Effects of Multi-Charge on Aerosol Hygroscopicity Measurement by HTDMA

Abstract. The Humidified Tandem Differential Mobility Analyzer (HTDMA) is widely used to obtain the hygroscopic properties of submicron particles. Aerosol size-resolved hygroscopicity parameter κ measured by HTDMA will be influenced by the contribution of multiply charged aerosols, and this effect has seldom been discussed in previous field measurements. Our calculation demonstrates that the number ratio of multiply charged particles is quite considerable for some specific sizes between 100 nm and 300 nm, especially during the polluted episode. The multi charges will further lead to the shrinking effect of aerosol hygroscopicity in HTDMA measurements. Therefore, we propose a new algorithm to do the multi-charge correction for the size-resolved hygroscopicity κ considering both the shrinking effect and multi-charge number contribution. The application in field measurements shows that the relatively high hygroscopicity in the accumulation size range will lead to the overestimation of the particle's hygroscopicity smaller than 200 nm. The low hygroscopicity in coarse mode particles will lead to the underestimation of accumulation particles between 200 nm and 500 nm. The difference between corrected and measured κ can reach as large as 0.05, highlighting that special attention needs to be paid to the multi-charge effect when the HTDMA is used for the aerosol hygroscopicity measurement.


Response: The following is a test for our correction algorithm. The algorithm cannot ensure that the corrected particle's size-resolved hygroscopicity is fully consistent with the true values because of the measurement size resolution (detailed hygroscopicity information between measured size is lost), but the correction can improve the result to bring it closer to the true values.
If we assume a group of ammonium sulfate particles with a constant κ of 0.53. Then the HTDMA is used to scan these aerosol particles. The sample/sheath ratio of the first DMA is 1/10 and the DMA will select those negatively charged particles (DMA type from BMI). According to the following two equations: the kernel function for each size set in DMA is shown below with the assumed particle number size distribution. Then we use the HTDMA to obtain the size-resolved hygroscopicity over the size of [50,100,150,200,250,300,400,500,600] (nm). For each diameter set * in the first DMA, it will give the corresponding measured hygroscopicity as the following equations: * ( * ) = 1 Based on our calculation, we can obtain the * ( * ). Then we apply our multi-charge correction algorithm in the calculated * ( * ) and retrieve a corrected one. The results are listed in the figure below. The black line is the true hygroscopicity distribution with a uniform κ of 0.53. It can be seen that the measured * ( * ) deviate much from the true distributions because of multi-charge effect. The sizes of 100 and 150 nm are influenced most because the high ratio of multiply charged particles. After the correction, the hygroscopicity distribution comes very close to the true value. The large error at the size of 50 nm is due to the missing information between 50 nm and 100 nm, and the size of 50 nm is mostly affected by particles from this size range. If the measurement size resolution improves, the corrected values will come closer to the true values.

The procedures of calculating the number ratio of particles carrying different charges.
Step 1. Calculate the particle charge distribution.
The particle charge distribution at each size is based on a theoretical model developed by Wiedensohler et al. (1986). To calculate the fraction of particles carrying zero, one or two charges, use the equation below: For the fraction of particles carrying three or more charges, use the equation below: Here we present bipolar particle charge distribution with number of charges up to 4 over the size range of 10-1000 nm. Step 2: Calculate the DMA transfer function and Kernel function for each size set at DMA. In our field measurement, the DMA (BMI, Model 2100) selected those negatively charged particles. The sample/sheath ratio of 0.75/4 is used to calculate the transfer function. Then the Kernel function can be obtained from: The following is an example for the DMA set size of 100 nm. Step 3. Calculate the (1) the total number concentration of particles that can pass through the DMA and (2) the number concentration of particles carrying charges. In this step, particle number size distribution data is needed. Here we present a particle number size distribution data during the relatively polluted period in our field measurement. When combined with the total kernel function or charge-resolved kernel function, we can obtain the corresponding number concentration of particles that can pass through the DMA. Fig.S3 shows an example when the DMA set size is 100 nm. It can be seen that when the accumulation mode particles increase, the doubly or triply charged particles also increase greatly. In this case, when integrated over the whole size range, the singly charged particles only constitute 55% of all the particles that can pass through the DMA.

The calculation and properties of f function
In the paper, f function is defined as:

= ( * , ν)
It describes the physical diameter of charged particles with the known parameters of electrical mobility diameter ( * ) and number of charges (ν).
We don't have an analytical expression for f function, but it can be calculated through two steps: (1) Calculate the electrical mobility from * using the following equation: = ( * ) 3 * (2) Solve the following nonlinear equation and get the best fit through the optimization method.
Here, we give an example of the Cunningham slip correction C with the temperature of 25 o C and pressure of 101300 Pa. ( * , ν) curves are also shown with 1 through 4 charges respectively. It can be seen that when ν = 1, the is equal to * . When ν > 1, the is larger than * .