Minimum sampling time/volume for liquid-borne particle counters and monitors
Xu, Mindi
ABSTRACT
A particle counter is an instrument that measures particles in all the fluid passing through its sensor, and a particle monitor measures particles only in a portion of the fluid. For liquid with an ultralow particle concentration, particles may not disperse uniformly in the liquid. Therefore, the concentrations may vary significantly from measurement to measurement if the sample volume is not large enough. To achieve the same precision, a minimum sampling time or minimum sample volume for a particle instrument needs to be specified. A Poisson distribution was used to describe the distribution of particle counts. Testing included a series of particle concentration measurements. Minimum sampling time or sample volume at a given average concentration with different error levels was determined for selected commercial particle instruments. At the same flow rate, a particle monitor always requires a longer sampling time than a particle counter to achieve a specific precision for a given concentration. The minimum sampling time also varies among instruments because of the difference in sample volume in which the particles are counted. Experiments with a particle monitor have been conducted to test the changes in average particle concentration and the standard deviation at different operating conditions.
Keywords: particles, particle counter, particle monitor, sampling time, concentration, ultrapure liquid
Liquid-borne particle counters and monitors are used extensively in the semiconductor and pharmaceutical industries to measure particles in liquids. An evaluation of liquid-borne particle instruments from different manufacturers has shown a significant variation in measurement results for different instruments. This variation could be explained by the inherent characteristics of the individual instrument design. With the limited choices for particle instruments, a user needs to fully understand the equipment and know how to operate it properly to obtain a reliable result.
The counters and monitors commonly used for particle measurement in liquids are the optical type. Typically, a laser light illuminates the fluid with particles in a capillary tube. The particles scatter light with an intensity depending on the particle size and the refractive index. The fluid media also scatter light, which contributes to the inherent background noise of the instrument. A particle with the same refractive index as that of fluid is not distinguishable from the fluid by light scattering. However, a particle consisting of material with a refractive index much different from the refractive index of fluid will produce a strong signal. Thus, the particle signal eventually depends on the refractive index ratio of the particle to fluid. Since most liquid-borne particle instruments are calibrated with polystyrene latex (PSL) particles in deionized water, the measured particle size may not be exactly the correct size if the particles and fluid have different refractive indices from those of PSL and deionized water.11-3 A particle instrument can be recalibrated with the particles and liquid in question. Theoretical calculations can be used for recalibration when the refractive indices of particles and liquid are known.
Some particle instruments are designed so all the fluid passing through the sensor is illuminated by a uniformly distributed light beam.4 Therefore, a particle will be subjected to the same intensity light when it passes through the sensing volume regardless of its transverse position. The instrument that measures all the particles passing through its sensor is usually called a particle counter. A current commercially available particle counter can measure particles down to 0.2 (mu)m. However, an instrument capable of measuring 0.2-(mu)m particles is not necessarily a particle counter.
In a particle counter, the interfacial area between the fluid and the capillary tube is also illuminated. Consequently, both the fluid column and the tube/fluid interface scatter light, contributing significantly to the instrument background noise. The inner surface of the capillary tube contributes to the background noise by light reflection due to the roughness of the tube surface and the material itself. Although the outer surface of the capillary tube can be smoothed and coated with optical materials to reduce or eliminate light reflection, the inner surface cannot be treated in a similar way because of the material corrosiveness and the limitation of the tube size. The noise due to the interfacial illumination significantly restricts the detection limit of a particle instrument. Only those particles large enough in size to produce a signal distinguishable from the background noise can be detected.
To eliminate background noise from the interfacial area, some particle instruments focus their light beams to a small central portion of the fluid in a capillary tube, such as the PMS M-65 and the HIAC/ROYCO M-01 particle monitors. The incident light may then have a higher intensity per unit area and thus a particle in the illuminated area can produce a stronger signal. The detection sensitivity of such an instrument is better than a particle counter because of its lower background noise and stronger signal.4 Since only a portion of the fluid is illuminated in this type of instrument, usually called a particle monitor, only a fraction of the particles sampled into the instrument are counted.
The sensitivity of a particle monitor is largely dependent on the sensing volume in which the particles are counted. Generally, the smaller the sensing volume or the more the laser beam is in focus, the smaller the particle size that can be measured. Most of the particle instruments that measure particles smaller than 0.2 (mu)m are monitors. The smallest particles measured with a currently available monitor are 0.05 gm for deionized water (PMS M-50) and 0.065 (mu)m for chemicals (PMS M-65).
It should be understood that a laser beam has a normal (Gaussian) distribution in intensity along its cross section, with a maximum intensity at the center. Therefore, a particle of given size passing through the center of a light beam will scatter more light or produce a stronger signal than that by the same particle passing through the edge of the beam. If a threshold for particle size is set based on the scattering light from a particle through the center of the beam (the threshold is usually set at a percentage of the scattering light at the center of the beam), the particle through the side will always be sized smaller. When a very focused light beam is used, most of the large particles may be counted as smaller particles because very few can pass through the beam center. In this case, the size and concentration information for large particles is not reliable. Thus, monitors are usually designed to segregate particles in a limited size range. For example, a PMS M-65 particle monitor has only four size channels, one each for the 0.065, 0.1, 0.15, and > 0.2-(mu)m sizes, respectively.
In a measurement, particle concentration is reported based on the total count and the total volume of fluid in which the particles are counted continuously in a given period of time. With most particle counters and monitors, this period of time can be preset by an operator. A delaying time (dead time between the end of one counting interval and the beginning of the next) can also be preset at a time interval longer than the built-in delaying time. This option allows the operator to maintain the data volume while operating the instrument at a fixed sampling time interval, especially during on-line monitoring for quality control. Our work with ultrapure liquids has shown that one count can dramatically change the concentration value if the sample volume is too small or the sampling time is too short. It is possible that more (or less) particles may consistently appear in a series of measurements if the total sampling time of all the measurements is short. In this case, the average particle concentration based on the measurements will be high (or low).
The performances of several liquid-borne particle counters and monitors were evaluated experimentally.56 Statistical methods were used to analyze the accuracy of the measurement data of the optical particle counters.5 7-11We have concluded that to achieve a precise particle-concentration measurement, a minimum sampling time or minimum sample volume for a particle counter or a monitor is required. In this paper, a Poisson distribution is assumed for a series of particle concentration measurements. Minimum sampling time or sample volume at a given average concentration with different error levels is calculated for some commercial particle instruments. A discussion of sizing accuracy is beyond the scope of this study and will be considered in the future.
THEORETICAL CONSIDERATION
Theoretically, this assumption is valid for any particle concentration if the particle source and the flow are stable during the measurement time period. However, the Poisson distribution cannot be applied to the measurements where the probability that more than one particle will be counted in a sampling time interval is too high.l2 This time interval is in the inverse of the average particle concentration. The measurements for low concentrations at a given time interval may fit the Poisson distribution, but they may not be accurate when high concentrations of particles are measured at the same time interval. It is also impossible to set the sampling time interval shorter than the limitation of an instrument. In this paper, we assume that this distribution is valid throughout all of the discussions.
In a practical situation, a precision requirement is often specified in advance. In this case, the sample volume or the sampling time needs to be determined to meet the requirement. For the liquid with a mean concentration of 2 particles/ml, the minimum sample volume (sampling flow rate multiplied by sampling time) should be 12.5 ml if a standard deviation of 20 percent mean concentration, or S = 0.2, is required.
EXPERIMENTS
Experiments were conducted to measure particles in deionized water with a PMS M-65 particle monitor. The quality of the deionized water remained the same during the experiments and thus it could be assumed that the particles in the water were at a stable concentration. The particle monitor was operated at a total flow rate of 100 ml/min and a sampling flow rate of 0.6 ml/min. Each experiment continued for more than 24 hr at a constant sampling time and a constant delaying time between the two contiguous measurements. The experiments with a sampling time of 5, 10, and 30 sec reported data every 5 min with a delaying or dead time of 295, 290, and 270 sec, respectively. The measurements at the sampling time of 300 and 1200 sec reported data every 10 and 40 min with a delaying or dead time of 300 and 1200 sec, respectively.
RESULTS AND DISCUSSION
Experimental data showed that the variation of particle concentrations or counts from a series of measurements depends on the sampling time or sample volume of the measurements. For example, Figure 1 shows the average and the variation of particle concentrations (particles > 0.065 (mu)m) from the experiments at different sampling times. The average concentrations were calculated by averaging the concentrations from all measurements at a given sampling time in 24 hr.
In Figure 1, the average concentration decays as sampling time (sample volume) increases and then maintains at a relative constant level after 100 sec. This phenomenon could be partially attributed to the effect of the sample volume on determining particle concentration. With our experimental conditions, the particle concentration in the deionized water is so low that, although a particle is counted, the average amount of fluid in which a particle is dispersed does not fully pass through the sensor in a short sampling time. It is also possible that some of the fluid (but not a particle) passes through the sensor before the delaying time starts. With the PMS-M65 particle monitor, the change of one particle count will result in a concentration difference of 20 particles/ml at the 5-sec sampling time (sample volume 0.05 ml), and only 0.33 particles/ml at the 5-min sampling time (sample volume 3 ml). The average concentration will be high if one more particle appears in a series of measurements with a high possibility. Statistically, however, the average concentrations should be the same regardless of the sampling time intervals if the number of samples is large enough. As indicated, each data point in Figure 1 is an average of a large number of samples in 24 hr. Therefore, there might be other reasons to explain the strong dependence of the average concentrations on the sampling time intervals.
It is understandable that sampling time for a relatively accurate concentration should at least allow the amount of fluid with one particle to pass through the sensor. For example, if an average concentration of 1.6 particles/ml is measured with a PMS M-65 monitor (sampling rate 0.6 ml/min), the sampling time should be at least 62 sec for a decently accurate (precise) concentration (relative standard deviation S = 100% of the average concentration). Better accuracy could be achieved in this example if the recommendation by FEDSTD-209E to collect 20 particles in a continuous measurement (S=22% of the average concentration but a much longer sampling time) were followed.13 Therefore, a minimum sampling time should be met to achieve a specified precision for a given average particle concentration.
For a particle counter or monitor, its sampling flow rate is always specified by the manufacturer. The sampling time can then be determined with minimum sample volume and sampling flow rate. If the particle counts in a given volume of fluid follow the Poisson distribution, as shown in Equation 1, then Equation 4 can be used to calculate the minimum sample volume.
Figure 2 shows the data from the experiments with a sampling time of 5 sec, and Figure 3 shows the data with a sampling time of 5 min. It is shown that the experimental data fit the Poisson distribution very well. The minimum sample volumes at different mean concentrations have been calculated for the relative standard deviations of 5 to 110 percent mean concentrations with Equation 4. (The results are plotted in Figure 4.)
When Figure 4 is used to determine the sample volume before an experiment, an average particle concentration should be estimated. Starting from this average concentration on the x-axis to intersect with a line for a specific relative standard deviation, the corresponding sample volume for this intersection point is the minimum sample volume (y-axis). The sampling flow rate can be found in the particle instrument manual. Thus, the minimum sampling time can be easily determined with the minimum sample volume and the sampling flow rate. Figures 5 and 6 show the minimum sampling time for a PMS M-65 and a HIAC/ROYCO MicroCount-01 particle monitor, respectively. According to the manufacturers, the M-65 has a sampling flow rate of 0.6 ml/min, and the MicroCount-01 has a sampling flow rate of 4 ml/min (maximum sampling flow rate as shown in the manual).
For comparison, Table 1 lists the minimum sampling times for the particle instruments from different manufacturers. Instrument sensitivities and flow rate are also listed in the table. It is shown that to achieve a specific precision of the average concentration, a particle monitor (measures particles in a portion of the fluid through its sensor) requires a longer sampling time than a particle counter (measures particles in all of the fluid through its sensor). The minimum sampling time also varies from instrument to instrument because of the difference in sampling flow rate. A series of measurements needs to be made at the selected sampling time to have a statistically accurate average concentration.
Note that the values of the minimum sampling time listed in Table 1 do not necessarily correspond to the magnitudes of measurement errors when the instrument is used. It might be true only if the background noise of an instrument is negligible compared with the true particle concentration.9
Indeed, the effective sensing volume of a particle monitor (those instruments with a sampling rate smaller than the total flow rate as shown in Table 1) will be increased when an extremely large particle (relative to the sensing volume of the monitor) passes through the sensor. This particle will be illuminated by the very weak light and produce a detectable signal even if it passes through the sensor outside of the defined sensing volume. The minimum sampling time will be shorter than that shown in the calculation. Since this large particle is very rare in the environment where the instruments are used, the minimum sampling time for the particle monitors in Table 1 can be used without change.
CONCLUSION
Particle counts from a series of measurements of a medium with a constant concentration of particles follow the Poisson distribution. With this distribution, minimum sample volume and sampling time were determined for various particle counters and monitors at different error levels. The plots and tables presented in this paper can be used to determine the minimum sample volume or sampling time to achieve a specified precision and accuracy in experimental data.
The sampling flow rate of a particle counter or monitor is always specified by the manufacturer. Therefore, the minimum sampling time for any instrument can then be determined from the minimum sample volume and sampling flow rate.
For ultrapure liquids, the average and variation of particulate concentrations are sampling-time or samplevolume dependent. As a rule, the sampling time for a relatively accurate measurement should be longer than the time allowed for the amount of fluid containing one particle to pass through the instrument sensor.
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Updated version of a paper presented at the 43rd Annual Technical Meeting of the Institute of Environmental Sciences and Technology, May 4-8, 1997, Los Angeles, California.
ABOUT THE AUTHORS
Dr. Mindi Xu is a research scientist at the Chicago Research Center of American Air Liquide. His work has focused on particulate contamination, ultrapure liquid chemical process development, and chemical delivery system. He received his Ph.D. degree from the University of Cincinnati.
Dr. Hwa-Chi Wang is the associate director of Research and Development at the Chicago Research Center of American Air Liquide where he is responsible for microcontamination research. He is also an adjunct professor at the Department of Chemical and Environmental Engineering, Illinois Institute of Technology. He received his Ph.D. degree from the University of Illinois at UrbanaChampaign.
Copyright Institute of Environmental Sciences Nov/Dec 1997
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