Coating thickness measurements on gas-borne nanoparticles by combined mobility and aerodynamic spectrometry

Abstract

An on-line method is described and validated to measure the thickness of coatings on gas-borne nanoparticles. The method is essentially a tandem technique which measures the aerodynamic diameter of a particle twice—before and after coating—by a single-stage low-pressure impactor (SS-LPI) for the same mobility equivalent diameter preselected via differential mobility analyzer (DMA). A shell thickness is then derived from the change in effective particle density determined by the SS-LPI. The method requires a difference in mass density between carrier particle and coating material. Its theoretical sensitivity is shown to range between about 0.1 and 1 nm, depending on the density ratio. One advantage of this approach is that both DMA and SS-LPI are situated in series but downstream of the coating step, so as not to interfere with the coating process. The method was validated against transmission electron microscopy (TEM) measurements, using spherical silica–titania particles coated with conformal shells of molybdenum and bismuth oxide by chemical vapor deposition (CVD). For such spherical particles, the agreement with TEM was excellent. The technique was able to provide layer thicknesses for sub-nanometer layers barely or not resolved by TEM. The paper also discusses the impact of ‘non-ideal’ phenomena such as the formation of doublet particles by coagulation, the effect of multiply charged particles, or the onset of homogeneous decomposition of the coating precursor. With supporting experimental data, it is shown that such phenomena can be interpreted reliably from certain features of the impactor penetration curve. The on-line method can thus be used for fast screening of process parameters and reliable process monitoring for gas-phase synthesis of composite nanopowders.

Appendix

Details of impactor calibration

Table 3 lists the measured pressures and corresponding St ₅₀ values calculated according to Eq. (15) for each particle size. Note that $St_{50}$ is based on the pressure upstream of the impactor nozzle, $p_{{50,{\text{up}}}}$ (which was not monitored in our set-up), while the pressure $p_{50}$ was actually measured downstream of the impactor nozzle. As the volume flow rate through the nozzle increases with decreasing chamber pressure, so does the pressure drop. This introduces a small but increasingly significant error in the “true” pressure, which needs to be corrected for. We have corrected for this pressure drop via a well-known expression for compressible flow

$$\dot{m} = 0.97 \cdot \frac{\pi }{4}D^{2} \cdot \sqrt {2\left( {\frac{\varepsilon }{\varepsilon - 1}} \right) \cdot p_{\text{up}} \cdot \rho_{\text{air,up}} \cdot \left[ {\left( {\frac{{p_{\text{down}} }}{{p_{\text{up}} }}} \right)^{{\frac{2}{\varepsilon }}} - \left( {\frac{{p_{\text{down}} }}{{p_{\text{up}} }}} \right)^{{\frac{\varepsilon + 1}{\varepsilon }}} } \right]},$$

(14)

wherein $\dot{m}$ is known from the inlet flow to the impactor, $p_{\text{down}}$ is taken to be the nominal pressure at the pressure gauge, and $p_{\text{up}}$ is the desired pressure $p_{{50,{\text{up}}}}$; $\varepsilon = 1.4$ is the isentropic exponent for air. $St_{50}$ was then calculated using the expression given by de la Mora

$$St_{50} = 0.178 \cdot \frac{{\rho \cdot d \cdot \dot{m} \cdot c_{0}^{3} }}{{p_{50}^{2} \cdot D^{3} }}$$

(15)

with $c_{0}^{{}}$ the speed of sound. The resulting values for $St_{50}$ (Table 3) still show a drift, similar to what was observed by other authors, which is probably due to other secondary effects (Fernandez de la Mora et al. 1990). For our purposes, we were able to disregard these differences because all subsequent validation experiments were performed in a pressure range of 25–45 mbar, so that St ₅₀ was sufficiently constant anyway.

Table 3 Calibration of the impactor with DEHS-Aerosol

Estimation for aerodynamic size of doublets

In the following, we estimate the shift in aerodynamic size—and thus the shift in the impactor penetration curves—induced by the presence of doublets of spheres. For this purpose, we introduce the mobility equivalent diameter d _me, the volume equivalent diameter d _ve, and the Stokes diameter d _st of an arbitrary particle.

For an ideal sphere of 80 nm diameter, all three diameters are identical.

For a doublet particle consisting of two spheres of diameter d ₁, the following expressions apply (Kasper 1982):

$$d_{\text{ve}} = 2^{1/3} \cdot d_{1}$$

(16)

$$\kappa = \frac{{d_{\text{me}} }}{{d_{\text{ve}} }} \cdot \frac{{C_{\text{ve}} }}{{C_{\text{me}} }}$$

(17)

$$\kappa = \left[ {\frac{{d_{\text{ve}} }}{{d_{st} }}} \right]^{2} \cdot \frac{{C_{\text{ve}} }}{{C_{st} }},$$

(18)

where κ is the dynamic shape factor and C _ve, C _me, and C _st the slip corrections at the respective diameters. κ depends on orientation of the doublet relative to its direction of movement. For doublets of spheres moving parallel and perpendicular to their principal axis, the respective values of κ are 1.05 and 1.15 (Kasper 1982). Since doublets are too short to be completely aligned (Kasper and Wen 1984; Zelenyuk and Imre 2007), the orientation-averaged shape factor will be about 1.11. For the present purposes of an estimate, it suffices, therefore, to estimate the effects on d _st in both orientations.

Two cases have to be considered: Doublets can be formed prior to mobility classification by the DMA, in which case they have an d _me of 80 nm. Such particles appear aerodynamically smaller than 80 nm. The resulting values for d _ve and d _st are shown in Table 4. If the doublets are formed after passage through the DMA, then they will consist of two 80-nm spheres and be aerodynamically larger, with corresponding values of relevant equivalent diameters again shown in Table 4.

Table 4 Equivalent sphere diameters for doublets