Conformations of three representative PPV chains. The radii of gyration of chains are chain A: 300 Å, chain B: 210 Å, and chain C: 154 Å. Chain , , and consists of 135, 145, and 150 respective number of effective PV chromophore units.
Each bracket denotes conformational subunit (segment) with unique color, which represents the shape of segments in the part of the polymer chains , , and . In our study, one large segment can have central conjugation breaks, it is mainly because these polymer chains can be “broken up” into segments with an acceptable cutoff (dihedral) angle. A cutoff of around 55° was typically used (Ref. 16). Reference 16 states that all of the segments are coupled and there is no discernible difference between one large segment with conjugation break or two smaller segments that are strongly coupled.
Delocalization of electronic eigenstate in the dressed eigenstate representation as the primary excitation moves along the polymer chain A. Here, , , etc, represent exciton relaxation among eigenstates such as 6 to 5, 5 to 4. The coloration indicates the net amplitude of an exciton eigenstate. Only the significant portion of the amplitude of a state is colored. Less than 10% of the amplitude is not shown. The color coding is shown with its particular amplitude, which indicates the participation of individual chromophore subunits (i.e., basis sites). For state #4, the color coding indicates that 67%, 19%, and 12% of the amplitudes are delocalized over three different segments in which the first two of them has conjugation breaks. For state #6, the color coding indicates that 86% of the amplitude is delocalized over a segment that has a conjugation break and 14% of the amplitude delocalized on another segment. For state #1, the color coding indicates that 96% of amplitude is delocalized over one larger segment with conjugation breaks and 4% of the amplitude is delocalized over the rest of the segments in the chain which is not shown. Lower energy states are generally associated with larger segments, whereas shorter segments give rise to higher energy states.
Simulated absorption spectrum and inverse participation ratio for PPV polymer chains: chain -dotted line (red), chain -solid line (black), and chain -dashed line (blue). There is no significant correlation between (a) absorption spectrum and (b) IPR. IPR represents continuous beta distribution function with a -value equal to 0.05 (i.e., probability of observing a difference between sample and population is less than 0.5%). Mean and standard deviation of the beta distribution for each chain is chain A: (, ), chain B: (, ), and chain C: (, ).
Plot of electron-phonon autocorrelation function in the dressed eigenstate representation [Eq. (30)]: with respect to phonon lifetime for states #1 and #2 of polymer chain at 300 K.
Normalized anisotropy decay upon averaging for three representative PPV polymer chains , , and at 300 K. The dressed eigenstate representation: (a) the black dashed line is the anisotropy decay averaged over three chains and (b) the biexponential fit to the average anisotropy decay . It shows two time constant, a faster component , and a slower component . The chromophore site (localized) representation: (c) the black dashed line is averaged over three chains and (d) an exponential fit to the average anisotropy decay . Average decay line shows a single time constant .
Graphical picture for the migration of an initial photoexcitation from state #60 to the kinetically trapped states. VE denotes the vertical excitation energy in eV. The coloring along the chain is based on the amplitude of eigenstate coefficients projected on to the chromophore basis sets.
Exciton energy vs time over the course of multiple hopping trajectories for chain C starting from two different initial states in the dressed eigenstate representation (a) state #60 and (b) state #126.
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