Tests of the homogeneous nucleation theory with molecular-dynamics simulations. I. Lennard-Jones molecules

Two kinds of the homogeneous nucleation theory exist at the present: the classical nucleation theory and the semiphenomenological model. To test them, we performed molecular-dynamics (MD) simulations of nucleation from vapor to liquid with 5000-20,000 Lennard-Jones-type molecules. Simulations were done for various values of supersaturation ratios (from 2 to 10) and temperatures (from 80 to 120 K). We compared the size distribution of clusters in MD simulations with those in the theoretical models because the number density of critical clusters governs the nucleation rate. We found that the semiphenomenological model achieves excellent agreements in size distributions of the clusters with all MD simulations we done. The classical theory underestimates the number density of the clusters in the temperature range of 80-100 K, but overestimates in 100-120 K. The semiphenomenological model also predicts well the nucleation rate in MD simulations, while the classical nucleation theory does not. Our results confirmed the validity of the semiphenomenological model for Lennard-Jones-type molecules.     

Molecular dynamics of homogeneous nucleation in the vapor phase of Lennard-Jones. III. Effect of carrier gas pressure

A molecular dynamics simulation of vapor phase nucleation has been performed with 40,000 Lennard-Jones particles for the target gas and 0-160,000 particles for the carrier gas. Three carrier gas models are adopted, including a soft-core model, a Lennard-Jones model, and a modified Lennard-Jones model in which the attractive interaction can be adjusted. The effect of the carrier-gas pressure is assessed through computing and comparing the rate of nucleation and cluster size distribution. It is found that the effect of the carrier-gas pressure can be strongly dependent on the carrier-gas model. A positive effect (enhancement of the nucleation rate) is found with the soft-core potential model, whereas negligible effect is found with the Lennard-Jones potential model. For the modified Lennard-Jones potential with a weak attractive interaction, the carrier-gas effect is positive. However, the effect is negligible with a stronger attractive interaction between the target and carrier-gas particles. A reason for the negligible effect is that the carrier-gas particles are adsorbed on the cluster surface when the density of target and carrier-gas particles are comparable. When the density of carrier-gas particles are four times that of the target particles, the carrier-gas particles tend to mix with the target particles in the clusters.     

Molecular dynamics simulations of ice nucleation by electric fields

Molecular dynamics simulations are used to investigate heterogeneous ice nucleation in model systems where an electric field acts on water molecules within 10-20 ? of a surface. Two different water models (the six-site and TIP4P/Ice models) are considered, and in both cases, it is shown that a surface field can serve as a very effective ice nucleation catalyst in supercooled water. Ice with a ferroelectric cubic structure nucleates near the surface, and dipole disordered cubic ice grows outward from the surface layer. We examine the influences of temperature and two important field parameters, the field strength and distance from the surface over which it acts, on the ice nucleation process. For the six-site model, the highest temperature where we observe field-induced ice nucleation is 280 K, and for TIP4P/Ice 270 K (note that the estimated normal freezing points of the six-site and TIP4P/Ice models are ～289 and ～270 K, respectively). The minimum electric field strength required to nucleate ice depends a little on how far the field extends from the surface. If it extends 20 ?, then a field strength of 1.5 × 10(9) V/m is effective for both models. If the field extent is 10 ?, then stronger fields are required (2.5 × 10(9) V/m for TIP4P/Ice and 3.5 × 10(9) V/m for the six-site model). Our results demonstrate that fields of realistic strength, that act only over a narrow surface region, can effectively nucleate ice at temperatures not far below the freezing point. This further supports the possibility that local electric fields can be a significant factor influencing heterogeneous ice nucleation in physical situations. We would expect this to be especially relevant for ice nuclei with very rough surfaces where one would expect local fields of varying strength and direction.     

Molecular dynamics simulations of cluster nucleation during inert gas condensation

Molecular dynamics simulations of vapor-phase nucleation of germanium in an argon atmosphere were performed and a unexpected channel of nucleation was observed. This channel, vapor-induced cluster splitting, is important for more refractory materials since the critical nucleus size can fall below the size of a dimer. As opposed to conventional direct vapor nucleation of the dimer, which occurs by three-body collisions, cluster-splitting nucleation is a second-order reaction. The most important cluster-splitting reaction is the collision of a vapor atom and a trimer that leads to the formation of two dimers. The importance of the cluster-splitting nucleation channel relative to the direct vapor nucleation channel is observed to increase with decreasing vapor density and increasing ratio of vapor to carrier gas atoms.     

Molecular dynamics simulations of n-Alkane melts confined between solid surfaces

Molecular dynamics simulations of polyethylene chains (C_nH_2n+2 for n = 13, 16, 28, 60) have been carried out to investigate both equilibrium and dynamic properties of polymer melts confined between flat solid surfaces. We observe an oscillatory monomer density in the direction normal to the solid surfaces, which depends on the size of the monomers (i.e., on the volume density of the system). The packing manner of monomer segments, segment orientation, and local conformations of chains are found to be independent of chain length. In addition, preferential interfacial adsorption of chain ends is observed. The chains are flattened close to the surface and many molecules assume essentially two-dimensional train configurations even in the case of C₆₀H₁₂₂ melts. The apparent self-diffusivities of the centers of mass of the molecules depend on their distance from a surface. Molecules adjacent to a surface exhibit a reduced mobility perpendicular to the surface and an increased one parallel to it. The self-diffusion constant parallel to a surface depends strongly on the size of the monomers. An increase of the united atom diameter by 10% reduces the diffusion constant by a factor of three, in good agreement with the experimental value. © 1994 John Wiley & Sons, Inc.     

Molecular dynamics simulations of liquid crystal molecules on a polyimide monolayer

Preliminary results are presented on the molecular dynamics simulations of alignment of the liquid crystal molecule, 4-n-octyl-4'-cyanobiphenyl (8CB), on a polyimide (pyromelltic dianhydride-p-phenylene diamine) oligomer monolayer. We actually simulated a three-layer system, i.e., liquid crystal molecule/polyimide oligomer/a basal plane of graphite. First, simulations of the oligomers adsorbed on graphite were done in order to obtain reasonable adsorption structures, as the pre-stage simulation of the three-layer system. Then, by placing a liquid crystal layer on top, the three-layer system was simulated. The stable liquid crystal alignment direction on the polyimide monolayer was found roughly to be the polyimide chain direction with zero pretilt in this combination of liquid crystal and polymer materials. The calculated adsorption energy of an 8CB molecule to the polyimide monolayer was 128 kJ mol^-1 and the carbonyl group of the polyimide was the main adsorption site.     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.     

Thermal conductivity of solid argon from molecular dynamics simulations

The thermal conductivity of solid argon in the classical limit has been calculated by equilibrium molecular dynamic simulations using the Green-Kubo formalism and a Lennard-Jones interatomic potential. Contrary to previous theoretical reports, we find that the computed thermal conductivities are in good agreement with experimental data. The computed values are also in agreement with the high-temperature limit of the three-phonon scattering contribution to the thermal conductivity. We find that finite-size effects are negligible and that phonon lifetimes have two characteristic time scales, so that agreement with kinetic theory is obtained only after appropriate averaging of the calculated phonon lifetimes.     

Molecular dynamics simulations of p-tert-butylcalix[4]arene with small guest molecules

Classical molecular dynamics simulations were used to study p-tert-butylcalix[4]arene inclusion compounds with xenon, nitrogen, hydrogen, methane, and sulfur dioxide guest molecules. The calixarene units were taken to be rigid and the intermolecular molecular interactions were modeled as a sum of the van der Waals interactions with parameters from the AMBER force field and electrostatic interactions. Simulations of the high-density alpha phase and low-density beta0 phase of p-tert-butylcalix[4]arene were used to test the force field. The predicted densities of the two phases were found to agree with experimental measurements at 173 K to within 5 %. Simulations were performed with guests placed inside the calixarene cages of the beta0 phase. Guest-host ratios of 1:1 to 1:4 were considered. Changes in the unit-cell volume and density of the phases with the addition of guest molecules and the inclusion energies for the guests were determined. Finally, the dynamics of the guest motion inside the cages were characterized by determining the root-mean-square displacements and velocity autocorrelation functions of the xenon and nitrogen guests.     

Monte Carlo simulations of Lennard-Jones nonionic surfactant adsorption at the liquid/vapor interface

We present Monte Carlo simulations of nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential using differing interaction parameters. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate quantitative thermodynamic adsorption and surface tension isotherms in addition to surfactant radius of gyration, tilt angles, and potentials of mean force. Surface tension simulations compared to those calculated from the simulated adsorbed amounts and the Gibbs adsorption isotherm agree confirming equilibrium in our simulations. We find that the classical Langmuir isotherm is obeyed for our LJ surfactants over the range of head and tail lengths studied. Although simulated surfactant chains in the bulk solution exhibit random orientations, surfactant chains at the interface orient roughly perpendicular and the tails elongate compared to bulk chains even in the submonolayer adsorption regime. At a critical surfactant concentration, designated as the critical aggregation concentration (CAC), we find aggregates in the solution away from the interface. At higher concentrations, simulated surface tensions remain practically constant. Using the simulated potential of mean force in the submonolayer regime and an estimate of the surfactant footprint at the CAC, we predict a priori the Langmuir adsorption constant, KL, and the maximum monolayer adsorption, Gammam. Adsorption is driven not by proclivity of the surfactant for the interface, but by the dislike of the surfactant tails for the solvent, that is by a "solvophobic" effect. Accordingly, we establish that a coarse-grained LJ surfactant system mimics well the expected equilibrium behavior of aqueous nonionic surfactants adsorbing at the air/water interface.     

Molecular dynamics simulations of the Li-ion diffusion in the amorphous solid electrolyte interphase

The solid electrolyte interphase (SEI), a passivation film covering the electrode surface, is crucial to the lifetime and efficiency of the lithium-ion (Li-ion) battery. Understanding the Li-ion diffusion mechanism within possible components in the mosaic-structured SEI is an essential step to improve the Li-ion conductivity and thus the battery performance. Here, we investigate the Li-ion diffusion mechanism within three amorphous SEI components (i.e., the inorganic inner layer, organic outer layer, and their mixture with 1:1 molar ratio) via ab initio molecular dynamic (AIMD) simulations. Our simulations show that the Li-ion diffusion coefficient in the inorganic layer is two orders of magnitude faster than that in the organic layer. Therefore, the inorganic layer makes a major contribution to the Li-ion diffusion. Furthermore, we find that the Li-ion diffusivity in the organic layer decreases slightly with the increase of the carbon chain from the methyl to ethyl owing to the steric hindrance induced by large groups. Overall, our current work unravels the Li-ion diffusion mechanism, and provides an atomic-scale insight for the understanding of the Li-ion transport in the SEI components.     

Molecular dynamics simulations of amphiphilic graft copolymer molecules at a water/air interface

Fully atomistic molecular dynamics simulations of amphiphilic graft copolymer molecules have been performed at a range of surface concentrations at a water/air interface. These simulations are compared to experimental results from a corresponding system over a similar range of surface concentrations. Neutron reflectivity data calculated from the simulation trajectories agrees well with experimentally acquired profiles. In particular, excellent agreement in neutron reflectivity is found for lower surface concentration simulations. A simulation of a poly(ethylene oxide) (PEO) chain in aqueous solution has also been performed. This simulation allows the conformational behavior of the free PEO chain and those tethered to the interface in the previous simulations to be compared.     

Molecular dynamics simulations of halide glasses

Summary Halide glasses have been extensively studied in recent years because of their potential application as infrared transmitting fibre optic materials. They are believed to be more ionic than glasses based on silica and should therefore be more amenable to molecular dynamics simulation using simple two-body potentials. Here the main features of structural models derived using such techniques are described and compared with available structural data. Possible future applications of this approach are outlined.     

Molecular dynamics simulations of peptide-surface interactions

Proteins, which are bioactive molecules, adsorb on implants placed in the body through complex and poorly understood mechanisms and directly influence biocompatibility. Molecular dynamics modeling using empirical force fields provides one of the most direct methods of theoretically analyzing the behavior of complex molecular systems and is well-suited for the simulation of protein adsorption behavior. To accurately simulate protein adsorption behavior, a force field must correctly represent the thermodynamic driving forces that govern peptide residue-surface interactions. However, since existing force fields were developed without specific consideration of protein-surface interactions, they may not accurately represent this type of molecular behavior. To address this concern, we developed a host-guest peptide adsorption model in the form of a G(4)-X-G(4) peptide (G is glycine, X is a variable residue) to enable determination of the contributions to adsorption free energy of different X residues when adsorbed to functionalized Au-alkanethiol self-assembled monolayers (SAMs). We have previously reported experimental results using surface plasmon resonance (SPR) spectroscopy to measure the free energy of peptide adsorption for this peptide model with X = G and K (lysine) on OH and COOH functionalized SAMs. The objectives of the present research were the development and assessment of methods to calculate adsorption free energy using molecular dynamics simulations with the GROMACS force field for these same peptide adsorption systems, with an oligoethylene oxide (OEG) functionalized SAM surface also being considered. By comparing simulation results to the experimental results, the accuracy of the selected force field to represent the behavior of these molecular systems can be evaluated. From our simulations, the G(4)-G-G(4) and G(4)-K-G(4) peptides showed minimal to no adsorption to the OH SAM surfaces and the G(4)-K-G(4) showed strong adsorption to the COOH SAM surface, which is in agreement with our SPR experiments. Contrary to our experimental results, however, the simulations predicted a relatively strong adsorption of G(4)-G-G(4) peptide to the COOH SAM surface. In addition, both peptides were unexpectedly predicted to adsorb to the OEG surface. These findings demonstrate the need for GROMACS force field parameters to be rebalanced for the simulation of peptide adsorption behavior on SAM surfaces. The developed methods provide a direct means of assessing, modifying, and validating force field performance for the simulation of peptide and protein adsorption to surfaces, without which little confidence can be placed in the simulation results that are generated with these types of systems.     

Molecular dynamics simulations of proteins and peptides: from folding to drug design

Computer simulations of proteins, lipids and nucleic acids at equilibrium have become essentially routine. However, the fact remains that complete sampling of conformational space continues to be a bottle-neck in the field. The challenge for the future is to overcome such problems and use computational approaches to understand recognition and spontaneous self-organization in biomolecular systems (folding, aggregation and assembly of complexes), processes that cannot be directly observed experimentally. In this review, examples illustrating the extent to which simulations can be used to understand these phenomena in biomolecular systems will be presented along with examples of methodological developments to increase our physical understanding of the processes. The study cases will cover the problems of peptide-receptor recognition and the use of the information obtained for the design of new non-peptidic ligands; the study of the folding mechanism of small proteins and finally the study of the initial stages of peptide self-aggregation.     

Molecular dynamics simulations of lipid bilayers

Computer simulation methods are becoming increasingly widespread as tools for studying the structure and dynamics of lipid bilayer membranes. The length scale and time scale accessible to atomic-level molecular dynamics simulations are rapidly increasing, providing insight into the relatively slow motions of molecular reorientation and translation and demonstrating that effects due to the finite size of the simulation cell can influence simulation results. Additionally, significant advances have been made in the complexity of membrane systems studied, including bilayers with cholesterol, small solute molecules, and lipid-protein and lipid-DNA complexes. Especially promising is the progress that continues to be made in the comparison of simulation results with experiment, both to validate the simulation algorithms and to aid in the interpretation of existing experimental data.     

Molecular dynamics simulations of biotin carboxylase

Biotin carboxylase catalyzes the ATP-dependent carboxylation of biotin and is one component of the multienzyme complex acetyl-CoA carboxylase that catalyzes the first committed step in fatty acid synthesis in all organisms. Biotin carboxylase from Escherichia coli, whose crystal structures with and without ATP bound have been determined, has served as a model system for this component of the acetyl-CoA carboxylase complex. The two crystal structures revealed a large conformational change of one domain relative to the other domains when ATP is bound. Unfortunately, the crystal structure with ATP bound was obtained with an inactive site-directed mutant of the enzyme. As a consequence the structure with ATP bound lacked key structural information such as for the Mg2+ ions and contained altered conformations of key active-site residues. Therefore, nanosecond molecular dynamics studies of the wild-type biotin carboxylase were undertaken to supplant and amend the results of the crystal structures. Specifically, the protein-metal interactions of the two catalytically critical Mg2+ ions bound in the active site are presented along with a reevaluation of the conformations of active-site residues bound to ATP. In addition, the regions of the polypeptide chain that serve as hinges for the large conformational change were identified. The results of the hinge analysis complemented a covariance analysis that identified the individual structural elements of biotin carboxylase that change their conformation in response to ATP binding.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

Molecular dynamics simulations of cardiolipin bilayers

Cardiolipin is a key lipid component in the inner mitochondrial membrane, where the lipid is involved in energy production, cristae structure, and mechanisms in the apoptotic pathway. In this article we used molecular dynamics computer simulations to investigate cardiolipin and its effect on the structure of lipid bilayers. Three cardiolipin/POPC bilayers with different lipid compositions were simulated: 100, 9.2, and 0% cardiolipin. We found strong association of sodium counterions to the carbonyl groups of both lipid types, leaving in the case of 9.2% cardiolipin virtually no ions in the aqueous compartment. Although binding occurred primarily at the carbonyl position, there was a preference to bind to the carbonyl groups of cardiolipin. Ion binding and the small headgroup of cardiolipin gave a strong ordering of the hydrocarbon chains. We found significant effects in the water dipole orientation and water dipole potential which can compensate for the electrostatic repulsion that otherwise should force charged lipids apart. Several parameters relevant for the molecular structure of cardiolipin were calculated and compared with results from analyses of coarse-grained simulations and available X-ray structural data.