Lattice density functional theory of molecular diffusion

How 2D Nanoflakes Improve Transport in Mixed Matrix Membranes: Insights from a Simple Lattice Model and Dynamic Mean Field Theory

Mixed matrix membranes (MMMs), incorporating graphene and graphene oxide structural fragments, have emerged as promising materials for challenging gas separation processes. What remains unclear is the actual molecular mechanism responsible for the enhanced permeability and perm-selectivity of these materials. With the fully atomistic models still unable to handle the required time and length scales, here, we employ a simple qualitative model based on the lattice representation of the physical system and dynamic mean field theory. We demonstrate that the performance enhancement results from the flux-regularization impact of the 2D nanoflakes and that this effect sensitively depends on the orientation of the nanoflakes and the properties of the interface between the nanoflakes and the polymer.

Connecting dynamic pore filling mechanisms with equilibrium and out of equilibrium configurations of fluids in nanopores

In the present study, using dynamic mean field theory complemented by grand canonical molecular dynamics simulations, we investigate the extent to which the density distributions encountered during the dynamics of capillary condensation are related to those distributions at equilibrium or metastable equilibrium in a system at fixed average density (canonical ensemble). We find that the states encountered can be categorized as out of equilibrium or quasi-equilibrium based on the magnitude of the driving force for mass transfer. More specifically, in open-ended slit pores, pore filling via double bridging is an out of equilibrium process, induced by the dynamics of the system, while pore filling by single bridge formation is connected to a series of configurations that are equilibrium configurations in the canonical ensemble and that cannot be observed experimentally by a standard adsorption process, corresponding to the grand canonical ensemble. Likewise, in closed cap slits, the formation of a liquid bridge near the pore opening and its subsequent growth while the initially detached meniscus from the capped end remains immobilized are out of equilibrium processes that occur at large driving forces. On the other hand, at small driving forces, there is a continuous acceleration of the detached meniscus from the capped end, which is associated with complete reversibility in the limit of an infinitesimally small driving force.

Application of the dynamic mean field theory to fluid transport in slit pores

We explore the applicability of the lattice model and dynamic mean field theory as a computationally efficient tool to study transport across heterogeneous porous media, such as mixed matrix membranes. As a starting point and to establish some basic definitions of properties analogous to those in the off-lattice systems, we consider transport across simple models of porous materials represented by a slit pore in a chemical potential gradient. Using this simple model, we investigate the distribution of density and flux under steady state conditions, define the permeability across the system, and explore how this property depends on the length of the pore and the solid-fluid interactions. Among other effects, we observe that the flux in the system goes through a maximum as the solid-fluid interaction is varied from weak to strong. This effect is dominated by the behavior of the fluid near the walls and is also confirmed by off-lattice molecular dynamics simulations. We further extend this study to explore transport across heterogeneous slit pore channels composed of two solids with different values of solid-fluid interaction strengths. We demonstrate that the lattice models and dynamic mean field theory provide a useful framework to pose questions on the accuracy and applicability of the classical theories of transport across heterogeneous porous systems.

Nonequilibrium Steady States in Fluid Transport through Mesopores: Dynamic Mean Field Theory and Nonequilibrium Molecular Dynamics

We present a dynamic mean field theory (DMFT) and nonequilibrium dual control volume grand canonical molecular dynamics (GCMD) simulation study of steady-state fluid transport in slit-shaped mesopores under an applied chemical potential gradient. The main focus is on states where the bulk conditions on one side of the pore would lead to a capillary condensed state in the pore at equilibrium while those on the other side would lead to a vapor state in the pore. This choice of conditions is motivated by certain separation applications in which condensable vapors permeate through mesoporous membranes. Under these circumstances, we have found partially filled states with a liquid-like state at the high chemical potential end of the pore and a vapor-like state at the low chemical potential end. This phenomenon is accompanied by hysteresis. The existence of partially filled states has been hypothesized in previous work but the present paper reveals them as an emergent feature of the systems. We find that predictions of DMFT are in good qualitative agreement with the overall GCMD results. However, the GCMD results demonstrate that the transport is faster through the partially filled pore than through the unfilled pore, a feature not captured by DMFT.

Gradient Energy Band Driven High-Performance Self-Powered Perovskite/CdS Photodetector

Self-powered photodetectors are highly desired to meet the great demand in applications of sensing, communication, and imaging. Manipulating the carrier separation and recombination is critical to achieve high performance. In this paper, a self-powered photodetector based on the integrated gradient O-doped CdS nanorod array and perovskite is presented. Through optimizing the degree of continuous built-in band bending in the gradient-O CdS, the photodetector demonstrates a remarkable detectivity of 2.1 × 10¹³ Jones. Under the self-powered voltage mode, the responsivity can be as high as 0.48 A W^-1 , and the rise and decay time are 0.54/2.21 ms. The comprehensive performance is comparable and even better than reported perovskite and other types of self-powered photodetectors. The improved mechanism reveals that the gradient band bending promotes the photogenerated carrier transfer and hinders the recombination at the interface.

A comparison of dynamic mean field theory and grand canonical molecular dynamics for the dynamics of pore filling and capillary condensation of fluids in mesopores

We use results from grand canonical molecular dynamics (GCMD) to test the predictions from dynamic mean field theory (DMFT) for the pore filling and capillary condensation mechanisms of a fluid confined in slit shaped mesopores. The theory predicts that capillary condensation occurs by a nucleation process in which a liquid bridge forms between the two walls, and the pore is filled via the growth of this bridge. For longer pores, multiple bridging is seen. These mechanisms are confirmed by the molecular dynamics simulations. The primary difference between the theory and simulations lies in the role of fluctuations. DMFT predicts a single nucleation time and location, while in GCMD (and in nature) a distribution of nucleation times and locations is seen.

Modeling the influence of side stream and ink bottle structures on adsorption/desorption dynamics of fluids in long pores

We apply dynamic mean field theory to study relaxation dynamics for lattice models of fluids confined in linear pores with side streams and with ink bottle structures. Our results show several mechanisms for how the pore structure affects the dynamics, and these are amplified in longer pores. An important conclusion of this work is that features such as side streams and ink bottle segments can substantially slow the equilibration of fluids confined in long pore systems where the pore lengths can be more than 100 micrometers, such as in porous silicon. This may make it difficult to properly equilibrate these systems for states close to those where the pores should be completely filled with liquids. The presence of trapped bubbles in the system may change the desorption characteristics of the system and the shape of the hysteresis loops.

Filling dynamics of closed end nanocapillaries

We have studied the filling dynamics of model capillaries using dynamic mean field theory for a confined lattice gas and Kawasaki dynamics simulations. We have found two different scenarios for filling of capped nanocapillaries from the vapor phase. As compared to channels with macroscopic width, in which the filling process occurs by the detachment of the meniscus from the cap, in mesoscopic channels there is an alternative mechanism associated with the spontaneous condensation of the liquid close to the pore opening and its subsequent growth toward the closed pore end. We show that these two scenarios have totally different filling dynamics, providing an additional mechanism for slow capillary condensation kinetics in nanoscopic objects.

Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials

We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes.

Nanobubble stability induced by contact line pinning

The origin of surface nanobubbles stability is a controversial topic since nanobubbles were first observed. Here, we propose a mechanism that the three-phase contact line pinning, which results from the intrinsic nanoscale physical roughness or chemical heterogeneities of substrates, leads to stable surface nanobubbles. Using the constrained lattice density functional theory (LDFT) and kinetic LDFT, we prove thermodynamically and dynamically that the state with nanobubbles is in fact a thermodynamical metastable state. The mechanism consistent with the classical nucleation theory can interpret most of experimental characteristics for nanobubbles qualitatively, and predict relationships among the gas-side nanobubble contact angle, nanobubble size, and chemical potential.

Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels

We present a theoretical study of spontaneous imbibition of liquid (4)He in silica aerogels focusing on the effect of porosity on the fluid dynamical behavior. We adopt a coarse-grained three-dimensional lattice-gas description like in previous studies of gas adsorption and capillary condensation and use a dynamical mean-field theory, assuming that capillary disorder predominates over permeability disorder as in recent phase-field models of spontaneous imbibition. Our results reveal a remarkable connection between imbibition and adsorption as also suggested by recent experiments. The imbibition front is always preceded by a precursor film, and the classical Lucas-Washburn √t scaling law is generally recovered, although some deviations may exist at large porosity. Moreover, the interface roughening is modified by wetting and confinement effects. Our results suggest that the interpretation of the recent experiments should be revised.

Rediscovering the problem of interpretation of chromatographically determined enthalpy and entropy of adsorption of different adsorbates on carbon materials

Adsorbate-adsorbent and adsorbate-adsorbate interactions having decisive influence on the distribution of adsorbate between gas-solid phases in inverse gas chromatography (IGC) have been thermodynamically explained. Specific retention volumes, second adsorption virial coefficients and Kováts retention indices, likewise their dependencies on column temperature, T, number of carbon atoms, n(C) (or methylene groups CH(2)) and mutual ones have been briefly presented. The results of the molar differential enthalpy and entropy of adsorption obtained for different carbon materials employing inverse gas chromatography have been collected and interpreted. An attempt has been made to elucidate abnormal behaviour of the specific and net retention volumes, the second adsorption virial coefficients and the Kováts retention indices, e.g., the magnitudes on which the values of the afore-mentioned thermodynamic values have been determined and compared. The detailed analysis of the errors associated with the experimental parameters necessary for calculating retention volumes, second adsorption virial coefficients and Kováts retention indices has been presented.

Self-Assembly of T-Structures in Molecular Fluids

A lattice density functional approach is used to describe the equilibrium assembly of three types of anisotropic patchy particles into a T-structure. The T-structure is comprised of one three-patch, three two-patch, and three one-patch particles. All patches are positioned orthogonal to each other. Temperature, particle concentration, and interaction energy ranges are determined that lead to T-structure formation. T-structure formation is investigated for two types of two-patch particles: Case 1 uses two identical patches and Case 2 employs two differing patches. Sets of parameters leading to T-structure assembly are determined for both cases. We find that in Case 1 the symmetric two-patch particle enforces T-structure formation, while the asymmetric two-patch particle in Case 2 leads to formation of chains, dimers, and incorrect and extended T-structures in addition to the T-structure. Synthetic strategies for both cases are discussed and reveal that Case 2 presents the more straightforward synthetic route.

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.

Diffusion Equation for Interacting Particles

A new approach to molecular diffusion is developed using density functionals for fluxes and the Metropolis algorithm in the mass balance equation. This procedure results in a new equation for diffusion of interacting particles which has multiple solutions and gives density distributions for coexisting and metastable phases. It is shown that the diffusion of interacting molecules is driven by two variables: the density gradient of molecules and the density of molecule-vacancy pairs ("pseudoparticles").

Cosorption effect in gas chromatography: flow fluctuations caused by adsorbing carrier gases

Adsorbing carrier gases have a number of advantages in analytical and preparative gas chromatography, such as clearer detector signals and higher column efficiencies. This work shows that adsorbing carrier gases also may be useful because they cause the mobile phase flow rate to become unsteady after injecting a small amount of sample. This work shows that a 100 microL sample of helium can liberate enough carbon dioxide carrier gas from a zeolite 5A packed column at 373 K, that the departure from the steady-state flow rate had an upper lobe area of 586 microL of carrier gas. This was confirmed by coupling a modified Langmuir kinetic model with the Ergun equation.