By far the most important physical property of particulate samples is particle size. Particle size distributions is routinely measured across a variety of industries and is usually critical in the manufacture of many products. Particle sizes are generally measured in micrometre (µm) or nanometre (nm) and usually refer to the average diameter. With a diameter traceable to the National Institute of Standards and Technology (NIST), Thermo Scientific™ Duke Standards was developed to serve as a third-party reference to calibrate and check performance when particle sizing instruments are used for solving real-world analytical problems.
“O amazement of things—even the least PARTICLE!” ('Song at Sunset'. In Leaves of Grass, 375) published by Walt Whitman on 1897 expressed his grateful feeling toward everything in the world, including the small particle. Today particle is referred as “a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass.”
By far the most important physical property of particulate samples is particle size. Particle size distributions is routinely measured across a variety of industries and is usually critical in the manufacture of many products. Particle sizes are generally measured in micrometre (µm) or nanometre (nm) and usually refer to the average diameter. With a diameter traceable to the National Institute of Standards and Technology (NIST), Thermo Scientific™ Duke Standards was developed to serve as a third-party reference to calibrate and check performance when particle sizing instruments are used for solving real-world analytical problems.
Figure 1 shows the microsphere designed for application of size standard, noted that the range of size falls within which the actual mean diameter will lie—that is less than or equal to 2.5% of the mean diameter. Here a simple protocol is provided for the calibration of particles size with microscope, which the calibrated particle can be applied to check the sizes of bacteria, viruses, ribosomes and sub-cellular as well as microscope calibration.
Figure 1: 4D Series Dry Microsphere Size Standards observed under optical microscope.
ABSTRACT
Monodisperse or highly uniform spheres, when placed on a flat surface in a liquid medium, align themselves into systematic hexagonal arrays characterized by straight rows of particles. Using an optical microscope, the length of a row can be measured and divided by the number of spheres in the row to calculate the average diameter of the spheres. Limitations of the traditional array methods have been avoided by improved sample preparation methods and careful selection of measurement rows. Using the improved method, a series of monodisperse spherical particles from 0.5 to 40 micrometers (μm) was calibrated and certified with a stage micrometer calibrated by the National Institute of Standards and Technology (NIST).
1. INTRODUCTION
When placed on a flat surface in a liquid medium, monodisperse or highly uniform spheres align themselves into systematic hexagonal arrays characterized by straight rows of particles. Using a calibrated optical microscope, the length of a row can be measured, then divided by the number of spheres in the row to calculate the average diameter of the spheres.
Array methods for determining the mean diameter of spherical particles have been in use at the authors’ laboratory since 1977. The methods were developed because of the difficulty of determining the edge of spherical particle images with high precision as shown in Figure 2(a). When the spheres are in contact in a straight line on a flat surface, the uncertainty of defining the outside edge of the first and last particle in an array is the same as for both edges of a single particle. When the uncertainty is divided by the number of spheres in the row, the edge uncertainty per sphere becomes very low, greatly improving the accuracy of the mean size determination. Figure 2 (b) shows a typical array.
(a)
(b)
Figure 2: (a) Typical edge images for 9.87 μm spheres, 8 μm per division. (b) 9.87 μm spheres in arrays, 4 μm per division.
Other laboratories have also used array methods successfully1. Kubitschek2 and Hartman3,4 have described errors in previous methods which can be overcome with the techniques we have developed. When the mean diameter of monodisperse particles is of primary importance, rather than the size distribution, the array method is a convenient and practical method. This report describes our method and gives the results of the measurement of selected reference standards from 0.46 to 40 μm.
2. EQUIPMENT AND METHODS
2.1. Microscope
The microscope used in this work is an Olympus BHA. It has 15x eyepieces equipped with an eyepiece reticle, and objectives of 10, 20, 40, 60 and 100x magnification.
2.2. Stage Micrometer - Primary Standard
The primary calibration standard is a stage micrometer calibrated for 31 intervals by laser interferometry by the National Institute of Standards and Technology (NIST)5. The uncertainty of the micrometer calibration, from NIST Report #5524, is less than 0.00004 mm (0.04 μm) for lengths less than 0.2 mm, the longest length used to calibrate the eyepiece reticle. The micrometer was calibrated at 20°C and has a thermal coefficient of expansion of 8.5 parts per million per °C. The maximum error due to thermal expansion is 0.004%. The micrometer is 2 mm in length divided in 200 divisions, with line widths of 2 μm, and sharp line edges as shown in Figure 3.
Figure 3: The NIST-calibrated stage micrometer, 10 μm per division.
2.3. Verification Standards
Our own in-house size standards and several certified particle size standards from NIST and from the Community Bureau of Reference (BCR)6 were used as verification standards. They were measured for spherical diameter using the improved array method. The three BCR Standard Reference Materials analyzed are BCR #165A (2.223 μm), BCR #166A (4.821 μm), and BCR #167A (9.475 μm), calibrated by the optical array method. The three NIST Reference Materials are SRM #1690 (0.895 μm), SRM #1960 (9.89 μm) and SRM #1961 (29.64 μm)7. The eight Nanosphere size standards were calibrated by transmission electron microscopy (TEM) using the internal standard method8,9 with SRM #1690 (0.895 μm) as the reference standard.
2.4. Calibration
The microscope eyepiece reticle was calibrated by measuring intervals on the NIST-calibrated stage micrometer with the eyepiece reticle (Figure 4). It is critical that the eyepiece reticle be well focused for the microscope operator, and that the eyepieces of binocular microscopes be carefully focused to the operator’s eyes.
Figure 4. The stage micrometer through the eyepiece reticle, 8 μm per reticle division.
To minimize the effect of spherical aberration, only the central 20% of the eyepiece reticle, which has no apparent distortion, was calibrated. No lengths were measured at more than 25 divisions (<20% of the field), as beyond this point, the field is not optically flat. In general, the reticle should be calibrated as close as possible to the length of the array being measured.
2.5 Array Preparation
There are several methods of preparing measurable arrays, but the general method involves inducing the spheres to array in monolayers by drawing the microsphere suspension between microscope slide and cover-glass by capillary action. Anything that disturbs this smooth flow will interrupt array formation. If the array formation is too slow, the microspheres will array loosely, making them appear larger than they are. This can be detected by measuring the array in two different directions; if there is any variation, the section of arrays in question should not be used. If the microspheres array too fast, they will pack too tightly, and not all of them will be in contact with the slide. This produces arrays that appear striated when slightly defocused and will show an average diameter smaller than the actual diameter. The greatest problems in producing measurable arrays are flocculation, or the presence of clumped particles or large spheres. These can cause the microspheres to array in multilayers. Near-size large and small particles can make holes or gaps in the arrays, causing the rows to crack or bend. Preparation of good, measurable arrays requires microsphere suspensions that contain a minimum of large or small outliers or clumps of particles and have proper dispersing agents to prevent flocculation during array formation.
2.6. Row Selection
Rows were selected that were in flat monolayer arrays, without large or small particles, cracks, or gaps. They were perfectly straight when compared to the eyepiece reticle and were at least 10 divisions long whenever possible. Row lengths were measured on the eyepiece reticle by placing a reticle line exactly between two beads and counting the number of beads until the edge of a bead corresponds closely with another line. The length (to the nearest tenth of a division) and the number of spheres in the row were recorded. At least 9 rows were measured for each sample. The row lengths can be measured directly by the microscope operator or photographed for later analysis. These values were entered in a double precision computer program created specifically for the array method which automatically adjusts for the scale calibrations. The mean is calculated as the sum of the row lengths in micrometers divided by the total number of spheres measured. Figure 5 shows a typical row with the eyepiece reticle in place.
Figure 5. 9.87 μm arrayed spheres through the eyepiece reticle, 4 μm per division.
2.7. Analysis of Uncertainty10
The total uncertainty is the sum of the random measurement error and the calibration uncertainty (Table 1). The calibration uncertainty was calculated as the sum of the stage micrometer calibration uncertainty (from NIST report #5524) and the estimated uncertainty of determining the edge of the stage micrometer lines by the microscope operator. To determine the random error of the measurements, the mean diameter of each row measurement was considered as one determination. The precision of the measurements is the standard deviation of the mean diameters for each individual row. Errors in locating the edges of the spheres are included in the row-length variation.
Table 1. Sources of Uncertainty for 10 μm Spheres
3. RESULTS
The expected values and the values observed by array method for the certified reference standards are summarized in Table 1. There was no bias observed, meaning that the systematic error was not significant. The average percent differences between the observed and expected values, 0.11%, can be considered random or measurement error. The measured value was within the uncertainty of the certified value for the standards in all cases. Figure 6 is a graph of the expected vs. observed values.
Table 2: Comparison of the Array Method with Certified Diameters of Reference Standards
Figure 6. Array Method: Observed vs. Expected Values for Standards.
4. CONCLUSIONS
Although limited primarily to the measurement of monodisperse microspheres, the array method offers improved mean size analysis compared to most one-by-one particle sizing methods, provided the arrays are measured by the recommended procedures. It correlates extremely well with more sophisticated and complicated methods for calibrating particle size standards, can be NIST traceable, and is relatively easy to perform. Using the improved array method, a new series of particle size standards (4000 series) from 1.0 to 100 μm has been calibrated and certified by the authors’ laboratories as shown in Figure 7. Noted particle size smaller than 1 μm (3000 series) was calibrated by Photo correlation spectroscopy (PCS) or TEM. Both Thermo Scientific Duke Standards 3000 and 4000 series calibrated particle are excellent for use with any application that requires a NIST™ traceable size standard with a very narrow standard deviation such as checking the sizes of bacteria, viruses, ribosomes and sub-cellular as well as microscope calibration.
Figure 7. Particle Counter Validation for 4000 and 3000 series of Thermo Scientific Duke Standards
Additional Resources:
Thom, R., H. Marchandise and E. Colinet, “The Certification of Monodisperse Latex Spheres in Aqueous Suspensions with Nominal Diameter 2.0μm, 4.8μm and 9.6μm”, Calibration Report EUR 9662 EN, Community Bureau of Reference (1985).
Kubitschek, Herbert E., “The Array Method of Sizing Monodisperse Particles”,in Ultrafine Particles, ed. W.E. Kuhn, Wiley, p.438-454, (1963).
Hartman, A.W., “Investigations in Array Sizing, Part 1: Accuracy of the Sizing Process”, Powder Technology 39, p. 49-59, (1984).
Hartman, A.W., “Investigations in Array Sizing, Part 2: The Kubitschek Effect”, Powder Technology 42, p. 269-272, (1985).
National Bureau of Standards Technical News Bulletin, Vol. 51, #3, March 1967. Now the National Institute of Standards and Technology.
Community Bureau of Reference, Commission of the European Communities, 200 rue de la Loi, B-1049, Brussels, Belgium.
National Institute of Standards and Technology, U.S. Department of Commerce, Gaithersburg, Maryland, 20899.
Mulholland, G.W., A.W. Hartman, G.G. Hembree, Egon Marx, and T.R. Lettieri, “Development of a One- Micrometer-Diameter Particle Size Standard Reference Material”, Journal of the National Bureau of Standards 90, p.3-26, (1985).
Duke, S.D., and E.B. Layendecker, “Internal Standard Method for Size Calibration of Sub-Micrometer Spherical Particles by Electron Microscope”, Proceedings of the Fine Particle Society, (1988).
The original publication of this paper pre-dates NIST Technical Note #1297, therefore the uncertainty calculation follows the guidelines in place at the time instead of the TN1297 / ISO GUM methods.
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By far the most important physical property of particulate samples is particle size. Particle size distributions is routinely measured across a variety of industries and is usually critical in the manufacture of many products. Particle sizes are generally measured in micrometre (µm) or nanometre (nm) and usually refer to the average diameter. With a diameter traceable to the National Institute of Standards and Technology (NIST), Thermo Scientific™ Duke Standards was developed to serve as a third-party reference to calibrate and check performance when particle sizing instruments are used for solving real-world analytical problems.
“O amazement of things—even the least PARTICLE!” ('Song at Sunset'. In Leaves of Grass, 375) published by Walt Whitman on 1897 expressed his grateful feeling toward everything in the world, including the small particle. Today particle is referred as “a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass.”
By far the most important physical property of particulate samples is particle size. Particle size distributions is routinely measured across a variety of industries and is usually critical in the manufacture of many products. Particle sizes are generally measured in micrometre (µm) or nanometre (nm) and usually refer to the average diameter. With a diameter traceable to the National Institute of Standards and Technology (NIST), Thermo Scientific™ Duke Standards was developed to serve as a third-party reference to calibrate and check performance when particle sizing instruments are used for solving real-world analytical problems.
Figure 1 shows the microsphere designed for application of size standard, noted that the range of size falls within which the actual mean diameter will lie—that is less than or equal to 2.5% of the mean diameter. Here a simple protocol is provided for the calibration of particles size with microscope, which the calibrated particle can be applied to check the sizes of bacteria, viruses, ribosomes and sub-cellular as well as microscope calibration.
Figure 1: 4D Series Dry Microsphere Size Standards observed under optical microscope.
ABSTRACT
Monodisperse or highly uniform spheres, when placed on a flat surface in a liquid medium, align themselves into systematic hexagonal arrays characterized by straight rows of particles. Using an optical microscope, the length of a row can be measured and divided by the number of spheres in the row to calculate the average diameter of the spheres. Limitations of the traditional array methods have been avoided by improved sample preparation methods and careful selection of measurement rows. Using the improved method, a series of monodisperse spherical particles from 0.5 to 40 micrometers (μm) was calibrated and certified with a stage micrometer calibrated by the National Institute of Standards and Technology (NIST).
1. INTRODUCTION
When placed on a flat surface in a liquid medium, monodisperse or highly uniform spheres align themselves into systematic hexagonal arrays characterized by straight rows of particles. Using a calibrated optical microscope, the length of a row can be measured, then divided by the number of spheres in the row to calculate the average diameter of the spheres.
Array methods for determining the mean diameter of spherical particles have been in use at the authors’ laboratory since 1977. The methods were developed because of the difficulty of determining the edge of spherical particle images with high precision as shown in Figure 2(a). When the spheres are in contact in a straight line on a flat surface, the uncertainty of defining the outside edge of the first and last particle in an array is the same as for both edges of a single particle. When the uncertainty is divided by the number of spheres in the row, the edge uncertainty per sphere becomes very low, greatly improving the accuracy of the mean size determination. Figure 2 (b) shows a typical array.
Other laboratories have also used array methods successfully1. Kubitschek2 and Hartman3,4 have described errors in previous methods which can be overcome with the techniques we have developed. When the mean diameter of monodisperse particles is of primary importance, rather than the size distribution, the array method is a convenient and practical method. This report describes our method and gives the results of the measurement of selected reference standards from 0.46 to 40 μm.
2. EQUIPMENT AND METHODS
2.1. Microscope
The microscope used in this work is an Olympus BHA. It has 15x eyepieces equipped with an eyepiece reticle, and objectives of 10, 20, 40, 60 and 100x magnification.
2.2. Stage Micrometer - Primary Standard
The primary calibration standard is a stage micrometer calibrated for 31 intervals by laser interferometry by the National Institute of Standards and Technology (NIST)5. The uncertainty of the micrometer calibration, from NIST Report #5524, is less than 0.00004 mm (0.04 μm) for lengths less than 0.2 mm, the longest length used to calibrate the eyepiece reticle. The micrometer was calibrated at 20°C and has a thermal coefficient of expansion of 8.5 parts per million per °C. The maximum error due to thermal expansion is 0.004%. The micrometer is 2 mm in length divided in 200 divisions, with line widths of 2 μm, and sharp line edges as shown in Figure 3.
Figure 3: The NIST-calibrated stage micrometer, 10 μm per division.
2.3. Verification Standards
Our own in-house size standards and several certified particle size standards from NIST and from the Community Bureau of Reference (BCR)6 were used as verification standards. They were measured for spherical diameter using the improved array method. The three BCR Standard Reference Materials analyzed are BCR #165A (2.223 μm), BCR #166A (4.821 μm), and BCR #167A (9.475 μm), calibrated by the optical array method. The three NIST Reference Materials are SRM #1690 (0.895 μm), SRM #1960 (9.89 μm) and SRM #1961 (29.64 μm)7. The eight Nanosphere size standards were calibrated by transmission electron microscopy (TEM) using the internal standard method8,9 with SRM #1690 (0.895 μm) as the reference standard.
2.4. Calibration
The microscope eyepiece reticle was calibrated by measuring intervals on the NIST-calibrated stage micrometer with the eyepiece reticle (Figure 4). It is critical that the eyepiece reticle be well focused for the microscope operator, and that the eyepieces of binocular microscopes be carefully focused to the operator’s eyes.
Figure 4. The stage micrometer through the eyepiece reticle, 8 μm per reticle division.
To minimize the effect of spherical aberration, only the central 20% of the eyepiece reticle, which has no apparent distortion, was calibrated. No lengths were measured at more than 25 divisions (<20% of the field), as beyond this point, the field is not optically flat. In general, the reticle should be calibrated as close as possible to the length of the array being measured.
2.5 Array Preparation
There are several methods of preparing measurable arrays, but the general method involves inducing the spheres to array in monolayers by drawing the microsphere suspension between microscope slide and cover-glass by capillary action. Anything that disturbs this smooth flow will interrupt array formation. If the array formation is too slow, the microspheres will array loosely, making them appear larger than they are. This can be detected by measuring the array in two different directions; if there is any variation, the section of arrays in question should not be used. If the microspheres array too fast, they will pack too tightly, and not all of them will be in contact with the slide. This produces arrays that appear striated when slightly defocused and will show an average diameter smaller than the actual diameter. The greatest problems in producing measurable arrays are flocculation, or the presence of clumped particles or large spheres. These can cause the microspheres to array in multilayers. Near-size large and small particles can make holes or gaps in the arrays, causing the rows to crack or bend. Preparation of good, measurable arrays requires microsphere suspensions that contain a minimum of large or small outliers or clumps of particles and have proper dispersing agents to prevent flocculation during array formation.
2.6. Row Selection
Rows were selected that were in flat monolayer arrays, without large or small particles, cracks, or gaps. They were perfectly straight when compared to the eyepiece reticle and were at least 10 divisions long whenever possible. Row lengths were measured on the eyepiece reticle by placing a reticle line exactly between two beads and counting the number of beads until the edge of a bead corresponds closely with another line. The length (to the nearest tenth of a division) and the number of spheres in the row were recorded. At least 9 rows were measured for each sample. The row lengths can be measured directly by the microscope operator or photographed for later analysis. These values were entered in a double precision computer program created specifically for the array method which automatically adjusts for the scale calibrations. The mean is calculated as the sum of the row lengths in micrometers divided by the total number of spheres measured. Figure 5 shows a typical row with the eyepiece reticle in place.
Figure 5. 9.87 μm arrayed spheres through the eyepiece reticle, 4 μm per division.
2.7. Analysis of Uncertainty10
The total uncertainty is the sum of the random measurement error and the calibration uncertainty (Table 1). The calibration uncertainty was calculated as the sum of the stage micrometer calibration uncertainty (from NIST report #5524) and the estimated uncertainty of determining the edge of the stage micrometer lines by the microscope operator. To determine the random error of the measurements, the mean diameter of each row measurement was considered as one determination. The precision of the measurements is the standard deviation of the mean diameters for each individual row. Errors in locating the edges of the spheres are included in the row-length variation.
Table 1. Sources of Uncertainty for 10 μm Spheres
3. RESULTS
The expected values and the values observed by array method for the certified reference standards are summarized in Table 1. There was no bias observed, meaning that the systematic error was not significant. The average percent differences between the observed and expected values, 0.11%, can be considered random or measurement error. The measured value was within the uncertainty of the certified value for the standards in all cases. Figure 6 is a graph of the expected vs. observed values.
Table 2: Comparison of the Array Method with Certified Diameters of Reference Standards
Figure 6. Array Method: Observed vs. Expected Values for Standards.
4. CONCLUSIONS
Although limited primarily to the measurement of monodisperse microspheres, the array method offers improved mean size analysis compared to most one-by-one particle sizing methods, provided the arrays are measured by the recommended procedures. It correlates extremely well with more sophisticated and complicated methods for calibrating particle size standards, can be NIST traceable, and is relatively easy to perform. Using the improved array method, a new series of particle size standards (4000 series) from 1.0 to 100 μm has been calibrated and certified by the authors’ laboratories as shown in Figure 7. Noted particle size smaller than 1 μm (3000 series) was calibrated by Photo correlation spectroscopy (PCS) or TEM. Both Thermo Scientific Duke Standards 3000 and 4000 series calibrated particle are excellent for use with any application that requires a NIST™ traceable size standard with a very narrow standard deviation such as checking the sizes of bacteria, viruses, ribosomes and sub-cellular as well as microscope calibration.
Figure 7. Particle Counter Validation for 4000 and 3000 series of Thermo Scientific Duke Standards
Additional Resources:
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