Thermodynamic regularities for associating fluids from statistical associating fluid theory equation of state

In this work, we used a statistical associating fluid theory to analyze two important thermodynamic regularities for some associating fluids, including water, methanol and ethanol. The studied regularities included: (i) the common bulk modulus point on the isotherms of the reduced bulk modulus versus reduced density, (ii) near linearity of the reduced isothermal bulk modulus as a function of reduced pressure. In this work, we also reported the influence of the molecular size and interaction strength on the bulk modulus point.     

Modified interfacial statistical associating fluid theory: a perturbation density functional theory for inhomogeneous complex fluids

A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.     

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.     

Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range

Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.     

A study of square-well statistical associating fluid theory approximations

Six square-well (SW) statistical associating fluid theory (SAFT) models, fitted to the experimental saturated liquid volume and saturated vapor pressure for pure n-alkanes, are analyzed for predicting the coexisting densities, second virial coefficients, and binary phase equilibria. The models that result in low values of the segment energy and weak molecular weight dependence of the parameters are found to be more accurate for real fluids. The inclusion of the dimer structure in the SW chain term seems to produce no significant benefit for representing real substances.     

Modified interfacial statistical associating fluid theory: application to tethered polymer chains

Modified interfacial statistical associating fluid theory density functional theory is extended to tethered polymer chains in the absence or presence of free polymer chains. The structures of the "dry" and "wet" polymer brushes have been calculated and compared with simulation results available in the literature. The comparisons show that the theory accurately predicts the structure of the tethered polymer brush. The average brush heights calculated from the theory agree with well-established scaling theories for tethered polymers. However, these scaling theories cannot predict the detailed structure, accurately. The effects of the segment-segment interactions of the tethered polymer and the free polymer have been effectively captured by the theory.     

Optimized theory for simple and molecular fluids

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.     

An extended rism equation for molecular polar fluids

The RISM integral equation is extended to molecules with charged sites via a renormalization of the Coulomb potentials and the introduction of appropriate closure relations. For a fluid of diatomics with atomic charges of ±0.2 e the equation yields site-site correlation functions in qualitative agreement with those from computer simulation.     

Predicting adsorption isotherms using a two-dimensional statistical associating fluid theory

A molecular thermodynamics approach is developed in order to describe the adsorption of fluids on solid surfaces. The new theory is based on the statistical associating fluid theory for potentials of variable range [A. Gil-Villegas et al., J. Chem. Phys. 106, 4168 (1997)] and uses a quasi-two-dimensional approximation to describe the properties of adsorbed fluids. The theory is tested against Gibbs ensemble Monte Carlo simulations and excellent agreement with the theoretical predictions is achieved. Additionally the authors use the new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon.     

Measuring distances between half-integer quadrupolar nuclei and detecting relative orientations of quadrupolar and dipolar tensors by double-quantum homonuclear dipolar recoupling nuclear magnetic resonance experiments

We studied the possibility of using double-quantum homonuclear dipolar recoupling magic angle spinning nuclear magnetic resonance experiments for structural analysis of systems of half-integer quadrupolar nuclei. We investigated symmetry-based recoupling schemes R2(2) (1) and R2(2) (1)R2(2) (-1) and showed that the obtained double-quantum filtered signals depend substantially on magnitudes and relative orientations of dipolar and quadrupolar tensors. Experimental results measured on aluminophosphate molecular sieve AlPO(4)-14, containing dipolar-coupled spin-52 aluminum nuclei, were compared to results of time-consuming numerical simulations. The comparison for short mixing times allowed us to roughly measure internuclear Al-Al distances, if constraints about relative tensor orientations were available. Inspection of relative orientations of dipolar and quadrupolar tensors, using known distances between nuclei, required experimental and simulated data for long mixing times and yielded less accurate results. Two experimental protocols were employed for measuring double-quantum filtered curves, the symmetric protocol, in which excitation and reconversion periods are incremented simultaneously, and the asymmetric protocol, in which only the length of the excitation period is incremented and the length of the reconversion period is kept constant. The former experimental protocol was more convenient for the detection of internuclear distances, and the latter one was more appropriate for the inspection of relative orientations of interaction tensors.     

Statistical associating fluid theory coupled with restrictive primitive model extended to bivalent ions. SAFT2: 1. Single salt + water solutions

Statistical associating fluid theory coupled with the restricted primitive model is extended to multivalent ions by relaxing the range of the square-well width parameter, which leads to a new dispersion term approximation and calls for a new set of salt and ion parameters. This new approximation, referred to as SAFT2, requires a single set of parameters derived from the salt (mean ionic) activity coefficients and liquid densities of single-salt solutions for five cations (Li(+), Na(+), K(+), Ca(2+), Mg(2+)), six anions (Cl(-), Br(-), I(-), NO(3)(-), SO(4)(-2), HCO(3)(-)), and 24 salts. These parameters, in turn, are shown to predict the osmotic coefficients for single salt + water solutions.     

Statistical associating fluid theory coupled with restrictive primitive model extended to bivalent ions. SAFT2: 2. Brine/seawater properties predicted

Statistical associating fluid theory coupled with restricted primitive model (SAFT2) represents the properties of aqueous multiple-salt solutions, such as brine/seawater. The osmotic coefficients, densities, and vapor pressures are predicted without any additional parameters using the salt hydrated diameters obtained for single-salt solutions. For a given ion composition of brine, the predicted vapor pressure, osmotic coefficient, activity of water, and density are found to agree with the experimental data.     

Thermodynamic properties of the Mie n-6 fluid: a comparison between statistical associating fluid theory of variable range approach and molecular dynamics results

Molecular dynamics (MD) simulations of direct and derivative thermodynamic properties of the Mie n-6 fluid (n=8, 10, and 12) have been performed for liquid to supercritical states. Using the results, an in depth test of the monomer-monomer interaction estimation of a recently derived statistical associating fluid theory of variable range (SAFT-VR) equation of state [Lafitte et al., J. Chem. Phys., 124, 024509 (2006)] has been carried out based on the Mie n-6 potential. For pure fluids, using an appropriate scaling, MD simulations show that density and isometric heat capacity are nearly independent of n, whereas sound velocity and thermal pressure coefficient tend to increase with n. In addition, the results show that predictions provided by the equation of state are consistent with those coming from MD and catch correctly the trends of each property with n except for the heat capacity. The comparison is next extended to binary mixtures with components differing only in the value of the n parameter and which demonstrate the reliability of the scheme (MX1b) used by Lafitte et al. to deal with this parameter in the SAFT-VR equation of state. In addition, a new empirical one-fluid approximation of the n parameter is proposed thanks to MD simulations, which very favorably compare with the one-fluid model on n previously proposed in the literature. The consistency of this approximation is addressed by making use of it in combination with the SAFT-VR Mie equation of state. It is shown that using such an approach, which is easier to handle than the MX1b one, yields slightly improved results compared to those of the MX1b.     

A site-renormalized molecular fluid theory

The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.     

Structure-property relationships for three-photon absorption in stilbene-based dipolar and quadrupolar chromophores

Based on essential-state models for three-photon absorption (3PA), we have investigated the structure-property relationships for stilbene-based dipolar and quadrupolar chromophores. The emphasis lies on the evolution of the 3PA cross section with the degree of ground-state polarization. For dipolar systems, we find a dominant role played by Deltamu, which expresses the change in dipole moment between the ground state and the 3PA active excited state. Thus, the strategies usually applied to maximize the second-order polarizability beta are also applicable to optimize the 3PA cross section. For quadrupolar systems, the 3PA response is dominated by contributions from channels including various low-lying two-photon allowed states, which limits the applicability of essential-state models. Optimization strategies can be proposed but vary for different ranges of ground-state polarization.     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

Coarse-grained molecular dynamics modeling of strongly associating fluids: thermodynamics, liquid structure, and dynamics of symmetric binary mixture fluids

Symmetric binary mixtures capable of strong association via a highly directional and saturable specific interaction between unlike molecules are investigated by canonical molecular dynamics simulations. The specific interaction of the molecules is defined in a new coarse-grained pair potential that can be applied in continuous molecular dynamics as well as in Monte Carlo simulations. The thermodynamic, structural, and dynamic properties of the associating mixture fluids are investigated as a function of density, temperature, and association strength of the specific interaction. Detailed analysis of the simulation data confirms a two-stage mechanism in the formation of specific bonds with increasing interaction strength, including a fast dimerization process and a subsequent stage of perfecting the bonds. A large heat capacity peak is found during the formation or breaking of the bonds, reflecting the large energy fluctuation introduced by the strong association. The fractions of nonbonded molecules obtained from the simulations as a function of density, temperature, and interaction strength are in excellent agreement with the predictions of Wertheim's thermodynamic perturbation theory. The translational and rotational dynamics of the Tmer mixture are effectively retarded with increasing association strength and are analyzed in terms of autocorrelation functions and a non-Gaussian parameter for the translational dynamics. The lifetimes of molecules in bonded and nonbonded states provide detailed information about the transformation of molecules between the bonded state and the nonbonded state. Finally, simulation sampling problems inherent to strongly interacting systems are easily overcome using the parallel tempering simulation technique. This latter result confirms that with the new continuous coarse-grained simulation potential we have a versatile and flexible interaction potential that can be used with many available molecular dynamics and Monte Carlo algorithms under various ensembles.