There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Equivalent weight (EW) is the number of grams of dry Nafion per mole of sulfonic acid groups when the material is in the acid form. This is an average EW in the sense that the comonomer sequence distribution (that is usually unknown to the investigator and largely unreported) gives a distribution in m in this formula. EW can be ascertained by acid-base titration, by analysis of atomic sulfur, and by FT-IR spectroscopy. The relationship between EW and m is EW ) 100m + 446 so that, for example, the side chains are separated by around 14 CF2 units in a membrane of 1100 EW. Common at the time of this writing are Nafion 117 films. The designation “117” refers to a film having 1100 EW and a nominal thickness of 0.007 in., although 115 and 112 films have also been available. Early-reported studies involved 1200 EW samples as well as special experimental varieties, some being rather thin. The equivalent weight is related to the property more often seen in the field of conventional ion exchange resins, namely the ion exchange capacity (IEC), by the equation IEC ) 1000/EW. The mention of the molecular weight of high equivalent weight (EW > 1000 g‚mol-1) Nafion is almost absent in the literature, although the range 105-106 Da has been mentioned. As this polymer does not form true solutions, the common methods of light scattering and gel permeation chromatography cannot be used to determine molecular weight as well as the size and shape of isolated, truly dissolved molecules. Studies of the structure of this polymer in solvent (albeit not a true solution) will be mentioned in the scattering section of this review. It should be noted that Curtin et al. performed size exclusion chromatography determinations of the molecular weight distribution in Nafion aqueous dispersions after they were heated to high temperatures (230, 250, and 270 °C).1 Before heating, there was a high molecular weight shoulder on a bimodal distribution, due to molecular aggregates, but this shoulder disappeared upon heating, which indicated that the aggregates were disrupted. The peaks for the monomodal distribution for the heated samples were all located at molecular weights slightly higher than 105 g‚mol-1. Also, light scattering experiments revealed that the radius of gyration had a linear dependence on the molar mass of the aggregates, which suggests that the particles are in the form of rods or ribbons, or at least some elongated structure. Nafion ionomers are usually derived from the thermoplastic -SO2F precursor form that can be extruded into sheets of required thickness. Strong interactions between the ionic groups are an obstacle to melt processing. This precursor does not possess the clustered morphology that will be of great concern in this article but does possess Teflon-like crystallinity which persists when the sulfonyl fluoride form is converted to, for example, the K+ form by reacting it with KOH in water and DMSO. Thereafter, the -SO3H form is achieved by soaking the film in a sufficiently concentrated aqueous acid solution. Extrusion of the sulfonyl fluoride precursor can cause microstructural orientation in the machine direction, * Address correspondence to either author. Phone: 601-266-5595/ 4480. Fax: 601-266-5635. E-mail: Kenneth.Mauritz@usm.edu; RBMoore@usm.edu. 4535 Chem. Rev. 2004, 104, 4535−4585

State of Understanding of Nafion

New, hydrophobic ionic liquids with low melting points (<−30 °C to ambient temperature) have been synthesized and investigated, based on 1,3-dialkyl imidazolium cations and hydrophobic anions. Other imidazolium molten salts with hydrophilic anions and thus water-soluble are also described. The molten salts were characterized by NMR and elemental analysis. Their density, melting point, viscosity, conductivity, refractive index, electrochemical window, thermal stability, and miscibility with water and organic solvents were determined. The influence of the alkyl substituents in 1, 2, 3, and 4(5)-positions on these properties was scrutinized. Viscosities as low as 35 cP (for 1-ethyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)amide (bis(triflyl)amide) and trifluoroacetate) and conductivities as high as 9.6 mS/cm were obtained. Photophysical probe studies were carried out to establish more precisely the solvent properties of 1-ethyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)amide). The hydrophobi...

Hydrophobic, Highly Conductive Ambient-Temperature Molten Salts

To date, copper is the only heterogeneous catalyst that has shown a propensity to produce valuable hydrocarbons and alcohols, such as ethylene and ethanol, from electrochemical CO2 reduction (CO2R). There are variety of factors that impact CO2R activity and selectivity, including the catalyst surface structure, morphology, composition, the choice of electrolyte ions and pH, and the electrochemical cell design. Many of these factors are often intertwined, which can complicate catalyst discovery and design efforts. Here we take a broad and historical view of these different aspects and their complex interplay in CO2R catalysis on Cu, with the purpose of providing new insights, critical evaluations, and guidance to the field with regard to research directions and best practices. First, we describe the various experimental probes and complementary theoretical methods that have been used to discern the mechanisms by which products are formed, and next we present our current understanding of the complex reaction networks for CO2R on Cu. We then analyze two key methods that have been used in attempts to alter the activity and selectivity of Cu: nanostructuring and the formation of bimetallic electrodes. Finally, we offer some perspectives on the future outlook for electrochemical CO2R.

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Progress and Perspectives of Electrochemical CO2 Reduction on Copper in Aqueous Electrolyte

The method of molecular dynamics is applied to a solvent‐averaged model of electrolyte solutions, described by a generalized Langevin equation. For Brownian motion without solute–solute interactions, we recover the characteristic features of an infinitely dilute solution. For interacting brownons, the results exhibit a noticeable dependence of the calculated self‐diffusion coefficients on the influence of the Coulomb forces. The model system exhibits ion association when the Coulomb forces are made strong enough.

Brownian dynamics: Its application to ionic solutions

We report a molecular simulation study of hydrodynamics in clay nanopores, with pore widths ranging from 2 to 9 nm. Understanding mass transfer through clay nanopores is necessary in many contexts such as groundwater hydrology, petroleum and gas reservoir engineering, as well as carbon dioxide sequestration or geological disposal of radioactive waste. Grand-canonical Monte Carlo simulations first allow us to determine the water content in the pores. We then analyze the structure and diffusion of confined water using equilibrium molecular dynamics (MD). Finally, nonequilibrium MD allow us to analyze the hydrodynamic behavior of the confined fluid and assess the relevance of continuum hydrodynamics to describe the flow under a pressure gradient. The Navier–Stokes equation, using the density and viscosity of the bulk fluid, provides a reasonable description of the flow provided that the pore width is larger than 3 nm and that a slip boundary condition is used. We determine a slip length of 2.1 A at the clay ...

/pdf/hydrodynamics-in-clay-nanopores-586nzondrb.pdf

Hydrodynamics in Clay Nanopores

Models of swelling clays are studied by computer simulations (Monte Carlo and molecular dynamics). We focus on the comparison of structural and dynamic properties of two montmorillonites with different kinds of counterions Na+ and Cs+. The calculated values are compared with available experimental quantities such as interlayer spacing as a function of water content and diffusion coefficients of both water molecules and counterions in the monohydrated state. The results are consistent with experimental values and previous simulations. For the dynamics, the short time behavior of water as observed with quasielastic neutron scattering is in agreement with simulated one. For the ions, the experimental values are related to macroscopic long time motions and are much smaller than the short time values calculated from MD. Thus, the present study provides a detailed insight in the microscopic dynamics of ions related to the structure of the clay: it is shown that Cs+ diffuse faster than Na+ and that the arrangeme...

Microscopic simulation of structure and dynamics of water and counterions in a monohydrated montmorillonite

We report a Monte Carlo and molecular dynamics simulations study of carbon dioxide in hydrated sodium montmorillonite, including thermodynamical, structural, and dynamical properties. In order to simulate the behavior of a clay caprock in contact with a CO2 reservoir, we consider clays in equilibrium with H2O−CO2 mixtures under conditions close to relevant ones for geological storage, namely a temperature T = 348 K, and pressures P = 25 and 125 bar, and under which two bulk phases coexist: H2O-rich liquid on the one hand and CO2-rich gas (P = 25 bar) or supercritical fluid (P = 125 bar) on the other hand. We first use grand canonical MC simulations to determine the number of stable states in clay, their composition, and the corresponding equilibrium interlayer distances. The vertical, horizontal, and radial distribution functions of the confined mixture, subsequently obtained using molecular dynamics, reveal some structural feature induced by the presence of CO2. Finally, the simulations indicate that car...

/pdf/carbon-dioxide-in-montmorillonite-clay-hydrates-agrazhlxrt.pdf

Carbon Dioxide in Montmorillonite Clay Hydrates: Thermodynamics, Structure, and Transport from Molecular Simulation

https://hal.archives-ouvertes.fr/hal-00369627/document

Pierre Turq

Papers

Brownian dynamics: Its application to ionic solutions

Hydrodynamics in Clay Nanopores

Microscopic simulation of structure and dynamics of water and counterions in a monohydrated montmorillonite

Carbon Dioxide in Montmorillonite Clay Hydrates: Thermodynamics, Structure, and Transport from Molecular Simulation

Water and ions in clays: Unraveling the interlayer/micropore exchange using molecular dynamics