Abstract
The ballistic regime of vibrational energy transport in oligomeric molecular chains occurs with a constant, often high, transport speed and high efficiency. Such a transport regime can be initiated by exciting a chain end group with a mid-infrared (IR) photon. To better understand the wavepacket formation process, two chemically identical end groups, azido groups with normal, 14N3-, and isotopically substituted, 15N3-, nitrogen atoms, were tested for wavepacket initiation in compounds with alkyl chains of n = 5, 10, and 15 methylene units terminated with a carboxylic acid (-a) group, denoted as 14N3Cn-a and 15N3Cn-a. The transport was initiated by exciting the azido moiety stretching mode, the νN≡N tag, at 2100 cm–1 (14N3Cn-a) or 2031 cm–1 (15N3Cn-a). Opposite to the expectation, the ballistic transport speed was found to decrease upon 14N3 → 15N3 isotope editing. Three mechanisms of the transport initiation of a vibrational wavepacket are described and analyzed. The first mechanism involves the direct formation of a wavepacket via excitation with IR photons of several strong Fermi resonances of the tag mode with the νN=N + νN–C combination state while each of the combination state components is mixed with delocalized chain states. The second mechanism relies on the vibrational relaxation of an end-group-localized tag into a mostly localized end-group state that is strongly coupled to multiple delocalized states of a chain band. Harmonic mixing of νN=N of the azido group with CH2 wagging states of the chain permits a wavepacket formation within a portion of the wagging band, suggesting a fast transport speed. The third mechanism involves the vibrational relaxation of an end-group-localized mode into chain states. Two such pathways were found for the νN≡N initiation: The νN=N mode relaxes efficiently into the twisting band states and low-frequency acoustic modes, and the νN–C mode relaxes into the rocking band states and low-frequency acoustic modes. The contributions of the three initiation mechanisms in the ballistic energy transport initiated by νN≡N tag are quantitatively evaluated and related to the experiment. We conclude that the third mechanism dominates the transport in alkane chains of 5–15 methylene units initiated with the νN≡N tag and the wavepacket generated predominantly at the CH2 twisting band. The isotope effect of the transport speed is attributed to a larger contribution of the faster wavepackets for 14N3Cn-a or to the different breadth of the wavepacket within the twisting band. The study offers a systematic description of different transport initiation mechanisms and discusses the requirements and features of each mechanism. Such analysis will be useful for designing novel materials for energy management.
Highlights
Ballistic energy transport via acoustic phonons is prevalent in ordered materials such as crystals and can occur to large distances
Ballistic energy transport via covalent bonds of linear oligomeric chains was discovered to occur via optical chain bands, delivering substantially larger energy quanta to distances exceeding 60 Å1−4 and featuring much higher efficiency compared with that in diffusive energy transport.[5−8] Oligomeric chains feature a range of chain bands differing in energy and bandwidth
The cross-peak spectra were measured for a range of waiting times, T, and waiting-time kinetics were constructed by integrating the 2DIR spectra over the cross-peak area and plotting the resulting amplitude as a function of the waiting time (Figure 1E)
Summary
Ballistic energy transport via acoustic phonons is prevalent in ordered materials such as crystals and can occur to large distances. Ballistic energy transport via covalent bonds of linear oligomeric chains was discovered to occur via optical chain bands, delivering substantially larger energy quanta to distances exceeding 60 Å1−4 and featuring much higher efficiency compared with that in diffusive energy transport.[5−8] Oligomeric chains feature a range of chain bands differing in energy and bandwidth. The bandwidth of a chain band determines the mean group velocity of the wavepacket supported by the band.[9] The ballistic through-chain transport was initiated via excitation with a midIR photon, a vibrational mode at the end group, which transferred its energy into the chain, initiating the transport. The energies of the end-group modes tested for ballistic transport range from 2100 cm−1 (azido group stretch)[1] to 1650−1750 cm−1
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