Stepan Hlushak

Temperature, pressure and pore-size dependence of  the heat of adsorption, adsorption stress, and adsorption capacity  of methane in simple models of slit and cylindrical carbon pores  is studied with classical density functional theory (CDFT) and grand-canonical  Monte-Carlo (MC) simulation. Studied properties depend nontrivially on the bulk pressure  and the size of the pores. Heat of adsorption increases with loading,  but only for sufficiently narrow pores. While the increase is advantageous for gas storage applications, it is less significant for cylindrical pores than for slits. Adsorption stress and the average adsorbed fluid density show oscillatory dependence on the pore size and increase with bulk pressure.  Slit pores exhibit stronger oscillating behavior  of the normal adsorption stress, but the stress  increase with bulk pressure is weaker for slits than for cylindrical pores.  Adsorption stress appears to be negative for a wide  range of pore sizes and external conditions. Pore size dependence of the average delivered density  of the gas is analyzed and the optimal pore sizes  for storage applications are estimated. The optimal width of slit pore appears to be almost independent  of storage pressure at room temperature and pressures above 10 bar. Similarly to the case of slit pores, the optimal radius of cylindrical pores  does not exhibit much dependence on the storage pressure above 15 bar. Both optimal width and optimal radius of slit and cylindrical  pores increase as temperature decreases. 
Comparison of the results of CDFT theory and MC simulations reveals subtle but important differences in the underlying  fluid models employed by the approaches. The differences in the high-pressure behaviour between  the hard-sphere 2-Yukawa and Lennard-Jones models of methane,  employed by the CDFT and MC approaches, respectively,  result in an overestimation of the heat of adsorption  by the CDFT theory at higher loadings. However, both adsorption stress and adsorption capacity appear to be much less sensitive to the differences between the models and demonstrate excellent agreement between the theory and computer  experiment.

We employ the 3D-RISM-KH molecular theory of solvation to study adsorption of several heterocyclic aromatic hydrocarbons (acridine, benzothiophene, carbazole, dibenzothiophene, indole, and phenanthridine), which are intended to represent bitumen fragments on the surfaces of a single-sheet kaolinite nanoparticle in cyclohexane and toluene solvents. Additionally to adsorption, we also examine solvent mediated effective interactions between two kaolinite nanoparticles in organic and aqueous solutions. The proposed adsorption model serves as a simple prototype of suspensions formed during non-aqueous extraction of bitumen from oil sands of Athabasca basin.  Using the proposed computational approach, excess adsorption isotherms of bitumen fragments on two different faces of kaolinite were calculated and compared in cyclohexane and toluene solvents at several temperatures. Almost all the studied molecules show strong preference for adsorption on the octahedral aluminum hydroxide surface of kaolinite. While adsorption of the molecules on the tetrahedral silicon oxide surface is weaker, it is still significant compared to the octahedral surface and for some of the studied molecules adsorption appears to be stronger than for the octahedral surface. Due to the better surface and bulk solvation properties of toluene, the adsorption of the bitumen fragments in toluene is weaker than in cyclohexane.  Potentials of mean force between kaolinite nanoplatelets in cyclohexane at several temperatures were calculated using the 3D-RISM-KH molecular theory of solvation. Evaluation of effective interactions by conventional molecular simulation techniques generally requires costly free energy integration and therefore is usually avoided by adopting simple and often unrealistic semiempirical effective potentials. On the other hand, the 3D-RISM-KH molecular theory of solvation offers fully atomistic description with all-atom force-fields and notable performance advantages over molecular simulations. Obtained in this way potentials of mean force in organic solvents exhibit complex oscillating behavior and generally possess deeper main minima and smaller aggregation barriers than the corresponding potentials in aqueous solution.

We developed a predictive model to study how flocculant additives alter the interactions among clay particles in colloidal suspensions, such as industrial mining tailings. Fully atomistic models of kaolinite
nanoplatelets constructed from X-ray crystal structure data feature a highly polarized charge distribution, which defines their solvation, adsorption and association properties. Effective interactions,
in the form of potential of mean force (PMF), between kaolinite platelets in aqueous electrolyte solution are calculated using the three-dimensional reference interaction site model with the Kovalenko-Hirata closure relation (3D-RISM-KH) molecular theory of solvation based on the first
principles of statistical mechanics. This theory is also employed to study the adsorption of ions and flocculant additive building blocks onto kaolinite surfaces. Three main mutual orientations of platelets
are studied in aqueous electrolyte solutions of several polymer building blocks represented by acrylamide, acrylic acid, acrylate and styrene. The results indicate that Na + are predominantly adsorbed
onto the siloxane surface of kaolinite while the chloride and acrylate anions prefer the aluminum hydroxide surface of kaolinite. Weaker preferential adsorption is observed for the neutral monomers.
The PMF between platelets depends nontrivially on the concentration of solvent components and exhibits a complex oscillating behavior with several minima and maxima that correspond to important
solvation and aggregation energy barriers. Among the three studied mutual orientations of the nanoplatelets, the most stable one corresponds to the direct contact of the aluminum hydroxide with
siloxane surfaces. Other highly probable arrangements correspond to nanoplatelets separated by a single layer of solvent. The effect of additives on interparticle interactions is correlated with the
strength of adsorption on kaolinite relative to water, as strongly and weakly adsorbing species cause increase and decrease, respectively, of the PMF at short distances. Moreover, hydrophobic additives
cause a decrease in the local solvent density between nanoparticles and consequently a decrease in the PMF. These results provide valuable insights into the mechanism of interactions of kaolinite nanoplatelets in thermodynamic conditions relevant to clay dispersions, as occurring in tailings produced by the process of hot water extraction of bitumen from oil sands and other mining tailings.

An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.

A theory based on the exponential approximation of the liquid-state theory is applied to study prop erties of several models of one-component Yukawa plasma characterized by different values of the screening parameter z. The results of the new theory are compared to the results of a conventional theory, which is based on the first-order mean spherical approximation, and to the results of a Monte
Carlo simulation. The new theory shows improvements in the predictions for the thermodynamic and structural properties of Yukawa plasmas with high and intermediate values of the screening parameter, z, and coupling parameter, . For low values of z and , the new theory is comparable in accuracy to the conventional theory, which in turn agrees well with the results of the Monte Carlo simulation.

A perturbation approach based on the first-order mean-spherical approximation (FMSA) is proposed. It con-
sists in adopting a hard-sphere plus short-range attractive Yukawa fluid as the novel reference system, over
which the perturbative solution of the Ornstein-Zernike equation is performed. A choice of the optimal range
of the reference attraction is discussed. The results are compared against conventional FMSA/HS theory and
Monte-Carlo simulation data for compressibility factor and vapor-liquid phase diagrams of the medium-ranged
Yukawa fluid. The proposed theory keeps the same level of simplicity and transparency as the conventional
FMSA/HS approach does, but turns out to be more accurate.

Exponential approximation based on the first order mean spherical approximation (FMSA) is applied to the
study of the structure and thermodynamics of hard-core repulsive Yukawa fluids. The proposed theory utilizes
an exponential enhancement of the analytical solution of the FMSA due to Tang and Lu [ J. Chem. Phys., 1993, 99,
9828] for the radial distribution function. From comparison with computer simulation data we have shown that
at low density and low temperature conditions, where original FMSA theory fails, the FMSA-based exponential
theory predicts a significant improvement.

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.