对微孔吸附常用经典分析模型的比较

doi:10.3866/PKU.DXHX202208134

Abstract

Abstract:

This paper briefly compares the source, application scope, development history and respective characteristics of the commonly used classical models of microporous adsorption. In order to facilitate the systematic understanding and mastery of classical microporous analysis methods in physical adsorption, the methods are divided into three categories: (1) methods developed from standard isotherms, including t-method, α_s-method, n-method and MP method; (2) methods based on micropore filling theory, including D-R method, D-A method and D-R-S method; (3) the currently commonly used methods include the original HK method (slit pore), HK-SF method (cylindrical pore), HK-CY method (spherical pore) and the improved HK method.

Key words: t-method, MP method, D-R equation, Original H-K equation, Improved H-K equation

Jianhui Zhang, Weiqing Zhang. Comparison of Common Classical Analytical Models for Microporous Adsorption[J].University Chemistry, 2023, 38(8): 326-332.

Figures/Tables 4

项目	t-图法	α_s-图法	n-图法
年代提出者	1966 de Boer等	1970 Sing等	1979 Lecloux等
适用温度吸附质	液氮温度氮气吸附	液氮及其他温度氮气及其他吸附质	同左同左
数学表达式	$ {t}{}{=}{}{{t}}_{\rm{m}}\frac{{V}}{{{V}}_{\rm{m}}} $	$ {{α}}_{\rm{s}}{}{=}{}\frac{{V}}{{{V}}_{{0.4}}} $	$ {n}{}{=}{}\frac{{V}}{{{V}}_{{m}}}{或}{n}{}{=}{}\frac{{t}}{{{t}}_{{m}}} $
纵轴轴标、单位及来源	吸附量V；cm³∙g⁻¹ STP 吸附等温线的纵轴数据列	同左同左	同左同左
横轴轴标、单位及来源	厚度t；单位为nm；由吸附等温线纵轴数据列经过标准等温线或膜厚方程变换获得	吸附量比值α_s；不同p/p₀下吸附量与p/p₀为0.4时吸附量的比值，单位为1；由吸附等温线纵轴数据列获得	吸附量比值n；不同p/p₀下吸附量(或膜厚)与单层吸附量(或单层膜厚)的比值，单位为1；由吸附等温线纵轴数据列(或经变换)获得
曲线是否过原点及不过原点的原因	t曲线在p/p₀较低时会存在部分曲(直)线不通过原点的可能，这与未考虑吸附剂的性质有关	α_s曲线在p/p₀较低时会存在部分曲(直)线不通过原点的可能，这与未考虑吸附质的性质有关	n曲线初始部分是直线且总是通过原点
曲线斜率单位及斜率的物理意义	斜率经变换后与比表面积单位相同，斜率表观单位为cm³∙g⁻¹∙nm⁻¹ STP 斜率可用来计算、换算成比表面积。此是MP方法的关键点	斜率单位为cm³∙g⁻¹ STP 若直线过原点，则其斜率等于p/p₀在0.4时的吸附量	斜率单位为cm³∙g⁻¹ STP 直线部分的斜率可用来计算比表面积
77 K氮气吸附相互关系	$ {t}{}{=}{}{0.538}{{α}}_{\rm{s}} $ $ {t}{}{=}{}{0.354}{n} $	$ {{α}}_{\rm{s}}{}{=}{}{1.859}{t} $ $ {{α}}_{\rm{s}}{}{=}{}{0.658}{n} $	$ {n}{}{=}{}{1.520}{{α}}_{\rm{s}} $ $ {n}{}{=}{}{2.825}{t} $
特点	几乎没有考虑吸附剂的性质；需要从BET方法中获得V_m	只考虑了吸附质的作用；不需要与吸附层相关的数据	同时考虑了吸附质和吸附剂两方面的作用。提出了选择标准等温线的一般化准则
分析结果	给出微孔范围的孔体积和孔面积，没有直接给出微孔分布	同左	同左

项目	D-R方程	D-A方程
年代	1947	1975
适用吸附质	蒸气，也用于气体	同左
适用吸附剂	活性碳，碳材料；适用于具备单一均匀微孔的材料，或者是具备很宽孔分布的材料中的均匀微孔部分的表征	微孔分布很宽的碳材料；适合具备微孔分布很宽的材料和完整的吸附曲线
适用p/p₀范围	$ {\text{10}}^{\text{-}\text{4}}\text{}\text{ < }\text{}{p}/{{p}}_{\text{0}}\text{ < }\text{}\text{0.1}\text{}\text{(}\text{或}\text{0.2)} $	$ \text{0.0}\text{}\text{ < }{p}/{{p}}_{\text{0}}\text{ < }\text{}\text{0.9} $
方程形式	$ \text{ln}{V}\text{}\text{=}\text{}\text{ln}{{V}}_{\text{micro}}\text{-}\text{}{\left(\frac{{RT}}{{β}{{E}}_{\text{0}}}\right)}^{\text{2}}{\left[\text{ln}\frac{{{p}}_{\text{0}}}{{p}}\right]}^{\text{2}} $	$ \text{ln}{V}\text{}\text{=}\text{}\text{ln}{{V}}_{\text{micro}}\text{}\text{-}\text{}{\left(\frac{{RT}}{{β}{{E}}_{\text{0}}}\right)}^{{m}}{\left[\text{ln}\frac{{{p}}_{\text{0}}}{{p}}\right]}^{{m}} $
纵、横轴标	$ \text{ln}{V}\text{；}{\left[\text{ln}\frac{{{p}}_{\text{0}}}{{p}}\right]}^{\text{2}} $	$ \text{ln}{V}{\text{；}\left[\text{ln}\frac{{{p}}_{\text{0}}}{{p}}\right]}^{{m}} $
切线斜率意义	$ \mathrm{斜}\mathrm{率}{\left(\frac{{RT}}{{β}{{E}}_{\text{0}}}\right)}^{\text{2}}，\mathrm{所}\mathrm{获}\mathrm{得}{{E}}_{\text{0}}\mathrm{包}\mathrm{含}\mathrm{有}\mathrm{微}\mathrm{孔}\mathrm{结}\mathrm{构}\mathrm{信}\mathrm{息} $	$ {\text{斜率}\left(\frac{{RT}}{{β}{{E}}_{\text{0}}}\right)}^{{m}}\text{，所获得}{{E}}_{\text{0}}\text{包含有微孔结构信息} $
截距数值意义	总微孔体积V_micro	同左
指数m	可看作是D-A方程中m = 2的特例	对宽微孔分布的吸附曲线，m = 1；单一均匀微孔分布的吸附曲线，m = 2；碳分子筛吸附曲线，m = 3
孔分布假设	吸附势能(相当于孔)服从Gaussian分布	吸附势能(相当于孔)服从Weibull分布
分析结果	给出特征能量、极限微孔容量(体积)和等效比表面积	除给出同左侧结果外，还给出平均孔宽、孔分布最大峰值

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项目	t-图法	MP法
年代及提出者	1966，de Boer等	1968，Mikhail等
适用温度及吸附质	液氮温度，氮气吸附	同左
纵轴轴标及单位	吸附量(气态)；cm³∙g⁻¹ STP	孔容积(液态)变化量与水力半径变化量的比值；cm³∙g⁻¹∙nm⁻¹
纵轴数值来源	吸附等温线的纵轴数列值	由t-图中两相邻数据点之间连线的斜率(相应于比表面积)差与其相应的两横坐标(厚度)的算术平均值之积，经换算得到微孔容积变化值，然后，除以相应的水力半径变化值
横轴轴标及单位	厚度t；单位为nm	水力半径r_h；单位为nm
横轴数值来源	从实测等温线经标准等温线或膜厚度方程变换得到	微孔容积与比表面积值之比(见纵轴数值计算过程), r_h = V/S
分析结果	给出微孔范围的孔体积和孔面积，不能给出微孔分布	给出微孔体积和比表面分布。累积孔比表面与BET表面积一致；累积孔体积与氮气可及的总孔体积一致

项目	Original HK方程	HK-SF方程	HK-CY方程
年代	1983	1991	1994
提出者	Horvath, G. and Kawazoe, K.	Saito, A. and Foley, H. C.	Cheng, Linda S. and Yang, Ralph T.
适用孔型	狭缝型	圆柱型	球型
常用测试温度	77 K、87 K、195 K、273 K和298 K	同左	同左
常用吸附质	N₂、Ar和CO₂	同左	同左
常见吸附剂	石墨碳分子筛、沸石分子筛等	同左	同左
分析结果	微孔孔径-累计体积分布等信息	同左	同左

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Comparison of Common Classical Analytical Models for Microporous Adsorption

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