Two types of particles were used for laboratory experiments, spherical particles of Polystyrene Latex beads (PSL, Duke Scientific Corp) with a factor shape equal to 1 and a density of 1.05 g mL-1, and ammonium nitrate particles (ACROS organics) with a factor shape equal to 0.8 and a density of 1.7 g mL-1.These particles were generated by an atomizer (model 3076, TSI, US). A diffusion dryer (model 3306, TSI, US) was used to decrease the humidity so it does not affect the hit rate and the particle size. The number concentration is regulated by a concentration controller. To control the number concentration in the sample flow, the particle flow is split into two, one flow path passing through the particle filter while the second one goes through a normal tube. The two flows are then merged at the outlet of the concentration controller. By increasing the fraction of the flow passing through the filter, the particle number concentration decreases.

The experimental configurations were designed to investigate the instrument's performance in the first mode of operation, with particle sizing. The first outline (Fig. 1b–c) was employed to study the repeatability, the size calibration and the effect of the particle size and the particle number concentration on the hit rate of the excimer laser (HR) and the scattering efficiency of the scattering lasers (E). The differential mobility analyzer (DMA 3081, TSI, US, impactor size 0.071 cm, sample flow = 0.3 L min-1 (liter per minute), sheath flow = 3.0 L min-1) was placed downstream of the particle generation assembly and was set to select particles in the required size range between 15 and 773 nm. The sized particle stream leaving the DMA was split between a condensation particle counter (CPC 3776, TSI) (F1= 0.3 L min-1) and the LAAP-ToF-MS (F2=F3= 0.08 L min-1), to obtain independent measurements of the number of particles per second and the particles' number in the DMA-selected size range, respectively, allowing calculation of the scattering efficiency and the detection rate.

The second configuration (Fig. 1d–c) was used for the measurement of atmospheric particles. This second configuration was designed to assess the potential effect of chemical composition on the hit rate and the scattering efficiency of real particles and to assess the effect of the number concentration. The chemical composition, particle size and the number evolution of the ambient particles were measured continuously by the LAAP-ToF-MS and an optical particle counter (OPC 1.109, Grimm, Germany).

To test the influence of particle size on the efficiency of the scattering lasers and the hit rate of the excimer laser, five different sizes of PSL particles (350, 450, 500, 600, 700 nm) were analyzed at constant particle concentration of 20 particles cm-3. For this particle concentration, particles smaller than 350 nm are undetectable. The RSD for each particle size, obtained from several replicate analyses, was compared to the coefficient of variation corresponding to different particle sizes. The particle size influences both the laser scattering efficiency and the hit rate, and therefore the detection efficiency of LAAP-ToF-MS (Fig. 6), as well.

Figure 6 shows that the hit rate decreases with the particle diameter, from 93 to 83 % when the diameter decreases from 600 to 350 nm. This behavior can be explained by the fact that smaller particles drift with higher velocity. Thus, the ions generated by the ionization laser have a higher kinetic energy resulting in aberrations (Murphy, 2007). A maximum efficiency of 2.5 % for the laser scattering diodes was observed for particles with a diameter of 450 nm and a lower efficiency for smaller particles. When the size of the individual particles becomes equivalent to or greater than the wavelength of the laser (λ= 403 nm), the scattering becomes a complex function with maxima and minima with respect to the incident angle according to Mie theory (Finlayson-Pitts and Pitts, 2000). As the diameter of the particle drops below the wavelength of the scattering laser the scatter intensity decreases rapidly, inversely proportional to the sixth power of the particle diameter (1/d6).

The scattering efficiency decreases again for particles with a dva diameter greater than 600 nm as only the particles in the range between 80 and 600 nm are transmitted at 100 % by the aerodynamic lenses.

A comparison between the scattering efficiencies of LAAP-ToF-MS, the single particle laser ablation mass spectrometer (SPLAM) (Gaie-Levrel et al., 2012) and the single particle laser ablation time-of-flight mass spectrometer (SPLAT) (Zelenyuk and Imre, 2005) has been undertaken (Fig. 6). The scattering efficiency of SPLAT decreases slightly for particles higher than 300 nm compared to SPLAM or LAAP-ToF-MS. The scattering efficiency shows the same behavior for LAAP-ToF-MS and SPLAM which can be ascribed to the same operating wavelengths of the scattering lasers (λ= 405 nm for SPLAM). However, the scattering efficiency of SPLAM is much higher than that of LAAP-ToF-MS, which can be explained by the much smaller distance (dd) between the two scattering lasers within SPLAM, i.e. 4.1 vs. 11.5 cm for LAAP-ToF-MS. Another advantage of SPLAM compared to the LAAP-ToF-MS is the higher value of Cmax which is ascribed to the small dd. The distance between the two scattering lasers influences the Cmax for a particle size of 350 nm and a velocity of 103 m s-1, the Cmax of LAAP-ToF-MS is 618 particles cm-3 whereas the Cmax of SPLAM for the same particle size and a velocity of 100 m s-1 is 1.7 × 103 particles cm-3. The ratio between the dd of SPLAM and LAAP-ToF-MS is 2.87 and is similar to the ratio between the Cmax of SPLAM and LAAP-ToF-MS (2.75), which explains that divergence of the particle beam increases with dd and is more pronounced for smaller particle sizes. In comparison to SPLAM, which uses ionization laser at λ= 248 nm, the ablation of the particles by LAAP-ToF-MS occurs at 193 nm which means that even metals can be ionized. A big advantage of LAAP-ToF-MS compared to SPLAM or SPLAT is the much higher hit rate. For LAAP-ToF-MS the effective hit rate is 90 % for PSL particles and 58 % for atmospheric particles, while the hit rate of SPLAT is only 8 % for atmospheric particles. Also, LAAP-ToF-MS is an easily transportable tool for fast field deployment.

Finally, a comparison was carried out with another similar instrument named Aerosol Time of Flight Mass Spectrometer (ATOFMS) (Gard et al., 1997). This instrument operates at 266 nm unlike the LAAP-TOF-MS (λ= 193 nm). The lower wavelength of the ionization laser enables the analysis of trace metals. There are few papers in the literature referring to the development of ATOFMS associated with detection of different size of particles (Allen et al., 2000; Su et al., 2004; Zauscher et al., 2011). For example, the detection efficiency of ATOFMS is highest for the ambient particles with diameter of 1.8 µm and decreases for about 3 orders of magnitude for the lowest size that is 320 nm (Allen et al., 2000). Su et al. (2004) reported that ATOFMS is able to detect small size particles ranging between 70 and 300 nm with detection efficiency varying between 0.3 and 44.5 %.

In any case, it should be noted that size has an impact on the detection efficiency as we mentioned above.

We assessed the size effect of ambient aerosols on the hit rate and on the scattering efficiency. For each size in the range between 10 nm and 2.5 µm (aerodynamic diameter) we are showing (Fig. 7) the total number of particles detected by the LAAP-ToF-MS during the measurements by the scattering lasers and also the total number of ionized particles during the measurements.

The optimum particle size for detection is in the range between 400 and 600 nm (aerodynamic diameter), in the same range as the wavelength of ionization (λ= 403 nm). The Fig. 7b shows the time evolution of the particle concentration. It can be seen that in the ambient air the maximum particle number concentration corresponds to the lowest size range (dva < 300 nm). The comparison between the results of the Fig. 7a and the results of the Fig. 7b confirm the conclusions from laboratory tests that the scattering efficiency is affected by the size of particles and its maximum is influenced according to the Mie theory.

In addition, Fig. 7a shows that the hit rate for ambient aerosol as function of the size range is different from the laboratory results. This difference can be ascribed to the effect of chemical composition which is detailed in Sect. 3.4.3.

Figure 7c shows the evolution of the number of spectra in each size range every 5 min during the measurements. Since the scattering efficiency and the hit rate are affected by the particle size, so is the detection efficiency (Fig. 7c). Most of the usable spectra are in the range between 400 and 500 nm. The effect of particle size is overcome by clustering the spectra obtained for each size range and multiplying the number of ionized particle by the detection efficiency (D%=E×HR) corresponding to each size range.

We investigated the transmission efficiency between the first and the second scattering laser, considering that the two laser diodes have the same characteristics. However, the first scattering laser exhibits a much higher efficiency (Ed1) than the second scattering laser (Ed2). This observation is a consequence of the divergence of the particles between the two laser diodes. In order to understand the magnitude of the particle divergence we researched into the relationship between the ratio of scattering efficiencies Ed2/Ed1 (%) and the particle size. Figure 8 displays a parabolic dependency of the ratio of the scattering efficiencies with the size of the PSL particles generated, indicating that velocity indeed plays an important role.

Smaller particles with a diameter of 350 nm exhibit higher velocities and diverge much more than bigger particles with a size of 600 nm. This curve also explains the lower scattering efficiency of particles with a diameter of 350 nm displayed in Fig. 8.

In this study there are no information about the values of detection limit in number concentration for each particle size, because this limit is different for each type of particle.

Liu et al. (1995) have demonstrated that the morphology of the particles is a very important parameter that influences the divergence of particles during their drift between the two scattering lasers. In fact, the divergence of the particles increases for non-spherical particles implying a reduction of the scattering efficiency of the laser diodes.

The ionization efficiency of the excimer laser depends on the chemical composition of the particles (Pratt and Prather, 2011). Experiments were carried out with two types of particles containing ammonium nitrate and ammonium sulfate in order to assess the effect of chemical composition on LAAP-ToF-MS performance. Although, both particles have the same density (1.74 ± 0.03 g cm-3) and the same shape factor (0.8), the hit rate is completely different. Because sulfate resists ionization (Kane and Johnston, 2001), the hit rate decreases from 60 % for the ammonium nitrate particles to 21 % for the ammonium sulfate particles. The hit rate also strongly depends on the alignment of the ionization laser and on the delay time. A change in the chemical particle composition induces a change in the refractive index. Yoo et al. (1996) evaluated the influence of the refractive index on the scattering efficiency of laser diodes. The higher the refractive index, the smaller the particles that can be measured. Moffet and Prather (2005) developed a method to calibrate the light scattering signal collected from individual particles using the Mie theory to calculate the partial scattering cross-section as a function of the particle diameter. The particle density was used to fit the partial scattering cross-section to the Mie theory (Moffet and Prather, 2005).

The complete set of spectra can be clustered using the software MATLAB version 2013b into different chemical classes of particles.

Figure 9a illustrates four of these clusters and their repartition every 5 min in different size range. These clusters were chosen as example to show different kind of inorganics particles, and one cluster with major carbonaceous ions. The inorganic particles are those containing sulfate and nitrate that are considered as secondary particles and particles containing TiO2 that are rather considered as primary particle (Delmas et al., 2005). It can be observed that nitrosium ion NO+ (m/z=  30) is abundant in the first cluster and potassium ion K+ (m/z= 39) is abundant in the second cluster. The third cluster represents particles with high signals of carbon, and in the fourth cluster characteristic peak of carbon C+ (m/z=  12), C2+ (m/z= 24), C3+ (m/z= 36) dominate.

Every cluster has its own repartition, which is defined as a number of particles detected every 5 min in different size range. Thus, the chemical composition of the particles detected during the measurements is not constant. To show the effect of chemical composition on the hit rate we calculated the hit rate of particles with different size range every 5 min during the entire time of the measurements. Then we calculated the RSD of the hit rate for each size range. The RSD varies between 51 % for the aerodynamic size range between 400 and 500 nm to 96 % for aerodynamic size range between 800 and 1000 nm (Fig. 9b). Comparing the RSD of ambient particles to the RSD calculated of spherical PSL particles during the laboratory tests (Sect. 3.2, repeatability 18 %), it can be concluded that chemical composition of particles affects the hit rate.

The effect of chemical composition on the hit rate was assessed for particles ranging between 400 and 500 nm (aerodynamic diameter). Figure 10a shows the evolution of the scattering efficiency and the hit rate for the detected particles between 400 and 500 nm (aerodynamic diameter).

It can be seen that the hit rate and the scattering efficiency are not constant all the time. As was already seen for a single type of particles the instrument exhibits good repeatability. Therefore the variation in HR (%) and E (%) is mainly the consequence of the variation of the chemical composition. In Fig. 10a and c the variation of the number of three types of particles is represented. The first type (Fig. 10b) represents the particles having an aerodynamic size between 400 and 500 nm and containing sulfate (cluster 1 and 2). The second type represents the particles having an aerodynamic size between 400 and 500 nm and containing a TiO2 (cluster 3). The third type (Fig. 10c) (cluster 4) represents the carbonaceous particles having a size between 400 and 500 nm. The increase and decrease of the percentage of particles containing sulfate is illustrated by the peak and trough (points G) depicted in Fig. 10b. The points G′ depicted in Fig. 10a correspond to a decrease of hit rate according to the peak of sulfate and an increase of hit rate caused by the decrease of the percentage of sulfate. The point A in Fig. 10b shows the highest percentage of sulfate in parallel to a low hit rate shown in Fig. 10a. The point S which corresponds to a maximum concentration of TiO2 (Fig. 10b) shows a very low value of scattering efficiency and hit rate (Fig. 10a). Regarding the points P, R and T the number of carbonaceous particles decreases while the number of TiO2 particles increases. For these three points the scattering efficiency decreases, as well. The evolution of the carbonaceous particles before and after S exhibits a similar behavior as the hit rate. Despite the effect that other particles could induce on these parameters, the comparison made in Fig. 10 emphasizes the importance of chemical composition toward the hit rate and the scattering efficiency.

Therefore, a simple separation by size range and a correction of the detection efficiency according to the size can no longer lead to the real concentration number because of the variation of the chemical composition. Thus, the average of the detection efficiency calculated for each size range is no longer adequate for a time interval of few minutes. Therefore, it is necessary to have a particle counter (like an OPC) to calculate the detection efficiency (Dn,t) for each size range for every time interval. On the other hand, the total amount of particles must be separated in different classes (Ci) based on their chemical composition. These classes must be separated in different size ranges (Ci,n). Every Ci,n, according to its distribution during the time, must be multiplied by its corresponding Dn,t. The description of this method is out of scope of this article and therefore will be detailed and validated by comparison to another instrument elsewhere.

Ambient measurements showed that a significant amount of particles could be related to particles with a diameter less than 350 nm, which is not the case for experiments with the spherical PSL particles during the calibration of the instrument. This can be explained by the fact that particles in ambient air have different optical characteristics, enabling them to scatter the light more efficiently at the scattering wavelength used in this instrument (λ= 405 nm). Therefore, in order to precisely determine the diameter of the particles we carried out measurements related to the size calibration of the particles.

When a particle drifts through the particle-time-of-flight (P-ToF) chamber, it crosses the beam of two light scattering lasers. Upon passing the first laser beam, the scattered light from the particle is detected by the first photomultiplier tube (PMT). As explained above in the description of LAAP-ToF-MS, the flight time of an individual particle between the first and second scattering lasers is used to determine its velocity and associated vacuum-aerodynamic diameter. For the given beam separation distance of 11.5 cm between the two scatterings lasers the particle velocity was determined and plotted against the aerodynamic particle diameter (Fig. 11).

Figure 11 shows the calibration curve for aerodynamic particle sizing measurements carried out for five certified sizes of PSL particles (a) and five different sizes of ammonium nitrate particles (b).

The experimental data were fitted with a first order exponential decay curve. The smallest PSL particles that can be precisely size-calibrated have a diameter of 350 nm. However, the fitting equation depicted in Fig. 11 can serve to roughly estimate the size of atmospheric particles with an aerodynamic diameter smaller than 350 nm.

Prior to study the effect of number concentration, an upper limit of the particle number concentration (Cmax) has been determined for each size to ensure that below this limit only a single particle is present in the space between the two scattering lasers. The obtained results presented in Fig. 12 indicate that Cmax is linear and inversely proportional to the particle size.

For a particle size of 350 nm, which is the smallest particle size that has been tested, Cmax is ≈ 618 particles cm-3. For higher particle number concentrations, more particles are present in the space between the two scattering lasers which indicates that smaller particulate matter with d < 200 nm can be detected but the obtained information corresponds to two different particles detected in very small frame of time. In other words, the spectrum obtained relates to a single, real particle, but the size information does not. Hence, the E (%) should decrease because the data of one single particle is recorded instead of two. In order to study the effect of a concentration higher than Cmax on the E (%), ferric sulfate particles (450 nm) were generated at 5 different concentrations between 50 and 1200 particles cm-3. The higher level 1200 was chosen according to the value of Cmax found at 562 particles cm-3 for particles with diameter of 450 nm. The influence of particle concentration on the detection efficiency was assessed by comparison of the obtained RSD values based on at least three independent measurements.

Concerning the scattering efficiency E (%), it was expected that it decreases, but the RSD between the different concentrations is lower than the RSD between the repetitions for the same concentration, so the E (%) is considered constant. To study the effect of concentration number higher than Cmax on the detection of particles lower than 200 nm to which the scattering lasers are blind, the percentage of these particles for the different concentration numbers studied was assessed (Fig. 13). Once the concentration is higher than the Cmax, 562 particles cm-3, the percentage of the particles with size lower than 200 nm increases from 1 % for a concentration number of 40 particles cm-3 to 19 % for a concentration number of 612 particles cm-3. This means that the detected particle with diameter lower than 200 nm corresponds to the detection of two different particles by the two scattering lasers.

The detected particles in the range between 250 and 350 nm (aerodynamic diameter) could be the result of two phenomena. The first one is the presence of a total concentration number higher than the Cmax for all the particle sizes and the second one is the increase of the refraction index of the particles. A comparison of the results obtained by the OPC and the LAAP-ToF-MS, that has been undertaken for the particles ranging between 250 and 350 nm shows the reason why these particles were detected. The comparison of the results is depicted in Fig. 14a where a similar evolution of the number of particles is shown for the two types of measurements. The figure indicates that the particles between 250 and 350 nm detected by the LAAP-ToF-MS are not a consequence of the total concentration of particles which was higher than the Cmax during the 6 days of measurements.

Considering that the scattering laser is blind with respect to the particles with dva<200 nm and that the aerodynamic lenses cannot transmit particles with dva < 80 nm, the effect of Cmax was evaluated as shown in Fig. 14b. Particles having an aerodynamic diameter between 0 and 80 and 0 and 200 nm were detected mainly when the number concentration of particles increased (Fig. 14b).