Theoretical investigation of the origins of abrupt thermochromism in the polysilanes

Abstract

Abstract Values of the conformation-dependent polymer-solvent interaction parameter VD have been calculated for some simple polysilane model compounds using quantum-mechanically derived molecular polarizabilities coupled with London's dispersion formula. The value VD = 0.97 kcal mol−1 obtained in the present study for the σ-conjugated polysilanes nearly equals the VD ≈ 1.1 kcal mol−1 estimated by Schweizer for the analogous π-conjugated carbon-backbone polymers, assuming similar physical conditions. The present results thus provide theoretical evidence in support of the pertinence of Schweizer's theory of abrupt thermochromism to the polysilanes. The conformational flexibility and versatility of the backbone is much greater for the polysilanes compared with most π-conjugated polymers, hence the conformational ‘defect energy’ ϵ of the former should be small or even negative. The combination of large VD (favouring the ‘ordered’ backbone) and small ϵ (favouring the ‘disordered’ backbone) predicted for the polysilanes would place the critical VD/ϵ parameter well in excess of the limiting value VD/ϵ ≥ 0.37 required for onset of abrupt thermochromism according the Schweizer. The (Austin Model 1) AM1-calculated change in polarizability Δα with respect to backbone rotation o was 0.63 A3 for the model polysilane but only 0.08 A3 for the analogous non-conjugated carbon-backbone model polymer. This substantial difference substantiates the existence of strong coupling between the molecular polarizability and the backbone conformation in the polysilanes. Only the longitudinal polarizability αxx contributes substantially to Δα, while the transverse polarizabilities αyy and αzz essentially combine with no net effect on Δα (i.e. Δαyy −Δαzz). The variation of the calculated band-gap energy Eg with α for corresponding values of o fits a second-order regression curve (correlation coefficient r = 0.98). As the silicon backbone approaches an all-trans conformation, the highest occupied molecular orbital (HOMO) energy increases while the lowest unoccupied molecular orbital (LUMO) energy decreases to reduce Eg. This increase in the HOMO energy is balanced by a nearly equal decrease in the HOMO-1 energy; likewise, the decrease in the LUMO energy is balanced by an increase in the LUMO+1 energy.