A theory of pitch for the hydrodynamic properties of molecules, helices, and achiral swimmers at low Reynolds number.

We present a theory for pitch, a matrix property that is linked to the coupling of rotational and translational motion of rigid bodies at low Reynolds numbers. The pitch matrix is a geometric property of objects in contact with a surrounding fluid, and it can be decomposed into three principal axes of pitch and their associated moments of pitch. The moments of pitch predict the translational motion in a direction parallel to each pitch axis when the object is rotated around that axis and can be used to explain translational drift, particularly for rotating helices. We also provide a symmetrized boundary element model for blocks of the resistance tensor, allowing calculation of the pitch matrix for arbitrary rigid bodies. We analyze a range of chiral objects, including chiral molecules and helices. Chiral objects with a Cn symmetry axis with n > 2 show additional symmetries in their pitch matrices. We also show that some achiral objects have non-vanishing pitch matrices, and we use this result to explain recent observations of achiral microswimmers. We also discuss the small but non-zero pitch of Lord Kelvin's isotropic helicoid.

The role of polarizability in the interfacial thermal conductance at the gold-water interface.

We have studied the interfacial thermal conductance, G, of the flat Au(111)-water interface using non-equilibrium molecular dynamics simulations. We utilized two metal models, one based on the embedded atom method (EAM) and the other including metallic polarizability via a density readjusting EAM. These were combined with three popular water models, SPC/E, TIP4P, and TIP4P-FQ, to understand the role of polarizability in the thermal transport process. A thermal flux was introduced using velocity shearing and scaling reverse non-equilibrium molecular dynamics, and transport coefficients were measured by calculating the resulting thermal gradients and temperature differences at the interface. Our primary finding is that the computed interfacial thermal conductance between a bare metal interface and water increases when polarizability is taken into account in the metal model. Additional work to understand the origin of the conductance difference points to changes in the local ordering of the water molecules in the first two layers of water above the metal surface. Vibrational densities of states on both sides of the interface exhibit interesting frequency modulation close to the surface but no obvious differences due to metal polarizability.

Real space electrostatics for multipoles. III. Dielectric properties.

In Papers I and II, we developed new shifted potential, gradient shifted force, and Taylor shifted force real-space methods for multipole interactions in condensed phase simulations. Here, we discuss the dielectric properties of fluids that emerge from simulations using these methods. Most electrostatic methods (including the Ewald sum) require correction to the conducting boundary fluctuation formula for the static dielectric constants, and we discuss the derivation of these corrections for the new real space methods. For quadrupolar fluids, the analogous material property is the quadrupolar susceptibility. As in the dipolar case, the fluctuation formula for the quadrupolar susceptibility has corrections that depend on the electrostatic method being utilized. One of the most important effects measured by both the static dielectric and quadrupolar susceptibility is the ability to screen charges embedded in the fluid. We use potentials of mean force between solvated ions to discuss how geometric factors can lead to distance-dependent screening in both quadrupolar and dipolar fluids.

Real space electrostatics for multipoles. I. Development of methods.

We have extended the original damped-shifted force (DSF) electrostatic kernel and have been able to derive three new electrostatic potentials for higher-order multipoles that are based on truncated Taylor expansions around the cutoff radius. These include a shifted potential (SP) that generalizes the Wolf method for point multipoles, and Taylor-shifted force (TSF) and gradient-shifted force (GSF) potentials that are both generalizations of DSF electrostatics for multipoles. We find that each of the distinct orientational contributions requires a separate radial function to ensure that pairwise energies, forces, and torques all vanish at the cutoff radius. In this paper, we present energy, force, and torque expressions for the new models, and compare these real-space interaction models to exact results for ordered arrays of multipoles. We find that the GSF and SP methods converge rapidly to the correct lattice energies for ordered dipolar and quadrupolar arrays, while the TSF is too severe an approximation to provide accurate convergence to lattice energies. Because real-space methods can be made to scale linearly with system size, SP and GSF are attractive options for large Monte Carlo and molecular dynamics simulations, respectively.

Real space electrostatics for multipoles. II. Comparisons with the Ewald sum.

We report on tests of the shifted potential (SP), gradient shifted force (GSF), and Taylor shifted force (TSF) real-space methods for multipole interactions developed in Paper I of this series, using the multipolar Ewald sum as a reference method. The tests were carried out in a variety of condensed-phase environments designed to test up to quadrupole-quadrupole interactions. Comparisons of the energy differences between configurations, molecular forces, and torques were used to analyze how well the real-space models perform relative to the more computationally expensive Ewald treatment. We have also investigated the energy conservation, structural, and dynamical properties of the new methods in molecular dynamics simulations. The SP method shows excellent agreement with configurational energy differences, forces, and torques, and would be suitable for use in Monte Carlo calculations. Of the two new shifted-force methods, the GSF approach shows the best agreement with Ewald-derived energies, forces, and torques and also exhibits energy conservation properties that make it an excellent choice for efficient computation of electrostatic interactions in molecular dynamics simulations. Both SP and GSF are able to reproduce structural and dynamical properties in the liquid models with excellent fidelity.

A Reverse Nonequilibrium Molecular Dynamics Algorithm for Coupled Mass and Heat Transport in Mixtures.

We present a new method for introducing stable nonequilibrium concentration gradients in molecular dynamics simulations of mixtures. This method extends earlier reverse nonequilibrium molecular dynamics (RNEMD) methods, which use kinetic energy scaling moves to create temperature or velocity gradients. In the new scaled particle flux (SPF-RNEMD) algorithm, energies and forces are computed simultaneously for a molecule existing in two nonadjacent regions of a simulation box, and the system evolves under a linear combination of these interactions. A continuously increasing particle scaling variable is responsible for the migration of the molecule between the regions as the simulation progresses, allowing for simulations under an applied particle flux. To test the method, we investigate diffusivity in mixtures of identical but distinguishable particles and in a simple mixture of multiple Lennard-Jones particles. The resulting concentration gradients provide Fick diffusion constants for mixtures. We also discuss using the new method to obtain coupled transport properties using simultaneous particle and thermal fluxes to compute the temperature dependence of the diffusion coefficient and activation energies for diffusion from a single simulation. Lastly, we demonstrate the use of this new method in interfacial systems by computing the diffusive permeability of a molecular fluid moving through a nanoporous graphene membrane.

Simulations of solid-liquid friction at ice-I(h)/water interfaces.

We have investigated the structural and dynamic properties of the basal and prismatic facets of the ice Ih/water interface when the solid phase is drawn through the liquid (i.e., sheared relative to the fluid phase). To impose the shear, we utilized a velocity-shearing and scaling approach to reverse non-equilibrium molecular dynamics. This method can create simultaneous temperature and velocity gradients and allow the measurement of transport properties at interfaces. The interfacial width was found to be independent of the relative velocity of the ice and liquid layers over a wide range of shear rates. Decays of molecular orientational time correlation functions gave similar estimates for the width of the interfaces, although the short- and longer-time decay components behave differently closer to the interface. Although both facets of ice are in "stick" boundary conditions in liquid water, the solid-liquid friction coefficients were found to be significantly different for the basal and prismatic facets of ice.

Heat Transfer in Gold Interfaces Capped with Thiolated Polyethylene Glycol: A Molecular Dynamics Study.

Reverse nonequilibrium molecular dynamics simulations were used to study heat transport in solvated gold interfaces which have been functionalized with a low-molecular weight thiolated polyethylene glycol (PEG). The gold interfaces studied included (111), (110), and (100) facets as well as spherical nanoparticles with radii of 10 and 20 Å. The embedded atom model (EAM) and the polarizable density-readjusted embedded atom model (DR-EAM) were implemented to determine the effect of metal polarizability on heat transport properties. We find that the interfacial thermal conductance values for thiolated PEG-capped interfaces are higher than those for pristine gold interfaces. Hydrogen bonding between the thiolated PEG and solvent differs between planar facets and the nanospheres, suggesting one mechanism for enhanced transfer of energy, while the covalent gold sulfur bond appears to create the largest barrier to thermal conduction. Through analysis of vibrational power spectra, we find an enhanced population at low-frequency heat-carrying modes for the nanospheres, which may also explain the higher mean interfacial thermal conductance (G) value.

Separation of Enantiomers through Local Vorticity: A Screw Model Mechanism.

We present a model to explain the mechanism behind enantiomeric separation under either shear flow or local rotational motion in a fluid. Local vorticity of the fluid imparts molecular rotation that couples to translational motion, sending enantiomers in opposite directions. Translation-rotation coupling of enantiomers is explored using the molecular hydrodynamic resistance tensor, and a molecular equivalent of the pitch of a screw is introduced to describe the degree of translation-rotation coupling. Molecular pitch is a structural feature of the molecules and can be easily computed, allowing rapid estimation of the pitch of 85 druglike molecules. Simulations of model enantiomers in a range of fluids such as Λ- and Δ-[Ru(bpy)3]Cl2 in water and (R, R)- and (S, S)-atorvastatin in methanol support predictions made using molecular pitch values. A competition model and continuum drift-diffusion equations are developed to predict separation of realistic racemic mixtures. We find that enantiomeric separation on a centimeter length scale can be achieved in hours, using experimentally achievable vorticities. Additionally, we find that certain achiral objects can also exhibit a nonzero molecular pitch.

A gentler approach to RNEMD: nonisotropic velocity scaling for computing thermal conductivity and shear viscosity.

We present a new method for introducing stable nonequilibrium velocity and temperature gradients in molecular dynamics simulations of heterogeneous systems. This method extends earlier reverse nonequilibrium molecular dynamics (RNEMD) methods which use momentum exchange swapping moves. The standard swapping moves can create nonthermal velocity distributions and are difficult to use for interfacial calculations. By using nonisotropic velocity scaling (NIVS) on the molecules in specific regions of a system, it is possible to impose momentum or thermal flux between regions of a simulation while conserving the linear momentum and total energy of the system. To test the method, we have computed the thermal conductivity of model liquid and solid systems as well as the interfacial thermal conductivity of a metal-water interface. We find that the NIVS-RNEMD improves the problematic velocity distributions that develop in other RNEMD methods.

Dipolar ordering in the ripple phases of molecular-scale models of lipid membranes.

Symmetric and asymmetric ripple phases have been observed to form in molecular dynamics simulations of a simple molecular-scale lipid model. The lipid model consists of an dipolar head group and an ellipsoidal tail. Within the limits of this model, an explanation for generalized membrane curvature is a simple mismatch in the size of the heads with the width of the molecular bodies. The persistence of a bilayer structure requires strong attractive forces between the head groups. One feature of this model is that an energetically favorable orientational ordering of the dipoles can be achieved by out-of-plane membrane corrugation. The corrugation of the surface stabilizes the long range orientational ordering for the dipoles in the head groups which then adopt a bulk anti-ferroelectric state. We observe a common feature of the corrugated dipolar membranes: the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis.

Langevin dynamics for rigid bodies of arbitrary shape.

We present an algorithm for carrying out Langevin dynamics simulations on complex rigid bodies by incorporating the hydrodynamic resistance tensors for arbitrary shapes into an advanced rotational integration scheme. The integrator gives quantitative agreement with both analytic and approximate hydrodynamic theories for a number of model rigid bodies and works well at reproducing the solute dynamical properties (diffusion constants and orientational relaxation times) obtained from explicitly solvated simulations.

Why is Ice Slippery? Simulations of Shear Viscosity of the Quasi-Liquid Layer on Ice.

The temperature and depth dependence of the shear viscosity (η) of the quasi-liquid layer (QLL) of water on ice-Ih crystals was determined using simulations of the TIP4P/Ice model. The crystals display either the basal {0001} or prismatic {101̅0} facets, and we find that the QLL viscosity depends on the presented facet, the distance from the solid/liquid interface, and the undercooling temperature. Structural order parameters provide two distinct estimates of the QLL widths, which are found to range from 6.0 to 7.8 Å, and depend on the facet and undercooling temperature. Above 260 K, the viscosity of the vapor-adjacent water layer is significantly less viscous than the solid-adjacent layer and is also lower than the viscosity of liquid water.

Spontaneous corrugation of dipolar membranes.

We present a simple model for dipolar elastic membranes that gives lattice-bound point dipoles complete orientational freedom as well as translational freedom along one coordinate (out of the plane of the membrane). There is an additional harmonic term which binds each of the dipoles to the six nearest neighbors on either triangular or distorted lattices. The translational freedom of the dipoles allows triangular lattices to find states that break out of the normal orientational disorder of frustrated configurations and which are stabilized by long-range antiferroelectric ordering. In order to break out of the frustrated states, the dipolar membranes form corrugated or "rippled" phases that make the lattices effectively nontriangular. We observe three common features of the corrugated dipolar membranes: (1) the corrugated phases develop easily when hosted on triangular lattices, (2) the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis, and (3) on triangular lattices, the dipole director axis is found to be parallel to any of the three equivalent lattice directions.

Breathing mode dynamics and elastic properties of gold nanoparticles.

We present calculations of the bulk modulus, heat capacity, and the period of the breathing mode for spherical nanoparticles following excitation by ultrafast laser pulses. The bulk modulus and heat capacities both exhibit clear transitions upon bulk melting of the particles. Equilibrium calculations of the heat capacity show that the melting transition is sharper and occurs at a lower temperature than one would observe from an ultrafast experiment. We also observe an intriguing splitting in the low-frequency spectra of the nanoparticles and analyze this splitting in terms of Lamb's classical theory of elastic spheres. We conclude that the particles either (1) melt during the observation period following laser excitation or (2) melt an outer shell while maintaining a crystalline core. Both mechanisms for melting are commensurate with our observations.

Reverse Non-Equilibrium Molecular Dynamics Demonstrate That Surface Passivation Controls Thermal Transport at Semiconductor-Solvent Interfaces.

We examine the role played by surface structure and passivation in thermal transport at semiconductor/organic interfaces. Such interfaces dominate thermal transport in semiconductor nanomaterials owing to material dimensions much smaller than the bulk phonon mean free path. Utilizing reverse nonequilibrium molecular dynamics simulations, we calculate the interfacial thermal conductance (G) between a hexane solvent and chemically passivated wurtzite CdSe surfaces. In particular, we examine the dependence of G on the CdSe slab thickness, the particular exposed crystal facet, and the extent of surface passivation. Our results indicate a nonmonotonic dependence of G on ligand-grafting density, with interfaces generally exhibiting higher thermal conductance for increasing surface coverage up to ∼0.08 ligands/Å(2) (75-100% of a monolayer, depending on the particular exposed facet) and decreasing for still higher coverages. By analyzing orientational ordering and solvent penetration into the ligand layer, we show that a balance of competing effects is responsible for this nonmonotonic dependence. Although the various unpassivated CdSe surfaces exhibit similar G values, the crystal structure of an exposed facet nevertheless plays an important role in determining the interfacial thermal conductance of passivated surfaces, as the density of binding sites on a surface determines the ligand-grafting densities that may ultimately be achieved. We demonstrate that surface passivation can increase G relative to a bare surface by roughly 1 order of magnitude and that, for a given extent of passivation, thermal conductance can vary by up to a factor of ∼2 between different surfaces, suggesting that appropriately tailored nanostructures may direct heat flow in an anisotropic fashion for interface-limited thermal transport.

A Method for Creating Thermal and Angular Momentum Fluxes in Nonperiodic Simulations.

We present a new reverse nonequilibrium molecular dynamics method that can be used with nonperiodic simulation cells. This method applies thermal and/or angular momentum fluxes between two arbitrary regions of the simulation and is capable of creating stable temperature and angular velocity gradients while conserving total energy and angular momentum. One particularly useful application is the exchange of kinetic energy between two concentric spherical regions, which can be used to generate thermal transport between nanoparticles and the solvent that surrounds them. The rotational couple to the solvent (a measure of interfacial friction) is also available via this method. As tests of the new method, we have computed the thermal conductivities of gold nanoparticles and water clusters, the interfacial thermal conductivity (G) of a solvated gold nanoparticle, and the interfacial friction of a variety of solvated gold nanostructures.

Nitrile vibrations as reporters of field-induced phase transitions in 4-cyano-4'-pentylbiphenyl (5CB).

4-Cyano-4'-pentylbiphenyl (5CB) is a liquid crystal forming compound with a terminal nitrile group aligned with the long axis of the molecule. Simulations of condensed-phase 5CB were carried out both with and without applied electric fields to provide an understanding of the Stark shift of the terminal nitrile group. A field-induced isotropic-nematic phase transition was observed in the simulations, and the effects of this transition on the distribution of nitrile frequencies were computed. Classical bond displacement correlation functions exhibit a ∼2.3 cm(-1) red-shift of a portion of the main nitrile peak, and this shift was observed only when the fields were large enough to induce orientational ordering of the bulk phase. Distributions of frequencies obtained via cluster-based fits to quantum mechanical energies of nitrile bond deformations exhibit a similar ∼2.7 cm(-1) red-shift. Joint spatial-angular distribution functions indicate that phase-induced anticaging of the nitrile bond is contributing to the change in the nitrile spectrum.

The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems.

We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the "Langevin Hull", can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work.