Fluorescence “Giant” Red Edge Effect
2.4 Theoretical studies of different properties of carbon quantum dots
2.4.1 Electronic structure
The electronic properties of CDs depend on the effect of quantum confinement and the surface passivating species. These two factors determine the energy gap between the highest occupied molecular orbital (HOMO) state and the lowest unoc- cupied molecular orbital (LUMO) state, as shown inFig. 2.4. GQDs have a nonzero band gap because of excitons in graphene. The main controllers for the energy gap are the bonding between C atoms like GQDs in the core region of the CDs and its surface species.
Figure 2.4 (A) Relation between the energy gap vs the size of the aromatic ring.
(B) Variation of energy gap with degrees of oxidation. (C) The effect of the introduction of oxygen atoms on the energy gap. (D) The impact of the introduction of nitrogen atoms on the energy gap. (E) The effect of introducing an electron-donating functional group or domain size of sp2hybridization. (F) Modification of PL after D-Lysine and L-Lysine.
(G) Synthesis of CDs guided by machine learning.
Source: Reproduced from S. Li, et al., The development of carbon dots: from the perspective of materials chemistry. Materials Today, 51 (2021) 188 207, with permission from Elsevier.
The design principles of different CDs with several parameters are schematically depicted inFig. 2.4, as shown by Li et al.[2]. The CDs have GQDs as core and sur- face functional groups. InFig. 2.4A, with the increasing size of the aromatic ring, the band gap decreases due to the effect of quantum confinement. The sp2domain size also increases with the growing length of the aromatic rings. Similarly, the energy gap of CDs reduces upon an increment of oxidation at the surface of the CDs. Incorporating oxygen atoms into the sp2 region generates an n-orbital level, which causesn-ᴨ transition (Fig. 2.4B and C). Furthermore, nitrogen functionaliza- tion at the surface of CQDs changes the HOMO and LUMO positions and hence the energy gap as shown inFig. 2.4D. This nitrogen-containing surface group could donate electrons, and it may generate n-orbital between ᴨ and ᴨ that affect the photoluminescence (PL).
Chirality is another factor that affects CDs’ electronic and chemical properties, as explained inFig. 2.4F. Chirality in CDs, modified by chiral ligands (e.g., amino acid), enhances their chemical stability and optical properties.
The state-of-the-art computational approach could help to design and control the electronic and optical properties and develop CDs. Han et al. recently showed from computation using machine learning (ML) technique that their advanced ML-based method can design the CDs with higher quantum yield[6].
2.4.2 Optical properties
The optical properties of any material depend entirely on its electronic structure, as discussed above. Several optical processes are observed in CDs, as shown in Fig. 2.5. These optical processes are only within the singlet state of CDs. PL and absorption depend entirely on the transition between two electronic states obeying selection rules. In general, the emission mechanism in CDs is exciton-dependent, and this occurs in three different ways, namely emissions due to the quantum con- finement effect of the 0D QDs, emissions due to more prominent surface states, and emissions due to molecular states.
Strong absorption occurs in CDs due to the transition betweenᴨtoᴨof the phe- nyl rings. This absorption of light belongs to the ultraviolet region. On the contrary, lower absorption by the transition betweenn toᴨ from C-C or C-O bonds lies in the visible and near-infrared region. The PL phenomenon is observed between two singlet states following internal conversion between nonradiative singlet states.
The excitation-dependent PL or fluorescence is the most promising phenomenon observed in CDs[3]. Due to excitation-dependent PL, a wide range of multicolor emissions makes CDs more useful in optoelectronic applications. These long- ranged emission processes occur from the transition between several surface defect states to ground states. On the contrary, the tunable PL in semiconductor QDs mainly arises from the changing size of the particle due to the quantum confine- ment effect. Several groups showed a direct relationship between surface state-to- PL. Hence, one can generate particular color of PL by modifying surface defect states from passivating agents in CDs. Fu et al. had shown that the luminescence in
CDs could be controlled by adjusting the structure of emitting surface species[7].
For example, they showed two-dimensional polycyclic aromatic hydrocarbons (PAHs) containing carbons having sp2hybridization, which mimic the nanodomains of CDs. Luo et al. also showed luminescence tuning in aryl functionalized GQDs, where aryl residues make covalent bonds with surface carbon atoms[8].
Furthermore, several photophysical processes were observed in the CDs, namely electrochemiluminescence, chemical luminescence, Foster resonance energy trans- fer (FRET), etc.
Figure 2.5 Different possible PL and fluorescence mechanisms. (A) Effect of quantum confinement; (B) multicomponent PL between core, molecular, and surface states; (C) effect of crosslink-enhanced emission.
Source: Reproduced from M. Langer, et al., Progress and challenges in understanding of photoluminescence properties of carbon dots based on theoretical computations. Applied Materials Today, 22 (2021) 100924, with permission from Elsevier.
2.4.3 Electrocatalytic properties
Beyond the PL application, the CDs have plenty of applications in energy storage via electrocatalytic processes. The advantages of using CDs as an electrocatalytic agent are that they are nontoxic, economically cheap, have large surface area, high conductivity, and reasonable charge transfer possibilities (see Fig. 2.6) [9]. These include oxygen reduction reaction (ORR), oxygen evolution reaction (OER), CO2 reduction, hydrogen evolution reaction (HER), etc.[10].
To know the intermediate steps of any electrocatalytic phenomena such as OER, ORR, HER, etc., we can calculate free energies for all steps using DFT, and details of the approach could be found in Ref. [11]. In DFT, we calculate Gibbs free energy from the following formula.
ΔG5 ΔE1 ΔZPE2T∙ΔS
whereΔG, ΔE, ΔZPE, T, andΔS are changes in Gibbs free energy for the reac- tion, change in binding energies for the reaction, change in zero-point energy, tem- perature, and change in entropy, respectively. All the parameters are calculated from DFT or the gas-phase database.
There are very few theoretical studies on the electrocatalytic properties of CDs.
We here discuss a few of the recent studies. W. A. Saidi explored ORR activity from first-principles calculations for N-doped GQDs, where pyridine and graphitic nitrogen are the most active sites with comparatively low overpotential[12].
Figure 2.6 Schematic representation of various electrocatalytic properties of CQDs and GQDs.GQDs, Graphene quantum dots;CQDs, carbon quantum dots.
Source: Reproduced from V. C. Hoang, K. Dave, V. G. Gomes, Carbon quantum dot-based composites for energy storage and electrocatalysis: Mechanism, applications and future prospects. Nano Energy, 66 (2019) 104093, with permission from Elsevier.
Li et al. showed that CDs could be used as a promising electrocatalyst for ORR [13]. These CDs can easily combine with noble metals, metal oxides, and other organic solvents. These integrated complexes help the electrocatalytic process through possible charge separation, opening new reactive sites and reducing the reaction’s acti- vation barrier. The GQDs combined with carbon nitride form nanohybrid, which helps in ORR. Hence, the CQDs could provide promising electrocatalytic applications.
The CDs combined with transition metal compounds such as CoP provide better OER activity, where the overpotential is lowered by 400 mV compared to pure CoP[10].
In fossil fuels, nitrogen-doped GQDs with the wrapping of Au nanoparticles help to reduce CO2in the natural carbon cycle. This is due to the enhancement of the absorp- tion of the carboxylic group at the N site of the pyridine ring of N-doped GQDs[14].
Furthermore, CDs can be used for HER activity, such as Ru with CDs hybrid, which requires only 10 mV of overpotential[15].
Therefore, CDs are promising as electrocatalysts due to their inherent properties, as shown inFig. 2.6, and are nontoxic and inexpensive, as discussed earlier.
2.4.4 Transport properties
Beyond the interesting optical properties, CDs, especially GQDs, also show exciting transport properties. The electronic and transport properties of nanostructures like QDs depend on the QDs’ confined geometry. The quantum confinement of the CDs avails of exciting phenomena like quantum interference, resonant tunneling, and localization. Recently, Gonzalez et al. found a resonant behavior for the con- ductance of the GQDs using tight-binding Hamiltonian and Green’s function (Landauer-Buttiker formalism) with the real space renormalization technique[16].
This can be controlled by changing their geometry, and the negative differential conductance appears upon applying low gate and bias voltage values.
Furthermore, the spin state beyond the charge transport in GQDs can be used as qubits in quantum computation, which is the future for superfast computations. The GQDs have advantages over semiconductor QDs like GaAs QDs because of the weaker spin-orbit coupling due to the low atomic weight, which provides a much longer spin coherence time, unlike GaAs[17,18]. The GQDs also have a larger spin g-factor (c. 2), so qubit manipulation could be done much faster than GaAs[19]. A simple illustration of the long-range interaction via Klein tunneling between spin qubits of QDs embedded within a graphene sheet is presented inFig. 2.7. To under- stand the behavior of spin qubits in GQDs, one can use the model Hamiltonian approach considering spin-orbit coupling and electron-phonon coupling within it.
More details about spin qubits and their interaction in different graphene and semi- conductor QDs could be found in Ref.[17 19].
2.4.5 Kondo effect in carbon quantum dots
The conduction electrons get scattered due to magnetic impurities in the materials, for which resistivity at zero temperature diverges. This phenomenon is known as
the Kondo effect. The first time experimentally Kondo effect in QDs was observed in 1998, confirming theoretical predictions[21]. In the case of GQDs, Kurzmann et al. showed the presence of the Kondo effect from the two-electron triplet ground states with small spin-orbit coupling[22].