaric densities, density profiles, and Gibbs relative adsorption of the volatile component with respect to the heavy component were also obtained. The properties were studied as a function of the temperature, molar concentration of the heavy component, and the asymmetry of the mixture. According to the results of this work, the temperature loses influence on the surface tension, vapor pressure, and Gibbs relative adsorption curves as the molecular length of the heavy component increases. This suggests that the universal behavior observed in pure fluids of Lennard-Jones chains also holds for binary mixtures. The contribution of the long-range interactions turned out to account for about 60%, 20%, and 10% of the surface tension, vapor pressure, and orthobaric density final values, respectively. This contribution was even larger at high temperatures and for large molecules. Strong enrichment of the volatile component at the interface was observed in the asymmetric mixtures. One of these mixtures even showed a barotropic effect at elevated pressures and a class III phase behavior.

An entropy scaling demarcation of gas- and liquid-like fluid behaviors.

In this work, we propose a generic and simple definition of a line separating gas-like and liquid-like fluid behaviors from the standpoint of shear viscosity. This definition is valid even for fluids such as the hard sphere and the inverse power law that exhibit a unique fluid phase. We argue that this line is defined by the location of the minimum of the macroscopically scaled viscosity when plotted as a function of the excess entropy, which differs from the popular Widom lines. For hard sphere, Lennard-Jones, and inverse-power-law fluids, such a line is located at an excess entropy approximately equal to -2/3 times Boltzmann's constant and corresponds to points in the thermodynamic phase diagram for which the kinetic contribution to viscosity is approximately half of the total viscosity. For flexible Lennard-Jones chains, the excess entropy at the minimum is a linear function of the chain length. This definition opens a straightforward route to classify the dynamical behavior of fluids from a single thermodynamic quantity obtainable from high-accuracy thermodynamic models.

A perturbed-chain equation of state based on Wertheim TPT for the fully flexible LJ chains in the fluid and solid phases.

In the framework of thermodynamic perturbation theory (TPT), a new perturbed-chain equation of state (EOS) is presented for a fully flexible Lennard-Jones (LJ) chain system. The EOS is the sum of repulsive and perturbation contributions. The reference term of the EOS is derived based on first- and second-order TPT of Wertheim for the chains interacting with each other through the Weeks-Chandler-Anderson potential model. In order to derive the perturbation term, we have used the radial distribution function of the hard-chain system with a chain range of m = 2-10 and packing fraction range of η = 0.10-0.72, which cover the entire density range from vapor to solid phases. The performance of the EOS is tested against simulation data of the compressibility factor, residual internal energy, and phase equilibrium. A close agreement was observed across all cases. The EOS has three pure component parameters and is able to describe the global vapor-liquid-solid phase diagram of the LJ chain.

O(N) Fluctuations and Lattice Distortions in 1-Dimensional Systems

Statistical mechanics harmonizes mechanical and thermodynamical quantities, via the notion of local thermodynamic equilibrium (LTE). In absence of external drivings, LTE becomes equilibrium tout court, and states are characterized by several thermodynamic quantities, each of which is associated with negligibly fluctuating microscopic properties. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the system are represented by the transport coefficients. In 1-dimensional systems, on the other hand, various anomalies are { reported}, such as the dependence of the {heat conductivity} on the global state, rather than on the local state. { Such deductions, that rely on the existence of thermodynamic quantities like temperature and heat, are here} interpreted within the framework of boundary driven 1-dimensional Lennard-Jones chains of $N$ oscillators. { It is found that these chains} experience non-negligible $O(N)$ lattice distortions and fluctuations, { in contrast with the requirements of LTE}.

Cluster sizes in a classical Lennard-Jones chain.

The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, 〈K〉, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that 〈K〉 increases exponentially with β=1/k_{B}T and with pressure, P in agreement with previous results in the literature. A method is illustrated for using 〈K〉(β,P) to generate a "phase diagram" for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.

Thermodynamic regimes over which homologous alkane fluids can be treated as simple liquids

We compare the extent to which the properties of simple liquids are pertinent to short to moderate chain n-alkanes ranging from ethane (C2) to dodecane (C12). Explicit geometric features such as bonds, angles and dihedral potentials in currently available models of n-alkanes make these systems more realistic, and distinct from the generalized Lennard-Jones chain fluids. Our study confirms that the presence of these flexible geometric constraints completely suppresses the energy-virial correlation in these systems. However, they are found to have a strong energy-virial correlation in high density region of their phase diagram when the contribution from these geometric constraints are excluded. For fluids having simple liquid like behavior, semi-quantitative relationships between structure, dynamics, and thermodynamics are well established. Range of state points is explored to test the applicability of such relationships for n-alkanes. Considering the collection of monomer beads as the reference state, thermodynamic and structural entropic measures are systematically compared with and without intramolecular contributions. We show that the pair entropy computed with explicit intramolecular geometric constraints correlates well with thermodynamic excess entropy. Both the thermodynamic and pair entropy have strong isochore dependence with reduced diffusivity. Intermolecular pair entropy correlates well with reduced diffusivity. The role of multiparticle correlations is highlighted for predicting thermodynamic and transport properties in these chain systems. Triplet correlations in addition to pair correlations are used as an attempt to improve the structural contribution to excess entropy. We show that if the three particle contribution is included in the computation of structural entropy, the resulting value overestimates the excess entropy.

Vapour–liquid phase equilibrium and surface tension of fully flexible Lennard–Jones chains

ABSTRACTWe report measurements of the vapour–liquid coexistence densities and surface tension of fully flexible Lennard–Jones chain molecules ranging in length from 4 to 60 beads. We demonstrate that the surface tension for all chain lengths collapses to a single master curve when plotted according to the universal parachor correlation. We find a universal parachor exponent 3.79 ± 0.05 for conditions close to the critical point, with a deviation observed for the longest chains far below the critical point.

Heat conduction in diatomic chains with correlated disorder

The paper considers heat transport in diatomic one-dimensional lattices, containing equal amounts of particles with different masses. Ordering of the particles in the chain is governed by single correlation parameter – the probability for two neighboring particles to have the same mass. As this parameter grows from zero to unity, the structure of the chain varies from regular staggering chain to completely random configuration, and then – to very long clusters of particles with equal masses. Therefore, this correlation parameter allows a control of typical cluster size in the chain. In order to explore different regimes of the heat transport, two interatomic potentials are considered. The first one is an infinite potential wall, corresponding to instantaneous elastic collisions between the neighboring particles. In homogeneous chains such interaction leads to an anomalous heat transport. The other one is classical Lennard–Jones interatomic potential, which leads to a normal heat transport. The simulations demonstrate that the correlated disorder of the particle arrangement does not change the convergence properties of the heat conduction coefficient, but essentially modifies its value. For the collision potential, one observes essential growth of the coefficient for fixed chain length as the limit of large homogeneous clusters is approached. The thermal transport in these models remains superdiffusive. In the Lennard–Jones chain the effect of correlation appears to be not monotonous in the limit of low temperatures. This behavior stems from the competition between formation of long clusters mentioned above, and Anderson localization close to the staggering ordered state.

Dilute gas viscosity of n-alkanes represented by rigid Lennard-Jones chains

ABSTRACTThe shear viscosity in the dilute gas limit has been calculated by means of the classical trajectory method for a gas consisting of chain-like molecules. The molecules were modelled as rigid chains made up of spherical segments that interact through a combination of site–site Lennard-Jones 12-6 potentials. Results are reported for chains consisting of 2, 3, 4, 6, 8, 12 and 16 segments in the reduced temperature range of 0.3–50 for site–site separations of 0.25σ, 0.333σ, 0.40σ, 0.60σ and 0.80σ, where σ is the Lennard-Jones length scaling parameter. The results were used to determine the shear viscosity of n-alkanes in the zero-density limit by representing an n-alkane molecule as a rigid linear chain consisting of nc − 1 spherical segments, where nc is the number of carbon atoms. We show that for a given n-alkane molecule, the scaling parameters ϵ and σ are not unique and not transferable from one molecule to another. The commonly used site–site Lennard-Jones 12-6 potential in combination with a rigid-chain molecular representation can only accurately mimic the viscosity if the scaling parameters are fitted. If the scaling parameters are estimated from the scaling parameters of other n-alkanes, the predicted viscosity values have an unacceptably high uncertainty.

Confining interparticle potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems

We provide molecular dynamics simulation of heat transport and energy diffusion in one-dimensional molecular chains with different interparticle pair potentials at zero and non-zero temperature. We model the thermal conductivity (TC) and energy diffusion (ED) in the chain of coupled rotators and in the Lennard-Jones chain either without or with the confining parabolic interparticle potential. The considered chains without the confining potential have normal TC and ED at non-zero temperature, while the corresponding chains with the confining potential are characterized by anomalous (diverging with the system length) TC and superdiffusion of energy. Similar effect is produced by the anharmonic quartic confining pair potential. We confirm in such a way that, surprisingly, the confining pair potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems. We show that the normal TC is always accompanied by the normal ED in the thermalized anharmonic chains, while the superdiffusion of energy occurs in the thermalized chains with only anomalous heat transport.

Liquid-crystal phase equilibria of Lennard-Jones chains

ABSTRACTLiquid-crystal phase equilibria of Lennard-Jones chain fluids and the solubility of a Lennard-Jones gas in the coexisting phases are calculated from Monte Carlo simulations. Direct phase equilibria calculations are performed using an expanded formulation of the Gibbs ensemble. Monomer densities, order parameters, and equilibrium pressures are reported for the coexisting isotropic and nematic phases of: (1) linear Lennard-Jones chains, (2) a partially-flexible Lennard-Jones chain, and (3) a binary mixture of linear Lennard-Jones chains. The effect of chain length is determined by calculating the isotropic-nematic coexistence of linear Lennard-Jones chain fluids made of 8, 10, and 12 segments (8-, 10-, 12-mer). The effect of molecular flexibility on the isotropic-nematic equilibrium is studied for a Lennard-Jones 10-mer chain fluid with one freely-jointed segment at the end of the chain. An isotropic-nematic phase split and fractionation are reported for a binary mixture of linear 7-mer and 12-mer chains. Simulation results are compared with theoretical results as obtained from a recently developed analytical equation of state based on perturbation theory. Excellent agreement between theory and simulations is observed. The solubility of a monomer Lennard-Jones gas in the coexisting isotropic and nematic phases is estimated using the Widom test-particle insertion method. A linear relationship between solubility difference and density difference at isotropic-nematic coexistence is observed. It is shown that gas solubility is independent of the nematic ordering of the fluid, at constant temperature and density conditions.

Properties of π-mode vibrations in strained carbon chains

Nonlinear vibrations in strained monoatomic carbon chains are studied with the aid of ab initio methods based on the density functional theory. An unexpected phenomenon of structural transformation at the atomic level above a certain value of the strain was revealed in cumulene chain (carbyne-β). This phenomenon is a consequence of stability loss of the old equilibrium atomic positions that occur at small strain, and appearance of two new stable equilibrium positions near each of them. The aforementioned restructuring gives rise to a softening of π-mode whose frequency tends to zero in a certain region of amplitudes when carbon atoms begin to vibrate near new equilibrium positions. This resembles the concept of soft mode whose “freezing” is postulated in the theory of phase transitions in crystals to explain the transitions of displacement type. The dynamical modeling of mass point chains whose particles interact via Lennard-Jones potential can approximate our ab initio results well enough. In particular, this study demonstrates an essential role of dipole-dipole interactions between carbon atoms in formation of their new equilibrium positions in the cumulene chain. We believe that computer studying of Lennard-Jones chains enables to predict properties of various dynamical objects in carbon chains (different nonlinear normal modes and their bushes, discrete breathers etc.) which then can be verified by ab initio methods.