Lennard-Jones Dimers Research Articles

Accurate thermodynamics of simple fluids and chain fluids based on first-order perturbation theory and second virial coefficients: uv-theory.

We develop a simplification of our recently proposed uf-theory for describing the thermodynamics of simple fluids and fluids comprising short chain molecules. In its original form, the uf-theory interpolates the Helmholtz energy between a first-order f-expansion and first-order u-expansion as (effective) lower and upper bounds. We here replace the f-bound by a new, tighter (effective) lower bound. The resulting equation of state interpolates between a first-order u-expansion at high densities and another first-order u-expansion that is modified to recover the exact second virial coefficient at low densities. The theory merely requires the Helmholtz energy of the reference fluid, the first-order u-perturbation term, and the total perturbation contribution to the second virial coefficient as input. The revised theory-referred to as uv-theory-is thus simpler than the uf-theory but leads to similar accuracy, as we show for fluids with intermolecular pair interactions governed by a Mie potential. The uv-theory is thereby easier to extend to fluid mixtures and provides more flexibility in extending the model to non-spherical or chain-like molecules. The usefulness of the uv-theory for developing equation-of-state models of non-spherical molecules is here exemplified by developing an equation of state for Lennard-Jones dimers.

Density functional theory for molecular liquids based on interaction site model and self-consistent integral equations for site-site pair correlation functions.

We propose a novel classical density functional theory (DFT) for inhomogeneous polyatomic liquids based on the grand canonical ensemble of a solute-solvent system. Different from the existing DFT for interaction site model developed by Chandler et al. [J. Chem. Phys. 85, 5971 (1986)], the fundamental quantities in the present theory are the radial density distributions around the atomic site of the solute molecule. With this development and the reference interaction site model equation, we provide self-consistent integral equations for calculating the site-site pair correlation function (PCF) and apply it to the structure of the Lennard-Jones dimer, HCl, and H2O molecular fluids. The site-site PCFs obtained from the new scheme agree well with those from Monte Carlo simulation results.

Modeling Thermodynamic Properties of Isomeric Alkanes with a New Branched Equation of State

In this paper we present an extension of the statistical associating fluid theory (SAFT) for branched molecules with a Lennard-Jones dimer reference fluid (SAFTD-LJ-Branch). The theory successfully predicts how branched architecture affects the attraction and repulsion between molecules. SAFTD-LJ-Branch takes a form similar to SAFTD-LJ with an additional parameter NB introduced to account for the branching effect. We propose an approach relating NB to the number of different types of articulation segments. The theory is used to study the effect of chain architecture on the thermodynamic properties of isomeric alkanes. SAFTD-LJ-Branch accurately predicts the phase diagram of pure butane, pentane or hexane isomers. Further, vapor pressures of n-triacontane and squalane are predicted without further fitting and shown to be in semiquantitative agreement with experimental data. Finally, SAFTD-LJ-Branch is demonstrated to be well applicable to mixtures as we model the vapor–liquid coexistence of binary alkane mixtures containing different hexane isomers and recover the experimental trends.

Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study.

Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures.

Development of molecular closures for the reference interaction site model theory with application to square-well and Lennard-Jones homonuclear diatomics

Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with ‘molecular closures’ (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their ‘atomic’ counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.

Surface impacts and collisions of particle-laden nanodrops

The surface impact and collisions of particle-laden nanodrops are studied using molecular dynamics computer simulations. The drops are composed of Lennard-Jones dimers and the particles are rigid spherical sections of a cubic lattice, with radii about 11 nm and 0.6 nm, respectively. Uniform suspensions of 21% and 42% particle concentrations and particle-coated drops are studied, and their behavior is compared to that of pure fluid drops of the same size. The relative velocities studied span the transition to splashing, and both wetting/miscible and non-wetting/immiscible cases are considered. Impacts normal to the surface and head-on collisions are studied and compared. In surface impact, the behavior of low-density suspensions and liquid marble drops is qualitatively similar to that of pure liquid, while the concentrated drops are solid-like on impact. Collisions produce a splash only at velocities significantly higher than in impact, but the resulting drop morphology shows a similar dependence on solid concentration as in impact. In all cases, the collision or impact produces a strong local enhancement in the kinetic energy density and temperature but not in the particle or potential energy densities. Mixing of the two colliding species is not enhanced by collisions, unless the velocity is so high as to cause drop disintegration.

Three new branched chain equations of state based on Wertheim's perturbation theory

In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.

Frictional Forces between Strongly Compressed, Nonentangled Polymer Brushes: Molecular Dynamics Simulations and Scaling Theory

By means of molecular dynamics simulations and scaling theory we study the response of opposing polymer brushes to constant shear motion under good solvent conditions. Model systems that contain explicit solvent molecules (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their molecular parameters, chain length and grafting density. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg number, W, beyond linear response. For instance, we find that the kinetic friction constant scales as mu approximately W(0.57) for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent experiments.

Computation of Surface Tensions Using Expanded Ensemble Simulations

A method for the direct simulation of the surface tension is examined. The technique is based on the thermodynamic route to the interfacial tension and makes use of the expanded ensemble simulation method for the calculation of the free energy difference between two inhomogeneous systems with the same number of particles, temperature, and volume, but different interfacial area. The method is completely general and suitable for systems with either continuous or discontinuous interactions. The adequacy of the expanded ensemble method is assessed by computing the interfacial tension of the planar vapor-liquid interface of Lennard-Jones, Lennard-Jones dimers, Gay-Berne, and square-well model fluids; in the latter, the interactions are discontinuous and the present method does not exhibit the asymmetry of other related methods, such as the test area. The expanded ensemble simulation results are compared with simulation data obtained from other techniques (mechanical and test area) with overall good agreement.

Monte Carlo simulation of homogeneous binary vapor–liquid nucleation: Mutual enhancement of nucleation in a partially miscible system

By means of a constrained canonical-ensemble Monte Carlo technique the equilibrium physical cluster distribution {nij} in a supersaturated vapor mixture is computed. From this the intensive Gibbs free energy of ij-cluster formation ΔGij is obtained via the relation nij=Ne−ΔGij/kBT, where N is the number of molecules in the system, T is temperature, and kB is the Boltzmann constant. The saddle point on the free energy surface ΔGij versus i and j provides a measure of the activation barrier to nucleation ΔG*. A statistical mechanical formula of ΔGij is derived based on the physical-cluster theory of nucleation, and from which a molecular interpretation of ΔGij is given. We applied the Monte Carlo method to investigate the mutual enhancement of nucleation in a binary model system which is composed of spherical Lennard-Jones monomers and rigid Lennard-Jones dimers consisting of a monophilic atom and a monophobic atom. This model system bears some qualitative similarity to the partially miscible water/higher alcohol systems in which the mutual enhancement of nucleation has been observed experimentally. The simulation confirms the existence of mutual enhancement of nucleation in monomer-rich vapors, as originally predicted by Napari and Laaksonen from a density-functional theory [Napari and Laaksonen, Phys. Rev. Lett. 84, 2184 (2000)]. The nucleation enhancement is also seen in dimer-rich vapors at high supersaturations.

Molecular fluids: site-site analysis and hypernetted chain results with bridge functions for Lennard-Jones dimers

Rigid site-site molecular fluids are analysed, and a formally exact expression for the virial pressure is obtained that involves the triplet site correlation function, which may be evaluated using a superposition approximation. Numerical results for a Lennard-Jones dimer are obtained using the hypernetted chain (HNC) closure with all bridge diagrams with two field points. The bridge diagrams induce the secondary peak in the site-site distribution function that is missing in the HNC. Although the internal energy and the pressure are improved by the inclusion of bridge functions, the latter is most reliably given by the bare HNC and the compressibility route.

The effect of molecular shape anisotropy on surface melting

We report molecular dynamics (MD) simulations of the behaviour of the (101̄0) and (0001) crystal-vapour interfaces of Lennard-Jones dimers near the triple point. For slightly anisometric molecules, where the bulk melts from an orientationally disordered state, both interfaces were found to surface melt, with behaviour resembling that of the atomic Lennard-Jones system. In contrast, at larger anisometries, where the molecules are orientationally ordered close to the triple point, the (101̄0) face exhibits a first-order surface melting transition, while the (0001) face does not surface melt at all.