Chemistry Reference
In-Depth Information
This expression was derived by Bell (1978), who used Kramers' theory to show
that bond lifetime can 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 x
b
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 literature, but they are outside the scope of this chapter and will not be
reviewed here.
A recent resurgence in mechanochemical research (Beyer and Clausen-
Schaumann 2005) provides technical and intellectual opportunities to correlate
the mechanical response of individual molecules to that of SPs, and quantitative,
single-molecule force spectroscopy studies have been completed for several supra-
molecular interactions that are important components of SPs. These interactions
have included, but are not limited to, host-guest interactions involving crown
ethers, cyclodextrins (CDs), and calixarenes; hydrogen bonding within double-
stranded oligonucleotides and between UPy units; hydrophobic interactions
between alkanes and fullerenes; and metal -ligand bonds, such as ruthenium(II)-
terpyridine [Ru
2
þ
-(tpy)
2
]. A summary of the forces associated with these interactions
is given in Table 3.1.
The experiments summarized in Table 3.1 are done under conditions in which the
applied force increases with time. The most-probable rupture force (F
), which is
taken from a distribution of measured values, reflects the competition between
force loading and bond rupture and, with the exception of the CD inclusion com-
pounds, rupture 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 (K
eq
. 10
8
M
21
, F
, 50 pN)
to the 4b
.
pyridine associations (K
eq
, 10
2
M
21
, F
. 50 pN) at comparable
loading rates. The kinetic nature of the mechanical influence expected from
Eq. (3.2) is further shown in a comparison of the rupture forces of the same pyridine
ligand from metal complexes 5a and 4b. The thermodynamics of ligand coordination
are nearly identical for the two Pd complexes, but larger rupture forces are observed
for the “slower” 4b complex.
Such effects are likely to be important. The use of SP interactions to create bio-
inspired material properties (e.g., see Chap. 9) implies that the ultimate yield behavior
of SP materials could depend on the mechanical response of supramolecular inter-
actions. 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 rupture of “sacrificial” supramolecular interactions protects a permanent,
underlying materials architecture. The dynamic repair of the SP component
in
