Chemistry Reference
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However, SP dissociation can be the primary relaxation pathway, and theoretical
scaling concepts developed by Cates (1987) to describe the relaxations of wormlike
micelles (such as those examined by Rehage and Hoffmann 1988, 1991) are often
successfully applied to experimental observations on SPs. The Cates theory provides
a useful probe of SP structure and relaxation mechanisms. For example, in their work
on reversible neodymium(III) coordination polymers, Vermonden et al. (2004)
found that dissociation, rather than reptation, is the fastest route for entanglement
relaxation and the wormlike micelle theory fits the data for the supramolecular assem-
blies well. Even when metals that have trivalent coordination are used, the scaling law
behavior is consistent with the Cates model. This result suggests that the trivalent
metals form linear chains that include alternating ring structures, although, as dis-
cussed in Section 3.3, similar scaling laws are observed in supramolecular networks
in which the lifetime of the stress-bearing cross-links determines the relaxation of
the network structure.
The overlaps between SPs in semidilute concentrations can be thought of in very
similar terms to the entanglements defined above. Supramolecular interactions create
large structures that physically interact to determine the mechanical response (in this
case, viscous flow). The primary relaxation is the diffusion of an SP that is effectively
intact on the timescale of the diffusion process. Thus, at a fixed concentration, the SP
properties in dilute solution are therefore quite similar to those of covalent polymers
of the same molecular weight and molecular weight distribution.
Similar behavior is observed in many SP solutions, and we highlight only a few
of the many examples. Castellano et al. (2000) were able to quantitatively relate
the semidilute transition observed in viscosimetry measurements of calixarene-
based SP capsules (“polycaps”) to that extrapolated from quasielastic light scattering.
Xu and coworkers (2004) made a similar analysis on DNA-based SPs. Scaling laws
above the critical concentration are similar in all cases. The generality of the behavior
supports the expected view that, in the semidilute regime, the SP mechanical response
is effectively equivalent to that of covalent systems. The observed viscosity depends
on the average SP size, and the dynamic nature of the SP is invisible in the flow
properties of the polymer solution.
Yount and colleagues (2003) recently presented a direct and fairly general probe
of SP dynamics. Their approach is based on the fact that a direct study of SP
dynamics would involve making a change in the dissociation/association kinetics
of the defining SP interaction and observing the corresponding changes in the
properties of the SP materials. Although this strategy is potentially very informative,
a subtle, yet persistent, difficulty exists in distinguishing the contributions of the
kinetics of a given molecular interaction (k
diss
, Fig. 3.4) from those of its thermodyn-
amics (K
eq
). In most reversibly assembled systems, for example, those based on
hydrogen bonding, association occurs at or near the diffusion rate and K
eq
and k
diss
are strongly anticorrelated. For SPs, the inverse correlation of k
diss
and K
eq
intrinsi-
cally frustrates efforts to determine the relative importance of the two contributions.
A high K
eq
leads to increased aggregation, higher SP molecular weights, and slower
dynamics within the equilibrium polymer structure. At the same time, a lower k
diss
leads to slower
reversible kinetics along the assembly. Dynamic properties,
