National Academies Press: OpenBook

Mesoscale Chemistry: A Workshop Summary (2015)

Chapter: 3 Catalysis

« Previous: 2 Growing (Up) from the Nanoscale to the Mesoscale
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

3

Catalysis

Key Points

  • Confinement and control of local environments are essential features of development of functional catalysts, and chemists can provide this control by using both chemical and biological approaches to modify mesoscale parameters.
  • Controlling the environment surrounding the active sites of catalysts within constrained environments has proved to be difficult, as is the understanding of the effects that the reaction products have on a constrained environment inside a pore.
  • For native enzymes and synthesized catalytic mimics, the outer coordination sphere plays a critical role in determining reactivity. Large, dynamic changes in the ligands around an active site can result in changes in the reactivity of functional groups in other parts of the protein.
  • There are many opportunities within modeling to address mesoscale phenomena and to develop new theoretical paradigms for examining mesoscale regimes within different types of catalysts. Such work would be particularly valuable for understanding mesoscale heterogeneity, fluctuations, and transport effects.
  • Heterogeneity and long-range interactions, which had not been factored into modeling studies until recently, are important for generating catalytic activity.
  • The role of entropy in driving the reactions at the mesoscale is recognized as important but not yet well understood, raising a challenge that needs to be addressed.
  • The tools available in mechanical engineering, fluid control, and synthesis provide a greater ability to design structures with varying pore diameters and shapes to create catalysts reliably for specific functions, but key synthetic challenges remain.
  • Processes developed for the semiconductor industry, such as atomic layer deposition, are being employed to build mesoscale catalyst structures via a bottom-up strategy.

The workshop’s first panel session featured five presentations on various aspects of how mesoscale chemistry is important for catalysis. Andrew Borovik, Professor of Chemistry at the University of California, Irvine, described the architectural features within local environments that are instrumental in regulating function at a catalytic center. Wendy Shaw, Scientist in the Physical Sciences Division at the Pacific Northwest National Laboratory (PNNL), discussed how an understanding of the interactions between an enzyme’s protein scaffold and its catalytic active site can inform efforts to improve molecular catalysts. Yi Lu, the Jay and Ann Schenck Professor of Chemistry at the University of Illinois, Urbana-Champaign, presented an example of how to elucidate and employ key features of mesoscale biocatalysis for designing artificial enzymes with catalytic efficiencies similar to that of native enzymes. Cynthia Jenks, Assistant Director for Scientific Planning and Division Director of Chemical and Biological Sciences at the Ames Laboratory, focused on hybrid multifunctional systems and their use in modulating catalytic activity and selectively controlling accessibility of an active site to reactants. She also discussed design concepts based on

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

mesoscale phenomena for tandem catalysts. Peter Stair, the John G. Searle Professor of Chemistry and Chair of the Chemistry Department at Northwestern University, concluded the presentations by reviewing two basic approaches to synthesizing mesoscale catalysts and then focusing on strategies for molecular and atomic assembly on solid platforms to create new catalysts. A panel discussion, moderated by session chair Bruce Garrett, Director of the Physical Sciences Division at the PNNL and a member of the workshop organizing committee, followed the five presentations.

ARCHITECTURAL COMPLEXITY AT THE MOLECULAR LEVEL

To start his presentation, Andrew Borovik showed images of four enzymes containing metal cofactors that are essential for their enzymatic activity and noted two key features shared by these enzymes. The first is that if the metal cofactors were removed from the active site, the chemistry these enzymes would perform would be pedestrian at best and of almost no use to chemists. “But when we insert these cofactors into the active site, they perform remarkable chemistry, efficient, robust, selective chemistry that as a synthetic chemist who tries to make catalysts, I have an amazingly difficult time to achieve,” said Borovik. The second important feature is that key forces or interactions that control the local environments around the metal atom cofactors are noncovalent.

These two features are not found solely in biology, however, and Borovik showed an example of a porous organic host that his group has synthesized (Sharma and Borovik 2000). It is able to bind and release oxygen using a confined cobalt atom within a suitable molecular complex. He also described a relatively simple copper complex that, when embedded within a zeolite, had very high activity as an oxidation catalyst for converting methane to methanol. He characterized this reaction as one of the most difficult chemical transformations to accomplish (Woertink et al. 2009). The lesson from these two examples, he said, is that confinement and control of local environments are essential properties for developing functional catalysts, and that the main challenge for chemists aiming to manipulate these two properties is to control noncovalent interactions. The key question, he said, is “How can you design something to promote these intramolecular processes in order to promote overall function?”

To illustrate this challenge, Borovik focused on a simple reaction—the oxidation of water to form oxygen—and the biological construct that promotes this reaction. The molecular complex that accomplishes this reaction in nature is called Photosystem II, and it orchestrates the movement of eight different particles with specific timing to catalyze this reaction, which lies at the heart of photosynthesis. Photosystem II is a large membrane-bound protein complex whose active site structure was solved in 2011 (Umena et al. 2011), revealing the arrangement of metal atoms within the active site and providing important information about how water is oxidized to molecular oxygen. There are four manganese centers and one calcium center that are surrounded by a rich network of hydrogen bonds which extends beyond the active site (Figure 3-1). While many of the steps of the water oxidation reaction are known, the details of the key step of generating the oxygen–oxygen bond are still largely a mystery. Identifying those details will likely depend on computational methods to provide some mechanistic insights.

One thought regarding potential mechanisms for the reaction, said Borovik, is that one of the manganese centers becomes highly oxidized, making it “amazingly electron deficient” and capable of forming a high-energy oxygen intermediate that can react with one of the water molecules in the active site to create molecular oxygen. That mechanism, however, would require chemistry that has not ever been observed in the laboratory. To explore possible mechanisms, Borovik and his colleagues have been creating small organic constructs that can bind metal ions and promote intermolecular hydrogen bonding networks similar to those in the active site of Photosystem II. These can then be used to study fundamental properties such as proton and electron flow, and findings of these studies can then be applied to the creation of synthetic catalysts.

One such organic construct contains a metal binding pocket and several nearby amine groups to promote intermolecular hydrogen bonding. Borovik’s research group has created a number of versions of this molecule with different functionality and obtained both structural data using x-ray diffraction and spectroscopic data to follow electron

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

images

Figure 3-1 The oxygen-evolving complex of Photosystem II. SOURCE: Cook and Borovik (2013). Reprinted with permission from Nature Chemistry.

transfer and proton movement. These data are supporting the development of a better understanding of the thermodynamics and kinetics of the oxidation reaction and how the key reactive intermediate could form in a biological active site.

Another key question his group is exploring is the role the calcium atoms play in active site function. To examine this question, they redesigned the active site in a construct to promote hydrogen bond formation and to include both manganese and calcium in the active site, which would resemble the active site of Photosystem II (Figure 3-2). The next step, he explained, is first to introduce more manganese atoms into this complex followed by water molecules to see if the resulting complex will oxidize water to molecular oxygen.

Borovik and his colleagues are also exploring ways of modifying their small molecule complexes to move protons out of the active site. One of the molecules they created was able to catalyze a related reaction that reduces molecular oxygen to water at room temperature. “This just shows you that by changing the local environment and managing the protons that we can actually install new catalytic function in our systems,” Borovik said. Taking this work to the next scale, his team is now inserting these metal–organic complexes into larger structures such as the Streptavidin protein complex. This work takes advantage of the interface between two of the Streptavidin subunits, known as the vestibule, and is attempting to tune the local environment around the vestibule to alter the mesoscale interactions in order to observe the effect of those environmental changes on inserted metal–organic complexes. Recently, his team created a structure that connects two spatially separate copper complexes—one bound to each Streptavidin subunit—via a water channel. “We can now combine chemistry and biology and in some cases genetics to create modifications within the vestibule to control the local environment,” said Borovik in closing. “The ultimate goal is to understand how these weak interactions control function and to make catalysts that can do the same kind of transformations that occur in biology.”

BRINGING MESOSCALE PROPERTIES TO MOLECULAR CATALYSTS BY ATTACHING AN OUTER COORDINATION SPHERE

Like Borovik, Wendy Shaw is attempting to gain insights into catalytic function by controlling the environment around the active site, but her approach is to use amino acids and peptides. She is also studying a different system—the enzyme known as hydrogenase, which converts protons to

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

images

Figure 3-2 A molecular structural comparison between a synthetic active site and that of the oxygen-evolving complex. SOURCE: Umena et al. (2011). Reprinted with permission from Nature Chemistry.

molecular hydrogen and back again. Hydrogenase is extremely efficient at catalyzing this reaction, operating at a rate of 10,000 conversions per second at less than 100 millivolts (mV) overpotential. She explained that overpotential is a measure of the extra energy required to initiate the reaction, and the lower the overpotential, the more energetically efficient the reaction.

There are multiple hydrogenases in nature, and the one Shaw studies has two iron atoms in the active site along with pendant amine groups that are positioned such that they can bring hydrogen into the active site for cleavage or bring protons together to be released as molecular hydrogen. These pendant amines are critical for the enzyme’s efficient function, and Shaw noted there are no known active catalysts that purely mimic the active site of the enzyme. She added that a colleague of hers has created active site mimics that reproduce the function of the pendant amines (Figure 3-3), producing some of the fastest hydrogen oxidation catalysts known; they operate at 50 conversions per second and with a 400-mV overpotential (DuBois 2014). Nevertheless, the underperformance of this synthetic catalyst relative to the native enzyme shows that the complexity of the outer coordination sphere is essential to function. It is for this reason that she focuses her work on introducing the outer coordination sphere to see if she can recapture some of that complexity and its function.

The outer coordination sphere of hydrogenase, explained Shaw, controls mesoscale functionality by creating channels that allow protons, hydrogen gas, and electrons to reach and leave the active site in a precise way, in terms of both location and timing. “It ends up being a very orchestrated process to get protons and electrons at the active site at the right time to react,” said Shaw. She also noted that each of the ligands in the hydrogenase active site is bound to metals or hydrogen-bonded to another group around it, which allows for the precise control at an atomic level around the active site. This hydrogen bonding controls redox potentials and the structure and dielectric potentials of the active site. Shaw said that there are many things about the environment of the active site that are not yet understood, but that it is clear that this environment is controlled by the large number of functional groups within the complex of 20 amino acids that surround the active site.

Ligand dynamics also plays an important role in the active site’s catalytic activity. Large, dynamic changes in the ligands around an active site can

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

images

Figure 3-3 Two mimics of the iron–iron hydrogenase: one that reproduces the active site of the enzyme but is inactive (left) and one that introduces pendant amine functionality and that is active (right). SOURCE: DuBois (2014). Reprinted with permission from Inorganic Chemistry.

result in changes in the reactivity of functional groups in other parts of the protein, a phenomenon known as allostery. At the same time, there are many smaller, slower structural changes occurring in the vicinity of the active site that can control the local dielectric and structure and cause the enzyme to catalyze the reverse reaction. “That’s something that we don’t have good control of in molecular catalysts,” said Shaw, who said that the important lesson when considering all of the dynamics described so far is that the interaction and cooperativity of the active site with the protein scaffold is necessary to generate function.

There are many mesoscale features in hydrogenase and Shaw discussed how the study of one of these features provides evidence of concerted proton and electron transfer. Data from a molecular dynamics study looking at motion as a function of protonation state show that when the protein is in a protonation state that is preferential for hydrogen oxidation, there is motion at the mouth of the channel that ferried protons out of the active site, as well as at the redox partner binding site (Ginovska-Pangovska et al. 2014, McCullagh and Voth 2013). However, when the protonation state changes to one that favors hydrogen production, motion at the proton channel stops while motion at the redox binding partner increases. “While this is by no means conclusive, it indicates that the redox partner binding region is sensitive to what is happening in the proton channel and is suggestive of proton-coupled electron transfer,” said Shaw.

One challenge is to understand how motion in one part of the enzyme is driving protonation at the active site or vice versa, she said. Another challenge is to incorporate these kinds of allosteric interactions into molecular catalysts, both to create novel catalysts and to better understand how enzymes work. There are two general methods for approaching the work, either from the “top down” or the “bottom up.” A top-down approach to control mesoscale complexity takes a molecular catalyst and inserts it into an already formed protein structure, such as the work that Borovik discussed using Streptavidin. The problem with this approach is that it produces a very large molecule that may provide challenges for studying and modeling the system.

Shaw has taken a bottom-up approach that begins with a molecular catalyst and uses peptides to build a scaffold that adds functional groups to the outer coordination sphere. She started with a nickel-phosphorous-nitrogen hydrogen oxidation catalyst and added various peptide-based outer coordination spheres that resemble the enzyme but are much smaller. The first construct she created to oxidize hydrogen operated at three reactions per second with an overpotential of 900 mV. Adding a proton channel to move protons more quickly out of the active site reduced the overpotential by 300 mV—a 30 percent improvement in efficiency—but it also slowed the reaction rate slightly (Lense et al. 2014). “I think this result captures the idea of the mesoscale in that you can introduce a feature that you think is going to do one thing and it does something completely different,” said Shaw.

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

The next step was to insert a glycine into the core catalyst and the result was “pretty interesting,” said Shaw. The resulting catalyst has a reaction rate that is competitive with the catalyst described previously but with a low overpotential that is competitive with what is seen in the enzyme. She credits a strategically positioned carboxylic acid group that can move a proton quickly between a nitrogen atom and an oxygen atom in the active site and allows for rapid proton transfer from the pendant amine (Dutta et al. 2013). Adding another proton relay using arginine instead of glycine, which adds guanidinium functionality in the outer coordination sphere, raises the overpotential slightly but increases the reaction rate by about an order of magnitude, she said (Dutta, Roberts, and Shaw 2014).

While these results indicate that guanidiniums are enhancing catalysis, it is not clear how they are doing so. To answer that question, Shaw and her colleagues looked at the catalytic cycle and began to test possible steps in the cycle, including deprotonation followed by hydrogen addition. Beginning with the idea that deprotonation was the initial step—a step that would be independent of hydrogen concentration—she and her colleagues increased the hydrogen pressure and expected to see no change in rate as deprotonation would be the rate-limiting step. In fact, they identified a linear dependence on hydrogen concentration, suggesting that the guanidiniums in the outer shell are in some way affecting hydrogen addition but not deprotonation. Subsequent experiments showed that there appears to be an arginine–arginine interaction within the protein that aids in catalysis. Shaw believes that the interaction between the two arginines helps stabilize the nickel-to-nitrogen distance slightly and that in turn is helping to facilitate hydrogen addition.

Reversibility is a hallmark of enzymes and mesoscale interactions, and though Shaw and her colleagues had managed to create a fairly efficient molecular catalyst, this catalyst is not reversible at room temperature. Shaw credits a decrease in mesoscale interactions between the active site and the protein scaffold for the reversibility displayed by the native enzyme. However, when the molecularly catalyzed reaction was run at 40°C to 50°C instead of room temperature, the molecular catalyst was completely reversible just as it is in the enzymes. In light of those results, she and her colleagues hypothesized that if arginine stabilizes the guanidinium–guanidinium interaction, then pi–pi interactions, such as those introduced by phenylalanine or tyrosine, could provide similar stabilization. In fact, when Shaw and her team replaced the arginine with tyrosine, the result was a catalyst that operates reversibly at room temperature. “What’s exciting here is that we’ve made a pretty small change really far from the active site, and we’ve completely changed the reversibility of these complexes as well as the temperature at which it operates,” said Shaw.

Going forward, Shaw and her colleagues plan to add more complexity by using peptides instead of amino acids in the outer shell and to employ computational methods to inform future designs. Computation, said Shaw, has the potential to predict structural stability and functional group positioning and to limit the experimental guessing that comes with trying to perform protein structure prediction. She noted that David Baker, a colleague at the University of Washington, made a structure prediction game that anyone can play on the Internet, and that work has identified two different solutions that look to be promising structures. She and her coworkers are doing some optimization work now, and she noted that they are at the point of introducing multiple functional groups to the system and seeing how those can control catalytic activity. Future work will also investigate the role of water within these catalytic structures. She stated that the ultimate question to answer will be how to implement various features so that they work together. “We’ve been able to implement two different functional groups, but when we add a third will it be complementary, or will we have to do something to make them talk to each other?” she asked in closing her remarks.

ELUCIDATING KEY FEATURES OF MESOSCALE BIOCATALYTIC SYSTEMS AND EMPLOYING THEM IN DESIGNING FUNCTIONAL ARTIFICIAL ENZYMES WITH HIGH ACTIVITY

Continuing the theme of exploring the role that mesoscale phenomena play in enabling the catalytic activity of enzymes, Yi Lu described his group’s work on the enzyme cytochrome c oxidase, which catalyzes the reduction of oxygen to water and in doing so creates the proton gradient that drives the

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

images

Figure 3-4 Cytochrome c oxidase catalyzes the reduction of oxygen to water, producing four protons and four electrons that are used to drive adenosine triphosphate (ATP) synthesis. SOURCE: Hwang and Lu (2004). Reprinted with permission from Proceedings of the National Academy of Sciences of the United States of America.

synthesis of adenosine triphosphate (ATP). Moreover, this enzyme is capable of catalyzing this reaction without releasing toxic reactive oxygen species (Figure 3-4). Lu noted that one of his interests in studying this enzyme is its potential importance as a model for creating new catalysts for the oxygen reduction reaction in fuel cells because of its fine control over the movement of electrons with high efficiency. While there is a relatively efficient platinum-based catalyst that is used in today’s fuel cells, this catalyst is not only expensive because of its platinum content, but it operates at a higher overpotential than does cytochrome c oxidase (Kjaergaard, Rossmeisl, and Norskov 2010). Besides wanting to identify the mesoscale features that make cytochrome c oxidase such an efficient catalyst, Lu said that he also wants to understand why chemists have been unable to create a synthetic biocatalyst with high activity despite 30 to 40 years of biomolecular modeling aimed at creating such a catalyst.

One answer to this second question is that most biomimetic modeling work has focused on the enzyme’s active site and has treated the environment surrounding the active site as being largely hydrophobic. In fact, said Lu, there are many hydrophilic, positively charged, and negatively charged residues around and near the active site and many water molecules that are strategically positioned around the active site. “So if you look at the true picture of the active site, it is no longer just a hydrophobic environment. It’s actually quite hydrophilic, particularly at the mesoscale,” said Lu, who added that the role of these mesoscale heterogeneous environments surrounding the active site had not been factored into synthetic modeling studies until recently.

A number of groups have created synthetic model systems for this enzyme, and James Collman’s group at Stanford has produced several different synthetic iron and copper biomimetic analogs of the copper-containing active site of cytochrome c oxidase that faithfully reproduce not only key physical features of the active site, but also its ability to catalyze the reduction of oxygen into water (Collman et al. 2007). Daniel Nocera’s group at the Massachusetts Institute of Technology has created a copper-containing complex that is also able to catalyze the reduction of oxygen to water (Dogutan et al. 2010). Both of these model systems use small organic molecules to mimic the enzyme’s active site.

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

Lu’s approach is to use the protein myoglobin as the scaffold for creating a catalytically conducive environment around a synthetic active site. Myoglobin is much smaller than cytochrome c oxidase, making it easier to work with, and its rigid protein scaffold allows for the facile incorporation of mesoscale interactions into the design of the biosynthetic catalyst. In addition, a large body of work by many research groups has created the means to produce modified myoglobin molecules that can be used to explore how well-characterized changes in the protein’s structure affect those mesoscale interactions and catalytic activity (Lu et al. 2009).

Lu’s initial work aimed at incorporating a heme-coordinated copper into myoglobin that had catalytic activity, but it only reduced oxygen to the peroxide species and not all the way to water (Sigman et al. 2003). Further modeling activity identified three key histidine residues and a tyrosine residue within cytochrome c oxidase, as well as an elaborate hydrogen-bonding network involving two water molecules, that are critical in creating catalytic activity (Blomberg, Siegbahn, and Wikstrom 2003). The challenge then became one of introducing these residues and this hydrogen bonding network into the structure of a modified myoglobin. The group’s first step was to use a different heme to coordinate copper—one that added a particular hydroxyl group to the active site. The second was to introduce a tyrosine residue into the active site next to one of the key histidine residues. The resulting synthetic enzyme was able to reduce oxygen to water at a rate of thousands of reactions per second (Miner et al. 2012). Lu summarized these findings by emphasizing the importance of the heterogeneous environment and long-range interactions for generating catalytic activity.

The next challenge his group addressed was to try to understand and control the cascade of electron and proton transfers that occur in cytochrome c oxidase and similar enzymes, such as the family of blue copper proteins in which the copper atom is coordinated to two nitrogen atoms and two sulfurs in the active site. One interesting feature of these blue copper proteins is that they have nearly identical structures yet have a wide range of overpotentials ranging from 130 to 618 mV. Lu’s group decided to explore the role that mesoscale structure plays in producing this wide range of catalytic activity by changing the hydrophobicity and the hydrogen bonding network near the active site using various combinations of four mutations to alter amino acid residues in the protein. Using these mutations, either singly or in combination, Lu’s team was able to tune the overpotential over a 700-mV range, surpassing the highest and lowest potentials reported for any member of this enzyme family without altering the metal binding site (Marshall et al. 2009). Lu and his colleagues have since used these proteins to generate the first experimental support for what is known as a Marcus inverted region that has been proposed to be important in tuning the forward and backward electron transfer rates that create the charge separation needed to drive reactions such as photosynthesis (Farver et al. 2013).

Lu’s team has since collaborated with a group in India to engineer these artificial enzymes onto the surface of an electrode, a necessary step for creating a commercially useful catalyst. To ensure that the proteins have a specific orientation on the surface of the electrodes, computer models were used. The collaboration has generated a model system that has a pseudo-first-order rate that is better than the native enzyme and with a turnover rate approaching a quarter of a million reactions per second. Lu’s group has since improved the catalytic activity of its biomimetic system by incorporating nonnative cofactors and unnatural amino acids into their designed myoglobin oxidase catalysts (Bhagi-Damodaran et al. 2014).

Turning to a different subject in the final few minutes of his presentation, Lu described the use of catalytic DNA to control the assembly and disassembly of nanoparticles at the mesoscale for use in sensing, imaging, and drug delivery applications. Using lessons learned from the error-correcting functions of the ribosome, Lu’s team has developed catalytic DNA that can find defects in nanoparticle assembly and remove them (Tan, Xing, and Lu 2014).

In summary, said Lu, it is possible to make functional biomimetic models of complex metalloenzymes such as cytochrome c oxidase with high activity using much simpler native proteins, by taking into account several mesoscale parameters:

  • the heterogeneous environment around the active site that includes many noncovalent interactions, such as water and associated hydrogen-bonding networks;
  • the control of cascade reactions; and
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
  • the role that the homo- and heterogeneous reactions play in catalytic activity.

MESOSCALE CONCEPTS FOR DESIGN AND BEHAVIOR IN HETEROGENEOUS CATALYSIS

Heterogeneous catalysts differ from their homogeneous counterparts in that they are easier to separate out of a reaction mixture and regenerate. They are typically robust and have higher activities than homogeneous catalysts and usually have good stability at higher temperature, but aside from those features, these two broad classes of catalyst have much in common, said Cynthia Jenks. As is the case with the homogeneous catalytic systems that the first three speakers described, controlling key features of the heterogeneous catalysts that she studies requires consideration of the environment surrounding the active sites. In this presentation, Jenks focused on her work on immobilizing heterogeneous molecular catalysts in mesoporous silica nanoparticles, an environment that is more constrained than when these catalysts are in solution. These nanoparticles have cylindrical pores whose shape, size, and chemical composition and surface functionalization can be controlled during nanoparticle synthesis.

Confinement was the first aspect of these catalysts that Jenks addressed. When creating these catalysts, it is possible to put them onto the convex surface of a solid particle or onto the concave inside of the pore. In one experiment, she and her colleagues ran a catalytic addition reaction in a hexane solution, with the catalyst tethered to the outside of a particle and inside a mesoporous silica nanoparticle. Tethering the catalyst to the nanoparticle surface enhanced the reaction rate slightly, but putting it inside a nanoparticle pore produced a huge jump in reaction rate. Changes in the morphology and size of the pore—both its length and diameter—also can have a significant impact on catalytic activity. In another experiment, Jenks and her colleagues ran an aldol condensation reaction using a catalyst that was embedded in nanoparticles with pores that were either 400 or 800 nm long. Activity—measured by the percent of starting materials converted to the final product—dropped substantially with the longer pore, perhaps because the reaction products could not exit the pore efficiently. On the other hand, said Jenks, increasing pore diameter had a significant positive impact on percent conversion, raising it from less than that of the homogeneous catalyst when it was in a 2.8-nm-diameter pore to approximately 10-fold higher than the homogeneous catalyst when pore size was enlarged to 3.6 nm in diameter. These results show that modifying the physical, mesoscale environment of the catalysts can significantly affect the reactivity of the systems. Given the tools available in mechanical engineering, fluid control, and synthesis, one can imagine designing structures with varying pore diameters and shapes to reliably create catalysts for specific functions.

Aside from tuning pore size and shape, Jenks and her colleagues have also explored tuning catalytic activity by modifying the chemical composition of the internal pore wall using pentafluorophenyl propyl groups, which creates a hydrophobic environment inside the pores and enhances catalytic activity. It appears that this hydrophobic environment causes water to be extruded from the mesopores, driving the equilibrium of the reaction toward completion. Changing solvents can also have a big effect on reaction and conversion rates, with the effect depending on the nature of the catalyst and the solvent being used (Kandel et al. 2013a). For example, when using an immobilized amine to catalyze an esterification reaction, the percent conversion is high when hexane is the solvent and the catalyst is a secondary amine, but the conversion rate is low when water is the solvent, probably because water stabilized a reaction intermediate, which in turn inhibits the reaction. Understanding the fundamental aspects of the interaction between the solvent and reactive intermediates at the catalytic site represents another area for future investigation.

Jenks has also been exploring the creation of systems in which two catalysts are immobilized, one on the particle surface, the other in the pores, to enable tandem reactions to occur, much as location-coupled enzymes do in nature. These could also provide opportunities to take advantage of a combination of enzymatic specificity in a mild, external environment and also allow for less selective, harsher reactions to occur in a designed, reactor-like environment within a pore. As an example, she described a system in which the enzymes alcohol dehydrogenase and catalase are tethered to the outside of the particle and an alkylamine oxidation catalyst is immobilized inside the pores to perform a sequence of oxidation and aldol coupling that transforms short-chain alcohols

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

into longer-chain molecules with high selectivity (Kandel et al. 2013b). She also noted that it is possible to do one reaction on the surface of the particle and then cap the pores using gold or silver to carry out a second reaction in a more confined environment or to employ some gatekeeper functionality that only admits certain molecules into the pores. Another way porous materials can enable interesting chemistry is by enabling reactions to be run under different temperature and pressure conditions, she added (Lewis et al. 2013).

There are a number of challenges in designing these types of systems that are related to mesoscale phenomena. Tethering homogeneous catalysts is often complicated, she said, as is being able to distribute reactive sites throughout the particles and controlling the chemistry within the pore. Controlling the environment surrounding active sites in the pore has proven difficult, and so too has been understanding the effect that the reaction products have on the constrained environment inside a pore. Unintended plugging of the pores can also be a problem. Solutions to some or all of these challenges could come from promising work in mesoscale modeling of reactions in these different environments (Nagasaka et al. 2007, Piccinin and Stamatakis 2014) and molecular tethering in pores (Wang et al. 2014).

Jenks concluded her presentation by noting that there are many opportunities within modeling to address mesoscale phenomena. “Being able to develop new paradigms to enable us to look at these mesoscale regimes within these particular types of catalysts would be particularly valuable to enable us to understand at the mesoscale spatial heterogeneity, fluctuations, and transport effects,” said Jenks. Key challenges that she sees include the ability to design catalytic groups where they are desired, to design in gatekeepers and caps, and to bridge length scales in modeling and combine and control chemistry and transport.

STRATEGIES FOR THE SYNTHESIS OF MESOSCALE CATALYST DESIGNS

In the final presentation of this first panel session, Peter Stair discussed methods and strategies for making solid catalytic materials using one of two approaches: the one-step assembly of preformed molecular units into porous scaffolds and the step-by-step assembly of molecular units on preformed porous platforms. In the former process, pore structures and catalytic sites are determined by the assembling units, and in the latter, pore structures and catalytic sites are adjusted by assembly.

The synthesis of zeolites starting with aluminum or silicon hydroxyl anions is one example of the one-step synthesis approach. Under the right conditions of pH and temperature, these anions will assemble into a gel, form secondary units that ultimately form larger building blocks, and then form a host of zeolite structures at the mesoscale. Stair reminded the audience that one particular zeolite made in this fashion catalyzes the production of gasoline from oil, the largest human-performed chemical transformation in history. One feature of this strategy, he said, is that it runs at equilibrium conditions throughout the reaction process, so even when there is a significant amount of solid material formed, the reaction of the smaller soluble units continues at equilibrium.

Another, more recent example of the one-step approach is one that produces metal organic frameworks. In this case, the building blocks are more complicated than simple anions; they include a large variety of linkers and metal salts. Typically, the linkers determine what the structure of the metal organic framework will be when they combine with the metal salts under the right solvent conditions. This approach is capable of producing structures with pores that are much larger than those found in zeolites, and because the synthesis occurs in near-equilibrium conditions, it tends to produce crystalline materials.

The second approach to solid catalyst synthesis—step-by-step synthesis—uses a solid, porous material, usually ceramic, into which catalytic function is added. The ceramic forms can take a wide variety of macroscopic shapes. A variety of methods such as precipitation, adsorption, and impregnation are used to add catalytic function to the preformed materials. In impregnation, which Stair characterized as the most important of these methods, the porous ceramic material is combined with a solution of a metal salt, for example, where the volume of solution is such that it matches the pore volume of the ceramic material. Once the liquid fills the pores, a simple drying process leaves the metal salt behind as little crystallites of various sizes and shapes located at different locations in the pores. The catalyst is then activated by calcining it in

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

oxygen or reducing in hydrogen at high temperature. Typically, said Stair, because of the porous structures of the ceramic materials and the variations of density and shape of the crystallites within those pores, the final catalyst is considered inhomogeneous in size, shape, and composition.

There are pros and cons to each of these approaches for making solid catalysts. The advantage of the one-step assembly process, said Stair, is that it produces materials with uniform crystalline structure and a large surface area, and it provides the ability to carefully control pore size and the uniformity of those pores. The disadvantage of this approach is that the resulting catalysts are of limited stability and complexity, particularly with the metal organic frameworks. The two-step or post-platform assembly method produces materials with good stability, flexibility, and complexity. Pore size and morphology are well controlled, but the main disadvantage is that the active sites are determined more by statistics than by molecular control in most cases.

A new third approach that Stair and his collaborators are developing is to create materials using the atomic layer deposition process developed by the semiconductor industry as a bottom-up strategy to build mesoscale catalyst structures. This strategy starts out with atomic and molecular building blocks and assembles catalysts with well-defined composition and structure. As an example of how atomic layer deposition works, Stair described one synthesis in which a metal oxide surface covered with hydroxyl groups was exposed to a reactive organometallic complex such as trimethylaluminum. The resulting vigorous reaction created a new surface in which all of the hydroxyl groups are gone, replaced by a new surface decorated by alkyl groups that could be converted to hydroxyl groups again by treatment with water. The advantage of this approach is that because it is self-limiting it provides control by allowing uniform, layer-by-layer deposition of the coating without concerns about clogging the mouth of the channel, which is a concern for other coating techniques such as vapor deposition (Figure 3-5). Stair noted, too, that “you can make all of the interesting catalytic compositions that you would ever want using atomic layer deposition.”

Atomic layer deposition can also be used to make nanoparticles when using precursors of late transition metals such as palladium and platinum (Lu and Stair 2010, Lu et al. 2014). The nanoparticles tend to be capped by the ligands that were in the original organometallic precursor, and the deposition process can therefore be repeated to create tiny nanoparticles of well-defined size and composition. It is also possible to deposit multiple metals on the same nanoparticle to explore mesoscale effects related to the proximity of one metal atom to another.

Stair then noted that atomic layer deposition can be used to create apertures, pores, and cavities, as well as structures with or without facets. He highlighted one surprising example from his group in which he and his collaborators took a bare supported palladium nanoparticle and tried to use it to catalyze the dehydrogenation of ethane to make ethylene. The result was that the reaction produced carbon, methane, and hydrogen but little ethylene. Wondering what would happen if they covered the palladium nanoparticle, they added a layer of aluminum oxide that eventually buried the particle, eliminating all catalytic activity since reactants could not reach the nanoparticle. However, this coating has a high water and hydroxyl content and heating the material generated pores in the deposited layers that reached down to the nanoparticle. Now, this construct is “beautifully selective for producing ethylene and hydrogen,” said Stair, characterizing it as an example of how changing the environment around the nanoparticle totally changes the particle’s catalytic chemistry.

Elaborating on this idea, Stair said it is possible to bury the nanoparticles in layers that themselves have catalytic activity such that when the channels are formed, the result is a metal-based catalyst at the bottom of the channel and a different function, such as an acid catalyst, higher up in the channel to carry a second chemical transformation within the same pore. It is also possible to envision creating layers that generate a gradient of composition along the pore that would allow a particular chemical species to diffuse along the surface of the pore in one direction. “You might be able to channel reagents in and out of the catalytic site by using such a gradient,” Stair explained. He noted that these are just possibilities as his group has yet to generate such structures.

Atomic layer deposition can also be used to make cavities by starting with a catalytic oxide and adding a template molecule that will not be covered during the deposition process. The cavities can be

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

images

Figure 3-5 Conformal zinc oxide coating of a silicon trench without buildup at the pore entrance. SOURCE: Stair (2014). Reproduced with permission from Jeffrey W. Elam.

constructed so that they only let certain molecules reach the catalyst sitting at the bottom of the pore to create selectivity. His group has demonstrated this approach is capable of discriminating between closely related chemical species in a competitive photoreduction reaction (Figure 3-6) (Canlas et al. 2012). Stair added that it should be possible to create sterically defined cavities that can perform chiral catalysis, though again his group has yet to make such catalysts. In response to a question about these chiral cavities from Donna Blackmond of the Scripps Research Institute, Stair explained that the premise here is that creating a spiral of functional groups in the cavity could create binding sites capable of discriminating between two enantiomers.

Stair concluded his presentation by noting that with the essentially limitless possibilities of atomic layer deposition it would be good to develop design rules to help guide future work. He added that he would also like chemists to develop more selective synthesis chemistries based on the atomic layer deposition reaction and analytical techniques that can provide more information about the structures and chemistries of the resulting cavities.

DISCUSSION

Neil Henson from the Los Alamos National Laboratory started the discussion by asking the panel for their thoughts on the statement in the Department of Energy report that, when thinking about mesoscale phenomena, the density of atoms is more important than the specific positions of those atoms (BESAC Subcommittee on Mesoscale Science 2012). He added that it was his opinion based on what he heard from the four speakers that this statement is wrong. Stair said that structure does matter and that maybe it would be

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

images

Figure 3-6 Catalysis by nanocavities over titanium dioxide with structural selectivity. SOURCE: Stair (2014). Reproduced with permission from Justin Notestein.

important to consider structure over a longer length scale. Shaw agreed completely that the report was wrong, particularly with regard to enzyme function where the position of specific atoms makes a difference in activity. Session Chair Bruce Garrett said that the Energy Department’s report was oriented more toward materials rather than chemistry and chemists worry about atomic position more. Jenks added that the density of sites does matter.

Garrett asked the panel to comment on the need to couple transport to reactivity, which several of the panelists mentioned in their talks. Stair said that moving reagents where you want them to go is important and is something that could be improved in heterogeneous catalysis. Borovik added that he and others working in homogeneous catalysis have not done a good job with this either. He also noted that understanding transport issues includes understanding the timing and reagents coordinated so that the molecules arrive at the active site in the right sequence to facilitate the reaction. Jenks said that her work has shown that transport dynamics is tremendously important and that one challenge is controlling transport as pores get deeper and reactions get more complex. Lu said that structural biology can provide clues on how nature accomplishes transport with high precision.

Jim de Yoreo of PNNL asked about solvent effects for catalytic reactions done in solution as opposed to the gas phase. Shaw said that solvent plays an important role in determining catalytic activity. Enzymes, for example, have pockets of water in them that have been demonstrated to be important, though the details are not yet well understood. Borovik said there is not yet much evidence that solvent effects can alter the catalytic process, but anecdotal evidence does support that idea. “But I don’t think we have much experimental evidence to know exactly how the solvent is manipulating the process,” Borovik said. Blackmond noted that the work Jenks described with the aldol condensation supports the idea that solvent effects are important.

Garrett then asked if there is a difference between mesoscale environmental effects around active sites and confinement. Shaw said that there is

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

a difference: “The environment around the active site is controlling what the chemistry around that active site looks like. Confinement could at its simplest be just making sure the molecules are close enough to react.” Garrett also wondered about the example that was discussed where confinement decreased the reaction rate when he would have expected it to increase because reagents are kept in closer proximity to one another. Jenks explained that confinement can mean that product molecules could also end up being confined in the active site which could block further reactions from occurring.

Yong Wang from PNNL asked Stair to elaborate on the kind of design rules he would like to see developed to help guide the use of atomic layer deposition. Stair replied that one place to start would be to have a better idea of what the structures created using this method actually looked like, such as when particles are being partially covered with some parts left exposed. It would be helpful, he added, to have some notion about what structures would be interesting to make and to have reagents that will react selectively with the edges of a nanoparticle versus its facets or vice versa. Garrett, in a follow-up question, asked if there was any real idea of whether edges or facets are left uncovered when creating these structures and Stair said that infrared spectroscopy does provide a fairly good picture of whether facets or edges are exposed and that the results agree with calculations based on theory.

Turning to the subject of measurement, Garrett asked the panel to comment on the challenges of characterizing active sites in these constructs. Lu said that the characterization of systems that can form crystals is well developed, but the interface between homogeneous and heterogeneous catalysis is where more work is needed. Also, characterizing structures on surfaces in three dimensions is extremely challenging, Lu added. “I think the biggest challenge is doing in situ characterization of heterogeneous catalysis on surfaces,” he said. Shaw added that a major challenge is developing methods for determining if minor species present in catalysts are actually doing most of the catalysis.

De Yoreo commented that with regard to measurement, it is easy to address the problem of what is happening at the atomic scale using computational methods, while from the measurement standpoint it is easy to address what is happening at the ensemble scale. Linking the two scales is where the difficulty lies. It would be useful, though, to resolve motions at the mesoscale and new measurement techniques are needed to do this. Some optical techniques have sufficient time resolution, he noted, but they do not have the necessary spatial resolution. Pulsed imaging techniques, such as those using free electron lasers, might be able to produce snapshots but only while destroying the system. De Yoreo suggested that low-dose dynamic transmission electron microscopy (TEM) might be able to get both the necessary time and spatial resolution, but that has yet to be demonstrated. Stair added that TEM is good at seeing something solid but poor at seeing voids in structures.

Lu said that his group is exploring the possibility of using the optical and magnetic properties of the metal atoms in their catalysts to see if they can get useful microscopic images of single proteins and observe their dynamics. So far, his collaborator has obtained single protein images and can measure spectroscopic changes that provide information on dynamics. “It’s quite challenging and we cannot see the complete catalytic process,” said Lu. Borovik asked if this method can see the movement of the protein 10 to 20 angstroms from the active site. Lu said when the microscopy and spectroscopy data are combined with calculations and information from crystal structures there is the potential to produce a series of snapshots of protein dynamics.

Gregory Schenter from PNNL stated that it is his opinion that the issue of a system being confined is closely coupled to the nature of the fluctuations that influence the reactions from the mesoscale, be it density fluctuations, vibrational fluctuations, electronic structure fluctuations, or electric field fluctuations, and he asked the panel for their comments. Borovik agreed with Schenter and that all of those properties are governed by the local environment. He noted that changes in the hydrogen-bonding network his group creates change the redox potential of the system and the acid–base properties, all of which are connected to function.

Miguel Garcia-Garibay, of the University of California, Los Angeles and a member of the organizing committee and the Chemical Sciences Roundtable, said that one way of looking at compartmentalization and reduction of dimensionality is to reduce the statistical entropy of the system. Given that nobody on the panel talked about entropy, he asked if the panel had any thoughts on this matter. Borovik said that he thinks entropy is important and has examined how the local

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

confinement provided by the cavity around a catalyst, particularly the hydrogen-binding cavity in one of the systems he studies, can influence the reaction process and impacts the energy of activation. His group found that there is a tremendous effect that can change the entire mechanism of the reaction and provide unexpected rate enhancements. He acknowledged, though, that he would like to have a better understanding of how to take advantage of the local confinement, which is an entropic effect to make systems function better. Although entropy is well defined, the entropic effect of this local confinement might be more difficult to quantify.

In response to a comment from William Noid of the Pennsylvania State University about the relative importance of entropy and atomic structure in high-energy versus low-energy reactions, Shaw said that she believes that, even at the mesoscale, atomic structure matters. “Maybe it’s possible that we don’t need to understand atomic structure in detail, but I think it’s critical to have different materials or different catalyst functions regardless of the length scale that you’re looking at,” she said. Jenks added that there just is not enough knowledge yet to know how understanding the atomic structure is impacting the macroscale behavior of a system. As a final comment, Borovik reiterated that structure does matter at the mesoscale and that the reason entropy is not discussed much is because the field does not know how to think about it yet, raising a challenge that needs to be addressed.

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×

This page intentionally left blank.

Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 9
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 10
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 11
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 12
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 13
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 14
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 15
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 16
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 17
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 18
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 19
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 20
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 21
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 22
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 23
Suggested Citation:"3 Catalysis." National Research Council. 2015. Mesoscale Chemistry: A Workshop Summary. Washington, DC: The National Academies Press. doi: 10.17226/21733.
×
Page 24
Next: 4 Membrane Behavior and Microchemical Systems »
Mesoscale Chemistry: A Workshop Summary Get This Book
×
Buy Paperback | $45.00 Buy Ebook | $35.99
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

In the last few decades great strides have been made in chemistry at the nanoscale, where the atomic granularity of matter and the exact positions of individual atoms are key determinants of structure and dynamics. Less attention, however, has been paid to the mesoscale--it is at this scale, in the range extending from large molecules (10 nm) through viruses to eukaryotic cells (10 microns), where interesting ensemble effects and the functionality that is critical to macroscopic phenomenon begins to manifest itself and cannot be described by laws on the scale of atoms and molecules alone.

To further explore how knowledge about mesoscale phenomena can impact chemical research and development activities and vice versa, the Chemical Sciences Roundtable of the National Research Council convened a workshop on mesoscale chemistry in November 2014. With a focus on the research on chemical phenomena at the mesoscale, participants examined the opportunities that utilizing those behaviors can have for developing new catalysts, adding new functionality to materials, and increasing our understanding of biological and interfacial systems. The workshop also highlighted some of the challenges for analysis and description of mesoscale structures. This report summarizes the presentations and discussion of the workshop.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

    « Back Next »
  6. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  7. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  8. ×

    View our suggested citation for this chapter.

    « Back Next »
  9. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!