Solvent- and Wavelength-Dependent Photoluminescence Relaxation Dynamics of Carbon Nanotube sp³ Defect States

Abstract

Photoluminescent sp defect states introduced to single wall carbon nanotubes (SWCNTs) through low-level covalent functionalization create new photophysical behaviors and functionality as a result of defect sites acting as exciton traps. Evaluation of relaxation dynamics in varying dielectric environments can aid in advancing a more complete description of defect-state relaxation pathways and electronic structure. Here, we exploit helical wrapping polymers as a route to suspending (6,5) SWCNTs covalently functionalized with 4-methoxybenzene in solvent systems including HO, DO, methanol, dimethylformamide, tetrahydrofuran, and toluene, spanning a range of dielectric constants from 80 to 3. Defect-state photoluminescence decays were measured as a function of emission wavelength and solvent environment. Emission decays are biexponential, with short lifetime components on the order of 65 ps and long components ranging from around 100 to 350 ps. Both short and long decay components increase as emission wavelength increases, while only the long lifetime component shows a solvent dependence. We demonstrate that the wavelength dependence is a consequence of thermal detrapping of defect-state excitons to produce mobile E excitons, providing an important mechanism for loss of defect-state population. Deeper trap states (i.e., those emitting at longer wavelengths) result in a decreased rate for thermal loss. The solvent-independent behavior of the short lifetime component is consistent with its assignment as the characteristic time for redistribution of exciton population between bright and dark defect states. The solvent dependence of the long lifetime component is shown to be consistent with relaxation via an electronic to vibrational energy transfer mechanism, in which energy is resonantly lost to solvent vibrations in a complementary mechanism to multiphonon decay processes.

Exciton relaxation in carbon nanotubes via electronic-to-vibrational energy transfer

“…Experimentally, the EVET decay rate in water was estimated to be ≈ 200 ps in Ref. [17]. Considering the level of approximations in this work, the obtained theoretical result (τ EVET ∼ 100 ps) is in good agreement with experiment.…”

“…In this subsection, we will evaluate the EVET rate corresponding to a localized exciton in a functionalized CNT. The detailed description of the system is given in our previous work [17]. Briefly, a chiral (6,5) CNT is assumed to be of radius R = 0.38 nm [28,29].…”

“…Distance between CNT surface and the first water solvation shell (for CNTs of similar diameters, but not specifically for (6,5) chirality) is estimated to be a − R ≈ 0.3 nm [30,31], so we estimate the cavity radius as a = 0.68 nm. CNT is functionalized with 4-methoxybenzene, resulting in the strong localized exciton transition at λ ≈ 1160 nm with the transition dipole moment of d = 38 D [17]. The dielectric constant of water at the frequency corresponding to this transition is taken to be out = 1.75 + i2.7 × 10 −5 [17].…”

“…CNT is functionalized with 4-methoxybenzene, resulting in the strong localized exciton transition at λ ≈ 1160 nm with the transition dipole moment of d = 38 D [17]. The dielectric constant of water at the frequency corresponding to this transition is taken to be out = 1.75 + i2.7 × 10 −5 [17]. Exciton localization size in axial direction is typically significantly larger than the CNT radius [32,33].…”

“…This is because the exciton, once trapped at the defect site, is no longer free to diffusively sample PL quenching sites along the length of the carbon nanotube [14]. Since the long exciton lifetime (hundreds of picoseconds) becomes critical for proposed functionalities, much effort has been directed lately towards understanding the nature of relaxation channels of the trapped exciton in functionalized CNTs [12,[15][16][17]. In particular, we have recently suggested that resonance energy transfer between the trapped exciton in CNT and solvent vibrational modes can be an important exciton relaxation channel [17].…”