Soliton confinement in polyacetylene due to interchain coupling

The energy involved in the relative ordering of the dimerization patterns of neighboring ${\left(\mathrm{CH}\right)}_x$ chains is evaluated with a model where the coupling is due to the interchain hopping of the $\pi$ electrons. It is shown that this mechanism favors antiferromagnetic order between neighboring chains. Furthermore, it leads to soliton confinement. The energy associated with a pair of solitons on the same chain separated by $\frac{l}{a}\left(\mathrm{CH}\right)$ units is given by $E_c\simeq \frac{\mathrm{Wl}}{a}$, where $W=\frac{4t_{\perp }^2}{\pi t_0}$. Substituting accepted values for the interchain and intrachain hopping energies $t_{\perp }$ and $t_0$, we find $W\sim 10-3$ K.