Exciton Conformational Dynamics of Poly(3-hexylthiophene) (P3HT) in Solution from Time-Resolved Resonant-Raman Spectroscopy

We have used time-resolved resonant-Raman spectroscopy to investigate the picosecond conformational relaxation of regioregular poly­(3-hexylthiophene) (RR-P3HT) in chlorobenzene after 510 nm photoexcitation. Vibrational signatures from modes along and peripheral to the exciton’s backbone have been identified according to the time dependence of excited-state Raman features and from comparisons to Raman spectra of other polymer states. Measured spectral dynamics reflect initial changes in the resonance enhancement of backbone modes on a time scale of 9 ± 1 ps. In contrast, contributions from peripheral modes exhibit time-dependent decay determined only by exciton intersystem-crossing kinetics. Spectral dynamics are interpreted in terms of evolution in bond lengths along the exciton’s backbone resulting from increased conjugation allowed by torsional reordering. Possible origins of peripheral features are discussed, including distorted inter-ring modes at exciton termini. Findings provide a glimpse of the underlying molecular dynamics responsible for the red shift in the exciton’s near-IR transient absorption occurring on the same time scale

Structural Relaxation of Photoexcited Quaterthiophenes Probed with Vibrational Specificity

Ultrafast structural relaxation of photoexcited 2,2′:5′,2″:5″,2‴-quaterthiophene (4T) and 3,3‴-Dihexyl-2,2′:5′,2″:5″,2‴-quaterthiophene (DH4T) in solution were interrogated with femtosecond stimulated Raman spectroscopy (FSRS). Relaxation was observed through time-dependent evolution in frequencies and intensity ratios of out-of-phase (Z) and in-phase (Я) intraring CC stretching features. Frequency shifts occurred on time scales of 0.4 and 0.86 ps, respectively, dominated by a blue shift in the Z mode (6.2 and 11.5 cm^–1 shifts for 4T and DH4T, respectively). Intensity ratios evolved on similar time scales due to correlated intensity decreases and increases of Z- and Я-mode features. Excited-state quantum-chemical calculations with bithiophene demonstrate that mode frequencies are coupled to the torsional dihedral, such that the spectral evolution observed reflects excited-state relaxation toward a planar conformation. This work demonstrates the power of ultrafast Raman spectroscopy for probing dynamics in photoexcited conjugated materials with structural detail given the parametric dependence of intraring vibrational modes on interring torsional dihedrals

Coexistence of behaviors, when the benefit <i>B</i> of pursuing the individually preferred behavior is larger than the advantage <i>A</i> of conforming with the behavior of the respective interaction partner.

<p>The model parameters used in this computer simulation are <i>A</i> = 1, <i>B</i> = 1.2, <i>R</i> = 10, <i>S</i> = 0.5, <i>p</i>₁ = <i>p</i>₂ = 0.5, <i>r</i> = 0.01, i.e. the only parameter that is different from the ones used in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104207#pone-0104207-g001" target="_blank">Fig. 1(a)</a> is <i>B</i>.</p

Proportions of sincere and hypocritical punishers as a function of time t in case of (a) behavior-based punishment and (b) preference-based punishment.

<p>The model parameters in both simulation scenarios are <i>A</i> = 1, <i>B</i> = 1.2, <i>L</i> = 1.5, <i>R</i> = 2, <i>r</i> = 0.01, <i>S</i> = 0.8, <i>p</i>₁ = 0.5, <i>p</i>₂ = 0.5.</p

Proportion of individuals showing behavior 2 as a function of the punishment level <i>L</i>, when individuals either apply behavior-based or preference-based punishment.

<p>(a) For <i>S</i> = 0.8, preference-based punishment is less successful in establishing a commonly shared behavior 1 than behavior-based punishment. (b) Preference-based punishment may fail completely, if both populations have a similar strength (<i>S</i> = 0.6). The other model parameters are <i>A</i> = 1, <i>B</i> = 1.2, <i>R</i> = 2, <i>p</i>₁ = 0.5, <i>p</i>₂ = 0.5, <i>r</i> = 0.01.</p

Persistence of a social norm, when sanctioning efforts are stopped at some point <i>t</i>₀ in time.

<p>Before this time, behavior 1 has been established as social norm. The model parameters used in the computer simulation are <i>A</i> = 1, <i>B</i> = 1.1, <i>R</i> = 2, <i>r</i> = 0.01, <i>S</i> = 0.6, <i>p</i>₁ = <i>p</i>₂ = 1, <i>k</i> = 3 and <i>C</i>₀ = 1 until <i>t</i>₀ = 1000, afterwards <i>C</i>₀ = 0.25.</p

Due to the path dependence of norm formation, unpopular norms can be established, if the unpopular behavior is initially overrepresented.

<p>In our computer simulations, 80% of individuals belong to population 1 and prefer behavior 1 (<i>S</i> = 0.8). The other model parameters are <i>A</i> = 1, <i>B</i> = 0.5, <i>R</i> = 10, <i>r</i> = 0.01. (a) If the initial average commitment is the same in both populations (<i>p</i>₁ = <i>p</i>₂ = 0.5), the behavior preferred by the majority wins through, as expected. (b) However, if the initial average commitment in the minority population is high (p₂ = 0.9), while it is low in the majority population (p₁ = 0.25), the behavior preferred by the minority establishes as a norm. (c) The dependence of the final outcome on the initial average commitments p₁ and p₂ can be illustrated by a phase diagram. In this case, the results are for <i>A</i> = 1, <i>B</i> = 0.5, <i>R</i> = 10, <i>r</i> = 0.01, <i>S</i> = 0.8.</p

Average payoff of all individuals in the course of time t for the two scenarios illustrated in Fig. 3, assuming the parameters <i>A</i> = 1, <i>B</i> = 0.5, <i>R</i> = 10, <i>r</i> = 0.01, <i>S</i> = 0.8.

<p>Dotted curve on the top: the behavior preferred by the majority wins through (<i>p</i>₁ = 0.5, <i>p</i>₂ = 0.5), Dashed curve on the bottom: the behavior preferred by the minority establishes the norm (<i>p</i>₁ = 0.5, <i>p</i>₂ = 0.5). Note that, compared to the (initial) coexistence of the two behaviors, the average payoff increases even, if the behavior preferred by the minority wins through.</p

Emergence of local conformity and global diversity, when the interaction range <i>R</i> is small.

<p>The displayed snapshots are from computer simulations for two equally strong populations (<i>S</i> = 0.5) and taken after <i>t</i> = 100 iterations (a) for <i>R</i> = 1 and (b) for <i>R</i> = 2. The other model parameters are <i>A</i> = 1, <i>B</i> = 0.4, <i>S</i> = 0.5, <i>p</i>₁ = 0.5, <i>p</i>₂ = 0.5, <i>r</i> = 0.01.</p

Payoffs of the focal individual in the multi-population norms game (<i>A</i> = advantage of conforming with the behavior of the interaction partner, <i>B</i> = benefit of showing the own preferred behavior).

<p>Payoffs of the focal individual in the multi-population norms game (<i>A</i> = advantage of conforming with the behavior of the interaction partner, <i>B</i> = benefit of showing the own preferred behavior).</p