Electron Density from Saha Equation

Here, dM/dlogdm is the mass concentration of each bin, normalized by bin width

and ρbis the bulk density of RbCl (2.80 g cm−3). The bulk density will be a good

approximation since the particles are compact. The total mass concentration (MRbCl)

can then be determined by multiplying each bin by the bin width and summing over all bins: M_RbCl=

_∑

The atomic concentration of rubidium in the gas at ambient conditions (NRb) can

be calculated from the total mass concentration of RbCl by accounting for the mass fraction of rubidium in the salt molecule:

N_Rb= M_RbClNa

M_m,Rb M_m,Rb+ Mm,Cl

, (4.8)

where Na is Avogadro’s number, and Mm,Rb and Mm,Cl are the molar masses of

rubidium and chlorine respectively. In the case of the size distribution in Figure 4.3d, the total RbCl concentration was calculated by considering only the larger lognormal distribution possessing a dgof 228.1 nm (which constitutes ∼90% of the total aerosol

mass). The mass distribution is also shown in Figure 4.3d in blue, and the total RbCl mass concentration at standard conditions is 35 562 µg m−3. The atomic Rb concentration is 1.77 × 1020m−3 before mixing with additional gas and entering the plasma. This represents an atomic fraction of rubidium of approximately one atom in a million relative to the nitrogen carrier gas entering the plasma.

4.6.2

Electron Density from Saha Equation

The system of equations in section 4.3.2 pertaining to the Saha equation was solved iteratively in Matlab, and the resulting plot of electron (and ion) density as a function of excitation temperature is displayed in Figure 4.3f. Argon is represented by the

4.6 Electron Density 75

dotted purple line, and its electron/ion density at the excitation temperature determined previously of 7162 K is 1.46 × 1020 m−3. This corresponds to a charge fraction of 1.42 × 10−4. This is slightly lower than the range of Choi et al. [70] who determined the electron density of their argon microplasma to be 6.5 − 7.4 × 1020m−3.

The electron density for the N2-H2-Rb plasma was also determined for the case in

Figure 4.3c where 1.0 SLPM H2is used. The multiple species present in the plasma

produce a more complex electron density profile as seen with the black line in Fig- ure 4.3f. The low ionization energy of rubidium (4.18 eV) means that a large fraction is ionized even at low temperatures. By comparison, the much higher ionization energies of nitrogen and hydrogen (∼15.5 eV) cause extremely low ion concentrations to be present below 5000 K. Therefore, for lower temperatures, the free electrons originate almost exclusively from the rubidium. In this case, rubidium ionization increases until 2900 K at which point nearly the entire population of rubidium will be ionized, and the electron density is limited by the concentration of rubidium atoms in the plasma. The electron density in this regime peaks at 2900 K at 2.08 × 1018 m−3 and gradually decreases as temperature decreases due to expansion from the ideal gas law. Above 5000 K, the ion and electron densities from nitrogen and hydrogen become appreciable and at 5300 K the same number of nitrogen atoms are ionized as rubidium atoms, at 1.20 × 1018m−3for each species. For temperatures above 5300 K, the electron density is dominated by nitrogen and hydrogen ionization.

Note that while nearly all of the rubidium is ionized, only two Rb+ lines were

observed (394 and 397 nm), and these were relatively low intensity in comparison to the Rb0lines. This is because like argon (shown schematically in Figure 4.2a), Rb+

lines are associated with de-excitation from high energy states (>19 eV). So while the plasma is sufficiently hot to nearly fully ionize the rubidium, it is not hot enough to promote a significant proportion of Rb+ electrons to energy levels where they are able

to de-excite and emit light. Therefore, the majority of the emission spectrum is still associated with Rb0.

From the Boltzmann plot in Figure 4.3c, the excitation temperature of the plasma using 1.0 SLPM H2of 4278 K corresponds to an electron density of 1.48 × 1018m−3.

Likewise, the overall charge fraction of this plasma is 8.62 × 10−7 although >99% of these electrons originate from the rubidium. Given that the charge fraction of nitrogen at this temperature is 4.06 × 10−10and is similar for hydrogen, it is not likely that the plasma would be sustainable at such a low temperature without the presence of the rubidium. Conversely, when rubidium is added to a pure nitrogen plasma such as that in Figure 4.3b, the majority of the ionization pertains to the nitrogen rather than the rubidium at temperatures typical for this MW system. Its excitation temperature of 6390 K corresponds to an electron density of 3.88 × 1019m−3 and a nitrogen charge fraction of 3.29 × 10−5. The electron density and ionization fraction from nitrogen

reported here are slightly lower than those observed by Leins et al. [69] whose values were approximately 1 × 1020m−3and 1 × 10−4, respectively. This is largely due to the fact that they used air rather than nitrogen, and the ionization energy of O2as well as

the NO2that forms at high temperature are both lower than that for nitrogen, causing

more electrons to be liberated. For further comparison, these results are similar to if not slightly lower than other atmospheric pressure microwave plasmas [67, 87]. In general, microwave plasmas exhibit electron densities several orders of magnitude higher than those from lower energy density plasmas such as dielectric barrier discharge [173] or those at low pressure [78]. Conversely, plasmas with higher energy densities such as arc discharge or RF induction often possess electron densities several orders of magnitude higher than those from microwave systems [76, 92, 101].