Forces and Supramolecular Interactions

2004b Kizhakkedathu et al. 2004 LeMieux et al. 2004), and the specific modulation of cross-finking kinetics is one method by which to exert control. As in the SP networks discussed above, the cross-linkiug in the brushes is reversed by chemical competition, but responsiveness to other stimuli, such as temperature, could be engineered. 

The mechanical properties of SPs described in Sections 3.2-3.4 are, in general, suc-cessfiiUy interpreted, often quantitatively, in terms of thermal rate and equilibrium constants, but it is reasonable to expect that the underlying molecular behavior should be perturbed by the application of a mechanical stress. On the whole, the mechanical properties of supramolecular interactions are not well known, and their study constitutes a relatively new but burgeoning research area related to the field of SPs. 

This expression was derived by Bell (1978), who used Kramers theory to show that bond lifetime ean be shortened by an applied force in processes such as cell adhesion. Although Eq. (3.2) is quite useful, it is in practice limited, most notably by the fact that it assumes that xp is constant. Typically, measurements of force dependency are made under conditions in which force changes with time, and it is likely that the position of the transition state will move as the shape of the potential surface is perturbed by an applied force (Evans and Ritchie 1997 Hummer and Szabo 2003). Theoretical and empirical treatments of various cases have been put forth in the hterature, but they are outside the scope of this chapter and will not be reviewed here. 

The experiments summarized in Table 3.1 are done under conditions in which the applied force increases with time. The most-probable mpture force (F ), which is taken from a distribution of measured values, reflects the competition between force loading and bond mpture and, with the exception of the CD inclusion compounds, mpture force increases with loading rate (Evans and Ritchie 1997). The data emphasize that the mechanical strength of the interactions do not necessarily reflect the thermodynamic strength, or association constant, of the interaction. This point is made by comparison of the DNA duplexes (i eq 

Such effects are likely to be important. The use of SP interactions to create bioinspired material properties (e.g., see Chap. 9) implies that the ultimate yield behavior of SP materials could depend on the mechanical response of supramolecular interactions. Paulusse and Sijbesma (2004) have also shown that ultrasound-generated shear stresses can mechanically tear apart coordination SPs, damage that is subsequently repaired during dynamic equilibration once the shear stresses are removed. The mechanical response of supramolecular interactions within materials has potentially important consequences in the context of self-repairing materials, where the mpture of sacrificial supramolecular interactions protects a permanent, underlying materials architecture. The dynamic repair of the SP component in 

---