Inferring pore connectivity from sorption hysteresis in multiscale porous media

Development and Application of an Advanced Percolation Model for Pore Network Characterization by Physical Adsorption

Physical adsorption is one of the most widely used techniques to characterize porous materials because it is reliable and able to assess micro- and mesopores within one approach. Challenges and open questions persist in characterizing disordered and hierarchically structured porous materials. This study introduces a pore network model aimed at enhancing the textural characterization of nanoporous materials. The model, based on percolation theory on a finite-sized Bethe lattice, includes all mechanisms known to contribute to adsorption hysteresis in mesoporous pore networks. The model accounts for delayed and initiated condensation during adsorption as well as equilibrium evaporation, pore blocking, and cavitation during desorption. Coupled with dedicated nonlocal-density functional theory kernels, the proposed method provides a unified framework for modeling the entire experimental adsorption-desorption isotherm, including desorption hysteresis scans. The applicability of the method is demonstrated on a selected set of nanoporous silica materials exhibiting distinct types of hysteresis loops (types H1, H2a, H1/H2a, and H5), including ordered mesoporous silica networks (KIT-6 and SBA-15/MCM-41 hybrid silica with plugged pores) and disordered mesoporous silica networks (hierarchical meso-macroporous monolith and porous Vycor glass). For all materials, a good correlation is found between calculated and experimental primary isotherms as well as desorption scans. The model allows us to determine key pore network characteristics such as pore connectivity and pore size distributions as well as a parameter correlated with the impact of pore network disorder on the adsorption behavior. The versatility and enriched textural insights provided by the proposed novel network model allow for a comprehensive characterization previously inaccessible and hence will contribute to further advancement in the textural characterization of novel nanoporous materials. It has the potential to provide important guidance for the design and selection of porous materials for optimizing various applications, including separation processes such as chromatography, heterogeneous catalysis and gas and energy storage.

Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices

In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.

SEM Image Processing Assisted by Deep Learning to Quantify Mesoporous γ-Alumina Spatial Heterogeneity and Its Predicted Impact on Mass Transfer

The pore network architecture of porous heterogeneous catalyst supports has a significant effect on the kinetics of mass transfer occurring within them. Therefore, characterizing and understanding structure-transport relationships is essential to guide new designs of heterogeneous catalysts with higher activity and selectivity and superior resistance to deactivation. This study combines classical characterization via N2 adsorption and desorption and mercury porosimetry with advanced scanning electron microscopy (SEM) imaging and processing approaches to quantify the spatial heterogeneity of γ-alumina (γ-Al2O3), a catalyst support of great industrial relevance. Based on this, a model is proposed for the spatial organization of γ-Al2O3, containing alumina inclusions of different porosities with respect to the alumina matrix. Using original, advanced SEM image analysis techniques, including deep learning semantic segmentation and porosity measurement under gray-level calibration, the inclusion volume fraction and interphase porosity difference were identified and quantified as the key parameters that served as input for effective tortuosity factor predictions using effective medium theory (EMT)-based models. For the studied aluminas, spatial porosity heterogeneity impact on the effective tortuosity factor was found to be negligible, yet it was proven to become significant for an inclusion content of at least 30% and an interphase porosity difference of over 20%. The proposed methodology based on machine-learning-supported image analysis, in conjunction with other analytical techniques, is a general platform that should have a broader impact on porous materials characterization.

A New Statistical Theory for Constructing Sorption Isotherms in Mesoporous Structures Represented by Bethe Lattices

In the present work, a new statistical theory is developed to describe adsorption and desorption in mesoporous materials (pore sizes ranging from 2 to 50 nm) represented by pore networks in the form of Bethe lattices. The new theory is an extension of a previous theory applied for Statistically Disordered Chain Model (SDCM) structures and incorporates the cooperative effects emerging during phase transitions in pore networks. The theory is validated against simulations and algorithmic models that describe sorption of lattice and real fluids in Bethe lattices. It is seen that the pore network coordination number, or pore connectivity, z, has a significant impact on two important processes observed in pore networks: pore assisting condensation during adsorption and evaporation by percolation during desorption. The inclusion of pore connectivity in the earlier developed framework accounting for cooperativity effects is an important step, rendering the existing models to mimic fluid behavior in real materials more accurately. Hence, the new theory inherently contains all essential elements that may offer the extraction of more reliable pore size distributions utilizing both the adsorption and desorption branches of the isotherm.

Evaluation of a graphitic porous carbon modified with iron oxides for atrazine environmental remediation in water by adsorption

In the last decades, the growth of world agricultural activity has significantly contributed to the increased presence of emerging pollutants such as atrazine (ATZ) in aquatic ecosystems. Due to its high stability to the natural or artificial degradation processes, the ATZ environmental remediation by adsorption has been investigated. In this study, a graphitic-porous-carbon- (GPC) based material with magnetic domains was applied to remove ATZ from aqueous solution. ATZ high adsorption efficiency in a reduced time was achieved in the presence of the GPC adsorbent, leading to a detailed investigation of the mechanisms involved in the adsorption processes. Pseudo-first-order (PFO), pseudo-second-order (PSO), Ritchie, Elovich, and Weber-Morris models were applied to calculate the kinetic process efficiency. Likewise, adsorption isotherms based on Langmuir, Freundlich, Temkin, and Redlich-Peterson models were applied for a detailed understanding of the adsorption mechanisms. GPC was successfully applied for ATZ remediation in natural waters, confirming its high potential for treating natural waters contaminated by ATZ using adsorption process. The material can also be recovered and reused for up to 4 application cycles due to its magnetic properties, showing that in addition to ATZ adsorption efficiency, its sustainable use can be achieved.

Field study on the characteristics of scales in damaged multi-material water supply pipelines: Insights into heavy metal and biological stability

Microbial corrosion and heavy metal accumulation in metal water supply pipelines aggravate scale formation and may result in pipeline leakage or bursting events. To better understand the corrosion and corrosion products in the damaged pipes, deposits excavated from three damaged pipes after 22-26 year service periods were analyzed. Using a combination of advanced micro-mineral techniques and 16S rRNA high-throughput sequencing, the micromorphology, chemical composition, and bacterial community were investigated systematically. Unlined pipe wall scales ruptured while lined pipes leaked due to joint scales. Dendrogram correlation results demonstrated that V/As, Al/Pb, and Cr/Mn clusters exhibited co-adsorption and co-precipitation characteristics. FTIR and XRD analysis detected the presence of γ-FeOOH, α-FeOOH in loose scales, and Fe₃O₄ in rigid scales. Scales were colonized by various corrosion bacteria, with sulfate reducing bacteria and ammonia producing bacteria being dominant in the scales of anticorrosive and non-corrosive pipe, respectively. Tl, Ca, Al, and Pb exhibited an extremely positive correlation with Rhodocyclaceae, Ferritrophicum, Thermodesulfovibrionia, and Clostridiaceae. Al and V presented a potential Hazard Quotient risk to consumers, while Cd was potentially bioavailable in all inner scales. Overall, this study provides valuable information for the effective management and avoidance of corrosion-induced pipeline damage and heavy metal release.

Impact of Geometrical Disorder on Phase Equilibria of Fluids and Solids Confined in Mesoporous Materials

Porous solids used in practical applications often possess structural disorder over broad length scales. This disorder strongly affects different properties of the substances confined in their pore spaces. Quantifying structural disorder and correlating it with the physical properties of confined matter is thus a necessary step toward the rational use of porous solids in practical applications and process optimization. The present work focuses on recent advances made in the understanding of correlations between the phase state and geometric disorder in nanoporous solids. We overview the recently developed statistical theory for phase transitions in a minimalistic model of disordered pore networks: linear chains of pores with statistical disorder. By correlating its predictions with various experimental observations, we show that this model gives notable insight into collective phenomena in phase-transition processes in disordered materials and is capable of explaining self-consistently the majority of the experimental results obtained for gas-liquid and solid-liquid equilibria in mesoporous solids. The potentials of the theory for improving the gas sorption and thermoporometry characterization of porous materials are discussed.

A Poromechanical Model for Sorption Hysteresis in Nanoporous Polymers

Sorption hysteresis in nanoporous polymer is an intriguing phenomenon that involves coupling between sorption and deformation. Based on the mechanism revealed at the microscopic level by use of molecular simulation, a poromechanical model is developed capturing all relevant physics and yielding a quantitative description. In this model, the coupling between sorption and deformation is described by a poromechanics framework. More in detail, an upscaling process from the molecular mechanism is implemented to model the hysteresis through the state change of each element upon deformation. We provide two solutions of the model: a numerical one based on the finite element method and an analytical one based on uniform strain assumption. The results from both solutions agree well with the molecular simulation and experimental results, therefore capturing and describing adequately sorption hysteresis. The developed model illustrates that water forms different structural distributions upon adsorption and desorption. A parametric study shows that sorption hysteresis is influenced by material properties. We find that a softer material with stronger adsorbent-adsorbate interaction tends to exhibit more profound sorption hysteresis. The developed model, which relies on the concepts of sorption-deformation coupling and multiscale modeling from atomistic simulations to domain dependent theory, paves the way for a new direction of modeling sorption hysteresis.

Modeling Anomalous Moisture Transport in Cement-Based Materials with Kinetic Permeability

The durability of reinforced concrete structures is closely related to moisture state in cement-based materials. Therefore, it is crucial to develop moisture models that can accurately predict moisture state in the materials. However, many studies reported anomalous moisture transport in cement-based materials that cannot be well simulated by the conventional models. Several reasons have been investigated in the literature, such as the complex pore structure, chemical reactions with water, dimensional changes of the tested specimen, etc. Nevertheless, only a few models are able to capture the anomaly of moisture transport. This study viewed the main moisture transport coefficient-permeability-as a kinetic variable that depends on both the degree of moisture saturation and the contact time. The time-dependence was formulated by the decay (for drying) or growth (for wetting) functions. The saturation-dependence was calculated by the van Genuchten-Mualem (VGM) model. These functions were then implemented into a moisture transport model that was developed in previous studies. The proposed model was validated by experimental data and showed a good agreement for cement pastes that were dried or wetted in the hygroscopic range. Numerical simulation results were also compared with the simplified solutions to a fractional derivative model (FDM) of anomalous diffusion and the empirical Weibull function. We found that the solutions to the FDM cannot provide appropriate results. Weibull function performs as well as the proposed model, but the empirical function lacks physical meanings.

Multiscale poromechanics of wet cement paste

Capillary effects, such as imbibition drying cycles, impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, which is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidity is obtained using a lattice gas density functional method together with a realistic nanogranular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well with nitrogen and water experiments. The standard method for pore size distribution determination from desorption data is evaluated. Second, the integration of the Korteweg liquid stress field around each cement hydrate particle provided the capillary forces at the nanoscale. The cement mesoscale structure was relaxed under the action of the capillary forces. Local irreversible deformations of the cement nanograins assembly were identified due to liquid-solid interactions. The spatial correlations of the nonaffine displacements extend to a few tens of nanometers. Third, the Love-Weber method provided the homogenized liquid stress at the micrometer scale. The homogenization length coincided with the spatial correlation length of nonaffine displacements. Our results on the solid response to capillary stress field suggest that the micrometer-scale texture is not affected by mild drying, while nanoscale irreversible deformations still occur. These results pave the way for understanding capillary phenomena-induced stresses in heterogeneous porous media ranging from construction materials to hydrogels and living systems.