Spin Modes

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What are spin modes?

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.












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