for ultra-sensitive sensors [4]. There have been many excellent tutorial papers and reviews on SPR that the reader is directed to for more in-depth explanation, as well as the many applications, from sensing to in vivo and in vitro biomedical applications [2–5].
2.3.2 Optical: quantum dots fluorescence
Metals conduct electricity because their mobile electrons can move through the material. Electrons are confined to their atomic orbitals in an insulator material. So what is it that allows electrons to move in metals and not in insulators? The answer is there are simply vacant orbitals (holes) to move into at the same (or very similar) energy of the mobile electrons in metals. This is described by band theory, where there is an energy band full of electrons, so there are no holes available for electron movement. This is the valance band. Above this is the conduction band. Metals have electrons in the conduction band, which is not full, so there are plenty of vacant sites to move between. Semiconducting materials have a full valance band and no electrons in the conduction band (similar to an insulator), but they differ from an insulator as they have a very small band gap between the two bands. As such they become conducting when the temperature is increased sufficiently for the electrons to be promoted into the higher energy conducting band, leaving an electron hole in the valence band (with both mobile electron and holes contributing to conduction). Examples of semiconducting materials include CdSe, InAs and GaP. Describing electronic properties with respect to bands is only possible in the bulk phase (as bands are a continuous macroscale phenomenon). As the particle size reduces in size to the nanoscale, the electrons become spacially confined (with fewer vacant orbitals to move into) and the bulk models break down. When the size of the particle becomes comparable to or smaller than the electron/hole pair (exciton) Bohr radius (usually ⩽10 nm), the electrons are confined in all directions and the material is considered to have zero dimensions (hence a dot); these materials are known as quantum dots or ‘artificial atoms’. The spacial confinement results in an increase in the size of the band gap and the banded continuum (valance and conducting bands) breaking into a quantised energy level, perfectly demonstrating how the nanoscale is the intermediate between the bulk and the atomic scale. When energy is supplied to a quantum dot (in the form of electromagnetic radiation), an exciton is created as the electron is promoted into the conduction band, and this then emits fluorescence when the electron relaxes back down into the valance band, recombining with the hole. The wavelength of this fluorescence is dependent on the size of the band gap (ΔE(r)) which is dependent on the band gap of the bulk material (Egap), plus an increase in this size as the radius of the quantum dot (r) decreases (this relationship is shown in equation (2.4) and figure 2.6). The higher energy (shorter wavelength/higher frequency) emission is generated from relaxation across a larger band gap which occurs for smaller quantum dots. Equation (2.4) can be rearranged to equation (2.5) to show the relationship of the quantum dot size (radius r) to the change in band gap energy (h is Planck’s constant, me is the mass of a free electron and mh is the mass of the hole).
ΔEnano(r)=ΔEbulk+h28r21me⁎+1mh⁎(2.4)
r=h28(ΔEnano−ΔEbulk)1me⁎+1mh⁎(2.5)
Quantum dots have exceptional and far superior fluorescent properties in comparison to traditional organic dye molecules. (1) Due to the relationship between size and emission their wavelength can be precisely tuned. (2) They can absorb a broad range of energy but have a very narrow emission band. (3) Their fluorescence is unparalleled with respect to brightness, lifetime and resistance to photobleaching, which makes them excellent optical probes. One downside is many of the best semiconductor materials for high florescence quantum dots with the band gap at the best wavelength for visualisation are often the most toxic (such as CdSe and Cd/S). This is being addressed by coating these materials in less toxic semiconductors, such as ZnS, and also developing new quantum dot materials by doping less toxic semiconductors to tune the band gap. Again, different morphologies can offer further tuning. Further reading on quantum dots and particularly their biomedical uses and the implications of their toxicity can be found in [6].
Figure 2.6. Description of how a band gap in a semiconductor increases as the size of the particle decreases. The left-hand side shows the band gap in the bulk material, while on the right an increased band gap is shown for the nanoparticle (bulk gap is shown as a dashed line on the right for comparison) as the frequency of the light emitted is proportional to this energy (and dependent on the material), the light emitted varies with size. CdSe/ZnS quantum dots of decreasing sizes from left to right are shown in the centre (image from [2] reproduced by permission of the Royal Society of Chemistry).
2.3.3 Electron spin and nanomagnetism
Nanomagnetism is another perfect illustration of a property on the boundary between bulk and atomic scale. Again we will see here how some nanoparticles behave like atoms (superparamagnets) while others behave more like the bulk (single-domain nanomagnets). Furthermore, we see how the quantum interplay between charge, electron spin and magnetic field can be harnessed in nanomaterials for spintronic applications. To understand the nanoscale properties we must first understand the interplay of electrons and magnetism at the atomic scale, appreciate how this builds to bulk scale, then interrogate the middle.
In fundamental terms, a magnetic field is generated when there is movement of charge. This is seen by the magnetic field surrounding a wire conducting electricity, which is due to the charged electrons moving in the wire (figure 2.7(Ai)). Electrons in an atom have two sorts of motion (orbital and spin (figure 2.7(Aii))) and as such have a magnetic moment: generally it is the electrons in a material that give it its magnetic properties. The moment of a single electron can be calculated from first principles, and is found to be
μB=πr2I=eℏ2me=9.274×10−24Am2,(2.6)
where r is the radius of the orbital, I is the current, e is the charge of an electron, me is the mass of an electron and ℏ is the reduced Planck constant.
Figure 2.7. Description of magnetism from the atomic to the bulk. (A) Two demonstrations of magnetic fields generated by electrons. (Ai) Macroscale example of magnetic field lines of magnetic field generated by a wire conducting electricity due to the flow of electrons (the current I) in the wire. (Aii) The motion of an electron within an atom (both orbital and spin) which generates an atomic magnetic field. (B) Any unpaired electrons contribute to a bulk magnetic property depending how they are arranged in the solid. Each arrow represents the direction and magnitude of a paramagnetic atom. (C) The nanomagnetic properties, demonstrating how the largest single domain magnetism have the highest coercivity due to no loss of energy through domain wall formation, while superparamagnetic nanoparticles have near zero coercivity. (D) Description of the magnetic properties of hysteresis, plotting the magnetisation with increasing field, then reversing the field and increasing again.
Two electrons only exist in the same atomic orbital if they have opposite spin values (either + 1/2 or −1/2). The electrons are ‘paired’ in an orbital and these two opposite electronic spins cancel out each other’s magnetic moment, so there is said to be no net overall magnetic effect. However, this is not technically true: such orbits actually have a week
