Marc D. Donohue

Density functional theory predictions of adsorption isotherms with hysteresis loops

Abstract Adsorption equilibrium is calculated for slit-like pores of various sizes using lattice density functional theory (LDFT). It is shown that LDFT can predict adsorption isotherms with hysteresis loops and that different types of hysteresis loops can be obtained by varying energies of adsorbate–adsorbate and adsorbate–adsorbent interactions for different widths and lengths of slit-like pores. LDFT also predicts hysteresis loops with multiple steps. Though such behavior has not been part of the characterization of isotherms with hysteresis loops, there are experimental data that exhibit steps within hysteresis loops.

Supercritical phase behavior: The entrainer effect

Abstract One of the keys to lowering the cost of supercritical extraction processes is to find appropriate cosolvents (entrainers) that maintain or improve selectivity while increasing the solubility. This solubility enhancement is of great commercial interest; however until recently there was no way to predict either for which systems or under what conditions it would occur. We show that the entrainer effect is caused by a chemical association between the cosolvent and the solute. Further, we present a model that explicitly accounts for these chemical associations. Finally, we show that data and analysis techniques already established for associations in liquid solvents (especially spectroscopic and solvatochromic techniques) can be used to make qualitative predictions of the entrainer effect in a supercritical fluid.

Adsorption isotherms for microporous adsorbents

Adsorption equilibria in slit pores are calculated using an analytic solution of the classical Ono-Kondo equation with modified boundary conditions. A new equation is developed for isotherms of gas adsorption on microporous adsorbents. This equation describes isotherms of Type I in the IUPAC classification scheme for temperatures below the critical point and also describes the unusual adsorption of supercritical fluids. This new equation predicts an isotherm that follows the behavior of the Dubinin-Radushkevich (DR) isotherm for relative pressures pps, between 10−1 and 10−5. However, while the DR equation does not give correct behavior either for very low pressures or for moderate to high pressures, this new equation is valid over the whole range of relative pressures. Results obtained are compared with experimental data for adsorption of nitrogen, carbon dioxide, hydrogen sulfide, propane, carbon tetrachloride, ethanol, benzene, iso-octane, n-butane, and methane on activated carbon.

Vapor-liquid equilibria for binary mixtures of carbon dioxide with benzene, toluene and p-xylene

Abstract Vapor-liquid equilibrium data for carbon dioxide - benzene, carbon dioxide - toluene, and carbon dioxide - p-xylene were measured for pressures up to 6.5 MPa, and at temperatures of 353 K, 373 K, and 393 K. The solubility of benzene in the dense carbon dioxide vapor phase is higher than that of either toluene or p-xylene. In the liquid phase, carbon dioxide is more soluble in p-xylene than in toluene or benzene. The experimental data obtained were compared with calculations from three correlations: the Peng-Robinson equation, the UNIFAC activity coefficient correlation, and the Perturbed-Anisotropic- Chain Theory (PACT). All three correlations predict phase compositions in good agreement with the experimental data.

Extension of the associated perturbed anisotropic chain theory to mixtures with more than one associating component

Abstract The Associated Perturbed Anisotropic Chain Theory (APACT), a theory useful for calculation of equilibrium thermodynamic properties for fluid mixtures presented recently by Ikonomou and Donohue has been extended to treat multicomponent mixtures in which two or more components associate. Mixtures containing non-associating components (diluents) also can be treated. Association equilibria for each component hydrogen bonding to itself as well as for cross-association between associating components are considered. Following an approach similar to that used previously in the derivation of APACT, a closed-form equation of state has been derived. Preliminary results show that APACT does well in fitting phase equilibrium data for binary mixtures involving alcohols and water with small values of k ij . The fits are not as good, however, for systems containing small molecules (water and methanol) and the reasons for this shortcoming are discussed.

Bubble nucleation mechanisms of liquid droplets superheated in other liquids

Abstract An investigation was made into the mechanism of nucleating a vapor bubble at a liquid—liquid interface. Depending on the magnitudes of the surface tensions of both liquids and of the interfacial tension, nucleation occurs totally in one of the liquid phases or at the interface. In the usual case, i.e., when a volatile liquid is superheated in a nonvolatile liquid, this means that the nucleation occurs homogeneously in the superheated liquid, at the interface, or by blowing bubbles into the nonvolatile liquid. In this paper we derive an expression for the rate of bubble formation at a liquid—liquid interface and also extend nucleation theory to describe the phenomena of bubble blowing nucleation. To test our theoretical predictions, experiments were made in which small droplets of n-pentane were superheated in ethylene glycol (homogeneous nucleation), and small droplets of water were superheated in a fluorinated ether, Freon E-9, (bubble blowing nucleation).

Lattice density functional theory of molecular diffusion

A density functional theory of diffusion is developed for lattice fluids with molecular flux as a functional of the density distribution. The formalism coincides exactly with the generalized Ono-Kondo density functional theory when there is no gradient of chemical potential, i.e., at equilibrium. Away from equilibrium, it gives Ficks first law in the absence of a potential energy gradient, and it departs from Fickian behavior consistently with the Maxwell-Stefan formulation. The theory is applied to model a nanopore, predicting nonequilibrium phase transitions and the role of surface diffusion in the transport of capillary condensate.

A new classification of isotherms for Gibbs adsorption of gases on solids

A systematic analysis of adsorption behavior has been performed. The results are presented here as a new classification of isotherms for fluid/solid equilibria.

The Perturbed-Soft-Chain Theory: an equation of state based on the Lennard-Jones potential

Abstract Perturbed-Soft-Chain theory is a perturbation theory for chain-like molecules which uses a soft-core (Lennard-Jones) intermolecular potential energy function. Three pure-component parameters are required for the PSCT equation of state. These parameters are reported for 13 normal alkanes and 25 other compounds. The PSCT equation of state does very well in predicting the thermodynamic properties of molecules over a wide range of fluid densities and molecular complexities. The PSCT equation of state is tested against the PHCT and Peng-Robinson equation of state by determining the errors in calculated liquid-densities and vapor pressures for normal alkanes. The PSCT equation of state predicts these properties slightly better than the PHCT equation of state and much better than the Peng-Robinson equation of state.

A new model for lattice systems

A new model is derived for lattice systems (lattice gas and binary mixtures of monomers). This model is based on a generalization to three dimensions of the Ono–Kondo equations for the density profile near a flat surface. The internal energy is calculated and compared with previous models. Unlike many previous theories, this new model has the correct limiting behavior at infinite dilution, at high densities, when the interchange energy goes to zero and for the lattice gas. In addition, it displays the correct behavior for systems with very strong interactions (such as hydrogen bonds) in that it predicts that the energy saturates to a constant value at a low density. For one‐component, monomer systems, the new theory also describes simulation data for square‐well (off‐lattice) molecules better than previous theories.