1、Designation: E 2490 09Standard Guide forMeasurement of Particle Size Distribution of Nanomaterialsin Suspension by Photon Correlation Spectroscopy (PCS)1This standard is issued under the fixed designation E 2490; the number immediately following the designation indicates the year oforiginal adoption
2、 or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide deals with the measurement of particle sizedistribution of suspen
3、ded particles, which are solely or pre-dominantly sub-100 nm, using the photon correlation (PCS)technique. It does not provide a complete measurement meth-odology for any specific nanomaterial, but provides a generaloverview and guide as to the methodology that should befollowed for good practice, a
4、long with potential pitfalls.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations
5、 prior to use.2. Referenced Documents2.1 ASTM Standards:2E 177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE 1617 Practice for Reporting Particle Size Characteriza-tion DataF 1877
6、 Practice for Characterization of Particles2.2 ISO Standards:ISO 13320-1 Particle Size AnalysisLaser DiffractionMethodsPart 1: General Principles3ISO 14488 Particulate MaterialsSampling and SampleSplitting for the Determination of Particulate Properties3ISO 13321 Particle Size AnalysisPhoton Correla
7、tionSpectroscopy33. Terminology3.1 Definitions of Terms Specific to This StandardSome ofthe definitions in 3.1 will differ slightly from those used withinother (non-particle sizing) standards (for example, repeatabil-ity, reproducibility). For the purposes of this Guide only, weutilize the stated de
8、finitions, as they enable the isolation ofpossible errors or differences in the measurement to be as-signed to instrumental, dispersion or sampling variation.3.1.1 correlation coeffcient, nmeasure of the correlation(or similarity/comparison) between 2 signals or a signal anditself at another point i
9、n time.3.1.1.1 DiscussionIf there is perfect correlation (the sig-nals are identical), then this takes the value 1.00; with nocorrelation then the value is zero.3.1.2 correlogram or correlation function, ngraphicalrepresentation of the correlation coefficient over time.3.1.2.1 DiscussionThis is typi
10、cally an exponential decay.3.1.3 cumulants analysis, nmathematical fitting of thecorrelation function as a polynomial expansion that producessome estimate of the width of the particle size distribution.3.1.4 diffusion coeffcient (self or collective), na measureof the Brownian motion movement of a pa
11、rticle(s) in amedium.3.1.4.1 DiscussionAfter measurement, the value is beinputted into in the Stokes-Einstein equation (Eq 1, see7.2.1.2(4). Diffusion coefficient units in photon correlationspectroscopy (PCS) measurements are typically m2/s.3.1.5 Mie region, nin this region (typically where the size
12、of the particle is greater than half the wavelength of incidentlight), the light scattering behavior is complex and can only beinterpreted with a more rigorous and exact (and all-encompassing) theory.3.1.5.1 DiscussionThis more exact theory can be usedinstead of the Rayleigh and Rayleigh-Gans-Debye
13、approxima-tions described in 3.1.7 and 3.1.8. The differences between theapproximations and exact theory are typically small in the size1This guide is under the jurisdiction of ASTM Committee E56 on Nanotech-nology and is the direct responsibility of Subcommittee E56.02 on Characterization:Physical,
14、 Chemical, and Toxicological Properties.Current edition approved April 1, 2009. Published June 2009. Originallyapproved in 2008. Last previous edition in 2008 as E 249008.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Ann
15、ual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C7
16、00, West Conshohocken, PA 19428-2959, United States.range considered by this standard. Mie theory is needed inorder to convert an intensity distribution to one based onvolume or mass.3.1.6 polydispersity index (PI), ndescriptor of the widthof the particle size distribution obtained from the second a
17、ndthird cumulants (see 8.3).3.1.7 Rayleigh-Gans-Debye region, nin this region (statedto be where the diameter of the particle is up to half thewavelength of incident light), the scattering tends to theforward direction, and again, an approximation can be used todescribe the behavior of the particle
18、with respect to incidentlight.3.1.8 Rayleigh region, nsize limit below which the scat-tering intensity is isotropicthat is, there is no angulardependence for unpolarized light.3.1.8.1 DiscussionTypically, this region is stated to bewhere the diameter of the particle is less than a tenth of thewavele
19、ngth of the incident light. In this region a mathematicalapproximation can be used to predict the light-scatteringbehavior.3.1.9 repeatability, nin PCS and other particle sizingtechniques, this usually refers to the precision of repeatedconsecutive measurements on the same group of particles andis n
20、ormally expressed as a relative standard deviation (RSD) orcoefficient of variation (C.V.).3.1.9.1 DiscussionThe repeatability value reflects the sta-bility (instrumental, but mainly the sample) of the system overtime. Changes in the sample could include dispersion (de-sired?) and settling.3.1.10 re
21、producibility, nin PCS and particle sizing thisusually refers to second and further aliquots of the same bulksample (and therefore is subject to the homogeneity or other-wise of the starting material and the sampling method em-ployed).3.1.10.1 DiscussionIn a slurry system, it is often thelargest err
22、or when repeated samples are taken. Other defini-tions of reproducibility also address the variability amongsingle test results gathered from different laboratories wheninter-laboratory testing is undertaken. It is to be noted that thesame group of particles can never be measured in such asystem of
23、tests and therefore reproducibility values are typi-cally be considerably in excess of repeatability values.3.1.11 robustness, na measure of the change of therequired parameter with deliberate and systematic variations inany or all of the key parameters that influence it.3.1.11.1 DiscussionFor examp
24、le, dispersion time (ultra-sound time and duration) almost certainly will affect thereported results. Variation in pH is likely to affect the degree ofagglomeration and so forth.3.1.12 rotational diffusion, na process by which theequilibrium statistical distribution of the overall orientation ofmole
25、cules or particles is maintained or restored.3.1.13 translational diffusion, na process by which theequilibrium statistical distribution of molecules or particles inspace is maintained or restored.3.1.14 z-average, nharmonic intensity weighted averageparticle diameter (the type of diameter that is i
26、solated in a PCSexperiment; a harmonic-type average is usual in frequencyanalyses) (see 8.9).3.2 Acronyms:3.2.1 APDavalanche photodiode detector3.2.2 CONTINmathematical program for the solution ofnon-linear equations created by Stephen Provencher and ex-tensively used in PCS (1)43.2.3 CVcoefficient
27、of variation3.2.4 DLSdynamic light scattering3.2.5 NNLSnon-negative least squares3.2.6 PCSphoton correlation spectroscopy3.2.7 PMTphotomultiplier tube3.2.8 QELSquasi-elastic light scattering3.2.9 RGBRayleigh-Gans Debye4. Summary of Guide4.1 This Guide addresses the technique of photon correla-tion s
28、pectroscopy (PCS) alternatively known as dynamic lightscattering (DLS) or quasi-elastic light scattering (QELS) usedfor the measurement of particle size within liquid systems. Toavoid confusion, every usage of the term PCS implies that DLSor QELS can be used in its place.5. Significance and Use5.1 P
29、CS is one of the very few techniques that are able todeal with the measurement of particle size distribution in thenano-size region. This Guide highlights this light scatteringtechnique, generally applicable in the particle size range fromthe sub-nm region until the onset of sedimentation in thesamp
30、le. The PCS technique is usually applied to slurries orsuspensions of solid material in a liquid carrier. It is a firstprinciples method (that is, calibration in the standard under-standing of this word, is not involved). The measurement ishydrodynamically based and therefore provides size informa-t
31、ion in the suspending medium (typically water). Thus thehydrodynamic diameter will almost certainly differ from othersize diameters isolated by other techniques and users of thePCS technique need to be aware of the distinction of thevarious descriptors of particle diameter before making com-parisons
32、 between techniques. Notwithstanding the precedingsentence, the technique is widely applied in industry andacademia as both a research and development tool and as a QCmethod for the characterization of submicron systems.6. Reagents6.1 In general, no reagents specific to the technique arenecessary. H
33、owever, dispersing and stabilizing agents often arerequired for a specific test sample in order to preserve colloidalstability during the measurement. A suitable diluent is used toachieve a particle concentration appropriate for the measure-ment. Particle size is likely to undergo change on dilution
34、, asthe ionic environment, within which the particles are dispersed,4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.E2490092changes in nature or concentration. This is particularly notice-able when diluting a monodisperse latex. A latex that ismeasured
35、 as 60 nm in 1 3 10-3M NaCl can have a hydrody-namic diameter of over 70 nm in 1 3 10-6M NaCl (close todeionized water). In order to minimize any changes in thesystem on dilution, it is common to use what is commonlycalled the “mother liquor”. This is the liquid in which theparticles exist in stable
36、 form and is usually obtained bycentrifuging of the suspension or making up the same ionicnature of the dispersant liquid if knowledge of this material isavailable. Many biological materials are measured in a buffer(often phosphate), which confers the correct (range of) condi-tions of pH and ionic s
37、trength to assure stability of the system.Instability (usually through inadequate zeta potential (2) canpromote agglomeration leading to settling or sedimentation ina solid-liquid system or creaming in a liquid-liquid system(emulsion). Such fundamental changes interfere with the sta-bility of the su
38、spension and need to be minimized as they affectthe quality (accuracy and repeatability) of the reported mea-surements. These are likely to be investigated in any robustnessexperiment.7. Procedure7.1 Verification:7.1.1 The instrument to be used in the determination shouldbe verified for correct perf
39、ormance, within pre-defined qualitycontrol limits, by following protocols issued by the instrumentmanufacturer. These confirmation tests normally involve theuse of one or more NIST-traceable particle size standards. Inthe sub-micron ( 60 nm)the light starts to be scattered towards the forward anglei
40、nlaymans terms it becomes egg-shaped with more forward thanback-scatterand up to l/2 ( 300 nm for a He-Ne laser at632.8 nm) then the Rayleigh-Gans-Debye approximationworks well as there is little structure to the observed polarpattern of scattering. Thus, in the 100 nm present in the sample (and thu
41、sthe distribution is broader than “monodisperse”). The situationis likely to be simpler (smaller values of polydispersity index)FIG. 1 Diagrammatic Representation of the Intensity Fluctuations with Small and Large ParticlesFIG. 2 Traditional PCS Measurement Indicating the Main Components of a Typica
42、l SystemE2490096for samples that are 100 % 100 nm and therefore not relevant to this Guide) thereis then a variation in scattering intensity with angle (thescattering is non-isotropic in contrast to the sub-100 nm(approximate) regime. Any angular variation in scattering canbe used (along with the kn
43、own optical properties of theparticulate system), in theory at least, to obtain particle sizedistribution information. This area (0.1 m and higher) is nowthe preserve of “laser diffraction” (for example, seeISO 13320-1) where light scattering is involved and a range ofother non-optical techniques (f
44、or example, sedimentation,sieves, electrical sensing zone) dependent on the size range ofthe system.8.4 Carrying Out the Measurement:8.4.1 A generic diagram is shown in Fig. 3.8.4.2 Fig. 3 shows the “classic” design where scattered lightis detected at a variable angle (often 90), although for dilute
45、small systems ( 0.7) then the sample is unlikely to be suitable forPCS and is not likely to give a stable distribution with time.8.10 Conversion of the Intensity Distribution to OtherParticle Size Distributions:8.10.1 In mathematical terms, this deconvolution is termedill-posed or ill-conditioned th
46、at means, in practical terms that itis ill advised. Small changes in collected data can give rise toenormous changes in derived result and as such treat anyderived result with caution and skepticism. To convert fromintensity to volume distribution would involve the manipula-tion of perfect noise-fre
47、e experimental data with accuratelymeasured refractive indices using Mie theory. A further con-version to number should never be attempted. If a numberdistribution is desired then an instrument that collects suchinformation should be used in the first place.8.10.2 The wider the initial distribution
48、the more serious arethe errors in the conversion, and we have previously shownthat the given solution(s) are derived from ill-posed mathemati-cal problems and thus possibly subject to unbounded errors.8.10.3 Notwithstanding the above caveats and cautions,conversion to a volume-weighted distribution
49、can often pro-vide an indication of the relative importance (prominence) oftwo or more reported peaks. A common situation is to see anapparently dominant large-size peak virtually disappearing anda low-intensity smaller-sized peak becoming the primary modeafter conversion to volume weighting. This conversion tends tobe relatively insensitive to the refractive index (the additionalparameter required for the conversion) except when the particleand medium have very similar values for the real refractiveindex ( 0.03).9. Report9.1 See Pract
