ChE 553 Lecture 6 Equilibrium Adsorption 1 Objective • Introduce Adsorption Isotherms – How much gas adsorbs at equilibrium as a function of pressure – Qualitative features of isotherms • Types 1-5 • More complex phase behavior 2 Topics • Introduction to Adsorption Isotherms Five types • Langmuir Adsorption Isotherm Simple Adsorption Isotherm Finite number of surface spaces to hold gas • More complex behavior: surface phase transitions due to adsorbate/adsorbate interactions 3 Introduction To Adsorption Isotherms Adsorption Isotherm – amount adsorbed as a function of pressure S-shaped curve typical at T>300K 4 Typical Behavior At Low Temperature Figure 4.2 Isotherms for adsorption of krypton, argon at 77 K, argon at 91.3 K, and ammonia on graphitized carbon black. (Data of Putnam and Fart [1975], Ross and Winkler [1955], Basset, Boucher, and Zettlemoyer [1968], and Bomchil et al. [1979], respectively.) 5 S-Shaped Curve At Low Pressure Figure 4.3 A blowup of the low-pressure part of the krypton data in Figure 4.2. 6 General Adsorption Isotherms Figure 4.4 The five types of adsorption isotherms described by Brunauer [1945]. 7 Next Langmuir’s Model Of Adsorption: Figure 4.5 Langmuir’s model of the structure of the adsorbed layer. The black dots represent possible adsorption sites, while the white and mauve ovals represent adsorbed molecules. 8 Key Features Of Langmuir’s Model • Finite sites to adsorb gas • Ideal behavior in surface phase (no interactions between adsorbed molecules? • At low pressures coverages proportional to pressure (or p1/2) • Eventually surface fills up – Adsorption limited by availability of sites – If multiple species – competition for sites – Maximum coverage 1ML 9 Kinetic Derivation Of Langmuir’s Model Assume equilibrium A g S Aad (4.1) rad kad PA S (4.2) At equilibrium rd=rad. Solving Aad PA S kad kd A K equ (4.4) rd kd Aad (4.3) 10 Isotherm Arises From A Site Balance S0 [S] [A ad ] (4.7) equation (4.4) are 4.7 are two equations in two unknowns ([S], [Aad]). Solving yields A A K equ PA A 1 K equ PA (4.10) 11 Qualitative Features of Langmuir’s Model 1 .2 1.2 1 0 .8 Co ve r a g e Co ve r a g e 1 0 .6 0 .4 0.8 0.6 0.4 0 .2 0.2 0 0 10 20 30 Pr e s s u r e 40 50 0 0.0 1 0.1 1 10 10 0 Pr es s ur e 12 Derivation Of Langmuir Isotherm For Competitive Adsorption Aad K A Bad K B equ equ PA S PB S (4.22) S S Aad Bad (4.23) 13 Solving Equations Simultaneously A A K equ PA 1 A K equ PA B K equ PB (4.24) B B K equ PB A B 1 K equ PA K equ PB (4.25) 14 1 .2 1.2 1 1 0 .8 0 0 .1 1 5 10 0 .6 0 .4 Co ve r a g e Co ve r a g e Qualitative Picture 0.8 0.6 0.4 0 0.1 1 5 10 0.2 0 .2 0 0 10 20 30 Pr e s s u r e 40 50 0 0.0 1 0.1 1 10 10 0 Pr es s ur e 15 Derivation Of Langmuir Adsorption For Dissociative Adsorption 1/2D2 + S Dad Dad K D equ 1/ 2 PD S 2 Qualitatively the same as non-dissociative (4.26) D D 1/ 2 K equ P2 D 1/ 2 1 K equ PD 2 (4.27) 16 Comparison To Data D 1/ 2 Kequ P2 D D 1/ 2 1 Kequ PD2 (4.27) 1 Rearranging 1 D 1 1 D 1/ 2 K equ P2 Figure 4.1 A plot of a series of adsorption isotherms for hydrogen adsorption on Pt(111). Dotted lines are symbols: data. Solid Lines: fits to the Langmuir adsorption isotherm. (Data of Ertl, Neuman, and Steit [1977].) 17 Real Situation: Interactions Between Molecules Attractive interactions lead to islands 18 Repulsive Interactions Order Overlayer Continued 19 Phase Diagrams For Adsorption Figure 4.13 A phase diagram for oxygen on W(110). (Adapted from one presented by Lagally et al. [1980].) 20 Qualitative Behavior 1/RT Strength of Attraction Figure 4.21 A replot of the data from Figure 4.20 as a function of dimensionless pressure. 21 Universal Curve: Monolayer Adsorption: Only Nearest Neighbor Interactions Equilibrium constant at half coverage Figure 4.23 A series of adsorption isotherms calculated via the lattice gas method for adsorption on a square lattice with first nearest neighbor interactions. Curves are shown for βh = -0.50, -0.25, 0, …, 2.0. 22 Complication: Multilayer Adsorption 23 The BET Equation Assume • Random distribution of sites with 1, 2, 3… adsorbed molecules • No lateral interactions between molecules A cB xB S 1 xB 1 cB 1xB (4.189) Does not work that well in practice 24 A Comparison Of The Krypton Data In Figure 4.12 To The Best Fit With The BET Equation 25 Comparison Continued Figure 4.45 A blowup of the portion of the date in Figure 4.44 below 4 torr. Used anyway 26 Why 5 Types Of Adsorption Isotherms? 27 Type I • Type I arises when only one type of site: – Initially surface fills randomly – Eventually saturates when surface filled (or pores filled with a porous material) 28 Type III • Type III arises when there are strong attractive interactions leading to condensation – Initially, no adsorption – Pressure increases lead to nucleation and growth of islands – Eventually liquids condense on the surface 29 Type II • Type II arises when the is more than one adsorption site – Initial rapid adsorption – Saturates when first site filled – Second rise when second site fills • Second site could be a second monolayer, a second site on the surface. In porous materials, it can also be a second type of pore. 30 Type V • Type V is another case for attractive interactions – Initially no adsorption – Next nucleation and growth of islands or liquid drops – Coverage saturates when no more space to hold adsorbates 31 Type IV • Type V occurs when there are multiple phase transitions due to a mixture of attractive and repulsive interactions • Can also arise in multilayer adsorption where adsorption on second layer starts before first layer saturates 32 Summary • Introduction to Adsorption Isotherms Five types • Langmuir Adsorption Isotherm Simple Adsorption Isotherm Finite number of surface spaces to hold gas • More complex behavior: surface phase transitions due to adsorbate/adsorbate interactions – Attractive Interactions: Classical two phase regions i.e. solids and gases – Repulsive interactions - adsorbate ordering – Leads to universality (general phase diagrams that do not depend on gas and solid) 33