介孔材料低温氮气吸脱附的孔道网络模型

doi:10.11949/0438-1157.20221406

摘要/Abstract

摘要：

介孔结构的表征和分析对于介孔材料的开发至关重要，其中低温氮气吸脱附法是最常用的介孔表征方法之一。然而，目前氮气吸脱附法采用的分析模型仍基于平行孔假设，无法描述脱附过程堵孔现象，以及获取孔道连通性等重要孔结构信息。本文建立了低温氮气吸脱附的孔道网络模型，用于分析介孔结构对氮气等温吸脱附行为的影响。通过对比氧化铝材料的氮气吸脱附实验数据和模拟结果，证实了建立的孔道网络模型能很好地描述介孔材料中低温氮气吸脱附行为。模拟结果表明平均孔径较小时，毛细凝聚分压低，液氮堵孔效应显著，氮气吸脱附曲线回滞环的范围和面积较大；孔径分布较宽时，小孔和大孔数量均较多，毛细凝聚和堵孔效应显著，回滞环面积较大；孔道连通性不会影响吸附过程，但会通过改变堵孔效应显著影响脱附过程，连通性越差，堵孔效应越强。证实了堵孔效应对氮气脱附过程影响显著，因而氮气吸脱附法需要考虑堵孔效应，建立的孔道网络模型也可为介孔结构分析提供合理的模型工具。

关键词: 介孔材料, 孔道网络模型, 氮气吸脱附, 孔径分布, 孔道连通性

Abstract:

Characterization and analysis of mesoporous structure are essential for the development of mesoporous materials, and one of the most commonly used mesoporous characterization methods is low-temperature nitrogen adsorption-desorption. However, the current analytical model used in the nitrogen adsorption-desorption method is still based on the assumption of parallel pores, which cannot describe the pore blocking phenomenon during desorption and obtain important pore structural parameters such as pore connectivity. In this work, a pore network model for low-temperature nitrogen adsorption-desorption is developed, which can be used to analyze the effect of mesoporous structure on the isothermal adsorption-desorption behavior of nitrogen. By comparing experimental data and simulation results of nitrogen adsorption-desorption in alumina materials, the established pore network model is proved can well describe the low-temperature nitrogen adsorption-desorption behavior in mesoporous materials. The simulation results show that when the average pore size is small, the partial pressure of capillary condensation is low, the pore blocking effect of liquid nitrogen is significant, and thus the range and area of the hysteresis loop of nitrogen adsorption-desorption curve are larger; when the pore size distribution is wide, the numbers of both small and large pores are larger, the capillary condensation and pore blocking effects are significant, and thus the area of the hysteresis loop is larger. The pore connectivity does not affect the adsorption process, but significantly affects the desorption process by changing the pore blocking effect, and the worse the connectivity, the stronger the pore blocking effect. This work indicates that pore blocking should be accounted for in method of nitrogen adsorption-desorption as pore blocking importantly affects the adsorption process, and also provides a pore network model for mesoporous structure analysis.

Key words: mesoporous materials, pore network model, nitrogen adsorption-desorption, pore size distribution, pore connectivity

中图分类号:

TQ 018

孟金琳, 汪宇, 张群锋, 叶光华, 周兴贵. 介孔材料低温氮气吸脱附的孔道网络模型[J]. 化工学报, 2023, 74(2): 893-903.

Jinlin MENG, Yu WANG, Qunfeng ZHANG, Guanghua YE, Xinggui ZHOU. Pore network model of low-temperature nitrogen adsorption-desorption in mesoporous materials[J]. CIESC Journal, 2023, 74(2): 893-903.

图/表 12

图1 液氮脱附时堵孔效应的示意图

Fig.1 Illustration of pore blocking during nitrogen desorption

图2 孔道连通性为4的二维正方形孔道网络示意图

Fig.2 Illustration of a two-dimensional pore network with a pore connectivity of 4

图3 孔道网络模型求解的算法步骤

Fig.3 Algorithm for solving the pore network model

表1 本工作中所用到的模型参数及变量

Table 1 Model parameters and variables used in this work

参数或变量	数值
氮气吸脱附温度(T)/K	77
氮气临界温度(T_c)/K	126
液氮密度(ρ)/( kg/m³)	807
吸脱附相对压力区间(P/P₀)	0.10~0.95
平均孔径(d_p)/nm	5~20
孔径分布标准偏差(σ)	0.2~0.8
孔道连通性(Z)	4~8

图4 氧化铝氮气吸脱附曲线的实验测量结果和孔道网络模型模拟结果对比

Fig.4 Comparison of nitrogen adsorption-desorption isotherms obtained from experiments and pore network model

图5 孔道网络尺寸对氮气吸附-脱附曲线的影响（Z = 4，dp = 5 nm，σ = 0.5）

Fig.5 Effect of pore network size on the nitrogen adsorption-desorption isotherms(Z = 4, dp = 5 nm, σ = 0.5)

图6 平均孔径对氮气吸附-脱附曲线的影响（Z = 4,σ = 0.5）

Fig.6 Effect of average pore diameter on the nitrogen adsorption-desorption isotherms(Z = 4, σ = 0.5)

图7 不同平均孔径的孔道网络在脱附过程相对压力为0.60时的液氮分布

Fig.7 Liquid nitrogen distribution in pore networks with different average pore diameter at P/P0 = 0.60 during desorption

图8 孔径分布标准偏差对氮气吸附-脱附曲线的影响（Z = 4, dp =10 nm）

Fig.8 Effect of standard deviation on the nitrogen adsorption-desorption isotherms(Z = 4, dp =10 nm)

图9 不同孔径分布标准偏差的孔道网络在脱附过程相对压力为0.60时的液氮分布

Fig.9 Liquid nitrogen distribution in pore networks with different standard deviation at P/P0 = 0.60 during desorption

图10 孔道连通性对氮气吸附-脱附曲线的影响（σ = 0.5， dp =10 nm）

Fig.10 Effect of pore connectivity on the nitrogen adsorption-desorption isotherms(σ = 0.5， dp = 10 nm)

图11 不同孔道连通性的孔道网络在脱附过程相对压力为0.60时的液氮分布

Fig.11 Liquid nitrogen distribution in pore networks with different pore connectivity at P/P0 = 0.60 during desorption

参考文献 41

1	李三妹, 陕绍云, 贾庆明, 等. 介孔分子筛改性研究进展[J]. 硅酸盐通报, 2013, 32(6): 1082-1086.
	Li S M, Shan S Y, Jia Q M, et al. Process on modified mesoporous molecular sieve[J]. Bulletin of the Chinese Ceramic Society, 2013, 32(6): 1082-1086.
2	耿旺昌, 吉志强, 张秋禹. 介孔金属氧化物的研究进展[J]. 材料导报, 2010, 24(7): 16-19.
	Geng W C, Ji Z Q, Zhang Q Y. Research progress of mesoporous metal oxides[J]. Materials Reports, 2010, 24(7): 16-19.
3	张宁, 李育珍, 夏云生, 等. 介孔碳材料的制备、功能化与应用研究进展[J]. 化学研究与应用, 2018, 30(7): 1048-1056.
	Zhang N, Li Y Z, Xia Y S, et al. Preparation, functionalization and application of mesoporous carbon materials[J]. Chemical Research and Application, 2018, 30(7): 1048-1056.
4	Linares N, Silvestre-Albero A M, Serrano E, et al. Mesoporous materials for clean energy technologies[J]. Chemical Society Reviews, 2014, 43(22): 7681-7717.
5	梁振金, 洪梓博, 解明月, 等. 介孔炭材料应用于电化学催化的研究进展[J]. 新型炭材料, 2022, 37(1): 152-179.
	Liang Z J, Hong Z B, Xie M Y, et al. Recent progress on mesoporous carbon materials used in electrochemical catalysis[J]. New Carbon Materials, 2022, 37(1): 152-179.
6	李刚, 华绍广, 吴将有. 硅基介孔材料及其改性对SO₂的吸附效能研究[J]. 化学工程, 2020, 48(12): 25-30, 36.
	Li G, Hua S G, Wu J Y. Adsorption efficiency of silica-based mesoporous materials and their modifications on sulfur dioxide[J]. Chemical Engineering (China), 2020, 48(12): 25-30, 36.
7	张文君, 梁喜龙, 吕江维, 等. 周期性介孔有机硅的合成及在生物医药领域的应用进展[J]. 精细化工, 2022, 39(2): 236-246.
	Zhang W J, Liang X L, Lyu J W, et al. Synthesis and biomedicine application progress of periodic mesoporous organosilicas[J]. Fine Chemicals, 2022, 39(2): 236-246.
8	Zhao C, Danish E, Cameron N R, et al. Emulsion-templated porous materials (PolyHIPEs) for selective ion and molecular recognition and transport: applications in electrochemical sensing[J]. Journal of Materials Chemistry, 2007, 17(23): 2446-2453.
9	Wargo E A, Kotaka T, Tabuchi Y, et al. Comparison of focused ion beam versus nano-scale X-ray computed tomography for resolving 3-D microstructures of porous fuel cell materials[J]. Journal of Power Sources, 2013, 241: 608-618.
10	Epting W K, Gelb J, Litster S. Resolving the three-dimensional microstructure of polymer electrolyte fuel cell electrodes using nanometer-scale X-ray computed tomography[J]. Advanced Functional Materials, 2012, 22(3): 555-560.
11	Litster S, Epting W K, Wargo E A, et al. Morphological analyses of polymer electrolyte fuel cell electrodes with nano-scale computed tomography imaging[J]. Fuel Cells, 2013, 13(5): 935-945.
12	Hoefner M L, Fogler H S. Pore evolution and channel formation during flow and reaction in porous media[J]. AIChE Journal, 1988, 34(1): 45-54.
13	Liu P S. Determining methods for aperture and aperture distribution of porous materials[J]. Titanium Industry Progress, 2006, 23(2): 29-34.
14	Roquerol F, Rouquerol J, Sing K. Adsorption by Powders and Porous Solids: Principles, Methodology, and Applications[M]. London: Academic Press, 1999.
15	Coasne B, Grosman A, Ortega C, et al. Adsorption in noninterconnected pores open at one or at both ends: a reconsideration of the origin of the hysteresis phenomenon[J]. Physical Review Letters, 2002, 88(25): 256102.
16	Cohan L H. Hysteresis and the capillary theory of adsorption of vapors1[J]. Journal of the American Chemical Society, 1944, 66(1): 98-105.
17	Horikawa T, Do D D, Nicholson D. Capillary condensation of adsorbates in porous materials[J]. Advances in Colloid and Interface Science, 2011, 169(1): 40-58.
18	张伟庆, 黄滨, 余小岚, 等. 对BJH方法计算孔径分布过程的解读[J]. 大学化学, 2020, 35(2): 98-106.
	Zhang W Q, Huang B, Yu X L, et al. Interpretation of BJH method for calculating aperture distribution process[J]. University Chemistry, 2020, 35(2): 98-106.
19	近藤精一. 吸附科学[M]. 北京: 化学工业出版社, 2006: 32-34, 40-45, 72-80.
	Kondo S. Adsorption Science[M]. Beijing: Chemical Industry Press, 2006: 32-34, 40-45, 72-80.
20	贾双珠, 吴林媛, 陈炷霖, 等. 微介孔材料的孔结构分析表征[J]. 分析测试技术与仪器, 2019, 25(3): 141-147.
	Jia S Z, Wu L Y, Chen Z L, et al. Analysis and characterization of pore structure of micro-mesoporous materials[J]. Analysis and Testing Technology and Instruments, 2019, 25(3): 141-147.
21	浦群, 杨杰, 吴启强, 等. 含中孔和微孔的多孔炭的孔结构表征[J]. 实验技术与管理, 2015, 32(4): 52-55, 61.
	Pu Q, Yang J, Wu Q Q, et al. Characterization of pore structure of carbons containing micro-and meso-pores[J]. Experimental Technology and Management, 2015, 32(4): 52-55, 61.
22	Wheeler A. Reaction rates and selectivity in catalyst pores[J]. Advances in Catalysis, 1951, 3: 249-327.
23	Carman P C. Fluid flow through granular beds[J]. Chemical Engineering Research and Design, 1997, 75: S32-S48.
24	Wakao N, Smith J M. Diffusion in catalyst pellets[J]. Chemical Engineering Science, 1962, 17: 825-834.
25	Wakao N, Smith J M. Diffusion and reaction in porous catalysts[J]. Industrial and Engineering Chemistry Fundamentals, 1964, 3: 123-127.
26	Beeckman J W, Froment G F. Catalyst deactivation by site coverage and pore blockage: finite rate of growth of the carbonaceous deposit[J]. Chemical Engineering Science, 1980, 35(4): 805-815.
27	Reyes S, Jensen K F. Estimation of effective transport coefficients in porous solids based on percolation concepts[J]. Chemical Engineering Science, 1985, 40(9): 1723-1734.
28	Hollewand M P, Gladden L F. Modelling of diffusion and reaction in porous catalysts using a random three-dimensional network model[J]. Chemical Engineering Science, 1992, 47(7): 1761-1770.
29	Ding W, Li H, Pfeifer P, et al. Crystallite-pore network model of transport and reaction of multicomponent gas mixtures in polycrystalline microporous media[J]. Chemical Engineering Journal, 2014, 254: 545-558.
30	Kharaghani A, Metzger T, Tsotsas E. An irregular pore network model for convective drying and resulting damage of particle aggregates[J]. Chemical Engineering Science, 2012, 75: 267-278.
31	Blunt M J, Jackson M D, Piri M, et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow[J]. Advances in Water Resources, 2002, 25(8/12): 1069-1089.
32	El Hannach M, Prat M, Pauchet J. Pore network model of the cathode catalyst layer of proton exchange membrane fuel cells: analysis of water management and electrical performance[J]. International Journal of Hydrogen Energy, 2012, 37(24): 18996-19006.
33	Wu R, Liao Q, Zhu X, et al. Pore network modeling of cathode catalyst layer of proton exchange membrane fuel cell[J]. International Journal of Hydrogen Energy, 2012, 37(15): 11255-11267.
34	Ye G, Sun Y, Zhou X, et al. Method for generating pore networks in porous particles of arbitrary shape, and its application to catalytic hydrogenation of benzene[J]. Chemical Engineering Journal, 2017, 329: 56-65.
35	Zhou Z M, Cheng Z M, Li Z, et al. Determination of effectiveness factor of a partial internal wetting catalyst from adsorption measurement[J]. Chemical Engineering Science, 2004, 59(20): 4305-4311.
36	汪蓉, 盛勇, 杨传路, 等. 液态低沸点气体的表面张力[J]. 化学物理学报, 2000, 13(3): 380-384.
	Wang R, Sheng Y, Yang C L, et al. The surface tension of liquid gases for low-boiling point[J]. Chinese Journal of Chemical Physics, 2000, 13(3): 380-384.
37	Yaws C L. Chemical Properties Handbook[M]. McGraw-Hill Education, 1999.
38	Androutsopoulos G P, Salmas C E. A new model for capillary condensation-evaporation hysteresis based on a random corrugated pore structure concept: prediction of intrinsic pore size distributions (part 1): Model formulation[J]. Industrial & Engineering Chemistry Research, 2000, 39(10): 3747-3763.
39	Pierce C. The Frenkel-Halsey-Hill adsorption isotherm and capillary condensation[J]. The Journal of Physical Chemistry, 1960, 64(9): 1184-1187.
40	Al-Futaisi A, Patzek T W. Extension of Hoshen-Kopelman algorithm to non-lattice environments[J]. Physica A: Statistical Mechanics and Its Applications, 2003, 321(3/4): 665- 678.
41	Murray K L, Seaton N A, Day M A. An adsorption-based method for the characterization of pore networks containing both mesopores and macropores[J]. Langmuir, 1999, 15(20): 6728-6737.

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