Fronts do not have to propagate as simple planar fronts. Analogously to oscillating
reactions, a steady state can lose its stability as a parameter is varied and
exhibit periodic behavior, either as pulsations or ‘spin modes’ in
which a hot spot propagates around the reactor as the front propagates, leaving
a helical pattern. This mode was first observed in (SHS). SHS fronts demonstrate
a rich variety of dynamical behavior, including planar fronts, spin modes
and chaotic reaction waves.
SHS with Nickel and Aluminum (Movie courtesy of Arvind Varma, Notre Dame)
Single-head spin mode (video is slowed down) in SHS with Nickel and Aluminum
(Movie courtesy of Arvind Varma, Notre Dame)
Many examples of beautiful patterns spontaneously
formed by frontal polymerization have been discovered..
The linear stability analysis of the longitudinally propagating fronts in
the cylindrical adiabatic reactors with one overall reaction predicted
that the
expected frontal mode for the given reactive medium and diameter of reactor
is governed by the Zeldovich number:
The planar mode is stable if Z < Zcr = 8.4, and unstable if Z > Zcr.
By varying the Zeldovich number beyond the stability threshold, more complicated
spin mode instabilities can be observed. We point out that polymerization is
not a one-step reaction, so that the above form of the Zeldovich number does
not directly apply. It does indicate that there are three ways to increase
the probability of observing spin modes: lower the initial temperature, raise
the front temperature and increase the energy of activation. The front temperature
is limited by the energy released per mass of monomer so a lower molecular
weight is advantageous. (This is also true for achieving frontal polymerization
at all.)
The most commonly observed case with frontal polymerization is the spin mode
in which a ‘hot spot’ propagates around the front. A helical pattern
is often observed in the sample. The first case was with the frontal polymerization
of e-caprolactam, and the next case was discovered in the methacrylic
acid system in which the initial temperature was lowered.
An interesting problem arises in the study of fronts with multifunctional (meth)acrylates.
At room temperature, fronts with monomers such as 1, 6 hexanediol diacrylate
(HDDA) and triethylene glycol dimethacrylate (TGDMA) exhibit spin modes. In
fact, if an inert diluent, such as dimethyl sulfoxide (DMSO) is added, the
spins modes are more apparent even though the front temperature is reduced.
Masere et al. found spin modes in the frontal polymerization of a diacrylate
at room temperature. The overall energy of activation for multifunctional
acrylates increases with conversion and is a stronger function of conversion
the higher is the functionality of the monomer.
Other geometries allow other modes. Matkowsky and Volpert analyzed the problem
of an expanding front in a disk in which hot spots in the front traced out
Archimedian spirals.52 Pojman et al. studied propagation modes in square
reactors and in funnels.
Frontal polymerization shares many similarities with SHS but a significant
difference is that the monomers are usually transparent while the starting
materials used in SHS are opaque. This difference affords the possibility
to observe a type of propagation that cannot be observed in SHS, viz.,
a spherically
propagating front that expands out from an initiating source.
Here is a beautiful spiral made visible in this 1.5 cm diameter tube
by using bromophenol blue to scavenge radicals. Dark spiral indicates path
of hot spot.
All movies were prepared with an Amber IR camera. The different dynamics
arises by changing the amount of the inert DMSO. More information can be found
at
Masere, J.; Pojman, J. A. "Free Radical-Scavenging Dyes as Indicators
of Frontal Polymerization Dynamics,"J. Chem. Soc. Faraday Trans. 1998, 94, 919-922.
Masere,J.; Stewart, F.; Meehan, T.; Pojman, J. A. "Period-doubling Behavior
in Frontal Polymerization of Multifunctional Acrylates," Chaos, 1999, 9, 315-322
Pojman, J. A.; Masere, J.; Petretto, E.; Rustici, M.; Huh, D.-S.; Kim, M.
S.; Volpert, V. "The Effect of Reactor Geometry on Frontal Polymerization
Spin Modes,"Chaos 2002,
56-65.
