The bottom-up approach, on the other hand, starts out with precursor solu-tions used to synthesise clusters with sub-nanometer sized features and subse-quently building up nanostructures in the desired dimensions. Strong candidates for these methods are stabilized chemical reactions that cut-offat specific sizes or supramolecular interactions (through electrostatic, hydrogen-bonding,π−π in-teraction, Van-der-Waals, hydrophilic-hydrophilic or hydrophobic-hydrophobic).
The former is often used to synthesize nanoparticles with different morphologies (spherical, rods or sheets),[13–15] while the latter is often brought into context with self-assembled structures.
This work takes advantages of mostly the top-down approach with the syn-thesis of CNC particles from microcrystalline cellulose and thin-film deposition of conductors and semiconductors through physical and chemical vapor deposi-tion techniques (Chapter 4). However, the bottom-up approach in the form of self-assembled nanostructures will be used to obtain mesoporous photonic films from suspended CNC particles (Chapter 3).
Nanotechnology was very accurately summed up in a phrase by the National Science Foundation in 1999: “nanoscience and technology will change the nature of almost every human-made object in the 21st century”.[16] They were not far off.
This work demonstrates how Nanotechnology is not only the study of the very small but truly an area of multidisciplinary proportions and vectors, where on the nanoscale, diverse areas such as soft-condensed matter (cellulose nanocrystals) and solid-states physics (semiconductors) can be combined and linked to create something truly new and exciting.
1.2 The History and Math behind Light and its
with specific CNC-semiconductor structures (see Chapter 5 and 6).
Fundamentally and classically, EM radiation (of photons) refers to an EM field, which propagates through space and carries radiant energy.[17] An EM wave is classified as a transverse wave, meaning that the electric and magnetic field components oscillations are perpendicular to the propagation direction of the wave (as opposed to longitudinal waves; for instance sound waves). Additionally, the electric and magnetic field components oscillate perpendicular to each other and in space. Consequently, for an EM wave travelling along the z-axis, the electric and magnetic field will oscillate in the xz– and yz-planes or vice-versa, respectively (see Figure 1.3).
Figure 1.3 – a) An electromagnetic wave travelling along the z-axis with its elec-tric E~0 and magnetic B~0 field components oscillating in the xz- and yz-planes, respectively. Observe that both components are perpendicular to each other. b) Considering a wave with arbitrary form lying in a local reference frame xy-plane, which is perpendicular to the propagation direction z. It should be noted that the components may not oscillate perfectly in the xz or yz plane (as in a). In this case they need to be decomposed into their respective components E~0x (or B~0x) and E~0y (orB~0y). Also note that the magnetic component is usually omitted and only the electric components are shown.
In vacuum an EM wave travels at the speed of light (c = 299792458 ms-1) and the distance it takes for the EM field to repeat itself is denoted as the wavelength λ(λ0 if in vacuum). Comparatively, the time it takes for a full oscillation to occur is denoted as the periodT, which as a reciprocal is the wave’s frequencyf.
To describe an EM wave mathematically the wavenumber (k – magnitude of the wavevector) and the angular frequency (ω) are used. These two quantities are defined as:
k=2π
λ (1.1)
ω= 2π
T = 2πf (1.2)
The speed (or phase velocity of the waveυ) is thus intrinsically linked to these quantities by:
υ=ω
k =f λ (1.3)
where υ is equal to c when the EM wave travels in vacuum (with refractive indexn= 1). However, if the EM wave travels in a medium where n > 1, the phase velocity decreases according to:
n= c
υ ↔υ= c
n (1.4)
This relationship between the phase velocity and the refractive index will become relevant in the context of liquid crystals and their birefringence in Section 1.3 and Chapter 3.
As already hinted in Figure 1.3 and in order to simplify the mathematical description, normally the electric field is described, while the magnetic one is omitted and is assumed to always oscillate perpendicular to the electric field.
Therefore, for the example in Figure 1.3b, with a sinusoidal EM wave travelling along the z-axis, it is possible to establish the following individual electric field components:
E~x(z, t) =E~0x(t)cos(kz−ωt) (1.5)
E~y(z, t) =E~0y(t)cos(kz−ωt+δ) (1.6) here t stands for time, E~0x and E~0y are the magnitudes of the electric field components ofE~0 in an arbitrary plane andδrepresents the phase shift between the two components. The phase shift is an important parameter for this work, as it spans over a range of 2π, originating various polarization states of the EM wave, including LCPL and RCPL. These are the Circular Polarization (CP) states that are reflected or transmitted by the chiral nematic CNC structres, that will be implemented in semiconducting devices for sensing appliacations. Considering Figure 1.4, it is possible to establish the following relations betweenδ and the polarization of the EM wave.
Figure 1.4 – Phase (δ) shift between the x- and y-components of the electric field.
a) and b)E~0x andE~0y components of an electromagnetic wave travelling along z without and with a phase shift, respectively. c) Polarization states for 0≤δ≤2π (for equal magnitudes of E-field components). Forδ =kπ, where k = 0, 1, 2, 3, . . . the light is linear polarized. For δ = (2k−21)π, wherek = 1, 2, 3, . . . the light is circular polarized. For all other values in between, elliptical polarization is obtained. The handedness of the polarization (for elliptical and circular) depends on the relative position of the x- and y- E-field components.
Since the CP state is the most important one in this work, the shown cases here are simplified to an extent where the local reference frame is constant, and the magnitudes of the E-field components are equal. If not stated otherwise these will be the conditions when dealing with CPL throughout this work. For a more complete description of the underlying phenomena and intermediate elliptical polarization states originating from distinct azimuthal, ellipticity and reference frame angles, the reader may revisit the introductory part of the work by José J. Gil and Razvigor Ossikovski on “Polarized Light and the Mueller Matrix Approach”.[18]
From the relations of Figure 1.4 it is thus possible to arrive at the two polar-ization states that are in focus in this work: LCPL and RCPL. The convention for the electric field vector rotation adapted throughout this manuscript will be from the point of view of the observer (IEEE convention) as depicted in Figure 1.5.[19]
Figure 1.5 – Schematic representation of CPL in 3D. a) and b) Electric field components for RCP and LCP, respectively. c) Adopted IEEE convention for CPL throughout this work.
To obtain CPL using polarizing filters normally the light beam is firstly linearly polarized by either a polymer or a wire grid polarizer, followed by a film which defines the phase shift and handedness of the exiting beam. The former of the two is known as the retardation or a quarter-wave plate since it shifts one of the E-field components over π/2 to reach CPL (see Figure 1.4). Wave plates are fabricated from birefringent materials (for example quartz, mica or plastic), where the thickness and the ordinary and extraordinary refractive indices define the nature of the wave plate (quarter-, half- or full-waveplate). A sandwich of these two layers (linear polarizer combined with a quarter-wave plate) transforms an arbitrary polarized light beam into CPL. The handedness is defined by the rotation of one of these layers in respect to the other, where the fast-axis serves as the reference axis that defines the handedness.