Liquid–vapour equilibrium ofn-alkanes using interface simulations

Effect of molecular branching and surface wettability on solid-liquid surface tension and line-tension of liquid alkane surface nanodroplets

HYPOTHESIS

Surface nanodroplets have important technological applications. Previous experiments and simulations have shown that their contact angle deviates from Young's equation. A modified version of Young's equation considering the three-phase line tension (τ) has been widely used in literature, and a wide range of values for τ are reported. We have recently shown that molecular branching affects the liquid-vapour surface tension γlv of liquid alkanes. Therefore, the wetting behaviour of surface nanodroplets should be affected by molecular branching. This study conducted molecular dynamics (MD) simulations to gain insight into the wetting behaviour of linear and branched alkane nanodroplets on oleophilic and oleophobic surfaces. We aim to examine the Young equation's validity and branching's effect on fundamental properties, including solid-liquid surface tension γsl and line tension τ.

SIMULATIONS

The simulations were performed on a linear alkane, triacontane (C30H62), as well as four of its branched isomers: 2,6,13,17-tetrapropyloctadecane,2,6,9,10,13,17-hexaethyloctadecane, 2,5,7,8,11,12,15-heptaethylhexadecane and 2,3,6,7,10,11-hexapropyldodecane. Nanodroplets with a diameter of approximately 15 nm were released onto the surfaces, and their contact angles were measured. Additionally, using a novel approach, the solid-liquid surface tension (γsl), the validity of Young's equation and line tension for all alkane and surface combinations are determined.

FINDINGS

It was discovered that the calculated γsl, deviated from the theoretical γsl,Young predicted from Young's equation for all alkanes on oleophilic surfaces. However, this deviation was minimal for branched alkanes on the oleophobic surfaces but more significant for the linear alkane. The findings indicated that γsl < 0 for oleophilic surfaces and γsl > 0 for oleophobic surfaces. Moreover, it was observed that |γsl| was lower for branched molecules and decreased as branching increased. Line tension values were then determined through a novel method, showing τ was positive for oleophilic surfaces ranging from 1.30 × 10-10 to 6.27 × 10-11N. On an oleophobic surface, linear alkane shows a negative line tension of -1.15 × 10-10N and branched alkanes up to two orders of magnitude lower values ranging from -2.09 × 10-12 to 2.43 × 10-11N. Line tension values between -1.15 × 10-10 and + 1.1 × 10-10N are calculated for various linear alkane and surface combinations. These findings show the dependence of line tension on the contact angle and branching, demonstrating that for linear alkanes, τ is significant, whereas, for branched alkanes, line tension is smaller or negligible for large contact angles.

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.

The Water-Alkane Interface at Various NaCl Salt Concentrations: A Molecular Dynamics Study of the Readily Available Force Fields

In this study, classical molecular dynamic simulations have been used to examine the molecular properties of the water-alkane interface at various NaCl salt concentrations (up to 3.0 mol/kg). A variety of different force field combinations have been compared against experimental surface/interfacial tension values for the water-vapour, decane-vapour and water-decane interfaces. Six different force fields for water (SPC, SPC/E, TIP3P, TIP3Pcharmm, TIP4P & TIP4P2005), and three further force fields for alkane (TraPPE-UA, CGenFF & OPLS) have been compared to experimental data. CGenFF, OPLS-AA and TraPPE-UA all accurately reproduce the interfacial properties of decane. The TIP4P2005 (four-point) water model is shown to be the most accurate water model for predicting the interfacial properties of water. The SPC/E water model is the best three-point parameterisation of water for this purpose. The CGenFF and TraPPE parameterisations of oil accurately reproduce the interfacial tension with water using either the TIP4P2005 or SPC/E water model. The salinity dependence on surface/interfacial tension is accurately captured using the Smith & Dang parameterisation of NaCl. We observe that the Smith & Dang model slightly overestimates the surface/interfacial tensions at higher salinities (>1.5 mol/kg). This is ascribed to an overestimation of the ion exclusion at the interface.

Molecular dynamics simulations of 2-(dimethylamino)ethanol (DMEA)

We develop a multipurpose force field to investigate the properties of the condensed phases of 2-(dimethylamino)ethanol (DMEA). We use ab initio computations at the HF/6-311++G(2d,2p) level to derive partial charges, obtain force constants, and compute the electrostatic potential of the DMEA. We find that the HF predictions for the dipole moment are in excellent agreement with the experimental result (2.6 D). The computations also show the strong preference of DMEA to form intramolecular hydrogen bonds between the hydrogen in the alcohol group and nitrogen. We have tested the accuracy of our force field by computing coexistence and interfacial properties as well as thermal conductivities in wide range of thermodynamic states. In all these instances we find excellent agreement with the available experimental data. We have further investigated the structure of the liquid by computing pair correlations. Our results indicate a clear preference for DMEA to form low-dimensional structures, such as linear and bifurcated chains, which are driven by the association of the DMEA molecules via the alcohol group. Overall, our force field provides a good basis to compute the bulk and interfacial properties of DMEA.

Development and application of a particle-particle particle-mesh Ewald method for dispersion interactions

For inhomogeneous systems with interfaces, the inclusion of long-range dispersion interactions is necessary to achieve consistency between molecular simulation calculations and experimental results. For accurate and efficient incorporation of these contributions, we have implemented a particle-particle particle-mesh Ewald solver for dispersion (r(-6)) interactions into the LAMMPS molecular dynamics package. We demonstrate that the solver's O(N log N) scaling behavior allows its application to large-scale simulations. We carefully determine a set of parameters for the solver that provides accurate results and efficient computation. We perform a series of simulations with Lennard-Jones particles, SPC/E water, and hexane to show that with our choice of parameters the dependence of physical results on the chosen cutoff radius is removed. Physical results and computation time of these simulations are compared to results obtained using either a plain cutoff or a traditional Ewald sum for dispersion.

Comparison of united-atom potentials for the simulation of vapor-liquid equilibria and interfacial properties of long-chain n-alkanes up to n-C100

Canonical ensemble molecular dynamics (MD) simulations are reported which compute both the vapor-liquid equilibrium properties (vapor pressure and liquid and vapor densities) and the interfacial properties (density profiles, interfacial tensions, entropy and enthalpy of surface formation) of four long-chained n-alkanes: n-decane (n-C(10)), n-eicosane (n-C(20)), n-hexacontane (n-C(60)), and n-decacontane (n-C(100)). Three of the most commonly employed united-atom (UA) force fields for alkanes (SKS: Smit, B.; Karaborni, S.; Siepmann, J. I. J. Chem. Phys. 1995,102, 2126-2140; J. Chem. Phys. 1998,109, 352; NERD: Nath, S. K.; Escobedo, F. A.; de Pablo, J. J. J. Chem. Phys. 1998, 108, 9905-9911; and TraPPE: Martin M. G.; Siepmann, J. I. J. Phys. Chem. B1998, 102, 2569-2577.) are critically appraised. The computed results have been compared to the available experimental data and those fitted using the square gradient theory (SGT). In the latter approach, the Lennard-Jones chain equation of state (EoS), appropriately parametrized for long hydrocarbons, is used to model the homogeneous bulk phase Helmholtz energy. The MD results for phase equilibria of n-decane and n-eicosane exhibit sensible agreement both to the experimental data and EoS correlation for all potentials tested, with the TraPPE potential showing the lowest deviations. However, as the molecular chain increases to n-hexacontane and n-decacontane, the reliability of the UA potentials decreases, showing notorious subpredictions of both saturated liquid density and vapor pressure. Based on the recommended data and EoS results for the heaviest hydrocarbons, it is possible to attest, that in this extreme, the TraPPE potential shows the lowest liquid density deviations. The low absolute values of the vapor pressure preclude the discrimination among the three UA potentials studied. On the other hand, interfacial properties are very sensitive to the type of UA potential thus allowing a differentiation of the potentials. Comparing the interfacial tension MD results to the available experimental data and SGT results, the TraPPE model exhibits the lowest deviations for all hydrocarbons.

A non-polarizable model of water that yields the dielectric constant and the density anomalies of the liquid: TIP4Q

A four-site rigid water model is presented, whose parameters are fitted to reproduce the experimental static dielectric constant at 298 K, the maximum density of liquid water and the equation of state at low pressures. The model has a positive charge on each of the three atomic nuclei and a negative charge located at the bisector of the HOH bending angle. This charge distribution allows increasing the molecular dipole moment relative to four-site models with only three charges and improves the liquid dielectric constant at different temperatures. Several other properties of the liquid and of ice Ih resulting from numerical simulations with the model are in good agreement with experimental values over a wide range of temperatures and pressures. Moreover, the model yields the minimum density of supercooled water at 190 K and the minimum thermal compressibility at 310 K, close to the experimental values. A discussion is presented on the structural changes of liquid water in the supercooled region where the derivative of density with respect to temperature is a maximum.

The surface tension of TIP4P/2005 water model using the Ewald sums for the dispersion interactions

The liquid-vapor phase equilibria and surface tension of the TIP4P/2005 water model is obtained by using the Ewald summation method to determine the long range Lennard-Jones and electrostatic interactions. The method is implemented in a straightforward manner into standard simulation programs. The computational cost of using Ewald sums in dispersion interactions of water is estimated in direct simulation of interfaces. The results of this work at 300 K show a dramatic change in surface tension with an oscillatory behavior for surface areas smaller than 5x5sigma(2), where sigma is the Lennard-Jones oxygen diameter. The amplitude of such oscillations substantially decreases with temperature. Finite size effects are less important on coexisting densities. Phase equilibria and interfacial properties can be determined using a small number of water molecules; their fluctuations are around the same size of simulation error at all temperatures, even in systems where the interfaces are separated a few molecular diameters only. The difference in surface tension of this work compared to the results of other authors is not significant (on the contrary, there is a good agreement). What should be stressed is the different and more consistent approach to obtain the surface tension using the Ewald sums for dispersion interactions. There are two relevant aspects at the interface: An adsorption of water molecules is observed at small surface areas and its thickness systematically increases with system size.

Molecular dynamics simulations of a reversibly folding beta-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions

Eight 100-ns molecular dynamics simulations of a beta-heptapeptide in methanol at 340 K (within cubic periodic computational boxes of about 6-nm edge) are reported and compared. These simulations were performed with three different charge-state combinations at the peptide termini, one of them with or without a neutralizing chloride counterion, and using either the lattice-sum (LS) or reaction-field (RF) scheme to handle electrostatic interactions. The choice of the electrostatic scheme has essentially no influence on the folding-unfolding equilibrium when the peptide termini are uncharged and only a small influence when the peptide is positively charged at its N-terminus (with or without inclusion of a neutralizing chloride counterion). However, when the peptide is zwitterionic, the LS scheme leads to preferential sampling of the high-dipole folded helical state, whereas the RF scheme leads to preferential sampling of a low-dipole unfolded salt-bridged state. A continuum electrostatics analysis based on the sampled configurations (zwitterionic case) suggests that the LS scheme stabilizes the helical state through artificial periodicity, but that the magnitude of this perturbation is essentially negligible (compared to the thermal energy) for the large box size and relatively polar solvent considered. The results thus provide clear evidence (continuum electrostatics analysis) for the absence of LS artifacts and some indications (still not definitive because of the limited sampling of the folding-unfolding transition) for the presence of RF artifacts in this specific system.

Master curves and radial distribution functions for shear dilatancy of liquid n-hexadecane via nonequilibrium molecular dynamics simulations

Shear dilatancy, a significant nonlinear behavior of nonequilibrium thermodynamics states, has been observed in nonequilibrium molecular dynamics (NEMD) simulations for liquid n-hexadecane fluid under extreme shear conditions. The existence of shear dilatancy is relevant to the relationship between the imposed shear rate gamma and the critical shear rate gamma(c). Consequently, as gamma<gamma(c), the intermolecular equilibrium distance of the fluid remains unchanged, while the nonequilibrium state of the fluid approaches equilibrium. In contrast to gamma>gamma(c), the intermolecular distance is lengthened substantially by strong shear deformation breaking the equilibrium thermodynamic state so that shear dilatancy takes place. Notably, a characteristic shear rate gamma(m), which depends on the root mean square molecular velocity and the average free molecular distance, is found in nonequilibrium thermodynamics state curves. Studies of the variations in the intermolecular radial distribution function (RDF) with respect to the shear rate provide a direct measure of the variation in the degree of intermolecular separation. Additionally, the variations of the RDF curve in the microscopic regime are consistent with those of the nonequilibrium thermodynamic state in the macroscopic world. By inspecting the overall shape of the RDF curve, it can be readily corroborated that the fluid of interest exists in the liquid state. More importantly, both primary characteristic values, the equilibrium thermodynamic state variable and a particular shear rate of gamma(p), are determined cautiously, with gamma(p) depending on the gamma(m) value and the square root of pressure. Thereby, the nonequilibrium thermodynamic state curves can be normalized as temperature-, pressure-, and density-invariant master curves, formulated by applying the Cross constitutive equation. Clearly, gamma(c) occurs at which a reduced shear rate gamma/gamma(p) approaches 0.1. Furthermore, the trends in the rates of shear dilatancy in both the constant-pressure and constant-volume NEMD systems under isothermal conditions conform to the cyclic rule of pressure, as a function of density and shear rate.

Application of Ewald summations to long-range dispersion forces

Results illustrating the effects of using explicit summation terms for the r(-6) dispersion term on the interfacial properties of a Lennard-Jones fluid and SPC/E water are presented. For the Lennard-Jones fluid, we find that the use of long-range summations, even with a short "crossover radius," yields results that are consistent with simulations using large cutoff radii. Simulations of SPC/E water demonstrate that the long-range dispersion forces are of secondary importance to the Coulombic forces. In both cases, we find that the ratio of the box size L( parallel) to the crossover radius r(c) (k) plays an important role in determining the magnitude of the long-range dispersion correction, although its effect is secondary when Coulombic interactions are also present.

Surface tension of the most popular models of water by using the test-area simulation method

We consider the calculation of the surface tension from simulations of several models of water, such as the traditional TIP3P, SPC, SPC/E, and TIP4P models, and the new generation of TIP4P-like models including the TIP4P/Ew, TIP4P/Ice, and TIP4P/2005. We employ a thermodynamic route proposed by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] to determine the surface tension that involves the estimate of the change in free energy associated with a small change in the interfacial area at constant volume. The values of the surface tension computed from this test-area method are found to be fully consistent with those obtained from the standard mechanical route, which is based on the evaluation of the components of the pressure tensor. We find that most models do not reproduce quantitatively the experimental values of the surface tension of water. The best description of the surface tension is given by those models that provide a better description of the vapor-liquid coexistence curve. The values of the surface tension for the SPC/E and TIP4P/Ew models are found to be in reasonably good agreement with the experimental values. From the present investigation, we conclude that the TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature. We also conclude that the test area is an appropriate methodological choice for the calculation of the surface tension not only for simple fluids, but also for complex molecular polar fluids, as is the case of water.