Statistical mechanics of binary mixture adsorption in metal-organic frameworks in the osmotic ensemble

Models of adsorption-induced deformation: ordered materials and beyond

Adsorption-induced deformation is a change in geometrical dimensions of an adsorbent material caused by gas or liquid adsorption on its surface. This phenomenon is universal and sensitive to adsorbent properties, which makes its prediction a challenging task. However, the pure academic interest is complemented by its importance in a number of engineering applications with porous materials characterization among them. Similar to classical adsorption-based characterization methods, the deformation-based ones rely on the quality of the underlying theoretical framework. This fact stimulates the recent development of qualitative and quantitative models toward the more detailed description of a solid material, e.g. account of non-convex and corrugated pores, calculations of adsorption stress in realistic three-dimension solid structures, the extension of the existing models to new geometries, etc. The present review focuses on the theoretical description of adsorption-induced deformation in micro and mesoporous materials. We are aiming to cover recent theoretical works describing the deformation of both ordered and disordered porous bodies.

Removal of 4-chloro-2-methylphenoxyacetic acid from water by MIL-101(Cr) metal-organic framework: kinetics, isotherms and statistical models

Effective removal of 4-chloro-2-methylphenoxyacetic acid (MCPA), an emerging agrochemical contaminant in water with carcinogenic and mutagenic health effects has been reported using hydrothermally synthesized MIL-101(Cr) metal-organic framework (MOF). The properties of the MOF were ascertained using powdered X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, thermal gravimetric analysis (TGA), field emission scanning electron microscopy (FESEM) and surface area and porosimetry (SAP). The BET surface area and pore volume of the MOF were 1439 m2 g-1 and 0.77 cm3 g-1, respectively. Artificial neural network (ANN) model was significantly employed for the accurate prediction of the experimental adsorption capacity (qe ) values with minimal error. A rapid removal of the pollutant (99%) was recorded within short time (approx. 25 min), and the reusability of the MOF (20 mg) was achieved up to six cycles with over 90% removal efficiency. The kinetics, isotherm and thermodynamics of the process were described by the pseudo-second-order, Freundlich and endothermic adsorption, respectively. The adsorption process is spontaneous based on the negative Gibbs free energy values. The significant correlation between the experimental findings and simulation results suggests the great potential of MIL-101(Cr) for the remediation of MCPA from water matrices.

Statistical Mechanical Model of Gas Adsorption in a Metal-Organic Framework Harboring a Rotaxane Molecular Shuttle

Metal-organic frameworks (MOFs) are modular and tunable nanoporous materials with applications in gas storage, separations, and sensing. Integrating flexible/dynamic, gas-responsive components into MOFs can give them unique or enhanced adsorption properties. Here, we explore the adsorption properties that could be imparted to a MOF by a rotaxane molecular shuttle (RMS) in its pores. In the unit cell of an RMS-MOF, a macrocyclic wheel is mechanically interlocked with a strut of the MOF scaffold. The wheel shuttles between stations on the strut that are also gas adsorption sites. At a level of abstraction similar to the seminal Langmuir adsorption model, we pose and analyze a simple statistical mechanical model of gas adsorption in an RMS-MOF that accounts for (i) wheel/gas competition for sites on the strut and (ii) gas-induced changes in the configurational entropy of the shuttling wheel. We determine how the amount of gas adsorbed, the position of the wheel, and the differential energy of adsorption depend on temperature, pressure, and the interactions of the gas and wheel with the stations on the strut. Our model reveals that, compared to a rigid, Langmuir material, the chemistry of the RMS-MOF can be tuned to render gas adsorption more or less temperature sensitive and to release more or less heat upon adsorption. The model also uncovers that, if gas-wheel competition for a station is fierce, temperature influences the position of the wheel differently depending on the amount of gas adsorbed.

Exact matrix treatment of the statistical mechanics of adsorption of large aromatic molecules on graphene

Experimental studies of adsorption from solution of the large aromatic molecules 1,2-dihydroxybenzene (catechol) and phenyl hydroquinone on graphene nanoplatelets show that at low coverage adsorption is followed by a transition which occurs from adsorbed molecules in flat to more vertically oriented states. Catechol adsorption isotherms exhibit 2 plateaus while phenyl hydroquinone shows 3 plateaus indicating 2 and 3 active conformers respectively participating in the adsorption process. Modelling such adsorption isotherms presents a challenge. Here, an exact matrix treatment of the statistical mechanics of a one-dimensional model of adsorption of catechol and dihydroquinone on graphene nanoplatelets is presented. The theoretical adsorption isotherms successfully reproduce all the features of both the catechol and dihydroquinone experimental adsorption isotherms. As suggested by the experimentalists, our theoretical model demonstrates that adsorbed phenyl hydroquinone molecules adopt a flat orientation at low concentrations and an edge orientation at higher coverage before eventually adopting a vertical configuration. Both catechol and phenyl hydroquinone can be described by our interconvertible monomer-dimer-trimer model. The theoretical adsorption isotherms obtained show several plateaus reflecting the types of conformer on the graphene surface.

Metal-Organic Framework Nanoparticles Induce Pyroptosis in Cells Controlled by the Extracellular pH

Ion homeostasis is essential for cellular survival, and elevated concentrations of specific ions are used to start distinct forms of programmed cell death. However, investigating the influence of certain ions on cells in a controlled way has been hampered due to the tight regulation of ion import by cells. Here, it is shown that lipid-coated iron-based metal-organic framework nanoparticles are able to deliver and release high amounts of iron ions into cells. While high concentrations of iron often trigger ferroptosis, here, the released iron induces pyroptosis, a form of cell death involving the immune system. The iron release occurs only in slightly acidic extracellular environments restricting cell death to cells in acidic microenvironments and allowing for external control. The release mechanism is based on endocytosis facilitated by the lipid-coating followed by degradation of the nanoparticle in the lysosome via cysteine-mediated reduction, which is enhanced in slightly acidic extracellular environment. Thus, a new functionality of hybrid nanoparticles is demonstrated, which uses their nanoarchitecture to facilitate controlled ion delivery into cells. Based on the selectivity for acidic microenvironments, the described nanoparticles may also be used for immunotherapy: the nanoparticles may directly affect the primary tumor and the induced pyroptosis activates the immune system.

Calculation of the water-octanol partition coefficient of cholesterol for SPC, TIP3P, and TIP4P water

We present a numerical study of the relative solubility of cholesterol in octanol and water. Our calculations allow us to compare the accuracy of the computed values of the excess chemical potential of cholesterol for several widely used water models (SPC, TIP3P, and TIP4P). We compute the excess solvation free energies by means of a cavity-based method [L. Li et al., J. Chem. Phys. 146(21), 214110 (2017)] which allows for the calculation of the excess chemical potential of a large molecule in a dense solvent phase. For the calculation of the relative solubility ("partition coefficient," log₁₀ P o / w ) of cholesterol between octanol and water, we use the OPLS/AA force field in combination with the SPC, TIP3P, and TIP4P water models. For all water models studied, our results reproduce the experimental observation that cholesterol is less soluble in water than in octanol. While the experimental value for the partition coefficient is log₁₀ P o / w = 3.7, SPC, TIP3P, and TIP4P give us a value of log₁₀ P o / w = 4.5, 4.6, and 2.9, respectively. Therefore, although the results for the studied water models in combination with the OPLS/AA force field are acceptable, further work to improve the accuracy of current force fields is needed.

Predicting the Features of Methane Adsorption in Large Pore Metal-Organic Frameworks for Energy Storage

Currently, metal-organic frameworks (MOFs) are receiving significant attention as part of an international push to use their special properties in an extensive variety of energy applications. In particular, MOFs have exceptional potential for gas storage especially for methane and hydrogen for automobiles. However, using theoretical approaches to investigate this important problem presents various difficulties. Here we present the outcomes of a basic theoretical investigation into methane adsorption in large pore MOFs with the aim of capturing the unique features of this phenomenon. We have developed a pseudo one-dimensional statistical mechanical theory of adsorption of gas in a MOF with both narrow and large pores, which is solved exactly using a transfer matrix technique in the Osmotic Ensemble (OE). The theory effectively describes the distinctive features of adsorption of gas isotherms in MOFs. The characteristic forms of adsorption isotherms in MOFs reflect changes in structure caused by adsorption of gas and compressive stress. Of extraordinary importance for gas storage for energy applications, we find two regimes of Negative gas adsorption (NGA) where gas pressure causes the MOF to transform from the large pore to the narrow pore structure. These transformations can be induced by mechanical compression and conceivably used in an engine to discharge adsorbed gas from the MOF. The elements which govern NGA in MOFs with large pores are identified. Our study may help guide the difficult program of work for computer simulation studies of gas storage in MOFs with large pores.

Addressing hysteresis and slow equilibration issues in cavity-based calculation of chemical potentials

In this paper, we explore the strengths and weaknesses of a cavity-based method to calculate the excess chemical potential of a large molecular solute in a dense liquid solvent. Use of the cavity alleviates some technical problems associated with the appearance of (integrable) divergences in the integrand during alchemical particle growth. The excess chemical potential calculated using the cavity-based method should be independent of the cavity attributes. However, the performance of the method (equilibration time and the robustness) does depend on the cavity attributes. To illustrate the importance of a suitable choice of the cavity attributes, we calculate the partition coefficient of pyrene in toluene and heptane using a coarse-grained model. We find that a poor choice for the functional form of the cavity may lead to hysteresis between growth and shrinkage of the cavity. Somewhat unexpectedly, we find that, by allowing the cavity to move as a pseudo-particle within the simulation box, the decay time of fluctuations in the integrand of the thermodynamic integration can be reduced by an order of magnitude, thereby increasing the statistical accuracy of the calculation.