Gregory L. Aranovich

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.

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.

Effect of cationic polyelectrolyte and surfactant on cohesion and friction in contacts between cellulose fibers

Abstract The methodics and devices are presented for quantitative study of the characteristics of interaction in contact between individual fibers: friction force F in shear test, and cohesion force, i.e. contact strength p in rupture test. In experiments with cellulose fibers in various liquid media, the friction coefficient μ has been estimated, and the molecular component of friction force related only to attraction of fibers, in the absence of any external normal load has been found. The specific free energy of interaction U has been evaluated in measurements using model samples with the nature of surface similar to that of cellulose fibers. The effects of cationic polyelectrolyte and surfactant: polyethyleneimin and tetrabuthylammonium iodid on these parameters have been quantitatively determined. Complicated, non-monotonic (with several extrema) dependence have been estimated between values F , μ , p , U and surfactant concentration C . Comparison of these data with the ζ -potential measurements of cellulose fibers in the same surfactant solutions allows one to propose an explanation of the mechanisms of these polyelectrolyte and surfactant influence on fiber interactions.

Thermodynamic Driving Force for Molecular Diffusion – Lattice Density Functional Theory Predictions

Abstract Ficks first law describes diffusive flux as a linear function of the concentration gradient; its most popular generalization describes flux as a linear function of the chemical potential gradient. This generalization and others have been used for modeling, but the relationships between the flux and the gradients are nonlinear because the coefficients generally depend on state variables. In this paper, lattice density functional theory equations for diffusive flux are recast into linear differential form to explore well-known diffusion equations. This shows that the diffusive flux is related to the gradients of state variables (e.g., to the chemical potential gradient) through integrating factors, much like the heat flux in Clausiuss theorem is related to the difference in entropy. Subsequent analyses show why diffusive flux is more linear with respect to the fugacity gradient than the chemical potential gradient; and that the gradient of another property has linear proportionality to the diffusive flux. This property can appear as the impingement rate onto vacancies and molecules of species whose density gradients can be influenced by diffusion; and it behaves similarly to the chemical potential and the fugacity. The results agree with the theory of non-equilibrium thermodynamics about the conjugate force vectors for the diffusive flux.

Thermodynamic driving force for diffusion: comparison between theory and simulation.

In previous work, lattice density functional theory equations have been recast into differential form to determine a property whose gradient is universally proportional to the diffusive flux. For color counter diffusion, this property appears as the impingement rate onto vacancies and molecules of a species whose density gradient can be influenced by diffusion. Therefore, the impingement rate of a diffusing molecule depends on the mobility of its surroundings. In order to determine the validity of this finding, molecular dynamics simulations of color counter diffusion were performed in which the mobility of the solvent was varied to determine if the flux of the diffusing species responded to the change when all other factors, such as density gradient, available volume, and temperature are held constant.

Anisotropic mean free path in simulations of fluids traveling down a density gradient.

Hard sphere molecular dynamics simulations are used to study the mean free path of molecules traveling down a density gradient at fluid densities ranging between 0.05sigma(-3) and 0.7sigma(-3). Gradients are developed using semipermeable boundaries in the x-direction and, as a result, a net flow develops in the positive x-direction. Over the course of the simulation, the free paths of colliding molecules are calculated and it was determined that the mean free path in the positive x-direction is greater than the mean free path in the negative x-direction at each density studied. These results are compared to the mean free paths in the positive and negative y- and z-directions (in which there is no net flow) and the distribution of free paths for molecules traveling in the positive and negative x-directions gives insight into the physics of the system. In addition, the dependency of the mean free path on speed is studied and compared to kinetic theory predictions. The results have application in the modification of the classical model of diffusion for low density systems undergoing flow in which the mean free path is finite, large, and can be anisotropic.

Pattern of adsorption isotherms in Ono-Kondo coordinates.

The Ono-Kondo lattice density functional theory is used to analyze adsorbate-adsorbate interactions for supercritical systems. In prior work, this approach has been used to study intermolecular interactions in subcritical adsorbed phases, and this has included the study of adsorbate-adsorbate repulsions in the regime of adsorption compression. In this paper, we present the general pattern of adsorption isotherms in Ono-Kondo coordinates; this has not been done in the past. For this purpose, experimental isotherms for adsorption of supercritical fluids (including nitrogen, methane, and carbon dioxide) are plotted in Ono-Kondo coordinates. In addition, we performed Grand Canonical Monte Carlo simulations of adsorption for Lennard-Jones molecules and plotted isotherms in Ono-Kondo coordinates. Our results indicate a pattern of isotherms with regimes of adsorbate-adsorbate attractions at low surface coverage and adsorbate-adsorbate repulsions at high surface coverage. When the generalized Ono-Kondo model is used over a wide range of pressures - from low pressures of the Henrys law regime to supercritical pressures - the slope of the isotherm varies from positive at low pressures to negative at high pressures. The linear sections of these graphs show when the adsorbate-adsorbate interaction energies are approximately constant. When these linear sections have negative slopes, it indicates that the system is in a state of adsorption compression.

Density functional theory calculations of the energy and free energy of anisotropic multicomponent mixtures

A lattice density functional theory for the nonrandom energy for multicomponent mixtures containing monomers with directional interactions is presented. This theory is a simplification and generalization of a lattice density functional theory developed by Aranovich and Donohue (AD) for two-dimensional and three-dimensional mixtures based upon ideas originally proposed for one-dimensional systems by Ono and Kondo. While quite accurate and general, the AD equations could not be integrated analytically to give expressions for the free energy. With an algebraic rearrangement of this model into a sum of a random mixing internal energy and the deviations from random mixing, an expression is obtained that is both accurate and integrable. Comparisons with Monte Carlo simulations confirm the accuracy of the theory. Unusual phase stability boundaries are predicted.