Polarons as nucleation droplets in nondegenerate polymers

Abstract

We present a study of the nucleation mechanism that allows the decay of the metastable phase (trans-cisoid) to the stable phase (cis-transoid) in quasi one-dimensional non-degenerate polymers within the continuum electronphonon model. The electron-phonon configurations that lead to the decay, i.e. the critical droplets (or transition state), are identified as polarons of the metastable phase. We obtain an estimate for the decay rate via thermal activation within a range of parameters consistent with experimental values for the gap of the cis-configuration. It is pointed out that, upon doping, the activation barriers of the excited states are quite smaller and the decay rate is greatly enhanced. Typical activation energies for electron or hole polarons are ≈ 0.1 eV and the typical size for a critical droplet (polaron) is about 1 20Å. Decay via quantum nucleation is also studied and it is found that the crossover temperature between quantum nucleation and thermal activation is of order T c ≤ 40 o K. Metastable configurations of non-degenerate polymers may provide examples for mesoscopic quantum tunneling.pacs No:71.10.+x;71.20.Hk;64.60.My

Macroscopic Quantum Nucleation in cis-Polyacetylene

“…In the present paper we will be mostly concerned with polaron excitations in trans-cisoid, which is expected to mediate the decay of the metastable phase into more stable cis-transoid phase. A similar problem has been treated (although not very strictly) in Boyanovsky et al 5 > and we will summarize the relevant aspects of their paper in this section.…”

“…It can be shown that, for a positive value of Lie, Llo-yields a higher energy than Llo+, and hence corresponds to the metastable trans-cisoid isomer. Boyanovsky et al 5 …”

“…It is, therefore, desirable to have a concrete field theoretical model from which one can derive an analogue of the phenomenological Lagrangian to justify the abovementioned analyses. Recently, Boyanovsky et al 5 > have studied the metastable phase (trans-cisoid) of cis-polyacetylene and proposed that the decay of this metastable phase proceeds by a formation of a polaron, which is an island of the stable phase (cis-transoid) embedded in a trans-cisoid chain. Once a polaron of a critical size nucleates in a trans-cisoid chain it expands to flip the metastable trans-cisoid to cis-transoid until all the cis-polyacetylene turns into the stable phase.…”

Thermal activation rates in the chirally asymmetric Gross-Neveu model

“…These solutions were also studied within the context of electron-phonon models of conjugate polymers [12,13,14,15] and we refer the reader to these references for a comprehensive analysis of these solutions.…”

“…For notational simplicity we will take it to be zero in the rest of the analysis. The fermion spectrum in presence of this non-topological semiclassical configuration is also known exactly [11,12,13,14,15]: N bound states at energies…”