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Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble were used to obtain vapor−liquid coexistence curves for a series of alkanes physisorbed on a flat gold substrate. The critical temperatures and densities of n-alkanes from methane to decane as well as the branched molecules 2-methylpropane, 2,2-dimethylbutane, and 2,3-dimethylbutane were determined through a mixed-field analysis. The ratio of the 2D (two-dimensional) to the 3D (three-dimensional) critical temperature was found to depend weakly on the chain length for n-alkanes, decreasing from Tc^2D/Tc^3D = 0.38 for methane to Tc^2D/Tc^3D = 0.31 for n-decane. In contrast to typical bulk fluid behavior, the branched isomers were found to have higher critical temperatures than their linear counterparts.

Configurational-bias Monte Carlo simulations in the isobaric−isothermal ensemble using the nonpolarizable TraPPE−UA (transferable potentials for phase equilibria−united-atom) force field were performed to study the aggregation of 1-hexanol in n-hexane. The spatial distribution of alcohols was sampled efficiently using special Monte Carlo moves. Analysis of the microscopic structures for 1, 3, and 5% solutions at a temperature of 298.15 K and a pressure of 101.3 kPa shows strong aggregation with a preference for tetramers and pentamers for all three concentrations. About half of these tetramers and pentamers are found in cyclic aggregates. The enthalpies for the formation of clusters of specific sizes were determined from simulations of a 3% solution at temperatures ranging from 298.15 to 328.15 K. The free energies and enthalpies of cluster formation show the large influences of hydrogen-bond cooperativity, which favors clusters larger than dimers, but a decreasing enthalpy gain and an increasing entropic penalty prevent the formation of very large clusters. These results have important implications for the thermodynamic modeling of hydrogen-bonding fluids, which commonly use a constant value for the free energy of hydrogen-bond formation. Overall agreement with Fourier transform infrared spectroscopic measurements on the extent of hydrogen bonding for the same mixtures is satisfactory.

The aggregation−volume−bias Monte Carlo (AVBMC) algorithm is reanalyzed, and on the basis of this analysis, two extensions of the AVBMC algorithm with improved sampling efficiency for super-strongly associating fluids are presented. The new versions of the AVBMC algorithm are based on the principle of super-detailed balance and retain the simplicity, generality, and robustness of the original AVBMC algorithm. The performances of the various versions of the AVBMC algorithm are compared via applications to the simple ideal-association model of van Roij and to the superheated vapor phase of hydrogen fluoride.

In gas−liquid chromatography with liquid-crystalline stationary phases and in liquid−liquid chromatography with polymeric bonded phases, the retention selectivity has been linked to the orientation of the retentive phase. In an effort to explore the nature of this effect, molecular simulations utilizing the configurational-bias Monte Carlo technique in the Gibbs ensemble were performed. Through this simulation technique, the partition coefficients of benzene, naphthalene, n-heptane, and n-dodecane were calculated when partitioning takes place between an oriented or an isotropic liquid n-octadecane phase of equal density and a helium gas phase. The calculated partition coefficients demonstrate that the n-alkane solutes prefer the oriented n-octadecane phase over the isotropic one, while the opposite behavior (but to a smaller extent) is observed for benzene and naphthalene solutes. The n-alkane solute transfer into the oriented n-octadecane phase is favored by a smaller entropic penalty and a minor enthalpic gain compared to that into the isotropic phase. While the entropic cost for partitioning into the liquid phases increases by about 40% from n-heptane to n-dodecane, there is only a small increase of about 8% from benzene to naphthalene. Minor preferential alignment was observed for n-dodecane and naphthalene in the oriented liquid phase, but no significant differences are observed for the solutes' conformational properties in the two solvent environments.

The Gibbs ensemble Monte Carlo method of Panagiotopoulos is extended to calculations of solid−vapor coexistence curves. As in the original Gibbs ensemble method, the new technique makes use of two simulation boxes that are in thermodynamic contact. However, the box that contains the solid phase is elongated along one axis and contains only a slab of solid material surrounded on both sides by vapor. Aggregation-volume-bias Monte Carlo moves are used to sample transfers from the solid to the vapor and vice versa in this box, whereas the usual particle swap moves are applied to transfers between the solid−vapor box and the other box that contains a bulk vapor phase. Volume moves for the solid−vapor box use separate displacements of individual cell lengths or of individual H-matrix elements. As one approaches the triple-point temperature from below, increased disorder at the solid−vapor interface is observed, and once the triple-point temperature is exceeded, the entire solid slab converts to a liquid. The use of configurational-bias Monte Carlo particle swap moves enables us to extend conventional Gibbs ensemble simulations of vapor−liquid equilibria beyond the triple point into the supercooled regime. Clausius−Clapeyron fits to the sublimation, and vapor pressure curves allow for the precise determination of the triple-point location. The simulation results for Lennard−Jonesium are in excellent agreement with Gibbs−Duhem integration simulations, and the results for carbon dioxide using the TraPPE force field reproduce well the experimental data (e.g., the predicted triple-point parameters are T = 212 ± 2 K and p = 430 ± 50 kPa).

The transferable potentials for phase equilibria-united atom (TraPPE-UA) force field for hydrocarbons is extended to primary, secondary, and tertiary alcohols by introducing the following (pseudo-)atoms:  common hydroxyl O and H for all alcohols, α-CH3, α-CH2, α-CH, and α-C for methanol, primary, secondary, and tertiary alcohols, respectively. In the TraPPE-UA force field, the nonbonded interactions of these sites are governed by Lennard−Jones 12−6 potentials and Coulombic interactions of fixed partial charges. The values of these partial charges were borrowed from the optimized potentials for liquid simulations-united atom (OPLS−UA) force field [Jorgensen, W. L. J. Phys. Chem. 1986, 90, 1276]. The Lennard−Jones well depth and size parameters for the new interaction sites were determined by fitting to the single-component vapor−liquid-phase equilibria of a few selected model compounds. Although the well-depth parameters for the α-carbons could be taken directly from the TraPPE-UA parameters for the corresponding pseudoatoms in alkanes, the size parameters required small adjustments to reflect the differences in C−C and C−O bond lengths and the reduced electron density for α-carbons. Coupled−decoupled configurational-bias Monte Carlo simulations in the Gibbs and grand-canonical ensembles were carried out to calculate the one-component vapor−liquid coexistence curves for methanol, ethanol, propan-1-ol, propan-2-ol, butan-2-ol, 2-methylpropan-2-ol, pentan-1-ol, pentane-1,5-diol, and octan-1-ol, and to determine the binary phase diagrams for the mixtures of n-hexane/methanol and n-hexane/ethanol. It was found that the phase equilibria of the pure alcohols are accurately described by the TraPPE-UA force field, with mean unsigned deviations of about 1% from the experimental data for the normal boiling points and the saturated liquid densities. The azeotropic compositions for n-hexane/methanol and n-hexane/ethanol were predicted to be 0.340 at T = 448.15 K and 0.454 at 413.15 K and (in mole fraction of n-hexane), which are in good agreement with the experimental results of 0.288 and 0.440, respectively. Analysis of the structures of the n-hexane/methanol mixtures shows evidence for significant enhancements in the local mole fraction of alcohols in the vicinity of other alcohols. The magnitude of these local enhancements decreases with increasing alcohol concentration, but the change is gradual and no discontinuity was observed at the azeotropic composition.

An extension to the configurational-bias Monte Carlo method is presented which allows for the efficient conformational sampling of the interior segments of chain molecules whose interactions include strong bonded terms (governing bond stretching, bond angle bending, and dihedral angle rotation). The ability to regrow interior segments overcomes the limitations of conventional configurational-bias methods (where the regrowth is always directed to a free chain end) and now allows for the simulation of chain systems with low concentrations of chain ends, that is, higher molecular weights, networks, or cyclic structures. As previously proposed by Dijkstra et al. [J. Chem. Phys. 1994, 101, 3179] for lattice polymers and by Vendruscolo [J. Chem. Phys. 1997, 106, 2970] for freely jointed polymers, an additional biasing (closing) probability is used that guides the bead-by-bead configurational-bias regrowth of interior segments toward its desired fixed target. However, while the previous methods are limited to chain models for which the number of random walks that lead to closure is known or which rely on simpler and less efficient geometric considerations, the algorithm presented here allows for the simulation of chain molecules using force fields of arbitrary complexity for which the closing probability is not known a priori. It is important to note that the additional biasing probability used to guide the move does not necessarily have to be the true closing probability but that a good approximation thereof is essential to improve the sampling efficiency. To this extent, we obtain an intial guess of the biasing probability from a short presimulation or an earlier simulation of a related system or simply use a uniform biasing probability. A self-adapting scheme is then used to optimize the biasing probability during the course of the simulation for the system of interest. In addition to the conformational sampling of interior segments, the new algorithm also enables efficient particle insertions and removals of cyclic molecules (of moderate length) and thereby opens the door to simulations in the grand canonical and Gibbs ensembles. Simulation results are presented for linear, branched, and cyclic alkanes using the transferable potentials for phase equilibria (TraPPE) force field.

A novel aggregation-volume-bias Monte Carlo (AVBMC) algorithm is presented which greatly enhances the efficiency of sampling the phase space of fluid systems consisting of strongly associating molecules. The algorithm is compared to the bond-bias Monte Carlo algorithm by Tsangaris and de Pablo (J. Chem. Phys. 1994, 101, 1477) and the monomer-addition-subtraction algorithm by Visco and Kofke (J. Chem. Phys. 1999, 110, 5493). The AVBMC algorithm is easy to implement, generally applicable, and robust. Its efficiency is demonstrated for a large variety of processes and systems, including the vaporization of a liquid methane droplet or a water cluster, an investigation of the temperature- and pressure-dependent properties of superheated hydrogen fluoride vapor, and the vapor−liquid coexistence curve of acetic acid.

The Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field for hydrocarbons is extended to alkenes and alkylbenzenes by introducing the following pseudo-atoms:  CH2(sp²), CH(sp²), C(sp²), CH(aro), R−C(aro) for the link to aliphatic side chains and C(aro) for the link of two benzene rings. In this united-atom force field, the nonbonded interactions of the hydrocarbon pseudo-atoms are solely governed by Lennard-Jones 12−6 potentials, and the Lennard-Jones well depth and size parameters for the new pseudo-atoms were determined by fitting to the single-component vapor−liquid-phase equilibria of a few selected model compounds. Configurational-bias Monte Carlo simulations in the NVT version of the Gibbs ensemble were carried out to calculate the single-component vapor−liquid coexistence curves for ethene, propene, 1-butene, trans- and cis-2-butene, 2-methylpropene, 1,5-hexadiene, 1-octene, benzene, toluene, ethylbenzene, propylbenzene, isopropylbenzene, o-, m-, and p-xylene, and naphthalene. The phase diagrams for the binary mixtures of (supercritical) ethene/n-heptane and benzene/n-pentane were determined from simulations in the NpT Gibbs ensemble. Although the TraPPE-UA force field is rather simple and makes use of relatively few different pseudo-atoms, its performance, as judged by comparisons to other popular force fields and available experimental data, is very satisfactory.

The adiabatic nuclear and electronic sampling Monte Carlo algorithm (ANES-MC) is extended to simulations in the Gibbs ensemble. Whereas the maximum displacements used for translational, rotational, and volume trial moves can be adjusted to foster efficient sampling in the adiabatic limit, the transfer (swap) of particles always causes a major disturbance of the electronic structures of the two phases (supplying and receiving the particle). To reequilibrate the electronic structures requires additional sampling of the electronic degrees of freedom. A simple, distance-dependent criterion for the preferential selection of the electronic degrees of freedom, for which a move is to be attempted, is shown to improve the efficiency of the particle swap move. The ANES-MC algorithm is applied to the polarizable simple point charge-fluctuating charge (SPC−FQ) and transferable intermolecular potential 4 point-fluctuating charge (TIP4P−FQ) models proposed by Rick et al. (J. Chem. Phys. 1994, 101, 6141). For both models simulations were performed using the standard constraint on the neutrality of individual molecules. In addition, for the SPC−FQ model the use of a constraint on the neutrality of an entire phase was investigated, which allows for intermolecular charge transfer. Simulations in the Gibbs ensemble were performed to calculate the vapor−liquid coexistence curves from 323 to 523 K, whereas simulations in the grand canonical ensemble were performed for the near-critical region. Dielectric constants at different state points were calculated from canonical ensemble simulations. Neither the SPC−FQ nor the TIP4P−FQ force fields give a satisfactory description of the vapor−liquid equilibria. In particular, the critical temperature is greatly underestimated by both models. Although intermolecular charge transfer has only a very small influence on the internal energy and the radial distribution functions at ambient conditions and along the coexistence curve, it increases the dielectric constant by approximately 30%.

Pressure-composition and temperature-composition phase diagrams are computed for the binary mixture of n-heptane and supercritical ethane using four different molecular models of increasing complexity. The ethane and heptane molecules were described using either (i) single-site Lennard−Jonesium (LJ) with fixed well-depth and size parameters, (ii) single-site LJ with temperature-dependent well depths, (iii) chains of methyl and methylene pseudo-atoms interacting via LJ potentials placed at the positions of all carbon nuclei, or (iv) an explicit-hydrogen representation with LJ interaction sites placed both at the carbon nuclei and at the centers of all carbon−hydrogen bonds. For comparison, simulations were also performed for the binary mixture of n-heptane and helium using the pseudo-atom model for the n-heptane molecules. All four models produce phase diagrams for the ethane/n-heptane mixture that are in reasonable agreement with experiment. However, the accuracy of the calculated phase diagrams improves markedly with increasing complexity of the model (and therefore increasing computational requirements). In both the liquid (n-heptane-rich, higher specific density) and supercritical (ethane-rich, lower specific density) phases center-of-mass radial distribution functions appear to show more enhanced structures for the two single-site models than the united-atom and explicit-hydrogen force fields. However, the number integrals of these radial distribution functions are strikingly similar for all models, that is the differences in molecular shape do not lead to a difference in the clustering of the solvent molecules around the solute. In particular, preferential solvation of n-heptane by ethane is not observed in the supercritical phase. Analysis of the contributions of the liquid and the supercritical phases to the decrease of the Gibbs free energy of transfer of n-heptane with increasing pressure suggest that the enhanced solubility of n-heptane in high-pressure supercritical ethane can be attributed to two causes of roughly equal importance:  “Pulling” of n-heptane into the supercritical phase by an increased density of ethane that acts as a nonspecific solvent, and “pushing” n-heptane out of the liquid phase by an increased concentration of ethane.

Recent simulation studies for four dipole-polarizable and for two fluctuating-charge water force fields have demonstrated that none of the force fields studied is capable of yielding a satisfactory description of the vapor−liquid coexistence curve from room temperature to the critical region. The performance of these polarizable force fields can be improved dramatically by introducing an additional coupling between the Lennard−Jones interaction parameters for a pair of oxygen sites and their partial charges (electronic configuration). Two different types of water models are presented which are based on either the three-site simple point charge (SPC) or the four-site transferable intermolecular potential 4 point (TIP4P) water representations. Adiabatic nuclear and electronic sampling Monte Carlo (ANES-MC) simulations in the Gibbs, isobaric−isothermal, and canonical ensembles were performed to calculate vapor−liquid coexistence curves, to determine the temperatures of maximum liquid density, and to evaluate dielectric constants along the coexistence line, respectively. The new SPC-pol-1 force field yields significantly better agreement with the experiment for the saturated vapor and liquid densities, the heats of vaporization, and the liquid-phase dielectric constants than the fixed-charge SPC, SPC/E (simple point charge/extended), TIP4P, and Errington/Panagiotopoulos (EP) force fields or than any other polarizable force field previously tested. However, the representation of the liquid water structure at ambient conditions is less satisfactory for the SPC-pol force fields. In contrast, the TIP4P-pol force fields produce much better low-temperature liquid structures and, in particular, a density maximum close to T = 277 K, but their performance for the vapor−liquid equilibria in the near-critical region is less satisfactory. Finally, it is important to note that the SPC-pol-1 force field yields an average molecular dipole moment of 2.5 D for the liquid phase at ambient conditions that is substantially smaller than the value of 2.7 D obtained for its minimum-energy hexamer cluster.

Motivated by shortcomings of the available united-atom models for alkanes, a new explicit-hydrogen model for n-alkanes (TraPPE-EH, transferable potentials for phase equilibria-explicit hydrogen) is developed from fitting to one-component fluid phase properties. In addition to Lennard−Jones sites on carbon atoms, this model utilizes Lennard−Jones sites on the centers of carbon−hydrogen bonds. Configurational-bias Monte Carlo simulations in the Gibbs and canonical ensembles were carried out to calculate the one-component vapor−liquid phase equilibria for methane to n-dodecane, to determine the phase diagram of supercritical ethane and n-heptane mixtures, to obtain the Gibbs free energies of transfer for n-pentane and n-hexane between helium vapor and n-heptane liquid phases, and to study the high-pressure region of the equation of state for n-pentane and n-decane. The explicit-hydrogen representation with its more faithful description of the molecular shape of alkanes allows us to find a set of Lennard−Jones parameters that yields significantly better agreement with experiment for one- and multicomponent phase equilibria than our united-atom alkane model, but the price is higher computational cost.

Accurate predictions of retention times, retention indices, and partition constants are a long sought-after goal for theoretical studies in chromatography. Configurational-bias Monte Carlo (CBMC) simulations in the Gibbs ensemble using the transferable potentials for phase equilibria−united atom (TraPPE−UA) force field have been carried out to obtain a microscopic picture of the partitioning of 10 alkane isomers between a helium vapor phase and a squalane liquid phase, a prototypical gas-liquid chromatography system. The alkane solutes include some topological isomers that differ only in the arrangement of their building blocks (e.g., 2,5-dimethylhexane and 3,4-dimethylhexane), for which the prediction of the retention order is particularly difficult. The Kovats retention indices, a measure of the relative retention times, are calculated directly from the partition constants and are in good agreement with experimental values. The calculated Gibbs free energies of transfer for the normal alkanes conform to Martin's equation which is the basis of linear free energy relationships used in many process modeling packages. Analysis of radial distribution functions and the corresponding energy integrals does not yield evidence for specific retention structures and shows that the internal energy of solvation is not the main driving force for the separation of topological isomers in this system.

A new generalization of the configurational-bias Monte Carlo method is presented which avoids the problems inherent in a Boltzmann rejection scheme for sequentially generating bond bending and torsional angles. The TraPPE-UA (transferable potentials for phase equilibria united-atom) force field is extended to include Lennard-Jones interaction parameters for methine and quaternary carbon groups by fitting to critical temperatures and saturated liquid densities of branched alkanes. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to determine the vapor−liquid coexistence curves (VLCC) for six alkane isomers with four to eight carbons. Results are presented for two united-atom alkane force fields:  PRF [Poncela, et al. Mol. Phys. 1997, 91, 189] and TraPPE-UA. Standard-state specific densities for the TraPPE-UA model were studied by simulations in the isobaric−isothermal ensemble. It is found that a single set of methyl, methylene, methine, and quaternary carbon parameters gives a reasonable description of the fluid phases of all alkanes with two or more carbon atoms. Whereas the size of the united atoms increases with increasing number of hydrogens for the PRF force field, it is demonstrated here that the opposite trend yields a better fit to the experimental VLCC data. The TraPPE-UA force field underpredicts the magnitude of the experimental second virial coefficients, while PRF gives good second virial coefficients but does not perform satisfactorily for the VLCC. As is also seen for the normal alkanes, the TraPPE-UA force field shows small, systematic deviations from the experimental saturated vapor pressures and densities for all molecules studied, and it slightly overpredicts the critical temperatures of the larger branched alkanes.

Experimentally measured partition coefficients show that the solubilities of small solutes in normal alkanes depend on the solvent chain length (nC). The causes for this nC dependence have not yet been unambiguously determined, and there is considerable controversy as to whether different interactions with methyl and methylene groups or entropic Flory−Huggins-like effects might play the major role. We have performed Gibbs-ensemble Monte Carlo simulations to study the vapor−liquid partitioning of methane in normal alkanes (with 6−12 carbon atoms) and related model solvents. The simulations show that the increase in solvent density with increasing nC is the main origin of the nC dependence for normal alkanes; that is, the solute molecule feels a different environment depending on the alkane chain length.

High-resolution 500 MHz solution-state ¹H and ¹³C NMR spectra of various poly(lactides) indicate at least hexad stereosequence sensitivity. The poly(lactides) were prepared in vials by melt polymerization of various combinations of l-lactide, d-lactide, and meso-lactide at 180 °C for 3 h using tin(II) bis(2-ethylhexanoate) (tin(II) octoate) as the catalyst in a 1:10 000 ratio. The intensity distribution of the various stereosequence resonances in the NMR spectra indicates a preference for syndiotactic addition during the polymerization process. Minimal evidence of transesterification was observed for these polymerization conditions.

The performance of several all-atom force fields for alkanes is compared and evaluated. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to calculate the vapor−liquid phase equilibria for methane, ethane, n-butane, n-pentane, and n-octane. The Williams, OPLS-AA, and MMFF94 force fields were selected as representative all-atom models for this study because they were fitted using three different strategies (Williams, crystal structures and heats of sublimation; OPLS-AA, liquid densities and heats of vaporization; MMFF94, rare gas pair potentials and quantum mechanics) and employ potentials with three different functional forms to describe nonbonded van der Waals interactions (Williams, Buckingham exp−r^-6 ; OPLS-AA, Lennard-Jones 12−6; MMFF94, buffered 14−7). It is shown that seemingly small differences in the potential functions can account for very large changes in the fluid-phase behavior. The Williams and OPLS-AA force fields yield liquid densities, boiling temperatures, and critical points that are in acceptable, albeit not in quantitative agreement with experiments, whereas the fluid-phase behavior of the MMFF94 model shows very large deviations.

A new set of united-atom Lennard-Jones interaction parameters for n-alkanes is proposed from fitting to critical temperatures and saturated liquid densities. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to determine the vapor−liquid coexistence curves for methane to dodecane using three united-atom force fields:  OPLS [Jorgensen, et al. J. Am. Chem. Soc. 1984, 106, 813], SKS [Siepmann, et al. Nature 1993, 365, 330], and TraPPE. Standard specific densities and the high-pressure equation-of-state for the transferable potentials for phase equilibria (TraPPE) model were studied by simulations in the isobaric−isothermal and canonical ensembles, respectively. It is found that one set of methyl and methylene parameters is sufficient to accurately describe the fluid phases of all n-alkanes with two or more carbon atoms. Whereas other n-alkane force fields employ methyl groups that are either equal or larger in size than the methylene groups, it is demonstrated here that using a smaller methyl group yields a better fit to the set of experimental data. As should be expected from an effective pair potential, the new parameters do not reproduce experimental second virial coefficients. Saturated vapor pressures and densities show small, but systematic deviation from the experimental data.

Molecular dynamics simulations have been used to investigate the effect of system size on the structure of model Langmuir monolayers. Several simulations with 64 molecules were performed in the range 0·185-0·40 nm2 per molecule. In addition, results were obtained for 16 and 256 molecule systems at 0·23, 0·25 and 0·27 nm2 per molecule. The simulations reveal a marked dependence on the number of molecules at 0·27 nm2 per molecule. System size effects play an important role at intermediate densities, mainly due to the competition between the formation of a large tilt angle and the appearance of domains.