UNIVERSITY OF MINNESOTA. This is to certify that I have examined this copy of a master s thesis by XIAOLIANG WANG

Transcription

1 UNIVERSITY OF MINNESOTA This is to certify that I have examined this copy of a master s thesis by XIAOLIANG WANG And have found that it is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made. Name of Faculty Advisor Signature of Faculty Advisor Date GRADUATE SCHOOL

2 OPTICAL PARTICLE COUNTER (OPC) MEASUREMENTS AND PULSE HEIGHT ANALYSIS (PHA) DATA INVERSION A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY XIAOLIANG WANG IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE JUNE 2002

3 Acknowledgements I am deeply indebted to my advisor Prof. Peter H. McMurry, whose stimulating suggestions and encouragement helped me throughout my research and preparation of this thesis. It is hard to believe that he looked at this thesis closely for more than three times, offering suggestions for improvement from English style, grammars to contents, although he is extremely busy. He is so knowledgeable in aerosol science and technology. I am very fortunate to obtain advice from such a versatile scientist and excellent mentor during the course of my graduate studies. I would like to sincerely thank Dr. Hiromu Sakurai, who has contributed a lot of helpful ideas, knowledge and time to this project. Thanks to Kueng Shan Woo, Jongsup Park, Kihong Park, Qian Shi, and all other PTL faculty and students who have helped me in either experiments or data analysis. Finally, this thesis is dedicated to my family, from where I obtain ceaselessly and tirelessly encouragement and support. Funding for this work was provided by the United States Environmental Protection Agency as a part of the Supersite Program through a subcontract from Washington University in St. Louis. i

4 Abstract Two types of Optical particle counters (OPCs) were used in this study: PMS Lasair 1002 and Climet Spectro.3. The table data provided by the instruments usually report optical equivalent sizes, and the resolutions are low. To obtain particle mobility sizes directly and to obtain higher size resolution, a multichannel analyzer (MCA) was connected to the OPC analog output to record OPC s voltage responses to particles (pulse height distribution). Kernel functions of monodisperse particles were needed to convert pulse height distributions to size distributions. According to my calibrations of the Lasair-MCA system with PSL, DOS and diesel exhaust particles, kernel functions were found to fit lognormal distributions very well. Therefore, two parameters: peak voltage and geometric standard deviation were needed to define a kernel function. For spherical particles, remarkable agreements between the calibrated peak responses of PSL and DOS and Mie theoretical responses were achieved. Hence the theoretical peak voltages of spherical particles with arbitrary refractive index could be calculated. PSL were found to be more nearly monodisperse than aerosols classified by the DMA, and the pulse height distributions of DMA classified aerosols could be predicted using the width of PSL responses and DMA transfer functions. Therefore, the geometric standard deviations of PSL kernel functions were used for kernel functions of other particles. For non-spherical particles, the shape played an important role in both OPC-MCA peak voltages and standard deviations. The kernel functions of these particles were determined by calibration. Twomey algorithm and its modified version (STWOM) were adapted to invert the pulse height distribution. Numerical experiments demonstrated that this algorithm could invert pulse height distributions to size distributions accurately and quickly. The inversion helped to realize the strength of the OPC-PHA technique: much higher resolution and more accurate sizing than the table data. However, the uncertainties of the ii

5 inverted distribution both ends of the size range were large due to the large uncertainties of counting efficiencies of these sizes. A Lasair and a Climet were used in the atmospheric aerosol measurement in Metropolitan St. Louis (IL-MO). Particles of 450nm were found to be externally mixed and have quite different optical properties. In this work, refractive indices of brighter particles obtained from hourly calibration were used for data analysis. OPC distributions obtained from different methods were compared to SMPS distributions. The original OPC table data were found to match SMPS data best, but the table data corrected by refractive index and inverted distributions were systematically higher than SMPS concentrations. A Lasair was also used in the diesel exhaust mass distribution measurement. A discrepancy of ±200% was found between the inverted OPC and SMPS size and mass distributions. The reason of the discrepancies between the SMPS and the Lasair is still under investigation. iii

6 Table of Contents Acknowledgements... i Abstract... ii Table of Contents...iv Chapter 1: Introduction Principles of Optical Particle Counter (OPC) Introduction of OPC PHA Data Inversion Thesis Content... 6 Chapter 2: Optical Particle Counter Calibration Introduction of OPC Calibration Experiment Apparatus Data Acquisition Software Lasair Calibration results Climet Calibration Results Summary Chapter 3: Adaptation of the STWOM Method for OPC Pulse Height Analysis Data Inversion The Twomey and STWOM Nonlinear Iterative Inversion Algorithms OPC Pulse Height Analysis Data Inversion Codes Some Details of the OPC PHA Inversion Codes and Numerical Experiments Discussions of Twomey Inversion Summary Chapter 4: Atmospheric Aerosol and Diesel Exhaust Measurements St. Louis Size Distribution Measurement Diesel Exhaust Measurements Summary Chapter 5: Conclusions and Suggestions for Future Work Conclusions Recommendations for Future Work References: Appendix A: OPC Calibration Results A.1 South Pole Lasair High Gain A.2 South Pole Lasair Low Gain A.3 St. Louis Lasair Low Gain A.4 Climet Low Gain Appendix B: Codes for the Twomey Inversion Package Appendix C: Codes for the Lasair and Climet Response Calculations Appendix D: Codes for Lasair and Climet Table Data Refractive Index Corrections iv

7 Chapter 1: Introduction 1.1 Principles of Optical Particle Counter (OPC) The scattering of light by homogenous spherical particles is well-defined by three scattering regimes according to the optical size parameter α, which is given by: πd α = (1.1) λ where d = particle geometric diameter λ = wavelength. The three scattering regimes are [1], [2]: Rayleigh scattering: (α<0.15) Lorenz-Mie scattering: 0.15 α 15 (approximate) Geometric scattering: α>15 (approximate) In our current atmospheric research, particle sizes are comparable to wavelength. Therefore, scattering occurs in the Lorenz-Mie regime. Since light scattering theory can provide exact results for homogenous spherical particles, it forms the basis for building sensitive and accurate particle measuring instruments [1]. Single optical particle counters (OPC) count and size aerosol particles by measuring the light that is scattered when individual particles pass through a light beam [3]. Figure 1.1 is a schematic diagram of a generic forward scattering optical particle counter. It illustrates the steps required to convert raw voltage pulse data to particle size distributions [4]. 1

8 Calibrated Response Pulse Height Distribution Size Distribution Figure 1.1 Optical particle counter and data process steps [4] In the OPC shown above, a narrow stream of aerosol particles surrounded by filtered sheath air flows through a scattering volume into which an illuminating beam of light is tightly focused. Only one particle is illuminated at a time. The photo-detector collects the scattered light in a defined angular range and generates a voltage pulse that is proportional to the amount of light collected. Then the signal processor amplifies the pulses and classifies them into several discrete voltage bins (this is usually done by a built-in pulse height analyzer (PHA) or a multichannel analyzer (MCA)) to form a pulse height distribution. A set of comparators compare the pulse height distribution to the threshold voltages determined by calibration, and the pulse height distribution is finally converted to particle size distribution and reported as tabulated data. Given the aerosol flow rate, we can measure the aerosol concentration by counting the number of the scattering events per unit time [1], [5]. Optical particle counters avoid physical contact with particles and provide realtime measurement. However, these advantages are offset by three major shortcomings. First, the built-in pulse height analyzer (PHA) board only sizes particles into a few channels (e.g. 8 channels for the PMS Lasair 1002, 16 channels for the Climet Spectro.3). This configuration doesn t take full advantage of the inherent resolutions provided by these instruments. Second, the threshold voltage of each size bin is usually determined by 2

9 polystyrene latex (PSL) calibrations. PSL is spherical and has a refractive index of (at 0.589µm wavelength). Particles measured with OPCs often have shapes and refractive indices that are quite different from those of PSL. Therefore, if we use the preset threshold voltages, the size information will be inaccurate. For example, if we are measuring di-octyl sebacate (DOS) spherical particles, whose refractive index is (at 0.589µm wavelength), the Lasair voltage response to DOS particles of a given size will be smaller than that to PSL of the same size. This means that the OPC tends to underestimate the DOS sizes. Third, in an ideal OPC, all particles with the same size would be classified into the same channel. However, real OPCs produce a distribution of pulse heights when sampling monodisperse particles. Therefore, there is not a unique relationship between the pulse height and particle size, as is suggested in Figure 1.1. In order to extract the maximum amount of information from measured pulse height distributions, it is necessary to take into account what is known about the response of the OPC to real, complex particles. To overcome these three problems, we connected an external Multichannel Analyzer (MCA) (produced by EG&G ORTEC) to the OPC analog voltage output instead of using the internal MCA board. We refer this as an Optical Particle Counter Pulse Height Analysis (OPC-PHA) System. The external MCA has 2048 channels, which significantly improves the particle size resolution. Furthermore, we used a differential mobility analyzer (DMA) to produce monodisperse calibration aerosols from the measured aerosols (e.g., atmospheric and diesel exhaust particles) as well as calibration standards such as PSL and DOS. These provided us accurate information on the OPC s response to measured aerosols. I developed an inversion algorithm to convert pulse height distributions measured by the OPC-PHA system to aerosol size distributions. This inversion algorithm utilized kernel functions, which define the probability that a particle of a given size will be counted in a given MCA channel. Kernel functions were obtained by calibration with monodisperse particles. Rather than assuming that all particles in a given channel were produced by particles of the same size, the inversion algorithm determined the contribution of particles in various sizes to the number of counts in each MCA channel. For example, suppose that 100 particles were counted in 3

10 channel 500. Kernel functions say that 10% of these particles are 200nm 300nm, 80% are 300nm 400nm, and 10% are 400nm 500nm. Then the 100 particles should be allotted to these three size intervals according to their percentages. 1.2 Introduction of OPC PHA Data Inversion As described in the previous section, the objective of OPC PHA data inversion is to unravel the true size distribution from the pulse height distribution recorded by the multi-channel analyzer (MCA). Mathematically, our object is to solve the following Fredholm integral equation of the first kind for the aerosol size distribution, f D ), at each channel: ( p where y = K D ) f ( D ) dd, i = 1, 2,, m, (1.2) 0 i y i i ( p p p = number of pulses counted by the i th MCA channel D p K i ( D p = particle diameter ) = the probability that a particle with size D p will be counted by MCA channel i (kernel function), 0 K ( D ) 1 f ( D p ) = particle size distribution function i p m = total number of MCA channels. The physical meaning of this equation can be interpreted in this way: f ( D ) dd p p is the number of particles in the size range [ D, D + dd ]. And K ( D ) f ( D ) dd is the number of particles in [ D, D + dd ] that will be classified into channel i. If all possible p p p sizes are integrated, we can get the total number of particles counted in the i th MCA channel, i.e. y i. p The most common approach of solving equation 1.2 is to evaluate f D ) at a discrete set of diameters, p p i p p ( p D pj. The number of sizes is called resolution. Equation 1.2 can be reduced into the following discrete sum form: p 4

11 where y i n n j= 1 i p j p j pj n K ( D ) f ( D ) D = A ( D ) f ( D ), i = 1, 2,, m, (1.3) j= 1 = resolution of data inversion i p j p j D pj = particle diameter where the size distribution is to be calculated A ( D ) = K ( D ) D. (1.4) i p j i p j pj This is a system of m equations with n unknowns ( f ( ) ). It can be rewritten in matrix notation as: D p j y = Af D ) (1.5) ( p where y is a m 1 vector, A is a m n matrix, and f D ) is a n 1 vector. A straightforward solution of f D ) can be obtained by simple matrix inversion: ( p 1 f ( D ) = A y. (1.6) p Unfortunately, there are several limitations preventing us from solving these equations in this way. First, if m(channel number) > n (resolution), this is an overdetermined problem, and 1 A does not exist. Second, if m(channel number) < n (resolution), this is an 1 underdetermined problem, and again A does not exist. Furthermore, the solution to this problem is not unique. Third, even when m(channel number) = n (resolution), the matrix A is nearly singular and ill conditioned for many aerosol measurements [6]. Therefore, 1 A is very large or does not exist at all. A variety of inversion methods have been derived to solve this problem. A comprehensive review was given by Milind Kandlikar [6]. Among these methods, the programs developed by Crump and Seinfeld, INVERSE and CINVERSE, were reported to be able to give good results for impactor and optical particle counter data. But INVERSE often gives negative values in the tail of the inverted size distribution, and CINVERSE is difficult to automate [7]. The MICRON package developed by Wolfenbarger and Seinfeld has been successfully used in inverting the Ultrafine Condensation Nucleus Counter pulse height distributions [8]. This code is very long and ( p 5

12 difficult to understand, so it is not easy to be modified or adapted for inversions of data from other instruments. Furthermore, it requires substantial computational resources. In this study, we have chosen Twomey s non-linear iterative algorithm [9] and its modified version STWOM [7] to invert the OPC pulse height distribution data. Our work shows that these algorithms can give good result and they are relatively simple to use. 1.3 Thesis Content The objective of this work is to develop a software package that: (1) generates kernel functions pertinent to the refractive index of measured particles; (2) inverts measured OPC pulse height data with their kernel functions to obtain mobility size distributions. An outline of this thesis work is shown in Figure 1.2. Refractive index of measured aerosols OPC response calculation Kernel functions of laboratory aerosols Measured pulse height distribution Kernel functions of measured aerosols Data Inversion program Inverted size distribution Figure 1.2 Overview of the research in this thesis Three optical particle counters were used in this work. One PMS Lasair 1002 and one Climet Spectro.3 were used in measurements of atmospheric aerosol size distributions in the St. Louis Supersite Program. Another PMS Lasair 1002 was used in measuring diesel engine exhaust and laboratory generated aerosol mass distributions. The detailed description of these two instruments is given in Chapter 2. OPC calibrations are 6

13 essential for checking the performance of instruments, determining OPC s response to particles of different sizes and refractive indices, and eventually obtaining good kernel functions and inverted size distributions. Chapter 2 presents the OPC calibration experiment setup and results. The calculation of kernel functions is discussed in detail. OPC theoretical responses are also calculated according to Mie theory and compared to the measured responses. Chapter 3 is devoted to describing the Twomey and STWOM non-linear data inversion method. A number of numerical experiments have been performed to evaluate the performance of this inversion algorithm for OPC PHA data. In chapter 4, the inversion package is applied to atmospheric and diesel exhaust aerosol measurements. Conclusions are presented in Chapter 5. 7

14 Chapter 2: Optical Particle Counter Calibration 2.1 Introduction of OPC Calibration The objective of calibrating the OPC is to obtain the instrument responses to monodisperse particles. We refer to these response functions as kernel functions. The kernel functions can help us to understand the OPC s responses to particles of different sizes, refractive index, and shape. As was explained in Chapter 1, kernel functions are required to obtain size distributions by inverting raw pulse height distribution data. In this chapter, the Lasair s response to monodisperse polystyrene latex (PSL), di-octyl sebacate (DOS), sodium chloride (NaCl), and diesel soot particles is discussed in detail. Some calibration results for the Climet are also presented. Some of the properties of the particles are listed in Table 2.1 [1]. Table 2.1 Properties of measured particles PSL DOS NaCl Diesel soot Shape Spherical Spherical Cubic Chain agglomerates Refractive index (λ=589nm) ( i) Density (g/cm 3 ) ~ In the first part of this chapter, I present the instruments and the experiment setup used for calibration. Then the calibration results are presented and discussed. (Detailed calibration results for each instrument are listed in Appendix A.) The theoretical OPC responses are calculated and compared to measurements. After that, the Lasair counting efficiency is discussed. Finally, I discuss the calculation of kernel functions for homogenous spherical particles with arbitrary refractive indices. 1 Data measured by Kihong Park 8

15 V in1 V in2 V out1 V out1 V out2 V out2 2.2 Experiment Apparatus The OPC calibration experiment system can be divided into two subsystems, a monodisperse particle generation system that generates the monodisperse particles, and an Optical Particle Counter Pulse Height Analysis (OPC-PHA) data acquisition system that measures the kernel functions. The entire system is shown in Figure 2.1. sheath flow q c HEPA H.V. Power Supply q a DMA neutralizer make up flow filter HEPA Lasair amplifier MCA x 1 * / * u 1 u 2 u 3 u 4 u x 2 u n PC excess flow filter diffusion dryer C.O q s q m excess flow to vacuum Climet CNC to vacuum 0 0 voltage divider x 1 * / * x 2 u 1 u 2 u 3 u 4 u 5 u n Lab-PC-1200 dry, clean compress air atomizer liquid trap Symbols: Critical Orifice Ball Valve Laminar Flowmeter Figure 2.1 OPC calibration experiment setup Monodisperse Particle Generation System The laboratory monodisperse particle generation system used in this experiment is a very typical system that has been widely used in the Particle Technology Laboratory for many years [10], [11], [12], [13]. In this system, particles were generated by atomizing solutions or suspensions. In my experiments, deionized water was used to atomize PSL or NaCl particles. Typical 9

16 concentrations were 5 drops of 1.5 % of PSL in 250cc DI water, and 0.1% (by weight) of NaCl. DOS was dissolved in isopropyl alcohol to make a 0.1% (by volume) solution. Compressed air was passed through a dryer and a filter before it enters the atomizer. The pressure of compressed air at the entrance to the atomizer was controlled at around 30 psi by a pressure regulator (These parts are not shown in Figure 2.1). Because the Lasair, Climet and CNC needed only part of the aerosol flow provided by the atomizer, the excess flow was directed through a filter into the room air. A liquid trap was used downstream of the atomizer to collect big droplets. This reduced the amount of water that must be collect by the diffusion dryer. The droplets coming out the atomizer contained a mixture of the solvent and solute. To get pure solute particles, a diffusion dryer filled with silica gel was used to absorb the water from the PSL and NaCl droplets. To remove the isopropyl alcohol from the DOS solution, the diffusion dryer was filled with activated carbon. In some cases, the concentration of the particles was so high that it exceeded the upper limit that could be counted by the OPC. When this occurred, multiple particles could be simultaneously present in the scattering volume, and the MCA dead time was high, causing large errors in sizing and concentration. Dilution, which was achieved by filtering a fraction of the aerosol flow, was then used to reduce the concentration. The particles produced by the atomizer had an unknown distribution of charges. A Po-210 neutralizer was used to ensure that particles entering the DMA had the Boltzmann equilibrium charge distribution. The Differential Mobility Analyzer (DMA) was the core instrument used to generate monodisperse aerosols used for calibration. The DMA selects particles according to the electrical mobility Zp, which is defined as the ratio of electrostatic drift velocity to the magnitude of electric field [1]: Zp v qc = E 3πηD = c (2.1) p where v E = particle velocity = electric field strength 10

17 q C c η D p = particle s charge = Cunningham slip correction factor = air viscosity = particle diameter As shown in Figure 2.1, the DMA analyzing region consists of a center rod that can be maintained at a known voltage and a grounded outer housing. Both clean sheath air and aerosol flow enter near the top of the DMA. The aerosol flows through a thin annular region near the inner wall of the DMA housing. Charged particles move across the sheath flow to the center rod due to the electrical force. Particles having a narrow range of electrical mobilities will reach the sampling slit near the bottom of the DMA analyzing region. This range is given by and Zp * ± Zp, where * Zp is the centroid mobility, Zp is half width of the mobility range of the extracted particles. These parameters can be expressed as [11], [14]: * qc + qm Zp = 4π ΛV where qa + qs Zp = 4πΛV (2.2) (2.3) L Λ = (2.4) ln( b / a) a b L q a = outer radius of the center rod = inner radius of the housing = distance between the mid-planes of the DMA entrance and exit slits = aerosol (polydisperse) flow rate q c q m q s V = clean (sheath) air flow rate = main (excess) outlet flow rate = sampling (monodisperse) flow rate = center rod voltage 11

18 12 Note that particles of different mobilities can be selected by varying the voltage applied to the center rod. The resolution of the DMA is defined as the relative half-width, which is m c s a p q q q q Zp Z + + = *. (2.5) Since the aerosol coming out of the DMA is not monodisperse, the DMA broadening effect is defined by the DMA transfer function Ω, which is the probability that an aerosol particle of electrical mobility Zp entering the DMA will leave the DMA via the monodisperse aerosol outlet. Figure 2.2 shows the DMA transfer function [14], [15]. Figure 2.2 Theoretical DMA transfer function [15] If a q = s q, c q = m q, the transfer function shown in Figure 2.2 can be simplified to the following form [15]: = Ω p p p p p p p p p p p p p p p p p p p p p p p p p Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z * * * * * * * * * 0 1) / ( / 1) / ( / 0 ),, (. (2.6)

19 In my experiment, the GMWDMA was used [16]. This instrument had dimensions of: L = cm, a = 0.943cm, b = 1.927cm. A critical orifice was used to control the sheath air flow rate. I used two methods to ensure that the DMA did not leak. First, I reduced the vacuum inside the DMA column to 600 mmhg and closed all the valves. My criterion for a leak free column was that the pressure did not drop more than 5 mmhg in a 30-minnute period [17]. Second, I set the DMA voltage to zero, balanced the aerosol and sheath flow, and monitored the outlet aerosol flow using a TSI Condensation Nucleus Counter (CNC 3760). No particles would be detected by the CNC if there were no leak. In this experiment, DMA flow rates were regulated such that q = q, and a s q m = q c. Therefore, * Zp was only a function of V and q c (see Equation 2.2). The high voltage supply operated over the range from 0V to 10000V, and the sheath flow rate qc could be varied to obtain particles in a desired size range. Different sizes of critical orifices were used to control the sheath air flow rate. In order to get good resolution, the aerosol flow rates were almost always set to 10 1 of the sheath air flow rate. Under this condition, Zp Z p = * Furthermore, because all particles I measured in these experiments were bigger than 100nm, the diffusion broadening of particle size distributions was not significant. However, I found that the OPC pulse height distribution produced by DMAgenerated particles were significantly wider than would be produced by truly monodisperse particles. This effect needed to be accounted for when obtaining kernel functions. This will be discussed in detail later in this Chapter. The DMA center rod voltage was supplied by a Bertan Model 205A-10R high voltage power supply. Usually, the voltage indicated on the front panel is not exactly equal to voltage applied. I used a mulitmeter and a high voltage probe to calibrate the voltage supply. After leaving the DMA, the monodisperse aerosol flow was mixed with filtered make up air before it was sampled by particle measuring instruments. 13

20 2.2.2 OPC-PHA Data Acquisition System The OPC data acquisition system consists of a PMS Lasair 1002, a Climet SPECTRO.3 and two multichannel analyzers. In our system, the OPC s responses to particles were recorded both by the OPCs themselves and by the MCAs. A TSI CNC 3760 sampled the aerosol in parallel with the OPCs to independently measure the total particle concentration. The OPC s counting efficiency for monodisperse particles could be calculated by dividing the MCA concentration by the CNC concentration. Table 2.2 shows some of the main specifications of the two optical particle counters. More information about the instruments can be found in Lasair User s Guide to Operate [18] and Lasair Technical Service Manual [19], Spectro.3 Laser Particle Spectrometer Operation Manual [20], and the web sites of the two manufacturers: Table 2.2 Some specifications of Lasair 1002[19] and Climet Spectro.3 [20] PMS Lasair 1002 Climet Spectro..3 Flow rate CFM (0.057 LPM) CFM (1.0 LPM) Max. concentration 50,000,000/ft 3 28,000,000/ ft 3 Optical design Wide angle 90 collecting optics Elliptical Mirror Laser source HeNe, 633nm 50mW laser Diode, 780nm 2 Analog output 0 ~ -10V 0 ~ +2.9V Computer interface RS-232 and RS-485 RS-232 and RS PMS Lasair 1002 The Lasair 1002 is produced by Particle Measuring Systems. Figure 2.3 and Figure 2.4 show the optical system and flow system diagrams of the Lasair 1002 [18]. 2 Data from personal communication with Randy Grater (Technical Service Manager of Climet Instruments) 14

21 Figure 2.3 Optical system of Lasair [18] Figure 2.4 Flow system for Lasair 1002 [18] The operation of the Lasair is similar to that for the generic OPC we discussed in Chapter 1. The source of illumination is a 633nm 10-milliwatt HeNe laser. As a particle passes through the sample cavity, it is illuminated by the laser beam and scatters light. The main signal processing steps are illustrated in Figure 2.5 and discussed below [19]: Photodector board: The photodetector senses the scattered light and produces a current pulse. This pulse is proportional to amount of the scattered light, and contains size and refractive index information about the particle. Then this current pulse is converted to a negative voltage pulse. The preamplifiers amplify the signal into several gain stages according to different amplification factors and send it to the internal pulse height analysis (PHA) board. 15

22 Scattered Light Photodector board Photodector Signal Pulse Preamplifiers Amplified signal in up to 4 gains Internal PHA board Amplifiers Analog Output External PHA Board Pulse Height Distribution Comparators Laser Reference Voltage Size information in 8 channels Table data Digital Board Screen/Printer RS-232/RS-485 Table Data File Figure 2.5 Lasair data process flow chart Internal PHA: The internal PHA board amplifies the signal from the detector board again. Then the signal goes on in two separate routines. One is sent to the rear panel I/O as a 0 to -10VDC analog output, which can be connected to an external MCA to record the pulse height distribution. The other routine goes to the comparators, where the signal is compared to preset threshold voltages for the eight channels and assigned to the appropriate size bin. This information is sent to the digital board to create the 16

23 table data. Table 2.3 shows the particle size channels of the Lasair 1002 provided by the manufacturer. The threshold voltages for the eight channels are based on calibrations done with monodisperse polystyrene latex spheres (PSL). The voltage vs. size curve provided by PMS is shown in Figure 2.6 [19]. Thresholds are automatically adjusted to account for the changes of laser reference voltage (LRV) by voltage dividers shown in Figure 2.7. This is done by setting Threshold = LRV R2/(R1+R2). Table 2.3 Size channels for Lasair 1002 table data High gain Low gain Channel Size (µm) >2.0 High gain Low gain Figure 2.6 Voltage vs Size Interval Curve Lasair 1001 and 1002 [19] 17

24 R1 R2 Lasair reference voltage input Threshold voltage output to internal MCA Figure 2.7 Voltage divider to set the threshold of each size bin Digital Board: The digital board controls the data in and out of the Lasair. It processes data from the internal PHA board and outputs it either as the Lasair screen display (table data) or a printed hard copy. It can also read from or write to RS-232/ RS-485 serial ports. In my LabVIEW program, I used RS-232 serial communication to control sampling and save the table data as a file in the computer. I used two Lasair 1002 s in my work. Serial number was used in St Louis Supersite aerosol measurements. For this Lasair, only the low gain was calibrated and used. Serial number was used at the South Pole during December I used this instrument to study diesel exhaust aerosols and laboratory-generated aerosols. Both the high gain and the low gain of this Lasair were calibrated and used. In this thesis, these two instruments are referred to as the St Louis (STL) Lasair and South Pole (SP) Lasair, respectively Climet SPECTRO.3 Climet Spectro.3 is produced by Climet Instruments Company. The operation principle of Climet is quite similar to the Lasair, but as shown in Table 2.2, there are four main differences between the Climet and the Lasair. First, the flow rate of the Climet is about twenty times higher than the Lasair. This enables the Climet to collect more particles than the Lasair during the same sample period. Second, the Climet covers a wider size range than the Lasair. It can detect particles as big as 10µm. Third, the Climet uses an elliptical mirror instead of mangin mirrors to focus the scattered light to the detector. (This will be discussed in more detail later in this Chapter.) Finally, as with the Lasair, the Climet also has both table data and analog DC voltage outputs. But the Climet 18

25 table data have 16 channels in 3 separate gains, as shown in Table 2.4. The analog voltage output is 0 ~ +2.9VDC [20]. Table 2.4 Size channels for Climet SPECTRO.3 table data [20] Digital 3 High gain Channel Size (µm) Low gain Channel Size (µm) > Multichannel Analyzer (MCA) The multichannel analyzer consists a Multichannel Buffer (MCB) card and a personal computer. The MCB takes the Lasair or Climet analog voltage output as its input, and classifies voltage pulses into different channels. The computer is used to control instruments and to display and record measurements. The MCB used in our experiments is the TRUMP-2K Multichannel Buffer Card produced by EG&G ORTEC. This card has a resolution of 2048 channels. The inputs to the card are voltage pulses in the range from 0 to 10V. However, the manufacturer reserved channel 2001 to 2048 to improve the linearity performance and the data in this area is not valid. Therefore, we can only use data from channel 0 to For proper performance of the MCA, two things should be addressed: dead time and lower level discriminator (LLD). The MCB is not able to count signals during the time required for ADC conversion and data transfer. This is called dead time. When the concentration is very high, the possibility of losing pulse counts increases, which yields incorrect particle concentration data. In our experiments, the concentrations of particles were controlled so that the MCA dead time is less than 8%. The Lower Level 3 The amplification factor of the digital gain is 5 times higher than the high gain. The signal from the digital gain is applied as a digital pulse, rather than as an analog pulse, to the comparators. This information was not used in the PHA analysis of this work. 4 From personnel communication with Joe Lassater, a technician in Ametec, Inc, (Joe.Lassater@ameteconline.com) 19

26 Discriminator (LLD) adjustment is used to prevent small noise pulses from being counted. If the noise is counted, the dead time will increase tremendously, and the recorded pulse height distribution will include data from both noise and particles. The manufacturer (ORTEC) generally set the LLD to 75 mv [21], which corresponds to channel 15. In order to adjust the LLD to the noise level of the OPCs, I put a filter at the OPC inlet so that no particles were entering the OPC. The lowest MCA channel at which noise was detected was identified. A safety factor of about 10 channels was added to this lowest channel to set the LLD. In contrast to LLD, there is a upper level discriminator (ULD) which sets the highest amplitude pulse that will be stored in MCA. The ULD was set to one channel less than the maximum channel as required by the manufacture. In my experiments, I assumed that the voltage response changed linearly with the channel number. Because the lower end of channel 1 corresponded to 0 V, and the upper end of channel 2048 corresponded to 10V, the upper voltage limit for channel i was: i V i = 10V. (2.7) Inverting and Non-inverting Amplifiers The Lasair analog outputs are voltages from 0 to 10V, and the MCB input voltage range is 0 to +10V. Therefore, I built an inverter to enable the MCB to detect the Lasair output signals. At the same time, in order to increase the resolution in a selected range of particle sizes, I sometimes amplified the Lasair output signal. For example, for the particle size distribution measurements in St Louis, we wanted the Lasair to cover the size range of 0.3µm to 1.0µm. The threshold voltages of these two sizes were about 0.171V and 3.937V (Figure 2.6), respectively. We amplified the Lasair output pulse by a factor of 2.5. Hence the adjusted voltage range was from 0.428V to 9.843V. This significantly improved the resolution over the size range of interest. However, the analog outputs of the Climet were voltage pulses in the range from 0 to +2.9V, I used a noninverting amplifier to amplify the signal to increase the resolution. The amplification factor was 4.282, which enabled the Climet-PHA data to cover the size range of 0.4µm to 1.3µm. 20

27 Typical inverting and non-inverting amplifiers are shown in Figure 2.8 and Figure 2.9, respectively. R 2 R 1 Input ( from Lasair ) +15V - OP 27G + output ( to MCA ) -15V Figure 2.8 Inverting Amplifier used with Lasair (Values for R 1 and R 2 are given in Table 2.5) R 2 R V Input ( from Climet ) OP 37G + -15V output ( to MCA ) Figure 2.9 Non-inverting Amplifier used with Climet (Values for R 1 and R 2 are given in Table 2.5) 5 In order to obtain the correct amplification factor and maintain the shape of the signal, the amplifiers should have appropriate slew rates (defined as the voltage change rate per unit time). The signal durations of the Lasair and the Climet are about 20µsec and 4µsec, respectively. This means the amplifier of the Climet should be faster than that 5 The amplifier used with this Climet was originally OP27G. Later we found this amplifier was too slow that it did not provide the performance we desired. So we replaced it with a faster amplifier OP37G. 21

28 of the Lasair. OP 27G and OP 37G have slew rates of 2.8V/µsec and 17V/µsec, respectively. Oscilloscope tests showed that these two amplifies worked very well for the Lasair and the Climet. For the inverting amplifier in Figure 2.8, the amplification factor is R 2 /R 1. The amplification factor of the non-inverting amplifier in Figure 2.9 is 1+R 2 /R 1. The amplifier settings for the two Lasairs and the Climet of my experiment are listed in table 2.5. Table 2.5 Amplifier parameters R1 6 (Ω) R2 (Ω) Amplification PHA size range factor (PSL) (µm) South Pole Lasair (high gain) 21.49K(22K) 27.59K(27K) South Pole Lasair (low gain) 9.8K (10K) 27.74K(27K) St Louis Lasair (low gain) (200) (470) St Louis Climet (high gain) 9.77K (10K) 32.07K (33K) Condensation Nucleus Counter and Lab-PC-1200 Data Acquisition Card In these experiments, a CNC 3760 was used to measure the total concentration of the monodisperse particles, which was then used to calculate the OPC counting efficiency. As shown in Figure 2.1, the CNC, Lasair and Climet sampled the calibration aerosol in parallel downstream of the DMA. In order to make sure that these three instruments sample aerosols of the same concentration, the aerosol flows and the make up flow must be very well mixed. To achieve this, the flow path between the mixing point 6 Values in parenthesis are the nominal values. 7 The amplifiers for the St. Louis Lasair worked well, but the resistor values were too small. Usually, the higher the input impedance, the better the op amp performance. On the other hand, too high resistor will suffer from Johnson noise. Therefore, resistors on an order of several kω are suggested for future work. 22

29 and the sampling point was extended to about 2 meters and an orifice (not shown in Figure 2.1) was added between the tubes to help mixing. Lab-PC-1200 is a data acquisition card manufactured by National Instruments. This card provides a counter to record the CNC counts. The digital output of CNC 3760 is a 15V square pulse, but the Lab-PC-1200 can only take 0~10V input. Therefore, a voltage divider was used between the CNC and Lab-PC-1200 to reduce the CNC output to the amplitude acceptable to the Lab-PC Data Acquisition Software I wrote LabVIEW programs Lasair_calib.vi and Climet_calib.vi to control the instruments, do measurements and record data. When the programs start, they send commands to the serial ports that control the OPCs to set the sampling parameters, such as the sample interval, and sample mode (continuous or not). Then they order the OPCs to start sampling. At the same time, the program sends one command to the counter to start the CNC 3760 counting, and another to the MCB card to start measurements with the PHA. At the completion of the sampling interval, both the OPC table data and PHA data are stored on the computer hard disk. 2.4 Lasair Calibration results PSL Kernel Functions As indicated earlier, the manufacturer of the Lasair (Particle Measuring Systems Inc.) uses polystyrene latex (PSL) to calibrate the Lasair. They did not report complete kernel functions. Instead, they provided the average Lasair voltage responses corresponding to the peaks in the pulse height distributions of several selected PSL sizes (Figure 2.6). These values were used to set the threshold voltages for size bins to create table data. PSL spheres have standard deviations of about 2%. The size range is so narrow that the dispersion in size can be neglected. Therefore, the measured PSL kernel functions were deemed as the true PSL kernel functions in our work. Kernel functions of particles generated by the DMA (DOS, NaCl, diesel soot, etc) can be estimated from the PSL kernels by Mie response calculation (homogenous, spherical particles) or by 23

30 calibration (non-spherical particles). The PSL kernel functions were also used to check the performance of the particle measuring system, and to study the effect of refractive index on kernel functions. The response of the Lasair to 404nm PSL monodisperse particles recorded by the MCA (pulse height distribution) is shown in Figure counts MCA channel number Figure 2.10 Pulse height distribution of 404nm PSL (Lasair low gain) In order to obtain size distributions by inverting measured pulse height distributions, we need to fit mathematical functions to the measured kernels. These functions can then be interpolated or extrapolated to provide estimates of kernel functions for particle sizes for which no measurements are available. The procedure that I used to obtain generic kernel functions is as follows: First, only the peak corresponding to the desired size was kept in analysis. Peaks of doublets, triplets, etc. (which appear more commonly in DOS calibrations) were deleted. Second, normalized pulse height distributions were obtained by dividing the number of counts in each channel by the total number of the counts in the main peak. Third, the channel numbers were converted to voltages (pulse height) by assuming that the channel numbers were linearly proportional to voltages (Equation 2.7). During the sampling, the Lasair reference voltage (LRV) varied from 6.5 to 9.0V. All pulse heights were normalized to a LRV of 10V to enable comparisons of 24

31 measurements obtained at different LRV levels. The conversion from channel i to the upper limit voltage V i used Equation 2.8: i V = 10 i 2048 LRV (2.8) Finally, the measured kernel functions were fit to lognormal distributions according to the following equations [1]: Ci lnvi ln Vg = (2.9) C i C (ln ln ) i Vi Vg lnσ = g (2.10) 1 Ci where V g σ g V i dc dv 1 (lnv lnv ) exp 2(lnσ g ) g = 2 2π V lnσ g = count median voltage = geometric standard deviation = voltage corresponding to the upper limit of channel i 2 (2.11) C i = normalized counts in channel i. C = normalized counts distribution (kernel function). The most frequent pulse height voltage (mode) V V p was calculated by Equation = exp( ln σ ). (2.12) p V g g Both the measured and fitted kernel functions for the 404nm PSL data in Figure 2.10 are shown in Figure Note that the lognormal curve fits the measurements very well. 25

32 5 4 measured kernel fitted kernel dc/dv Pulse Height (V) Figure 2.11 Measured and fitted kernel function of 404nm PSL All of the PSL kernel functions for calibrated sizes were obtained by the method described above. Figure 2.12 shows the measured and fitted PSL kernels in the size range from 305nm to 1099nm for the South Pole Lasair low gain. Note that the lognormal distribution fits the PSL kernels quite well for most sizes. dc/dv nm 482nm 404nm 505nm 672nm 595nm 653nm 701nm 720nm 845nm 913nm 1099nm Pulse Height (V) Figure 2.12 Measured and fitted PSL kernel function (SP Lasair low gain) If we take the peak of each pulse height distribution (the fitted Vp from Equation 2.12), we can draw a graph of peak voltage vs. particle mobility size, which is shown in Figure

33 12 Peak Voltage (V) Dp (nm) PSL Measured PMS Provided Figure 2.13 Peak voltage versus size from my measurement and from calibration data provided by PMS (SP Lasair low gain) As we can see from this plot, the peak voltage (Vp) increases monotonically with particle diameter, except for the data point of 672nm. Also shown in Figure 2.13 are some peak voltages calculated from the PMS calibration data (Figure 2.6). They were obtained by multiplying the PMS calibration data by the amplification factor of the external inverting amplifier. Note that these data fit my calibration very well. Figure 2.14 shows a plot of geometric standard deviations (σ g ) of PSL pulse height distributions. A straight line was fitted to these points, and the fitted line equation was used to calculate standard deviations of all sizes. I found that when particle diameter exceeded 2µm, the extrapolated standard deviation was very close to 1 (see Figure A.3.2 in Appendix A). Since we did not have PSL calibration data above 2µm, the standard deviation of 2µm PSL was used for particles bigger than 2µm. 27

34 1.06 y = -3E-05x R 2 = σg Dp (nm) Figure 2.14 Geometric standard deviations of fitted PSL kernel functions (SP Lasair low gain) DOS Kernel Functions and DMA Broadening Effect The response of the Lasair to DMA selected monodisperse 404nm DOS particles is shown in Figure Note that there are two peaks in Figure 2.15: a main peak at channel 136, and a minor peak around channel 456. I believe that the minor peak was produced by doublets. The doublets have the same electrical mobility as the singly charged particles, but they are doubly charged, and are therefore larger Counts MCA channel number Figure 2.15 Pulse height distribution of 404nm DOS (Lasair low gain) 28

35 According to Equation 2.1, Zp V qc and Zp 1 = Zp2, 2q 1 = q2 q C c = = (2.1) E 3πηD p = q C 1 c1 2 c2 3πηD p1 3πηD p2 2 Cc2 D p1 D p2 = (2.13) C c1 where the subscripts 1 and 2 represent singly and double charged particles, respectively. In this case, D p 1 = 404nm ; From Equation 2.13 it follows that D p 2 = 705nm. On the other hand, my calibration showed that the peak of 701nm DOS pulse height distribution appears at channel 437. This confirms that the particles in the minor peak were doublets. In Chapter 3, this pulse height distribution is inverted to obtain the size distribution. Again, we will see these two peaks in the size distribution. Since we can calculate the size of doublets precisely, the peak of doublets can be considered as a calibration data point [22]. However, in this study, only the main peak was used to calculate the kernel function, and peaks of doublets, triplets etc. were deleted. Both the fitted and the measured pulse height distributions for the 404nm DOS data in Figure 2.15 are shown in Figure Note that the lognormal curve also fits the monodisperse DOS measurement data very well measured kernel fitted kernel 2.0 dc/dv Pulse Height (V) 29

36 Figure 2.16 Measured and fitted pulse height distribution of 404nm DOS However, the pulse height distribution shown in Figure 2.16 is not the true kernel function for 404nm DOS particles because of the DMA broadening effect. As was indicated in Section 2.2.1, particles coming out of DMA had a mobility range of * Zp ± Zp (in most of my experiments, Z p = * Zp 1 10 ). This mobility range corresponds to a diameter range of 375.6nm to 438.5nm. This range is much wider than that of 404nm PSL, which according to the manufacturer is 400nm to 408nm. Figure 2.17 compares the measured 404nm PSL and DOS pulse height distributions. We can see that the measured DOS pulse height distribution is much wider than the measured PSL kernel function. dc/dv measured 404nm PSL measured 404nm DOS scaled 404nm DOS Pulse Height (V) Figure 2.17 Pulse height distributions for 404nm PSL and DOS. The measured 404nm PSL and DOS were obtained directly from measurement. The scaled 404nm DOS curve was obtained by scaling the 404nm PSL kernel. The scaling method is discussed below. [8], Theoretically, the true DOS kernel functions can be solved through Equation 1.2 y = K D ) f ( D ) dd, i = 1, 2,, m, (1.2) 0 i i ( p p p where y i represents measured pulse height distribution of DMA selected monodisperse DOS particles, K D ) are true kernel functions, and f D ) is the aerosol distribution i ( p exiting the DMA. If we assume that the DMA inlet particle concentration over the narrow 30 ( p

37 range of Zp * ± Zp is constant, then f ( D p ) dd becomes the DMA transfer function p (Equation 2.6). Equation 1.2 can be changed to the matrix form as shown below: Y Y M Y 1 2 m m 1 = K K 1 M ( D m p1 ( D ) LK1( D ) pn O M ) LK m ( D pn ) p1 m n Ω( D Ω( D M Ω( D p1 p2 pn ) ) ) n 1 (2.14) However, because the number of unknowns ( K D ) ) generally exceeds the number of i ( p equations, it is not possible to solve this matrix to get the true kernel functions. Instead, I scaled the PSL kernel function to obtain the true DOS kernel function. The scaling factor was the ratio of the Mie response to DOS and to PSL of the same size (The Mie response calculation is discussed later in this chapter). The scaled 404nm DOS kernel is also shown in Figure It was obtained by multiplying the x value (pulse height) of PSL kernel by the scaling factor, while dividing the y value (dc/dv) by the same scaling factor. If the scaled kernels are true kernels, then I can solve Equation 2.14 to get Y i, which is the pulse height distribution of DMA selected 404nm DOS particles. The measured and calculated pulse height distributions are shown in Figure Note that the two curves are pretty close. The small peak shift is due to the small difference between the measured and calculated peak voltages of 404nm DOS and PSL particles measured 404nm DOS calculated 404nm DOS 2.0 dc/dv Pulse Height (V) Figure 2.18 Measured and calculated pulse height distributions 31