Rapid analysis of phase behavior with density functional theory. II. Capillary condensation in disordered porous media

Cationic microcrystalline cellulose - Montmorillonite composite aerogel for preconcentration of inorganic anions from dairy wastewater

Development of efficient adsorbents to inorganic anions as a solid phase extraction (SPE) material is highly desirable for chromatographic analysis and pollution control. In this work we developed a new hybrid cationic microcrystalline cellulose aerogel composite. Cationic cetylpyridinium imbedded montmorillonite (CPC-MT) was uniformly entrapped in microcrystalline cellulose (MCC) to enhance anionic adsorption efficiency and mechanical stability. The developed CPC-MT@MCC aerogel was used as an SPE adsorbent for anions from dairy wastewater by coupling with ion-column chromatography. Further quaternized CPC-MT@MCC aerogel (CPC-MT@QMCC) showed unique low density (10.6 mg cm^-3), large specific surface area (320 m² g^-1), porosity 70%, 800 mg g^-1 nitrate adsorption capacity within 60 min and ease of elution in alkaline solutions. The CPC-MT@QMCC aerogel showed efficient regeneration and reuse performances for up to 10 cycles. More importantly, a dynamic binding efficiency of 710 mg g^-1 highlights its excellent performance for practical applications. 96% of nitrate anion from environmental manure wastewater samples were adsorbed with 98.7% recovery. A good linear relationship was obtained in the range of 0.01-10 mg L^-1 and the limits of detection was 0.5 mg L^-1 using CPC-MT@QMCC aerogel as a preconcentration column. The successful synthesis of such intriguing and economic CPC-MT@QMCC aerogel may provide a promising matrix for high-performance and high efficiency chromatographic media.

The Effect of Topology on Phase Behavior under Confinement

This work studies how morphology (i.e., the shape of a structure) and topology (i.e., how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (cDFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These cDFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the phase behavior of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a continuous or a discrete (first-order) transition.

Effect of capillary condensation on gas transport properties in porous media

We investigate the effect of capillary condensation on gas diffusivity in porous media composed of randomly packed spheres with moderate wettability. To simulate capillary phenomena at the pore scale while retaining complex pore networks of the porous media, we employ density functional theory (DFT) for coarse-grained lattice gas models. The lattice DFT simulations reveal that capillary condensations preferentially occur at confined pores surrounded by solid walls, leading to the occlusion of narrow pores. Consequently, the characteristic lengths of the partially wet structures are larger than those of the corresponding dry structures with the same porosities. Subsequent gas diffusion simulations exploiting the mean-square displacement method indicate that while the effective diffusion coefficients significantly decrease in the presence of partially condensed liquids, they are larger than those in the dry structures with the same porosities. Moreover, we find that the ratio of the porosity to the tortuosity factor, which is a crucial parameter that determines an effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.

Scalable Fabrication of Electrospun Nanofibrous Membranes Functionalized with Citric Acid for High-Performance Protein Adsorption

Fabricating protein adsorbents with high adsorption capacity and appreciable throughput is extremely important and highly desired for the separation and purification of protein products in the biomedical and pharmaceutical industries, yet still remains a great challenge. Herein, we demonstrate the synthesis of a novel protein adsorbent by in situ functionalizing eletrospun ethylene-vinyl alcohol (EVOH) nanofibrous membranes (NFM) with critic acid (CCA). Taking advantage of the merits of large specific surface area, highly tortuous open-porous structure, abundant active carboxyl groups introduced by CCA, superior chemical stability, and robust mechanical strength, the obtained CCA-grafted EVOH NFM (EVOH-CCA NFM) present an excellent integrated protein (take lysozyme as the model protein) adsorption performance with a high capacity of 284 mg g(-1), short equilibrium time of 6 h, ease of elution, and good reusability. Meanwhile, the adsorption performance of EVOH-CCA NFM can be optimized by regulating buffer pH, ionic strength, and initial concentration of protein solutions. More importantly, a dynamic binding efficiency of 250 mg g(-1) can be achieved driven solely by the gravity of protein solution, which matches well with the demands of the high yield and energy conservation in the actual protein purification process. Furthermore, the resultant EVOH-CCA NFM also possess unique selectivity for positively charged proteins which was confirmed by the method of sodium dodecyl sulfate polyacrylamide gel electrophoresis. Significantly, the successful synthesis of such intriguing and economic EVOH-CCA NFM may provide a promising candidate for the next generation of protein adsorbents for rapid, massive, and cost-effective separation and purification of proteins.

In situ cross-linked and highly carboxylated poly(vinyl alcohol) nanofibrous membranes for efficient adsorption of proteins

In situ cross-linked and highly carboxylated poly(vinyl alcohol) nanofibrous membranes for lysozyme adsorption were fabricated by a combination of electrospinning and graft polymerization of poly(vinyl alcohol) and maleic anhydride.

Capillary condensation of adsorbates in porous materials

Hysteresis in capillary condensation is important for the fundamental study and application of porous materials, and yet experiments on porous materials are sometimes difficult to interpret because of the many interactions and complex solid structures involved in the condensation and evaporation processes. Here we make an overview of the significant progress in understanding capillary condensation and hysteresis phenomena in mesopores that have followed from experiment and simulation applied to highly ordered mesoporous materials such as MCM-41 and SBA-15 over the last few decades.

Algorithms for the computation of solutions of the Ornstein-Zernike equation

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Capillary phase transitions of linear and branched alkanes in carbon nanotubes from molecular simulation

Capillary phase transitions of linear (from C(1) to C(12)) and branched (C(5) isomers) alkanes in single-walled carbon nanotubes have been investigated using the gauge-cell Monte Carlo simulation. The isotherm at a supercritical temperature increases monotonically with chemical potential and coincides with that from the traditional grand canonical Monte Carlo simulation, whereas the isotherm at a subcritical temperature exhibits a sigmoid van der Waals loop including stable, metastable, and unstable regions. Along this loop, the coexisting phases are determined using an Maxwell equal-area construction. A generic confinement effect is found that reduces the saturation chemical potential, lowers the critical temperature, increases the critical density, and shrinks the phase envelope. The effect is greater in a smaller diameter nanotube and is greater in a nanotube than in a nanoslit.

Prediction of phase behavior of nanoconfined Lennard-Jones fluids with density functional theory based on the first-order mean spherical approximation

The recently proposed first-order mean spherical approximation (FMSA) [Y. Tang, J. Chem. Phys. 121, 10605 (2004)] for inhomogeneous fluids is extended to study the phase behavior of nanoconfined Lennard-Jones fluids, which is consistent with the phase equilibria calculation of the corresponding bulk fluid. With a combination of fundamental measure theory, FMSA provides Helmholtz free energy and direct correlation function to formulate density functional theory, which implementation is as easy as the mean-field theory. Following previous success in predicting density profiles inside slit pores, this work is focused specially on the vapor-liquid equilibrium of the Lennard-Jones fluids inside these pores. It is found that outside the critical region FMSA predicts well the equilibrium diagram of slit pores with the sizes of 5.0, 7.5, and 10 molecular diameters by comparing with available computer simulation data. As a quantitative method, FMSA can be treated as an extension from its bulk calculation, while the mean-field theory is only qualitative, as its bulk version.

Modeling fluid diffusion using the lattice density functional theory approach: counterdiffusion in an external field

The dependence of the diffusivity on temperature, pressure, and composition is not understood well; consequently, data is preferred significantly over correlations in most practical situations. Even in dilute gases, the contributions of attractions and repulsions to the diffusivity are difficult to understand on a molecular level without performing simulations. We have developed a Lattice Density Functional Theory (LDFT) approach for modeling diffusion to supplement existing methods that are very rigorous but computationally demanding. The LDFT approach is analogous to the van der Waals equation in how it accounts for molecular interactions in that it has first-order corrections to ideal behavior; it is an extension of the Equilibrium LDFT for adsorption and phase behavior. In this work, the LDFT approach is presented and demonstrated by modeling the problem of color counterdiffusion in an externally-applied potential field. This potential field, in combination with the intermolecular potential function, creates a diffusion regime in which repulsions cause oscillations in the density profile. Using the LDFT approach, the oscillations were described and attributed to nearest-neighbor and next nearest-neighbor interactions. The LDFT approach gives qualitative and quantitative agreement with dual control-volume Grand Canonical Molecular Dynamics simulations.

Water adsorption in disordered mesoporous silica (Vycor) at 300K and 650K: A Grand Canonical Monte Carlo simulation study of hysteresis

This numerical simulation paper focuses on the adsorption/desorption of water in disordered mesoporous silica glasses (Vycor-like). The numerical adsorbent was previously obtained by off lattice method, and was shown to reproduce quite well the micro- and mesotextural properties of real Vycor, as well as morphological (pore size distribution) and topological (pore interconnections) disorder. The water-water interactions are described by the SPC model while water-silica interactions are calculated in the framework of the PN-TrAZ model. The water adsorption/desorption isotherms and the configurational energies are calculated by the Grand Canonical Monte Carlo simulation method. The low pressure results compare well with experiments, showing the good transferability of the intermolecular potential. It is shown that if the hysteresis loop observed in the adsorption/desorption isotherm is considered as a true phase transition (which is actually still an open question in the case of disordered porous materials), then it is possible to calculate the grand potential by applying the thermodynamic integration scheme. The grand potential is shown to be multivalued for low (subcritical) temperature, and continuous for high (supercritical) temperature. A coexistence point is found within the hysteresis loop, actually close to the vertical desorption line. Below the equilibrium chemical potential, the gaslike branch is stable whereas the liquidlike branch is metastable. The situation is reversed above the coexistence point.

Torsion-induced phase transitions in fluids confined between chemically decorated substrates

In this paper we investigate the phase behavior of a "simple" fluid confined to a chemically heterogeneous slit pore of nanoscopic width s(z) by means of Monte Carlo simulations in the grand canonical ensemble. The fluid-substrate interaction is purely repulsive except for elliptic regions of semiaxes A and B attracting fluid molecules. On account of the interplay between confinement (i.e., s(z)) and chemical decoration, three fluid phases are thermodynamically permissible, namely, gaslike and liquidlike phases and a "bridge phase" where the molecules are preferentially adsorbed by the attractive elliptic patterns and span the gap between the opposite substrate surfaces. Because of their lack of cylindrical symmetry, bridge phases can be exposed to a torsional strain 0<or=theta;<or=pi/2 by rotating the upper substrate while holding the lower one in position. Depending on the thermodynamic state of the confined fluid, torsion-induced first-order phase transitions are feasible during which a bridge phase may be transformed into either a gaslike (evaporation) or a liquidlike phase (condensation). Since the chemical patterns decorating the substrates are finite in size, system properties are not translationally invariant in any spatial direction. Therefore, in order to study these phase transitions, we resorted to the thermodynamic integration scheme developed earlier to calculate the grand potential Omega in a system of low symmetry.

Nanoscopic liquid bridges exposed to a torsional strain

In this paper we investigate the response to a torsional strain of a molecularly thin film of spherically symmetric molecules confined to a chemically heterogeneous slit pore by means of Monte Carlo simulations in the grand canonical ensemble. The slit pore comprises two identical plane-parallel solid substrates, the fluid-substrate interaction is purely repulsive except for elliptic regions attracting fluid molecules. Under favorable thermodynamic conditions the confined film consists of fluid bridges where the molecules are preferentially adsorbed by the attractive elliptic regions, and span the gap between the opposite substrate surfaces. By rotating the upper substrate while holding the lower one in position, bridge phases can be exposed to a torsional strain 0< or =theta< or =pi/2 and the associated torsional stress T(theta) of the (fluidic) bridge phases can be calculated from molecular expressions. The obtained stress curve T(theta)(theta) is qualitatively similar to the one characteristic of sheared confined films: as the torsion strain increases, T(theta) rises to a maximum (yield point) and then decays monotonically to zero. By changing the ellipses' aspect ratio while keeping their area constant, we also investigate the influence of the attractive elliptic patterns' shape on T(theta)(theta).

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 Fick's 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.

Capillary condensation and interface structure of a model colloid-polymer mixture in a porous medium

We consider the Asakura-Oosawa model of hard sphere colloids and ideal polymers in contact with a porous matrix modeled by immobilized configurations of hard spheres. For this ternary mixture a fundamental measure density functional theory is employed, where the matrix particles are quenched and the colloids and polymers are annealed, i.e., allowed to equilibrate. We study capillary condensation of the mixture in a small sample of matrix as well as demixing and the fluid-fluid interface inside a bulk matrix. Density profiles normal to the interface and surface tensions are calculated and compared to the case without matrix. Two kinds of matrices are considered: (i) colloid-sized matrix particles at low packing fractions and (ii) large matrix particles at high packing fractions. These two cases show fundamentally different behavior and should both be experimentally realizable. Furthermore, we argue that capillary condensation of a colloidal suspension could be experimentally accessible. We find that in case (ii), even at high packing fractions, the main effect of the matrix is to exclude volume and, to high accuracy, the results can be mapped onto those of the same system without matrix via a simple rescaling.