EJERCICIOS DESARROLLADOS Tasas de Interés
Capítulo 2 Interés Simple e Interés Compuesto
1. Interés Simple
1.1. Valor actual
Currently, there exists a great deal of interest in the development of new supramolecular materials with various functional properties that are different from their monomeric or discrete molecular components.4 Interest in gels has grown in many scientific disciplines including tissue engineering and wound healing, drug delivery, and also sensing.4,6 Some examples where development of these materials is ongoing, particularly in relation to metal- containing gels, will be discussed in the following sections. Firstly, a detailed description of what these interesting materials are, how they are formed and the techniques which are used to study their properties will be carried out.
Flory defined a gel as a two-component colloidal dispersion, with a continuous structure and macroscopic dimensions which are permanent on the time scale of the experiment, and is solid-like in its rheological behaviour.177 There are several denominations of gels ranging from lamellar structures to covalently-polymerised networks.6,172 However, a supramolecular gel can be described as an aggregation of directionally-dependent three- dimensional structures in solution, self-assembled through non-covalent interactions such as hydrogen bonds, π-π interactions, van der Waals and ionic forces, and metal coordination, etc.6 Ideally, a gel consists of a relatively small amount gelling component (the gelator) and a significant volume of solvent. Upon self-assembly of the gelators into hierarchical structures the solvent molecules are immobilized within the gel matrix. Gels can be classified as hydrogels or organogels, within which the solvent encapsulated is water or an organic solvent, respectively. Gels possess a relatively disordered nature, the short range order not extending from the molecular to multimicrometer scale and as such it is challenging to understand the structure of the gel. The mechanism of gel formation is a hierarchical process which can be broken down into a primary, secondary, and tertiary structure. The self- assembly process involves the following steps, in which the primary component is the result
of dimerisation of two or more individual gelators, leading to the formation of oligomers through interaction with other dimers, demonstrated using urea-tape as an example in Figure 1.31(A).172 Other urea dimerising interactions such as extended hydrogen bonding and π–π interactions in the solid state were demonstrated by Pandurangan et al. using X-ray crystallography of novel aryl-pyridyl ureas like 47, see Figure 1.31(B).178 In selected cases, these ureas formed supramolecular gels with antimicrobial properties against Staphylococcus aureus and/or Escherichia coli. The secondary component in the self- assembly process arises from the extension of these oligomers into polymeric fibril formations of approximately similar width as the molecular building blocks (≈ 1-10 nm), and finally the tertiary process of the cross-linking of fibrils at junction points into fibres (≈ 20-50 nm width) and ‘splinters’ (≈ 10 µm width, Figure 1.31(C))178 which interact to give a long range, intertwined network stretching the whole sample. Finally, immobilisation of the solvent in the gel matrix is induced through surface tension. Surface tension effects allow the gel to be stable towards gravitational force when the vessel encasing it is turned upside down. This ‘inversion test’ is a crude technique typically used to identify whether or not gelation has occurred.5
Despite the plethora of gels which have been reported to date,6,172,179-180 there is a large gap between functional gel design efforts and actual knowledge of the supramolecular structure of the gels, i.e. the molecular arrangement of gelator molecules within the gel fibres. Of
Figure 1.31 (A) Hierarchical assembly process of supramolecular gel formation using urea derivatives as the gelators. Figure reproduced from Ref.172 Copyright 2004: American Chemical
Society. (B) Crystal structure of pyridyl urea 47 displaying oligomeric extended hydrogen bonding interactions. (C) SEM imaging (scale bar at 10 μm) of fibrous morphology of an organogel formed from an aryl-pyridyl urea analogue of 47 in a 4:1 THF:H2O mixture (1% wt.). Figure reproduced
fundamental concern is the structure of the gel both on the micro- and nanoscale i.e. at the cross-linking junction zones, the fibre-liquid interface and also at the molecular level.6,172 The macroscopic structure or morphology of these materials can be imaged by Scanning Electron Microscopy (SEM), Cryo-SEM, Transmission Electron Microscopy (TEM), Cryo-TEM, Scanning Tunnelling Electron Microscopy (STEM), and Helium Ion Beam Microscopy (HIBM). Other techniques used to study gels are optical and confocal microscopy, dynamic light scattering (DLS), and SAXS (Small-Angle X-ray Scattering) and SANS (Small-Angle Neutron Scattering).172 Techniques such as UV-vis/CD absorption can be used to detect changes in the ground state electronic properties in the generation of the supramolecular systems. Luminescence spectroscopic techniques is another very informative tool for gaining insights into the primary structure of the gels.6,172,181 Ln(III) centred phosphorescence can be very valuable in the characterisation of the metal ion chemical environments within the gel matrix.182
The gel rheological behaviour is perhaps its most important defining feature. Rheology183 is the study of the deformation and flow of matter under the influence of an applied stress. In general terms, when the mechanical properties of a material are under investigation, if the application of a continuous weak stress results in an overall resistance to further deformation, the material is a solid. However, the material is a liquid if flow is observed as a result of the deformation from the applied stress. Gels display both solid-like and liquid-like properties, depending on the strength of the applied stress. Thixotropy is an interesting property in which mechanical stress induces the break-up of the solid gel network, allowing the material to “flow”, but the gel’s elastic properties recover spontaneously upon release of the force, thus the network reforms over time.184 This will be discussed in more detail in Chapter 3 in studying the thixotropic properties of the btp derived supramolecular gels. Inducing such “self-healing” properties are a particularly topical area of research due to its potential to improve how reliable, useful and long-lived the resulting materials become.185-188 Gels which have the ability to self-heal are a subset of what are referred to as stimuli-responsive materials. A discussion of the interesting properties of both self-healing and other classes of stimuli-responsive soft materials in the literature will be made in the following section.
1.10.1.1
Stimuli-responsive Gels
The ability of certain stimuli-responsive polymer gels to autonomously heal upon damage are a consequence of the inherent dynamic nature of the non-covalent bonds of which they consist. In general, responsive materials that can change their physical state in response to
physical or chemical stimuli do so through the reorganisation of their molecular make-up upon exposure to an external trigger. Supramolecular gels have been shown to be responsive when external stresses such as ultrasound,189 light190 or chemical triggers86,174,191 are applied. This reversible nature is a vital part of the development of functional gel-based systems. Gels with sensing capabilities are an example of functional responsive materials which undergo a change in spectroscopic, electronic, or magnetic properties upon detection of a particular analyte. The incorporation of metal ions into gels, i.e. metallogels, broadens the possibilities for engineering the response of these materials. Coordination-based gels can be endowed with the metal’s physicochemical properties, e.g. magnetism, colour, rheology, photophysical properties, catalytic activity and redox behaviour. Therefore, there is an increased range of chemical and physical stimuli that these gels can react to in contrast to their non-metal containing counterparts.
There are two types of metallogels generally reported.5-6,172 Firstly, non-covalently interacting “standalone” coordination complexes linked together in the gel matrix. In this scenario the discrete complexes are joined through other non-covalent interactions. For example, Yan et al. reported a series of Pt(II):terpy complexes 48a and 48b (Figure 1.32) which showed gelation in DMSO, driven by Pt…Pt, π…π and hydrophobic-hydrophobic
Figure 1.32 Functional metallogels formed from non-covalent interactions where metal-48a/b
coordination is not central to the formation of the extended gel network. Gel to sol transition results in a colour change and loss of luminescence properties. Figure reproduced from Ref.192 Copyright
interactions.192 Here, the dative coordination bond is a secondary interaction in the assembly design and not involved in linking the gelator molecules together.6 It was also demonstrated that dramatic colour and emission changes were observed during the sol-gel transition. Secondly, however, there are gel structures consisting of organic molecules, such as multi- topic ligands with at least two binding sites for metals which facilitate the formation of branched two and three dimensional coordination polymer gel networks.86 A short review of some examples of functional supramolecular metallogels, beginning with the most recent reports, will be presented in the following section, with a particular focus on autonomously healing systems consisting of the btp motif, or analogues thereof, playing the role of the ligating host. Weng et al. most recently reported the formation of self-healing metallo- supramolecular polymer gels from btp ligand macromolecule 49. The macromolecule was synthesised via chain extension of two components: a CuAAC prepared bis-propene functionalised btp ligand which underwent a UV initiated thiol-ene “click” reaction with bis-thiol functionalised polytetrahydrofuran prepolymer linkers culminating in multiple btp-units incorporated throughout the polymer backbone, Figure 1.33.193 Three metallo- supramolecular gel materials formed by separately cross-linking btp macromolecule 49 with Eu(III), Tb(III) and Zn(II) displayed self-healing behavior when stacking the three respective metallogels together in a saturated toluene atmosphere for one hour. The resulting joined material composite was then subject to bending and stretching but breakage at the joints was not observed. This work was an extension of similar systems125,194 which displayed similar
Figure 1.33 Multiple btp motifs (represented as bricks) incorporated into ligand macromolecule 49
which coordinate with Zn(II) ions (represented as balls) to form a metallo-supramolecular gel. Figure reproduced from Ref.193 Copyright 2014: The Royal Society of Chemistry.
self-healing behaviour on account of the metal-btp complexation sites. It was rationalised that these cross-linking points were responsible for the healable nature of the final materials which were robust enough to be picked up and placed under bending and compressive strain.125 The gels demonstrated the thermodynamically stable but kinetically labile nature of the metal:btp complexation, a property which is of valuable significance in systems where a fast response is required. These systems also exhibited mechanical properties such as high tensile strength (up to 18 MPa), and exceptional toughness (up to 70 MPa).
There are several other examples of self-healing metallogels which contain metal chelating groups analogous to btp. Rowan et al. developed ditopic ligand 50 featuring the 2,6- bis(benzimidazol-2-yl)pyridine (bbp) binding motif, joined by a penta(ethylene glycol) unit which exhibited linear chain extension binding with either Co(II) and Zn(II) ions.195 The Zn(II) containing polymeric sequence was also cross-linked with Eu(III) or La(III) giving rise to globular colloidal particles that crystallised followed by phase separation leading to the formation of metallogels, Figure 1.34. The gelation mechanism was investigated using rheological study and techniques mentioned previously, namely, optical and confocal microscopy, DLS, and XRD.179 This work was further developed using related bpp ditopic polymer 51 featuring a low molecular-weight poly(ethylene-co-butylene) linker. Despite being based on weakly coordinating complexes optically healable and exceptionally strong metallo-supramolecular gel networks were formed.190 Upon exposure to light, the Zn(II)/La(III):51 complexes comprising the gel cross-links absorbed energy which was converted into heat. The effect of this was the temporary dissociation of Zn(II)/La(III):51
Figure 1.34 (A) Ditopic ligands 50 and 51. (B) Schematic showing the mixed f-d metallogel formations A-C with ditopic bpp ligand 50. Figure reproduced from Ref.179 Copyright 2006:
cross-links, with subsequent decrease in viscosity of the material, which then recombined, thus healing any defects caused by strains or damage done to the system. In other work, it was shown that upon solvent evaporation of similar Eu(III):51 based gels, followed by compression moulding, films were formed which displayed appreciable elastomeric mechanical properties.196 This was not a feature of the dried sample of 51. The metal ions played a vital role in imparting these film materials with useful functions, namely the ability to be healed, after cutting, by treatment with ultrasound. Various reversible and irreversible mechanically activated reactions were used to study the disassembly process using the characteristic photoluminescent properties of the system.
Finally, Martínez-Calvo et al. investigated the role of the guest Ln(III) ion in the formation of highly luminescent metallo-supramolecular gels, from a morphological and rheological perspective using a dpa derived multidentate ligand 52 (Figure 1.35).197 The gelation process used the 1:3 Ln(III):52 stoichiometric ratio to form pre-organised metal complexes which were then cross-linked through Ln(III)-carboxylate coordination upon additional equivalents of Ln(III). SEM imaging and rheological studies showed that the gels prepared using only Eu(III) or only Tb(III) possessed different morphological and rheological properties to each other, which also differed from those consisting of mixed Eu(III) and Tb(III) in the gel formation. This was despite Eu(III) and Tb(III) having similar coordination properties which would indicate that self-recognition in the individual gels was different from that of the mixed system. The gels showed the ability to self-heal after being cut and allowed to recombine. Futhermore, the luminescent properties of the soft materials could be tuned depending on the Eu(III):Tb(III) stoichiometric ratios used in their synthesis, resulting in a
Figure 1.35. Dpa amide derivative 52. (A) Tb(III) metallogel and Eu(III) metallogel in daylight and (C) Luminescence of Eu(III), Tb(III), and mixed Eu(III)/ Tb(III) gels on quartz plates. (D)-(G) Healing experiment of Tb(III) gel with (D) Tb(III) gel in daylight, (E) under UV irradiation, (F) gel after being cut, and (G) self-healing.
variety of luminescent colours.
These articles demonstrate the ability of metallo-supramolecular interactions, through their dynamic nature, to achieve the production self-healing, functional soft materials. The multiple coordinating directionality together with the conformational capability range of similar ligands to those discussed above in the generation of functional soft materials also make them very appealing for the design of new architecturally diverse MOFs possessing desirable functional properties. The importance of functional MOFs based on using 1,4-disubstituted-1,2,3-triazoles, or analogues thereof, as tectons will be discussed in the next section using relevant examples.