Advantages of Multidimensional Biasing in Accelerated Dynamics: Application to the Calculation of the Acid pKa for Acetic Acid.

The use of accelerated sampling methods such as metadynamics has shown a significant advantage in calculations that involve infrequent events, which would otherwise require sampling a prohibitive number of configurations to determine the difference in free energies between two or more chemically distinct states such as in the calculation of acid dissociation constants Ka. In this case, the most common method is to bias the system via a single collective variable (CV) representing the coordination number of the proton donor group, which yields results in reasonable agreement with experiments. Here we study the deprotonation of acetic acid using the reactive force field ReaxFF and observe a significant dependence of Ka on the simulation box size when biasing only the coordination number CV, which is due to incomplete sampling of the deprotonated state for small simulation systems and inefficient sampling for larger ones. Incorporating a second CV representing the distance between the H3O+ cation and the acetate anion results in substantially more efficient sampling, both accelerating the dynamics and virtually eliminating the computational box size dependence.

Adsorption-Induced Expansion of Graphene Oxide Frameworks with Covalently Bonded Benzene-1,4-diboronic Acid: Numerical Studies.

Graphene oxide frameworks (GOFs) are interesting adsorbent materials with well-defined slit-shaped pores of almost monodisperse separation of ∼1 nm between graphene-like layers; however, the exact nature of the structure has remained undetermined. Recently, GOFs were observed to swell monotonically upon the adsorption of methane and xenon under supercritical conditions. Here, we present the results of molecular dynamics simulations of the adsorption of methane and xenon for various proposed GOF structures based upon force fields based on ab initio B3LYP density functional theory calculations. The simulations reproduce well both the adsorption isotherms and the expansion of the interlayer spacing for methane and xenon for a model of GOFs formed by covalently bonded benzene-1,4-diboronic acid oriented at quasirandom angles with respect to the graphene layers.

Adsorption of Natural Gas Mixtures of Methane, Ethane, and Propane in Nanoporous Carbon: Fully Atomistic Numerical Studies.

Natural gas (NG) is an interesting primary fuel; its larger-scale use is hindered by the difficulties of storing it under high pressures or low temperatures; a viable alternative is its storage via physisorption in porous materials. Most NG adsorption studies have focused on adsorption of pure methane, its primary component. Here we investigate the influence of heavier alkanes commonly found in NG (propane, ethane) on the adsorption process. We present the results of extensive molecular dynamics simulations of mixtures of methane-propane and methane-ethane at T = 300 and 400 K and P = 0-1500 bar in slit-shaped pores with interlayer spacings H = 8-20 Å. We observed that heavier hydrocarbons adsorb preferentially but remain mobile, which is promising for the intended application. We also solved a common problem with simulations of molecules with high adsorption affinity: the difficulty to determine their partial pressure. We developed an Arrhenius-type relationship allowing the calculation of these partial pressures from relationships between energy distributions of the different molecules in the simulations in conditions where a direct determination of these is impractical or impossible.

Self-Assembled Two-Dimensional Nanoporous Crystals as Molecular Sieves: Molecular Dynamics Studies of 1,3,5-Tristyrilbenzene-Cn Superstructures.

Due to their unique geometry complex, self-assembled nanoporous 2D molecular crystals offer a broad landscape of potential applications, ranging from adsorption and catalysis to optoelectronics, substrate processes, and future nanomachine applications. Here we report and discuss the results of extensive all-atom Molecular Dynamics (MD) investigations of self-assembled organic monolayers (SAOM) of interdigitated 1,3,5-tristyrilbenzene (TSB) molecules terminated by alkoxy peripheral chains Cn containing n carbon atoms (TSB3,5-Cn) deposited onto highly ordered pyrolytic graphite (HOPG). In vacuo structural and electronic properties of the TSB3,5-Cn molecules were initially determined using ab initio second order Møller-Plesset (MP2) calculations. The MD simulations were then used to analyze the behavior of the self-assembled superlattices, including relaxed lattice geometry (in good agreement with experimental results) and stability at ambient temperatures. We show that the intermolecular disordering of the TSB3,5-Cn monolayers arises from competition between decreased rigidity of the alkoxy chains (loss of intramolecular order) and increased stabilization with increasing chain length (afforded by interdigitation). We show that the inclusion of guest organic molecules (e.g., benzene, pyrene, coronene, hexabenzocoronene) into the nanopores (voids formed by interdigitated alkoxy chains) of the TSB3,5-Cn superlattices stabilizes the superstructure, and we highlight the importance of alkoxy chain mobility and available pore space in the dynamics of the systems and their potential application in selective adsorption.

Computer modeling of 2D supramolecular nanoporous monolayers self-assembled on graphite.

Nano-porous two-dimensional molecular crystals, self-assembled on atomically flat host surfaces offer a broad range of possible applications, from molecular electronics to future nano-machines. Computer-assisted designing of such complex structures requires numerically intensive modeling methods. Here we present the results of extensive, fully atomistic simulations of self-assembled monolayers of interdigitated molecules of 1,3,5-tristyrilbenzene substituted by C6 alkoxy peripheral chains (TSB3,5-C6), deposited onto highly-ordered pyrolytic graphite. Structural and electronic properties of the TSB3,5-C6 molecules were determined from ab initio calculations, then used in Molecular Dynamics simulations to analyze the mechanism of formation, epitaxy, and stability of the TSB3,5-C6 nanoporous superlattice. We show that the monolayer disordering results from the competition between flexibility of the C6 chains and their stabilization by interdigitation. The inclusion of guest molecules (benzene and pyrene) into superlattice nanopores stabilizes the monolayer. The alkoxy chain mobility and available pore space defines the systems dynamics, essential for potential application.

Adsorption-Induced Expansion of Graphene Oxide Frameworks: Observation by in Situ Neutron Diffraction.

We have investigated adsorption-induced deformation in graphene oxide framework materials (GOFs) using neutron diffraction at sample pressures up to 140 bar. GOFs, made by the solvothermal reaction of graphite oxide and benzene-1,4-diboronic acid, are a suitable candidate for deformation studies due to their narrow (∼1 nm), monodispersed, slit-shaped pores whose width can be measured by diffraction techniques. We have observed, in situ, a monotonic expansion of the slit width with increasing pressure upon adsorption of xenon, methane, and hydrogen under supercritical conditions. The expansion of ∼4% observed for xenon at a pressure of 48 bar is the largest deformation yet reported for supercritical adsorption on a carbonaceous material. We find that the expansion of the three gases can be mapped onto a common curve based solely on their Lennard-Jones parameters, in a manner similar to a law of corresponding states.

Molecular simulations of intermediate and long alkanes adsorbed on graphite: tuning of non-bond interactions.

The interplay between the torsional potential energy and the scaling of the 1-4 van der Waals and Coulomb interactions determines the stiffness of flexible molecules. In this paper we demonstrate for the first time that the precise value of the nonbond scaling factor (SF)--often a value assumed without justification--has a significant effect on the critical properties and mechanisms of systems undergoing a phase transition, and that, for accurate simulations, this scaling factor is highly dependent on the system under consideration. In particular, by analyzing the melting of n-alkanes (hexane C6, dodecane C12, tetracosane C24) on graphite, we show that the SF is not constant over varying alkane chain lengths when the structural correlated transformations are concerned. Instead, monotonic decrease of SF with the molecular length drives a cross-over between two distinct mechanisms for melting in such systems. In a broad sense we show that the choice for SF in any simulation containing adsorbed or correlated long molecules needs to be carefully considered.

Enhanced hydrogen adsorption in boron substituted carbon nanospaces.

Activated carbons are one of promising groups of materials for reversible storage of hydrogen by physisorption. However, the heat of hydrogen adsorption in such materials is relatively low, in the range of about 4-8 kJ/mol, which limits the total amount of hydrogen adsorbed at P=100 bar to approximately 2 wt % at room temperature and approximately 8 wt % at 77 K. To improve the sorption characteristics the adsorbing surfaces must be modified either by substitution of some atoms in the all-carbon skeleton by other elements, or by doping/intercalation with other species. In this letter we present ab initio calculations and Monte Carlo simulations showing that substitution of 5%-10% of atoms in a nanoporous carbon by boron atoms results in significant increases in the adsorption energy (up to 10-13.5 kJ/mol) and storage capacity ( approximately 5 wt % at 298 K, 100 bar) with a 97% delivery rate.

Hydrogen storage in engineered carbon nanospaces.

It is shown how appropriately engineered nanoporous carbons provide materials for reversible hydrogen storage, based on physisorption, with exceptional storage capacities (approximately 80 g H2/kg carbon, approximately 50 g H2/liter carbon, at 50 bar and 77 K). Nanopores generate high storage capacities (a) by having high surface area to volume ratios, and (b) by hosting deep potential wells through overlapping substrate potentials from opposite pore walls, giving rise to a binding energy nearly twice the binding energy in wide pores. Experimental case studies are presented with surface areas as high as 3100 m(2) g(-1), in which 40% of all surface sites reside in pores of width approximately 0.7 nm and binding energy approximately 9 kJ mol(-1), and 60% of sites in pores of width>1.0 nm and binding energy approximately 5 kJ mol(-1). The findings, including the prevalence of just two distinct binding energies, are in excellent agreement with results from molecular dynamics simulations. It is also shown, from statistical mechanical models, that one can experimentally distinguish between the situation in which molecules do (mobile adsorption) and do not (localized adsorption) move parallel to the surface, how such lateral dynamics affects the hydrogen storage capacity, and how the two situations are controlled by the vibrational frequencies of adsorbed hydrogen molecules parallel and perpendicular to the surface: in the samples presented, adsorption is mobile at 293 K, and localized at 77 K. These findings make a strong case for it being possible to significantly increase hydrogen storage capacities in nanoporous carbons by suitable engineering of the nanopore space.

Structural and phase properties of tetracosane (C24H50) monolayers adsorbed on graphite: an explicit hydrogen molecular dynamics study.

We discuss molecular dynamics (MD) computer simulations of a tetracosane (C24H50) monolayer physisorbed onto the basal plane of graphite. The adlayer molecules are simulated with explicit hydrogens, and the graphite substrate is represented as an all-atom structure having six graphene layers. The tetracosane dynamics modeled in the fully atomistic manner agree well with experiment. The low-temperature ordered solid organizes into a rectangularly centered structure that is not commensurate with underlying graphite. Above T=200 K, as the molecules start to lose their translational and orientational order via gauche defect formation a weak smectic mesophase (observed experimentally but never reproduced in united atom (UA) simulations) appears. The phase behavior of the adsorbed layer is critically sensitive to the way the electrostatic interactions are included in the model. If the electrostatic charges are set to zero (as for a UA force field), then the melting temperature increases by approximately 70 K with respect to the experimental value. When the nonbonded 1-4 interaction is not scaled, the melting temperature decreases by approximately 90 K. If the scaling factor is set to 0.5, then melting occurs at T=350 K, in very good agreement with experimental data.

Explicit hydrogen molecular dynamics simulations of hexane deposited onto graphite at various coverages.

We present results of molecular dynamics (MD) computer simulations of hexane (C6H14) adlayers physisorbed onto a graphite substrate for coverages in the range 0.5 < or = rho < or = 1 monolayers. The hexane molecules are simulated with explicit hydrogens, and the graphite substrate is modeled as an all-atom structure having six graphene layers. At coverages above about rho congruent with 0.9 the low-temperature herringbone solid loses its orientational order at T(1) = 140 +/- 3 K. At rho = 0.878, the system presents vacancy patches and T(1) decreases to ca. 100 K. As coverage decreases further, the vacancy patches become larger and by rho = 0.614 the solid is a connected network of randomly oriented islands and there is no global herringbone order-disorder transition. In all cases we observe a weak nematic mespohase. The melting temperature for our explicit-hydrogen model is T(2) = 160 +/- 3 K and falls to ca. 145 K by rho = 0.614 (somewhat lower than seen in experiment). The dynamics seen in the fully atomistic model agree well with experiment, as the molecules remain overall flat on the substrate in the solid phase and do not show anomalous tilting behavior at any phase transition observed in earlier simulations in the unified atom (UA) approximation. Energetics and structural parameters also are more reasonable and, collectively, the results from the simulations in this work demonstrate that the explicit-hydrogen model of hexane is substantially more realistic than the UA approximation.

Universality away from critical points in two-dimensional phase transitions.

The p-state clock model in two dimensions is a system of discrete rotors with a quasiliquid phase in a region T14. We show that, for p>4 and above a temperature T(eu), all macroscopic thermal averages become identical to those of the continuous rotor (p=infinity). This collapse of thermodynamic observables creates a regime of extended universality in the phase diagram and an emergent symmetry, not present in the Hamiltonian. For p> or =8, the collapse starts in the quasiliquid phase and makes the transition at T2 identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition of the continuous rotor. For p< or =6, the transition at T2 is below T(eu) and no longer a BKT transition. The results generate a range of experimental predictions, such as the motion of magnetic domain walls, and limits on macroscopic distinguishability of different microscopic interactions.