Current Issue

Black carbon (BC) is an important object in many areas including climate change and the growth rates of Asian forest tree species (Yamaguchi et al., 2012). Currently, several filter-based instruments such as a Particle Soot Absorption Photometer (PSAP), a Continuous Soot Monitoring System (COSMOS), a Continuous Light-Absorption Photometer (CLAP), an aethalometer and a MultiAngle Absorption Photometer (MAAP) are widely used to measure BC concentration even though they suffer from artifacts associated with the materials of the filter membrane and moisture issues (Shrestha et al., 2014; Kanaya et al., 2013; Reche et al., 2011). A Single Particle Soot Photometer (SP2) as a non-intrusive method is suggested to overcome the issues arisen from the filter-based methods for the characterization of BC. However, the SP2 is also known to be unable to detect loosely packed particles that have very small primary particles even though the particles are black (Gysel et al., 2012). In this situation, a photothermal spectroscopy does provide a filter-free technique as a challenge toward a sensitive measurement of BC via quantification of light absorption. Light energy absorbed by subsequent emission from the aerosol results in the heating of sample and consequently causes a temperature change as well as changes in temperature-related thermodynamic parameters of the sample. PhotoThermal Interferometry (PTI) traces the refractive index change induced by the thermal dissipation of the spectrally absorbed light (Bialkowski, 1996). Recently, image based PTI was also introduced to measure light absorption from absorbing particles (Lee and Kim, 2012). Similarly, PhotoAcoustic Spectroscopy (PAS) measures the sound wave produced due to light absorption, heating of the ambient gas, and subsequent pressure fluctuations detected through microphone. Here, the author considered the effect of temperature in estimating the absorption coefficient of aerosol particles from photothermal spectroscopy. It is suggested that the detection limit of the photothermal spectroscopy can be influenced by the introduction of a slip correction factor at high temperature environment.

The basis of photothermal spectroscopy is a photoinduced change in the thermal state of the sample as its name suggested. Photothermal spectroscopy involves thermal effect caused by the optical interaction of airborne samples through energy transfer. The thermal effect finally creates the temperature difference surrounding the airborne samples (Bialkowski, 1996). Thus, it is important to consider the temperature effect during the photothermal process.

First, the relative minimum detectable absorption coefficient without considering the slip correction factor was estimated. For the case of PTI, when the temperature of the environment is 400 K, the relative minimum detectable absorption coefficient increases approximately 0.3% higher than the case of 300 K as can be seen in Fig. 1. For the case of photoacoustic spectroscopy, the relative minimum detectable absorption coefficient was estimated only 0.2% less than the case of 300 K. Thus, it is believed that the photothermal interferometry is comparable to the photoacoustic spectroscopy under 400 K. The deviation of 0.3% for the PTI at the temperature of 400 K is probably due to enhanced molecular interaction between the airborne samples and air at the elevated energy state. The equations of polynomial fitting for both cases were presented in the Fig. 1. Extrapolation using these equations allows us to estimate the discrepancy between photothermal interferometry and photoacoustic spectroscopy. The discrepancy was calculated to be approximately 30% for the temperature of 2000 K, which is common in combustion study.

Fig. 1. 
Relative minimum detectable absorption coefficients for PTI (Photothermal Interferometry) and PAS (Photoacoustic Spectroscopy) at different temperature higher than room temperature without considering a slip correction factor.

The author showed the relative minimum detectable absorption coefficients for PTI estimated using different models of slip correction factor in Fig. 2. The relative minimum detectable absorption coefficients relative to that calculated with T=300 K were reduced as temperature increased. When it is assumed that the heat capacity is proportional to the slip correction factor to the -1/3 (model 1), the relative minimum detectable absorption coefficient decreased about 7.5% when the temperature was 400 K. For the case of model 2 and 3, the relative minimum detectable absorption coefficients were reduced by 11% and 21%, respectively. The equations for linear regression fitting were imbedded in Fig. 2. These equations could be used to estimate the relative minimum detectable absorption coefficient for the temperatures higher than 400 K. Extrapolation using these equations allows us to estimate the deviation from the relative minimum detectable absorption coefficient at 300 K for the photothermal interferometry. The relative minimum detectable absorption coefficients at 2000 K, which is a typical example of combustion study, were calculated to be approximately 31%, 49% and 78% for the model 1, 2 and 3, respectively.

Fig. 2. 
Relative minimum detectable absorption coefficient estimated by PTI (Photothermal Interferometry) for different models of slip correction factor.

Similar to the case of PTI, the relative minimum detectable absorption coefficients estimated for PAS were reduced as temperature increased. Fig. 3 shows that the relative minimum detectable absorption coefficient decreased about 8% when the temperature was 400 K for the model 1 case. The trend for the model 2 and 3 is very similar to the case of PTI. The equations for linear regression fitting were imbedded in Fig. 3. These equations could be used to estimate the relative minimum detectable absorption coefficient for the temperatures higher than 400 K. Extrapolation using these equations allows us to estimate the deviation from the relative minimum detectable absorption coefficient at 300 K for the photoacoustic spectroscopy. The relative minimum detectable absorption coefficients at 2000 K were calculated to be approximately 48%, 61% and 84% for models 1, 2 and 3, respectively.

Fig. 3. 
Relative minimum detectable absorption coefficient estimated by PAS (Photoacoustic Spectroscopy) for different models of slip correction factor.

Both PTI and PAS use optical heating to obtain relevant signals. During the optical interaction, the thermal energy is absorbed into the volume of particles which depends on d_p³. Airborne samples that spectrally absorb light dissipate heat radially. If slip between molecules and particles takes place, the specific heat could decrease since the particles can move actively under the condition of reduced drag, resulting in a fast heat transfer. This implies that the specific heat can be decreased. Thus, it is appropriate that specific heat can be modified by the slip correction factor to the -1/3. Fig. 4 shows that slip correction factor up to 400 K, the relative minimum detectable absorption coefficients for both the PTI and the PAS are maintained almost same and decreased linearly to the temperature. The relative minimum detectable absorption coefficients decreased only by 8% up to the temperature of 400 K. Therefore, both the PTI and the PAS can be applied up to this temperature without considering the slip correction if the error of 8% is assumed to be acceptable. However, slip correction needs to be considered in environments higher than 400 K. The equations for linear regression fitting were imbedded in Fig. 4. These equations could be used to estimate the relative minimum detectable absorption coefficient for the temperatures higher than 400 K. Extrapolation using these equations shows that the relative minimum detectable absorption coefficient for the photothermal interferometry is 17% point higher than that for the photoacoustic spectroscopy at 2000 K.

Fig. 4. 
Comparison of relative minimum detectable absorption coefficients between PTI and PAS for the model 1.

As far as the author knows, this research investigated the temperature effect on the PAS and PTI technique for the first time. The PAS is comparable to the PTI up to T=400 K from room temperature. When considering slip correction, the relative minimum detectable absorption coefficients using PAS were also comparable to those using PTI up to T=400 K. The detection limit of the photothermal interferometry can be affected by the slip correction factor in the environment higher than room temperature. The minimum detectable absorption coefficient for the photothermal interferometry depends only on some thermodynamic properties such as the density, the specific heat and the temperature. Without considering the slip correction, when the temperature is 400 K, the relative minimum detectable absorption coefficient for the photothermal interferometry increased approximately 0.3%. The relative minimum detectable absorption coefficient for the photoacoustic spectroscopy decreased 0.2%. The difference of the minimum detectable absorption coefficient between the photothermal interferometry and the photoacoustic spectroscopy is only 0.5% points. Thus, it is believed that photothermal interferometry is reliably comparable to photoacoustic spectroscopy under 400 K. At a temperature of 2000 K, however, the relative minimum detectable absorption coefficient for the photothermal interferometry deviated approximately 30% from that for the photoacoustic spectroscopy. Therefore, it is believed that more detailed research needs to be done to elucidate which technique is reliable.