HORIBA Scientific Particle Analysis Carl Lundstedt BET Theory and how its used to calculate surface area June 25, 2019 © 2018 HORIBA, Ltd. All rights reserved. 1 BET Theory seeks to explain the physical adsorption of gas molecules onto solid surfaces © 2018 HORIBA, Ltd. All rights reserved. 2 Particles of similar size can vary drastically in surface area © 2018 HORIBA, Ltd. All rights reserved. 3 Physical adsorption occurs due to Van der Waals forces when at low temperatures and without chemical reactions Adsorbate Adsorbent © 2018 HORIBA, Ltd. All rights reserved. 4 BET Theory extends the Langmuir theory from monolayer adsorption to multilayer adsorption © 2018 HORIBA, Ltd. All rights reserved. 5 We use the BET equation to determine the monolayer absorbed gas volume (vm) 1 1 1 = + [( / ) – 1] − 0 0 = adsorbed gas quantity = saturation pressure of adsorbate = equilibrium pressure of adsorbate 0 = BET constant = exp 1 = heat of adsorption for −the first layer = heat of vaporization 1 © 2018 HORIBA, Ltd. All rights reserved. 6 BET equation can be plotted to determine monolayer adsorbed gas quantity and the BET constant 1 1 1 = + [( / ) – 1] − 0 = + 0 1 [( / ) – 1] 0 1 − 1 © 2018 HORIBA, Ltd. All rights reserved. 7 0 Take numerical values for slope and intercept to solve for vm and c 1 = − intercept = 1 1 = + = 1 + © 2018 HORIBA, Ltd. All rights reserved. 8 From the monolayer absorbed gas volume (vm), we can determine total and specific surface area = = total surface area of sample material = monolayer absorbed gas volume = Avogadro’s number = 6.02 x 1023 molecules/mol = cross-sectional area of adsorbed gas molecule = molar volume of adsorbed gas = [=] m2/g = specific surface area = mass of sample © 2018 HORIBA, Ltd. All rights reserved. 9 Can only assume linear relationship for adsorption isotherms in the range of 0.05 < / < 0.30 0 © 2018 HORIBA, Ltd. All rights reserved. 10 Pore width can make a big difference on shape of isotherm Micropores Mesopores Macropores Zeolite, Mesoporous silica, Sintered metals Activated Activated carbon and ceramics carbon, Metal organic framework 2 nm 50 nm © 2018 HORIBA, Ltd. All rights reserved. 11 Usually apply BET theory to Type 2 and Type 4 isotherms, apply to Type 1 with caution Macroporous/ Microporous non-porous (C > 150) (C > 80) (C < 2) Mesoporous Step-wise (C > 80) (C < 2) multilayer © 2018 HORIBA, Ltd. All rights reserved. 12 Have to insert sample into cell and degas sample to remove excess moisture on surface © 2018 HORIBA, Ltd. All rights reserved. 13 BET measurement includes calibration of 1 cm3 of nitrogen, adsorption, and desorption © 2018 HORIBA, Ltd. All rights reserved. 14 Large surface area samples will adsorb and desorb more nitrogen © 2018 HORIBA, Ltd. All rights reserved. 15 BET multipoint measurement example 1st point 2nd point 3rd point © 2018 HORIBA, Ltd. All rights reserved. 16 Plot at least 3 points to obtain multi-point plot, solve for BET constant (c) and Vm (monolayer volume) BET constant = 145.84 Surface area = 11.36 m2/g © 2018 HORIBA, Ltd. All rights reserved. 17 © 2018 HORIBA, Ltd. All rights reserved. 18 19 © 2018 HORIBA, Ltd. All rights reserved..