NBS

PUBLICATIONS

OF

V:).-- NBS SPECIAL PUBLICATION 260-95

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

-QC100

U57

260-95

1985

Standard Reference Materials:

Development of a

One-Micrometer- Diameter

Particle Size Standard,

SRM 1690
TM he National Bureau of Standards was established by an act of Congress on March 3, 1901. The m Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Center for Materials

Science.

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

coordinates the system with measurement systems of other nations and

furnishes essential services leading to accurate and uniform physical and

chemical measurement throughout the Nation's scientific community, in- dustry, and commerce; provides advisory and research services to other Government agencies; conducts physical and chemical research; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Basic Standards^ Radiation Research Chemical Physics

Analytical Chemistry

TTie National Engineering Laboratory

Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops and proposes new engineering practices; and develops and improves mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

Applied Mathematics

Electronics and Electrical Engineering' Manufacturing Engineering

Building Technology

Fire Research Chemical Engineering^

TTie Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

Programming Science and

Technology Computer Systems

Engineering

The Center for Materials Science

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information funda- mental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Center consists of the following Divisions:

Inorganic Materials Fracture and Deformation^ Polymers

Metallurgy Reactor Radiation

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address

Gaithersburg, MD 20899. 'Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
Standard Reference Materials:

Development of a One-MicrometerDiameter Particle Size Standard,

SRM 1690

G. W. Mulholland

Fire Measurement and Research Division Center for Fire Research

A. W. Hartman, G.G. Hembree, Egon Marx,

and T R. Lettieri Mechanical Production Metrology Division Center for Manufacturing Engineering

National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

Sponsored by:

Office of Standard Reference Materials National Measurement Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director Issued May 1985
Library of Congress Catalog Card Number: 85-600539

National Bureau of Standards Special Publication 260-95

Natl. Bur. Stand. (U.S.), Spec. Publ. 260-95, 32 pages (May 1985)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1985 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
PREFACE

Standard Reference Materials (SRM's) as defined by the National Bureau of Standards are "well -characterized

materials, produced in quantity, that calibrate a measurement system to assure compatibility of measurement in the Nation." SRM's are widely used as primary standards in many diverse fields of science, industry, and technology,

both within the United States and throughout the world. For many of the Nation's scientists and technologists it

is of more than passing interest to know the measurements obtained and methods used by the analytical community

when analyzing SRM's. An NBS series of papers, of which this publication is a member, called the NBS Special Publication - 260 Series is reserved for this purpose.

This 260 Series is dedicated to the dissemination of information on all phases of the preparation, measurement,

and certification of NBS SRM's. In general, more detail will be found in these papers than is generally allowed,

or desirable, in scientific journal articles. This enables the user to assess the validity and accuracy of the measurement processes employed, to judge the statistical analysis, and to learn details of techniques and methods utilized for work entailing the greatest care and accuracy. It is also hoped that these papers will provide sufficient additional information not found on the certificate so that new applications in diverse fields not foreseen at the time the SRM was originally issued will be sought and found. Inquiries concerning the technical content of this paper should be directed to the author. Other questions concerned with the availability, delivery, price of specific SRM's should be addressed to: Office of Standard Reference Materials

National Bureau of Standards Gaithersburg, MD 20899

Stanley D. Rasberry, Chief

Office of Standard Reference Materials
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference Materials

(1984-85 edition), Catherine H. Hudson, ed., NBS

Spec. Publ. 260 (February 1984). $5.50* SN003-

003-02558-5.

Michaelis, R. E., and Wyman, L. L. Standard

Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards. NBS Misc. Publ. 260-1 (June 1964). COM74-1 1061**

Michaelis, R. E., Wyman, L. L., and Flitsch, R., Standard Reference Materials: Preparation of NBS Copper-Base Spectrochemical Standards. NBS Misc. Publ. 260-2 (October 1964). COM74-

11063**

Michaelis, R. E., Yakowitz, H., and Moore, G. A., Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric LowAlloy Steel Standard. NBS Misc. Publ. 260-3 (October 1964). COM74-1 1060** Hague, J. L. Mears, T. W., and Michaelis, R. E., Standard Reference Materials: Sources of

Information, NBS Misc. Publ. 260^ (February

1965). COM74-11059

Alvarez, R., and Flitsch R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys. NBS

Misc. Publ. 260-5 (March 1965). PB168068**

Shultz, J. I., Standard Reference Materials: Methods for the Chemical Analysis of White

Cast Iron Standards, NBS Misc. Publ. 260-6

(July 1965). COM74-11068**

Bell, R. K., Standard Reference Materials: Methods for the Chemical Analysis of NBS

Copper-Base Spectrochemical Standards. NBS

Misc. Publ. 260-7 (October 1965). COM74-

11067** Richmond, M.S., Standard Reference Materials: Analysis of Uranium Concentrates at the

National Bureau of Standards. NBS Misc. Publ. 260-8 (December 1965). COM74-1 1066** Anspach, S. C, Cavallo, L. M. Garfmkel, S. B. Hutchinson, J. M. R., and Smith, C. N., Standard Reference Materials: Half Lives of Materials Used in the Preparation of Standard Reference Materials of Nineteen Radioactive Nuclides

Issued by the National Bureau of Standards NBS Misc. Publ. 260-9 (November 1965). COM74-11065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F. J., and

Michaelis, R. E., Standard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards II: Cartridge Brass and LowAlloy Steel, NBS Misc. Publ. 260-10 (December

(1965). COM74-1 1064** Napolitano, A., and Hawkins, E. G., Standard Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-1 1 (November 1966). NBS Misc. Publ. 260-11** Yakowitz, H., Vieth, D. L., and Michaelis, R. E., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards III: White Cast Iron and Stainless Steel Powder Compact, NBS Misc. Publ. 260-12

(September 1966). NBS Misc. Publ. 260-12**

Spijkerman, J. L., Snediker, D. K., Ruegg, F. C,

and DeVoe, J. R.. Standard Reference Materials: Mossbauer Spectroscopy Standard for the Chemical Shift of Iron Compounds, NBS Misc. Publ. 260-13 (July 1967). NBS Misc. Publ.

260-13**

Menis, O., and Sterling, J. T., Standard Reference

Materials: Determination of Oxygen in Ferrous

Materials - SRM 1090, 1091, and 1092. NBS

Misc. Publ. 260-14 (September 1966). NBS Misc.

Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard Refer- ence Materials; Recommended Method of Use

of Standard Light-Sensitive Paper for Calibrat- ing Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Misc. Publ. 260-15 (June 1967). (Replaced by NBS Spec. Publ.

260-41.) Yakowitz, H., Michaelis, R. E., and Vieth, D. L., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of W-20% MO Alloy Fabricated by Powder Metallurgical Methods, NBS Spec.

Publ. 260-16 (January 1969). COM74-1 1062** Catanzaro, E. J., Champion, C. E., Garner, E. L., Marinenko. G., Sappenfield, K. M., and Shields, W. R., Standard Reference Materials: Boric

Acid; Isotopic and Assay Standard Reference

Materials, NBS Spec. Publ. 260-17 (February

1970). Out of Print. Geller, S. B., Mantek, P.A., and Cleveland, N.

G., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape Amplitude Measurement

"Process A," NBS Spec. Publ. 260-18 (November

1969). (See NBS Spec. Publ. 260-29.) Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measure- ments on the Vapor Pressure of Gold (Certifica- tion of Standard Reference Material 745). NBS

Spec. Publ. 260-19 (January 1970). PB190071**

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and

Silver, NBS Spec. Publ. 260-21 (January 1971). COM74-11359**

Yakowitz, H., Fiori, C. E., and Michaelis, R. E., Standard Reference Materials: Homogeneity

Characterization of Fe-3 Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec. Publ. 260-23 (December 1970). COM7I-00157**

Sappenfield, K. M., Marineko, G., and Hague, J. L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24 (January 1972). COM72-50058**

iv
Hicho, G. E., Yakowitz, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials: A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec.

Publ. 260-25 (February 1971). COM74-1 1356** Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel Corporation Joint Program for Determining Oxygen and Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). 85 cents* PB 81176620

Garner, E. L., Machlan, L. A., and Shields, W. R., Standard Reference Materials: Uranium

Isotopic Standard Reference Materials, NBS

Spec. Publ. 260-27 (April 1971). COM74-

11358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D., and Michaelis, R. E., Standard Reference Materials: Preparation and Evaluation of SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM71-50365**

Geller, S. B., Standard Reference Materials: Cali- bration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using

the Reference Tape Amplitude Measurement

"Process A-Model 2," NBS Spec. Publ. 260-29 (June 1971). COM71-50282

Gorozhanina, R. S., Freedman, A. Y., and

Shaievitch, A. B. (translated by M. C. Selby), Standard Reference Materials: Standard

Samples Issued in the USSR (A Translation from the Russian). NBS Spec. Publ. 260-30 (June

1971). COM71-50283**

Hust, J, G., and Sparks, L. L., Standard Reference

Materials: Thermal Conductivity of Electrolytic Iron SRM 734 from 4 to 300 K, NBS Spec. Publ. 260-31 (November 1971). COM7 1-50563** Mavrodineanu, R., and Lazar, J. W., Standard

Reference Materials: Standard Quartz Cuvettes,

for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). 55 cents* SN003-003-012I3-1 Wagner, H. L., Standard Reference Materials: Comparison of Original and Supplemental SRM 705, Narrow Molecular Weight Distri- bution Polystyrene, NBS Spec. Publ. 260-33 (May 1972). COM72-50526**

Sparks, L. L., and Hust, J. G., Standard Reference

Materials: Thermoelectric Voltage, NBS Spec.

Publ. 260-34, (April 1972). COM72-50371**

Sparks, L. L., and Hust, J. G., Standard Refer- ence Materials: Thermal Conductivity of

Austenitic Stainless Steel, SRM 735 from 5

to 280 K, NBS Spec. Publ. 260-35 (April 1972.) 35 cents* COM72-50368**

Cali, J. P., Mandel, J., Moore, L. J., and Young, D.

S., Standard Reference Materials: A Referee Method for the Determination of Calcium in Serum, NBS SRM 915, NBS Spec. Publ. 260-36 (May 1972). COM72-50527**

Shultz, J. I. Bell., R. K. Rains, T. C, and Menis,

O., Standard Reference Materials: Methods of Analysis of NBS Clay Standards, NBS Spec.

Publ. 260-37 (June 1972). COM72-50692**

Richmond, J. C, and Hsia, J. J., Standard Refer- ence Materials: Preparation and Calibration of Standards of Spectral Specular Reflectance, NBS Spec. Publ. 260-38 (May 1972). COM72-

50528**

Clark, A. F., Denson, V.A., Hust, J. G., and

Powell, R. L., Standard Reference Materials: The Eddy Current Decay Method for Resistivity Characterization of High-Purity Metals, NBS

Spec. Publ. 260-39 (May 1972). COM72-50529**

McAdie, H. G., Gam, P.D., and Menis, O., Standard Reference Materials: Selection of Thermal

Analysis Temperature Standards Through a Cooperative Study (SRM 758, 759, 760), NBS

Spec. Publ. 260-40 (August 1972.) COM72-

50776** Wood, L. A., and Shouse, P. J., Standard

Reference Materials: Use of Standard LightSensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Spec. Publ. 260-41 (August 1972) COM72-50775**

Wagner, H. L. and Verdier, P. H., eds.. Standard

Reference Materials; The Characterization of Linear Polyethylene, SRM 1475,' NBS Spec. Publ. 260-42 (September 1972). COM72-

50944**

Yakowitz, H., Ruff, A. W., and Michaelis, R. E., Standard Reference Materials: Preparation and Homogeneity Characterization of an Austenitic Iron-Chromium-Nickel Alloy, NBS Spec. Publ. 260-43 (November 1972). COM73-50760**

Schooley, J. F., Soulen, R. J., Jr., and Evans, G. A.,

Jr., Standard Reference Materials: Preparation and Use of Superconductive Fixed Point

Devices, SRM 767, NBS Spec. Publ. 260-44 (December 1972). COM73-50037**

Greifer, B., Maienthal, E. J., Rains, T. C, and

Rasberry, S. D., Standard Reference Materials: Powdered Lead-Based Paint, SRM 1579, NBS

Spec. Publ. 260-45 (March 1973). COM73-

50226**

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K, NBS Spec. Publ. 260-46 (March 1975). SN003-003-0 1278-5* Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and Austenitic Stainless Steel, SRM 798, from 5

to 280 K, NBS Spec. Publ. 260-47 (February

1974). COM74-50176** Mangum, B, W., and Wise, J. A., Standard Refer- ence Materials: Description and Use of Precision Thermometers for the Clinical Laboratory, SRM 933 and SRM 934, NBS Spec. Publ. 260-48 (May 1974). 60 cents* SN003-003-0 1278-5 Carpenter, B. S., and Reimer, G. M., Standard

Reference Materials: CaHbrated Glass Standards for Fission Track Use, NBS Spec. Publ. 260-49 (November 1974). CO"M74-51185

V
Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975). $1.00* SN003-003-0 1425-7 Mavrodineanu, R., and Baldwin, J. R., Standard

Reference Materials: Glass Filters As a Standard Reference Material for Spectrophotometry;

Selection; Preparation; Certification; Use-SRM

930, NBS Spec. Publ. 260-51 (November 1975). $1.90* SN003-003-O1481-8

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials 730 and 799, from 4 to 3000 K, NBS Spec. Publ. 260-52 (September 1975). $1.05* SN003-003-

01464-8 Durst, R. A., Standard Reference Materials: Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1975, Revised). $1.05 SN003-003-01551-2

Burke, R. W., and Mavrodineanu, R., Standard

Reference Materials: Certification and Use of Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard, NBS Spec.

Publ. 260-54 (August 1977). $3.00* SN003-O03-

01828-7

Ditmars, D. A., Cezairliyan, A., Ishihara, S., and

Douglas, T. B., Standard Reference Materials: Enthalpy and Heat Capacity; Molybdenum SRM 781, from 273 to 2800 K, NBS Spec. Publ. 260-55 (September 1977). $2.20* SN003-003-

01836-8

Powell, R. L., Sparks, L. L., and Hust, J. G., Standard Reference Materials: Standard

Thermocouple Materials, Pt.67: SRM 1967, NBS

Spec. Publ. 260-56 (February 1978). $2.20* SN003-003-0 18864

Cali, J. P. and Plebanski, T., Guide to United

States Reference Materials, NBS Spec. Publ. 260-57 (February 1978). $2.20* PB 277173

Barnes, J. D., and Martin, G. M., Standard Refer- ence Materials: Polyester Film for Oxygen Gas

Transmission Measurements SRM 1470, NBS

Spec. Publ. 260-58 (June 1979) $2.00* SN003-

003-02077 Chang, T., and Kahn, A. H. Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard; SRM 2601, NBS Spec.

Publ. 260-59 (August 1978) $2.30* SN003-

003-01975-5 Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., and Moody, J. R., Standard Refer- ence Materials: A Reference Method for the Determination of Sodium in Serum, NBS Spec.

Publ. 260-60 (August 1978). $3.00* SN003-003

01978-0

Verdier, P. H., and Wagner. H. L., Standard Refer- ence Materials: The Characterization of Linear Polyethylene (SRM 1482, 1483, 1484), NBS

Spec. Publ. 260-61 (December 1978). $1.70* SN003-003-02006-1

Soulen, R. J., and Dove, R. B., Standard Reference

Materials: Temperature Reference Standard

for Use Below 0.5 K (SRM 768). NBS Spec. Publ. 260-62 (April 1979). $2.30* SN003-003-

02047-8 Velapoldi, R. A., Paule, R. C, Schaffer, R. Mandel, J., Machlan, L. A., and Gramlich, J. W., Standard Reference Materials: A Reference Method for the Determination of Potassium in Serum. NBS Spec. Publ. 260-63 (May 1979). $3.75* SN003-003-02068

Velapoldi, R. A., and Mielenz, K. D., Standard

Reference Materials: A Fluorescence Standard

Reference Material Quinine Sulfate Dihydrate (SRM 936), NBS Spec. Publ. 260-64 (January

1980). $4.25* SN003-003-02 148-2 Marinenko, R. B., Heinrich, K. F. J., and Ruegg,

F. C, Standard Reference Materials: Micro- Homogeneity Studies of NBS Standard Reference

Materials, NBS Research Materials, and Other Related Samples. NBS Spec. Publ. 260-65

(September 1979). $3.50* SNOO3-O03-021 14-1 Venable, W. H., Jr., and Eckerle, K. L., Standard

Reference Materials: Didymium Glass Filters for Calibrating the Wavelength Scale of Spectro- photometers (SRM 2009, 2010, 2013). NBS Spec. Publ. 260-66 (October 1979). $3.50* SN003-003-

02127-0

Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel,

J., Murphy, T. J., and Gramlich, J. W., Standard

Reference Materials: A Reference Method for the Determination of Chloride in Serum, NBS Spec.

Publ. 260-67 (November 1979). $3.75* SN003-

003-02136-9 Mavrodineanu, R. and Baldwin, J. R., Standard

Reference Materials: Metal-On-Quartz Filters as a Standard Reference Material for Spectrophoto- metry-SRM 2031, NBS Spec. Publ. 260-68

(April 1980). $4.25* SN003-003-02 167-9 Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., Machlan, L. A., Garner, E. L., and

Rains, T. C, Standard Reference Materials: A

Reference Method for the Determination of Lithium in Serum, NBS Spec. Publ. 260-69 (July)

1980). $4.25* SN003-003-02214-4 Marinenko, R. B., Biancaniello, F., Boyer, P. A., Ruff, A. W., DeRobertis, L., Standard Reference

Materials: Preparation and Characterization of an Iron-Chromium-Nickel Alloy for Microanalysis, NBS Spec. Publ. 260-70 (May 1981). $2.50* SN003-OO3-O2328-1 Seward, R. W., and Mavrodineanu, R., Standard

Reference Materials: Summary of the Clinical Laboratory Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-71 (November 1981). $6.50* SN003-003-02381-7

Reeder, D.J., Coxon, B., Enagonio, D.,Christensen, R. G., Schaffer, R., Howell, B. F., Paule, R. C,

Mandel, J., Standard Reference Materials: SRM

900, Antiepilepsy Drug Level Assay Standard, NBS Spec. Publ. 260-72 (June 1981). $4.25* SN003-003-02329-9

vi
Interrante, C. G., and Hicho, G. E., Standard Refer- ence Materials: A Standard Reference Material Containing Nominally Fifteen Percent Austenite (SRM 486), NBS Spec. Publ. 260-73 (January

1982). $2.75* SN003-003-02386-8 Marinenko, R. B., Standard Reference Materials: Preparation and Characterization of K-411 and

K-414 Mineral Glasses for Microanalysis: SRM

470. NBS Spec. Publ. 260-74 (April 1982). $3.50 SN003-003-023-95-7

Weidner, V. R., and Hsia, J. J., Standard Reference

Materials: Preparation and Calibration of First Surface Aluminum Mirror Specular Reflectance Standards (SRM 2003a), NBS Spec. Publ. 260-75 (May 1982). $3.75 SN003-003-023-99-0

Hicho, G. E. and Eaton, E. E., Standard Reference Materials: A Standard Reference Material

Containing Nominally Five Percent Austenite (SRM 485a), NBS Spec. Publ. 260-76 (August

1982). $3.50 SN003-O03-O24-33-3 Furukawa, G. T., Riddle, J. L., Bigge, W. G., and

Pfieffer, E. R., Standard Reference Materials: Application of Some Metal SRM's as Thermometric Fixed Points, NBS Spec. Publ. 260-77 (August 1982). $6.00 SN003-003-024-34-I

Hicho, G. E. and Eaton, E. E., Standard Reference

Materials: Standard Reference Material Containing Nominally Thirty Percent Austenite (SRM

487), NBS Spec. Publ. 260-78 (September 1982). $3.75* SN003-003-024-35-0 Richmond, J. C, Hsia, J. J. Weidner, V. R., and

Wilmering, D. B., Standard Reference Materials: Second Surface Mirror Standards of Specular

Spectral Reflectance (SRM's 2023, 2024, 2025), NBS Spec. Publ. 260-79 (October 1982). $4.50* SN003-003-024-47-3

Schaffer, R., Mandel, J., Sun, T., Cohen, A., and

Hertz, H. S., Standard Reference Materials: Evaluation by an ID/ MS Method of the AACC

Reference Method for Serum Glucose, NBS

Spec. Publ. 260-80 (October 1982). $4.75* SN003-

003-024-43-1 Burke, R. W., and Mavrodineanu, R. (NBS retired). Standard Reference Materials: Accuracy in Analytical Spectrophotometry, NBS Spec. Publ.

260-81 (April 1983). $6.00* SN003-003-024-8

Weidner, V. R., Standard Reference Materials: White Opal Glass Diffuse Spectral Reflectance Standards for the Visible Spectrum (SRM's 2015 and 2016). NBS Spec. Publ. 260-82 (April 1983). $3.75* SN003-003-024-89-9**

Bowers, G. N., Jr., Alvarez, R., Cali, J. P. (NBS

retired), Eberhardt, K. R., Reeder, D. J., Schaffer, R., Uriano, G. A., Standard Reference

Materials: The Measurement of the Catalytic

(Activity) Concentration of Seven Enzymes in NBS Human Serum SRM 909, NBS Spec.

Publ. 260-83 (June 1983). $4.50* SN003-003-024-

99-6

Gills, T. E., Seward, R. W., ColHns, R. J., and

Webster, W. C, Standard Reference Materials: Sampling, Materials Handling, Processing, and Packaging of NBS Sulfur in Coal Standard

Reference Materials, 2682, 2683, 2684, and 2685, NBS Spec. Publ. 260-84 (August 1983). $4.50* SN003-003-025-20-8

Swyt, D. A., Standard Reference Materials: A Look

at Techniques for the Dimensional Calibration of Standard Microscopic Particles, NBS Spec. Publ. 260-85 (September 1983). $5.50* SN003-003-

025-21-6 Hicho, G. E. and Eaton, E. E., Standard Reference Materials: A Standard Reference Material

Containing Two and One-Half Percent Austenite, SRM 488, NBS Spec. Publ. 260-86 (December

1983) . $1.75* SN003-003-025-41-1 Mangum, B. W., Standard Reference Materials: SRM 1969: Rubidium Triple-Point - A Temperature Reference Standard Near 39.30 °C, NBS

Spec. Publ. 260-87 (December 1983). $2.25* SN003-003-025-44-5 Gladney, E. S., Burns, C. E., Perrin, D. R., Roelandts, I., and Gills, T. E., Standard Reference Materials: 1982 Compilation of Elemental

Concentration Data for NBS Biological, Geological, and Environmental Standard Reference

Materials. Spec. Publ. 260-88 (March 1984). $7.00* SN003-003-02565-8

Hust, J. G., Standard Reference Materials: A Fine- Grained, Isotropic Graphite for Use as NBS

Thermophysical Property RM's from '5 to 2500 K, NBS Spec. Publ. 260-89 (September 1984). $4.50* SN003-003-02608-5

Hust, J. G., and Lankford, A. B., Standard Reference Materials: Update of Thermal

Conductivity and Electrical Resistivity of

Electrolytic Iron, Tungsten, and Stainless Steel, NBS Spec. Publ. 260-90 (September 1984). $3.00* SN003-003-02609-3

Goodrich, L. F., Vecchia, D. F., Pittman, E. S., Ekin, J. W., and Clark, A. F., Standard Reference

Materials: Critical Current Measurements on an NbTi Superconducting Wire Standard Reference

Material, NBS Spec. Publ. 260-91 (September

1984) . $2.75* SN003-003-02614-0

Carpenter, B. S., Standard Reference Materials: Calibrated Glass Standards for Fission Track Use (Supplement to NBS Spec. 260-49). NBS

Spec. Publ.. 260-92 (September 1984). $1.50* SN003-003-02610-7

Ehrstein, J., Preparation and Certification of Standard Reference Materials for Calibration of Spreading Resistance Probes, NBS Spec. Publ. 260-93 (January 1985).

Gills, T. E., Koch, W. F. Stolz, J. W., Kelly, W. R., Paulsen, P. J., Colbert, J. C. Kirklin, D. R., Pei, P.T.S., Weeks, S., Lindstrom, R. M.

Fleming, R. F., Greenberg, R. R., and

Paule, R. C, Methods and Procedures Used at the National Bureau of Standards to Certify Sulfur

in Coal SRM's for Sulfur Content, Calorific Value, Ash Content, NBS Spec. Publ. 260-94 (December 1984). Mulholland, G. W., Hartman, A. W., Hembree,

G. G., Marx, E., and Lettieri, T. R., Standard

Reference Materials: Development of a 1 jjm Diameter Particle Size Standard, SRM 1690, NBS Spec. Publ. 260-95 (In Press).

* Send order with remittance to Superintendent

of Documents, US Government Printing Office Washington, DC 20402. Remittance from

foreign countries should include an additional one-fourth of the purchase price for postage. ** May be ordered from: National Technical Information Services (NTIS). Springfield

Virginia 22 161.

vii

standard Reference Materials: Development

of a One-Micrometer-Diameter

Particle Size Standard, SRM 1690

G. W. Mulholland, A. W. Hartman, G. G. Hembree,

Egon Marx, and T. R. Lettieri

National Bureau of Standards, Gaithersburg, MD 20899

Accepted: October 11, 1984 The average diameter of the first micrometer particle size standard (Standard Reference Material 1690), an aqueous suspension of monosized polystyrene spheres with a nominal 1 )xm diameter, was accurately determined by three independent techniques. In one technique the intensity of light scattered by a diluted suspension of

polystyrene spheres was measured as a function of scattering angle, using a He-Ne laser polarized in the vertical direction. The second technique consisted of measuring as a function of angle the intensity of light scattered from

individual polystyrene spheres suspended in air, using a He-Cd laser with light polarized parallel and perpendicular to the scattering plane. The measurement of row length by optical microscopy for polystyrene spheres arranged in close-packed, two-dimensional hexagonal arrays was the basis of the third technique. The measurement errors for each technique were quantitatively assessed. For the light scattering experiments, this required simulation with numerical experiments. The average diameter determined by each technique agreed

within 0.5% with the most accurate value being O.895±0.OO7 ^m based on light scattering by an aqueous

suspension. Transmission electron microscopy, flow through electrical sensing zone counter measurements, and

optical microscopy were also used to obtain more detailed information on the size distribution including the standard deviation (0.0095 p-m), fraction of off-size particles, and the fraction of agglomerated doublets (1.5%). Key words: array sizing; index of refraction; light scattering; Mie scattering; particle countmg; particle size standards; polystyrene spheres; size distribution; transmission electron microscopy.

1. Introduction

This paper describes the measurements performed to accurately characterize the average particle size of the nominal one-micrometer polystyrene spheres particle

size standard (Standard Reference Material 1690). The

spheres were purchased from Dow Chemical Company.' They have a nearly monosize distribution and are dispersed in water at a weight concentration of 0.5%.

About the Authors: G. W. Mulholland is a research chemist in NBS' Center for Fire Research. A. W.

Hartman, G. G. Hembree, Egon Marx, and T. R.

Lettieri are physicists in the Bureau's Center for Manufacturing Engineering.

'Certain materials are identified in this paper in order to adequately

specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the materials or equipment identified are

necessarily the best available for the purpose.

The three techniques used for measuring average particle size were: light scattering from individual spheres suspended in air, light scattering from an aqueous sus- pension of the spheres, and optical row-length measurements of spheres arranged in two dimensional ar- rays. The selection of these techniques resulted in part from a detailed review of all the generic measurement

techniques appropriate for the dimensional calibration of microscopic-particle size standards by Swyt [1]^ These same three techniques were used previously by

others in characterizing a batch of monosize polystyrene

spheres produced by Dow Chemical Co. (batch number

LS-1028-E). Phillips et al. [2] obtained a diameter of 1.20 jxm by single particle scattering measurements, Rowell

et al. [3] obtained 1.21 jiim by measurement of light scattering from a suspension of particles, and Bierhuizen and Perron [4] obtained 1.20 jam based on array sizing. The good agreement among these independent

^Figures in brackets refer to literature references at the end of this paper.

1
measurements gave us confidence that an accurate particle size standard was achievable. Our study represents an extension of the earlier work

in regard to the accuracy achievable by the three techniques. The major effort of our study was directed at performing the measurements in such a way as to maximize the accuracy in the determination of the mean

particle size. This required the use of accurate cali- bration standards for magnification and angular align- ment in addition to a quantitative error analysis. Perhaps the most widely accepted technique for measuring the particle size of polystyrene spheres has been

transmission electron microscopy (TEM). This is the

basis of the particle size information that is provided

with the monosize polystyrene spheres marketed by the manufacturer. We also had intended to use the TEM as one of our primary techniques, but we were unable to

find an accurate method for calibrating the magnification of the microscope. The relatively wide range

of values for particle diameter (from 1.10 to 1.26 ixm) reported by five independent TEM measurements [3] for Dow Latex LS-1028-E also suggests that the method

is unsatisfactory for highly accurate particle size measurements. While we did not use the TEM for deter- mining average size, we did use it for determining the standard deviation, orp, of the size distribution. Methods that have been used by others for measuring

the particle size of polystyrene spheres include flow

ultramicroscopy, ultracentrifugation, quasi-elastic scattering, and small-angle x-ray scattering. Some general design limitations of these instruments are given below. Our choice of light scattering and optical array sizing techniques was based on their being at least competitive with other methods in regard to sizing accuracy, and on

our familiarity with the measurement methods and the

theoretical basis. Both the quasi-elastic scattering technique and small- angle x-ray scattering work best for particles smaller than about 1 jum. The former technique [5] measures, in

effect, the particle diffusion coefficient, which increases with decreasing particle size. The resolution is limited

for 1 )Lim particles but improves with decreasing size. This is just the opposite of angular-intensity light scat- tering and array sizing where the resolution drops off markedly for particle sizes less than about 0.5 /im di- ameter. Small-angle x-ray scattering [6] is also best for small particle sizes because of the small wavelengths of

the x-rays. Davidson et al. [7] obtained an uncertainty of about ±4% at the 95% confidence level for flow ultra- microscopy based on counting 300 particles. The major

source of uncertainty was attributed to the statistical uncertainty in the average counting rate. The uncertainty in the number of particles counted is simply equal

to the square root of that number. Van den Hul and Vanderhoff [8] obtained a mean diameter for Dow Latex LS-1028-E about 18% less than the mean of the other techniques listed by Rowell et al. [3] using ultra- centrifugation. A major drawback in the technique for

this application is the small density difference, 1.00 versus 1.05, between water and the polymer. Nevertheless, Van den Hul et al. point out that all the deviation from

other measurements cannot be accounted for by the uncertainty in the density difference. Apparently no detailed error analysis has been made for the ultra- centrifuge applied to particle measurements. While the major focus of our study was the accurate determination of the number average particle diameter

D„, we also obtained information regarding the size dis- tribution including the standard deviation, crp, of the

particle size distribution, the fraction of off-size particles, and the fraction of agglomerated doublets. In addition, we obtained an estimate of the deviation from

sphericity based on TEM measurements. A brief description of the emulsion polymerization technique for producing polystyrene spheres and the factors affecting the stability of the suspension is given in the Appendix.

2. Light Scattering From Individual Spheres

We determined the diameter of the polystyrene

spheres by measuring the angular distribution of the

intensity of the light scattered by a single sphere and comparing measured intensities with those computed

for different values of the diameter, D, and the refractive index, n. The particles were levitated electrostatically in a Differential II light-scattering photometer developed by Wyatt and Phillips [9]. This type of instrument has been

used to determine D and n for spheres with diameters

1.099 ^m (Phillips et al. [2]), 0.796 ;xm (Cook and Kerker [10]), 1.011, 0.794, and 0.600 jam (McRae [11]), and

1.01, 5.7, and 11.9 pun (Davis and Ravindran [12]). The

sizes given above are nominal sizes provided by Dow

Chemical Company, the manufacturer of the particles. Bottiger et al. [13] have developed the capability of measuring all 16 components of the Mueller matrix, the

light-scattering phase matrix, for a single polystyrene

sphere. They also collected the particles on the tip of a needle for subsequent observation in an electron microscope. A detailed error analysis enabled us to make a quantitative statement regarding the accuracy of this technique. This and other aspects of the experiment and data

analysis have been previously reported by Marx and

Mulholland [14].

2
2.1 Experimental Method aT,{D,n)y (1) An aerosol made up of polystyrene spheres is generated by nebulizing a suspension of the spheres in distilled, filtered water; the water evaporates rapidly leav- ing charged spheres. One of these spheres is then

levitated electrostatically in an optical cell with elec- trodes as shown in figure 1. The particle is kept in the

light beam of a He-Cd laser (\ = 441.6 nm) by means of

a servocontrol. The scattered light reaches a photomuitiplier (having an S-21 response) via a traveling periscope, which has an acceptance angle of about 2° and which moves in a horizontal arc of almost 180°. We found that the output

of the angle encoder deviates by as much as 3° from the

true angle, and we performed an angle calibration using an accurately indexed protractor. We use a half-wave retardation plate to change the

polarization of the incident light. A typical sequence of measurements begins with a scan of the background, then a particle is captured and one or more scans is performed to measure the light scattered by that particle. A rotation of the half-wave

plate by 45° then changes the polarization of the incident beam by 90°, and one or more scans is performed to measure the scattered light, followed by a background

measurement for the new polarization. The light intensity-angle data pair closest to each integer angle over the range 20° to 160° is stored on magnetic tape.

2.2 Data Analysis The data are matched to the results of the calculations of the angular distribution of the intensity of the light scattered by a uniform sphere, as found by Mie and

others [15-171. The values of D and n are determined by minimizing

the quality of fit Ground

where A'^ is the number of data points, E, is the measured

intensity at the angle B,, T, is the computed value for the same angle, and a is an overall scaling factor required because we do not measure absolute intensities. The

expression for the a that minimizes Q is given by

A'2 T,\ (2) The least-squares fit is then determined by a grid search in the Z)« -plane for progressively finer grids. This procedure can be speeded up using an iterative search such as the Marquardt-Levenberg algorithm af- ter an initial coarse grid search. Other measures of the quality of fit are possible, and we consider mainly those that involve a change of variables. Specifically, we use the transformed intensity

I,{d) =I{e)sm\e/l), (3) because it tends to equalize the height of all the peaks for

a particle of a size around 1 jum in diameter. In the

original variable I{6), the large peak at small angles is overemphasized. On the other hand, the use of I\id) overemphasizes the values at angles close to 180°, which

are small with large relative errors.

2.3 Results The theoretical best fit curves are plotted in figure 2 for a single polystyrene sphere with and without the weighting function. There are four independent deter- minations of the best fit diameter; two based on vertical polarization and two based on horizontal polarization

data. The best fit values range from 0.898 to 0.905 /xm, which is a range of about 0.8%. A small portion of the

table of values of Q(n,D) near the minimum is given in y— Aerosol inlet

Figure 1-Single particle scattering instrument (Differential II). The

pillbox shaped scattering cell has

a pin electrode (V,) separated by

an insultor from the ground

plate electrode and opposite to the base plate electrode (Vz).

\

V2 1_ HeCd laser

^g^^^ Periscope

\~

^—To photomuitiplier tube

Half-wave plate

3
200 -

180

160 140

t-(A 120

UJ 100

UJ>

1-< 80

60

40

204

200 r 180

160

140

CMz

>< 120

>-w 10080 >

< 6040

20

BEST VERTICAL FIT D=0.905 pm

n =1.608

200

180

20° 40° 60° 80° 100° 120° 140° 160° 180° SCATTERING ANGLE

BEST VERTICAL FIT D=0.902 urn n=1.608

1ij

1

1

'1a /

1

1

1

1

'v

0° 20° 40° 60° 80° 100° 120° 140° 160° 180° SCATTERING ANGLE

BEST HORIZONTAL FIT D=0.899 pm

'l n = 1.616

0° 20° 40° 60° 80° 100° 120° 140° 160° 180° SCATTERING ANGLE

200

180

160 ^ 140 ! 120 w 100

BEST HORIZONTAL FIT D=0.898 \im n = 1.617

20° 40° 60° 80° 100° 120° 140° 160° 180° SCATTERING ANGLE

Figure 2-Best fits to the intensity of scattered light versus angle data for a single polystyrene sphere as determined by the least squares method

with (bottom) and without (top) the sin^0/2 weighting factor. Data ( x x); theory ( ).

table 1. The quantity Q varies rapidly with respect to D

for fixed n (column) and rapidly with respect to n for fixed D (row) but is rather insensitive in the diagonal

direction along which the product nD is almost constant. In a three-dimensional plot of \/Q as a function of

n and D, there is a very sharp peak when the surface is viewed in one direction but almost a ridgelike appearance in the other as shown in figure 3. The relative

insensitivity of Q to correlated changes in n and D necessitates that careful angle calibrations and detailed data

analysis be performed in order to obtain accurate values

for n and D. The results for the eight SRM 1690 particles analyzed

are contained in table 2 including the averages for the

4
Table 1. Normalized values of Q near the minimum for a SRM 1690 particle.

Vertical Polarization Horizontal Polarization

n 1.600 1.604 1.608 1.612 1.616 n 1.608 1.612 1.616 1.620 1.624 D,^m D,/i,m 0.899 4.75 3.18 2.18 1.70 1.69 0.893 14.22 9.78 6.36 4.07 3.03 0.901 2.34 2.15 1.48 1.29 1.50 0.895 9.58 5.93 3.37 2.01 1.92 0.903 2.31 1.47 1.09 1.15 1.58 0.897 5.90 3.11 1.51 1.16 2.13 0.905 1.65 1.10 1.29 1.92 0.899 3.35 1.55 1 1.81 4.06 0.907 1.32 1.06 1.20 1.70 2.52 0.901 2.15 1.46 2.16 4.35 8.13 0.909 1.32' 1.33 1.70 2.40 3.39 0.903 2.59 3.24 5.40 9.25 14.92 "The minimum value of Q in each column is underlined to illustrate the slow variation of ^ on a diagonal.

Figure 3--Two views of the three-dimensional surface of the inverse of the quality of fit, l/Q, as a function of the index of refraction, n, and the diameter, D, over a range of a few percent from the best value. The ridges cause difficulties for an accurate determination of the correct values of n and D.

5
Table 2. Radius and index of refraction for eight particles from SRM 1690.

Harmonic Mean'

Refractive

Vertical

Polarization Horizontal

PolarizationRefractive Radius Index Radius

fxm Index Radius

p.m Index

0.4545 1.614 0.4550 1.614 0.4535 1.610 0.4570 1.613 0.4570 1.613 0.4530 1.623 0.4490 1.618 0.4530 1.605 0.4490 1.618 0.4465 1.612 0.4510 1.600 0.4460 1.614 0.4480 1.613 0.4515 1.610 0.4480 1.613 0.4505 1.613 0.4535 1.610 0.4505 1.613 0.4535 1.608 0.4535 1.608 0.4535 1.610 0.4394 1.606 0.4402 1.603 0.4394 1.610 Average 0.4498 1.612 0.4518 1.608 0.4491 1.614

(T 0.0051 0.004 0.0048 0.005 0.0045 0.004 'Harmonic mean refers to the determination of the best fit radii horizontally polarized light, and Qh respectively (i.e., 2/Q|,=

js and refractive index by taking the harmonic mean, Q^, l/fJv+l/^H)-

, of the ^'s for the ca;ses of vertically and

diameter and index of refraction, 0.900 fxm and 1.612, respectively. The average particle size in this report

refers to the number average defined as follows:

(4) where A'^ refers to the number of particles measured. The

particle size is not perfectly uniform (ct/, = 0.010) and we

expect to see a spread in the measured diameters. On the other hand, the refractive index should be the same for

all particles, and we attribute the variation to experi- mental error.

For one particle we took nine scans with vertically polarized light and three more with horizontal polarization. The results of the analysis are shown in table 3. The standard deviation for the diameter, 0.0022 jam, is smaller than the one previously calculated for groups of

particles, but that for the index of refraction, 0.005, is about the same, suggesting that this parameter does not change, at least for particles of the same size.

2,4 Error Analysis To study the effects of experimental errors on the best

fit parameters, we modified the program that produces

the theoretical values of the scattered intensities to add

Table 3. Results for repeated scans for one particle. Run Unweighted Fit Weighted Fit Refractive Refractive n= 1.608" 0=1.615

Radius Index Radius Index Radius Radius

p,m |Lim p.m 1-V 0.4402 1.601 0.4380 1.612 0.4384 0.4366 2-V 0.4364 1.620 0.4376 1.614 0.4398 0.4378 3-V 0.4392 1.606 0.4366 1.618 0.4386 0.4372 4-V 0.4402 1.603 0.4398 1.605 0.4388 0.4372 5-V 0.4394 1.606 0.4410 1.601 0.4390 0.4372 6-V 0.4380 1.610 0.4398 1.604 0.4386 0.4368 7-V 0.4398 1.604 0.4386 1.610 0.4388 0.4370 8-V 0.4394 1.606 0.4388 1.609 0.4390 0.4372 9-V 0.4394 1.607 0.4400 1.604 0.4392 0.4374 1-H 0.4394 1.610 0.4402 1.601 0.4398 0.4384 2-H 0.4380 1.612 0.4402 1.612 0.4386 0.4374 3-H 0.4384 1.614 0.4364 1.620 0.4394 0.4382 Average 0.4390 1.608 0.4389 1.609 0.4390 0.4374

or 0.00110 0.0053 0.00150 0.0063 0.00047 0.00053

"The last two columns correspond to values of the radii obtained for a fixed value of the refractive index (unweighted fit). The first value is obtained for the best

fit to all particles of this size, and the second one is the published bulk value.

6
simulated errors and generate a file of "data" to be pro- cessed by the same procedure as described above. Noise

obtained using a random number generator with a max- imum amplitude of 1-3% of the intensity at each angle was added to all curves. The major component of the random error is attrib- uted to the noise in the intensity of the scattered light. This noise can be monitored by fixing the angle and

recording a trace of the intensity versus time. The general characteristics of such a trace show that there are two components of this noise. The smaller component,

about 2% of the intensity, affects each angle reading

independently; the larger component, which we think comes from the motion of the particle within the laser beam when the servocontrol is activated, is about 5%

and has a lower frequency so that it affects intensity readings in groups of about 10 degrees for the data col- lection speed that we used. The uncertainty in particle

size for a 0.900 /xm particle diameter was found to be at most 0.3% or 0.0027 /xm. As described above, the ob- served variability in particle diameter for 12 repeat scans of the same particle resulted in a cr of 0.0022 /xm, which

is consistent with most of the error being attributed to noise in the intensity of the scattered light. The quantity of primary interest is the random error associated with the determination of the average particle diameter. The standard deviation of the size distri- bution, CTp, is much larger than the cr associated with

repeat measurements and will ultimately limit the accu- racy in the mean size determination. Our measured crpoi

the particle diameters based on eight particles is 0.010

/x,m; an estimate based on our electron microscopy for about 160 particles, as discussed below, is slightly smaller, 0.0095 /xm. The component of the overall uncertainty in particle diameter resulting from the width of

the size distribution is given by

/? =r,„ (0.025)-^, (5) where n is the number of particles (eight in this case) and

(0.025) is the Student f -value for m degrees of freedom

and for 95% confidence level. The number of degrees of freedom relates to the determination of errand is one less than the number of particles sized by electron micros- copy, 159. We obtain a value of R equal to 0.0066 /Am. The sources of systematic errors include angle drift, 80, polarization misalignment, 8p, wavelength uncertainty, 8x, and non-volatile impurities, 81. There is an

error on the order of 2% if the angle encoder output is not calibrated. To this is added the problem of a slight

drift in the calibration that was apparently electronic in origin. Over the two days during which the light scat- tering measurements were performed on the eight poly- styrene spheres, the angle drift was about 0.08°. Including this drift in a numerical simulation, we find the uncertainty in particle size due to the drift, 89, to be

0.0028 /xm. The mixture of polarization states comes primarily from imperfections in the optical components and the misalignment of the periscope. The imperfections in the half-wave plate and other optical components allow the leakage of a small fraction of light (1 part in 200) at the orthogonal polarization direction. The error from the

inclination of the periscope with respect to the scatter- ing plane is comparable to the error due to the optical imperfections. A combined estimate of these effects comes to 8p =0.0018 /xm. The least important error is the uncertainty in the wavelength of the He-Cd laser, 8x =0.00007 /xm. In addition to instrumental errors, there are uncertainties associated with the nature of the particle. While

the polystyrene spheres are often considered to be ho- mogeneous, we expect the existence of a surface coating from the non-volatile emulsifier added during the preparation of the particles. If we assume that all the emulsifier resides on the particle surface, we find that the diameter is increased by 0.0008 /xm, so that 81= —0.0008. There is also a contribution to the surface coating from the 2 ppm impurities in the distilled water

in which the particles are suspended, but it is negligible

in comparison with the emulsifier contribution. An estimate of the total uncertainty, Ui, is obtained by adding the random error, R , to the sum of the absolute values of the systematic errors. £/t=J? + |8,1 + |8p| + |8,| (6) Using the values given above, we obtain i7T =0.012 /xm with a number average size of 0.900 /xm. The above analysis includes effects for which we

have quantitative estimates. Two other possible systematic error sources are slight asphericity of the particle and possible inhomogeneity of the particle resulting from strain as the water evaporates from the particle. Transmission electron microscope measurements of the

particle described in section 5 indicate an asphericity of 0.6% at a precision of about 0.3%. Over the course of our measurements the particle would have undergone

extensive rotation as a result of Brownian motion. We

have no quantitative estimate of this effect, though we

intuitively expect our value to be close to the volume

equivalent sphere diameter.

3. Light Scattering From a Suspension of Spheres

Light scattering measurements on a suspension of particles is complementary to single-particle scattering measurements. The signal-to-noise performance for sin7
gle-particle measurements is limited by the small scatter- ing intensity and by particle movement in the beam. For

scattering from a particle suspension the signal-to-noise

ratio is much improved because of the large number of

particles in the scattering volume and because of the use of photon counting. An accurately indexed rotary table was used for our light-scattering measurements with a suspension, whereas a rapidly-traversing periscope with some drift in the angle calibration was used for the

single-particle measurements. One disadvantage of measurements with a suspension is that there is one more unknown in the measurement, namely the size distribution, compared to the single-particle measurements where particle size and the index of refraction are the only unknowns. There have been a number of studies of light scatter- ing by nearly monosized suspensions. Kerker's book [17] includes several studies of the determination of the mean

size and standard deviation based on the angular de- pendence of the polarization ratio. Our instrument design is similar to the one described by Wims and Myers

[18]. The recent determination of particle size of poly- styrene spheres by Rowell et al. [3] by light scattering measurements is similar to our study in terms of measurement technique and data analysis.

3.1 Design of the Photometer A schematic diagram of the light scattering photometer for particle suspension is shown in figure 4. A 5-mW

intensity-stabilized He-Ne laser beam is directed to the center of a 10-cm diameter scattering cell with optical

flat windows on opposite sides. Incident light is verti- cally polarized and only the vertically polarized component of the scattered light is detected (VV scattering). A beam stop is positioned in the cell to minimize the amount of reflected light reaching the detector. The

collection optics (figs. 4 and 5) consist of two apertures,

a 1 X microscope objective, a vertical polarizer, and a

glass diffusing screen. The scattered light is detected by

a low-noise photomultiplier tube with a small (2.5 mm

diameter) photo cathode. The output pulses from the anode are amplified, discriminated, and then counted

over a 10-second time interval. The typical number of

counts per 10-second interval at the first peak is about

200,000, with repeat measurements agreeing within about 1%. The lowest count was on the order of 10,000. For some measurements, part of the laser beam is split off and sent into a reference photomultiplier. Output

counts from the reference amplifier-discriminator are used as clock pulses to the photon counter. In this manner, a ratio is taken between the signal photon counts and reference photon counts, thus cancelling out the

laser intensity fluctuations. This is not a significant effect for the intensity stabilized He-Ne laser, but it is signifi- cant for the He-Cd laser to be discussed later. A rotary table with an accuracy and reproducibility of ±1 arc second (0.0003°) is used for the angle measurements. The rotary table is indexed at two-degree

increments. The PMT is mounted rigidly to an arm at- tached to the rotary table. Using a micrometer adjust- ment and a dial indicator, the center of the scattering

cell is made coincident with the center of rotation of the

8
35mm 35mm

Beam stop

Sample volume

Laser beam

(unfocused)

Figure 5-Design of detector optics for minimizing acceptance angle.

Diffuser — 2.5mm dia. aperture IX microscope objective w/ 7mm dia. aperture — Polarizer 0.6mm dia. aperture

rotary table. Next the laser is mounted so that the beam

goes through the center of the two optical flats and

reflects back on itself. The pinholes in the detector sys- tem are then positioned in the center of the laser beam. The estimated deviation of the zero angle alignment,

including a slight error in positioning the cell (about 0.05 mm) and in the pinhole positioning (about 0.2 mm), leads

to an uncertainty in the zero angle of about 0.07°. The

effect of this uncertainty on the particle size deter- mination will be discussed in subsection 3.4.

It is important to have a small acceptance angle for the detector in order to obtain good size resolution. This is accomplished in our design by using two pin- holes before the detector as inc^cated in figure 5. In addition, a collection lens is used to limit the depth of

field. With these optics in the collection arm, the measured acceptance angle is about ± 1

° as measured at the 70% transmission points. This compares favorably with

the calculated acceptance angle of ±1.3° at the zero

transmission points. The two-degree acceptance angle

gives a calculated sample volume on the order of 1.3X10-W (13 mm^).

3.2 Sample Preparation and Experimental Procedure Clean glassware and "particle free" water are used to minimize extraneous particles in the suspension. After each experiment, the cell is washed with detergent,

rinsed, and then cleaned in hot nitric acid for a couple of

hours. After rinsing the cell and cover glass 8 to 10 times with deionized, filtered water, the cell is dried without water marks by directing a particle-free flow of air over

the external surface of the cell. Deionized water with a

resistivity of about 18 megohm-centimeter is used for rinsing glassware and for sample dilution. A pleated membrane filter with a 0.2-;xm pore size is also used on

the water outlet to remove particulates. In order to minimize multiple scattering, the particle suspension is diluted to a concentration on the order of

10'' particles/cm\ Dilution of approximately four orders of magnitude is required to dilute the standard samples, which are 0.5% by weight. After positioning the optical cell, a beam stop is in- serted in the cell to minimize reflected light. Measurements are performed every two degrees from 20° to about 140°, requiring about 30 minutes per experiment. At each angle, two intensity measurements are made to check for consistency and to avoid spurious data re- sulting from contamination particles which occasionally

enter the scattering volume.

3.3 Data Analysis For the case of light scattering from a suspension,

there are three unknown parameters: the numberaverage size, Dn, the standard deviation of the size distri- bution, CTp, and the index of refraction of the poly- styrene sphere. We assume the size distribution to be

normal. For the narrow size distribution of interest here, there is little difference between a log-normal distribution, which others have assumed for the polystyrene

spheres, and a normal distribution. Determinations of

size distributions of polystyrene spheres by electron mi- croscopy support this assumption. In carrying out our

data analysis, we assume the index of refraction to be known, and treat D„ and a-p as unknown parameters. In

9
subsection 3.5 we consider the sensitivity of the results to the assumed value of the index of refraction. For a distribution of particle sizes, the theoretically predicted scattering intensity, I{6,,D„,n), is the single- particle scattering intensity, T{0,,D^,n), averaged over

the size distribution and the acceptance angle of the

detector.

+ 0. 7 - 1 ,Dj,/t ) + Q.lT{d, + 1 ,£>j,« )} (7) where m represents the number of size increments and

the terms with B, + 1 and Q, — 1 take into account the

effects due to the finite acceptance angle of the detector. The quality of fit, Q, for the particle suspension experi- ment is defined by the same type of expression as eq (1), Q=^l[E,-aI{e„D„,crp)\\ (8) where the index i refers to angle, and E, is the measured

scattered mtensity at 6,. The expression for a is the same

as given by eq (2) but with replacing T,. For the refractive index of the polystyrene spheres, we use the value 1.588 for bulk polystyrene at A. = 632.8 nm given by Boundy and Boyer [19]. The refractive index of water at 23 °C was taken to be 1.3315 based on

measurements by Tilton and Taylor [20]. The appropriate wavelength and index of refraction for a particle suspended in water are the ratios of the respective val- ues in vacuum to the refractive index of water giving ^^=0.4752 )j,m

ical experimental data and best-fit results are shown in figure 6. We also consider a second definition of quality of fit based on weighting the intensities by a function of the

angle. Specifically, we consider

/,(0,) =/(0,)sin^(|), (10) which reduces the contributions to the quality of fit from the large peaks at small scattering angles. As seen

in figure 7, which is based on the same data as figure 6, the weighted peaks and valleys are approximately uni- form in amplitude throughout the angular range. The

30° 60° 90° 120° SCATTERING ANGLE

Figure 6-Best fit curve for the intensity of scattered light as a function of angle with Z)„=0.893 \im and a-,. = 0.027 fi,m. Data ( ); theory ( ).

npsL (vac) _j jg25

"water The number of intervals in the size distribution, m , is typically taken to be 10 or 20. The size increment. A, from £)j to £)j+i is chosen to be

so that the average in eq (7) covers the full size distribu- tion regardless of the value of a-p. For a specified value of /)„ and ap, the quantity / is calculated at two degree

intervals from 20° to 140°. The value of Q is determined from eqs (8) and (2). The best-fit values for £)„ and cr/.are determined by finding the minimum Q for a range of

values for D„ and CTp. The range for D„ is typically 0.893-0.898 jtim in increments of 0.0005 jiim, and, for a-p, from 0.021 to 0.039 /xm in increments of 0.002 /nm. Typ30° 60° 90° 120° SCATTERING ANGLE

Figure 7-Best fit curve for the intensity of scattered light weighted by

s\n*(d/2) as a function of angle with Z)„= 0.896 /xm and a? =0.023

/xm. The experimental data is the same as for figure 6. Data ( ); theory ( ).

10
values of ^ as a function of D„ and cr/>are given in table 4 for this case (experiment A3). We consider this second

definition of quality of fit to be superior to the first because all the data are significant. For our data, both

techniques produce very nearly the same result; for ex- ample, D„ for the first method is 0.894 compared to 0.896

for the second method.

3.4 Results One drop from one of the SRM 1690 vials, selected at random from 1000 vials, was used in preparing each of

the 10 samples. Light-intensity-versus-angle data were

taken for each sample and the best-fit parameters were

calculated. The results of the measurements are presented in table 5. The average value of £)„, for experiments A2 through Jl was found to be 0.895 jum with a standard deviation associated with the average

size, ctd^, of 0.0007. The average value of the standard

deviation of the size distribution, crp, was found to be

0.029 \im. Also indicated in table 5 are four repeat meaTable 4. The quality of fit, Q, for experiment A3 with weighting

factor

o-/.,fim 0.021 0.023 0.025 0.027 D,^m

0.8945 0.158 0.147 0.149 0.165 0.8950 0.147 0.140 0.146 0.167 0.8955 0.140 0.137 0.148 0,172 0.8960 0.139 0.140 0.154 0.181 0.8965 0.143 0.147 0.164 0,192

Table 5. Best-fit values for D„ for 10 samples of SRM 1690 based on

light scattering from a particle suspension.

photon

Sample" cr counts/ lOs"* Q

A2 0,8945 0,029 197,000 0.276 B 0.8965 0.025 165,000 0.287 C 0.8945 0.031 177,000 0.321 D 0.8940 0.031 179,500 0.272 E 0,8955 0.029 172,900 0.288 F 0,8950 0.029 150,500 0.224 G 0.8945 0.027 166,000 0.246 H 0.8950 0.027 97,500 0.166

I 0.8945 0.031 142,700 0.231

Jl" 0.8955 0.029 137,200 0.280

J2 0.8950 0.029 137,000 0.221 J3 0.8955 0.027 137,500 0.234 J4 0.8955 0.029 136,000 0.217 A.y 0.8955 0.023 167,500 0.137

"The sample concentration is approximately 7,0x lO' particles/cm', •The numerals refer to repeat measurements of the same sample. ^Sample A3 was prepared and the measurements made six months after the other measurements.

""Measured at 30 °C.

surements for one sample with the scans performed se- quentially over a period of about three hours. The stan- dard deviation for the average size for the repeat measurements is less than 0.0003 \xm. We think that the

larger standard deviation obtained for the 10 samples is a result of the sample preparation and cell positioning and not of differences in the vials; in any event, both

standard deviations are small and represent a minor component of the overall error as discussed in subsection 3.5. Scattering measurements were also performed with a He-Cd laser with X =441.6 nm, as a test for consistency. The appropriate values for the indices of refraction of water and polystyrene for this wavelength at 23 °C are

1.3395 and 1.615, respectively. Because of the lower

intensity stability of the He-Cd laser, the ratio of signal photon counts to reference co unts was taken as de- scribed in subsection 3.1. In this case,Z)n was found to be

0.896 with orp =0.031.

3.5 Error Anal> , > The major elements of the random error component

of the overall uncertainty are the photon counting noise and the fluctuation in the nu aber of particles in the

scattering volume. The percentage noise arising from

the statistical nature of photon counting goes as 1/Va^

so that even for a low count of 10,000 the noise is only 1%. Another \/\/N ievm is caused by the fluctuation in the number of particles in the scattering volume. For a number concentration of 7 x 10' particles/cm' and a typical scattering volume of 1.3 X 10"^ cm\ the number of

particles is 9.1x10' leading to a noise of 1.0%. As- suming the two fluctuations to be independent, we obtain a combined noise of 1.5%. The effect of this noise was simulated by the same technique as described in subsection 2.4 and found to change the particle size by

0.0006 \xm. This is comparable to the observed cr, 0.0007, for the measurements with the 10 samples. The

random component of the uncertainty is calculated as in subsection 2.4,

i?=r„_, (0.025)-^, (11)

where n refers to the number of samples. In this case the number of degrees of freedom is « — 1. We obtain for R

a value of 0.0005 \im, which is a factor of 13 less than for the single-particle measurements. The primary component of the systematic error is uncertainty in the refractive index of the particle with

lesser contributions from multiple scattering, finite ac- ceptance angle of detector, misalignment of detector, and reflected light. The uncertainty in the angle mea11
surement and in the wavelength of light is negligible in comparison to these others. The values of the refractive index of polystyrene

spheres obtained by various investigators were extrapolated to the He-Ne laser wavelength using the following

dispersion equation: n=A (12) The constants A and B are obtained from the measured

value of n at one wavelength together with Starkie's [21] value of 31.0 for the dispersion ratio defined as

:31. (13) The resulting values given in table 6 are close to the bulk

value of 1.588 but, based on these data, we cannot rule out the possibility of the refractive index of the particle being slightly different from that of the bulk. The range

of values obtained for liquid suspensions of the particles

Table 6. Refractive index of polystyrene.

Investigator n(0.6328)" Boundy and Boyer

bulk value

Heller and Pugh

0.132-0.295 )nm Smart and Willis 0.132-0.295 ;xm Marx and MulhoUand D = 0.460 jam" D = 0.600 ^x.m D = 0.914 ^im D=1.101 fxm McRaeD = 0.600 fim" D = 0.794 fxm D= 1.011 ;im Davis and Ravindran D=11.9 and 5.7 ^^m

Bottiger, Voss, and FryD=1.112 urn

Phillips, Wyatt, and Berkman D= 1.099 jj.m" 1.59+0.001

603 ±0.029

599±0.013 612±0.0O4

619±0.002

63±0.019

58±0.0O8

57±0.012

0.4416

0.4416

0.4416

0.4416

0,5145

0.5145

0.5145

1.579

1.575 1.588

1.595

1.618 1.569

1.559

'The refractive index has been extrapolated to X = n=A +B/\^.

"The values of D are the values obtained by Dow

mission electron microscopy.

0.6328 using the equation Chemical Co. using transextends from 1.577 to 1.594 and is based, respectively, on transmitted light intensity measurements by Smart

and Willis [22] and interferometric measurements by

Heller and Pugh [23]. In both cases the data analysis is the most straightforward for small particle sizes, and

only the small particle size results are given in table 6. All the other values in the table correspond to light- scattering measurements of single particles levitated in

air. We consider Marx and Mulholland's value [14] of

1.588 for the nominal 0.914 \xm particles to be the best of

the single-particle measurements in regard to SRM

1690, since the measurements were made on the SRM

particles and great care was taken with regard to angle

calibration and data analysis. The low value obtained by McRae [11] might have resulted from an error in the

calibration of the angle encoder. We observed an apparent size-dependence of the refractive index similar to that reported by McRae when our angle calibration was

off by about 3°. The measurements of Davis and Ravindran [12] were done on much larger polystyrene

spheres (5.7 and 11.9 jam) and the quality of the data appears to be lower than that of the other studies. The

poorer data may have resulted from a slight asphericity or inhomogeneity in the particles. We take as our range

of uncertainty in refractive index 1.577 to 1.595, which

encompasses all the values in table 6 except the values of Davis and Ravindran, McRae, and Marx and Mulholland's value for the 0.600-jj,m particle size which had

a large uncertainty. To estimate the effect of this uncertainty on we

repeated the data analysis for experiment A3 using the two extreme values of n. The value 1.577 leads to a

slightly increased value of 0.899, while the larger value of 1.595 leads to a slightly reduced mean diameter

of 0.893 \im. So the contribution to the uncertainty from

this effect, b„, equals ±0.003. The effect of multiple scattering on the results was

estimated by performing measurements at two concentrations. According to the criterion established by Napper and Ottewill [24], multiple-scattering effects be- come insignificant for the ratios of the average distance between particles, /, and the particle diameter, D,

greater than 100. For concentrations of 7.0x10^ and

3.5 X 10* particles/cm\ we find that l/D is 125 and 70

respectively. From analyzing the Hght-scattering data

for these two cases, we obtain 0.894 ]xm at the lower

concentration and 0.890 \xm at the higher concentration. We estimate as +0.001 jam allowing for a slight residual effect even though the criterion given above is satisfied for the 10 samples analyzed. The effect of the finite acceptance angle of the photometer was determined by computer simulation in which a slit width integration was performed over the

theoretically-predicted intensity pattern for £)„ =0.900

12
and 0-/, = 0.010 jam. The "data" were then analyzed by

the same procedure with the intensity weighted by

sm\d/2), and the resulting values of D„ and crp were

0.900 and 0.01 1 jam respectively. So we find 80 to be at most 0.0005 jam. If the intensities were analyzed directly without the angular weighting function, the values of D„

and o-p, 0.899 and 0.015, changed more as a result of the

finite acceptance angle than the values obtained using

the intensity weighted by the angular function. We also used computer simulation to estimate the error associ- ated with a slight misalignment at zero angle, about

0.07°, and found Sd to be 0.0004 fim. Without a beam stop, on the order of 4% of the laser beam is reflected from the glass-air interface back into the cell. This would lead to some fraction of the light reaching the detector having been scattered through the supplement of the scattering angle. We obtain an in- crease of 0.002 jam size without the beam stop and esti- mate an error, Sr, of at most +0.001 jam due to residual

reflection. As discussed in section 5, about 1.5% of the particles

is in the form of agglomerated doublets. Bottiger et al. [13], having measured all 16 components of the Mueller

matrix for a doublet of 1.112 jam polystyrene spheres,

find that the peaks and valleys in the scattering pattern appear at the same angles as for the single sphere but

that the amplitudes are smaller. We have no quantitative estimate of this agglomeration error, 5a, but we intuitively expect it to be less than 0.001 jam. Estimating the total uncertainty in the same manner as

in subsection 2.4, we obtain an expression for Uj shown

below together with estimates of the different terms,

C/T=i? + |8„| + |8„| + |89| + |SD| + |0R| + |8A|. 0.0005 0.003 0.001 0.0005 0.0004 0.001 0.001

Using these estimates, we obtain i[7T =0.007 jxm with a number-average size, D^, of 0.895 jam. The uncertainty

is lower than for the single-particle measurement be- cause of the much smaller random component of error, 0.0005 jam compared to 0.007 jam. While the average size can be determined quite accurately by scattering from a suspension, this is not the

case for the standard deviation of the size distribution,

(Tp. Our best estimate of crp based on light scattering is 0.029 jam while, as discussed in section 5, the value obtained by electron microscopy is about 0.0095 jam. We suspect that the major cause of the discrepancy is the contribution of scattered light from off-size particles and agglomerated doublets. The off-size particles are excluded from the determination of crp by electron mi- croscopy and the doublets are treated as pairs of individual spheres.

4. Optical Array Sizing

Array sizing by optical microscopy provides an inde- pendent measure of D„ since the technique is based on

geometrical optics rather than diffraction theory. This is one of the oldest techniques for the measurement of average size of micrometer-sized particles. Perrin [25] used this technique in his study of Brownian motion, from which Avogadro's number was first determined.

Its ability to produce accurate values for the average

diameter results from a combination of a highly accurate

length standard for optical microscopy and the fact that monosize polystyrene spheres can form close-packed, two-dimensional hexagonal arrays. The microscopic im- age of a row of micrometer-size spheres consists of a

string of circular images blurred by diffraction as indi- cated in figure 8; however, the center of the sphere can

be pinpointed with considerable accuracy. In fact, when

rows of, say, lO spheres are used, the potential exists for finding the average size of 1 jam spheres to a resolution of about 1% of the sphere diameter. Our methods for preparing the arrays and performing the measurements

are similar to those described by Kubitschek [26].

4.1 Formation of Two-Dimensional Arrays To minimize non-volatile residue, the particles were "washed" with 18-megohm-centimeter deionized water

filtered with a 0.2 jam pore size pleated membrane filter. The washing consisted of pouring off the supernatant

after allowing the particles to settle and then adding

filtered, deionized water. The particle concentration was about 0.5% by mass. A drop of the particle sus- pension was placed at one end of a microscope slide and

smeared out by means of a second slide held such that one of its long edges would wipe slowly over the first slide. The evaporating water sweeps the particles in- ward though it appears that surface tension is re- sponsible for the small scale motion leading to the or- dered array. In the early phase of evaporation, the

particles tend to congregate in assemblies similar in shape to ice floes in a freezing ice field. As the evaporation continues, the spheres arrange themselves into well-ordered hexagonal arrays, with rows 10-50 spheres

long. This ordering occurrs too rapidly to be observed by eye. The ordered arrays extending perhaps 7 spheres in one direction and 20 in another are separated by microcracks as seen in figure 9. The cracks occur during the drying when an array field is pulled apart perhaps to relieve a stress on the array. Another type of crack, also

illustrated in figure 9, is much shorter and is V-shaped.

It seems to indicate intensive drying within an array

13
Figure 8-Hexagonal array of nominal one-^m polystyrene spheres (Standard Reference Material

1690).

field. Close inspection shows that such cracks can be

detected when they are about 0.05 jam wide, and they

are easily visible when the width exceeds 0.1 jam.

4.2 Measurement of Arrays The arrays were measured by scaled micro- photography rather than by microscopy with a graduated eyepiece. Microphotography has the advantage of providing a permanent record from which array defects such as microcracks can be accounted for. The image

distortion in the optical train was measured to be less than 0.2%, and scale changes from repeated focusing were 0.1-0.2%. The microscope was a Zeiss Universal' with Polaroid attachment and with a 63x, 0.90 N.A.

objective.

The micrographs, with a typical scale of 1.6 mm per

jam, were measured to 0.05-0. 1 mm. The magnification

calibration and the image distortion were measured us- ing a 19.990±0.005 ixm linewidth spacing on SRM 474

Line Width Standard from NBS. The arrays were prepared on six microscope slides. One to three arrays were measured on each slide for a

total of 12 arrays. For each array, 15 row lengths were

measured. The number-average diameter for a single row is determined by dividing the length of the row, L, by the number of spheres in the row minus one, A^ — 1.

The — 1 results from using the center-to-center row

length rather than the edge-to-edge row length.

14
Figure 9-The same field of view is slightly defocussed for the photograph on the right to allow better visualization of the microcracks.

In our measurements the row length varied from 10 to 30 spheres.

4.3 Results The results for two arrays are shown in table 7. Measurements along each of the three lattice directions are included. In some cases the row lengths in different

Table 7. Measured row lengths for two arrays.

Orientation Row Length Readings Row Average Diameter Average (mm) (/xm) (fxm)

Slide No. 0° 120° 240° 0° 120° 240°

3 28.6 29.0 29.15

28.8 29.0 29.15

28.9 28.0 29.2 0.891 0.901 0.896 0.896

28.85 28.95 29.1 28.9 28.9 29.1

6 14.55 14.55 14.7

14.5 14.55 14.7

14.5 14.5 14.7 0.898 0.898 0,908 0.901

14.5 14.4 14,7

14.5 14.55 14.6

directions differ by as much as 0.2 mm for an 1

1 -sphere array leading to differences in the average diameter of

0.01 jam. The reason for this anisotropy is not clear. Kubitschek [26] attributes this effect to undetected mi- crocracks. If the cause were a single microcrack, then it would be on the order of 0.1 to 0.2 mm and would thus have been detected. For those arrays located at the pe- riphery of the ordered region, we found that in general

the average diameters calculated from rows parallel to the edge were somewhat larger than values calculated from rows in the other two directions, suggesting loos- eness in that direction. The drying speed of the array

also seemed to have some influence. The row-average diameter, D„ is obtained as a simple average of the values AO) for the R rows. 2 AO) A=-y- (15) The standard deviation in A -ctd, is given by 2 (AO) -A)'

A summary of the values of A and ctd, for each of 12

arrays, which includes 240 rows, is given in table 8. The

15
Table 8. Array sizing results for SRM 1690.

Slide Array Row No. of A Anisotropy No. No.

' ' 20 j5 0 905 0 0027 0 001 20 15 0 909 0 0027 0 006

0 906 0 0037

J 20 15 0 905 0 001

8

0 002

1 1 20 15 0.904 0.0028 0.002

2 ] 5 ] 5 0 895 0 0027 0 005

3 1 5 30 ] 5 0.896 0.0027 0 005

2 4 20 ] 5 0 896 0 0022 0 002

5 20 0 898 0 0049 0 011 4 13 15 0.886 0.0057 0 012

4 7 13 15 0.888 0.0038 0.009

4 8 13 15 0.889 0.0039 0.007

5 9 20 15 0.882 0.0029 0.004

6 10 20 15 0.898 0.0023 0.003

6 11 10 15 0.903 0.CO44 0.010

6 12 10 15 0.902 0.0039 0.010 Average: £>„ = 0.898 0.0026 0.006 = 0.008

average of all the values of D, in table 8, defined as D„,

is 0.898 with a standard deviation among the row averages, (To , of 0.008 jxm. The anisotropy, defined as the range in the row-averaged diameters in the three lattice directions of an array, is found to have an average value of 0.006 ixm. This is comparable in magnitude to ctd^-

It is also possible to determine the standard deviation of the size distribution, CTp, from cr^ . Assuming the spheres to be randomly distributed along a row in terms

of particle size, it can be shown that the crp is related to

(Td^ by the expression, ctp^VN-I a-o,, (17) where A'^ is the number of spheres in a row.

In arriving at this result, one makes use of the fact that the variance of the sum of random variables (the row

length) is the sum of the variances of the individual random variables (sphere diameter). The resulting value, 0.013 jam, has a statistical uncertainty of about ±0.003 /xm and is somewhat larger than the value obtained by electron microscopy, 0.0095 \im.

4.4 Error Analysis While the experimental technique of optical array siz- ing is relatively simple compared to light-scattering measurements, there are more potential sources of uncertainty, both random and systematic. The random

component of the total uncertainty is related to the stan- dard deviation of the average diameters for the arrays

measured, o-o„. We estimate the magnitude of the vari- ous components of the random error including image

distortion, readout of microphotographs, local motion

in the photographic material, and anisotropy. These are combined and compared with cr^^. There are also a number of systematic errors arising from the finite width

of the size distribution, microcracks, solute impurities, and shape distortion. Image distortion results in the length scale changing

over the photographic field of view. Because of axial symmetry of the optical train, it needs to be measured in relation to one plane containing the optical axis. The

Standard Reference Materia! 474 Line Width Standard was used as a two-line resolution target. A series of 150 measurements was made, covering

five photographs, each with 10 areas and each area be- ing measured three times. The result was a scale factor of 0.6 19 ±0.001 jam/mm (— at center, -I- at edge). Using one scale value for the entire field of view introduces an image distortion error, cr,, no greater than 0.002 \xm. Row lengths were measured to 0.05-0.1 mm

(0.03-0.06 /xm) using a film scale. The rows contained 10-20 spheres; thus the error contribution to the average

diameter value (1.0 fxm nominal) was 0.003 to 0.006 ju,m. In practice the film readout error, cti, was held below

0.005 [im.

It is known that slight motion can occur in photographic materials primarily as a result of uneven drying.

In the Polaroid material used here, there was no detectable motion at the 0.05 mm level. The error contribution, 0-3, is thus less than 0.003 jam for 20-sphere rows. The anisotropy in the array will also manifest itself as a component of the random error, 0-4. We estimate this effect as half the range in the average anisotropy, 0.003 jam. We obtain a combined estimate of all the sigmas by

using the formula

o-,^= i cr.\ (18)

In using this standard formula, we are assuming the

errors to be independent. The resulting value of cr„ 0.007 jam, is comparable to GrD„ so our error budget

accounts for the observed value of the random error. The random component of the overall uncertainty based on 16 sets of measurements is found to be 0.0044 /am based on the formula i?=r,3(0.025)^. (19)

It is thought that the mean distance between particle centers in monodisperse arrays, such as those shown in figure 8, is greater than the mean particle diameter be16
cause many smaller particles fail to be in contact with all of their neighbors. Thus, gaps in the array add to the length of a line of particles, causing an overestimate of

their true mean diameter. For hexagonal arrays formed

from machined washers of known size, Kubitschek [27] found that the overestimate AZ) for particles with stan- dard deviation crp was given by

A£)=0.46o-p. (20) For our case, crp obtained from electron microscopy is 0.0095 ]u.m, so the resulting systematic error, 8w, is —0.0044 /xm. We have chosen to treat this effect as a systematic error rather than correcting for it, because

there has been no direct verification of eq (20) for micrometer-size spheres. A second source of systematic error arises from microcracks. When a row is measured across one or two

undetected cracks, one can expect an error contribution

to the average diameter of about 0.01 jam for rows 10 spheres long, and less for longer rows. We take as our

error estimate, Sc, a value of —0.005 juim. The presence of impurities in the polystyrene sus- pensions is another source of error. Assuming that the

emulsifier and inorganic impurities form a uniform coat- ing around the spheres when the water evaporates, one

finds the following expression for the thickness, t, of the coating

where C is the volume concentration of the polystyrene and C, the concentration of the non-volatile impurities. For our case the non-volatile impurity concentration was about two orders of magnituide lower than the vol- ume concentration of the polystyrene spheres, and the maximum resulting error is about 0.003 \im. An attempt was made to detect this effect by using one sample of the stock solution and a different one in which the original solute impurity content had been reduced by an order of magnitude by settling, decanting, and addition of filtered, deionized water. The measured

diameter for the second sample was slightly less, by

0.004 ±0.003 jam. Therefore, all reported measurements were performed on samples with reduced impurity content. We estimate the error resulting from residual nonvolatile impurity of washed particles, 8i, as 0.001 jam. Two other potential systematic errors include the ef- fect of unequal-size spheres on a flat substrate and the

effect of curved rows. If we have a row of spheres of unequal diameters, the centers of the spheres will not be on a straight line and the row length will be less than the

sum of the diameters. If the size distribution is not too broad {crp/D <0.03), the error in the calculated average

diameter, c^/.V2Z)^ is small (less than 0.001 /am) compared to other errors. Occasionally arrays will exhibit curved or wavy

rows. For typical curvatures, replacing the arc by the chord introduces only a small error (on the order of

0.001 jam) in the measured diameter. However, we

found that curved rows are sometimes as much as 1%

longer than the corresponding straight rows found in the same array. This suggests the presence of slack in the curved rows, and therefore such rows were omitted from our measurements.

It is possible that spheres in contact flatten slightly. We made an attempt to measure the average size of

isolated spheres and arrays of spheres with a trans- mission electron microscope, but we were not able to prepare arrays on TEM grids. There were instances of

particles in contact as in figure 10, and from measuring

Figure 10-Electron micrograph of nominal one-/a.m polystyrene

spheres (SRM 1690) at a magnification of 10,000x. The spacing for the diffraction grating lines is 0.46 /xm.

17
such particles we found that the flattening effect is less than 0.005 fxm. More quantitative measurements are necessary to refine dp. As in the error analyses in the previous sections, we

obtain the combined uncertainty from the sum of the random error, R , and the absolute values of the systematic errors,C/t=/? + |Sw| + |8c| + |8,| + |8f| We obtain a value of 0.020 for Uj with the overall average value for £)„ of 0.898 jitm.

5. Measurements of Size Distribution/Concentration

We have used transmission electron microscopy,

flow-through electrical-sensing zone counter measurements, and optical microscopy to obtain more detailed information about the size distribution. Using

these techniques, we measure crp, the standard deviation of the size distribution, the fraction of off-size particles, and the fraction of agglomerated doublets. Our only

direct measure of number concentration was obtained with electrical sensing zone counter measurements.

5.1 Transmission Electron Microscopy The sample was prepared for electron microscopy by

evaporating a small drop of diluted suspension of the spheres on a diffraction grating replica mounted on a TEM grid. Three grids were prepared from one SRM

1690 vial. The grids were coated with approximately 20 nm of carbon and then examined with a JEOL 200CX

electron microscope' at an accelerating potential of 100 KV and at a nominal 1 0,000 X magnification. The particle size was measured directly from the negative using

a 7x magnifier with an accurate millimeter scale reti- cule. A series of concentric circles on the reticule en- abled quick location of the sphere diameter. A typical micrograph is shown in figure 10. As mentioned in the introduction, we had hoped to make an accurate determination of the average particle

size from the TEM measurements. However, we found

significant variability in the commercially available grating replicas in regard to the line spacing even among

those from the same supplier. We also found variations

as much as 3% in the line spacing in different regions of

the same grating. So from our assessment, transmission

electron microscopy is not competitive with the light scattering and array sizing measurements for accurate

particle size measurement without a suitable calibration

artifact.

However, the high resolution of the TEM makes it suitable for the measurement of the standard deviation of the narrow size distribution. The size distribution typically consists of a very sharp central peak plus broadly distributed off-size particles. The inclusion of

the off-size particles in the data analysis will greatly broaden the apparent value of crp. In one case crp changed from 0.031 to 0.011 as a result of removing

three off-size particles from a sample of 102 particles. It

is, therefore, important to have a systematic procedure

for rejecting off-size particles. We used a discordancy

test [28] based on the sample kurtosis as the test statistic,

sample kurtosis = '-j^ r-. (22) (2 (A -A)']'

If the sample kurtosis exceeds a value of about 3.77 for

a 100-sphere sample, then one or more spheres are off- size at the 5% level of discordancy. The spheres with

diameters farthest from the average size are eliminated consecutively until the sample kurtosis reaches the ap- propriate value. The particles at the edge of the field of view were eliminated because of evidence of magnification distortion in this region. Using a common magnification for all the micro- graphs resulted in a smaller value of crp than the value obtained using a magnification for each photograph de- rived from the li.ie spacing on the diffraction grating

replica. The smaller value of crp is the better value be- cause experimental errors only tend to increase crp. The

constancy o. the magnification was to be expected, since

all the micrographs were taken at one magnification

setting over a period of a few hours. We obtained values of 0.0083 /j,m and 0.0106 jitm for cr/> based on samples of

59 and 99 particles. We take the mean value of 0.0095 as our estimate of crp. The major source of uncertainty in crp is statistical in origin. The sample variance has a distribution, and for a sample size of 100 there is an uncertainty of about ±13% at the 95% confidence level. The size distribu- tion is represented as a histogram in figure 11. Other information obtained from TEM includes the

asphericity of the particles and the fraction of "new"

particles. The asphericity, A„ is defined as

A, =

(^'""^^'"'")xl00%. (23) The diameter measurements were made every 45° for

particles located near the center of the field of view. The

asphericity is small, 0.6% ±0.3%, with large uncertainty because of the resolution limit of the TEM. We found a total of eight particles with diameters less than 0.5 /xm out of some 1350 particles (0.6%). As ex18
20

15

DC

UJ

QQ1-

\

\

\\

0.90 0.91 0.92 0.93 0.94 0.95 DIAMETER, pm

Figure 11-Size distribution of nominal one-jam polystyrene spheres

(with off-size particles excluded) obtained by transmission electron microscopy. The dashed curve is the normal distribution with £)„ (0.932 (Lim) and crp (0.0106 fxm) obtained from the experimental data.

plained in the Appendix, it is possible to nucleate a new

population of particles in the process of using seed particles to produce larger particles. We believe that this nucleation process is responsible for the small off-size spheres.

5.2 Electrical Sensing Zone-Counter Measurements We used the Coulter ZB Counter with Coulter Channelyzer Pulse Sizer' to measure the fraction of doublets, the fraction of large off-size particles, and the number

concentration, and to estimate the variability of D„ in the SRM 1690 samples. To apply this technique, the particles must be prepared in an electrolyte solution at a concentration of about 1% by mass. The technique consists of measuring the electrical current due to the elec- trolyte flowing through an orifice; in our case, 30- and

19-jLim diameter orifices were used. As a particle flows through the orifice, the current is reduced by an amount

approximately proportional to the volume of the particle [29]. For our application, we used nominal 0.9- and 2-jLim size polystyrene spheres for a particle size calibration of

the instrument, and then used the Coulter Counter to measure the concentration and size distribution. The

Coulter Counter is not an absolute sizing instrument.

It was found that if the polystyrene spheres were

directly diluted with electrolyte, then about 10% ag- glomerated doublets resulted from the combined effects of high particle concentration and the reduction in electrostatic repulsion between the particles. The agglomerated doublets were minimized by first diluting with fil- tered, deionized water (dilution factor 2.5x10^) and

then diluting by another factor of 10 with the electrolyte

solution. The percentage of doublets was found to be

1.5 ±0.4% of the total population for fresh samples, compared to about 1 % obtained by visual microscopy of

the suspended particles diluted without electrolyte. Based on the limited sample size, there does not appear

to be any significant difference in the fraction of doublets between the sample diluted without electrolyte and the fresh samples diluted with electrolyte at the last step.By changing the electronic settings of the Coulter

Counter, it was possible to estimate the percentage of

large single particles with diameters in the range of 2 —

jam. The observed count was on the order of 200 out of

a total population of about 235,000 particles, which cor- responds to slightly less than 0.1%. Based on the measured number-concentration of two

diluted samples for particles in the 0.6 to 1.4 /j,m size range, we obtain number concentrations of the undiluted samples of 1.18 and 1.45x10'° particles/cm\ These values agree well with a calculated value of 1.25x10'° particles/cm^ based or a concentration of 0.5% by mass of the polystyrene spheres, a particle density of 1.052 g/cm\ and a particle size of 0.9 jam. Diluted samples were prepared from each of 10 SRM

vials and two portions of each sample were sized with

the Coulter Counter using the 30-jam-diameter orifice. A typical size distribution based on sizing about 85,(X)0 particles is given in figure 12. A complete listing of the

Figure 12-Size distribution of SRM 1690 obtained by a Coulter Counter for aperture current, amplification, and lower threshold settings of 1/3, 1/2, and 100 respectively. The instrument output is linear with respect to particle volume and consequently appears stretched when plotted versus particle diameter.

19
average particle size, £)„, and the standard deviation of

the central peak are given for each sample in table 9. The

standard deviation associated vi'ith 10 independent de- terminations of £>„ has a value of 0.0027 jam. This value

is approximately three times greater than the value obtained by light scattering and is due to instrumental

noise rather than sample-to-sample variability. Even when measurements are made on the same sample such

as Fl to F4, variations in Ai as large as 0.005 /im are observed.

Table 9. £>„ and cr,. for Coulter Counter measurements of SRM 1690.

Sample D„, \xm cTp, jum D„, \x.m CTp, /J,m A 0.9226 0.0370 0.9239 0.0336 B 0.9225 0.0380 0.9240 0.0344 C 0.9266 0.0351 0.9286 0.0349 D 0.9226 0.0336 0.9240 0.0339 E 0.9264 0.0351 0.9251 0.0357 Fl" 0.9308 0.0392 0.9302 0.0332 F2 0.9251 0.0329 F3 0.9246 0.0326 F4 0.9245 0.0325 G 0.9245 0.0328 0.9247 0.0356 H 0.9231 0.0333 0.9222 0.0338

1 0.9223 0.0338 0.9236 0.0340

J 0.9226 0.0323 0.9228 0.0311 "The numeralis refer to repeat n s of the same sample. The average value of the standard deviation of the

size distribution, 0.033 ju.m, for the central peak based on

Coulter Counter measurements is more than a factor of

three greater than the value obtained by electron mi- croscopy. The primary cause of this broadening is the

variation in the electrical pulse resulting from different

particle trajectories through the orifice. The amplitudetime history of the electrical pulse for a particle moving

near the aperture wall is different from that of a particle moving near the centerline. Thom [30] demonstrated

this effect on a model system with plastic washers and

Spielman and Goren [31] demonstrated that the resolution of the Coulter Counter could be improved by hy- drodynamically focusing the particles through the center of the orifice. The Coulter Counter we used did not have hydrodynamic focusing, but it did have a pulse analyzer for rejecting counts in part due to particles with atypical trajectories.

6. -Summary

The values of and the associated uncertainty for three techniques are: 0.895+0.007 jixm for light scatter- ing from particles suspended in water, 0.900+0.012 ju,m for single-particle light-scattering measurements, and

0.898 ±0.020 \xm for optical array sizing. For each technique there is a consistency test in addition to a quantitative error analysis. For the single-particle light- scattering measurements, the particle diameter obtained

for the incident light polarized in the vertical direction

(0.903 }xm) agreed well with the diameter obtained for

light polarized in the horizontal direction (0.898 ju.m). For light scattering from a particle suspension, the particle diameter obtained with two different laser sources, He-Ne (0.633 jam) and He-Cd (0.442 |Ltm) differed by

only 0.001 }xm. In the case of array sizing, six indepen- dent samples were prepared and the variation in the average particle diameter, 0.882 to 0.903 )j,m, was less than the overall uncertainty. We use 0.895 jam as the certified value because of the lower uncertainty associated with light scattering from

a suspension. Another advantage of this value is that the measurements characterize the particles in the same

form as provided in the SRM 1690, this is, in suspension

rather than as a dried sample where there is the possibility of a coating of non-volatile impurities on the surface. It is reassuring that the variability among the three values of D„ is less than the uncertainty associated with any one technique. We expect that our estimates of uncertainty are, if anything, conservative. The value obtained by Dow Chemical Co. for D„ by TEM, 0.914 jam,

is about 2% greater than our certified value.

In table 10 we summarize all the information regarding the size distribution obtained by our measurements. Only for D„ and the index of refraction have detailed error analyses been made. The different features of the global size distribution extending from 0. 1 to 6 jam are indicated qualitatively in figure 13. A wide range of values is found for the standard deviation of the size distribution, crp, extending from

Table 10. Summary of results for SRM 1690.

D„,ixm 0.895+0.007' light scat, from suspension (LSS)

0.90O±0.012 single part, scattering (SPS) 0.898±0.020 opt. array sizing (OAS)

o-f.jum 0.0095±0.002 TEM, 0.010 SPS, 0.013 OAS, 0.029 LSS,

0.033 Coulter Counter % doublets % large off-size

particles % "new" particles % asphericity number concentration

index of refraction sample variability

1.5±0.4

0.1 0.6+0.2

0.6±0.3 1.3+0.2X 10" 1.612+0.009

0.0005 p,m

0.0009 fxm

part/cmCoulter Counter

Coulter Counter TEM TEM

Coulter

single particle scattering

light scat, from

suspension Coulter Counter

'The first value in each case is the best estimate.

20
97.8%

1.5% doublets

Figure 13-Global size distribution. 0.1% large

spheres

0.3 1.0 3.0 DIAMETER, ^im

0.0095 jam to 0.033 jam. This is because each instrument

has a sigma associated with repeat measurements of the same objects, cr„ and measured values of crp given in table 10 represent a combined effect of the cr of the true

size distribution and cr,. The single-particle scattering measurement has the smallest cr„ 0.002 \xm, but the statistical uncertainty due to the small number of particles measured (eight) limits the accuracy of (Xp. The best estimate of cr comes from TEM with a slightly larger

cr,, about 0.003-0.004 \xm, compared to the single particle measurements, but this is offset by the improved

statistics from a much larger sample size (100). The large values of cr, for the other instruments result from the dependence of the electrical pulse on the particle tra- jectory through the orifice for the Coulter Counter, the presence of doublets and off-size particles for light- scattering measurements of a particle suspension, and

array nonuniformities for the case of optical array siz- ing.Each measurement method requires a slightly differ- ent sample preparation. A necessity in almost all cases is particle free water for dilution. We found 18 megohm- cm deionized water passed through a 0.2 jam pore size

filter to be adequate for our measurements. Clean glass- ware is a necessity for diluting the samples and a clean

optical cell free of water marks is required to obtain good light scattering data. As described in section 3, we

used both detergent and hot, concentrated nitric acid for cleaning our glassware. In the case of diluting a sample,

especially if an electrolyte is used, there is always the

possibility of promoting agglomeration through the re- duction in the electrostatic repulsion between the particles. We found that even for a 1 % by weight solution of sodium chloride little agglomeration occurred in an hour for a particle concentration of about 10* part/cm^

if the electrolyte were introduced only at the final dilu- tion stage as described in subsection 5.2.

7. Concluding Remarks

Our measurements have resulted in a particle size standard with an uncertainty in particle diameter of about 0.8%. Modest improvements in sizing accuracy,

say a twofold reduction in uncertainty, may be possible with the existing techniques. About half the total uncertainty in the scattering measurements for suspensions is associated with the uncertainty in the refractive index. The refractive index of liquids is known to an uncertainty of a few parts in 10^ while the uncertainty in the

refractive index of the polystyrene spheres is a few parts

in 10\ It is possible that at least a tenfold reduction in the uncertainty in the refractive index of the spheres could be achieved by index matching the spheres with a liquid. A second improvement would be to remove the ag- glomerated doublets by sedimentation before per- forming the scattering measurements. An accurate value of the refractive index of the poly- styrene spheres would also improve the sizing capabilities of single particle scattering measurements since there would be only one unknown parameter, the particle diameter, to be determined from the scattering measurements. We have found that the sizing resolution improves by a factor of two to three if the refractive index is fixed when performing the data analysis. The

single greatest source of uncertainty arises from the small number of particles sized (eight); this component

of the error could be cut in half if 40 particles were sized. Half of the uncertainty for optical array sizing results from smaller particles not touching neighboring particles and from slight flattening of the spheres on contact. Hartman [32] has demonstrated that it is possible to make square arrays of particles, where, unlike in- hexagonal arrays, every particle is in contact with its neighbors. A systematic analysis of such arrays is possi- ble but would be time-consuming because of the rela21
lively rare occurrence of square arrays. A quantitative

analysis of flattening could be made by transmission

electron microscopy if arrays could be prepared on TEM grids. Major improvements in sizing accuracy, say a tenfold reduction in uncertainty, will require a more detailed characterization of the particle structure. Specific structural information of intercut includes particle shape, es- pecially in regard to deviation from sphericity, particle inhomogeneity in regard to a variable index of refraction within the particle, and the surface structure both

for particles in suspension where an electrical double

layer exists and in aerosol form where nonvolatile impurities coat the surface. The pertinent structural infor- mation must also be included in the light scattering the- ory for determining particle size from scattering

intensity as a function of angle. Of course, if particles could be made with a high degree of sphericity and low

inhomogeneity within the particle, the analysis would

be simplified. Ultimately it is planned to develop particle size stan- dards over the diameter range of 0.1 to 100 jLx.m. For

such a wide range, a variety of techniques will be used. One promising instrument for larger particle sizes in- volves optical interferometry coupled to an electron microscope. One of us (G.G. Hembree) has developed

such an instrument with a piezoelectric stage, the dis- placement of which is monitored interferometrically with an uncertainty on the order of 0.02 jiim. Another

technique for larger particles consists of the measurement of resonances in the polarization ratio of scat- tered light. Lettieri et al. [33] measured the diameter of

droplets in the size range 6 to 12 jam to a resolution of

0.003 fim using this technique. Work is currently in progress to develop a nominal

0.3 jLim particle size standard. In this case, quasielastic scattering is being used in conjunction with transmission

electron microscopy with the magnification calibration based on the 0.895 jxm spheres (SRM 1690).

References

[1] Swyt, D. A. A look at techniques for the dimensional calibration of standard microscopic particles. Natl. Bur. Stand. (U.S.) Spec. Publ. 260-85 (1983).

[2] Phillips, D. T.; P. J. Wyatt and R. M. Berkman. Measurement of

the Lorenz-Mie scattering of a single particle: polystyrene

latex. J. Colloid Interface Sci, 34: 159 (1970).

[3] Rowell, R. L.; R. S. Farinato, J. W. Parsons, J. R. Ford, K. H.

Langley, J. R. Stone, T. R. Marshall, C. S. Parmenter, M.

Seaver and E. B. Bradford. Polystyrene latex particle size by electron microscopy and light scattering. J. Colloid In- terface Sci. 69(3): 590-595 (1979).

[4J Bierhuizen, H. W. J., and G. A. Ferron. Determination of the diameter of two monodisperse lattices by the free fall

method and the length of particle arrays. J. Aerosol Sci. 6: 19-21 (1975).

[51 Gulari, Es.; Er. Gulari, Y. Tsunashima, and B. Chu. Photon

correlation spectroscopy of particle distributions. J. Chem.

Phys. 70: 3965-3972 (1979).

[6] Bonse, J., and M. Hart. Small angle x-ray scattering by spherical

particles of polystyrene and polyvinyltoluene. J. Phys. 189:

151 (1966).

[7] Davidson, J. A.; C. W. Macosko and E. A. Collins. Latex particle size analysis I. flow microscopy. J. Colloid Interface

Sci. 25: 381-388 (1967).

[8] van den Hul, H. J., and J. W. Vanderhoff. "Clean" monodisperse latexes as model colloids, chapter 1 in Polymer Colloids. R. M. Fitch, ed. New York, NY: Plenum Press (1971)

pp. 1-27.

[9] Wyatt, P. J., and D. T. Phillips. A new instrument for the study

of individual aerosol particles. J. Colloid Interface Sci. 39(1): 125-135 (1972).

[10] Cooke, D. D., and M. Kerker. Particle size distribution of colloidal suspensions by light scattering based upon single particle counts—polystyrene latex. J, Colloid Interface Sci. 42(1): 150-155 (1973),

[11] McRae, D. D. The refractive index of individual cigarette smoke droplets. J. Colloid Interface Sci. 87: 1 17-123 (1982).

[12] Davis, E. J., and P. Ravindran. Single particle light scattering measurements using the electrodynamic balance. Aerosol

Sci. and Tech. 1: 337-350 (1982).

[13] Bottiger, J. R.; E. S. Fry and R. C. Thompson. Phase matrix measurements for electromagnetic scattering by sphere ag- gregates in light scattering by irregularly shaped particles. D. W. Shuerman, ed: New York: Plenum Press (1980) pp. 280-290.

[14] Marx, E., and G. W. Mulholland. Size and refractive index determination of single polystyrene spheres. J. Res. Natl. Bur. Stand. (U.S.) 88: 321-338 (1983).

[15] Mie, G. A contribution to the optics of turbid media, especially

colloidal metallic suspensions. Ann. Physik 25: 337-445

(1908).

[16] Born, M., and E. Wolf Principles of optics. Oxford: Pergamon

Press (1980).

[17] Kerker, M. The scattering of light and other electromagnetic

radiation. New York: Academic Press (1969).

[18] Wims, A. M., and M. E. Myers, Jr. An automated, laser light- scattering photometer (0.1 to 170° range) with a single photon counting system. J. Colloid Interface Sci. 39(3): 447-461

(1972).

[19] Matheson, L. A., and J. L. Saunderson. Optical and electrical properties of polystyrene, chapter 1 1 in Styrene: its poly- mers, copolymers, and derivatives, R. H. Boundy and R. F. Boyer, ed. New York, NY: Reinhold Publishing Corp.

(1952) 524.

[20] Tilton, T. W., and J. K. Taylor. Refractive index and dispersion of distilled water for visible radiation of temperatures 0 to 60° C. J. Res. Natl. Bur. Stand. (U.S.) 20: 419 (1938).

[21] Starkie, D. Brit. Plastics 19: 46 (1946).

[22] Smart, C. and E. Willis. Determination of refractive indices of polystyrene latices by light scattering. J. Colloid Interface

Sci. 25: 577-583 (1967).

[23] Heller, W, and T. L. Pugh. Experimental investigations on the

effect of light scattering upon the refractive index of colloidal paticles. J. Colloid Interface Sci. 12: 299-307 (1957).

[24] Napper, D. H., and R. H. Ottewill. Multiple scattering effects in polystyrene latex dispersions. J. Colloid Interface Sci. 19: 72-80 (1964).

[25] Perrin, M. J. Brownian movement and molecular reality, An22
nales de Chimie et de Physique, 8"" series, (1909) translated by F. Soddy. London: Taylor and Francis (1910).

[26] Kubitschek, H. E. Array method of sizing monodisperse particles, in Ultrafine particles, W. E. Kuhn, ed. Wiley (1961)

p. 438.

[27] Kubitschek, H. E. Optical calibration of some monodisperse

polystyrene latexes in arrays. Nature 192: 1 148-1 150 (1961).

[28] Barnett, V., and T. Lewis. Outliers in statistical data. New York: Wiley (1978) p. 101.

[29] Allen, T. Particle Size measurements. London: Chapman and

Hall (1975).

[30] Thorn, von R. Vergleichende untersuchungen zur elec- ktronischen zillvolumen-analyse, AEG-Telefunken report, Ulm, Germany, (around 1970).

[31] Spielman, L. and S. L. Goren. Improving resolution in Coulter counting by hydrodynamic focusing. J. Colloid Interface

Sci. 26: 175-182 (1968).

[32] Hartman, A. W. Experimental confirmation of the Kubitschek

effect. Journal of Powder Technology, in press.

[33] Lettieri, T. R.; W. D. Jenkins and D. A. Swyt. Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio. Appl. Opt.

20: 2799-2805 (1981).

[34] Blackley, D. C. Emulsion polymerisation theory and practice. New York; Wiley (1975).

[35] Verwey, E. J. W., and J. Th. G. Overbeek. Theory of stability of lyophobic colloids. New York: Elsevier (1948).

APPENDIX

Preparation and Stability of Polystyrene Sphere Suspensions

Preparation—The procedure used by Dow Chemical

Co. to produce monosize polystyrene spheres is known

as emulsion polymerization. A brief description of the general process is provided here, though the specific emulsifying agent and chemical initiator used by Dow

are confidential. A more detailed description of emulsion polymerization is given by Blackley [34]. Emulsion polymerization involves four components:

water, styrene monomer, an emulsifying agent, and a

free radical initiator. A typical emulsifying agent is so- dium lauryl sulfate. The emulsifier will permit the dis- persion of the stirred monomer phase into a stable sys- tem of micrometer-size droplets. At a sufficiently high

concentration of emulsifier, hydrated aggregates called

micelles, made up of 50 to 100 molecules of emulsifier,

will form. The concentration of micelles is approxi- mately six orders of magnitude greater than that of the monomer droplets. The polymerizafion reaction begins when the free radical initiator is heated to sufficiently high temperature to dissociate into radical ions. This is around 50 °C for persulfate anions. The sulfate radical anions at- tack the styrene dissolved in the aqueous phase to form new ion radicals. The polymer chain begins growing by

the addition of more styrene molecules to the radicals in the aqueous phase. The polymer-containing radicals soon enter the micelles where propagation of the chain

is continued by attack on the monomer within the micelle. The growth of the polymer chain is supported by

the rapid diffusion of the styrene from the droplets into the growing micelles. This growth is terminated by re- action with a second free radical. At this point the chain polymer may have reached a molecular weight on the order of 10*. Later the chain growth is reinitiated by

another radical, and this process will continue until most

of the styrene is consumed. While the polymer growth is a chain process, the intermolecular forces and surface tension lead to a spherical shape analogous to a ball of string. The nar- rowness of the size distribution results from the uni- formity of styrene concentration throughout the reactor and the growth time being long compared to the ini- tiation time. The concentration of the initiator and emulsifier are also important for obtaining a narrow size dis- tribution. Too much emulsifier can lead to new particle formation. This is especially true when small poly- styrene spheres are used as seed particles for growing

larger ones. The growth of 1-ju.m-diameter spheres for SRM 1690 required the use of seed particles, and there was evidence of a new generation of small particles.

Stability—The electrostatic charge on the surface of

the particles, created by the outward pointing ionic endgroups, is crucial to the stability of the suspension. Changes in the surface layer can lead to agglomeration

of the spheres. Dilution and the addition of electrolyte, required for some of the measurement techniques, can

affect the stability of the suspension. The VerweyOverbeek theory [35] describes the stability of colloidal suspensions in terms of the electrostatic forces of re- pulsion between colloidal particles and London-van der Waals forces of attraction. The electrostatic repulsion

arises from the surface charge; for example, from the adsorbed emulsifier ions. The repulsion is greatest at the point of contact between the electrical double layers on

the two particles. This is on the order of a nanometer

from the polymeric surface, since the ionic portion of

23
the emulsifier is directed away from the sphere. At

greater distances between the particles' centers, the re- pulsion drops off exponentially. The magnitude of the

repulsion depends on the surface particle charge and

electrolyte concentration. The London-van der Waals

forces are greatest close to the particle surface (a few

tenths of a nanometer from the polymeric surface) and

are not strongly affected by the surface charge of elec- trolyte concentration. Of course, there are very strong

repulsive forces as the polymeric molecules of two

spheres come in contact. The sum of these three forces leads to a potential with

a minimum at short distances, a repulsive barrier due to

electrostatic ^pu'sion at -reater dist 'nces, and possibly

a second minimum at relatively large distances, resulting from the longer range of the London-van der Waals

forces. If the particle has suflicient energy to penetrate

the electrostatic barrier of another particle, the two particles will stay together in an aggregate. An increase in the electrolyte concentration or a decrease in the sur- face charge density caused by diluting the suspension with electrolyte will lower the repulsive barrier and may lead to agglomeration. Such an effect was a concern in the electrical-sensing zone counter measurments

as discussed in subsection 5.2, since the particle sus- pension was diluted with electrolyte.
NBS-n4A iREv. 2-8C

U.S. DE'^'T. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See inst'jctiors.i

1. PUBLICATION OR REPORT NO. NBS/SP-260/95

2. Performinf Organ. Report No, 3. Publication Date May 1985

4. -TITLE AND SUBTITLE Standard Reference Materials: Development of a One-Micrometer-Diameter

Particle Size Standard, SRM 1690

5. AUTHOR(S)

G. W. Mulholland, A. W. Hartman, G. G. Hembree , E. Marx, and T. R. Lettieri

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. National Bureau of Standards

U.S. Department of Commerce 8. Type of Report & Period Covered Gaithersburg, MD 20899 Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State. ZIP) Same as item 6

10. SUPPLEMENTARY NOTESLibrary of Congress Catalog Card Number: 85-600539

1

I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information . Ij document inclucies a si gnificont

bi bliogra^hy or literature survey, motion it here) The average diameter of the first micrometer particle size standard (Standard Reference Material 1690), an aqueous suspension of monosized polystyrene spheres

with a nominal 1 ym diameter, was accurately determined by three independent

techniiques. In one technique the intensity of light scattered by a diluted

suspension of polystyrene spheres was measured as a function of scattering angle,

using a He-Ne laser polarized in the vertical direction. The second technique con- sisted of measuring the intensity of light scattered from individual polystyrene

spheres suspended in air as a function of angle, using a He-Cd laser with light

polarized parallel and perpendicular to the scattering plane. The measurement of row length by optical microscopy for polyst5rrene spheres arranged in close-packed,

two-dimensional hexagonal arrays was the basis of the third technique. The measurement errors for each technique were quantitatively assessed. For the light

scattering experiments, this required simulation with numerical experiments. The average diameter determined by each technique agreed within 0.5/^ with the most accurate value being 0.895 + 0.007 ym based on light scattering by an aqueous

suspension. Transmission electron microscopy, flow through electrical sensing zone counter measurements, and opLical microscopy were also used to obtain more detailed

information on the size distribution including the standard deviation (0.0095 ym) , fraction of off-size particles, and the fraction of agglomerated doublets (1.5%).

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) array sizing; index of refraction; light scattering; Mie scattering; particle

counting; particle size standards; polystyrene spheres; size distribution;

transmission electron microscopy

13. AVAILABILITY

rxi Unlimited

I

I For Official Distribution. Do Not Release to NTIS

[~Xl Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. on Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF PRINTED PAGES

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15. Price

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technical and scientific programs. Issued six times a year.

Nonperiodicals

Monographs—Major contributions to the technical literature on various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other

special publications appropriate to this grouping such as wall charts, pocket cards, and bibliographies. Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and

technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide pro- gram coordinated by NBS under the authority of the National Standard Data Act (Public Law 90-396). NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is pubUshed quarterly for NBS by

the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints, and supplements are available from ACS, 1155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials, components, systems, £ind whole structures. The series presents research results, test methods, and perfor- mance criteria related to the structural and environmental functions and the durability £ind safety

characteristics of building elements and systems. Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject

area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies. Voluntary Product Standards—Developed under procedures published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations. The standards establish nationally recognized re- quirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private

sector standardizing organizations. Consumer Information Series—Practical information, based on NBS research and experience, covering areas of interest to the consumer. Easily understandable language and illustrations provide useful background

knowledge for shopping in today's technological marketplace. Order the above NBS publications from: Superintendent of Documents, Government Printing Office, Washington, DC 20402. Order the following NBS publications—FIPS and NBSIR 's—from the National Technical Information Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the official source of

information in the Federal Government regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 1 1717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations). NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS

for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service, Springfield, VA 22161, in paper copy or microfiche form.
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