Formation of Periodically Arranged Nanobubbles in Mesopores: Capillary Bridge Formation and Cavitation during Sorption and Solidification in an Hierarchical Porous SBA-15 Matrix

Machine-Learned Free Energy Surfaces for Capillary Condensation and Evaporation in Mesopores

Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores.

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.

The effect of interconnections on gas adsorption in materials with spherical mesopores: A Monte Carlo simulation study

Gas adsorption is a standard method for measuring pore-size distributions of nanoporous materials. This method is often based on assuming the pores as separate entities of a certain simple shape: slit-like, cylindrical, or spherical. Here, we study the effect of interconnections on gas adsorption in materials with spherical pores, such as three-dimensionally ordered mesoporous (3DOm) carbons. We consider interconnected systems with two, four, and six windows of various sizes. We propose a simple method based on the integration of solid-fluid interactions to take into account these windows. We used Monte Carlo simulations to model argon adsorption at the normal boiling point and obtained adsorption isotherms for the range of systems. For a system with two windows, we obtained a remarkably smooth transition from the spherical to cylindrical isotherm. Depending on the size and number of windows, our system resembles both spherical and cylindrical pores. These windows can drastically shift the point of capillary condensation and result in pore-size distributions that are very different from the ones based on a spherical pore model. Our results can be further used for modeling fluids in a system of interconnected pores using Monte Carlo and density functional theory methods.

Adsorption-induced deformation of mesoporous materials with corrugated cylindrical pores

Mesoporous materials play an important role both in engineering applications and in fundamental research of confined fluids. Adsorption goes hand in hand with the deformation of the absorbent, which has positive and negative sides. It can cause sample aging or can be used in sensing technology. Here, we report the theoretical study of adsorption-induced deformation of the model mesoporous material with ordered corrugated cylindrical pores. Using the classical density functional theory in the local density approximation, we compared the solvation pressure in corrugated and cylindrical pores for nitrogen at sub- and super-critical temperatures. Our results demonstrate qualitative differences between solvation pressures in the two geometries at sub-critical temperatures. The deviations are attributed to the formation of liquid bridges in corrugated pores. However, at super-critical temperatures, there is no abrupt bridge formation and corrugation does not qualitatively change solvation pressure isotherms. We believe that these results could help in the analysis of an adsorption-induced deformation of the materials with distorted pores.

Capillary bridge formation between hexagonally ordered carbon nanorods

Capillary condensation within the pore space formed by a hexagonal arrangement of carbon nanorods is investigated using a thermodynamic model. Numerical solution of the corresponding non-linear differential equations predicts two characteristic equilibrium phase transitions corresponding to liquid-bridge formation between adjacent rods, and the subsequent filling of the entire pore space with liquid adsorbate at higher relative pressure, respectively. These separate transitions are predicted for a wide range of porosities, as demonstrated for two non-polar fluids, nitrogen and n-pentane, employing experimentally determined reference isotherms to model the fluid–solid interactions. The theoretical predictions are compared to experimental data for nitrogen and n-pentane adsorption in an ordered mesoporous CMK-3 type material, with the necessary structural parameters obtained from small-angle X-ray scattering. Although the experimental adsorption isotherms do not unambiguously show two separate transitions due to a high degree of structural disorder of the mesopore space, their general trends are consistent with the theoretical predictions for both adsorbates.

Nucleation of Capillary Bridges and Bubbles in Nanoconfined CO2

Using molecular simulation, we examine the capillary condensation and the capillary evaporation of CO₂ in cylindrical nanopores. More specifically, we employ the recently developed μV T-S method to determine the microscopic mechanism associated with these processes and the corresponding free energy profiles. We calculate the free energy barrier for capillary condensation and identify that the key step consists in the nucleation of a liquid bridge of a critical size. Similarly, the free energy maximum found for the capillary evaporation process is found to correspond to the nucleation of a vapor bubble of a critical size. In addition, we assess the impact of the strength of the wall-fluid on the height of the free energy barrier and on the critical size of liquid bridges (condensation process) and vapor bubbles (evaporation process). We observe that the height of the free energy barrier increases with the strength of the wall-fluid interactions. Finally, we build a theoretical model, based on capillary theory, to rationalize our findings. In particular, the simulation results reveal a linear scaling of the free energy barrier with the critical size, in excellent agreement with the theoretical predictions.

Simple and accurate isochoric differential scanning calorimetry measurements: phase transitions for pure fluids and mixtures in nanopores

A simple way to measure capillary condensation in nanopores for applications in engineering and science.

Confinement Facilitated Protein Stabilization As Investigated by Small-Angle Neutron Scattering

While mesoporous silicas have been shown to be a compelling candidate for drug delivery and the implementation of biotechnological applications requiring protein confinement and immobilization, the understanding of protein behavior upon physical adsorption into silica pores is limited. Many indirect methods are available to assess general adsorbed protein stability, such as Fourier-transform infrared spectroscopy and activity assays. However, the limitation of these methods is that spatial protein arrangement within the pores cannot be assessed. Mesoporous silicas pose a distinct challenge to direct methods, such as transmission electron microscopy, which lacks the contrast and resolution required to adequately observe immobilized protein structure, and nuclear magnetic resonance, which is computationally intensive and requires knowledge of the primary structure a priori. Small-angle neutron scattering can surmount these limitations and observe spatial protein arrangement within pores. Hereby, we observe the stabilization of fluid-like protein arrangement, facilitated by geometry-dependent crowding effects in cylindrical pores of ordered mesoporous silica, SBA-15. Stabilization is induced from a fluid-like structure factor, which is observed for samples at maximum protein loading in SBA-15 with pore diameters of 6.4 and 8.1 nm. Application of this effect for prevention of irreversible aggregation in high concentration environments is proposed.

Bubble nucleation and growth in nanochannels

We apply micro- and nanofluidics to study fundamental phase change behaviour at nanoscales, as relevant to shale gas/oil production. We investigate hydrocarbon phase transition in sub-100 nm channels under conditions that mimic the pressure drawdown process. Measured cavitation pressures are compared with those predicted from the nucleation theory. We find that cavitation pressure in the nanochannels corresponds closer to the spinodal limit than that predicted from classical nucleation theory. This deviation indicates that hydrocarbons remain in the liquid phase in nano-sized pores under pressures much lower than the saturation pressure. Depending on the initial nucleation location - along the channel or at the end - two types of bubble growth dynamics were observed. Bubble growth was measured experimentally at different nucleation conditions, and results agree with a fluid dynamics model including evaporation rate, instantaneous bulk liquid velocity, and bubble pressure. Collectively these results demonstrate, characterize, and quantify isothermal bubble nucleation and growth of a pure substance in nanochannels.