Supramolecular Polymerizations

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516 A. Ciferri tion. [77] Growth-coupled-to-orientation could in principle occur even for systems displaying only soft interactions, when mesophases are expected in the melt or in very concentrated solutions. [11] However, if growth due to alternative mechanisms (MSOA or HG) has produced a wormlike chain exceeding the persistent length (L A q) at these high concentrations, further growth by the SLC mechanism will not be relevant. The original theory, [20, 21] developed to explain the linear assembly of cylindrical micelles in nematic solutions, was later extended to discotic molecules in a wide range of concentrations at which hexagonal and higher-order phases were predicted. [31, 78, 79] A common feature of the cases considered above is the occurrence of polydispersity. [80] It is also apparent that SPs attain average DPs that are concentration-dependent, but may nevertheless far exceed those obtained in molecular polycondensation (cf. ref. [73] and Section 5.1.4). 4.2 Multidimensional Assemblies The above description of supramolecular polymerization for linear systems has involved the identification of proper unimers and corresponding growth mechanism. Unimers with functionality A2 can express strong supramolecular interactions in two and three dimensions. How can the approach developed for linear SPs be extended to multidimensional systems? General thermodynamic considerations regarding the growth of multidimensional assemblies were summarized by Israelachvili. [80] The standard chemical potential per unit (ln 0 ) decreases with the number n of aggregating units according to l 0 n = l 0 v + a kT/n p (4) where l 0 v is the bulk free energy for an infinite aggregate, a reflects the strength of contact energy, and p is a dimensionality index (p = 1 for linear systems, 1/2 for discs, 1/3 for spheres). Elaboration of the approach leads to the expectation that, whenever p a 1, macroscopic aggregates (n ev) grow abruptly above a critical concentration by a mechanism corresponding to a crystallization. Thus, at variance with the linear systems, no concentrationdependent broad size distributions are expected and there is no need to invoke a growth-coupled-to-orientation mechanism. These considerations apply to the growth of monolayers, single lamella, and also to the growth of three-dimensional assemblies of unimers having symmetrical and equivalent functionality. For some 2D systems, finite-size effects may frustrate growth to infinite assemblies. [81] The description of the growth of 3D systems is also more complex whenever a preferential growth direction occurs, reflecting, for instance, the geometrical anisotropy of the polymer, or the presence of two components. In such cases it might be possible to follow the Figure 5. Schematic assembly of the side and top views of a rigid polyanion and a cationic surfactant. This assembly may grow longitudinally by stacking, and laterally by interdigitation and hexagonal packing taken (taken from ref. [81] ). modes of growth along the longitudinal and transversal directions. The situations that may be encountered are illustrated by the assembly of a rigid polyanion (e.g., DNA) and a cationic surfactant in water (Figure 5). [82] The observation of the conventional nematic phase expected for the DNA/ H2O system is precluded by the strong reduction of solubility when the surfactant is present. Growth along the lateral direction (D) occurs by consecutive interdigitation of DNA helices with bound surfactant and produces aggregates with hexagonal symmetry. Growth along the longitudinal direction (L) may also occur due to the hydrophobic interaction occurring at the exposed North and South surfaces of the assembly. Provided L prevails over D, the nematic and hexagonal phases, crucial for the spatial orientation of the growing columns, should develop through the linear growthcoupled-to-orientation mechanism. On the other hand, when D prevails over L, planar growth leads to aggregates of infinite size (crystallization). Due to the fact that the helix and surfactant molecules are not chemically bound, it ought to be possible, through compositional control, to monitor growth along the two directions, possibly evidencing a liquid-crystalline phase, enhancing growth along the longitudinal direction. In general, one would expect a difference in the growth rate along the longitudinal and lateral directions. Indeed, such differences have been observed in block copolymers, when the components are chemically bound. [83] The foregoing considerations justify the empirical identification of linear growth components even in bulk composite assemblies, to be discussed in more detail in Section 5.6. A sounder mean-field approach was developed to interpret the solid-state morphology of (A)n–(B)m amorphous diblock copolymers exhibiting a microsegregation of components into cylindrical, lamellar or spherical domains. [48] The approach is based on the thermodynamic incompatibility of copolymer components that cannot be crystallized, theoretically shown to generate an unstable mode in an homogeneous, undiluted melt. [84–87] The formation of interfaces reduces the enthalpic cost of mixing (measured by the v parameter) but entails an entropy loss due to chain stretching to fill space uniformly. The latter depends upon the relative length and
Supramolecular Polymerizations 517 Figure 6. Mean-field phase diagram for amorphous diblock copolymers (A)n-(B)m. Main phases are: lamellar (L), hexagonal cylindrical (H), closed packed spheres (CPS), disordered (DIS). f is the volume fraction of A segments. (i Am. Chem. Soc. 1996 [87] ). flexibility of the A and B blocks. On this basis, cubic, hexagonal, lamellar, and other phases are predicted in discrete regions of v N N versus m/n phase diagrams as that illustrated in Figure 6 (N: total number of A and B units). A review of the most recent elaboration that unifies the weak [85] and strong [86] segregation regimes is given in the literature. [87] Noolandi et al. [88] extended the (self-consistent) mean-field approach to the calculation of the relative stability of liquid-crystalline phases occurring in solutions of copolymers composed of three flexible blocks. 5 Polymers from Supramolecular Polymerization 5.1 Linear Chains and Applications 5.1.1 H-Bonded Polymers This class of systems has attracted considerable interest due to the intrinsic characteristics of H-bonds, such as directionality and the possibility of increasing bond strength by multiple pairwise interactions. Figure 7 illustrates typical cases in which flexible or rigid segments are functionalized with groups able to form single or multiple H-bonds. The binding constant K is the primary parameter controlling DP in terms of the simple MSOA mechanism schematized in Figure 4a, predicting, according to Equation (1), K A 106 –107 m –1 needed for DP above the oligomeric range. If one takes K = 500 m –1 as an average value for a single H-bond (reported for the pyridine/ benzoic acid dimerization), [7] it appears that at least 4 Hbonds are needed to produce DPs of interest. In fact, the polymer in Figure 7c based on the dimerization of ureidopyrimidone residues (K =66107 m –1 in CDCl3), [4] was Figure 7. Supramolecular polymers stabilized by main-chain links based on (a) one, [11] (b) three, [2, 15] and (c) four [4, 52] Hbonds. reported to attain DP in the order of 1000 in dilute, iso- [4, 52] tropic solution. In the case of polymer (b), based on the 3 H-bond scheme of rigid anthracene segments terminated by uracil (A-A) or pyridine residues (B-B), one therefore would not expect a significant DP to occur in virtue of the MSOA mechanism. In fact, no evidence for appreciable DP was reported for isotropic solutions. However, the development of liquid crystallinity evidenced the formation of large DPs in moderately concentrated solutions in organic solvents, [14] likely triggered by the mechanism of growth-coupled-to orientation. When the rigid segments in (b) were replaced by flexible, tartaric acid spacers, the occurrence of liquid crystallinity was observed only in undiluted (thermotropic) systems. [13] Polymer (c), based on flexible segments terminated by diacid (A-A) and dipyridil (B-B) residues forming single H-bonds, [8–12] displayed analogously only thermotropic behavior. The occurrence of liquid crystallinity in the melt does not provide evidence of significant polymerization. [1] In fact, the role of the growth-coupled-toorientation mechanism for worm-like chains displaying soft interaction was shown to be extremely small. [10, 11] On the other hand, Equation (1) offers compelling evidence that no large DPs are produced in the case of a single Hbond. Other linear H-bonded systems of interest include the polycaps [89] based on the polymerization of capsular host complexes (calixarenes) functionalized with urea. The formation of main-chain bonds occurred only when a guest molecule was hosted in the capsule (CHCl3 acted both as a capsule host and as a solvent). Whitesides and coworkers [16] who had discussed the formation of closed structures by the self-assembly of melanine and cyanuric acid earlier, reported the formation of linear nanorods by introducing a mismatch in the spacers of the AA and BB groups of these monomers. Ladder-type supramolecular polymers, [10] and ribbon-type polymers have also been reported. [17]
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