作者： Iris Niu

Decoding Porosity: The Unsung Hero of Function

Catalysts: Tailoring Pores for Precision Chemistry

Batteries: Engineering Pores for Speed and Stability

Beyond Measurement: Enabling Cross-Disciplinary Innovation

Conclusion: Pores as Gateways to Progress

Introduction

Fundamental Principles: Beyond Basic Surface Area Measurement

SBET​=Mnm​NA​σ​

Advanced Application 1: Pore Size Distribution Analysis for Hierarchical Nanomaterials

• Micropore analysis: The t-plot method or Horvath-Kawazoe (HK) model distinguishes between monolayer adsorption and micropore filling, quantifying pore volumes as small as 0.3 nm. For instance, activated carbon nanotubes (CNTs) with embedded micropores show enhanced CO₂ capture due to their ultrahigh micropore surface area (>1500 m²/g).
• Mesopore characterization: The Barrett-Joyner-Halenda (BJH) model, applied to desorption branches of isotherms, resolves mesopore sizes (2–50 nm). This is critical for evaluating mesoporous silica nanoparticles (MSNs) used in drug delivery, where pore size dictates payload encapsulation efficiency.
• Hybrid modeling: Combining density functional theory (DFT) with experimental data allows simultaneous analysis of micro-, meso-, and even macropores. For example, hierarchical TiO₂ photocatalysts synthesized via soft-templating exhibit dual PSD peaks (micropores at ~1.5 nm and mesopores at ~15 nm), correlating with improved visible-light absorption and charge separation.

Advanced Application 2: Specific Surface Area Quantification for Functional Nanomaterials

• Carbon-based materials: Graphene oxide (GO) and reduced GO (rGO) have surface areas of 200–1000 m²/g, depending on oxidation degree and reduction method. BET analysis reveals that rGO with fewer oxygen groups retains higher surface area, enhancing its performance in supercapacitors.
• Metal oxides: Nanoscale TiO₂ (anatase phase) exhibits a surface area of ~50 m²/g, but when synthesized as hollow nanospheres, this increases to >200 m²/g, boosting photocatalytic degradation of organic pollutants.
• 2D materials: Transition metal dichalcogenides (e.g., MoS₂ nanosheets) have surface areas exceeding 600 m²/g, making them ideal for lithium-ion battery anodes. BET measurements confirm that exfoliated MoS₂ nanosheets retain >80% of their theoretical surface area after 500 cycles, outperforming bulk counterparts.

Advanced Application 3: Catalytic Performance Correlation with Porosity

• Zeolite catalysts: H-ZSM-5 zeolites with hierarchical porosity (micropores + mesopores) show 30–50% higher conversion rates in methanol-to-olefins reactions compared to purely microporous analogs. BET analysis confirms that mesopores reduce diffusion limitations, allowing reactants to reach internal acid sites more efficiently.
• Supported metal catalysts: Pt nanoparticles supported on ordered mesoporous carbons (OMCs) exhibit superior CO oxidation activity. BET data reveal that OMCs with a narrow mesopore size distribution (~4 nm) maximize Pt dispersion (particle size <2 nm) while minimizing pore blockage, leading to turnover frequencies (TOFs) 2× higher than non-porous supports.

Advanced Application 4: Stability Assessment Under Operational Conditions

• Battery materials: Silicon nanowire anodes expand by ~300% during lithiation, causing pore collapse. In situ BET measurements track surface area loss over 100 cycles, identifying optimal electrolyte additives that mitigate structural degradation.
• Environmental adsorbents: Metal-organic frameworks (MOFs) like UiO-66 degrade in humid air due to ligand hydrolysis. Isothermal BET tests at 90% relative humidity show a 40% drop in surface area within 24 hours, guiding the development of hydrophobic MOF coatings for water-stable applications.

Limitations and Emerging Trends

• Adsorbate specificity: N₂ adsorption may underestimate surface area for low-surface-energy materials (e.g., graphene) or those with pore sizes below 0.5 nm (requiring Ar or CO₂ physisorption at lower temperatures).
• Sample preparation: Agglomeration of nanomaterials (e.g., CNT bundles) can mask true surface area, necessitating careful degassing protocols.

• Multivariate analysis: Integrating BET data with X-ray diffraction (XRD), transmission electron microscopy (TEM), and positron annihilation lifetime spectroscopy (PALS) enables multiscale characterization of nanomaterials.
• High-throughput automation: Robotic sample handlers now allow simultaneous analysis of 96 samples, accelerating screening of nanomaterial libraries for industrial applications.

Conclusion

Abstract

1. Introduction

2. Principles of the BET Theory

V(1−P/P0​)P/P0​​=Vm​C1​+Vm​CC−1​⋅P0​P​

• $P$: equilibrium pressure of adsorbate gas
• P0​: saturation vapor pressure at measurement temperature
• $V$: volume of gas adsorbed
• Vm​: monolayer adsorption capacity
• $C$: BET constant related to the energy of adsorption

SBET​=Vmol​Vm​NA​σ​

3. Instrumentation and Experimental Procedure

• Sample cell​ with controlled temperature (commonly liquid nitrogen temperature for N₂ adsorption)
• Gas dosing system​ for precise pressure control
• Pressure transducers​ and vacuum pumps
• Data acquisition and analysis software

Procedure:

1. Sample pretreatment: degassing under vacuum or inert gas flow to remove physisorbed contaminants.
2. Adsorption measurement: incremental doses of adsorptive gas (e.g., N₂, Ar, CO₂) are introduced, and equilibrium pressure is recorded after each dose.
3. Desorption measurement​ (for hysteresis analysis and pore size distribution calculations).
4. Data processing: linear BET range identification, calculation of surface area, and pore structure analysis via t-plot, BJH, or DFT models.

4. Advanced Data Analysis

• Automated BET range selection​ using statistical criteria to avoid subjective errors.
• Combined methods: integrating BET surface area with DFT pore size distributions for comprehensive pore structure characterization.
• Multigas adsorption studies​ to probe site-specific interactions and chemical heterogeneity.

5. Applications

5.1 Nanomaterials

5.2 Activated Carbons

5.3 Zeolites and MOFs

5.4 Industrial Quality Control

6. Conclusion

Abstract

1. Introduction

2. Classical Theories of Static Adsorption

2.1 Langmuir Adsorption Model

• Adsorption occurs at specific sites on the adsorbent surface.
• Each site can accommodate only one adsorbate molecule.
• No interaction between adsorbed molecules.
• Monolayer coverage is the maximum possible.

θ=1+KL​PKL​P​

qe​=qm​1+KL​PKL​P​

• $\theta$is the fractional surface coverage,
• KL​is the Langmuir constant related to the affinity of binding sites,
• $P$is the pressure (or concentration) of the adsorbate,
• qe​is the amount of adsorbate adsorbed at equilibrium,
• qm​is the maximum adsorption capacity corresponding to monolayer coverage.

• Simple and intuitive.
• Effective for systems exhibiting monolayer adsorption on uniform surfaces.

• Assumes homogeneity and no lateral interactions, which may not hold for real systems.
• Limited applicability to multilayer adsorption scenarios.

2.2 Freundlich Adsorption Model

qe​=KF​P1/n

• KF​and $n$are Freundlich constants related to adsorption capacity and intensity, respectively.

• Applicable to heterogeneous surfaces and multilayer adsorption.
• Empirical flexibility allows it to fit a wide range of experimental data.

• Lacks a theoretical basis for the constants, making physical interpretation challenging.
• Predictive capabilities are limited outside the range of experimental conditions used for parameter determination.

2.3 BET Theory (Brunauer–Emmett–Teller)

• Adsorption occurs in multiple layers without limit.
• The first layer has different adsorption energy compared to subsequent layers.
• Equilibrium is achieved between adsorbed and vapor phases.

Vm​V​=(P0​−P)(1+(C−1)P0​P​)CP​

• $V$is the volume of gas adsorbed at pressure $P$,
• Vm​is the volume of gas required to form a monolayer,
• P0​is the saturation vapor pressure,
• $C$is the BET constant related to the heat of adsorption.

• Effective for determining surface area and porosity of adsorbents.
• Applicable to multilayer adsorption processes.

• Assumes a homogeneous surface and specific interactions between layers, which may not be accurate for all materials.
• Limited accuracy for very low or very high relative pressures.

3. Modern Theories of Static Adsorption

3.1 Potential Theory

• Adsorbate molecules are drawn to regions of favorable potential energy.
• The potential field influences the distribution and density of adsorbed species.

• Useful for understanding adsorption on energetically heterogeneous surfaces.
• Provides insights into the spatial distribution of adsorbed molecules.

• Conceptually explains adsorption behavior based on energy landscapes.
• Can be integrated with other theories to enhance predictive capabilities.

• Often requires complex mathematical treatments and assumptions.
• Experimental validation can be challenging.

3.2 Molecular Simulation and Statistical Mechanics

• Monte Carlo Simulations:​ Use random sampling to explore the configuration space of adsorbate molecules on surfaces.
• Molecular Dynamics:​ Simulate the movement and interactions of molecules over time to understand dynamic aspects leading to adsorption equilibria.
• Statistical Mechanics:​ Apply principles of statistical physics to derive macroscopic properties from microscopic behaviors.

• Provides detailed insights into adsorption mechanisms, including molecular orientations, interactions, and energetics.
• Capable of predicting adsorption behavior for complex systems and novel materials.

• Computationally intensive, limiting applicability to large-scale or real-time predictions.
• Requires accurate force fields and models, which may not always be available or reliable.

4. Emerging and Specialized Models

4.1 Quantum Mechanical Models

• Density Functional Theory (DFT):​ Investigates the electronic structure to understand adsorption energies and mechanisms.
• Ab Initio Methods:​ Use first-principles calculations without empirical parameters to predict adsorption behavior.

• Offers fundamental insights into the nature of adsorbate-surface interactions.
• Can predict novel adsorption phenomena and guide material design.

• Highly computationally demanding.
• Typically applicable to small systems or simplified models.

4.2 Dynamic and Hybrid Models

• Dynamic Adsorption Models:​ Account for transient behaviors, diffusion processes, and time evolution of adsorption equilibria.
• Hybrid Models:​ Integrate aspects of classical, molecular, and quantum theories to provide a more comprehensive description of adsorption phenomena.

• Enhanced ability to predict real-world adsorption behaviors under varying conditions.
• Flexibility in addressing complex systems with multiple interacting factors.

• Increased complexity in model formulation and parameterization.
• Requires extensive experimental data for validation and calibration.

5. Comparative Analysis and Selection of Appropriate Models

6. Applications of Static Adsorption Theories

• Catalysis:​ Understanding how reactants adsorb on catalyst surfaces to optimize reaction rates and selectivity.
• Environmental Remediation:​ Designing adsorbents for the removal of pollutants from air and water.
• Gas Storage and Separation:​ Enhancing the efficiency of gas storage systems and separation processes through optimized adsorption.
• Material Science:​ Developing advanced materials with tailored adsorption properties for specific applications.
• Pharmaceuticals and Biotechnology:​ Controlling the adsorption of biomolecules for drug delivery and bioseparation processes.

7. Challenges and Future Directions

• Complexity of Real Systems:​ Many real-world adsorption scenarios involve heterogeneous surfaces, multiple adsorbate species, and complex interactions that are difficult to model accurately.
• Scalability:​ High-fidelity models, especially those based on molecular simulations and quantum mechanics, are often limited in scalability for industrial applications.
• Data Availability:​ Accurate model parameterization requires extensive experimental data, which may not always be readily available or consistent.
• Integration of Theories:​ Developing integrated models that seamlessly combine different theoretical frameworks to leverage their respective strengths remains a challenge.

• Advanced Computational Techniques:​ Leveraging artificial intelligence and machine learning to enhance model predictive capabilities and reduce computational demands.
• Multiscale Modeling:​ Developing models that can bridge molecular-level interactions with macroscopic adsorption behaviors.
• Novel Materials:​ Designing and characterizing new adsorbent materials with tailored properties guided by theoretical insights.
• Experimental Validation:​ Strengthening the synergy between theoretical predictions and experimental data to refine and validate models.

8. Conclusion

1. Introduction

2. Current Approaches to Desorption Isotherm Modeling

2.1 Empirical and Semi-Empirical Models

• Modified BET Model:​ While the Brunauer-Emmett-Teller (BET) model is primarily for multilayer adsorption, modified versions attempt to fit desorption branches, particularly for high-moisture content regions. However, they often fail to capture the hysteresis loop adequately.
• GAB Model:​ The Guggenheim-Anderson-de Boer (GAB) model is a successful extension of BET for food applications, describing water sorption well over a wide range of moisture contents. Its application to desorption requires careful parameter fitting but is widely used for practical predictions.
• Halsey and Harkins-Jura Models:​ These are simple exponential models that provide reasonable fits for specific segments of the desorption curve but lack universality.
• Iglesias-Chirife Model:​ Specifically developed for food dehydration, this model accounts for the “constant rate period” and the falling rate period, linking desorption to heat and mass transfer phenomena.

2.2 Thermodynamic and Mechanistic Models

• Capillary Condensation Theory (Kelvin Equation):​ This classical approach explains the sharp increase in uptake at high relative pressures by invoking the condensation of vapor in cylindrical capillaries. The desorption branch is modeled by considering the evaporation from menisci with a different radius than during condensation. This theory successfully predicts the onset of hysteresis but fails to close the loop quantitatively due to oversimplified pore geometry assumptions.
• Independent Domain Theory (Potential Theory):​ Proposed by Everett, this theory suggests that the adsorbate occupies independent sites with a distribution of energies. Hysteresis arises from the difference in energy required for adsorption (nucleation) versus desorption (evaporation). It provides a qualitative framework but is mathematically complex for practical use.
• Pore Network Models (PNMs):​ These models represent the porous medium as a network of interconnected pores of various shapes (cylinders, slits, ink-bottle). The dynamics of liquid/vapor interfaces through this network are simulated using Young-Laplace equation. PNMs can reproduce realistic hysteresis loops and are powerful for studying the impact of pore structure. However, they are computationally intensive and require detailed knowledge of the microstructure.
• Density Functional Theory (DFT) for Pores:​ DFT, originally a quantum mechanical method, has been adapted for fluids in nanoporous materials. It calculates the local density profile of the fluid within a pore of a specific geometry, providing a molecular-level explanation for capillary condensation and hysteresis. It is highly accurate for model pores but becomes prohibitively expensive for complex, disordered real materials.

2.3 Modern Computational & Hybrid Approaches

• Molecular Dynamics (MD) Simulations:​ MD tracks the motion of individual atoms/molecules over time. It can simulate the entire desorption process in a small material volume, capturing both thermodynamic and kinetic aspects. It reveals atomic-scale mechanisms but is limited to very small length and time scales.
• Monte Carlo (MC) Simulations:​ Particularly Grand Canonical Monte Carlo (GCMC), MC simulations determine equilibrium configurations by sampling states according to statistical weights. It is excellent for calculating adsorption isotherms in model geometries and has been extended to study desorption pathways. Like MD, it is limited by computational cost.
• Machine Learning (ML) Models:​ Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), and Gaussian Process Regression are being trained on large databases of experimental isotherms. ML models can predict desorption behavior with high accuracy if sufficient data is available. Their major drawback is being “black boxes” with poor interpretability and generalizability outside the training domain.
• Hybrid Multi-Scale Models:​ The frontier of research involves coupling models across scales. For example:
  • Using DFT to calculate adsorption energies for specific pore types, which then inform a larger-scale Pore Network Model.
  • Using experimental data to train an ML model that acts as a surrogate for a computationally expensive MD simulation.

3. Key Challenges in Desorption Isotherm Modeling

1. Accurate Representation of Hysteresis:​ No single model perfectly closes the hysteresis loop for all materials and conditions. Capturing the “main” loop and nested scanning curves remains a formidable task. The choice of model often depends on the material’s porosity (microporous vs. mesoporous).
2. Multi-Component Systems:​ Most models are developed for single-component desorption (e.g., pure water vapor). Real-world systems involve mixtures (e.g., air-water-vapor, organic solvents). Competitive adsorption and co-desorption introduce immense complexity, and reliable models are scarce.
3. Temperature Dependence:​ Desorption is strongly temperature-dependent. While some models incorporate thermal effects via the Clausius-Clapeyron relation, accurately predicting desorption behavior across a wide temperature range for complex materials is challenging. Thermal gradients during actual desorption processes add another layer of difficulty.
4. Material Heterogeneity and Structural Complexity:​ Real materials have irregular, hierarchical pore structures (macro-, meso-, micro-pores) and surface chemical heterogeneity. Capturing this complexity in a tractable model is extremely difficult. Most models rely on idealized geometric representations.
5. Kinetics vs. Equilibrium:​ Traditional isotherm models describe equilibrium states. In practice, desorption is a dynamic, non-equilibrium process influenced by heat and mass transfer resistances. Bridging the gap between equilibrium isotherm models and transient kinetic models is crucial for industrial applications like drying.
6. Parameter Identification and Uniqueness:​ Many mechanistic models have multiple adjustable parameters. Fitting these parameters to experimental data can lead to non-unique solutions, making physical interpretation ambiguous. Robust inverse modeling techniques are needed.
7. Data Scarcity and Quality:​ High-quality, reproducible experimental desorption data, especially for novel materials or under extreme conditions, is often lacking. This limits the development and validation of new models, particularly for ML approaches.

4. Future Perspectives

• Integrated Multi-Scale Frameworks:​ The development of seamless workflows that link atomistic simulations (DFT, MD) to mesoscopic models (PNM) and finally to continuum-scale engineering models will be paramount.
• Advanced Machine Learning:​ Moving beyond simple regression, the use of physics-informed neural networks (PINNs) that embed known physical laws (e.g., mass conservation, thermodynamics) directly into the loss function could lead to more robust and interpretable AI models.
• Focus on Complex Fluids and Mixtures:​ There is a pressing need to develop theories and models for desorption of supercritical fluids, ionic liquids, and complex mixtures relevant to carbon capture, hydrogen storage, and pharmaceutical manufacturing.
• Dynamic and Non-Equilibrium Modeling:​ Coupling isotherm models with computational fluid dynamics (CFD) to simulate real-world desorption processes in reactors, dryers, and geological formations will enhance design and optimization.
• Standardization of Protocols:​ Establishing standard protocols for measuring and reporting desorption data would greatly facilitate model comparison and validation.

5. Conclusion

What is the BET Method?

How Does a BET Adsorption Analyzer Work? (The Principle)

1. Sample Preparation:​ The material is first heated under vacuum to remove any contaminants or pre-adsorbed gases, ensuring a clean surface for measurement.
2. Adsorption (Gas Uptake):​ The prepared sample is placed in a temperature-controlled chamber (the sample cell). It is then dosed with precise pulses of nitrogen gas. As the gas pressure increases, nitrogen molecules begin to adsorb onto the available surface sites of the material, much like dust settling on a table. The instrument measures the volume of gas adsorbed at various equilibrium pressures.
3. Desorption (Gas Release – Optional):​ In many modern analyzers, the process is reversible. By reducing the pressure, the adsorbed gas is desorbed, allowing for the analysis of pore size distribution as well.
4. Data Analysis & The BET Equation:​ The magic lies in analyzing the data. The volume of gas adsorbed is plotted against the relative pressure (P/P₀). The resulting graph typically shows an initial linear region. The famous BET equation​ is fitted to this linear section. From the slope and intercept of this line, we can directly calculate the monolayer capacity—the total volume of gas needed to form a single, complete layer over the entire surface of the sample.
5. Calculating Surface Area:​ Knowing the monolayer capacity and the cross-sectional area of a single nitrogen molecule, the instrument software calculates the total specific surface area of the sample in square meters per gram (m²/g).

Key Application Fields

• Catalysis & Chemical Engineering:​ Catalysts work by providing a large surface area for reactions to occur. The BET surface area is a primary indicator of catalyst activity and efficiency. A higher surface area generally means more active sites and a more effective catalyst.
• Porous Materials & Filtration:​ Activated carbon for water filters, zeolites for molecular sieves, and MOFs (Metal-Organic Frameworks) for gas storage rely on their intricate pore structures. BET analysis helps characterize these pores and optimize their performance for separation and storage.
• Pharmaceuticals:​ The dissolution rate and bioavailability of many drugs are directly influenced by the surface area of the active pharmaceutical ingredient (API). Controlling surface area during manufacturing ensures consistent drug performance and efficacy.
• Energy Storage:​ The capacity of batteries and supercapacitors is heavily dependent on the surface area of electrode materials. Nanomaterials with high surface areas are engineered to maximize energy storage and charge/discharge rates.
• Coatings & Adhesives:​ The performance of paints, varnishes, and adhesives depends on how well they wet and adhere to a surface. Measuring the substrate’s surface area helps in formulating products with optimal coverage and bonding strength.
• Nanotechnology:​ As materials enter the nanoscale, surface-area-to-volume ratio becomes the dominant property. BET analysis is fundamental for characterizing nanoparticles, nanotubes, and other nanostructures.

Conclusion

What Is PSA?

PSA in Small-Scale Applications

• Medical Oxygen Concentrators: Portable or home-use devices that generate oxygen-enriched air for patients with respiratory conditions. These systems typically operate at low flow rates and are optimized for reliability, quiet operation, and minimal maintenance.
• Laboratory Gas Generators: PSA is used to produce high-purity nitrogen, hydrogen, or zero-air for analytical instruments such as GC-MS, LC-MS, and ICP spectrometers. These generators offer a cost-effective and safe alternative to gas cylinders.
• On-Site Nitrogen Generators: Small businesses, such as electronics manufacturers or food packaging facilities, use compact PSA units to produce nitrogen for inerting and preservation processes.

PSA in Large-Scale Industrial Applications

• Hydrogen Production in Refineries: Large PSA units are integral to petroleum refining processes, where they recover high-purity hydrogen from hydrotreating and steam methane reforming off-gas streams. These systems can process tens of thousands of normal cubic meters per hour (Nm³/h) and support critical processes like hydrodesulfurization and ammonia synthesis.
• Biogas Upgrading: In wastewater treatment plants and anaerobic digestion facilities, PSA systems remove CO₂, H₂S, and moisture from biogas to produce pipeline-grade biomethane (≥97% CH₄).
• Air Separation for Industrial Oxygen and Nitrogen: Although cryogenic air separation dominates ultra-large capacity needs, PSA remains competitive for mid-to-large scale operations (e.g., steelmaking, glass manufacturing) where moderate purity and lower capital costs are priorities.

Key Advantages Supporting Scalability

1. Modular Design: PSA systems can be configured with multiple parallel modules to increase capacity incrementally, allowing seamless scaling based on demand.
2. Energy Efficiency: Since PSA operates near ambient temperature and avoids phase changes, it consumes less energy than many conventional separation techniques, especially in smaller applications.
3. Process Flexibility: Parameters such as cycle time, bed size, adsorption pressure, and number of stages can be adjusted to optimize performance for specific scales and feed compositions.
4. Low Operating Costs: With no moving parts in the adsorption beds and minimal utility requirements (mainly electricity and compressed air), PSA offers long-term cost savings.
5. Rapid Start-Up and Shut-Down: PSA systems can be started or stopped quickly, making them suitable for batch processes or intermittent demand scenarios common in smaller operations.

Conclusion

Understanding Diffusion Coefficients

D=6πηrkB​T​

• kB​= Boltzmann constant
• $T$= absolute temperature
• $\eta$= dynamic viscosity of the medium
• $r$= radius of the diffusing particle

Role of Diffusion in Chemical Reactions

1. Diffusion-Controlled Reactions

• The reaction rate is directly proportional to the diffusion coefficients​ of the reactants.
• A higher diffusion coefficient means faster reactant encounter rates, leading to a higher reaction rate.

2. Activation-Controlled vs. Diffusion-Controlled Reactions

• Activation-controlled reactions​ are limited by the energy barrier (activation energy)​ that must be overcome for the reaction to proceed.
• Diffusion-controlled reactions​ are limited by how fast reactants can physically meet​ due to diffusion.

Mathematical Relationship: Smoluchowski Equation

kd​=10004πNA​(DA​+DB​)(rA​+rB​)​

• NA​= Avogadro’s number
• DA​,DB​= diffusion coefficients of reactants A and B
• rA​,rB​= radii of reactants A and B

Practical Implications

1. Industrial Catalysis & Reaction Engineering

• In heterogeneous catalysis, reactants must diffuse to the catalyst surface. A higher diffusion coefficient​ means faster mass transport, improving reaction efficiency.
• Reactor design​ (e.g., stirred tanks, packed beds) considers diffusion effects to optimize reaction rates.

2. Biological Systems

• In enzyme-substrate reactions, diffusion influences how quickly substrates reach the active site.
• Cellular environments​ (e.g., cytoplasm) have varying viscosities, affecting diffusion and thus reaction speeds.

3. Environmental & Atmospheric Chemistry

• The diffusion of pollutants in air or water​ affects reaction rates with other species, influencing degradation processes.

Conclusion

1. Theoretical Foundations of BET Analysis

V(P0​−P)P​=Vm​C1​+Vm​CC−1​⋅P0​P​

2. Experimental Workflow

Sample Preparation

• Degassing: Samples are pretreated under vacuum or inert gas at elevated temperatures (e.g., 200–350°C) to remove physisorbed contaminants like water or hydrocarbons. This step ensures accurate adsorption measurements .
• Sample Loading: The degassed sample is loaded into a sample cell, which is then sealed and cooled to cryogenic temperatures.

Adsorption Isotherm Measurement

• Nitrogen Adsorption: The analyzer gradually increases the relative pressure (P/P0​) from 0.05 to 0.995, measuring the equilibrium adsorbed gas volume at each step. This generates an adsorption isotherm, which reflects the material’s pore structure .
• Desorption Isotherm: After saturation, pressure is decreased to record desorption data, which helps analyze pore filling and emptying mechanisms.

3. Pore Size Distribution Analysis

Barrett-Joyner-Halenda (BJH) Method

• Principle: The BJH model uses Kelvin’s equation to relate adsorption isotherms to pore diameters. It assumes cylindrical pores and calculates pore volumes based on capillary condensation at specific P/P0​values.
• Application: Primarily used for mesopores (2–50 nm). BJH plots adsorbed volume vs. pore diameter, creating a distribution curve .

Non-Local Density Functional Theory (NLDFT)

• Advancements: For micropores (<2 nm), BJH underestimates pore volumes due to interactions between adsorbed layers. NLDFT addresses this by incorporating quantum mechanical effects, providing accurate micropore characterization. It is now standardized in ISO 15901-3 .

Data Interpretation

• Adsorption vs. Desorption: Adsorption isotherms are preferred for pore size analysis to avoid artifacts like the “4 nm spike” caused by desorption hysteresis in composite pore systems .
• Software Tools: Modern analyzers use software (e.g., Gold APP’s V-Sorb) to automate data fitting, generate pore size histograms, and export reports .

4. Key Applications

• Catalysts: Evaluating pore structures to optimize active site accessibility .
• Energy Materials: Analyzing battery electrodes and fuel cells for pore-related performance metrics .
• Environmental Science: Characterizing adsorbents (e.g., activated carbon) for pollutant removal .

5. Limitations and Considerations

• Closed Pores: BET cannot assess pores inaccessible from the surface .
• Sample Requirements: Requires sufficient sample quantity (0.5–6 cm³) and homogeneous particle size .
• Pressure Range: Accuracy diminishes outside P/P0​=0.05–0.35for BET and 2–50 nm for BJH .

Conclusion