Van der Waals supercritical fluid: exact formulas for special lines

In the framework of the van der Waals model, analytical expressions for the locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, density fluctuation, and sound velocity in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into single Widom line only at T < 1.07T(c), P < 1.25P(c) and become smeared at T < 2T(c), P < 5P(c), where T(c) and P(c) are the critical temperature and pressure. The behavior of the Batschinski lines and the pseudo-Gruneisen parameter γ of a van der Waals fluid were analyzed. In the critical point, the van der Waals fluid has γ = 8/3, corresponding to a soft sphere particle system with exponent n = 14.     

聚合物流体的范德华凝聚行为

研究了由聚合物的范德华作用导致的凝聚行为. 研究发现, 尽管聚合物同小分子的相行为的形成原因不同(聚合物体系的相行为是由动能、构象熵项和范德华作用能三项相互竞争的结果, 而小分子的相行为是由动能和范德华作用能相互竞争的结果), 但是它们表现出了极为相似的相行为.     

Adsorption of square and rectangular plate-like molecules on a planar surface

A mean-field statistical thermodynamic analysis of monolayer adsorption of rigid square and rectangular plate-like molecules on a homogeneous planar surface is developed. The analysis is simplified by only considering facewise and edgewise modes of adsorption in restricted orthogonal orientations parallel to the surface. The free energy density, adsorbate population distribution and surface spreading pressure are obtained as a function of adsorbate density and compared for square plate molecules using three different sequences of adsorbate molecule placement on the surface to evaluate the configurational degeneracy. It is found that edgewise adsorbed molecules can be anisotropically ordered if the edge length of square and rectangular plate-like molecules exceeds three length units in the absence of anisotropic dispersion interactions. If intermolecular dispersion interactions are present and of sufficient strength, the spreading pressure-density isotherms can exhibit one or two van der Waals loops for square plate molecules with three van der Waals loops possible for rectangular plate adsorbate molecules. The phase transitions for the adsorbed monolayer corresponding to the appearance of these van der Waals loops are discussed.     

Hydration and dewetting near fluorinated superhydrophobic plates

The water dynamics near nanoscale fluorinated (CF(3)(CF(2))(7)(CH(2))(2)SiH(3)) monolayers (plates) as well as possible dewetting transitions in-between two such plates have been studied with molecular dynamics simulations in this paper. A "weak water depletion" is found near the single fluorinated surface, with an average water density in the first solvation shells 6-8% lower than its hydrogenated counterpart. The fluorinated molecules are also found to be water impermeable, consistent with experimental findings. More surprisingly, a dewetting transition is found in the interplate region with a critical distance D(c) of 10 A (3-4 water diameters) for double plates with 8 x 8 molecules each (plate size approximately 4 nm x 4 nm). This transition, although occurring on a microscopic length scale, is reminiscent of a first-order phase transition from liquid to vapor. The unusual superhydrophobicity of fluorocarbons is found to be related to their larger size (or surface area) as compared to hydrocarbons, which "dilutes" their physical interactions with water. The water-plate interaction profile shows that the fluorinated carbons have a 10-12% weaker water-plate interaction than their hydrogenated counterparts in the nearest solvation shell, even though the fluorocarbons do have a stronger electrostatic interaction with water due to their larger partial charges. However, the van der Waals interactions dominate the water-plate interaction within the nearest shell, with up to 90% contributions to the total interaction energy, and fluorocarbons have a noticeably weaker (by 10-15%) van der Waals interaction with water in the nearest shell than do hydrocarbons. Both the slightly weaker water-plate interaction and larger surface area contribute to the stronger dewetting transition in the current fluorinated carbon plates.     

Convergence of fine-lattice discretization for near-critical fluids

In simulating continuum model fluids that undergo phase separation and criticality, significant gains in computational efficiency may be had by confining the particles to the sites of a lattice of sufficiently fine spacing, a(0) (relative to the particle size, say a). But a cardinal question, investigated here, then arises; namely, How does the choice of the lattice discretization parameter, zeta identical with a/a(0), affect the values of interesting parameters, specifically, critical temperature and density, T(c) and rho(c)? Indeed, for small zeta ( less, similar 4-8) the underlying lattice can strongly influence the thermodynamic properties. A heuristic argument, essentially exact in d = 1 and d = 2 dimensions, indicates that, for models with hard-core potentials, both T(c)(zeta) and rho(c)(zeta) should converge to their continuum limits as 1/zeta((d)(+1)/2) for d infinity; but the behavior of the error is highly erratic for d >/= 2. For smoother interaction potentials, the convergence is faster. Exact results for d = 1 models of van der Waals character confirm this; however, an optimal choice of zeta can improve the rate of convergence by a factor 1/zeta. For d >/= 2 models, the convergence of the second virial coefficients to their continuum limits likewise exhibits erratic behavior, which is seen to transfer similarly to T(c) and rho(c); but this can be used in various ways to enhance convergence and improve extrapolation to zeta = infinity as is illustrated using data for the restricted primitive model electrolyte.     

Unveiling the Molecular Origin of Vapor-Liquid Phase Transition of Bulk and Confined Fluids

At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular mechanisms of fluids that involve the vapor–liquid phase transition in bulk and confinement, utilizing grand canonical (GCE) and meso-canonical (MCE) ensembles of the Monte Carlo simulation. Different geometries of the mesopores, including slit, cylindrical, and spherical, were studied. During phase transitions, condensation/evaporation hysteretic isotherms can be detected by GCE simulation, whereas employing MCE simulation allows us to investigate van der Waals (vdW) loop with a vapor spinodal point, intermediate states, and a liquid spinodal point in the isotherms. Depending on the system, the size of the simulation box, and the MCE method, we are able to identify three distinct groups of vdW-type isotherms for the first time: (1) a smooth S-shaped loop, (2) a stepwise S-shaped loop, and (3) a stepwise S-shaped loop with just a vertical segment. The first isotherm type is noticed in the bulk and pores having small box sizes, in which vapor and liquid phases are close and not clearly identified. The second and the third types occurred in the bulk, cylindrical, and slit mesopores with sufficiently large spaces, where vapor and liquid phases are distinctly separated. Results from our studies provide an insight analysis into vapor–liquid phase transitions, elucidating the effect of the confinement of fluid behaviors in a visual manner.     

The generalized van der waals partition function. I. basic theory

Sandler, S.I., 1985. The generalized van der Waals partition function. I. Basic theory. Fluid Phase Equilibria, 19:233-257 In this paper we provide a new derivation of the generalized van der Waals partition function for pure fluids and mixtures, and show how this partition function can be used as a basis for understanding equations of state, their mixing rules, and excess free energy (activity coefficient) models. The results presented here clarify some of the confusion which presently exists in the literature concerning the ramifications of local composition thermodynamic models, and provide the theory for papers to follow which combine the generalized van der Waals partition function and our computer simulation results to obtain new, statistical mechanical-based thermodynamic models.     

C-H/π-interaction-guided self-assembly in π-conjugated oligomers

We report CH/π hydrogen-bond-driven self-assembly in π-conjugated skeletons based on oligophenylenevinylenes (OPVs) and trace the origin of interactions at the molecular level by using single-crystal structures. OPVs were designed with appropriate pendants in the aromatic core and varied by hydrocarbon or fluorocarbon tails along the molecular axis. The roles of aromatic π-stack, van der Waals forces, fluorophobic effect and CH/π interactions were investigated on the theromotropic liquid crystallinity of OPV molecules. Single-crystal structures of hydrocarbon OPVs provided direct evidence for the existence of CH/π interactions between the π-ring (H-bond acceptor) and alkyl C-H (H-bond donor). The four important crystallographic parameters, d(c-x)=3.79 ?, θ=21.49°, φ=150.25° and d(Hp-x)=0.73 ?, matched in accordance with typical CH/π interactions. The CH/π interactions facilitate the close-packing of mesogens in x-y planes, which were further protruded along the c axis producing a lamellar structure. In the absence of CH/π interactions, van der Waals interactions drove the assembly towards a Schlieren nematic texture. Fluorocarbon OPVs exhibited smectic liquid-crystalline textures that further underwent Smectic A (SmA) to Smectic C (SmC) phase transitions with shrinkage up to 11%. The orientation and translational ordering of mesogens in the liquid-crystalline (LC) phases induced H- and J-type molecular arrangements in fluorocarbon and hydrocarbon OPVs, respectively. Upon photoexcitation, the H- and J-type molecular arrangements were found to emit a blue or yellowish/green colour. Time-resolved fluorescence decay measurements confirmed longer lifetimes for H-type smectic OPVs relative to that of loosely packed one-dimensional nematic hydrocarbon-tailed OPVs.     

Theoretical and computational investigations on thermodynamic properties, effective site diameters, and molecular free volume of carbon disulfide fluid

A newly proposed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was extended to polyatomics and applied to compute the density and temperature dependence of the effective site diameters of carbon disulfide fluids. The generic van der Waals (GvdW) theory was also extended to polyatomics in order to calculate the GvdW parameters and the molecular free volume using the effective site diameters as the repulsion-attraction separation distance. A three-site Lennard-Jones potential available in the literature was slightly modified and used in Monte Carlo simulations to obtain the functions appearing in the effective site diameter and GvdW expressions. The interaction potential was examined to reproduce the fluid phase thermodynamic properties using Gibbs ensemble Monte Carlo simulations and also the equation of state in the liquid phase using NVT Monte Carlo (NVT-MC) simulations. Comparison between the simulation results and experimental data shows excellent agreement for the densities of the coexisting phases, the vapor pressure, properties of the predicted critical point, and the equation of state. NVT-MC simulations were performed over a wide range of densities and temperatures in sub- and supercritical regions to compute the effective site diameters, the GvdW parameters, and the molecular free volume. The molecular structure in terms of the site-site pair correlation functions, the density dependence of the effective site diameters, and the density and temperature dependence of the GvdW parameters and molecular free volume were studied and discussed. The GvdW parameters were fitted to empirical expressions as a function of density and temperature. The computed molecular free volume will be used in future investigations to study the transport properties of carbon disulfide.     

Enveloping distribution sampling: a method to calculate free energy differences from a single simulation

The authors present a method to calculate free energy differences between two states A and B "on the fly" from a single molecular dynamics simulation of a reference state R. No computer time has to be spent on the simulation of intermediate states. Only one state is sampled, i.e., the reference state R which is designed such that the subset of phase space important to it is the union of the parts of phase space important to A and B. Therefore, an accurate estimate of the relative free energy can be obtained by construction. The authors applied the method to four test systems (dipole inversion, van der Waals interaction perturbation, charge inversion, and water to methanol conversion) and compared the results to thermodynamic integration estimates. In two cases, the enveloping distribution sampling calculation was straightforward. However, in the charge inversion and the water to methanol conversion, Hamiltonian replica-exchange molecular dynamics of the reference state was necessary to observe transitions in the reference state simulation between the parts of phase space important to A and B, respectively. This can be explained by the total absence of phase space overlap of A and B in these two cases.     

Molecular recognition thermodynamics of pyridine derivatives by sulfonatocalixarenes at different pH values

The complex stability constants (Ka) and thermodynamic parameters (DeltaG degrees, DeltaH degrees, and TDeltaS degrees) for 1:1 complexation of water-soluble calix[4]arene, thiacalix[4]arene, and calix[5]arene sulfonates with pyridine and their methylated derivatives have been determined by means of isothermal titration calorimetry at pH 2.0 and 7.2 at 298.15 K, and their binding modes have been investigated by NMR spectroscopy. The results obtained show that sulfonatocalixarenes afford stronger binding ability toward pyridine guests at pH 2.0, attributable to the positive electrostatic interactions and the more extensive desolvation effects, but present higher molecular selectivity at pH 7.2 owing to the strengthened C-H...pi interactions. The pH-responsible binding ability and molecular selectivity are discussed from the viewpoint of electrostatic, pi-stacking, van der Waals interactions and size-fit relationship between host and guest. A close comparison further demonstrates that the C-H...pi interactions and van der Waals interactions play a more important role than pi...pi interactions in the present inclusion complexation.     

Molecular theory of phase equilibria in model and real associated mixtures III. Binary solutions of inert gases and n-alkanes in ammonia and methanol

Using new molecular models of ammonia and methanol and thermodynamic perturbation theory, the global phase diagrams of model mixtures of these compounds with a van der Waals fluid, representing a simple nonpolar fluid, have been calculated. The global phase diagram of these mixtures is much richer than that of corresponding aqueous mixtures. More types of critical line behavior are found, including the presence of van Laar points and a small region where the mixtures exhibit a closed liquid-liquid immiscibility loop (Type VI phase behavior). The individual mixture components are characterized by two molecular parameters, which can be adjusted to their critical temperature and critical volume; the mixture model itself contains no adjustable parameters. It is shown that the theory gives qualitatively correct predietions of mixtures with n-alkanes. This includes the prediction of Type III critical line behavior for small and large values of the ratio of the critical temperatures of the components, and Type II over a large range of conditions, including the presence or absence of absolute or limited azeotropy, and temperature and pressure extrema of critical lines and their dependence on the number of carbon atoms.     

Thermodynamic scaling of the viscosity of van der Waals, H-bonded, and ionic liquids

Viscosities eta and their temperature T and volume V dependences are reported for seven molecular liquids and polymers. In combination with literature viscosity data for five other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TV(gamma), where the exponent gamma is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of gamma for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing gamma in going from van der Waals fluids to ionic liquids. For some strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the nontrivial change of chemical structure (degree of H bonding) with thermodynamic conditions.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Simulation of phase equilibria in lamellar surfactant systems

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.     

Liquid-vapor equilibrium and surface tension of nonconformal molecular fluids

Molecular dynamics simulations at constant temperature have been performed on the liquid-vapor interface for fluids characterized by a recently introduced three-parameter potential. This potential is a modification of the well-known spherical Kihara interaction and is termed approximate nonconformal (ANC). It has been used successfully to describe many real molecules in the gaseous phase. Besides the usual molecular energy and size, the ANC potential introduces a third parameter s, called softness, to measure the form of the potential profile. Study of these systems shows that their critical and interfacial properties follow very closely those of four selected substances: argon, methane, propane, and hexane. Deviations of the properties predicted from the experimental values are analyzed and their probable causes are determined. The critical properties of ANC fluids and their dependence on s are also obtained via first-order perturbation theory in the form of an augmented van der Waals model. Analysis of the results shows that ANC potential functions can be used as reliable effective interactions for real dense fluids.     

Critical behavior in microemulsions

Interactions in dispersions have been studied using light scattering techniques applied to microemulsions. In these systems, hard sphere interactions are dominant. The remaining interactions (van der Waals, etc.) are usually attractive and short-ranged and can be treated as perturbations. However, close to phase transitions where the microemulsion separates into two other microemulsions, the attractive part of the potential becomes large and behaves as if long range interactions were present; the characteristics of the scattered light can also be interpreted by assuming that the system is close to a critical consolute point. The low interfacial tensions (measured between the two microemulsions in equilibrium using surface light scattering techniques) and the large interfacial thicknesses (deduced from optical reflectivity) are consistent with the picture in terms of critical phenomena.     

Molecular thermodynamics of flexible-molecule fluids

Some of the most important problems encountered -in the statistical-mechanical treatment of dense, complex molecular fluids are indicated. Particular attention is given to the application of the generalized van der Waals concept to flexible-molecule fluids. Perturbed-hard-chain theory and chain-of-rotators theory are reviewed. This is followed by a brief summary of recent experimental work on thermodynamic excess properties of liquid mixtures of type (Y + an n-alkane). Several novel effects connected with local correlation of molecular orientation in the n-alkanes, with medium-induced conformational changes and with preferential orientation of strongly polar molecules are discussed (order/disorder phenomena).     

Importance of van der Waals Interactions in QM/MM Simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.