Phase Coexistence Curves for Off-lattice Polymer-Solvent Mixtures: Gibbs-Duhem Integration Simulations

The Gibbs-Duhem integration scheme is combined with the osmotic Gibbs-ensemble simulation method presented in previous work [Brennan, J.K. and Madden, W.G. "Phase coexistence curves for off-lattice polymer-solvent mixtures: Gibbs-ensemble simulations." Macromolecules , 2002, 35, 2827.] to calculate the phase coexistence of a polymer-solvent mixture. Gibbs-Duhem integration simulations are carried out at temperatures for which the osmotic Gibbs-ensemble method is not valid because the solvent-rich phase contains a significant amount of polymer. This combined strategy allows for the calculation of the full coexistence curve for polymer-solvent systems in the continuum. An alternative formulation of the Gibbs-Duhem integration algorithm is also presented. A major strength of the technique is that neither chain insertions nor deletions are required. The method allows for the calculation of the phase behavior of polymer-solvent mixtures containing long chains or branched and networked chains not previously possible.     

Chemical Potential,Partial Enthalpy and Partial Volume of Mixtures by NPT Molecular Dynamics

Abstract

Equilibrium NPT molecular dynamics computer simulations have been used to determine the chemical potential, partial enthalpy and partial volume of model Ar-Kr mixtures using newly devised non-intrusive particle insertion and particle swap techniques [P. Sindzingre et al. Chemical Physics, 129 (1989) 213]. In this report we examine, for the first time, in some detail the relative convergence statistics of the particle swap and particle insertion methods for these properties for binary Lennard-Jones (LJ) mixtures. Both species are represented by single-site Lennard-Jones pair potentials with Lorentz-Berthelot rules for the cross-species interactions. We show that, over the whole phase diagram and especially in the vicinity of the fluid-solid coexistence line, the particle swap method gives significantly better statistics than the particle insertion method for the difference in chemical potential of the two species, partial enthalpy and partial volume of each species. Also, we find that, using the particle swap method, the difference in the chemical potential converges more rapidly than the differences in the partial enthalpy and volume.     

Molecular Dynamics Simulations With First Order Coupling to a Bath of Constant Chemical Potential

Abstract

In molecular dynamics simulations the temperature or pressure can be controlled by applying a weak first-order coupling to a bath of constant temperature or pressure. This weak coupling technique to control system properties using a first-order relaxation equation is analyzed from a statistical mechanics point of view. It is shown, how the weak coupling scheme can be generalized and applied to a bath of contstant chemical potential. The presented method, to which in the following will be referred to as chemical potential weak coupling, is applied and tested on a Lennard-Jones fluid. The thermodynamic quantities known from the literature are accuratly reproduced.

The temperature and chemical potential weak coupling methods aim to sample the canonical and grand canonical ensembles respectively. By analyzing the fluctuations in energy and number of particles, the tight relation between the ensembles and the distributions obtained from the weak coupling simulations is demonstrated. The influence of the choice of the coupling parameters on the quality of the approximation of the ensemble distribution is discussed.     

Molecular Dynamics Simulation of Structural Phase Transition of AlPO4 Induced by Pressure

Abstract

The mechanism of pressure-induced phase transition of AlPO₄ has been investigated by means of a molecular dynamics method of constant temperature and pressure. A new crystalline phase with space group C2, which has not yet been experimentally found, appears by an instantaneous compression of 60, 70 and 80 GPa at 300 K. At high temperature (2500 K) and pressure (58 GPa), another new phase of AlPo₄ (y-phase), which is composed of PO₆ and AlO₆ octahedra, has been observed.     

Classical cumulant dynamics for statistical chemical physics

Abstract

We developed classical cumulant dynamics for statistical mechanics in order to evaluate thermal equilibrium properties of a given system. The equations of motion (EOMs) for momentum and position were formulated together with those for second-order cumulant variables, which are functions of second-order moments. From the Kramers equation, and simplified EOMs were obtained by assuming a stationary state limit. The present method combined with the umbrella integration method was applied to evaluate free energy surface of a seven-particle Morse cluster. With low computational costs, the present approach gave almost equivalent free energy barrier those by conventional classical molecular dynamics.     

Fluctuation Simulations and the Calculation of Mechanical Partial Molar Properties

Abstract

A method for the direct calculation of partial molar volumes, energies, and enthalpies in multicomponent mixtures in which all species have finite concentrations is presented. The approach, which is based on fluctuation theory, allows the simultaneous determination of the properties of all components in the mixture. The advantages and limitations of the method are illustrated through the (N, U, V) molecular dynamics calculation of the mechanical partial molar properties of two binary Lennard-Jones mixtures.     

Gibbs-Ensemble Molecular Dynamics: Liquid-Gas Equilibria for Lennard-Jones Spheres and n-Hexane

Abstract

We present a novel method to simulate phase equilibria in atomic and molecular systems. The method is a Molecular Dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles (or molecules) in a thermodynamically consistent fashion. Here we pres the derivation of the generalized equations of motion and discuss the relation of the resulting trajectory averages to the relevant ensemble. We test this Gibbs-Ensemble Molecular Dynamics algorithm by applying it to an atomic and a molecular system, i.e. to the liquid-gas coexistence in a Lennard-Jones fluid and in n-hexane. In both cases our results are in good accord with previous mean field and Gibbs-Ensemble Monte Carlo results as well as with the experimental data in the case of hexane. We also show that our Gibbs-Ensemble Molecular Dynamics algorithm like other Molecular Dynamics techniques can be used to study the dynamics of the system. Self-diffusion coefficients calculated with this method are in agreement with the result of conventional constant temperature Molecular Dynamics.     

Structural Transformations of Ice at High Pressures Via Molecular Dynamics Simulations

Abstract

A simple classical model is used for the study of the structural transformations of ice under high pressures, such as ice VIII to VII and X, via classical molecular dynamics (MD) simulation. In the present MD simulation, pair potentials of a simple form between pair of atoms and a thee-body potential representing the H-O-H angle dependence, originally developed by Kawamura et al., were used. Starting with a stable ice VIII at low pressure and low temperature, we have carried out two different MD runs, one with increasing pressure keeping the temperature constant (simulation I) and the other with increasing temperature under constant pressure (simulation II). From these MD simulations we have obtained the structural transformations from ice VIII to VII for both simulations; the former was finally transformed into ice X for the simulation I. The present results are compatible with recent experiments on high pressure ices.     

Assessment of Root System Dynamics of Species Grown in Mixtures under Field Conditions using Herbicide Injection and 15N Natural Abundance Methods: A Case Study with Pea, Barley and Mustard

Two methods were developed and used to study the root system dynamics of two species grown together or separately under field conditions. The first method, based on herbicide injection at different soil depths, was used to determine the rooting depth penetration rate of each species in pea–barley and pea–mustard mixtures. The roots absorbed the herbicide when they reached the treated zone leading to visible symptoms on the leaves which could be readily monitored. The second method used differences in ¹⁵N natural abundance and N concentration between legume and non-legume species to quantify the contribution of each species to root biomass of a pea–barley mixture. Each contribution was calculated using ¹⁵N abundance and N concentration of root mixtures and of subsamples of roots of individual species within mixtures. Both methods can indeed be used to distinguish roots of species in mixtures and thus to study belowground competition between associated species. The use of these methods demonstrated species differences in root system dynamics between species but also significant effects of interactions between species in mixtures. The rooting depth penetration rate was mainly species specific whereas root biomass was dependant on plant growth, allocation of dry matter between shoot and root components and growth factors such as N fertilization. Root biomass of each species may vary therefore with the level of competition between species.     

Isobaric and Isothermal Molecular Dynamics Simulations of Diatomic Systems

Abstract

Isobaric molecular dynamics simulations were carried out for diatomic systems using different algorithms available in the literature. Two-centered Lennard-Jones potentials with and without quadrupolar interactions were used. Thermodynamic properties obtained from the isobaric algorithms compared very well with those of an equivalent simulation in the microcanonical ensemble; however, some differences were observed when similar comparisons were carried out for dynamic properties. More specifically, the constant pressure constraint affects the translational dynamics of the system because of the non-negligible differences between the momenta and the instantaneous velocities of the molecules.

Furthermore, the following studies were carried out using isobaric MD simulations: 1. Low temperature spontaneous FCC-orthorhombic (and vice versa) transition of a diatomic system with quadrupolar interactions as a function of the molecular bond length. 2. Effect of quadrupolar interaction on isobaric melting of a model diatomic system. 3. Effect of pressure on melting properties of a model diatomic system with quadrupolar interactions.     

Hydration pressure and phase transitions of phospholipids: I. Piezotropic approach

Dehydration reduces the main phase transition pressure of phospholipids. An analysis based on the Gibbs-Duhem equation shows how the shift of the transition pressure is correlated to the hydration pressure.By using Fourier transform infrared (FT-IR) spectroscopy we determined the hydration-dependent phase transition pressure. The application of our new approach gives hydration pressure values which agree with the values obtained with the osmotic stress method.     

Self-aggregation of trehalose in the mixed solvents of 1,3-dimethylimidazolium ionic liquid and water

Abstract

Conformational variations of solvated trehaloses in binary mixtures of 1,3-dialkylimidazolium ([dmim]Cl) ionic liquids and trehalose as well as ternary mixtures of trehalose, [dmim]Cl and water have been studied by molecular dynamics (MD) simulations with and without polarisable force fields. The interaction energy between anion Cl^? and water is stronger than that between water itself in the [dmim]Cl-water mixtures. Isolated water clusters were found in the binary [dmim]Cl-water mixtures with 60.0 and 75.0% mole fraction of water, but a continuous water network appears when the concentration of the mixture increases to 99.9%. In the case of binary mixtures of trehalose and [dmim]Cl, both non-polarisable and polarisable models demonstrated that the pyranose rings of trehalose displayed chair conformations. MD simulations with polarisation model could sample larger conformation space than that with non-polarisable model. A self-aggregation behaviour of trehalose was found in the ternary trehalose-[dmim]Cl-water mixtures, which can be rationalised by the stronger non-bonded interaction energy between trehalose molecules and anion Cl^? than that between trehalose molecules and water.     

Convergence patterns and multiple species interactions in a designed plant mixture of five species

It is known that convergence and divergence can occur in complex plant communities, but the relative importance of biotic and abiotic factors driving these processes is less clear. We addressed this issue in an experiment using a range of mixed stands of five species that are common in Swiss fens (Carex elata, C. flava, Lycopus europaeus, Lysimachia vulgaris and Mentha aquatica) and two levels of water and nutrients. One hundred and seventy-six experimental mixtures were maintained in large pots (75 l) for two consecutive growing seasons in an experimental garden. The stands varied systematically in the initial relative abundance of each of the five species and in overall initial stand abundance. The changes in biomass over 2 years were modelled as linear functions of treatments and the initial biomass of each species. The dynamics of the system were mainly driven by differences in the identity of species and by a negative feedback mechanism but also by different abiotic conditions. In all mixtures, C. elata became more dominant over time, which caused an overall convergence of community composition. In addition, the rate of change of each species’ biomass was negatively related to its own initial abundance. Thus, a negative feedback further contributed to the convergence of communities. Species responded differently to water level and nutrient supply, causing community dynamics to differ among treatments. However, the different abiotic conditions only slightly modified the overall convergence pattern. Competitive interactions between more than two species were weaker than the negative feedback but still significantly influenced the species’ final relative abundance. The negative feedback suggests that there is niche partitioning between the species, which permits their coexistence. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Hydration pressure and phase transitions of phospholipids. I. Piezotropic approach

Dehydration reduces the main phase transition pressure of phospholipids. An analysis based on the Gibbs-Duhem equation shows how the shift of the transition pressure is correlated to the hydration pressure. By using Fourier transform infrared (FT-IR) spectroscopy we determined the hydration-dependent phase transition pressure. The application of our new approach gives hydration pressure values which agree with the values obtained with the osmotic stress method.     

Temperature fluctuation facilitates coexistence of competing species in experimental microbial communities

1. Temperature fluctuation is a general phenomenon affecting many, if not all, species in nature. While a few studies have shown that temperature fluctuation can promote species coexistence, little is known about the effects of different regimes of temperature fluctuation on coexistence. 2. We experimentally investigated how temperature fluctuation and different regimes of temperature fluctuation ('red' environments in which temperature series exhibited positive temporal autocorrelation vs. 'white' environments in which temperature series showed little autocorrelation) affected the coexistence of two ciliated protists, Colpidium striatum Stein and Paramecium tetraurelia Sonneborn, which competed for bacterial resources. 3. We have previously shown that the two species differed in their growth responses to changes in temperature and in their resource utilization patterns. The two species were not always able to coexist at constant temperatures (22, 24, 26, 28 and 30 degrees C), with Paramecium being competitively excluded at 26 and 28 degrees C. This indicated that resource partitioning was insufficient to maintain coexistence at these temperatures. 4. Here we show that in both red and white environments in which temperature varied between 22 and 32 degrees C, Paramecium coexisted with Colpidium. Consistent with the differential effects of temperature on their intrinsic growth rates, Paramecium population dynamics were largely unaffected by temperature regimes, and Colpidium showed more variable population dynamics in the red environments. 5. Temperature-dependent competitive effects of Colpidium on Paramecium, together with resource partitioning, appeared to be responsible for the coexistence in the white environments; resource partitioning and the storage effect appeared to account for the coexistence in the red environments. 6. These results suggest that temperature fluctuation may play important roles in regulating species coexistence and diversity in ecological communities.     

Monte Carlo Simulation Study of Adsorption Characteristics in Slit-Like Micropores Under Supercritical Conditions

Abstract

Adsorption characteristics of a solute diluted in supercritical fluids has been investigated by using the Monte Carlo simulation techniques. The Lennard-Jones potential function is used for describing interactions for a model system of CO₂ + benzene in slit-like micropores with infinite graphitic carbon walls. A modified μVT ensemble method with particle exchange proposed by Cracknell, Nicholson and Quirke (1993) is found to be much superior to the conventional μVT ensemble method especially for dense mixtures in a pore. Adsorption isotherms of CO₂ and benzene, in equilibrium with a dilute benzene mixture in CO₂ (mole fraction of benzene = 0.001), are computed by varying pressure, temperature, the benzene–surface interaction potential, and the slitwidth. Adsorption isotherm curve of CO₂ increases with an increase in pressure while that of benzene shows a maximum at a pressure far below the critical pressure of CO₂ and then it decreases with increasing pressure. The decrease in benzene adsorption with increasing pressure is attributable to both the enhanced solubility in supercritical CO₂ and the competitive adsorption of CO₂. The isotherm curves of each component at two temperatures, 313.2 K and 323.2 K, show to cross at a pressure near the critical pressure due to the “density effect” on the chemical potentials of a solute at supercritical fluid conditions. When the interaction between a solute and a surface increases, the adsorption isotherm increases. Narrowing the slitwidth results in the increase in the adsorption of solute since the external potential from two walls becomes deeper.     

System Relaxation and Thermodynamic Integration

Abstract

The thermodynamic integration (TI) method for calculating free energy differences has three inherent problems: statistics, numerical integration, and relaxation. In this paper the latter is analyzed for the nonequilibrium TI method introduced by Postma which combines molecular dynamics simulation and TI in a very effective way. A nontrivial extrapolation technique is presented to remove the relaxation error and to calculate the underlying relaxation time. It is shown that the optimal choice of grid points, derived in a previous paper, for minimizing statistical errors not only removes integration errors, but also minimizes relaxation errors. The methods are applied in a calculation of the free energy of cavity formation in water.     

Differential scanning calorimetry and 2H NMR studies of the phase behavior of gramicidin-phosphatidylcholine mixtures

The extents of two-phase coexistence in the phase diagrams of mixtures of gramicidin with 1,2-bis(perdeuteriopalmitoyl)-sn-glycero-3-phosphocholine (DPPC-d62) and with 1,2-bis(perdeuteriomyristoyl)-sn-glycero-3-phosphocholine (DMPC-d54) mixtures have been explored with differential scanning calorimetry (DSC) and deuterium nuclear magnetic resonance (2H NMR). For both systems, increased gramicidin content causes a decrease in transition enthalpy and a broadening of the peak in excess heat capacity at the transition. In DMPC-d54-based mixtures, the broadening is roughly symmetric about the pure lipid transition temperature. Addition of gramicidin to DPPC-d62 extends the excess heat capacity peak on the low-temperature side, resulting in a slightly asymmetric scan. Deuterium NMR spectra showing a superposition of gel and liquid-crystalline components, observed for both mixtures, indicate the presence of two-phase coexistence. For the DPPC-d62-based mixtures, two-phase coexistence is restricted to an approximately 2 degrees C temperature range below the pure transition temperature. For DMPC-d54-based mixtures, the region of two-phase coexistence is even narrower. For both mixtures, beyond a gramicidin mole fraction of 2%, distinct gel and liquid-crystal contributions to the spectra cannot be distinguished. Along with the broad featureless nature of the DSC scan in this region, this is taken to indicate that the transition has been replaced by a continuous phase change. These results are consistent with the existence of a closed two-phase region having a critical concentration of gramicidin below 2 mol%.     

Eutectic formation analysis of amino acid mixtures using molecular dynamics simulations

The mechanism of eutectic formation was investigated via computer-aided molecular dynamics techniques based on experimental results. The CBZ group mixtures CBZ-l-Asp/d-AlaNH2 x HCl/methanol, CBZ-l-Asp/l-PheOMe x HCl/methanol, and CBZ-l-Tyr/l-ArgNH2 x 2HCl/methanol formed transparent eutectic melts. The non-CBZ group mixtures l-Asp/d-AlaNH2 x HCl/methanol, l-Asp/l-PheOMe x HCl/methanol, and l-Tyr/l-ArgNH2 x 2HCl/methanol did not form eutectic melts. According to molecular dynamics simulation results, increase in the kinetic energy values of eutectic forming mixtures was much larger than the increase in potential energy over a temperature shift from 298 to 333 K. However, the results for non-eutectic forming mixtures were reversed. The Coulomb interaction energies of eutectic forming mixtures significantly decreased, because eutectic melting can increase the mobility of molecules in the mixtures. The enhancement of molecular mobility was confirmed by increased self-diffusion constant values, and the change of solid-to-liquid phase was detected by radial distribution function results. The periodic boundary conditions for calculation of molecular dynamics were found to be reliable.     

Determination of the molecular weight of proteins in heterogeneous mixtures: use of an air-driven ultracentrifuge for the analysis of protein--protein interactions.

A high-speed air-driven ultracentrifuge (Airfuge) has been used to study the molecular weights of proteins in heterogeneous mixtures. The method is based on previous studies (M. A. Bothwell, G. J. Howlett, and H. K. Schachman, 1978, J. Biol. Chem., 253, 2073–2077) which showed that at sedimentation equilibrium in the Airfuge the fraction of a protein remaining in an upper fraction of the Airfuge tube is almost linearly related to the exponential of the reduced molecular weight of the protein. In this study the total fraction of each particular protein remaining in an upper fraction of the Airfuge tube is determined by quantitative sodium dodecyl sulfate-gel electrophoresis. This procedure allows a wide range of proteins to be analyzed in a single Airfuge experiment. The method yields the “native” molecular weights of the protein components and is independent of the shape of the macromolecules being studied. Interactions occurring between the components in solution can be detected from the Airfuge data, and procedures are described which allow the experimental data for such interactions to be analyzed in terms of an equilibrium constant for the interaction. Results obtained for the electrostatic interaction at neutral pH between lysozyme and ovalbumin (K = 1.1 × 10⁵, m^?1) and lysozyme and bovine serum albumin (K = 1.0 × 10⁵, m^?1) agree well with literature values.