Diffusion in Nanoporous Materials E-Book

Jörg Kärger

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1465

Veröffentlichungsjahr: 2012

Beschreibung

Atoms and molecules in all states of matter are subject to continuous irregular movement. This process, referred to as diffusion, is among the most general and basic phenomena in nature and determines the performance of many technological processes.

This book provides an introduction to the fascinating world of diffusion in microporous solids. Jointly written by three well-known researchers in this field, it presents a coherent treatise, rather than a compilation of separate review articles, covering the theoretical fundamentals, molecular modeling, experimental observation and technical applications.

Based on the book Diffusion in Zeolites and other Microporous Solids, originally published in 1992, it illustrates the remarkable speed with which this field has developed since that time.

Specific topics include: new families of nanoporous materials, micro-imaging and single-particle tracking, direct monitoring of transient profiles by interference microscopy, single-file diffusion and new approaches to molecular modeling.

Leseprobe

Contents

Cover

Related Titles

Title Page

Copyright

Dedication

Preface

Acknowledgements

Part I: Introduction

Chapter 1: Elementary Principles of Diffusion

1.1 Fundamental Definitions

1.2 Driving Force for Diffusion

1.3 Diffusional Resistances in Nanoporous Media

1.4 Experimental Methods

References

Part II: Theory

Chapter 2: Diffusion as a Random Walk

2.1 Random Walk Model

2.2 Correlation Effects

2.3 Boundary Conditions

2.4 Macroscopic and Microscopic Diffusivities

2.5 Correlating Self-Diffusion and Diffusion with a Simple Jump Model

2.6 Anomalous Diffusion

References

Chapter 3: Diffusion and Non-equilibrium Thermodynamics

3.1 Generalized Forces and Fluxes

3.2 Self-Diffusion and Diffusive Transport

3.3 Generalized Maxwell–Stefan Equations

3.4 Application of the Maxwell–Stefan Model

3.5 Loading Dependence of Self- and Transport Diffusivities

3.6 Diffusion at High Loadings and in Liquid-Filled Pores

References

Chapter 4: Diffusion Mechanisms

4.1 Diffusion Regimes

4.2 Diffusion in Macro- and Mesopores

4.3 Activated Diffusion

4.4 Diffusion in More Open Micropore Systems

References

Chapter 5: Single-File Diffusion

5.1 Infinitely Extended Single-File Systems

5.2 Finite Single-File Systems

5.3 Experimental Evidence

References

Chapter 6: Sorption Kinetics

6.1 Resistances to Mass and Heat Transfer

6.2 Mathematical Modeling of Sorption Kinetics

6.3 Sorption Kinetics for Binary Mixtures

References

Part III: Molecular Modeling

Chapter 7: Constructing Molecular Models and Sampling Equilibrium Probability Distributions

7.1 Models and Force Fields for Zeolite–Sorbate Systems

7.2 Monte Carlo Simulation Methods

7.3 Free Energy Methods for Sorption Equilibria

7.4 Coarse-Graining and Potentials of Mean Force

References

Chapter 8: Molecular Dynamics Simulations

8.1 Statistical Mechanics of Diffusion

8.2 Equilibrium Molecular Dynamics Simulations

8.3 Non-equilibrium Molecular Dynamics Simulations

References

Chapter 9: Infrequent Event Techniques for Simulating Diffusion in Microporous Solids

9.1 Statistical Mechanics of Infrequent Events

9.2 Tracking Temporal Evolution in a Network of States

9.3 Example Applications of Infrequent Event Analysis and Kinetic Monte Carlo for the Prediction of Diffusivities in Zeolites

References

Part IV: Measurement Methods

Chapter 10: Measurement of Elementary Diffusion Processes

10.1 NMR Spectroscopy

10.2 Diffusion Measurements by Neutron Scattering

10.3 Diffusion Measurements by Light Scattering

References

Chapter 11: Diffusion Measurement by Monitoring Molecular Displacement

11.1 Pulsed Field Gradient (PFG) NMR: Principle of Measurement

11.2 The Complete Evidence of PFG NMR

11.3 Experimental Conditions, Limitations, and Options for PFG NMR Diffusion Measurement

11.4 Different Regimes of PFG NMR Diffusion Measurement

11.5 Experimental Tests of Consistency

11.6 Single-Molecule Observation

References

Chapter 12: Imaging of Transient Concentration Profiles

12.1 Different Options of Observation

12.2 Monitoring Intracrystalline Concentration Profiles by IR and Interference Microscopy

12.3 New Options for Experimental Studies

References

Chapter 13: Direct Macroscopic Measurement of Sorption and Tracer Exchange Rates

13.1 Gravimetric Methods

13.2 Piezometric Method

13.3 Macro FTIR Sorption Rate Measurements

13.4 Rapid Recirculation Systems

13.5 Differential Adsorption Bed

13.6 Analysis of Transient Uptake Rate Data

13.7 Tracer Exchange Measurements

13.8 Frequency Response Measurements

References

Chapter 14: Chromatographic and Permeation Methods of Measuring Intraparticle Diffusion

14.1 Chromatographic Method

14.2 Deviations from the Simple Theory

14.3 Experimental Systems for Chromatographic Measurements

14.4 Analysis of Experimental Data

14.5 Variants of the Chromatographic Method

14.6 Chromatography with Two Adsorbable Components

14.7 Zero-Length Column (ZLC) Method

14.8 TAP System

14.9 Membrane Permeation Measurements

References

Part V: Diffusion in Selected Systems

Chapter 15: Amorphous Materials and Extracrystalline (Meso/Macro) Pores

15.1 Diffusion in Amorphous Microporous Materials

15.2 Effective Diffusivity

15.3 Diffusion in Ordered Mesopores

15.4 Diffusion through Mesoporous Membranes

15.5 Surface Diffusion

15.6 Diffusion in Liquid-Filled Pores

15.7 Diffusion in Hierarchical Pore Systems

15.8 Diffusion in Beds of Particles and Composite Particles

15.9 More Complex Behavior: Presence of a Condensed Phase

References

Chapter 16: Eight-Ring Zeolites

16.1 Eight-Ring Zeolite Structures

16.2 Diffusion in Cation-Free Eight-Ring Structures

16.3 Diffusion in 4A Zeolite

16.4 Diffusion in 5A Zeolite

16.5 General Patterns of Behavior in Type A Zeolites

16.6 Window Blocking

16.7 Variation of Diffusivity with Carbon Number

16.8 Diffusion of Water Vapor in LTA Zeolites

16.9 Deactivation, Regeneration, and Hydrothermal Effects

16.10 Anisotropic Diffusion in CHA

16.11 Concluding Remarks

References

Chapter 17: Large Pore (12-Ring) Zeolites

17.1 Structure of X and Y Zeolites

17.2 Diffusion of Saturated Hydrocarbons

17.3 Diffusion of Unsaturated and Aromatic Hydrocarbons In NaX

17.4 Other Systems

17.5 PFG NMR Diffusion Measurements with Different Probe Nuclei

17.6 Self-diffusion in Multicomponent Systems

References

Chapter 18: Medium-Pore (Ten-Ring) Zeolites

18.1 MFI Crystal Structure

18.2 Diffusion of Saturated Hydrocarbons

18.3 Diffusion of Aromatic Hydrocarbons

18.4 Adsorption from the Liquid Phase

18.5 Microscale Studies of other Guest Molecules

18.6 Surface Resistance and Internal Barriers

18.7 Diffusion Anisotropy

18.8 Diffusion in a Mixed Adsorbed Phase

18.9 Guest Diffusion in Ferrierite

References

Chapter 19: Metal Organic Frameworks (MOFs)

19.1 A New Class of Porous Solids

19.2 MOF-5 and HKUST-1: Diffusion in Pore Spaces with the Architecture of Zeolite LTA

19.3 Zeolitic Imidazolate Framework 8 (ZIF-8)

19.4 Pore Segments in Single-File Arrangement: Zn(tbip)

19.5 Breathing Effects: Diffusion in MIL-53

19.6 Surface Resistance

19.7 Concluding Remarks

References

Part VI: Selected Applications

Chapter 20: Zeolite Membranes

20.1 Zeolite Membrane Synthesis

20.2 Single-Component Permeation

20.3 Separation of Gas Mixtures

20.4 Modeling Permeation of Binary Mixtures

20.5 Membrane Characterization

20.6 Membrane Separation Processes

References

Chapter 21: Diffusional Effects in Zeolite Catalysts

21.1 Diffusion and Reaction in a Catalyst Particle

21.2 Determination of Intracrystalline Diffusivity from Measurements of Reaction Rate

21.3 Direct Measurement of Concentration Profiles during a Diffusion-Controlled Catalytic Reaction

21.4 Diffusional Restrictions in Zeolite Catalytic Processes

21.5 Coking of Zeolite Catalysts

References

Notation

Index

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To Birge, Patricia and Fani

Preface

Diffusion at the atomic or molecular level is a universal phenomenon, occurring in all states of matter on time scales that vary over many orders of magnitude, and indeed controlling the overall rates of many physical, chemical, and biochemical processes. The wide variety of different systems controlled by diffusion is well illustrated by the range of the topics covered in the Diffusion Fundamentals Conference series (http://www.uni-leipzig.de/diffusion/). For both fundamental and practical reasons diffusion is therefore important to both scientists and engineers in several different disciplines. This book is concerned primarily with diffusion in microporous solids such as zeolites but, since the first edition was published (in 1992 under the title Diffusion in Zeolites and Other Microporous Solids), several important new micro- and mesoporous materials such as metal organic frameworks (MOFs) and mesoporous silicas (e.g., MCM-41 and SBA-15) have been developed. In recognition of these important developments the scope of this new edition has been broadened to include new chapters devoted to mesoporous silicas and MOFs and the title has been modified to reflect these major changes.

In addition to the important developments in the area of new materials, over the past 20 years, there have been equally important advances both in our understanding of the basic physics and in the development of new theoretical and experimental approaches for studying diffusion in micro- and mesoporous solids. Perhaps the most important of these advances is the remarkable development of molecular modeling based on numerical simulations. Building on the rapid advances in computer technology, Monte Carlo (MC) and molecular dynamic (MD) simulations of adsorption equilibrium and kinetics have become almost routine (although kinetic simulations must still be treated with caution unless confirmed by experimental data). In recognition of the importance of these developments the new edition contains three authoritative new chapters, written mainly by Doros Theodorou, dealing with the principles of molecular simulations and their application to the study of diffusion in porous materials.

With respect to experimental techniques, over the past 20 years, neutron scattering has advanced from a scientific curiosity to a viable and valuable technique for studying diffusion at short length scales. Interference microscopy (IFM) has also become a practically viable technique, providing unprecedented insights into diffusional behavior by allowing direct measurement of the internal concentration profiles during transient adsorption or desorption processes. In contrast, the early promise of light scattering techniques has not yet been fulfilled as the practical difficulties have, so far, proved insurmountable. We are, however, witnessing impressive advances in our understanding of a wide variety of systems through the application of single-molecule visualization techniques. As a highlight of this development the book includes experimental confirmation of the celebrated ergodic theorem.

As with the first edition our intention in writing this book has been to present a coherent summary and review of both the basic theory of diffusion in porous solids and the major experimental and theoretical techniques that have been developed for studying and simulating the behavior of such systems. The theoretical foundations of the subject and indeed some of the experimental approaches borrow heavily from classical theories of diffusion in solids, liquids, and gases. We have therefore attempted to include sufficient background material to allow the book to be read without frequent reference to other sources.

The book is divided into six parts, of which the first four, dealing with basic theory, molecular simulations, and experimental methods are included in Volume I. The “experimental” chapters cover both macroscopic measurements, in which adsorption/desorption rates are followed in an assemblage of adsorbent particles, and microscopic methods (mainly PFG NMR and QENS) in which the movement of the molecules themselves is followed, as well as the new imaging techniques such as IFM and IRM in which concentration profiles or fluxes within a single crystal are measured. Parts Five and Six, in Volume II, deal with diffusion in selected systems and with the practical application of zeolites as membranes and catalysts.

The first edition contained considerable discussion of the discrepancies between microscopic and macroscopic measurements. These discrepancies have now been largely resolved, but it turns out that in many zeolite crystals structural defects are much more important than was originally thought. As a result, in such systems, the measured diffusivity is indeed dependent on the length scale of the measurement and the diffusivity as a structurally perfect crystal is often approached only at the very short length scales probed by neutron scattering. Another important feature that has become apparent only through the application of detailed IFM measurements is the prevalence of surface resistance. In many zeolite and MOF crystals the resistance to transport at the crystal surface is significant and has been shown to result from the blockage of a large fraction of the pore openings. Such detailed insights, which depend on the application of new experimental techniques, have become possible only recently.

Throughout the text and in the major tables we have generally used SI units although our adherence to that system has not been slavish and, particularly with respect to pressure, we have generally retained the original units.

The selection of the material for a text of this kind inevitably reflects the biases and interests of the authors. In reviewing the literature of the subject we have made no attempt to be comprehensive but we hope that we have succeeded in covering, or at least mentioning, most of the more important developments.

Jörg Kärger, Leipzig, GermanyDouglas M. Ruthven, Orono, Maine, USADoros N. Theodorou, Athens, Greece

Acknowledgments

A book of this kind is inevitably a collaborative project involving not only the authors but their research students, colleagues, and associates, many of whom have contributed, both directly and indirectly, over a period of many years. Our early collaboration, in the days of the GDR, would not have been possible without the support and encouragement of two well-known pioneers of zeolite research, Professor Wolfgang Schirmer (Academy of Sciences of the GDR) and Professor Harry Pfeifer (University of Leipzig). Much of the early experimental work was carried out by Dr Jürgen Caro (now Professor of Physical Chemistry at the University of Hanover), using large zeolite crystals provided by Professor Zhdanov (University of Leningrad) and the home-made PFG NMR spectrometer that was constructed and maintained by Dr Wilfried Heink.

Since German re-unification both the formal and financial difficulties of research collaboration have been greatly reduced and the list of collaborators, many of whom are mentioned in the cited references, has become too long to name individuals. For the historical record it is, however, appropriate to mention the contributions of a few key people who were involved in the development of the new experimental and molecular modeling techniques that were used to obtain most of the information presented in this new edition. Jeffrey Hufton (now with Air Products Inc.) and Stefano Brandani (now Professor of Chemical Engineering at Edinburgh University) were mainly responsible for the development of “tracer ZLC,” which allowed the first direct comparisons of “macroscopic” and “microscopic” measurements of self-diffusion in zeolites. The successful development of interference microscopy to allow direct visualization of the transient intracrystalline concentration profiles was largely due to the efforts of Ulf Schemmert and Sergey Vasenkov (now professors at the University of Applied Sciences in Leipzig and the University of Florida, respectively) and the parallel development of infrared microscopy to allow the visualization of the profiles of individual species in a multicomponent system was largely due to Dr Christian Chmelik (University of Leipzig). The development of molecular simulation techniques for studying sorption and diffusion in zeolites owes much to Larry June (now with Shell Oil), Randy Snurr, and Ed Maginn (now professors at Northwestern University and the University of Notre Dame, respectively), Professor Alexis Bell (University of California, Berkeley), and Dr George Papadopoulos (NTU Athens). We should also mention the work of Hervé Jobic (CNRS, Villeurbanne), who has developed neutron scattering as a viable experimental technique for studying intracrystalline diffusion over very short time and distances, comparable to those accessible by molecular dynamics simulations.

We are grateful to numerous funding agencies, especially the National Research Foundations of Germany, Canada, and the United States, the Alexander von Humboldt Foundation, DECHEMA and the Fonds der Chemischen Industrie, the European Community, and several companies, notably, ExxonMobil who have provided research support as well as valuable technical assistance over many years.

Finally, we would also like to thank Wiley-VCH and especially our editor Bernadette Gmeiner for her efficient collaboration in the preparation and editing of the manuscript and also our wives, Birge, Patricia, and Fani, for all their help and support throughout the course of this project.

Jörg KärgerDouglas M. RuthvenDoros N. Theodorou5 December 2011

Part I

Introduction

Chapter 1

Elementary Principles of Diffusion

The tendency of matter to migrate in such a way as to eliminate spatial variations in composition, thereby approaching a uniform equilibrium state, is well known. Such behavior, which is a universal property of matter at all temperatures above absolute zero, is called diffusion and is simply a manifestation of the tendency towards maximum entropy or maximum randomness. The rate at which diffusion occurs varies widely, from a time scale of seconds for gases to millennia for crystalline solids at ordinary temperatures. The practical significance therefore depends on the time scale of interest in any particular situation.

Diffusion in gases, liquids, and solids has been widely studied for more than a century [1–3]. In this book we are concerned with the specific problem of diffusion in porous solids. Such materials find widespread application as catalysts or adsorbents, which is a subject of considerable practical importance in the petroleum and chemical process industries and have recently attracted even more attention due to their potential as functional materials with a broad range of applications ranging from optical sensing to drug delivery [4]. To achieve the necessary surface area required for high capacity and activity, such materials generally have very fine pores. Transport through these pores occurs mainly by diffusion and often affects or even controls the overall rate of the process. A detailed understanding of the complexities of diffusional behavior in porous media is therefore essential for the development, design, and optimization of catalytic and adsorption processes and for technological exploitation of porous materials in general. Moreover, systematic diffusion studies in such systems lead to a better understanding of such fundamental questions as the interaction between molecules and solid surfaces [5] and the behavior of molecular systems of reduced dimensionality [6–8].

One class of microporous materials that is of special interest from both practical and theoretical points of view is the zeolites, where this term is used in its broad sense to include both microporous crystalline aluminosilicates and their structural analogs such as the titanosilicates and aluminophosphates. These materials form the basis of many practical adsorbents and catalysts. They combine the advantages of high specific area and uniform micropore size and, as a result, they offer unique properties such as size selective adsorption that can be exploited to achieve practically useful separations and to improve the efficiency of catalytic processes. The regularity of the pore structure, which is determined by the crystal structure rather than by the mode of preparation or pretreatment, offers the important advantage that it is possible, in such systems, to investigate the effect of pore size on the transport properties. In more conventional adsorbents, which have a very much wider distribution of pore size, such effects are more difficult to isolate. In the earlier chapters of this book diffusion in nanoporous solids is treated from a general perspective, but the later chapters focus on zeolitic adsorbents; because of their practical importance, these materials have been studied in much greater detail than amorphous materials.

Since the first edition of this book was published [9], an important new class of nanoporous materials based on metal–organic frameworks (MOFs) has been discovered and studied in considerable detail. Although their composition is quite different, MOFs are structurally similar to the zeolites and show many similarities in their diffusional behavior. Some of the recent studies of these materials are reviewed in Chapter 19.

1.1 Fundamental Definitions

1.1.1 Transfer of Matter by Diffusion

The quantitative study of diffusion dates from the early work of two pioneers, Thomas Graham and Adolf Fick (for a detailed historical review, see, for example, Reference [10]), during the period 1850–1855. Graham's initial experiments, which led to Graham's law of diffusion, involved measuring the rate of interdiffusion of two gases, at constant pressure, through a porous plug [11, 12]. He concluded that:

The diffusion or spontaneous inter-mixture of two gases in contact is, in the case of each gas, inversely proportional to the density of the gas.

In later experiments with salt solutions he, in effect, verified the proportionality between the diffusive flux and the concentration gradient, although the results were not reported in precisely those terms. He also established the very large difference in the orders of magnitude of gas and liquid diffusion rates.

Fick's contribution was to recognize that Graham's observations could be understood if the diffusion of matter obeys a law of the same general form as Fourier's law of heat conduction, an analogy that remains useful to this day. On this basis he formulated what is now generally known as Fick's first law of diffusion, which is in fact no more than a definition of the “diffusivity” ():