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1、,Micropore Size Calculations,Quantachrome,I N S T R U M E N T S, 2004-2006 Quantachrome Instruments,Multilayer adsorption,Estimation of Micropores.the t-plot method,This method uses a mathematical representation of multi-layer adsorption. The thickness, t, of an adsorbate layer increases with increa
2、sing pressure. The t-curve so produced is very similar in appearance to a type II isotherm.,The t-plot,Resembles a type II isotherm,Relative Pressure (P/Po),Statistical thickness,A statistical monolayer,A statistical multilayer,Not Only Multilayer Correction to the Kelvin Equation, But Also Estimati
3、on of Micropores.,For every value of P/Po, the volume adsorbed is plotted against the corresponding value of “t”.If the model describes the experimental data a straight line is produced on the t-plot.,The t-plot method,Statistical Thickness, t,Halsey equation Generalized Halsey deBoer equation Carbo
4、n Black STSA,t-plot Method (mesoporous only),t-plot Method(in the presence of micropores),Micropore Size Determination by Gas Sorption,Comparisons,Gas Sorption Calculation MethodsP/Po rangeMechanismCalculation model1x10-7 to 0.02micropore fillingDFT, GCMC, HK, SF, DA, DR0.01 to 0.1sub-monolayer form
5、ationDR0.05 to 0.3monolayer completeBET, Langmuir 0.1 multilayer formationt-plot (de-Boer,FHH), 0.35 capillary condensationBJH, DH0.1 to 0.5 capillary filling DFT, BJH in M41S-type materials,DR & DA Dubinin-Radushkevic and Dubinin-Astakov,DRSimple log(V) vs log2(Po/P) relationship which linearizes t
6、he isotherm based on micropore filling principles. “Best fit” is extrapolated to log2(Po/P) (i.e. where P/Po = 1) to find micropore volume.DAClosely related to DR calculation based on pore filling mechanism. Equation fits calculated data to experimental isotherm by varying two parameters, E and n. E
7、 is average adsorption energy that is directly related to average pore diameter, and n is an exponent that controls the width of the resulting pore size distribution. The calculated pore size distribution always has a skewed, monomodal appearance (Weibull distribution).,Estimation of MicroporesDubin
8、in-Radushkevich (DR) Theory,W = volume of the liquid adsorbateW0 = total volume of the microporesB = adsorbent constant = adsorbate constant,A linear relationship should be found between log(W) and log2(Po/P).,Log2(Po/P),Log (W),Extrapolation yields Wo,Estimation of MicroporesDubinin-Radushkevich (D
9、R) Plot,0,HK & SFHorvath-Kawazoe & Saito-Foley,HKDirect mathematical relationship between relative pressure (P/Po) and pore size. Relationship calculated from modified Young-Laplace equation, and takes into account parameters such as magnetic susceptibility. Based on slit-shape pore geometry (e.g. a
10、ctivated carbons). Calculation restricted to micropore region ( 2nm width). SFSimilar mathematics to HK method, but based on cylindrical pore geometry (e.g. zeolites). Calculation restricted to micropore region ( 2 nm diameter).,DFTDensity Functional Theory,Provides a microscopic treatment .Complex
11、mathematical modelling of fluid interactions plus geometrical considerations (pore geometry).Fluid interactions are “calibrated”.“Kernel” consists of up to 100 theoretical, individual pore isotherms.,Gas- and Liquid Density Profiles in a Slit Pore by GCMC (Walton and Quirke,1989),Pore Filling Pressu
12、res for Nitrogen in Cylindrical Silica Pores at 77 K (Neimark et al, 1998),Pore Size Analysis of MCM 41 (Templated Silica) by N2 Sorption at 77 K,Pore Size Analysis of MCM 41: Calculations Compared,Recent Advances in Pore Size Characterization by Physical Adsorption,Author: Dr. Matthias ThommesDirec
13、tor of Applied Science, Quantachrome InstrumentsBoynton Beach, Florida, USAPresented by Dr. Martin A. ThomasDirector of Business Development and Applied TechnologyQuantachrome InstrumentsBoynton Beach, Florida, USA,Adsorption Potentials : Planar Surface, Meso- and Micropores,Planar Surface,Mesopores
14、 (2-50 nm),Micropore (2 nm),IUPACs Classification of Sorption Isotherms,Adsorption in Micro- and Mesopores,Micropores (pore size 2 nm): Micropore filling (continuous process) at very low relative pressures P/P0 0.15 Type I isotherm (IUPAC Classification) Mesopores (pore size 2 - 50 nm): Multilayer a
15、dsorption, pore condensation and hysteresis (pore condensation reflects as 1st order phase transition, i.e., discontinuous process) in relative pressure (P/P0) range from 0.15 1 Type IV, and V isotherm (IUPAC Classification),Recent Advances in Micropore ( 2 nm) Analysis,Commonly Used Adsorptives for
16、 Surface Area and Pore size Analysis,Nitrogen: at 77.35 K (liquid nitrogen temperature, T/Tc = 0.61) pore size analysis of micro-,meso and macropores surface area analysis Argon: at 77.35 K (T Tr = - 6.5 K; Tr : bulk triple point temperature; T/Tc = 0.50) at 87.27 K (liquid argon temperature, T/Tc =
17、 0.57 ) pore size analysis of micro- , meso- and macropores surface area analysis CO2 : at 195 K (T/Tc = 0.63) at 273 K (T/Tc = 0.89) pore size analysis of micropores of widths 1.5 nm (particularly for microporous carbons)Krypton : at 77.35 K (T Tr = - 38.5 K) measurement of very low surface areas at 87.27 K (T Tr = - 28.5 K) pore size analysis of thin micro/mesoporous films (M. Thommes et al, 2005),
