Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions

Solvation pressure due to adsorption of fluids in porous materials is the cause of elastic deformation of an adsorbent, which is accessible to direct experimental measurements. Such a deformation contributes to the Helmholtz free energy of the whole adsorbent-adsorbate system due to accumulation of compression or tension energy by the solid. It means that in the general case the solid has to be considered as not solely a source of the external potential field for the fluid confined in the pore volume, but also as thermodynamically noninert component of the solid-fluid system. We present analysis of nitrogen adsorption isotherms and heat of adsorption in slit graphitic pores accounting for the adsorption deformation by means of nonlocal density functional theory.     

Quenched solid density functional theory method for characterization of mesoporous carbons by nitrogen adsorption

Quenched solid density functional theory (QSDFT) model for characterization of mesoporous carbons using nitrogen adsorption is extended to cylindrical and spherical pore geometries. The kernels of theoretical isotherms in the range from 0.4 to 50 nm are constructed accounting for different possible variations of the pore shapes in micropore and mesopore regions. The results of QSDFT method are illustrated with experimental data on adsorption on novel CMK-3 and 3DOm carbons. The proposed method is recommended for pore size distribution calculations for micro–mesoporous carbons obtained through various templating mechanisms.     

Quenched solid density functional theory and pore size analysis of micro-mesoporous carbons

We present a new model of adsorption on micro-mesoporous carbons based on the quenched solid density functional theory (QSDFT). QSDFT quantitatively accounts for the surface geometrical inhomogeneity in terms of the roughness parameter. We developed the QSDFT models for pore size distribution calculations in the range of pore widths from 0.4 to 35 nm from nitrogen at 77.4 K and argon at 87.3 K adsorption isotherms. The QSDFT model improves significantly the method of adsorption porosimetry: the pore size distribution (PSD) functions do not possess gaps in the regions of ∼1 nm and ∼2 nm, which are typical artifacts of the standard non-local density functional theory (NLDFT) model that treats the pore walls as homogeneous graphite-like plane surfaces. The advantages of the QSDFT method are demonstrated on various carbons, including activated carbons fibers, coal based granular carbon, water purification adsorbents, and mirco-mesoporous carbon CMK-1 templated on MCM-48 silica. The results of PSD calculations from nitrogen and argon are consistent, however, argon adsorption provides a better resolution of micropore sizes at low vapor pressures than nitrogen adsorption.     

碳基吸附剂储氢吸附热的密度泛函理论

为比较狭缝孔、纳米管两种典型碳基吸附剂的储氢性能,应用非局域密度泛函理论、微观物理学、吸附平衡原理、典型吸附剂储氢试验结果计算并分析了典型碳基吸附剂的氢等量吸附热.结果表明,两类吸附剂的氢等量吸附热相差不大,等温线变化规律相似,并且只有在低温（液氮）、适度压力时吸附储氢的质量密度才有望达到DOE标准.     

2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation

In this work, we show that the standard slit pore model widely used for the characterization of activated carbons may be improved by introducing structural and/or energetical heterogeneity to the surface of pore walls. The existing one dimensional slit pore model assumes graphite-like energetically uniform pore walls. As a result of this assumption adsorption isotherms calculated by the non local density functional theory (NLDFT) do not fit accurately the experimental N₂ data measured for real activated carbons. Assuming a graphene-based structural framework for activated carbons and using a 2D-NLDFT treatment of the fluid density in the pores we consider two options for model pores: energetically heterogeneous (EH) and geometrically corrugated (GC). For testing, we applied these two models to the pore size analysis of porous carbons that were giving poor results of the analysis with the standard slit model. We found that the typical artifacts of the homogeneous slit pore model were eliminated. Also, the agreement of the new models with experimental data was significantly better than that of the standard slit model.     

An improved theoretical procedure for the pore-size analysis of activated carbon by gas adsorption

Amorphous carbon materials play a vital role in adsorbed natural gas (ANG) storage.One of the key issues in themore prevalent use of ANG is the limited adsorption capacity,which is primarily determined by the porosity and surface characteristics of porous materials.To identify suitable adsorbents,we need a reliable computational tool for pore characterization and,subsequently,quantitative prediction of the adsorption behavior.Within the framework of adsorption integral equation (AIE),the pore-size distribution (PSD) is sensitive to the adopted theoretical models and numerical algorithms through isotherm fitting.In recent years,the classical density functional theory (DFT) has emerged as a common choice to describe adsorption isotherms for AIE kernel construction.However,rarely considered is the accuracy of the mean-field approximation (MFA) commonly used in commercial software.In this work,we calibrate four versions of DFT methods with grand canonical Monte Carlo (GCMC) molecular simulation for the adsorption of CH4 and CO2 gas in slit pores at 298 K with the pore width varying from 0.65 to 5.00 nm and pressure from 0.2 to 2.0 MPa.It is found that a weighted-density approximation proposed by Yu (WDA-Yu) is more accurate than MFA and other non-local DFT methods.In combination with the trapezoid discretization of AIE,the WDA-Yu method provides a faithful representation of experimental data,with the accuracy and stability improved by 90.0％ and 91.2％,respectively,in comparison with the corresponding results from MFA for fitting CO2 isotherms.In particular,those distributions in the feature pore width range (FPWR)are proved more representative for the pore-size analysis.The new theoretical procedure for pore characterization has also been tested with the methane adsorption capacity in seven activated carbon samples.     

Evaluation of Adsorption Properties of Low Surface Area Carbons—Comparison of Experiments with a Theoretical Study

Adsorption isotherms of nitrogen, argon and methane were experimentally measured at 77 K on low surface area graphitised carbons and natural graphite. For direct comparison, theoretical isotherms for the same gases were calculated on a model, flat surface by using NL DFT. Vulcan (a graphitised carbon black, often used as a surface area standard) was shown to represent a good approximation of a flat graphite surface. It is a suitable material for evaluation of potential parameters in modelling of adsorption in micropores. It was also confirmed that the non-local density functional theory provided a good and reliable fit to experimental adsorption isotherms. SEM microscopy and x-ray diffraction revealed surface properties consistent with those evaluated by adsorption.     

氮气吸附法和压汞法测定Al2O3载体孔结构

作为催化剂载体的活性氧化铝,其孔径分布主要集中在中孔范围内,压汞法和氮气吸附法是测定多孔材料比表面积、孔径及其分布的经典方法,采甩压汞仪和比表面积、孔径测定仪对活性氧化铝载体孔结构进行测定。氮气吸附法采用BET原理进行比表面积测定,采用BJH原理进行孔径分布和孔容的测定,压汞法采用Wasburn公式测定比表面、孔径分布和孔容。对两种方法实验结果进行了讨论,认为氮气吸附法更适合氧化铝载体孔结构的测定。     

用近似Broekhoff方程计算孔径分布

本文对计算孔径分布的Broekhoff方程做了简化,得到一组近似方程,实例计算结果证明它和原方程等效.近似方程的优点在于能制成专用机与吸附仪联用,加快数据处理.近似方程的适用范围为:10(?)—300(?)     

Synthesis,gas adsorption and reliable pore size estimation of zeolitic imidazolate framework-7 using CO2 and water adsorption

Reliable estimation of the pore size distribution(PSD) in porous materials such as metal–organic frameworks(MOFs) and zeolitic imidazolate frameworks(ZIFs) is crucial for accurately assessing adsorption capacity and corresponding selectivity. In this study, the so-called zeolitic imidazolate framework-7(ZIF-7) is successfully synthesized via relatively fast and convenient microwave technique. The morphology and structure of the obtained MOF were characterized by XRD, SEM and N_2 and CO_2adsorption/desorption isotherms at 77 K and0 °C respectively. Then, to determine the PSD of the fabricated MOF, carbon dioxide isotherms are experimentally measured at various temperatures up to atmospheric pressure. Afterward, the experimental CO_2 isotherms data are utilized in two recently proposed in-house algorithms of SHN1 and SHN2 to extract the true PSD of manufactured ZIF-7. The obtained results revealed that median pore diameter of the fabricated ZIF-7 is estimated around 0.404 nm and 0.370 nm by using CO_2 isotherms at 273 K and 298 K respectively. These values are in good agreement with the real pore diameter of 0.42 nm. Moreover, experimental data of water adsorption isotherms over four different MOFs, borrowed from literature, are employed to illustrate further effectiveness of the above algorithms on successful determination of the corresponding pore size distributions. All predicted PSDs are proved to be in good agreement with those obtained from independent methods such as topology and morphology studies.     

基于密度泛函理论的活性炭孔径分布改进算法

为提高非定域密度泛函理论（NLDFT）预测活性炭孔径分布（PSD）的精度,考虑了活性炭孔壁面晶体粗糙度对结果的影响。在传统NLDFT基础上,结合吸附壁面碳原子的密度分布,推导出改进NLDFT,预测了氩在光滑及具粗糙碳晶体表面的吸附平衡,并根据87.3 K、氩在活性炭上的吸附平衡数据,在由两种NLDFT确定了不同孔径的理论等温线核后,由寻优函数确定活性炭在0.35~12 nm区间的PSD。结果表明,以改进的NLDFT预测活性炭的PSD时,确定的活性炭孔径呈连续分布,预测平衡数据的相对误差小于10%;传统NLDFT确定的孔径在1 nm处出现断点,最大的预测相对误差范围达45%。改进NLDFT能较准确预测氩在具有粗糙晶体碳表面活性炭的PSD。     

水蒸气活化法制备椰壳活性炭的孔结构特征

以农林废弃物椰壳在600℃炭化2h后的炭化料为原料,以水蒸气为活化剂,研究了活化温度、活化时间、水蒸气用量对活性炭的比表面积、微孔容积和收率等的影响。结果表明：椰壳炭化料的比表面积仅为185m^2／g,且以中孔为主。在活化过程中,通过提高活化温度和水蒸气用量缩短了活化时间,扩宽了孔径;当水蒸气用量和活化温度较为适宜时,延长活化时间,有利于微孔的形成。活性炭的比表面积、总孔容积、微孔容积可达：1465m^2／g,0．9703cm^3/g,0．7519cm^2／g。并通过非定域密度函数理论（NLDFT）对活性炭的孔径分布进行了表征。     

有序介孔TiO2溶剂挥发自组装法的合成研究

以三嵌段聚醚P123（PEO20-PPO70-PEO20,M=5875）为模板剂,用溶剂挥发自组装法（EISA法）制备了介孔二氧化钛粉体。采用高温焙烧的方法除去模板剂,对合成的样品TiO2粉体进行了XRD、N2等温吸附-脱附等实验表征,研究了焙烧温度对样品比表面、孔径、孔容的影响。     

Microstructures of PAN-ACF modified by catalytic benzene deposition

Benzene pyrolysis was successfully introduced to modify the pore size distributions (PSD) of polyacrylonitrile based activated carbon fibers (PAN-ACF) into a sharp distribution, at the presence of nickel catalyst. The microstructures of samples were studied by means of nitrogen adsorption, XRD, and SEM. The nitrogen isotherms were analyzed in detail using the routine BET method, α_s plot, DR equation, Horvath-Kawazoe (HK) equation, and regularized density functional theory (DFT), by which the surface area, micropore volume, and PSD were obtained. The results showed that the pore size of PAN-ACF can be effectively narrowed by catalytic benzene deposition and the PSD showed a unimodal nature, exhibiting potential behavior as a molecular sieve. A fraction residue of catalyst located in the ultramicropores can be washed by acid, resulting in increased BET surface area and micropore volume, which can also be confirmed by XRD and SEM measurements.     

Comparative study of nanopores in activated carbons by HRTEM and adsorption methods

Detailed analysis of nanopores (IUPAC micropores at pore half-width x < 1 nm) of carbonised porous phenolformaldehyde resin microbeads used as a precursor of activated carbon (AC) and CO₂ activated carbon (at 50% burn-off) has been performed on the basis of high-resolution transmission electron microscopy (HRTEM) image analysis and nitrogen adsorption data analysed using several density functional theory (DFT) methods. The results of quenched solid DFT (QSDFT) and nonlocal (NLDFT) are in agreement with the pore size distributions of nanopores based on the HRTEM image analysis. Development of porosity with progressive activation degree in a series of ACs leads to enhancement of the deviation of the pore shape from the used pore models. The TG/DTA data and Raman spectra show nonlinear but weak changes in the AC characteristics with increasing burn-off degree.     

Adsorption of N2, Ar, acetone, chloroform and acetone-chloroform mixture on carbon black in the framework of molecular layer structure theory (MLST)

Adsorption of pure nitrogen, argon, acetone, chloroform and acetone-chloroform mixture on graphitized thermal carbon black is considered at sub-critical conditions by means of molecular layer structure theory (MLST). In the present version of the MLST an adsorbed fluid is considered as a sequence of 2D molecular layers, whose Helmholtz free energies are obtained directly from the analysis of experimental adsorption isotherm of pure components. The interaction of the nearest layers is accounted for in the framework of mean field approximation. This approach allows quantitative correlating of experimental nitrogen and argon adsorption isotherm both in the monolayer region and in the range of multi-layer coverage up to 10 molecular layers. In the case of acetone and chloroform the approach also leads to excellent quantitative correlation of adsorption isotherms, while molecular approaches such as the non-local density functional theory (NLDFT) fail to describe those isotherms. We extend our new method to calculate the Helmholtz free energy of an adsorbed mixture using a simple mixing rule, and this allows us to predict mixture adsorption isotherms from pure component adsorption isotherms. The approach, which accounts for the difference in composition in different molecular layers, is tested against the experimental data of acetone-chloroform mixture (non-ideal mixture) adsorption on graphitized thermal carbon black at 50 °C.     

Using DFT analysis of adsorption data of multiple gases including H2 for the comprehensive characterization of microporous carbons

Hydrogen and nitrogen adsorption isotherms at cryogenic temperatures (77 and 87 K) were used to characterize the microporosity of a series of activated carbons, representing various pore size distributions (PSD). The PSD for each carbon was calculated by simultaneous fitting of the DFT model isotherms to their experimental counterparts. The resulting PSD represents robust characteristics of the carbon structure that is consistent with all the data used in the analysis. The range of pore size analysis in this method is extended to smaller pore sizes compared to the standard nitrogen adsorption analysis. In addition, it is shown that this approach allows to detect and exclude experimental points that are not fully equilibrated due to diffusion problems in narrow micropores. The results of the analysis of a series of carbons activated with systematically increasing burn-off show that the presented approach is a useful tool for a comprehensive characterization of microporous carbons, and for obtaining detailed and reliable carbon PSDs.