2.3 Optical properties of charged and uncharged particles
2.3.1 Scattering of uncharged and charged particles
For uncharged particles, the scattering of light is determined by the size param-eter α, the dielectric constant (ω), which depends on frequency. In general ω is complex:
(ω) = 0(ω) + i00(ω) (2.41) where 0 is the real part of the dielectric function, and 00is the complex part. If the particle does have an electric charge, light scattering is also affected by the electric conductivity of the surplus electrons. Surplus electrons can be trapped
in the particle itself, or in a layer around the particle [10]. This depends on the electronic affinity of the particle, noted as χ.
For particles with a small size parameter, i.e. ρ << 1, the formula for extinction resonance efficiency is derived according to Heinisch et al :
Qt= 12ρ(” + α” + 2τ0/ρ)
(0+ α0+ 2 − 2τ ”/ρ)2+ (” + α” + 2τ0/ρ)2 (2.42) In this equation, a single prime denotes the real parts of the dielectric constant, polarizability and surface conductivity (, α, τ respectively), and a double prime denotes the imaginary part. The excess charges enter through τ with α = 0 for χ < 0 or through α with χ > 0. The limit of Rayleigh scattering occurs at τ, α = 0 [9]. For these values, equation 2.42 simplifies to equation 2.43 (below).
The resonance is located at the wave number where
0+ α0+ 2 − 2τ00/ρ = 0 (2.43) If the particle has no electric charge, then α0 and τ00 are 0, so the resonance is at wavelength λ−10 , for which 0 = −2. Depending on the value of χ (positive or negative), the shift of resonance can be characterized in two ways. If χ < 0 then the shift is proportional to τ00, and thus to ns, the surface charge. The resonance location is then at
λ−1= λ−10 + cτns/(πcaλ−10 ) (2.44) where cτ and c are constant, denoting the change of 0 with respect to λ−1 at λ0 and the change of τ00 with respect to ns at λ0. In Heinisch et al. these equations are derived. [9]
Likewise, if χ > 0, then the shift is due to the bulk surplus charge, and the resonance is located at:
λ−1 = λ−10 − cαnb/c (2.45) In which cαdenotes the change of α0 with respect to the bulk surplus charge nb at λ0.
Figure 2.2: Position of extinction resonance depending on surface charge [9]
For Al2O3, the surface charge is plotted against wavenumber for different par-ticle sizes, see figure 2.2. The dotted line represent the solutions of equations 2.43, the solid lines are exact Mie solutions. As can be seen on the figure, the dotted and real solutions agree well with each other.
Chapter 3
Experimental Set-up
The goal of the experiment is to measure the charge using the shift of phonon-resonance of Al2O3. The methodology and set-up is similar to Kr¨ugers work [14]. The key difference is that a newer type of spectrometer is used and particles are deagglomerated in a different way.
The set-up consists of three main parts as described below: i) Injection of nano Al2O3 particles ii)Implementation of plasma chamber iii) FTIR resonance shift measurements
i) Injection of nano Al2O3 particles For optimal FTIR measurements, particles need to be (ideally) homogeneously distributed across the plasma. Homogeneous injection of Al2O3 particles is a difficult challenge, because nanoparticles stick together due to van der Waals forces. An injection method needs to deagglom-erate particles before they are brought into the plasma. The injection set-up is given below in figure 3.1
The injection valve allows to fill the reservoir with nanoparticles. During FTIR
Figure 3.1: Injection and de-agglomeration of dust particles [14]
Figure 3.2: Sketch of set-up (top), drawing of the set-up of the plasma chamber in the FTIR spectrometer (bottom)
[14]
measurements, the argon gas is brought into the reservoir using a pressure re-ducer and valve, reaching a pressure about 0.5 bar. An electric valve then allows a small amount of argon gas and nanoparticle mixture to escape the reservoir and immediately closes afterwards. The large pressure difference To further de-agglomerate the dust particles, the mixture passes through a tiny hole which has a size of 600 µm. Several methods have been performed in order to over-come this issue [14], such as dust shakers, Due to shear stress, particles could be further broken apart. Finally, particles pass through the plasma nozzle and are brought into the plasma chamber.
ii) Plasma chamber
It is needed to show that the phonon resonance can be identified from Al2O3
particles trapped in the plasma. So, in order to measure the IR spectrum, the entire chamber is placed inside a Bruker Vector 80 FTIR spectrometer (Fourier Transformed Infrared Spectrometry), which has a resolution of 4 cm−1. The set-up is shown in figure 3.2 below:
The plasma chamber has two KBr windows on opposite sides, which are trans-parent for IR light. KBr is extremely sensitive to moisture. To minimize the exposure to ambient air, and to optimize FTIR measurements, the detector and
laser source are placed close to the windows. In addition, there are two opposite glass windows and a vertical laser beam, perpendicular to the FTIR laser source to verify the shape and presence of a confined particle cloud.
iii) FTIR measurements
FTIR is used in this setup because it has great advantages over ordinary IR spectroscopy. Unlike ordinary IR spectroscopy, a FTIR spectrometer collects a large number of spectra over a wide spectral range. This greatly reduces the measurement time, and makes it possible to identify multiple resonance peaks at once. Furthermore, FTIR increases the signal-to-noise ratio, because the background noise gets reduced by the increased number of spectra (relative to the background noise)
Typically, a measurement consist of two stages: background measurement and dust measurement. A background measurement is performed when no particles are injected. Afterwards particles are injected until the confined particles are stable, a sample measurement is taken. The sample measurement contains several hundred of averaged FTIR scans and typically takes about 5 to 10 minutes each, provided that the dust particles stay stable during this time.
Chapter 4
Results and discussion
The electric charge is calculated using the OML approach and is −8.91 · 10−17 C. This means particles accumulate at most 556 electrons. The OML theory is assumed to be valid, because of the high Knudsen number (particles have a considerably large mean free path relative to the particle size). It is questionable however if it is an accurate way to determine electric charge. The ion and electron density are too high (of order 1014) to consider a collision-less regime.
This means that by following the OML theory, the ion current is underestimated, and the predicted electric charge is overestimated. Furthermore, Goree et al [7]
showed that charged dust grains in a plasma can trap positive ions in confined orbits, shielding the grain from external electromagnetic fields. Furthermore, the plasma is considered to be quasi neutral, meaning charge fluctuations can occur.
A force balance analysis showed that the particle size strongly affects the loca-tion in which particles are confined. Despite efforts to minimize the agglomer-ation (breaking up agglomerates using a large pressure gradient, and injecting through a small hole to utilize shear stress), it’s still not yet possible to get a perfectly de-agglomerated plasma. This means that there is an inhomogenous distribution of particle size (regarding clustered particles as single particles), causing an inhomogenous dust cloud in the plasma. Perhaps it is possible to use this as advantage, one could measure FTIR scans across a given area of the plasma, neglecting particles that are clustered.
The optical signatures of charged particles are investigated and compared to neutral particles. It turns out, based on Heinisch et al anomalous resonance shifts depending on particle charge are visible. For Al2O3 particles, the reso-nance shift in fig 4.1 is observed.
Based on this theory, Kr¨uger et al. developed a way to determine this shift.
Using FTIR spectroscopy, extinction resonances are identified on transmission spectra. The challenge however is that the spectrometer has a spectral resolution
Figure 4.1: Position of extinction resonance depending on surface charge ns[10]
of 4 cm−1 It is therefore necessary to adjust the conditions of the plasma in a way the net charge is increased. This leads to a more visible shift of resonance spectra and makes it possible to overcome the resolution. The next section describes possible ways to enhance the spectroscopy difference between charged and neutral particles.
4.1 Optimizing measurement set-up: MiePlot analysis
To perform optimal measurements, the scattering behavior of particles in the set-up is examined using MiePlot software.
MiePlot is a tool which uses a Bohren and Huffman algorithm [4] for Mie scat-tering off a sphere. The software calculates exact solutions of the Mie theory, and can be applied for a wide range of simulations. Two characteristics are determined: i) The Intensity versus scattering angle is modeled to determine the transmission for different angles. ii) The crossection vs wavelength is deter-mined.
Both characteristics will be determined for two cases: a) Neutral particles, b) charged particles. MiePlot does not provide an option to insert an electric charge directly, however, the scattering behavior can be modeled by indirectly imple-menting an electric charge by altering the index of refraction. The following ranges of values are used for MiePlot analysis: λ = 4000 - 10000 nm , r = 150 - 10000 nm, n = 1.79 + 1.38 i , θ = 0 - 180 degrees. The index of the medium
Figure 4.2: Intensity vs scatter angle for r = 150 nm
is approximately 1. The wavelength range is entirely in IR region, because the phonon resonance shift is expected in this region.
Secondly, clustering of particles is again investigated. No clustering at all (r is same as one particle radius) all the way up to highly clustered particles (r
= 10000 nm) are investigated. The results could provide information on how much (unavoidable) clusters of particles affect the measurement results.
i) Intensity vs scattering angle
First of all, the intensity as function of scatter angle is determined for a fixed wavelength and neutral particles (λ = 4000 nm and r = 150 nm, see fig 4.1.) As can be seen on fig 4.1, the parallel polarized (dark red) part of waves have zero intensity at θ = 90, whereas the perpendicular polarized part (bright red) appears to be independent of the scatter angle. This yields a total transmission of 12I0 for θ = 90, I0 being the intensity before the laser strikes the particle.
An optimal measurement angle is θ = 0 degrees (forward scattering) or θ = 180 degrees (back-scattering), both yield an intensity of I0, meaning no loss of intensity.
For r = 5 · 105 nm, a cluster consisting of approximately 106 particles, the scattering behavior is changed significantly, see figure 4.1
For large clusters, the average intensity (the mean of both parallel and perpen-dicular components) decreases across all angles. There is a significant difference between forward and backward scattering, meaning an inhomogeneous size dis-tribution It can be concluded that clusters do alter the optimal measurement angle. The de-agglomeration methods should be sufficient such that clusters of particles do not have an influence on Intensity vs Scatter angle measurements.
Altering the particle has no noticeable effect on this behavior ii) Crosssection vs wavelength
Figure 4.3: Intensity vs scatter angle for r = 5 · 105 nm
Figure 4.4: Extinction efficiency vs wavelength.
Secondly, the scatter crossections efficiencies as defined in equations 2.31 are determined using MiePlot. The same default values are used initially, resulting in fig 4.4
In this figure, the extinction cross section efficiency decreases monotonically as the wavelength increases. For default values, Qabs ≈ 0 across the whole region (not visible in the graph). This means Qext = Qsca. This result implies that the wavelength should be as low as possible, because for an optimal yield Qext should be as large as possible.
If the particle gains an electric charge, the complex component of the index of refraction increases. A qualitative representation is shown in figure 4.5 . The bright red, dark red and black line represent Qext, Qsca and Qabs respectively.
At an order of magnitude of k ≈ 10−3, k representing the complex part of index of refraction, (see equation 2.33), the absorption efficiency no longer becomes
Figure 4.5: Extinction vs wavelength for charged particles.
Figure 4.6: Extinction vs wavelength for uncharged particles, r = 15µm
negligibly small, and even exceeds the scatter efficiency at 5200 nm. The total scatter efficiency stays the same, but the extinction increases as result of the non-zero absorption efficiency. This means that for a shift in resonance to be as clear as possible, the electric charge should also be as high as possible.
If particle clusters occur, the scatter efficiencies have very sharp discontinuities and hence the resonance shift is inconsistent across the spectrum, as seen in figure 4.6. This further emphasizes the necessity of preventing particles from sticking together.