Supramolecular Chemistry Self-Assembly PDF

Self-Assembly 10 ‘On from room to room I stray Yet mine host can ne’er espy And I know not to this day Whether guest or captive I.’...

Self-Assembly 10 ‘On from room to room I stray Yet mine host can ne’er espy And I know not to this day Whether guest or captive I.’ Sir William Watson (1858–1936), World-Strangeness  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 592 Self-Assembly 10.1 Introduction Lindoy, L. F., Atkinson, I., Self-assembly in Supramolecular Systems. Royal Society of Chemistry: Cambridge, 2000. 10.1.1 Scope and Goals Whitesides, G. M., Grzybowski, B., ‘Self-assembly at all scales’, Science 2002, 295, 2418–2421. The synthesis of even small molecules by conventional organic or coordination chemistry may often be a tedious and repetitive process. With every new stage in the synthetic pathway, more and more product is lost, even in relatively high-yielding steps. The cost, both in materials and specialist endeavour, rises steeply. Indeed, entire chemistry-related disciplines such as chemical engineering have, as a primary goal, the task of simplifying chemical syntheses as much as possible. However, in the preparation of many speciality or fine chemicals this is often a very difficult task. Even more difficult is the extension of conventional chemistry to the preparation of intermediate and large-size molecules, assemblies and nanometre-scale (nanoscale) machines. Yet it is the preparation of such large aggregates that many supramolecular chemists believe will pave the way to the construction of new ultra-miniaturised com- ponents for computational, electronic and optical devices (Chapter 11). As a result, a great deal of work has gone into the development of preprogrammed systems in which small, readily prepared molecular components automatically converge to produce a much larger, more complicated aggregate. By the term ‘preprogramming’ we understand a chemical system in which the very nature of the molecular building blocks (in terms of size, shape, symmetry and the electronic properties of their binding sites) contains all the information necessary to selectively produce the desired superstructure. The supramo- lecular complex assembles itself. Thus we can define self-assembly as the spontaneous and reversible association of molecules or ions to form larger, more complex supramolecular entities according to the intrinsic information contained in the molecules themselves. This kind of approach is potentially of central importance in bridging the gap between the scale of structures and components available within the molecular world and those available on the tens to hundreds on nanometer scale via current lithographic techniques (particularly in the electronics indus- try). Production of electronic devices on the molecular scale would enable dramatic increases in speed and computing power, as well as the enhanced versatility that comes from small space requirements. Indeed, already computer hard disks have a read head flying at only 25 nm or 200 atoms above the surface of the disk. In order to function, however, molecular bistable devices (switches) must be pro- vided with the input/output infrastructure necessary for them to communicate with the outside world. Furthermore, they must be completely controllable, reversible and readable at the molecular level through millions of ‘on–off’ cycles. Current lithographic etching techniques result in the production of components of silicon wafers of sizes down to about 0.1 µm (i.e. 1000 Å or 100 nm). Already, even at that scale, problems are encountered with electron tunnelling and difficulty of heat dissipation, as well as more subtle effects such as quantum mechanical confinement of charge carriers, which results in each component having a different range of energy levels depending on its size. It is possible that fabrication of components by lithography is fundamentally limited to the tens of nanometre size scale. On the other hand, the largest well-characterised synthetic supermolecules to date are of the order of a few tens of nanometre in size, and have much more well-defined properties. Unfortunately, they lack the integrated suite of functionality requirements for practical device manufacture. This suggests Supramolecular Chemistry, 2nd edition J. W. Steed and J. L. Atwood © 2009 John Wiley & Sons, Ltd ISBN: 978-0-470-51233-3  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Introduction 593 Figure 10.1 Self-assembly of twelve autofabricated pentameric tiles linked by magnetic interactions inspired by the self-assembly of the protein capsid of the poliovirus (Copyright National Academy of Sciences, U.S.A.). that there is a point in between the worlds of electronic engineering and chemical synthesis, on the size scale 10–1000 nm, in which well-defined, functional and networked supramolecules might form the basis for a new kind of electronic design. Precedent for this molecular engineering comes from the world of molecular biology (Chapter 2) in which functional molecular devices of sizes between 1 and 10 000 nm regulate all of the chemistry of life, and indeed there is no fundamental reason why artificial molecular devices may not similarly exist. The vast majority of such biochemical systems are self-assembling in order to economise on the amount of genetic information required to synthe- sise them. For example the coats or capsids of virus particles generally comprise multiple copies of the same protein that self-assemble into highly regular geometric arrangements. Figure 10.1 shows a macroscopic model that gives at least a cartoon-type insight into the principles that underlie complex processes such as viral self-assembly. The model uses tiles based on the pentameric shape of poliovi- rus intermediates in capsid assembly. The tiles interact with one another via magnets which simulate the supramolecular interactions involved in linking them together. Manual shaking of twelve such curved pentagonoids in a container results in the ‘self-assembly’ of a closed, dodecahedral structure in just 1–2 minutes.1 In order to bridge the gap between current electronic and chemical technology, two distinct ap- proaches may be distinguished: ‘engineering down’ and ‘synthesising up’. We have already seen that there is little room for manoeuvre in engineering down due to current technological limitations, and thus the challenge to chemical technology is to develop ways to ‘synthesise up’ into the required range of scale and functionality through the use of supramolecular techniques. We will look in more detail at the ‘synthesising up’ and ‘engineering down’ approaches to nanotechnology in Chapter 15. For the time being we will explore the unit chemical steps that have so far been explored in the synthesis of large scale supramolecular systems and show what has been achieved so far in terms of the programmed or templated self-assembly of functional multi-nanometre scale supramolecular aggregates. Closely linked to the concept of self-assembly is the idea of self-replication: the ability of one mol- ecule or entity to produce a copy of itself. The analogy to biological (asexual) reproduction is clear and the ability to self-replicate has been suggested to constitute a basic criterion of life. Abundant examples in nature demonstrate that self-replication is a feasible, and indeed commonplace, occur- rence at the molecular level. Biological cell division involves the unwinding of the DNA double helix and the templated synthesis, via interstrand hydrogen bond base pairing, of a complementary copy of each single strand to generate two new double helices (Section 2.9.5). A single DNA strand contains all the information necessary to produce its complementary partner leading to self-replication of the  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 594 Self-Assembly double helix without the prohibitively frequent introduction of mistakes or variations (mutations). By comparison, the conventional synthesis of even a small oligonucleotide by stepwise condensation of phosphate residues would be a monumental task. Indeed, the surmounting of this barrier to oligonu- cleotide production by the polymerase chain reaction (PCR) (a process by which small amounts of oligonucleotides template the formation of a large number of copies of themselves) earned the 1993 Nobel Prize in Chemistry for Kary B. Mullis for his work in this area (Section 2.9.3). Increasingly in biochemical and chemical systems the concept of dynamic or time-resolved self-assembly is being recognised leading to a temporal hierarchy. Generally speaking this concept means that in complex systems self-assembly occurs in a sequence of stages with the higher stages ( j) not assembling until the self-assembly of a building block step ( j – 1) is complete. The lifetime of each self-assembled stage (τ) is inversely proportional to its position in the hierarchy, thus the highest stages are much longer lived than the stages below them, i.e. τj >> τj
1. The relevance of this kind of hierarchial self-organisation in biology is clear – the dimerisation of two nucleobases is individually short lived but a biological cell and thence an organism has an indefinitely long lifetime. All of self-assembly is based on some kind of templating (i.e. information-based assembly). We have already seen the operation of the template effect in synthesis (Section 3.9.1), in which a metal cation is used as a simple spherical template for the assembly of macrocyclic organic ligands. In this chapter we will examine much more generalised applications of templates and the self-templation that consti- tutes self-assembly, including the synthesis of elaborate supramolecular structures such as molecular knots, catenanes and rotaxanes. The next chapter, Chapter 11, then deals with large-scale functional devices, while the efforts of the supramolecular chemistry community to produce biomimetic and artificial, abiotic (i.e. non-biological) self-replicating systems is discussed along with supramolecular (templated) catalysis in Chapter 12. 10.1.2 Concepts and Classification Lindsey, J. S., ‘Self-Assembly in synthetic routes to molecular devices: biological principles and chemical perspectives – a review’, New J. Chem. 1991, 15, 153–180. Before embarking upon a survey of both natural and synthetic template-assembled and self-assembling systems, it is important to define and distinguish some of the language that will be required. Much of the terminology of supramolecular chemistry is still in a state of rapid change, and many terms are used either interchangeably or loosely with different terms being applied to very similar phenomena in chemistry and biochemistry in particular. Jean-Marie Lehn has distinguished a hierarchical order of the terms ‘templating’, ‘self-assembly’ and ‘self-organisation’. Together, these terms cover the processes that enable preprogrammed molecular components or tectons (from the Greek tekto-n, meaning builder, cf. Section 8.1.2) to come together spontaneously, in a well-defined way, to give assemblies presenting order in one, two or three dimensions and perhaps (although not necessarily) time. We have already discussed the template effect (Section 3.9.1) as a useful aid to synthesis through the involvement of temporary or permanent ‘helper’ species (e.g. an alkali metal cation). Self-assembly may or may not involve an actual template, such as a metal cation, and thus the template effect itself is not strictly an example of self-assembly, but has been classified by Lehn as ‘the unit step in self-assembly processes that comprise several steps occurring spontaneously in a single operation’. Within self-assembly pro- cesses, we must distinguish molecular self-assembly and supramolecular self-assembly. Molecular self-assembly concerns the formation of covalent bonds as part of a special synthetic procedure. The assembly is subject to control by the reaction stereochemistry and the conformational features of the intermediates, e.g. the formation of amine–aldehyde condensation macrocycles, as in Scheme 3.21. Supramolecular self-assembly concerns the recognition-directed, reversible spontaneous association  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Introduction 595 Figure 10.2 Fullerenes such as C60 and carbon nanotubes self-assemble covalently under extreme conditions. of a limited number of tectons (components) under the intermolecular control of relatively labile, noncovalent interactions such as coordination interactions, hydrogen bonds and dipolar interactions. The reversibility of supramolecular self-assembly is key to the resulting systems’ ability to sift through the available components to form the thermodynamically most favourable structure. This incorporates the potential for self-repair and correction of defects, as in biological systems. Fundamentally self- assembly is a convergent process in which a number of components assemble into, ideally, a single final, stable structure. Self-assembly is thus very distinct from chemical emergence which is a diver- gent process in which complexity evolves over time (Section 1.10.2). We will return to the interesting concept of emergence in chemical systems in Chapter 15. An interesting borderline case between covalent and supramolecular self-assembly concerns the formation of fullerenes, such as C60 and C70, and related species such as extended carbon nanotubes (Figure 10.2) within a high-temperature carbon vapour. While strictly an example of irreversible covalent bond formation, the extreme conditions of the carbon vapour permit a certain amount of reversibility in the formation of even strong covalent bonds, allowing them to behave somewhat like weaker supramolecular interactions do under ambient conditions. This means that more stable closed structures such as C60, which does not have any dangling bonds, are formed in preference to fragments of graphitic sheet, for example. On a higher level, the term self-organisation incorporates both the interaction between constituent parts of self-assembled entities and the integration of those interactions leading to collective behaviour such as is found in phase changes, for example. Self-organisation admits the possibility of emergent behaviour that is a property arising from complex interactions between self-assembled entities. In 1991 Lindsey introduced a definitive classification scheme for various types of self-assembly across biochemistry and chemistry which still remains the basis for the way in which we think about self-assembly today. Lindsay’s scheme divides self-assembly into seven broad, overlapping classes. Class 1. Strict Self-Assembly In a strict self-assembly process, the final product is produced entirely spontaneously when the compo- nents are mixed together in the correct ratios under a given set of conditions of temperature, pH, con- centration etc. The product formation must be completely reversible and represent the thermodynamic minimum for the system. In essence, all the information necessary for the assembly to occur is coded into the constituent parts. The concept of strict self-assembly is rooted in the ‘Thermodynamic Hypoth- esis’ of Afinison who suggested that under physiological conditions the native structure of a protein is  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 596 Self-Assembly the one in which the Gibbs free energy of the system is at its lowest.* Later work showed that this basic concept is not true of all proteins, some of which are assembled by entities such as chaperones. Class 2. Irreversible Self-Assembly Irreversible self-assembly involves the formation of a product through a series of irreversible (usually covalent) bond-forming steps under kinetic control. There is no margin for self-correction and any ‘mistakes’ are fatal to the formation of the final assembly. This class of reaction is not of significant inter- est in supramolecular chemistry but is topical in organic synthesis as ‘tandem’ or ‘domino’ reactions.2 Class 3. Precursor Modification Followed by Self-Assembly This process involves precursors that cannot undergo self-assembly until they are chemically modified – they are thus in a kind of ‘resting state’ until activated by some trigger or change. An example is the biosynthesis of collagen, the fibrous protein that are the major components of skin and bone. Collagen forms long fibrous bundles outside the cell, called fibrils. It would be fatal to the cell if these fibrils self-assembled inside it and so the collagen precursor, procollagen, is prevented from doing so by end- capping amino acid chains termed ‘propeptides’. Once synthesised the procollagen is secreted out of the cell where the capping propeptides are removed by proteolytic enzymes, triggering the self-assembly process (cf. prions and amyloids in Section 14.6.1). Class 4. Self-Assembly with Postmodification This process involves the covalent ‘locking in’ of structures formed by reversible self-assembly. The irreversible, post-assembly step switches off the equilibrium process involved in the self-assembly. As we will see in the following sections, self assembly with covalent postmodification is involved in a range of biochemistry (e.g. insulin synthesis) and elegant abiotic supramolecular synthesis as in the formation of catenanes and knots. Class 5. Assisted Self-Assembly In an assisted self-assembly process external factors that are not part of the final assembly are involved in mediating the assembly process rather like a catalyst. This concept became important with the recogni- tion of the role played by molecular chaperones in protein folding. The chaperone does not influence the thermodynamics of the assembly process and thus it leaves the ratio of folded and unfolded polypeptide chains the same but it stabilises intermediates along the folding pathway, accelerating the folding rate. Chaperones are important in prevention of peptide aggregation and in refolding denatured proteins.3 Class 6. Directed Self-Assembly Directed self-assembly processes are those which involve a template, whether or not it ends up in the final structure. Typical examples are vesicle-directed biomimetic mineralisation strategies (Section 15.3) Class 7. Self-Assembly with Intermittent Processing This class of self-assembly incorporates elements from all of the preceeding classes and involved com- plex processes in which there are sequential steps involving self-assembly and covalent or irreversible modification. In general such processes are only found in biology at the present state of the field. * US biochemist Christian Anfinsen 1916–1995, winner of the 1972 Nobel Prize in Chemistry for ‘his work on ribonuclease, especially concerning the connection between the amino acid sequence and the biologically active conformation’.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Introduction 597 For the most part, in abiotic supramolecular chemistry which is overwhelmingly based on either metal-ligand coordination interactions or hydrogen bonding, we will be concerned only with classes 1 and 4, i.e. either strict self-assembly or self-assembly with postmodification. Even within these classes, however, we can distinguish some subtleties of the kinds of bonding that can be involved with often more than one kind of interaction, perhaps of different strength, being involved. Depending on the number and types of interaction we can classify self-assembly processes as either a Single or Multiple Interaction Self-Assembly. These descriptive terms pertain to the number of different kinds of interaction that are present within the assembled structure. Single interaction self-assemblies might depend only on metal ligand interactions, for example, while multiple interaction processes might involve metal-ligand interactions and hydrogen bonding. We can also subdivide multiple interaction self-assemblies based on the number of a particular type of interaction present. If the self-assembled system contains different categories of interaction (e.g. both metal-ligand bonds and hydrogen bonds) then the term multimediated assembly is used, whereas if the assembly contains two different metal coordination environments but no other types of interaction then we refer to it as a unimediated assembly because even though there are two distinct interactions, they are both metal-ligand interac- tions, Figure 10.3. In general, in self-assembly, we can identify three main drivers that pervade a wide variety of chemi- cal systems, particularly metal-ligand complexes: 1. Efficient self-assembly occurs when there is a match between the geometric or stereochemical pref- erences of the components, e.g. the coordination polyhedron of a metal ion and the possible binding site arrangement(s) on a ligand. These pairings are sometimes referred to as incommensurate sym- metry interactions or interactional algorithms 2. All binding sites must be involved in the assembly. 3. Assemblies are influenced by the efficient packing of geometrical shapes in crystals or macroscopic materials. Before we go on to discuss artifical self-assembly, particular the current intense interest in self- assembling coordination complexes, we will look for inspiration at how Nature does it! Figure 10.3 (a) A single interaction assembly using one specific type of metal-ligand interac- tion, (b) A unimediated multiple interaction assembly, using two different metal-ligand interactions, (c) A multimediated multiple interaction assembly using both metal-ligand interactions and hydrogen bonding.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 598 Self-Assembly 10.2 Proteins and Foldamers: Single Molecule Self-Assembly 10.2.1 Protein Self-Assembly Okabayashi, H.-F., Ishida, M. and O’Connor, C. J., ‘The self-assembly of oligo-peptides’, in Self-Assembly, Robinson, B. H. (ed.), pp. 331–338, IOS Press: Amsterdam, 2003. In a strict self-assembly process all of the interactions contribute to the overall free energy of the assembly and the fi nal product will be the one with the lowest overall free energy. The sequence of events by which the assembly forms may well depend on the magnitude of the interactions, however, with the stronger or primary interactions (e.g. metal-ligand bonds) needing to form fi rst before the structure is further stabilised by secondary interactions such as hydrogen bond- ing between partially assembled fragments. This process is termed hierarchial assembly and is a common feature in both abiotic and biological self-assembly. In proteins, the linear polypeptide sequence folds fi rst into significant secondary structural features such as α-helices and β-sheets, held together by amide NH···OC hydrogen bonding interactions and hydrophobic effects in aqueous solution. The repetition of these features within a particular strand is often termed supersecondary structure. The overall folding of each polymer strand gives the protein tertiary structure and is responsible for many of the protein’s properties including the catalytic activity of enzymes which is often closely linked to the geometry and environment of the active site. Interac- tions between folded polymers to give self-assembled aggregates of a number of folded protein chains is termed the quaternary structure (Figure 2.20). For example, haemoglobin is made up from four separate myoglobin subunits (Section 2.5). Clearly the quaternary structure cannot assemble until the tertiary structure has formed, and so on. This hierarchical mechanism allows proteins to fold into their active conformations in a matter of minutes. For comparison, it is estimated that for a small 100 amino acid residue protein a random search for the lowest energy conformer would take about 1027 years. Such slow speeds are not biochemically viable – this figure is about 1018 times longer than the age of the universe! In abiotic systems we can also recognise some of these kinds of features. For example in the case of a metal helicate the primary structure involves the metal-ligand bonds with the secondary structure being the helical conformational folding. We might also recognise tertiary structure in the circular helicates (Section 10.8.6) The hierarchical nature of protein folding to give the precise conformation based on the information encoded into the primary sequence of amino acid residues is vital from a biological viewpoint. Errors in protein folding can have disastrous consequences. For example, many serious diseases such as BSE, CJD, Diabetes and Alzheimer’s Disease are caused by the misfolding of proteins into toxic, aggregated β-sheet fibrils termed amyloids, Figure 10.4. The tightly packed β-sheet structure of amyloid fibres is characterised by two characteristic X-ray diffraction maxima at 4.7 and 10 Å, corresponding to the interstrand and stacking distances in β-sheets These represent cases where the biological self-assembly process has ‘gone wrong’ in some way. This might be due to the malign influence of an external agent such as a prion (proteinaceous infectious particle) which infects and propagates by refolding abnormally into a structure which is able to convert normal molecules of the protein into an abnormally structured form. The fact that normal proteins can be refolded in this way suggests that they may not represent true examples of strict self-assembly since the refolded form is in some way more stable (although the insolubility of amyloids is also a significant driving force). Indeed while many proteins do self-assemble, others require some kind of assistance in their folding in the form of other proteins called molecular chaperones that guide or catalyse the assembly process.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Proteins and Foldamers: Single Molecule Self-Assembly 599 Figure 10.4 Electron microscope image of negatively stained amyloid fibrils formed by islet amy- loid polypeptide showing long, unbranching fibrils of 100 Å in diameter (reproduced with permission from ). 10.2.2 Foldamers Goodman, C. M., Choi, S.. Shandler, S. and DeGrado, W. F., ‘Foldamers as versatile frameworks for the design and evolution of function’, Nature Chem. Biol. 2007, 3, 252–262. Given the importance of single molecule self-assembly in proteins it is natural that supramolecular chemists have tried to mimic this property in biological models and in artificial systems. Artificial or biomimetic molecules that self-assemble into a particular conformation are termed foldamers and they represent a popular area of current research not just as aids in our understanding of protein folding but also as artificial scaffolds used to place functional or sensing groups in a precise way relative to one another – a step towards chemical nanotechnology. Foldamers can be amino acid based short polypeptide sequences as in non-natural peptide oligomers such as aliphatic β-, γ-, and δ-peptides, which are significant because of their similarity to α-peptides (a β-peptide has the amine group on the second carbon atom of the chain instead of the first as in natural α-amino acid derived peptides, similarly a γ-peptide has the amine group on the third carbon atom and so on). Aromatic amides are particularly popular foldamer components because of the restricted rotation about the Ar–C(O)NH bond that is a result of the delocalisation of the amide lone pair, Scheme 10.1a. The confor- mation of the group can also be locked in by particular hydrogen bonding interactions, Scheme 10.1b.5 R O O O O O O + NH + N R N R N R N R N N R O H H H O H H N R H (a) (b) Scheme 10.1 (a) resonance forms in aryl amides illustrating the restricted rotation of the Ar–C(O)NH bond because of the partial double bond character and (b) examples of hydrogen bonding motifs stabi- lising particular aryl amide conformers.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 600 Self-Assembly OR OR RO OR O O RO OR N R = (CH2)13CH3 N O O O O O2N N N N N NO 2 H H H H NH HN 10.1 Figure 10.5 (a) solution structure of the ‘tailbiter’ foldamer (10.1) (reproduced by permission of The Royal Society of Chemistry) and (b) Lucas Jennis’ engraving of the wyrm Ouroboros that swallows its own tail, published on an alchemical emblem-book entitled De Lapide Philisophico (1625). A particularly attractive aryl amide foldamer is ‘talibiter’ (10.1) named after the mythological wyrm Ouroboros that Kekulé claimed inspired his structure of benzene (Figure 10.5),6 which folds back on itself in a spiral conformation such that the pyrrole unit on one end is close to the other end of the molecule. The solution conformation of the foldamer was determined using NMR spectroscopic methods as described in Box 6.1. 10.3 Biochemical Self-Assembly 10.3.1 Strict Self-Assembly: The Tobacco Mosaic Virus and DNA Klug, A., ‘The tobacco mosaic virus particle: structure and assembly’, Phil. Trans. Royal Soc. Ser. B, Biol. Sci. 1999, 354, 531–535. We have already dealt with some general aspects of biochemical self-assembly in Section 2.10 includ- ing the remarkable formation of viral capsids. There are some biochemical examples, however, that translate readily into supramolecular chemical concepts and have been pivotal in defining the field. One such system is the tobacco mosaic virus, a virus that is very harmful to a variety of crops including tobacco, tomato, pepper, cucumbers and species such as ornamental flowers. This system consists of a helical virus particle measuring some 300  18 nm (Figure 10.6). A central strand of RNA is sheathed by 2130 identical protein subunits, each of which contains 158 amino acids. What is remarkable about  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Biochemical Self-Assembly 601 Figure 10.6 (a) Electron micrograph and (b) Schematic representation of the tobacco mosaic virus. (Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced by permission). the virus, compared to a purely chemical entity, is that if it is decomposed into its component parts and these fragments are mixed under physiological conditions, then the virus particle is accurately self- reassembled and regains full functionality. The mechanism of this impressive piece of self-assembly is well established and consists of the formation of a disk-shaped module by the aggregation of two layers of the protein sheath subunits. The protein disk is transformed into two helix turns by threading a loop of RNA into the central hole of the disk. The process is repeated by threading additional disks until the viral particle is complete, (Figure 10.7). The advantage of this convergent, modular approach to viral assembly, in which identical subunits are assembled into the complete entity, is that much less genetic information is required to program the formation of the assembly compared to coding the location of each residue individually. The formation of the tobacco mosaic virus serves to illustrate the role played in nature of noncovalent interactions. The entire self-assembly process is driven by nothing stronger than hydrogen bonding, electrostatic and solvophobic effects and other very weak interactions, all acting in concert. The final structure rep- resents a thermodynamic product and is favoured by a high equilibrium constant of formation (forma- tion constant). The self-assembly of the tobacco mosaic virus is thus an example of strict self-assembly in Lindsey’s scheme. The weak nature of the interactions means that if a mistake is made during the assembly process, then it is rectified automatically because the process is reversible and the ‘mistaken’ product is simply not as stable as the correct arrangement. The most famous example of a strict self-assembly process is the formation of the DNA double helix (Figure 2.27), by the spontaneous association (by hydrogen bonding) of complementary Figure 10.7 (a)–(d) Stepwise self-assembly of the tobacco mosaic virus. (Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced by permission).  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 602 Self-Assembly Figure 10.8 Stages in the self-assembly of adenine–uracil nucleic acid double helices. nucleobase pairs such as guanine and cytosine (Fig. 2.28). The thermodynamics of ‘zipping up’ the double-helical structure are of interest since the association of the two helical strands results in a thermodynamically unfavourable decrease in entropy, suggesting that there might be a significant thermodynamic barrier to be overcome. Studies on relatively small model systems such as the adenine- and uracil-based complementary pair of nucleic acids (A)17 and (U)17 show that the entwin- ing of the two strands to form a double helix is a two-stage process consisting fi rstly of a nucleation phase followed by a cascade propagation sequence, which completes the process (Figure 10.8). The nucleation phase brings together the two strands and is dominated by the thermodynamically unfavourable entropy component, since the favourable enthalpy term arising from the formation of hydrogen bonds between a few base pairs is relatively insignificant. Once nucleation has occurred, the association of every new base pair results in further increases to the magnitude of the favoura- ble enthalpy term with little change in entropy, resulting in a complete double helix (Figure 10.9). 10.3.2 Self-Assembly with Covalent Modification The term ‘self-assembly with covalent modification’ is generally applied to systems in which the formation of covalent linkages is irreversible, particularly as in classes 3 and 4 in Lindsey’s scheme. If the covalent bond formation occurs after the self-assembly (class 4) then, unlike a strict self- assembly, the final product does not necessarily need to be a thermodynamic minimum structure. On the other hand class 3 self-assembly does result in a thermodynamically stable structure once the covalent initiation step has taken place. Figure 10.10a shows a cartoon representation of the concept of precursor preprocessing. The interlocking of the two self-assembling components cannot occur until a covalent chemical change is carried out on the precursor of one of them. This may result in a change in size, shape or orientation, or the removal of a blocking effect. The two subunits are then free to self-assemble. Self-assembly with covalent modification may also involve post-assembly processing in which non-covalent interactions are used to assemble a precursor complex that is then fixed in the desired state by covalent modification, Figure 10.10b. This may be regarded as a kind of template effect, and indeed parts of the structure needed to template the initial self-assembly may subsequently be cleaved away if no longer required. An excellent biological example is the biosyn- thesis of the mammalian hormone, insulin. Insulin consists of two polypeptide chains (A and B)  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Biochemical Self-Assembly 603 Figure 10.9 Energetics of the self-assembly of nucleic acid double helices as a function of increasing number of base pairs. linked by a pair of disulfide bridges. Reduction of these —S—S— bridges leads to the break-up of the insulin molecule. Unlike the tobacco mosaic virus, however, the individual polypeptide chains do not contain the information necessary to self-assemble and hence reoxidation does not result in the reformation of active insulin. In fact, insulin is synthesised from a much larger polypeptide, preproinsulin, by two post-translational processing steps. Preproinsulin is able to self-assemble, using noncovalent forces, into a conformation that places the A and B fragments of the nascent insulin in their correct relative orientations. The two strands are then linked together via the irre- versible formation of the two disulfide linkages to give proinsulin. With the strands safely joined, the excess polypeptide can then be removed to form the final product (Figure 10.11). Figure 10.10 (a) Combination of covalent preprocessing modification and self-assembly, (b) self- assembly followed by covalent postmodification.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 604 Self-Assembly Figure 10.11 Biosynthesis of insulin by self-assembly followed by covalent modification. 10.4 Self-Assembly in Synthetic Systems: Kinetic and Thermodynamic Considerations 10.4.1 Template Effects in Synthesis Busch, D. H., Vance, A. L. and Kolchinski, A. G., ‘Molecular template effect: historical view, principles and perspectives’, in Comprehensive Supramolecular Chemistry, Atwood, J. L., Davies, J. E. D., MacNicol, D. D. and Vögtle, F. (eds), Pergamon: New York, 1996, vol. 9, 1–42. In Section 3.9, we distinguished between the kinetic and thermodynamic template effects in macro- cycle synthesis. Under the operation of a kinetic template effect, the distribution of the products of a cyclisation reaction is altered by the binding of the reactants in an enforced and relatively rigid geom- etry about the metal ion template. Crucially, the reaction should not be reversible under the prevailing conditions since the templated species is unlikely to be the most thermodynamically stable reaction product. Indeed, the cost of unfavourable interactions within the macrocycle must be borne during its synthesis. This is the origin of the enhancement of the metal ligand binding constant as a result of macrocyclic preorganisation (Section 1.6). The purpose of the synthetic template is to enable us to take advantage of this energetic ‘pay in advance’ gain in complexation ability. Effectively we are taking advantage of the self-assembly of a template complex followed by covalent postmodification to ‘fix’ the macrocycle. The use of metal ions as kinetic synthetic templates is extremely widespread, and is an excellent way in which to bring about the organisation of a number of reacting components in order to direct the geometry of the product. Because some metal ions, such as the transition metals, often have preferred coordination geometries (e.g. tetrahedral, square planar, octahedral etc.), changes in metal ion may have a profound effect on the nature of the templated product. Metal-ion-templated syntheses may be classified more generally as examples of self-assembly with covalent postmodification. For example, the synthesis of the artificial siderophore 10.2 is effected by the use of an octahedral Fe3 template.8 In this case, the macrobicyclic product is obtained as the Fe3 complex from which it is difficult to separate. In contrast, use of metalloid elements, such as silicon, tin antimony or boron, which can form weak covalent bonds with oxygen, nitrogen or sulfur substituents during the course of the reaction, results in templated products that may be obtained metal-free by simple hydrolysis. These ‘covalent template reactions’ (the M—X bond is essentially covalent in these cases) also have the advantage that the  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Self-Assembly in Synthetic Systems: Kinetic and Thermodynamic Considerations 605 O N O H O NH N N O O O NH O O O O 1. N(CH2CH2NH2)3 O 3+ 3+ Fe Fe 2. 60 oC, 10 d. O O O O O O O O N HN NH 3 O N N H O O 10.2 bound O, N or S remains relatively nucleophilic. The first example of this process was the condensation of tetrahedral silicon tetraisocyanate with glycol to give 10.3. This spiro intermediate was then reacted with C(O)Im2 as a source of ‘CO’ to give the silyl macrocyclic complex 10.4. Hydrolysis yields the free macrocycle 10.5 (Scheme 10.2). Ions other than metal cations may also act as templating agents, for example in the synthesis of zeo- lites and mesoporous silicas by templating about alkali metal cations and large quaternary ammonium ions (Section 9.2.2). Similarly the synthesis of large polyoxovanadate cages is templated by the pres- ence of ions such as Cl
or a combination of NH4 and Cl
. In contrast, the thermodynamic template effect in macrocycle synthesis is a process by which the presence of a metal ion template stabilises thermodynamically, or removes (e.g. by precipitation) one particular (usually cyclic) product from an equilibrating mixture, driving the equilibrium towards this thermodynamic minimum. This leads us to the conclusion that any thermodynamically stabilising influence may drive an equilibrium mixture towards a particular product according to Le Chatalier’s Principle (in an equilibrating situation, the system will react to diminish the effects of externally applied changes in conditions). On the border between kinetic and thermodynamic synthetic template effects are processes involving stepwise self-assembly followed by covalent modification. Electrostatic forces may be readily employed in this kind of templating role, for example in the synthesis of more unusual kinds of cyclic molecules, including interpenetrated catenane compounds. Face-to-face π-stacking interactions between electron-rich and electron-poor aromatic rings have been used to induce the interpenetration of one aryl ring within a cavity formed by a separate macrocycle (Figure 10.12). If the resulting inclusion compound can be cyclised, the result is an interpenetrated catenane in which one macrocyclic ring is threaded irreversibly through another. Alternatively, addition of bulky end groups results in a rotaxane, a compound in which a thread-like guest is inserted irreversibly within a cyclic host. The initial inclusion via π – π stacking interactions is an example of thermodynamic H H OCN NCO O O O O O O N N O Si OCN NCO O HH O O O C(=O)Im2 N N H2O O O O + N N Si Si HO N N N N O O O O O O O 2 H H O O O O O O N N O HO H H 10.3 10.4 10.5 Scheme 10.2 Covalent template synthesis of an 18-membered macrocycle.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 606 Self-Assembly O OH O electron rich p-alkoxy disubstituted precursor N+ O N+ electron poor bis(bipyridinium) host N+ O N+ OH O O Figure 10.12 Interpenetration of an electron-rich catenane or rotaxane precursor within an electron- poor macrocycle. self-assembly, while the subsequent covalent cyclisation or capping reaction that fixes the compo- nents in place is controlled kinetically. This latter stage in catenane synthesis is carried out under high-dilution conditions, with assistance from weaker, extra-cavity π – π stacking interactions. Once the second, kinetically controlled stage is complete, the templating interaction is no longer neces- sary, although it is not necessarily removed. The extensive chemistry of catenanes and rotaxanes is discussed in Section 10.7. As we have seen in biological systems, hydrogen bonding is also a powerful templating factor. While an individual hydrogen bond may constitute a relatively weak interaction, arrays of hydrogen bonds arranged in a complementary fashion can stabilise large aggregates. Hydrogen-bonding inter- actions have been used in the development of the first self-replicating systems (Section 12.9.3). In these autocatalytic molecules, a self-complementary amide derivative is able to organise a ternary (three-component) complex under thermodynamic control between itself and two precursor compo- nents. These precursors are brought into close proximity to one another in a well-defined orientation within the ternary assembly and react to produce a copy of the templating molecule. Such systems again make use of a templating effect in which thermodynamic self-assembly is followed by kinetic covalent modification. 10.4.2 A Thermodynamic Model: Self-Assembly of Zinc Porphyrin Complexes Chi, X. L., Guerin, A. J., Haycock, R. A., Hunter, C. A. and Sarson, L. D., ‘The thermodynamics of self-assembly’, J. Chem. Soc., Chem. Commun. 1995, 2563–2565. There have been several approaches to modelling the thermodynamic self-assembly of coordination complexes and hydrogen bonded assemblies, often taking a specific set of compounds as a representa- tive model. One of the earlier, successful models which gives a good feel for the factors involved is based on the zinc porphyrin complexes 10.6–10.8 (Figure 10.13). This systems represents an interesting test case to demonstrate the thermodynamics of the self-assembly of closed, cyclic oligomers (dimers, trimers tetramers etc.) as opposed to ‘open’ coordination polymers. Compounds 10.6–10.8 all self- assemble spontaneously from their constituent monomer units under thermodynamic control under well- defined conditions. Their formation is entirely equilibrium driven, since the Zn2—N(pyridyl) bond is relatively labile (rapidly and reversibly broken and reformed) in organic solvents (CH2Cl2, toluene etc.)  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Self-Assembly in Synthetic Systems: Kinetic and Thermodynamic Considerations 607 O N Zn O H O N N Zn HN NH N N O NH 10.6 HN O N O NH N 10.7 Zn H Zn N N N H O N O HN O O N Zn N N N Zn H H Zn N N O R O NH 10.8 NH O N N = Zn R Zn N N N O N Zn R = solubilising group R Zn N H Figure 10.13 Closed, cyclic, self-assembling zinc porphyrin oligomers. at room temperature. This lability arises from the hard nature of the Zn2 centre (Section 3.1) and the lack of any significant covalent component to the bonding. Note, however, that the Zn2 ion is held very strongly within the porphyrin N4 framework because of stabilisation by both the chelate and macro- cyclic preorganisation effects of the porphyrin ring. The formation of the three closely related cyclic oligomers is in competition with polymer formation as outlined in Scheme 10.3. The system as a whole may be characterised by the following quantities. [cycle] 1. K closed = (10.1) [monomer]n The equilibrium constant for the self-assembly of the cyclic oligomer containing n monomer units. [ n − mer ] 2. K open = (10.2) [(n − 1) − mer ][monomer] The equilibrium constant for the open (noncyclic) association of a monomer with a growing linear oligomer containing n – 1 monomer units. This is a difficult parameter to measure because strictly  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 608 Self-Assembly Scheme 10.3 Competitive formation of open (polymeric) and closed (cyclic) zinc porphyrin species. there should be a different value for each open association step. Furthermore, even the measure- ment of one such stepwise parameter is rendered extremely difficult by competing formation of the closed structure. However, Kopen may be approximated by measurement of the equilibrium constant for the association of a Zn(porphyrin) unit with pyridyl ligands incapable of assembling to form a closed structure. The association constant for these model, or reference species is denoted Kref; Kref ≈ Kopen. K closed K closed 3. Effective molarity, EM = n = n (10.3) K open K ref The effective molarity is a very useful parameter that represents the concentration at which polymer formation begins to compete with the self-assembly of closed oligomers, i.e. it is the upper limit at which the cyclic structure is stable. n[cycle] 4. Critical self-assembly concentration, csac = [monomer], when =1 (10.4) [monomer]n and [cycle] = K closed [monomer ]n (10.5) The csac is the minimum monomer concentration at which self-assembly of the closed structure begins. It is defined as the concentration at which the complex is half assembled, i.e. mole fraction of  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Self-Assembly in Synthetic Systems: Kinetic and Thermodynamic Considerations 609 Table 10.1 Self-assembly parameters for cycles 10.6 – 10.8 (room temperature, CH2Cl2). Complex n Kref (dm3 mol
1) csac (mol dm
3) EM (mol dm
3) ε 10.6 2 5.6  10
3 3  10
9 6 9.3 10.7 3 3.9  10
3 2  10
7 100 8.7 10.8 4 1.9  10
3 33  10
5 0.6 4.5 monomer units present in the form of the fully assembled complex is 0.5. Given a knowledge of EM, csac may be calculated from Equations (10.4) and (10.5), thus: 1 csac = 1 (n - 1) 1 (n − 1) (10.6) n K closed Substituting into Equation (10.3) for Kclosed gives 1 csac = (10.7) n1 ( n − 1) EM 1 ( n − 1) K ref n ( n − 1) Data for the zinc macrocyclic compounds 10.6–10.8 are given in Table 10.1. This data shows clearly that the macrocycles consisting of fewer monomer units (n) are more stable than those with increasing n. We can explain this trend on entropic grounds by the greater decrease in the number of degrees of freedom as more and more monomer units aggregate. This factor fundamentally limits the number of monomer units that can come together to form a closed structure. In turn we can surmise that this number may be increased by designed decreases in the number of degrees of conformational freedom and preorganisation of the oligomeric units for cyclisation, e.g. by steric constraints or multiple binding interactions. The experimental values of EM compare reasonably well with the theoretical maximum values, which may be obtained from Equation (10.8).9  −∆Sref  EM max = exp   (10.8)  R  For zinc pyridine reference complexes in toluene ∆S values are about 50 J K
1 mol
1, and hence the upper limit for EM is in the region of 400 mol dm
3. For the trimer 10.7, the experimental value (in CH2Cl2) of 100 mol dm
3 is close to the theoretical maximum, which suggests that this system is nearly geometrically optimal (i.e. the monomer units are highly complementary). In contrast, factors such as ring strain may contribute to the lower value for the dimer 10.6. Taken together, the EM and the csac represent the concentration window over which the closed, self- assembled structure is thermodynamically stable. The wider this window, the more stable the complex is. Thus an overall efficiency of the self-assembly process (ε) may be defined in terms of csac and EM.  EM  ε = log  (10.9)  csac  hence  n  log(n ) ε= log( EM K ref )  + (10.10)  n − 1  n −1  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 610 Self-Assembly Figure 10.14 Distribution of solution species for the self-assembling tetramer 10.8. (Reproduced by permission of The Royal Society of Chemistry). The lower limit of ε for which self-assembly may be realistically studied is ε ⯝ 4, since at this efficiency the self-assembled complex constitutes more than 90 % of the species present over a concen- tration range of only 102 mol dm
3. Even then, it is in equilibrium with significant amounts of oligomers. This may be readily appreciated from the speciation diagram for the tetramer 10.8 (Figure 10.14). Given a knowledge of the binding enthalpy for a realistic reference system, ∆Href, a theoretical esti- mate of the maximum ε may be obtained by substituting Equation (10.8) into (10.10) to give:  n ∆H ref  log(n ) ε max =  + (10.11)  n − 1 2.303RT  n − 1 Likewise, a minimum value for csac may also be obtained from Equations (10.7) and (10.8): 1  n ∆H ref ∆S  csac min = 1 ( n − 1) exp  − ref  (10.12) n  (n − 1)RT R  10.4.3 Cooperativity and the Extended Site Binding Model Hamacek, J., Borkovec, M. and Piguet, C., ‘Simple thermodynamics for unravelling sophisticated self-assembly processes’, Dalton Trans. 2006, 1473–1490. Given the beauty and elegance of some self-assembling processes it is tempting to attribute some magi- cal properties that allow complex mixtures to sort themselves out into a multi-component single prod- uct. In reality the stability of self-assembled complexes is often just the result of additive supramolecular interactions coupled with the need to use all possible binding sites at minimum entropic cost. In some cases, but by no means all, assemblies are more stable than the sum of their individual interactions. This phenomenon is termed positive cooperativity. Alternatively the binding of a first component may destabilise the binding of a second component. In the case of multiple metal cations binding to a ligand or series of ligands this negative cooperativity may arise as a result of electrostatic repulsions between the ions. We discussed in Section 1.5 a variety of graphical tests such as Scatchard and Hill plots that can be used to identify positive or negative cooperativity in systems involving purely intermolecular equilibria. These methods derive from a model called the site binding model originally used to describe intermolecular protein ligand interactions. The situation is more complex for self-assembled compounds  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Self-Assembly in Synthetic Systems: Kinetic and Thermodynamic Considerations 611 K open 2 K closed Figure 10.15 Schematic showing competing intermolecular and intramolecular equilibria. The rec- tangles represent binding sites. exhibiting both inter- and intramolecular equilibria and, apart from the treatment detailed in Section 10.4.2 (which does not explicitly consider metal–ligand complexation processes), it was not until 2003 that a proper description of their thermodynamics was derived by Gianfranco Ercolani at the University of Rome, Italy. Ercolani’s model has since been extended to give the extended site binding model by Claude Piguet (Geneva, Switzerland).10 We will briefly summarise these new thermodynamic treat- ments and look at some of their predictive implications. A more detailed explanation of the derivation of the models is given in the key reference. Ercolani’s Model In the previous section we came across the concept of effective molarity, EM, an empirical parameter that is used extensively (e.g. in polymer chemistry) to assess the relative efficiency of intra versus inter- molecular complexation processes; EM  Kclosed / Kopen (Equation 10.3 and Figure 10.15). If we express EM in terms of free energies we obtain Equation 10.13 and we can recognise that –RTln(EM) is an empirical correction factor when an intermolecular process is replaced by an in- tramolecular one. If we substitute into Equation 10.13 the separate enthalpy and entropy terms and recognise that in a strain free ring ∆Hinter ≈ ∆Hintra we get Equation 10.14. − RT ln( EM ) = − RT ln( K closed ) + RT ln( K open ) = ∆Gclosed − ∆Gopen (10.13) − RT ln( EM ) = ( ∆H closed − ∆H open ) − T ( ∆Sclosed − ∆Sopen ) ≈ −T ( ∆Sclosed − ∆Sopen ) (10.14) It is convenient to replace EM with the identical but theoretical parameter effective concentration (ceff ). Substituting this nomenclature change into Equation 10.14 we get Equation 10.15 and hence we can derive Equation 10.16 from the original definition of EM (Equation 10.3). c eff = e ( ∆Sclosed − ∆Sopen )/ R (10.15) ( ∆Sclosed − ∆Sopen )/ R K closed = c eff K open = e K open (10.16) The same approach can be applied not only to the bulk equilibrium constants (K) but also to the microscopic connection processes (given the symbol k). Recall that the macroscopic equilibrium con- stant is simply the sum of all the microscopic equilibrium constants. For example, if an acid (H2A) has two non-equivalent ionisable protons there are two distinct but equivalent ways to remove a proton to produce HA
and hence there are two microscopic equilibrium constants (k1 and k2) for this deprotona- tion process. Thus the macroscopic acid dissociation constant, Ka  k1k2. Don’t get confused between microscopic equilibrium constants and rate constants, both of which have the symbol k. So, in terms of  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 612 Self-Assembly micro constants, Ercolani proposed that the overall assembly equilibrium constant (β mn where m and n are the numbers of metal (M) and ligand (L) components) for an equilibrium of the type shown in Equation 10.17 involving both intra- (closed) and intermolecular (open) association can be calculated by multiplying together the micro constants as in Equation 10.18. m M  n L  [MmLn] (10.17) β mn = ω mn ∏ kclosed ∏ kopen (10.18) closed open The parameter ωmn is what is called a degeneracy parameter. It corrects for the number of different ways that any particular microspecies [MmLn] can be formed. For example if we have a single octa- hedral metal with three bidentate ‘binding domains’ (i.e. region where a metal can bind), interacting with a single ligand with two chelate binding domains to form a 1:1 ML complex then ω11  6. Each of the three metal binding sites can interact with either one of the ligand binding sites. The most stable assemblies are those in which all binding sites are occupied and these are the only ones we are con- cerned with, so in an assembly of ligands possessing m binding sites between them with metals having in total n coordination sites between them to give a complex [MmLn] (Equation 10.17) there is a total of N components, where N  m  n. These components are linked by a total number of connections C where C  mn. Of these connections N − 1 are intermolecular and C − (N − 1)  C − N  1  mn − m − n  1 are intramolecular. If we substitute these numbers into Equation 10.18 we get Equation 10.19. Equation 10.19 also contains a symmetry parameter, σmn, that describes the change in degeneracy of the microspecies involved in the assembly process. In complexes such as helicates this may include the formation of enantiomers. β mn = σ mn ( kclosed )mn− m − n+1 ( kopen )m + n−1 (10.19) Equation 10.19 allows us to calculate the overall stability constant for multi-component self-assembly processes provided we have a knowledge of the two micro constants kopen and kclosed. In general these are measured approximately by determining the macroscopic equilibrium constant for simple model reactions that mimic the more complex assembly. We can then determine the cooperativity of the sys- tem by examining whether the measured macroscopic stability constant for the assembly is greater than, less than or equal to that calculated from Equation 10.19, corresponding, to positive, negative and non-cooperative processes, respectively. An illustration of the operation of Equation 10.19 is shown in Figure 10.16. This process involves the self-assembly of two metals with two ligands to give a complex [M2L2]. Imagine that the metals are tetrahedral ions such as Cu(I) and the ligands have two bidentate binding domains such as a quaterpyridine ligand. The first three processes are all intermolecular (open) β22(open) = ω22(open).(kopen)3 1 2 3 4 β11 = ω11.kopen β21 = ω21.(kopen)2 β22 = ω 22.(kopen)3.(kclosed) Figure 10.16 Description of the formation of a M2L2 complex by Equation 10.19.10 Open circles rep- resent ligand binding sites and closed circles represent metal ions.  10.1002/9780470740880.ch10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/9780470740880.ch10 by Uva Universiteitsbibliotheek, Wiley Online Library on [16/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Self-Assembly in Synthetic Systems: Kinetic and Thermodynamic Considerations 613 processes corresponding to the binding of first one, then two metals to a single ligand and then the addition of the second ligand to one of the metals. The final step is an intramolecular ring closure process in which the dangling end of one ligand locks on to the vacant binding domain of the second metal. In Section 10.8.5 we will see Erolani’s equation in action in assessing the cooperativity of a helicate system. The Extended Site Binding Model While very powerful, Ercolani’s model has two drawbacks. First, because only two microscopic affini- ties are used (kopen and kclosed) only assemblies involving more or less equivalent binding sites can be treated. Secondly cooperativity, i.e. any deviations from statistical binding, are not clearly assigned to extra energy gains or losses arising from interactions between components that are not considered in the metal–ligand connections. These issues are addressed by adapting of Ercolani’s model to give the extended site binding model which allows the assignment of the origin of cooperativity to the combina- tion of intermetallic and interligand interactions such at metal-metal electrostatic repulsion and ligand- ligand interactions such as hydrogen bonding. The extended site binding model breaks down the free energy of formation of complex multi-component assemblies such as that described by Equation 10.17 into five distinct energetic terms, Equation 10.20. m ⋅n m⋅n− m −n+1 ∆Gmn = − RT ln(βmn ) = − RT ln(σ chir ωmn ) − ∑ RT ln( ki ) − ∑ RT ln ( cieff ) + ∑ ′′ ( ∆EijMM ) + ∑ ′′′ ( ∆EklLL ) i =1 i =1 i< j k