A new non-cubic equation of state

A new non-cubic equation of state is presented in this work. This expression is obtained from the original Redlich—Kwong equation of state by assuming that the attraction parameter depends not only on temperature, but also on density. Vapour—liquid equilibria in the coexistence region and PVT properties for the liquid, gas and supercritical fluid phases are accurately calculated with four parameters per isotherm. The generalization of this equation by a corresponding states correlation enables it to be applied over wide ranges of temperature, pressure and hydrocarbon molecular weight.     

Thermodynamics of the liquid states of Langmuir monolayers

The liquid states and the liquid-liquid equilibrium of surfactant molecules forming an interphase between air and water have been considered using Monte Carlo computer simulations. Specifically, the expanded and compressed liquid phases observed for surfactant molecules were characterized as a function of pressure and temperature. Simple modified beadlike potentials were implemented in order to describe the interparticle forces between the hydrophobic and hydrophilic portions of surfactant molecules at the air/water interface. A simulation box was defined such that the monolayer was exposed to an externally applied lateral pressure in a modified isothermal-isobaric ensemble, whereas the water bath was modeled in a canonical ensemble. The simulation resembles the experimental setup used to measure lateral pressure (Pi) versus area isotherms obtained with Langmuir troughs. The applied lateral pressure-surface area phase diagram clearly showed the coexistence of the expanded and compressed liquid phases within certain temperature and pressure ranges. Distribution functions of distances and enthalpies for the monolayer were computed to clearly identify each liquid phase and the coexistence region.     

Self-organization of a wedge-shaped surfactant in monolayers and multilayers

The self-organization behavior of a wedge-shaped surfactant, disodium-3,4,5-tris(dodecyloxy)phenylmethylphosphonate, was studied in Langmuir monolayers (at the air-water interface), Langmuir-Blodgett (LB) monolayers and multilayers, and films adsorbed spontaneously from isooctane solution onto a mica substrate (self-assembled films). This compound forms an inverted hexagonal lyotropic liquid crystal phase in the bulk and in thick adsorbed films. Surface pressure isotherm and Brewster angle microscope (BAM) studies of Langmuir monolayers revealed three phases: gas (G), liquid expanded (LE), and liquid condensed (LC). The surface pressure-temperature phase diagram was determined in detail; a triple point was found at approximately 10 degrees C. Atomic force microscope (AFM) images of LB monolayers transferred from various regions of the phase diagram were consistent with the BAM images and indicated that the LE regions are approximately 0.5 nm thinner than the LC regions. AFM images were also obtained of self-assembled films after various adsorption times. For short adsorption times, when monolayer self-assembly was incomplete, the film topography indicated the coexistence of two distinct monolayer phases. The height difference between these two phases was again 0.5 nm, suggesting a correspondence with the LE/LC coexistence observed in the Langmuir monolayers. For longer immersion times, adsorbed multilayers assembled into highly organized periodic arrays of inverse cylindrical micelles. Similar periodic structures, with the same repeat distance of 4.5 nm, were also observed in three-layer LB films. However, the regions of organized periodic structure were much smaller and more poorly correlated in the LB multilayers than in the films adsorbed from solution. Collectively, these observations indicate a high degree of similarity between the molecular organization in Langmuir layers/LB films and adsorbed self-assembled films. In both cases, monolayers progress through an LE phase, into LE/LC coexistence, and finally into LC phase as surface density increases. Following the deposition of an additional bilayer, the film reorganizes to form an array of inverted cylindrical micelles.     

Ab initio calculations of the melting temperatures of refractory bcc metals

We present ab initio calculations of the melting temperatures for bcc metals Nb, Ta and W. The calculations combine phase coexistence molecular dynamics (MD) simulations using classical embedded-atom method potentials and ab initio density functional theory free energy corrections. The calculated melting temperatures for Nb, Ta and W are, respectively, within 3%, 4%, and 7% of the experimental values. We compare the melting temperatures to those obtained from direct ab initio molecular dynamics simulations and see if they are in excellent agreement with each other. The small remaining discrepancies with experiment are thus likely due to inherent limitations associated with exchange-correlation energy approximations within density-functional theory.     

Global phase diagram for the honeycomb potential

We calculate the global phase diagram using classical statistical mechanics for an isotropic pair potential that has been previously [Rechtsman et al., Phys. Rev. Lett. 95, 228301 (2005)] shown to produce the low-coordinated two-dimensional honeycomb crystal as the ground-state structure. Low-coordinated crystals are of practical interest because they have desirable photonic band-gap properties. The phase diagram is obtained from Helmholtz free energies calculated using thermodynamic integration and Monte Carlo simulations. Our results show that the honeycomb crystal remains stable in the global phase diagram even after temperature effects are taken fully into account. Other stable phases in the phase diagram are high and low density triangular phases and a fluid phase. We find no evidence of gas-liquid or liquid-liquid phase coexistence.     

Films of novel mesogenic molecules at air-water and air-solid interfaces

Discotic molecules are known to form highly anisotropic structures at the air-water (A-W) interface. We have studied two novel ionic discotic mesogenic molecules, viz., pyridinium tethered with hexaalkoxytriphenylene with bromide counterion (Py-Tp) and imidazolium tethered with hexaalkoxytriphenylene with bromide counterion (Im-Tp) at A-W and air-solid interfaces. The monolayer phases were investigated at the A-W interface employing surface manometry and Brewster angle microscopy techniques. They indicate a uniform monolayer phase which shows negligible hysteresis on expanding and compressing. Also, in both the systems the collapsed state completely reverts to the monolayer state. These monolayer films transferred at different surface pressures by Langmuir-Blodgett technique were studied by employing atomic force microscopy. The topographies of these films transferred at the low and high surface pressure region of the isotherm indicate a transformation of the monolayer from face-on to edge-on structure.     

Dynamic in situ characterization of organic monolayer formation via a Novel substrate-mediated mechanism

Ultrahigh vacuum scanning tunneling microscopy data investigating octylsilane (C8H17SiH3) monolayer pattern formation on Au(111) are presented. The irregular monolayer pattern exhibits a 60 A length scale. Formation of the octylsilane monolayer relaxes the Au(111) 23 x square root3 surface reconstruction and ejects surface Au atoms. Au adatom diffusion epitaxially extends the Au(111) crystal lattice via step edge growth and island formation. The chemisorbed monolayer covers the entire Au surface at saturation exposure. Theoretical and experimental data suggest the presence of two octylsilane molecular adsorption phases: an atop site yielding a pentacoordinate Si atom and a surface vacancy site yielding a tetracoordinate Si atom. Theoretical simulations investigating two-phase monolayer self-assembly dynamics on a solid surface suggest pattern formation results from strain-induced spinodal decomposition of the two adsorption phases. Collectively, the theoretical and experimental data indicate octylsilane monolayer pattern formation is a result of interfacial Au-Si interactions and the alkyl chains play a negligible role in the monolayer pattern formation mechanism.     

Phase transition in an adsorption layer of a soluble surfactant at the air-water interface

In this paper we provide experimental evidence for a phase transition between a liquid- and gas-like phase occurring in an adsorption layer of a soluble surfactant at the air-water interface. The equilibrium surface tension sigma(e) versus bulk concentration sigma(e) (c) isotherm of surface chemically pure sodium 2-[4-(4-trifluoromethyl-phenylazo) phenoxy]-ethane sulfonate was measured at a temperature of 295 K up to the solubility limit of the amphiphile. The sigma(e) (c) isotherm could be fitted by Frumkin's equation of state. The lateral interaction energy is just above the limit for which Frumkin's model predicts a phase transition. The corresponding surface pressure pi versus surface area A isotherm possesses striking similarities to first-order phase transitions in the Langmuir monolayer. The fact that the difference in the two-dimensional density is only a factor of 2 indicates that the system is very close to the critical point. The surface phases were further characterized by surface second harmonic generation. The major structural difference between the two surface phases is the amphiphile's molecular orientation. A mean orientation of the amphiphile of about 80 degrees was found in the gas analogous phase, whereas a molecular tilt of 38 degrees has been identified in the liquid-like phase.     

Sulfur hexafluoride's liquid-vapor coexistence curve, interfacial properties, and diffusion coefficients as predicted by a simple rigid model

We present here molecular-dynamics simulation results of the vapor-liquid coexistence curve, surface tension, and self-diffusion coefficients of sulfur hexafluoride. Sulfur hexafluoride is modeled as a rigid molecule, following the model proposed by Pawley [Mol. Phys. 43, 1321 (1981)]. Vapor-liquid coexistence curve and surface tension are obtained through direct molecular-dynamic simulations in the NVT ensemble. Simulation results are able to reproduce the qualitative shape of the vapor-liquid envelope. However, lower densities, a higher critical temperature, and an overestimated surface tension are obtained here. Those deviations are explained on the basis of the rigidity of the molecular model used. Self-diffusion coefficients are calculated from simulations in the NVE ensemble for different gas states at atmospheric pressure. The rigid model performs better for dynamical properties since simulation results provide very good agreement with available experimental data in this case.     

Performance of a rigid rod statistical mechanical treatment to predict monolayer ordering: a study of chain interactions and comparison with molecular dynamics simulation

A statistical mechanical model that treats hydrocarbon self-assembled monolayer (SAM) chains as rigid rods is examined to interrogate the mechanisms involved in monolayer ordering. The statistical mechanical predictions are compared to fully atomistic molecular dynamics simulations of SAMs with different packing densities. The monolayer chain order is examined as a function of surface coverage, chain-surface interactions, and chain–chain interactions. Reasonable interaction potentials are deduced from ab initio electronic structure calculations of small model systems. It is found that the chain-surface interaction is the most important parameter in formation of flat-lying monolayer phases, while formation of standing phase monolayers is driven most importantly by increased density of molecules at the surface. A brief discussion of the utility and validity of the rigid rod treatment is given in light of the molecular dynamics results.     

Phase equilibria in model surfactants forming Langmuir monolayers

The study of Langmuir monolayers has generated the attention of researchers because of their unique properties and their not well understood phase equilibrium. These monolayers exhibit interesting phase diagrams where the unusual liquid-liquid equilibrium can be observed for a single component monolayer. Monte Carlo computer simulations in the virtual Gibbs ensemble were used to obtain the phase diagram of Langmuir monolayers. The liquid-vapor and liquid-liquid phase equilibria were considered by constructing the Cailletet-Mathias phase diagrams. By using the Ising model and the rectilinear approximations the identification of the critical properties for both equilibria was determined. These critical parameters were calculated as a function of the strength of the interaction between the surfactant molecules and the aqueous subphase. As a result, we have identified the coexistence between a liquid expanded state (LES)-vapor and the liquid condensed state-LES, in agreement with experimental and theoretical evidence in the literature. We obtained a clear separation of phases and a strong dependence on the strength of the solvent used. Namely, as the interaction between the solvent and the head of the surfactant increases, the critical properties also increase. Equilibrium states were characterized by computing thermodynamic quantities as a function of temperature and solvent strength.     

Sum-frequency spectroscopic study of Langmuir monolayers of lipids having oppositely charged headgroups

Sum-frequency vibrational spectroscopy, with the help of surface pressure-area (π-A) isotherm, was used to study lipid Langmuir monolayers composed of molecules with positively and negatively charged headgroups as well as a 1:1 neutral mixture of the two. The spectral profiles of the CH(x) stretch vibrations are similar for all monolayers in the liquid-condensed (LC) phase. They suggest a monolayer structure of closely packed alkyl chains that are nearly all-trans and well oriented along the surface normal. In the liquid-expanded (LE) phase, the spectra of all monolayers appear characteristic of loosely packed chains with significant gauche defects. The OH stretch spectra of interfacial water for both positively and negatively charged monolayers are significantly enhanced in comparison with a neutral water interface, but the phase measurement of SFVS indicates that OH in the two cases points toward the bulk and the interface, respectively. The enhancement results mainly from surface-field-induced polar ordering of interfacial water molecules. For a charge-neutral monolayer composed of an equal number of positively and negatively charged lipid molecules, no such enhancement is observed. This mixed monolayer exhibits a wide range of LC/LE coexistence region extended to very low surface pressure and its CH(x) spectral profile in the coexistence region resembles that of the LC phase. This result suggests that in the LC/LE coexistence region, the mixed monolayer consists of coexisting LC and LE patches in which oppositely charged lipid molecules are homogeneously mixed and dispersed.     

Thermodynamic and structural characterization of amphiphilic melamine-type monolayers

Monolayers of amphiphilic melamine derivatives are good candidates for the formation of supramolecular structures by hydrogen-bonding of nonsurface active species dissolved in the aqueous subphase by molecular recognition. In the present work, the thermodynamic and structural properties of the Langmuir monolayers of a homologous series of a selected amphiphilic melamine-type are characterized. Good candidates for such studies are the decyl, undecyl, and dodecyl homologues of the 2,4-di(n-alkylamino)-6-amino-1,3,5-triazine (2CnH(2n+1)-melamine) monolayers because of their two-phase coexistence region in the accessible temperature range. The characterization of the structural and phase behavior is performed by a combination of surface pressure studies with Brewster angle microscopy (BAM) imaging and Grazing incidence X-ray diffraction (GIXD) measurements. A comprehensive thermodynamic analysis provides good agreement between the experimental surface pressure - area (Pi-A) isotherms and the theoretical curves that were calculated on the basis of equations of state for a large region of monolayer stages developed by us in J. Phys. Chem. 1999, 103, 145. Theoretical curves calculated by application of equations of state only for the fluid monolayer state proposed recently by Rusanov (J. Chem Phys. 2004, 120, 10736) are in good agreement with the experiments in a limited temperature range. A rigorous equation is derived and applied to the experimental results for the calculation of the enthalpy of two-dimensional phase transition. The combination of BAM and GIXD illustrates that the microscopic long range ordering of the condensed monolayer phases is related to the lattice structure of the condensed monolayer.     

Adsorbed monolayer of H-bonded water molecules with and without neutral polymer molecules: A statistical mechanical treatment accounting for local order

A statistical mechanical treatment of a monolayer consisting both of H-bonded solvent molecules adsorbed in an unspecified number of orientations and of polymeric molecules of a neutral solute is provided. The different size of solvent and solute molecules is accounted for using Flory—Huggins statistics, whereas local order within the monolayer is accounted for using the quasi-chemical approximation. The above treatment is applied to a hexagonal array of adsorbed water molecules oriented in such a way as to be in a condition to be singly or double H-bonded laterally in the monolayer; a further water orientation characterized by full alignment of the dipole moment in the direction away from the electrode and simulating chemisorbed water monomers is included in the molecular model treatment. An adsorption isotherm is derived upon generalizing the molecular model at hand so as to include the presence of polymeric neutral solute molecules adsorbed in a single orientation. The model accounts satisfactorily for a number of salient features of experimental capacity curves at metal—water interphases in the absence of adsorbed solute species, as well as for the adsorption behaviour of aliphatic compounds on mercury, provided that the doubly H-bonded water molecules are excluded from the molecular model. A justification for this exclusion, based on the existence of H-bonds between the first and second layer of water molecules, is provided.     

Grand canonical ensemble molecular dynamics simulation of water solubility in polyamide-6,6

Grand canonical ensemble molecular dynamics simulation is employed to calculate the solubility of water in polyamide-6,6. It is shown that performing two separate simulations, one in the polymeric phase and one in the gaseous phase, is sufficient to find the phase coexistence point. In this method, the chemical potential of water in the polymer phase is expanded as a first-order Taylor series in terms of pressure. Knowing the chemical potential of water in the polymer phase in terms of pressure, another simulation for water in the gaseous phase, in the grand canonical ensemble, is done in which the target chemical potential is set in terms of pressure in the gas phase. The phase coexistence point can easily be calculated from the results of these two independent simulations. Our calculated sorption isotherms and solubility coefficients of water in polyamide-6,6, over a wide range of temperatures and pressures, agree with experimental data.     

Determination of the melting point of hard spheres from direct coexistence simulation methods

We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the (planar) fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p=11.54(4)k(B)T/sigma(3), which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p=11.54(4)k(B)T/sigma(3). We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.     

Static, transient, and dynamic phase coexistence in metal nanoclusters

Molecular dynamics simulations are used to examine static and dynamic coexistence between solid and liquid phases in nanoscale silver, copper, and nickel clusters. We find static coexistence in the 561-atom copper icosahedron, the 561-atom silver icosahedron, and the 923-atom nickel icosahedron, and in cluster sizes above these thresholds, but not in smaller clusters. Nonetheless, in smaller clusters we typically observe either dynamic coexistence between fully solid and liquid states or transient coexistence which is essentially dynamic coexistence between a fully solid state and a solid-liquid state.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.