The chromism observed in the MEH-PPV polymer in tetrahydrofuran (THF) solution is discussed as a function of the structural morphology of the backbone chains. To evaluate this phenomenon, we carried out simulations employing a hybrid methodology using molecular dynamics and quantum mechanical approaches. Our results support the hypothesis that the morphological order–disorder transition is related to the change from red to blue phase observed experimentally. The morphological disorder is associated with total or partial twisted arrangements in the polymer backbone, which induces an electronic conjugation length more confined to shorter segments. In addition, the main band of the MEH-PPV UV–Vis spectrum at the lower wavelength is related to the blue phase, in contrast to the red phase found for the more planar backbone chains.
A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov–Milne–Pinney equation. Killing isometries include spatial translations and rotations, Newton–Hooke boosts and translation in the null direction. Geodesic motion in Ermakov–Milne–Pinney cosmoi is analyzed. The derivation of the Ermakov–Lewis invariant, the Friedmann equations and the Dmitriev–Zel'dovich equations within the Eisenhart–Duval framework is presented.