Comparison of several classical density functional theories for the adsorption of flexible chain molecules into cylindrical nanopores.

Adsorption of flexible oligomers into narrow cylindrical pores has been studied by means of several versions of classical density functional theory (CDFT) and Monte Carlo simulation. The adsorption process is interesting to study due to the competition between the entropic depletion of oligomers from the pores and the wall-oligomer attraction. It is also challenging to describe using current CDFTs, which tend to overestimate the amount of the adsorbed fluid. From a comparison of several different CDFT approaches, we find that this is due to the assumption of ideal or freely jointed chain conformations. Moreover, it is demonstrated that it is impossible to obtain a reasonable description of the adsorption isotherms without taking into account accurate contact values in the distribution functions describing the structure of the reference monomer fluid. At low densities, more accurate result are obtained in comparison with Monte Carlo simulation data when accurate contact values are incorporated into the theory rather than the more commonly used hard-sphere contact value. However, even the CDFT with accurate contact values still overestimates the amount of the adsorbed fluid due to the ideal or freely jointed chain approximation, used for the description of chain conformations in most CDFT approaches. We find that significant improvement can achieved by employing self-consistent field theory, which samples self-avoiding chain conformations and decreases the number of possible chain conformations, and, consequently, the amount of the adsorbed fluid.

An improved first-order mean spherical approximation theory for the square-shoulder fluid.

The theory, which utilizes an exponential enhancement of the first-order mean spherical approximation (FMSA) for the radial distribution functions of the hard-core plus square-well fluid, is adopted to study the properties of the simplest model of the core-softened fluids, i.e., the hard spheres with a square-shoulder interaction. The results for structure and thermodynamic properties are reported and compared against both the Monte Carlo simulation data as well as with those obtained within the conventional FMSA theory. We found that in the region of low densities and low temperatures, where the conventional FMSA theory fails, the exponential-based FMSA theory besides being qualitatively correct also provides with a notable quantitative improvement of the theoretical description.

Speciation in aqueous solutions of nitric acid.

In this study, speciation in aqueous solutions of nitric acid at 25 °C was assessed in two independent ways. First, Raman experiments were carried out and interpreted in terms of free nitrate ions, ion pairs and neutral HNO(3) molecules. In parallel, a model was developed to account for the formation of these two kinds of pairs. It was based on an extension of the binding mean spherical approximation (BiMSA), or associative MSA (AMSA), in which the size and the charge of the ions in the chemical pair may differ from those of the free ions. A simultaneous fit of the osmotic coefficient and of the proportion of free ions (obtained from Raman spectroscopy experiments) led to an estimation of the speciation in nitric acid solutions. The result obtained using this procedure was compared with the estimation obtained from the Raman experiments.

An improved thermodynamic perturbation theory for square-well m-point model of the patchy colloids.

We propose an improved version of Wertheim's first order thermodynamic perturbation theory for the square-well m-point model of patchy colloids. Our version of the theory takes into account changes in the free volume of the system due to bond formation. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model.

Direct correlation function for complex square barrier-square well potentials in the first-order mean spherical approximation.

The direct correlation function of the complex discrete potential model fluids is obtained as a linear combination of the first-order mean spherical approximation (FMSA) solution for the simple square well model that has been reported recently [Hlushak et al., J. Chem. Phys. 130, 234511 (2009)]. The theory is employed to evaluate the structure and thermodynamics of complex fluids based on the square well-barrier and square well-barrier-well discrete potential models. Obtained results are compared with theoretical predictions of the hybrid mean spherical approximation, already reported in the literature [Guillen-Escamilla et al., J. Phys.: Condens. Matter 19, 086224 (2007)], and with computer simulation data of this study. The compressibility route to thermodynamics is then used to check whether the FMSA theory is able to predict multiple fluid-fluid transitions for the square barrier-well model fluids.

Density functional study of flexible chain molecules at curved surfaces.

Density profiles of flexible hard-sphere chain molecules in hard cylindrical pores and around hard cylindrical rods of various diameters were obtained by means of density functional theory of Yu and Wu [Y.-X. Yu and J. Wu, J. Chem. Phys. 117, 2368 (2002)] and grandcanonical Monte Carlo simulation. The density profiles show stronger depletion of long chain molecules from narrow cylindrical pores at low densities, when compared to slit pores of the same width. Additionally, positive surface curvature of cylindrical pores increases the magnitude of wall depletion of chain molecules at low and intermediate densities. For negative surfaces curvature around the cylindrical rod, the wall depletion of chains is weaker than for a flat surface.

Direct correlation function of the square-well fluid with attractive well width up to two particle diameters.

Analytical expression for direct correlation function of the square-well fluid with an attractive well width up to two particle diameters (2 < lambda < or = 3) is reported. This result is obtained within the first-order mean-spherical approximation (FMSA) and represents the nontrivial extension of the recent study due to Tang [J. Chem. Phys. 127, 164504 (2007)], where the width of square-well attraction was limited by one particle diameter (1 < lambda < or = 2). Prediction of the FMSA theory is validated by direct comparison against Monte Carlo simulation data. Additionally, an impact of the increase in the range of attraction on the parameters of the critical point of the square-well fluid is discussed using the compressibility route to thermodynamics.

Phase coexistence in the hard-sphere Yukawa chain fluid with chain length polydispersity: dimer thermodynamic perturbation theory.

An extension of the dimer version of Wertheim's thermodynamic perturbation theory is proposed and used to treat polydisperse mixture of the hard-sphere Yukawa chain fluid with chain length polydispersity. The structure and thermodynamic properties of the reference system, represented by multicomponent mixture of the Yukawa hard-sphere dimers, are described using polymer mean spherical approximation. Explicit analytical expressions for the Helmholtz free energy, chemical potential, and pressure in terms of the two chain length distribution function moments are derived. The theory is used to calculate the full liquid-gas phase diagram, including critical binodal, cloud and shadow curves, and distribution functions of the coexisting phases. Effects of fractionation in terms of the distribution function and its first and second moments are studied. Predictions of the theory for these effects are in qualitative agreement with the corresponding experimental predictions, obtained recently for the polydisperse mixture of polymers in a single solvent. In particular, both theory and experiment predict that longer chain polymers equilibrate to the liquid phase while shorter chain polymers are predominantly encountered in the gas phase.

Phase coexistence in polydisperse athermal polymer-colloidal mixture.

A theoretical scheme developed earlier [Y. V. Kalyuzhnyi et al., Chem. Phys. Lett. 443, 243 (2007)] is used to calculate the full phase diagram of polydisperse athermal polymer-colloidal mixture with polydispersity in both colloidal and polymeric components. In the limiting case of bidisperse polymer-colloidal mixture, theoretical results are compared against computer simulation results. We present the cloud and shadow curves, critical binodals, and distribution functions of the coexisting phases and discuss the effects of polydispersity on their behavior. According to our analysis polydispersity extends the region of the phase instability, shifting the critical point to the lower values of the pressure and density. For the high values of the pressure polydispersity causes strong fractionation effects, with the large size colloidal particles preferring the low-density shadow phase and long chain length polymeric particles preferring the high-density shadow phase.

Phase coexistence in polydisperse multi-Yukawa hard-sphere fluid: high temperature approximation.

High temperature approximation (HTA) is used to describe the phase behavior of polydisperse multi-Yukawa hard-sphere fluid mixtures. It is demonstrated that in the frames of the HTA the model belongs to the class of "truncatable free energy models," i.e., the models with thermodynamical properties (Helmholtz free energy, chemical potential, and pressure) defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram (i.e., cloud and shadow curves as well as binodals) and size distribution functions of the coexisting phases of several different models of polydisperse fluids. In particular, we consider polydisperse one-Yukawa hard-sphere mixture with factorizable Yukawa coefficients and polydisperse Lennard-Jones (LJ) mixture with interaction energy parameter and/or size polydispersity. To validate the accuracy of the HTA we compare theoretical results with previously published results of more advanced mean spherical approximation (MSA) for the one-Yukawa model and with the Monte Carlo (MC) computer simulation results of [Wilding et al. J. Chem. Phys. 121, 6887 (2004); Phys. Rev. Lett. 95, 155701 (2005)] for the LJ model. We find that overall predictions of the HTA are in reasonable agreement with predictions of the MSA and MC, with the accuracy range from semiquantitative (for the phase diagram) to quantitative (for the size distribution functions).