One-dimensional nanostructure-guided chain reactions: Harmonic and anharmonic interactions

Abstract

We have performed a parametric study of self-propagating chain reactions along a one-dimensional bead-spring array. The coupling between beads is modeled using harmonic and anharmonic Fermi-Pasta-Ulam (FPU)-β and φ[superscript 4] potentials. The parameters that define the system are the activation energy (E[subscript a]) of the reactive group and the fraction (α) of the reaction enthalpy that is converted to the kinetic energies of the reacted products. The mean conversion for a 100-bead lattice was investigated as a function of these handles. Assemblies of pristine chains with reactive groups having E[subscript a]<25 kcal/mol are shown to be inherently unstable. At loads of 3–4 energetic molecules/bead (E[subscript a]=35 kcal/mol, α=0.7), the FPU and harmonic lattices behaved similarly with reaction velocities ranging between 8 and 8.5 km/sec. The φ[superscript 4] lattice exhibited lower conversions along with the formation of a reaction initiation zone where the velocity was at least half of the bulk value at the aforementioned loads. Fourier analyses of the kinetic energy traces of the φ[superscript 4] lattice revealed that only high-frequency excitations led to viable wave propagation, which explains the prominence of the start-up zone at lower loadings of the energetic molecules. High velocity reaction waves are only observed in perfect crystal arrays. The presence of defects in the chain, i.e., beads with weaker force constants, hampers the progress of the wave.