Unmasking quantum effects in the surface thermodynamics of fluid nanodrops.

The focus of our study is an in-depth investigation of the quantum effects associated with the surface tension and other thermodynamic properties of nanoscopic liquid drops. The behavior of drops of quantum Lennard-Jones fluids is investigated with path-integral Monte Carlo simulations, and the test-area method is used to determine the surface tension of the spherical vapor-liquid interface. As the thermal de Broglie wavelength, λB, becomes more significant, the average density of the liquid drop decreases, with the drop becoming mechanically unstable at large wavelengths. As a consequence, the surface tension is found to decrease monotonically with λB, vanishing altogether for dominant quantum interactions. Quantum effects can be significant, leading to values that are notably lower than the classical thermodynamic limit, particularly for smaller drops. For planar interfaces (with infinite periodicity in the direction parallel to the interface), quantum effects are much less significant with the same values of λB but are, nevertheless, consequential for values representative of hydrogen or helium-4 at low temperatures corresponding to vapor-liquid coexistence. Large quantum effects are found for small drops of molecules with quantum interactions corresponding to water, ethane, methanol, and carbon dioxide, even at ambient conditions. The notable decrease in the density and tension has important consequences in reducing the Gibbs free-energy barrier of a nucleating cluster, enhancing the nucleation kinetics of liquid drops and of bubble formation. This implies that drops would form at a much greater rate than is predicted by classical nucleation theory.

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft repulsive colloidal rods.

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio L^{★}=5, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

Confined Quantum Hard Spheres.

We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter σ and mass m at temperature T, confined between parallel hard walls separated by a distance Hσ, within the range 1≤H≤∞. Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles ρ*=N/V, where V is the accessible volume, the inverse length H-1 and the de Broglie's thermal wavelength λB=h/2πmkT, where k and h are the Boltzmann's and Planck's constants, respectively. For the case of extreme and maximum confinement, 0.5

Assessment of the Wolf method using the Stillinger-Lovett sum rules: From strong electrolytes to weakly charged colloidal dispersions.

The Ewald method has been the cornerstone in molecular simulations for modeling electrostatic interactions of charge-stabilized many-body systems. In the late 1990s, Wolf and collaborators developed an alternative route to describe the long-range nature of electrostatic interactions; from a computational perspective, this method provides a more efficient and straightforward way to implement long-range electrostatic interactions than the Ewald method. Despite these advantages, the validity of the Wolf potential to account for the electrostatic contribution in charged fluids remains controversial. To alleviate this situation, in this contribution, we implement the Wolf summation method to both electrolyte solutions and charged colloids with moderate size and charge asymmetries in order to assess the accuracy and validity of the method. To this end, we verify that the proper selection of parameters within the Wolf method leads to results that are in good agreement with those obtained through the standard Ewald method and the theory of integral equations of simple liquids within the so-called hypernetted chain approximation. Furthermore, we show that the results obtained with the original Wolf method do satisfy the moment conditions described by the Stillinger-Lovett sum rules, which are directly related to the local electroneutrality condition and the electrostatic screening in the Debye-Hückel regime. Hence, the fact that the solution provided by the Wolf method satisfies the first and second moments of Stillinger-Lovett proves, for the first time, the reliability of the method to correctly incorporate the electrostatic contribution in charge-stabilized fluids. This makes the Wolf method a powerful alternative compared to more demanding computational approaches.

Assessment by Monte Carlo computer simulations of the phase behavior of hard spherocylinders confined within cylindrical cavities.

The phase behavior of hard spherocylinders (HSCs) confined in cylindrical cavities is studied using Monte Carlo simulations in the canonical ensemble. Results are presented for different values of the particles' aspect ratio l/σ, where l and σ are the length and diameter of the cylinder and hemispherical caps, respectively. Finite cavities with periodic boundary conditions along the principal axis of the cavities have been considered, where the cavity's principal axis is along the z-direction. We first focus our study in the structure induced by varying the degree of confinement, determining the HSC phase diagram for aspect ratios l/σ = 3, 5, 7, and 9, at a fixed packing fraction η = 0.071. By compressing the cavities along the radial direction, the isotropic phase becomes stable before the nematic phase as the length of the cavities is increased, resulting in a second-order transition. The occurrence of phase transitions has also been determined by varying η for constant values of the cavity's length L. Systems with low aspect ratios, l/σ = 3, 5, 7, and 9, exhibit first-order transitions with chiral, paranematic, and isotropic phases, whereas for larger HSCs, l/σ = 50, 70, and 100, the transitions are second order with paranematic, nematic, and isotropic phases, in contrast with the behavior of non-confined systems, with first-order transitions for isotropic, nematic, smectic-A, and solid phases.

Microcanonical ensemble simulation method applied to discrete potential fluids.

In this work we extend the applicability of the microcanonical ensemble simulation method, originally proposed to study the Ising model [A. Hüller and M. Pleimling, Int. J. Mod. Phys. C 13, 947 (2002)0129-183110.1142/S0129183102003693], to the case of simple fluids. An algorithm is developed by measuring the transition rates probabilities between macroscopic states, that has as advantage with respect to conventional Monte Carlo NVT (MC-NVT) simulations that a continuous range of temperatures are covered in a single run. For a given density, this new algorithm provides the inverse temperature, that can be parametrized as a function of the internal energy, and the isochoric heat capacity is then evaluated through a numerical derivative. As an illustrative example we consider a fluid composed of particles interacting via a square-well (SW) pair potential of variable range. Equilibrium internal energies and isochoric heat capacities are obtained with very high accuracy compared with data obtained from MC-NVT simulations. These results are important in the context of the application of the Hüller-Pleimling method to discrete-potential systems, that are based on a generalization of the SW and square-shoulder fluids properties.

Monte Carlo computer simulation of sedimentation of charged hard spherocylinders.

In this article we present a NVT Monte Carlo computer simulation study of sedimentation of an electroneutral mixture of oppositely charged hard spherocylinders (CHSC) with aspect ratio L/σ = 5, where L and σ are the length and diameter of the cylinder and hemispherical caps, respectively, for each particle. This system is an extension of the restricted primitive model for spherical particles, where L/σ = 0, and it is assumed that the ions are immersed in an structureless solvent, i.e., a continuum with dielectric constant D. The system consisted of N = 2000 particles and the Wolf method was implemented to handle the coulombic interactions of the inhomogeneous system. Results are presented for different values of the strength ratio between the gravitational and electrostatic interactions, Γ = (mgσ)/(e(2)/Dσ), where m is the mass per particle, e is the electron's charge and g is the gravitational acceleration value. A semi-infinite simulation cell was used with dimensions Lx ≈ Ly and Lz = 5Lx, where Lx, Ly, and Lz are the box dimensions in Cartesian coordinates, and the gravitational force acts along the z-direction. Sedimentation effects were studied by looking at every layer formed by the CHSC along the gravitational field. By increasing Γ, particles tend to get more packed at each layer and to arrange in local domains with an orientational ordering along two perpendicular axis, a feature not observed in the uncharged system with the same hard-body geometry. This type of arrangement, known as tetratic phase, has been observed in two-dimensional systems of hard-rectangles and rounded hard-squares. In this way, the coupling of gravitational and electric interactions in the CHSC system induces the arrangement of particles in layers, with the formation of quasi-two dimensional tetratic phases near the surface.

Computer simulation of liquid-vapor coexistence of confined quantum fluids.

The liquid-vapor coexistence (LV) of bulk and confined quantum fluids has been studied by Monte Carlo computer simulation for particles interacting via a semiclassical effective pair potential Veff(r) = VLJ + VQ, where VLJ is the Lennard-Jones 12-6 potential (LJ) and VQ is the first-order Wigner-Kirkwood (WK-1) quantum potential, that depends on ß = 1∕kT and de Boer's quantumness parameter Λ=h/σ√mε, where k and h are the Boltzmann's and Planck's constants, respectively, m is the particle's mass, T is the temperature of the system, and σ and ε are the LJ potential parameters. The non-conformal properties of the system of particles interacting via the effective pair potential Veff(r) are due to Λ, since the LV phase diagram is modified by varying Λ. We found that the WK-1 system gives an accurate description of the LV coexistence for bulk phases of several quantum fluids, obtained by the Gibbs Ensemble Monte Carlo method (GEMC). Confinement effects were introduced using the Canonical Ensemble (NVT) to simulate quantum fluids contained within parallel hard walls separated by a distance Lp, within the range 2σ ≤ Lp ≤ 6σ. The critical temperature of the system is reduced by decreasing Lp and increasing Λ, and the liquid-vapor transition is not longer observed for Lp∕σ < 2, in contrast to what has been observed for the classical system.

Monte Carlo simulation of flexible trimers: from square well chains to amphiphilic primitive models.

In this work, we present Monte Carlo computer simulation results of a primitive model of self-assembling system based on a flexible 3-mer chain interacting via square-well interactions. The effect of switching off the attractive interaction in an extreme sphere is analyzed, since the anisotropy in the molecular potential promotes self-organization. Before addressing studies on self-organization it is necessary to know the vapor liquid equilibrium of the system to avoid to confuse self-organization with phase separation. The range of the attractive potential of the model, λ, is kept constant and equal to 1.5σ, where σ is the diameter of a monomer sphere, while the attractive interaction in one of the monomers was gradually turned off until a pure hard body interaction was obtained. We present the vapor-liquid coexistence curves for the different models studied, their critical properties, and the comparison with the SAFT-VR theory prediction [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. Evidence of self-assembly for this system is discussed.

Generalized information entropies depending only on the probability distribution.

In the framework of superstatistics it has been shown that one can calculate the entropy of nonextensive statistical mechanics. We follow a similar procedure; we assume a Γ(χ(2)) distribution depending on ß that also depends on a parameter p(l). From it we calculate the Boltzmann factor and show that it is possible to obtain the information entropy S=k∑(l=1)(Ω)s(p(l)), where s(p(l))=1-p(l)(p(l)). By maximizing this information measure, p(l) is calculated as function of ßE(l) and, at this stage of the procedure, p(l) can be identified with the probability distribution. We show the validity of the saddle-point approximation and we also briefly discuss the generalization of one of the four Khinchin axioms. The modified axioms are then in accordance with the proposed entropy. As further possibilities, we also propose other entropies depending on p(l) that resemble the Kaniakadis and two possible Sharma-Mittal entropies. By expanding in series all entropies in this work we have as a first term the Shannon entropy.

Evaluation of the pressure tensor and surface tension for molecular fluids with discontinuous potentials using the volume perturbation method.

In this article we apply the volume-perturbation method to systems of particles interacting via discontinuous potentials. We have found that an accurate Monte Carlo simulation protocol can be used in order to study properties of very general non-spherical systems with discontinuous potentials, such as chain molecules and spherocylinders with square-well interactions, and chain molecules with square-well and square-shoulder interactions. From the simulation results obtained for these systems we verify that: (1) the method reproduces the pressure as used in NPT simulations; (2) discontinuous infinite repulsive interactions give asymmetric contributions to the pressure when compression and expansion movements are used; however for finite interactions these contributions are symmetric; and (3) the pressure contributions preserve the additivity of the potential interactions. Density profiles and surface tension for subcritical conditions are accurately predicted.

Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range.

Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.

Computer simulation of sedimentation of ionic systems using the Wolf method.

We present computer simulation results for 1:1 and 2:1 electrolyte solutions in the presence of a gravitational field, using the Monte Carlo method in the NVT ensemble for the restrictive primitive model. Coulombic interactions were taken into account comparing the Ewald and Wolf methods. Three variations of Ewald summations were considered: the exact method for slab geometries (EW2D), and the three-dimensional (3D) versions with and without a dipolar correction (EW3DC and EW3D, respectively). The equivalent 3D Wolf protocols were applied under the same conditions (WF3DC and WF3D, respectively). The Wolf and Ewald methods agree accurately in the prediction of several thermodynamic and structural properties for these inhomogeneous systems: excess internal energies, isochoric heath capacities, and density and electrostatic potential profiles. The main advantage using the Wolf method is the significant saving in computing time, which is approximately six times faster than EW3D and EW3DC, and sixty times faster than EW2D.

Computer simulation of charged hard spherocylinders.

In this work we present a computer simulation study of charged hard spherocylinders of aspect ratio L/sigma=5, using NVT and NPT Monte Carlo methods. Coulombic interactions are handled using the Wolf method [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. Thermodynamic and structural properties are in excellent agreement with the results obtained with the standard Ewald summation method. A partial prediction of the corresponding phase diagram is obtained by studying two isotherms of this system. The stability of the liquid crystalline phases is examined and compared with the phase diagrams of neutral hard spherocylinders and dipolar hard spherocylinders.

Predicting adsorption isotherms using a two-dimensional statistical associating fluid theory.

A molecular thermodynamics approach is developed in order to describe the adsorption of fluids on solid surfaces. The new theory is based on the statistical associating fluid theory for potentials of variable range [A. Gil-Villegas et al., J. Chem. Phys. 106, 4168 (1997)] and uses a quasi-two-dimensional approximation to describe the properties of adsorbed fluids. The theory is tested against Gibbs ensemble Monte Carlo simulations and excellent agreement with the theoretical predictions is achieved. Additionally the authors use the new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon.

Predicting the phase behavior of nitrogen + n-alkanes for enhanced oil recovery from the SAFT-VR approach: examining the effect of the quadrupole moment.

The phase behavior of nitrogen + n-alkanes is studied within the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). The effect of the quadrupole moment of nitrogen on the phase behavior is considered through an extension of the SAFT-VR equation that includes an additional contribution to the Helmholtz free energy due to quadrupolar interactions. A significant improvement in the description of the phase diagram of the binary mixtures of nitrogen with different n-alkanes is obtained with the new approach when compared to predictions from the original SAFT-VR EOS (i.e., without the quadrupolar term). The experimental value for the quadrupole moment of nitrogen is used in the new equation; thus, no additional parameters are employed. Given the nonideal nature of the binary mixtures, a binary interaction parameter is needed to describe the full-phase diagram and high-pressure critical lines of these systems; however, this can be fitted to a single system and successfully used to predict the phase behavior of other binary mixtures without additional fitting. Furthermore, only a single, transferable, cross-energy parameter is required when the quadrupolar term is considered, whereas a cross-range parameter is also needed with the original SAFT-VR approach. The inclusion of the quadrupolar term in the equation of state therefore reduces the need to use effective parameters by explicitly including at the molecular level interactions due to the quadrupole moment.

Predicting the phase diagram of two-dimensional colloidal systems with long-range interactions.

The phase diagram of a two-dimensional model system for colloidal particles at the air-water interface was determined using Monte Carlo computer simulations in the isothermic-isobaric ensemble. The micrometer-range binary colloidal interaction has been modeled by hard disklike particles interacting via a secondary minimum followed by a weaker longer-range repulsive maximum, both of the order of kBT. The repulsive part of the potential drives the clustering of particles at low densities and low temperatures. Pinned voids are formed at higher densities and intermediate values of the surface pressure. The analysis of isotherms, translational and orientational correlation functions as well as structure factor gives clear evidence of the presence of a melting first-order transition. However, the melting process can be also followed by a metastable route through a hexatic phase at low surface pressures and low temperatures, before crystalization occurs at higher surface pressure.