Density functional theory for inhomogeneous associating chain fluids

We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.     

Monte Carlo study of interfacial properties of associating fluids

Canonical Monte Carlo Simulations have been performed to calculate liquid-vapor properties of the associating square well and Lennard-Jones fluids with one and two sites. Simulations were carried out by using several values of reduced temperatures and association energies. The orthobaric densities, as well as the surface tension of associating square well fluids, were calculated and compared with those reported previously in literature; a good agreement was found among them. Results of surface tension of two-sites associating Lennard-Jones fluids are presented here for the first time.     

Computer simulation of the liquid crystal formation in a semi-flexible polymer system

Molecular dynamic simulations are reported for system of semi-flexible linear rod-like molecules. The molecules are composed of N_c tangent soft spheres, connected by elastic springs. Rigidity is introduced by additional springs between all pairs of spheres along the molecule. The formation of only a nematic LC phase is shown for all systems with N_c = 8 and different flexibility. The effect of flexibility on the order parameter and the volume fraction at the LC phase transition is compared with theoretical predictions by Khokhlov-Semenov and with available simulation data. The dependence of the anisotropy of diffusion on chain flexibility in LC phase was studied. The polymer brushes consisting of flexible and semi-flexible (composed of linear rod-like segments) chains were simulated at different grafting densities. Height of brush, order parameter, distribution of density and chain ends in brush were obtained in both cases and compared with theoretical predictions.     

Transport coefficients for hard-chain fluid

Diffusion coefficient and shear viscosity are calculated for fluids containing molecules modelled as chains of tangent hard spheres. A formula for the Stokes–Einstein relation is proposed for hard chain fluids to calculate the shear viscosity from the diffusion coefficient. The numerical results show a good agreement between theoretical values and molecular dynamics results     

Thermodynamics of mixtures of amines with n-alkanes and 1-alkanols

The LFAS (Lattice-Fluid Associated Solution) model, which has been applied to alkanol + alkane and to alkanol + alkanol mixtures is now extended to mixtures consisting of one self-associated and one active or weakly self-associated component. The types of association complexes considered are A_nB_m and A_nB with a single A-B bond each. The model is subsequently applied to binary alkanol + amine mixtures with an emphasis on vapor-liquid equilibria. Self-association constants for n-alkyl amines and dialkyl amines are presented along with the pure component lattice-fluid scaling constants. These parameters are used for correlating pure component data on vapor pressures, heats of vaporization, and orthobaric densities as well as mixing properties of amine + alkane mixtures.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

The vaporization properties of krypton and xenon

The vaporization properties of krypton and xenon are reassessed from the experimental results published in the literature, more sparsely since the 1970s. The measured vapour pressure and the saturated liquid density of both substances are adjusted to empirical, reliable equations. Results are presented for the calculated vapour pressures and the orthobaric densities of the two substances. The coordinates of the triple point, the normal boiling temperature, and the critical point are discussed as well as the corresponding values of the enthalpies of vaporization. Argon, for which recent experimental, accurate work has been published, was kept out of the present review.     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Numerical analysis of capillarity in packed spheres: planar hexagonal-packed spheres

General solutions of the capillary pressure for liquids as a function of contact angle and volume in planar close-packed spheres have been calculated numerically using Surface Evolver software. Applied pressure differences between liquid and vapor result in undulating (puckered) menisci exhibiting anticlastic curvature in the narrower spaces near particle contacts. The corresponding capillary pressures exhibit maxima with infiltration volume (minima with drainage), corresponding to critical pressures for engulfment of the spheres by the liquid (vapor). The analysis also reveals the formation of residual pendular rings of the wetting phase around particle contacts. Pendular ring formation is explored further by analyzing hexagonally packed spheres separated by 1/10 their radius. The results are discussed relative to the wide range of approximate solutions available in the literature.     

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.     

Electronic and Magnetic Properties of Linear and Dimerized Titanium Nanochains Under Compressive and Tensile Strain

The magnetic and electronic properties of both linear and dimerized nanochains of titanium at different atomic distances are calculated within density functional theory with the generalized gradient approximation. Titanium which is a nonmagnetic in its bulk form is shown to become magnetic in its nanochain structure. Also, a close relationship is found between magnetic state and geometry of chain structure and the dependence of electronic properties on the atomic structures of chains is revealed. It is found that, for dimerized nanochains from equilibrium constant, compressive strain leads to a reduction in magnetism. Moreover, characteristics of the systems near the Fermi level are investigated and the charge densities of both nanostructures are studied in the ferromagnetic order. The results show that metallic bonding is mainly responsible for the linear structure; however, for the dimerized structure, the bonding is more directional, i.e. has a more covalent character. With increasing tension along the axis of the nanostructures, a change in the types of bonding is found.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Evolution of intermolecular structure and dynamics in supercritical carbon dioxide with pressure: an ab initio molecular dynamics study

The effect of pressure on supercritical carbon dioxide (scCO2) has been characterized by using Car-Parrinello molecular dynamics simulations. Structural and dynamical properties along an isotherm of 318.15 K and at pressures ranging from 190 to 5000 bar have been obtained. Intermolecular pair correlation functions and three-dimensional atomic probability density map calculations indicate that the local environment of a central CO2 molecule becomes more structured with increasing pressure. The closest neighbors are predominantly oriented in a distorted T-shaped geometry while neighbors separated by larger distances are likely oriented in a slipped parallel arrangement. The structure of scCO2 at high densities has been compared with that of crystalline CO2. The probability distributions of intramolecular distances narrow down with increasing pressure. A marginal but non-negligible effect of pressure on the instantaneous intramolecular OCO angle is observed, lending credence to the idea that intermolecular interactions between CO2 molecules in an inhomogeneous near neighbor environment could contribute to the observed instantaneous molecular dipole moment. The extent of deviation from a perfect linear geometry of the carbon dioxide molecule decreases with increasing pressure. Time constants derived from reorientational time correlation functions of the molecular backbone compare well with experimental data. Within the range of thermodynamic conditions explored here, no significant changes are observed in the frequencies of intramolecular vibrational modes. However, a blue shift is observed in the low-frequency cage rattling mode with increasing pressure.     

Vapor pressure and density of thermotropic liquid crystals: MBBA, 5CB, and novel fluorinated mesogens

The vapor pressures and densities of six thermotropic liquid crystal-forming molecules (mesogens) have been determined experimentally as functions of temperature. The ubiquitous mesogenic compounds n-(4-methoxybenzylidene)-4-butylaniline (MBBA) and 4'-cyano-4-n-pentylbiphenyl (5CB), which both exhibit room-temperature nematic phases, are examined in this study, as are a number of trifluorinated bicyclohexyl and cyclohexylbiphenyl derivatives which find modern use in display applications. Although thermotropic mesogens are of prime importance in modern optoelectronic technologies, there is a scarcity of reliable saturation pressure data for such systems. An apparatus suitable for measurements of vapor pressures between 0.1 and 1333 Pa in the temperature range 298-523 K has been constructed. The adequacy of the apparatus has been verified by measurements on n-hexadecane at temperatures between 304 and 372 K, corresponding to vapor pressures between 0.4 and approximately 100 Pa. To our knowledge, our measurements represent the first reliable data for the saturation pressure of the fluid phase of these types of thermotropic compounds; we show that existing data for MBBA is thermodynamically inconsistent. The densities of the fluid phases of these compounds are also measured by means of a glass pycnometer at temperatures between 293 and 368 K.     

Interfacial Properties of Asymmetric Polymer Mixtures

Using a Monte‐Carlo simulation of a continuous space Rod Bead Model the interface properties of systems of flexible polymer chains with different sizes of monomers are investigated. An immiscible polymer blend in the strong segregation state is modeled by a double sandwich system of chains differing by an factor of two in the size of the beads and the interfacial tension is calculated by a virial theorem method. The simulation data are compared to self‐consistent mean field and experimental data. The results show that the simulation data agree very satisfactory with mean‐field results. The interfacial tension decreases for asymmetric systems in comparison to symmetric systems with comparable volume contents of monomers and interaction strengths due to a decrease of the effective interaction. The parameters of the investigated systems are close to the properties of PS, PMMA and PI melts. A comparison with experimental results yields a very good agreement with data for PS/PMMA and less satisfactory for PS/PI. Additionally to the interfacial tension we have studied the interfacial width, the deformation of polymer chains near the interface, distributions of chain ends, monomer densities and distributions of centers of mass of chains.

Snapshot of a typical configuration for chains with different monomer sizes and equal number of monomers per chain.     

Dynamics of polypropylene chains in their binary blends of different stereochemical sequences studied by Monte Carlo simulations

The conformational and dynamic properties of polypropylene （PP） for both pure melts and blends with different chain tacticity were investigated by Monte Carlo simulation of isotactic （iPP）, atactic （aPP） and syndiotactic （sPP） polypropylenes. The simulation of coarse-grained PP models was performed on a high coordination lattice incorporating short- and long-range intramolecular interactions from the rotational isomeric state （RIS） model and Lennard-Jones （LJ） potential function of propane pairs, respectively. The dynamics of chains in binary PP/PP mixture were investigated with the composition of C150H302 with different chain taciticity. The diffusion rates of PP with different stereochemistry are generally in the order as： iPP 〉 aPP 〉〉 sPP. For PP/PP blends with 50：50 wt% binary mixtures, immiscibility was observed when sPP was introduced into the mixtures. The diffusion rate of iPP and aPP became slower after mixing, while sPP diffuses significantly faster in the binary mixtures. The mobility of PP chains depends on both intramolecular （molecular size and chain stiffness） and intermolecular （chain packing） interactions. The effect of intramolecular contribution is greater than that of intermolecular contribution for iPP and aPP chains in binary mixtures. For sPP chain, intermolecular interaction has greater influence on the dynamics than intramolecular contribution.     

Polyelectrolytes in solutions with multivalent salt. Effects of flexibility and contour length

It has been experimentally observed that trivalent ions are capable of promoting compaction of semi-flexible polyelectrolyte chains. In this work we perform Monte Carlo simulations on single chain model systems with varying chain size and stiffness and evaluate the action of multivalent salt on the chain conformation. It is observed that longer chains tend to achieve relatively more compact conformations than shorter ones, and the dimensions of the collapsed structures do not significantly vary with contour length. The influence of contour length and intrinsic stiffness in the process of ion condensation is studied by analysis of the ion-ion nearest-neighbor distribution. The general trend is an increase of the degree of ion condensation as the chain length increases, in accordance with experimental evidence. A decreased importance of end-effects and, especially, larger volume charge densities are responsible for such behavior. The influence of chain stiffness is nontrivial, and depends on salt concentration. The results emphasize the complex nature of ion-correlation phenomena in flexible or semi-flexible chains and call for the development of more sophisticated analytical theories.     

Molecular dynamics simulation of potassium along the liquid-vapor coexistence curve

The applicability of pair potential functions to liquid alkali metals is questionable. On the one hand, some recent reports in the literature suggest the validity of two-parameter pair-wise additive Lennard-Jones (LJ) potentials for liquid alkali metals. On the other hand, there are some reports suggesting the inaccuracy of pair potential functions for liquid metals. In this work, we have performed extensive molecular dynamics simulations of vapor-liquid phase equilibria in potassium to check the validity of the proposed LJ potentials and to improve their accuracy by changing the LJ exponents and taking into account the temperaturedependencies of the potential parameters. We have calculated the orthobaric liquid and vapor densities of potassium using LJ (12–6), LJ (8.5–4) and LJ (5–4), effective pair potential energy functions. The results show that using an LJ (8.5–4) potential energy function with temperature-independent parameters, ε and σ, is inadequate to account for the vapor-liquid coexistence properties of potassium. Taking into account the temperature-dependencies of the LJ parameters, ε(T) and σ(T), we obtained the densities of coexisting liquid and vapor potassium in a much better agreement with experimental data. Changing the magnitude of repulsive and attractive contributions to the potential energy function shows that a two-parameter LJ (5–4) potential can well reproduce the densities of liquid and vapor potassium. The results show that LJ (5–4) potential with temperature-dependent parameters produces the densities of liquid and vapor potassium more accurately, compared to the results obtained using LJ (12–6) and LJ (8.5–4) potential energy functions.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Bulk and interfacial properties of binary polymer mixtures

A microscopic density functional theory is used to investigate a binary mixture of polymers, built of freely jointed tangent hard spheres. The difference in the chain length and in the segment diameter of polymers gives rise to a demixing transition. We evaluate the bulk fluid phase equilibria (binodal) and the limit of stability of a mixed state (spinodal) for selected systems, and analyze the decay of the critical packing fraction, critical mole fraction, and critical pressure with an increase of the chain length. The bulk results are subsequently used in the calculations of the density profiles across the fluid-fluid interface. The obtained profiles are smooth and do not exhibit any oscillations on the length scale of the segment diameter. Upon approaching the critical point the interfacial tension vanishes as (Deltarho)3, where Deltarho is the difference between bulk densities of one component in bulk phases rich and poor in that species. This indicates that the microscopic density functional theory applied here is of a mean-field type.     

Chemisorption of thiolated poly(ethylene oxide) to gold: surface chain densities measured by ellipsometry and neutron reflectometry

Physical property studies of surfaces formed by chemisorption of polyethylene oxide (PEO) onto gold are reported. Such surfaces have potential as model materials for elucidation of the mechanism of resistance to protein adsorption by PEO surfaces. Thiolated monomethoxy poly(ethylene oxide) (PEO) was chemisorbed onto gold-coated silicon wafers under various conditions such that different surface chain densities were achieved. Chain density was varied by controlling PEO solubility (proximity to cloud-point conditions) as well as chemisorption time. Films prepared with PEO of molecular weight 750, 2000, and 5000 g/mol were studied. Chain densities determined in the dry state by ellipsometry were found to be in the range of 0.4-0.7, 0.33-0.58, and 0.12-0.30 chains/nm(2) for MW 750, 2000, and 5000 PEO, respectively. Chain density was found to decrease with increasing molecular weight and to increase as cloud-point conditions were approached. PEO-layer mass densities and chain densities were determined independently by neutron reflectometry. Under low-solubility conditions and for a 4-h chemisorption time, film mass and chain density values of 1.0 +/-0.3 g cm(-3) and 1.8 +/- 0.9 chains/nm(2) were found for MW 750 PEO, and 0.82 +/- 0.02 g cm(-3) and 0.23 +/- 0.07 chains/nm(2) for MW 5000 PEO. Ellipsometry data for these systems yielded graft densities of 0.63 +/- 0.13 and 0.30 +/- 0.02 chains/nm(2), respectively. Using the mass densities obtained from the neutron data in the ellipsometry calculations, chain densities of 0.6 +/- 0.3 and 0.25 +/- 0.02 chains/nm(2), respectively, were obtained for the MW 750 and 5000 films. The ellipsometry and neutron data for the MW 5000 system are thus in agreement within experimental error. In general, the chain-density values are much higher than those corresponding to layers of unperturbed random coil PEO ("mushrooms"), suggesting that the PEO layers are in the brush regime with the chains in an extended conformation.