Supramolecular Polymerizations

More documents

Recommendations

Info

514 A. Ciferri Figure 3. (a) Bifunctional units with binding sites along the N and S (or E and W) directions, yielding linear polymers. (b) Tetrafunctional units with two sites along N and S, and two sites along N-E and S-E (same side of the assembly), yielding linear or helical double chains. (c) Tetrafunctional units with sites at right angles within the cross-sectional or equatorial area of the unimer, yielding planar polymers. (d) Hexafunctional units with sites as in (c), and two additional sites on the flat surfaces or poles, yielding three-dimensional polymers. 2. Classical supramolecular interactions (Coulombic, hydrogen and van der Waals bonds) are localized at specific sites or atoms of the unimers. These sites may be distributed at discrete locations over the surface of the unimers: the direction of interaction determines the functionality of the unimer and, in turn, the dimensionality of the assembly (cf. next section and Figure 3). These localized interactions are described by the respective set of potential functions involving combinations of point charges, dipolar interaction and separation distances. Several combinations of the above interactions may occur over the surface of the unimer, additively contributing to the overall binding free energy. [56, 72] Cooperative effects (when the formation of the first pairwise interaction increases the binding constant at successive sites along the chain) are also possible. In the case of H-bonds that – due to their strong directionality – are a primary source of stabilization of several SPs in class A, the parallel or antiparallel arrangement of multiple bonds may increase or decrease the product of the single binding constants on account of secondary electrostatic interaction. [5, 6] In addition to the above site-localized classical interactions, other stabilizing interactions play an important role in polymeric assemblies. [1] The solvophobic bond is responsible for the micellization of amphiphiles in the presence of a solvent. Even in the absence of a solvent, the incompatibility of amphiphilic components produces their ordered microsegregation. These interactions can be described by thermodynamic parameters that control micro- and macrophase separations. For instance, the Flory-Huggins thermodynamic parameter v plays a primary role in the theoretical description of microsegregation in block copolymers (cf. ref. [1, 81] and Section 4.2). The occurrence of liquid crystallinity in solutions of several polymeric assemblies is an example of hierarchical structurization (“macroscopic expression of molecular recognition” [2] ). Again, a thermodynamic effect (e.g., volume exclusion resulting from the shape anisotropy of rigid SPs) is the primary driving force for structurization. Note that it is convenient to distinguish the role of shape in the stabilization of individual unimers (shape I effect, cf. (iii) above) from the role of shape anisotropy in the development of liquid crystallinity by rigid SPs (shape II effect, cf. ref. [1] and Section 4.1). 3 Functionality of the Unimer and Dimensionality of the Assembly The assessment of unimer functionality is a primary requirement for determining the dimensionality of the assembly. Bifunctional rod-like, disk-like or spherical unimers (see scheme in Figure 3a) having binding sites pointing toward the North and South directions (or toward East and West) yield linear polymers. Note that it is the directionality of the interaction that specifies the functionality, e.g., the same functionality is assumed if four H-bonds rather than a single one point in the same direction. Increasing the functionality of the unimers produces more complex structures. The presence of two additional sites produces extended or helical double chains, [1, 7] provided the additional sites are located at the same side of the assembly (e.g., NE and SE, Figure 3b). However, planar assemblies are expected when four sites point toward perpendicular directions within a cross-section of cylindrical and disk-like unimers, or the equatorial plane of a spherical unimer (Figure 3c). The occurrence of two additional sites on the flat surfaces of cylinders and disks, or the poles of a sphere, generates a three-dimensionally ordered network (Figure 3d). The symbols +, –, 0, and 9, in Figure 3 indicate the functionality and refer to any possible localized supramolecular bond (Coulombic, hydrogen, van der Waals). In the case of non-localized effects, such as incompatibility and shape II-induced mesophases, a more uniform distribution of repulsive interaction ought to be assumed. In a few cases a polymer is undoubtedly formed, but the specification of unimer size and shape may not be straightforward.
Supramolecular Polymerizations 515 Figure 4. Theory of linear supramolecular polymerization. Schematic variation of the length (or DP) of a growing linear or helical assembly with the unimer concentration C according to three different growth mechanisms. MSOA: multi-stage open association, [1, 74] HG: helical growth, [26] SLC: open supramolecular liquid crystal. [1, 28– 30] C* is the critical concentration for helical growth, C i is the critical concentration for the formation of the mesophase. [77] 4 Theory of Supramolecular Polymerization 4.1 Linear, Helical Assemblies There are three different supramolecular polymerization mechanisms by which a linear or helical polymer could assemble consistently with the schemes in Figure 3a and b. [1] (i) Multistage open association (MSOA) resembles the step-by-step mechanism of the molecular polycondensation of bifunctional unimers. [73] The increase in the degree of polymerization of the growing assembly with the (total) [1, 74, 75] unimer concentration C is given by C L [M0/(4KNa)] N [(DP w) 2 –1] (1) where M0 is the unimer molar mass, Na the Avogadro’s number and K is the site binding constant. A plot of Equation (1) is schematized in Figure 4a. A continuous increase in DP, or length L of the assembly, with concentration is expected and the rate of increase is strongly affected by the binding constant. For K a 10 6 m –1 , corresponding to one or two H-bonds per site, only oligomers (DP a 10) occur in dilute (a1%) solution. However, in the case of the ureidopyrimidone polymers reported by Meijer and coworkers, [4, 52] characterized by four H-bonds per site and K A 10 7 , extremely high DPs (e 1000) may be reached in dilute isotropic solution. The familiar Car- others equation and the control of DP by monofunctional unimers [73] apply to MSOA. (ii) Helical growth (HG) is achieved when step-by-step growth is reinforced by an intra-assembly cooperative effect, [26] originating from a peculiar functionality such as that schematized in Figure 3b. Since more bonds per unimers occur with respect to the situation in Figure 3a, Kh A K and a critical unimer concentration C*occurs at which the MSOA regime encroaches helix formation with a sudden increase in DP according to [26] DPn =(Ch/C*) 1/2 N r –1/2 (2) where r s 1 is the familiar cooperativity parameter (easily in the order of 10 –8 ) and Ch is the concentration of helical polymer (increasing when C A C*). Figure 4b shows the step-jump increase in DP, orL, accompanying the nucleation of the helix at C*. The theory was intended to describe the reversible aggregation of globular proteins attaining extremely high DPs(A4000, cf. Section 5.2). Van der Schoot and coworkers [76] have recently generalized Oosawa’s theory to cover general situations with Kh A K, including high and weakly cooperative helical aggregation. The theory was applied to the case of columnar assemblies of chiral discotic molecules (cf. Section 6.3.2). (iii) Growth-coupled-to-orientation (SLC) is alternatively described as the open supramolecular liquid crystal. [77] It is an inter-assembly cooperative process that encroaches MSOA causing a sudden enhancement of the step-by-step growth of bifunctional unimers at a critical concentration C i at which nematic order appears. [1, 21–23] The polymer must have considerable chain rigidity, [22] as expressed by its persistent (q) or deflection length (k), and the DP attained at C i may be approximated as DP V q/L0 where L0 is the length of the unimer. The schematization of the theoretical behavior in Figure 4c shows the sudden jump of DP, orL, atC i (note C i is generally S C*), followed by a minor increase in L upon further increasing the unimer concentration. [23] Values of q for SPs frequently exceed the lm range, [1] enabling DPs higher than 1000. Note that while attractive interactions stabilize the assembly along the N-S direction, no lateral (soft) anisotropic attraction among the formed assemblies is postulated to occur in the nematic state: only excluded volume (hard) interaction stabilizes the mesophase. In view of its fundamental significance, the difference between an open SLC and a conventional, molecular liquid crystal should be emphasized. In the latter, no association/dissociation equilibria accompany the transition from the isotropic solution: the nematic field has only an orienting effect. In the open SLC, development of orientation is simultaneous to an enhancement of supramolecular polymeriza- (3)
Page 1 and 2: Macromol. Rapid Commun. 2002, 23, 5
Page 3: Supramolecular Polymerizations 513
Page 7 and 8: Supramolecular Polymerizations 517
Page 19: Supramolecular Polymerizations 529

Supramolecular Polymerizations

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?