ABSTRACT
In many instances, such functionalities are related to the exchange of electrons, either within the nanoassembly or involving external species [13]. As in the case of molecular devices, the rational design of functional assemblies that exploit electron-transfer processes for their operation requires a prior knowledge of the redox properties of the components; in fact, the fine-tuning of these parameters is essential to achieve the desired function [11, 12, 14-16]. In such a context, the amount of information available on the structural and electronic properties of organic and inorganic molecular components is invaluable. Unfortunately, the same level of understanding has not yet been achieved in the case of semi-conductor nanocrystals. In particular, it is still not entirely clear how the dimension of the core, the thickness of the inorganic shell and the nature of the organic ligands can influence the redox properties of semiconductor nanocrystals. Since their discovery in the 80s, quantum dots have attracted much attention and a large amount of literature is available on their synthesis, properties and applications [6, 17-20]. On the other hand, systematic investigations on the relationship between the structural parameters and the redox properties of QDs are rare [21]. The aim of this chapter is to collect and discuss the results of electrochemical studies carried out on binary semiconductor nanocrystals (core and core-shell) of spherical shape. The chapter starts with a brief overview of the peculiar electronic properties of QDs (Section 3.2), and of the electrochemical techniques commonly used for the study of such systems (Section 3.3). Sections 3.4 and 3.5 contain a description of examples taken from the literature. We will focus on CdSe and CdTe nanocrystals, because the relatively large number of papers dealing with these QDs enable a more insightful discussion on their redox properties. Whenever possible, we will compare the data obtained with different techniques by different groups in order to attempt an interpretation of sometimes contradictory results. Sections 3.6 and 3.7 are dedicated to emerging or potential applications that exploit the electroactivity of quantum dots. Finally, limitations and perspectives of these systems are summarized in Section 3.8. 3.2 Basic Electronic Properties of QDsSeveral physical properties of bulk materials change substantially when they are in the form of particles with a size on the order of
nanometers [5]. Examples of this behavior are melting points and other parameters related to phase transformations, charging energies, spectroscopic properties, etc. For semiconductors nanoparticles the most noticeable consequence of the size effect is that the band gap — namely, the energy difference between the top edge of the valence band and the bottom edge of the conduction band — can be modified on varying the particle size. In a semiconductor, absorption of a photon with energy equal or greater than the bandgap results in excitation of an electron from the valence to the conduction band, leaving a hole in the valence band. Such an electron-hole pair, or exciton, is bound by the electrostatic attraction between the opposite charges. The Bohr radius measures the extension of the exciton wavefunction over the crystal lattice; for example, the Bohr radius for excitons in CdSe is about 5 nm. When the size of the particle approaches the Bohr radius, the optical and electrical properties of the material become dependent on its physical dimension, owing to the so-called quantum confinement effect [1-6, 22]. In these conditions, the band structure of the semiconductor changes into discrete levels, and the energy difference between the highest occupied level and the lowest unoccupied level widens as the particle size decreases, following in many cases the behavior expected for an electron inside a three-dimensional box. In some cases a description in terms of molecular orbitals is more appropriate than that of band theory, reflecting the nature of QDs as systems lying between bulk materials and molecular species. Electrochemical measurements are usually employed to estimate the energy of HOMO and LUMO levels of electroactive molecular species. They can also provide information on the electron-transfer kinetics and give access to other parameters such as diffusion coefficients, interfacial properties, thermodynamic and kinetic constants of reactions coupled with the redox process [15, 16, 23]. Similarly, voltammetric experiments can give information on the absolute energies of the valence and conduction bands of quantum dots. The process of charge transfer in quantum dots can be schematized in three ways (Fig. 3.1) [24]: (a) electron or hole addition [25] to a neutral nanoparticle; (b) simultaneous injection of a hole and an electron in two non-interacting quantum dots; (c) formation of an electron hole pair within the same particle by optical excitation. The charging energy for addition of one electron (Fig. 3.1a) is given by Eq. 3.1:
μ1 ≡ E1[e1] – E0 = ε0e1 + Σe1pol (3.1)where E1[e1] is the energy of the nanoparticle after addition of one electron to the e1 energy level, E0 is the initial energy, ε0e1 describes quantum confinement, Σe1pol is the dielectric confinement. The energy required for the formation of a non-interac-ting electron-hole pair (quasi-particle gap) (Fig. 3.1b) is given by Eq. 3.2: εqpgap = E1[e1] – E-1[h1] – 2E0 = ε0gap + Σe1pol + Σh1pol (3.2) The quasi-particle gap can be determined by voltammetric experiments, and it corresponds to the electrochemical bandgap (∆Eel). The optical gap (Fig. 3.1c) is given by Eq. 3.3: ∆Eop = ∆Eel – Je1,h1 (3.3)where Je1,h1 is the total Coulomb interaction of the electron-hole pair. Hence, for any given quantum dot, the electrochemical energy gap is expected to be larger than the optical energy gap.
