Particle Standards : Their Development and Application +

With the increase in the importance of dispersed materials (powders, aerosols, emulsions etc.) to trade, there is an increasing awareness of the need to verify that instruments which measure particle properties, particularly size, are operating within defined limits of accuracy. As a minimum, this process requires some form of verification with reference to standard particles whose properties are known in relation ultimately to the international standards of mass and length (so-called traceability chain). In some cases, a formal calibration to establish instrument response in terms of size, shape or concentration may be required. This article reviews the particle standards that are available to establish the performance of measurement equipment, placing most emphasis on particle size, as this is the variable that is generally of most importance to industry. However, secondary properties, such as shape, density and refractive index, influence the response of many types of particle size analyzer. Attempts to provide standard materials that may enable independent assessment to be made of the effect of some of these variables on instrument performance are therefore also considered.


Introduction 1.1 Background
There is an increasing awareness that instruments used to measure the properties of disperse systems (powders, aerosols, particles suspended in liquid etc.) cannot by themselves provide absolute values.Quality systems, such as the ISO 9000 series [1] require that the performance of instrumentation used in the measurement of properties deemed critical to the process for which the materials under investigation are being used, be verified on a regular basis as part of a method validation process, or standard operating procedure (SOP).The intention behind this requirement is to enable measurements made on a particular product at one location to be reproducible within well-defined limits anywhere else.Standard or reference materials (RMs) that are particle-based have an important part to play in this process.

Concept of Particle Size
The definition of 3-dimensional particle size itself requires clarification before proceeding to look at particle standards.The concept of particle diameter has unambiguous physical meaning only for spherical particles.It is not possible to define a single diameter that describes the geometric size of particles that are irregular-shaped, which comprise the vast majority of t Received: May 16, 2000 KONA No. 18 (2000) cases where measurements are sought.There are many techniques that can be used to measure particle size; some are more suited to liquid-based particle systems [2] (coarse particle suspensions and colloids) and others are applicable to gas-based systems [3] (aerosols).Each technique measures a particular dimension that is dependent on the measurement principle (Table 1).Hawksley has postulated that there are only three fundamental diameters [4]: • volume equivalent diameter (Dv): the diameter of a sphere having the same volume as the particle being studied • surface equivalent diameter CD a): the diameter of a non-porous sphere having the same surface area as the particle being studied • drag or Stokes diameter (D 51 ): the diameter of a sphere having the same resistance to motion as the particle in question, in a fluid of the same viscosity More recently, Scarlett [5] has presented a view that Dv is the most basic parameter to choose as the calibrating size, because it is directly proportional to the quantity of matter in the particle, regardless of shape.Da has limited use, except in applications where surface properties (e.g.catalysis) are under consideration.Ds 1 is not strictly a fundamental diameter, but one of a series of equivalent sphere diameters (including aerodynamic and mobility diameters) that relate to the interaction of a particle of any shape with the fluid within which it is contained.Dst is measured stg [1] where PP is the particle density and Uts is the particle terminal settling velocity, Pb and P11 are the particle density immersed in the fluid and fluid density respectively, 11 is fluid viscosity and g, acceleration due to gravity.Dv and Dst are related through the expression [3]: where x is a correction that adjusts for the effect of 3-dimensional particle shape on sedimentation behavior (dynamic shape factor).X is unity for spheres, and always exceeds this value for irregular-shaped particles.It may also have more than one value for certain shapes (e.g.spheroids), depending upon their orientation with respect to their motion in the suspending fluid [6].
Particle size analysis techniques that operate on other measurement principles measure one of several different equivalent sphere diameters (Table 1 each of which can ultimately be related to Dv. though not necessarily in the form of a simple relationship, such as that given by equation [2].It follows that the response of particle size analysis equipment to irregular particles with few exceptions is modified by shape (as well as in some cases by bulk properties such as density, porosity etc.).This behavior becomes especially important when it becomes necessary to compare data from instruments that operate on different principles, a not uncommon situation.The question to be posed is 'can particle standards provide meaningful reference values to enable such comparisons to be made accurately?'The answer depends on the properties of the standards themselves, and the approach taken to verify analyzer performance (Section 1.3).Size-based standard particles are the most widely used RMs, and several options are available for their use.
Reference particles which have specific non-spherical shapes (so-called 'particle shape standards' are considered separately from particles used in connection with particle sizing (Section 4.1), as their function in performance verification is fundamentally different.

Verification of Sizing Accuracy
There are two distinctly different approaches that can be taken to verify the accuracy of measurements based on particle size, on which this article is primarily focused.
In one approach, particle standards produced from bulk powders, whose size distributions and related properties (e.g.density) have been corroborated by independent laboratories, are used as so-called 'certified reference materials' (CRMs).The particles may be spherical or of irregular shape, but their range of size will be chosen to encompass the measurement range of the instrument being evaluated.This process is termed performance verification.The attractiveness of this process to industry is obvious; it is usually rapid to carry out, as only a single RM is normally required for the purpose, and analyzers operating on different measurement principles can be readily compared.
Performance verification should be distinguished from instrument calibration, which is the other approach for which particle standards are widely used.The calibration process in its most generic form, involves measurement of analyzer response and associated bias conversion factor, when presented with particles having known size properties by an independent procedure that is traceable ultimately to the international standard of length.The various documented international (Table 2) and national (Table 3) standards that relate to many of the particle size analysis methods in widespread use generally call for the use of standard particles as part of the calibration or performance verification process, particularly in instances where the instrument response is not a straightforward monotonic function of particle size.Even techniques, such as laser diffractometry (low-angle laser light scattering (LALLS)), which provide volumeweighted size distribution data for spherical particles by rigorous solution of Lorenz-Mie equations [7], so that formal calibration is not strictly necessary, should ideally be validated on a regular basis with particle size-based RMs [8], or at least by the use of a suitable reticle [9].The purpose of such measurements is as a check on the continued stability of the complete measurement system, including the software.The precise requirements for such RMs will vary from one instrument type to another.In the case of laser diffractometers, the ideal RMs should be spherical with maximum light absorption to avoid anomalous responses due to light reflection and refraction, and for examining liquid-based suspensions at least, the particle density should be close to that of the dispersion fluid [8].Their size distribution should also be preferably uni-modal and log-normal.Rothele and Witt [8] have gone as far as to provide indicative size distributions for 3-CRMs that might be developed specifically for this class of analyzer with the following size distribution properties based on Dv: • CRMl: range 0.1-10 11m: D 10 0.126 IJ.m, D 50 1.00;D 90 7.941J.m• CRM2: range 1.0-100 11m: D 10 1.261J.m,D 50    (BCR) will come close to meeting these criteria (Section 2.3).
The calibration process can be considerably more time consuming than performance verification, as it is necessary to utilize more than one RM to gauge the sensitivity of the response function to change in particle size.It is important that the properties of the RMs likely to be used for calibration purposes (particularly their shape, but also other properties that relate to the instrument response e.g.density in the case of techniques that measure Stokes or aerodynamic diameter) are well specified.In general, the most useful RMs for this activity will therefore be formulated from spherical, rather than irregular-shaped particles.

RM Hierarchy
It is useful to consider the hierarchy of particle size standards as having the form of an equilateral triangle (Figure 1), in which the international standard of length as the fundamental unit pertaining to size, forms the apex.Immediately beneath are the limited range of certified or standard reference materials (CRMs or SRMs) produced by governmental agencies, usually in partnership with industry and academia.CRMs/SRMs have been subjected to rigorous inter-laboratory evaluation by independent methods that are directly traceable to international standards, and are normally supplied with a data report in which their specification is defined.These standards are available in limited amounts and the process of certification, being labor intensive, results in their high cost.A compromise between the rigor of a formal certification process and the need for standards in appropriate quantities at reasonable cost is therefore necessary, resulting in the growth of secondary standard materials (SSMs).These calibrants are available from many sources, making them particularly useful for processes where frequent calibration is necessary or with techniques, such as sieve analysis, where rela- Calibration hierarchy in terms of particle size standards tively large quantities of calibrant is needed to achieve acceptable precision in the size analysis process.
There is often less information available on the properties of SSMs, other than size distribution, more often than not measured by a single technique.At the lowest level in the hierarchy are so-called tertiary standards.These particles are prepared in-situ for calibration purposes, frequently by aerosol generation methods.The twin advantages of tertiary standards are their low relative cost (although the equipment used to create the aerosol can be expensive), and the convenience in being able to both control and vary particle size within fairly wide limits.In some cases, it may be possible to control other properties, such as shape, density and refractive index, each of which may modify the response of the equipment under calibration.Since the process is essentially local to the laboratory undertaking the calibration, inter-laboratory data are by definition unavailable.Ultimately, the traceability of the size measurements is dependent upon the calibration of size analysis equipment that is used to verify correct operation of the particle generation equipment, even in instances such as the vibrating orifice monodisperse aerosol generator (VOMAG), where the modal particle size can be predicted directly from the operating variables of the system [10] (Section 4.3).

The Certification Process
The approach taken by the two organizations that have been responsible for almost all the particle size-based CRMs/SRMs produced to date is radically different.At the US National Institute for Standards and Technology (NIST-formerly the National Bureau of Standards), their own laboratory has been responsible for the production of ranges of SRMs with limited assistance from outside bodies.In the case of the SRMs based on uniform-sized particles (Table 4) [11][12][14][15][16][17], the basic approach has been to certify by means of a so-called 'first principle' technique that is directly traceable to the international length standard, supported by one other sizing technique.Certifying techniques chosen for each of the SRMs based on uniform-sized polymer latex particles were as follows: • optical microscopy of close-packed arrays of the larger spherical particles (SRMs having nominal Dv of 3, 10 and 30 !Jill) [11,12,14]  t based on total uncertainty (certification by single laboratory) 'uncertainty based on 95% confidence interval (consensus certification by several independent laboratories) NIST SRMs are each supplied in ca. 5 cm 3 aqueous suspension at a mass concentration of about 0.5% w/v solids BCR CRMs are each supplied in 2 cm 3 aqueous suspension: CRM 165 contains 0.02% w /v solids, CRM 166 contains 0.2% w /v solids and CRM 167 contains 1.4% w /v solids • transmission electron microscopy, to size the SRM having nominal Dv of 0.3 f.tm [16]-difficulties associated with the establishment of an accurate edge defining each particle boundary and distortion at the image periphery were overcome by including 1 f.tm diameter spheres from the previously calibrated SRM • electrical mobility of particles having a known charge to size the SRM having nominal Dv of 0.1 flm [17].In addition to the certifying techniques, quasi-elastic light scattering (QELS), in which the decay of coherence of the scattered light from the particles suspended in water, was used as the second method with the SRM having a nominal Dv of 0.3 f.tm.Resonance light scattering, in which sharp Mie resonances were observed in the plots of scattered light intensity versus size, was used with the SRM having nominal Dv of 10 f.tm.Metrology electron microscopy was utilized to size the SRMs having nominal Dv of 3, 10 and 30 f.tm).
In this secondary technique, the focused beam of a scanning electron microscope (SEM) was held stationary whist a single sphere (or row of spheres) was moved beneath the beam by means of a scanning stage.An interferometer was used to measure stage travel, whilst the SEM indicated where the leading and trailing edge of each particle passed by the beam.
The size distribution data provided for these SRMs, accurate though they are, represent the outcome of each certifying method, but are limited to measurements made within the laboratories at that single organization.In contrast, the certification process undertaken at the BCR has been by consensus measurements between several independent laboratories, also using techniques directly traceable to the international length standard.The BCR has no internal laboratory, but operates by contracts with outside organizations, almost always, but not necessarily within the European Union.The procedure is no less rigorous than that utilized by NIST, in that the certifying procedure (undertaken at each participating laboratory) is a 'first principle' method.However, there is added strength to the process by requiring corroboration of results from independent sources before certification takes place.In the case of the three sizes of uniform CRMs produced to date (Table 4), the certifying method has been optical microscopy of closepacked particle arrays, similar to that used by NIST with their larger sized SRMs [13].Supporting measurements of these CRMs were also made by an individual participating laboratory using the electrical sensing zone (ESZ) method (to estimate the disper-sion of particle size about the modal value -distribution skewness and kurtosis), and also by TEM (3-participants).
Similar considerations apply with the range of polydisperse CRMs also certified by the BCR (Table 5) [18][19] each based on a bulk sample of powder derived from materials in common use (e.g.quartz sand, gravel).However, the certifying techniques had to be quite different from those employed with the uniformsized CRMs.Array sizing by optical microscopy would not work, since the particles were irregular in shape as well as varying substantially in size.Alternative methods were therefore chosen (gravitational sedimentation in liquid suspension under Stokesian flow conditions for the CRMs containing particles with Dv finer than ca. 100 flm and sieve analysis for those comprising larger particles).The certified size was therefore an equivalent sphere (Stokes) diameter (Dst) in cases where sedimentation in a liquid suspension was used.In the instances where sieve analysis was the certifying technique, the near-mesh procedure, in which particles held firmly in the sieve mesh are brushed out for microscopy-based size analysis, was used to establish Dv for particles close in size to the mean aperture size of each sieve.The link between Dst and Dv is relatively straightforward [equation 2], although the immersed particle density (pb) had to be determined as accurately as possible in the dispersant medium (0.1% w/v sodium pyrophosphate in aqueous solution [19]).

Spherical or Irregular-Shaped Particles for
SRMs/CRMs Two equally valid, but distinctly different options exist when utilizing SRMs/CRMs to evaluate equipment in terms of particle size, and these options apply equally to other RMs.
In one approach that is becoming increasingly popular, standard particles that are spherical and have well-defined density as well as other relevant properties, such as refractive index, may be used.In the case of CRMs/SRMs of this type, the particles have been processed to control the primary properties of concern with the intention of being primarily used as calibrants.The CRMs/SRMs that have been prepared from polymer latex sources (Table 4), as well as being highly uniform in size (monodisperse), have well-defined, though not certified particle density (1.05 x 10 3 kg/m 3 for polystyrene) and refractive index (m=1.59+0i(polystyrene)).However, they are relatively expensive and are available only in small quantities, and in limited sizes (Section 1.4).RMs may also be used to relate measurements as part of performance verification to check the collective reliability of procedure, operator and instrument (arguably the true purpose of a so-called 'reference material' [20]), rather than as calibrants per se.The 8-polydisperse CRMs from the BCR (Section 2.1) are available in several overlapping size ranges, in many cases encompassing about half an order of magnitude in size per CRM, and are supplied in amounts varying from 10 g (CRMs 66, 67, 69 and 70) to as much as 700 g (CRM 132).Although Pb for many of these CRMs was established by pyknometry, the individual particles are irregular in shape, and their optical properties are ill-defined.The four SRMs from NIST in this category all comprise spherical glass microspheres, having relatively narrow but still polydisperse unimodal size distributions.
The use of spherical SRMs/CRMs as particle standards implies that the theoretical behavior of a sphere of the material in question is known, and that for the purpose of instrument calibration a check is being made between the presumed behavior and the actual response of the equipment on test.It follows that if a particular instrument has been calibrated using spherical particles, any irregular particle that gives KONA No. 18 (2000) the same response as a spherical particle with that instrument, is presumed to have the same equivalent size (equivalent sphere diameter (Section 1.2)).Scarlett et al. have argued that in cases where the response of a particular instrument (e.g. one that operates by the ESZ principle) is proportional to the volume of each particle entering the measurement zone, calibration with spheres of known volume is no different in principle to calibration with irregular particles of known volume [20].However, in instances where the relationship between the response function of the instrument and size is complex (especially with techniques such as laser diffractometry, that involve some form of deconvolution), true calibration may only be achievable with irregular-shaped RMs in fact, the particles which are themselves to be measured.To judge from experience where systematic comparisons of the performance of laser diffractometers from different manufacturers have been carried out using polydisperse BCR CRMs, the process still leaves much to be desired, with deviations as large as ±70% in reported size compared with certified size ob-served in some instances, albeit with excellent reproducibility [21][22][23].It is interesting to note that in one study, significant deviations were also observed with methods based on sedimentation/ centrifugation of particles in liquid suspension, attributed to a variety of causes, including software error and dilution corrections [22].The variability between techniques of similar principle has been attributed to a combination of the following factors [23]: • poor sampling (from the 10 g bottles of powder supplied by the BCR) • inadequate dispersion (both with surfactant and by ultrasonic methods) • non-prescriptive analytical procedures, including statistical interpretation of data • in the case of laser diffractometers, differences in interpretation of light scattering from the angular quartz particles (including ill-defined and variable refractive index) The development of SOPs that describe good sample handling and analytical practices would alleviate the impact of the first three factors, but the fourth factor reflects a more fundamental limitation in the CRMs themselves.

The Planned Certification of Spherical,
Polydisperse CRMs Studies of the sort already described [19][20][21] illustrate that the performance verification of many types of particle size analyzers with polydisperse, irregular shaped particles is a valid procedure, notwithstanding SOP-related issues that are best defined in written procedures, such as those already published and in development through ISO (Table 2).However, it is increasingly recognized that it is important that the RM be homogeneous, not simply in terms of certified size distribution, but also that different samples have equivalent secondary properties within the range of particle size that is present.Such homogeneity is, in fact, essential if acceptable agreement is to be achieved, even between instruments operating on the same principle.Furthermore, it should be possible to reconcile measurements by instruments that operate on different principles on the basis of the equivalent sphere diameter, once RMs having consistent properties have been created.In response to these demands, the BCR since the late 1980s, has been pursuing the development of a new range of CRMs comprising polydisperse, spherical particles having both homogeneous and well-defined secondary properties.However, it can be argued that current demand cannot be met with the quantities of powder that were originally envisaged even if certification of these CRMs eventually takes place.
The original specification was to provide a series of CRMs, each comprising a narrow width, uni-modal and near log-normal size distribution occupying an order of magnitude in size [24].The overall size range between 0.1 and 650 11m volume equivalent diameter was to have been encompassed by these CRMs having overlapping size ranges.On a volume (mass) weighted basis, between 5% and 95% of the spherical particles in each CRM would be within the upper and lower nominal size boundaries and the modal size would be welldefined.Most size fractions were to be produced with a uniform, measured refractive index, having the following appearances: (a) transparent-non absorbing, (b) colored-absorbing.
The development of the CRMs based on sub-micron particles were, to the author's best knowledge, not pursued beyond the initial materials sourcing stage.However, the need for these CRMs could be even more urgent now than in the early 1990s, as many techniques are being developed or extended in capability to size sub-micron particles without the necessary means to verify performance satisfactorily.
The International Fine Particle Research Institute (IFPRI) was responsible for coordinating the production of the bulk powders to manufacture the 8-CRMs comprising particles larger than 1 11m, and these materials (Table 6) were delivered to the BCR by the mid 1990s.They are currently sub-divided and awaiting certification by traceable techniques in accordance with the principles defined by the BCR [25].The technical document supporting the current Call for Proposals defines the following methodology for consensus certification [26]: • 100-100 11m and 150-650 11m: sieve analysis (near mesh technique) • 3-30 11m, 10-100 11m and 150-650 11m: optical microscopy • 1-10 11m, 3-30 11m and 10-100 11m: gravitational sedimentation (in liquid suspension) • 1-10 11m; 3-30 11m and 10-100 11m: ESZ analysis • density measurements by helium or water pyknometry In addition, each CRM is required to be characterized by non-directly traceable size analysis procedures (laser diffractometry and sedimentation methods not involving direct gravimetric assay).Finally, additional properties of importance (refractive index, porosity (if significant) and surface area (BET-method) as well as stability of the particle size distribution are to be established with their tolerances wherever possible.
It is encouraging to note that, in a study in preparation for the main certification program, inter-laboratory agreement by each of the certifying techniques proposed for the new CRMs was within ±20% of the consensus mean between 10 and 90% of each numberor volume (mass)-weighted size distribution [27].Several RMs based on glass particles that 'mirrored' the size distributions of the proposed CRMs were sized by several independent laboratories.Great care was taken to ensure homogeneity of important particle properties (e.g.sphericity, density and refractive index) during manufacture of the bulk powder.Furthermore, the size distribution of the sub-divided samples of 'mirror' standards from the bulk powder sources was accomplished in the minimum number of operations by custom-made spinning rifflers.It is understood that similar rigor has been applied to the CRMs themselves.
The addition of methods to characterize the proposed CRMs with widely used techniques to the certification methods will add to their value as tools for comparing analyzers of different kinds, as a significant database will be available that is directly applicable to instrumentation in actual laboratory use.However, caution will still required in the interpretation of data from these materials.For instance, Scarlett et al. have observed that in cases where proprietary deconvolution techniques are used to transform measured data into a size distribution (e.g.laser diffractometry), compatibility between instruments operating on the same principle may not be achievable even with spherical CRMs [20].Access to proprietary software is a commercially sensitive issue, and until international agreement can be achieved on standards for such software, each basic instrument and its attendant software must be separately specified and tested, regardless of the type of size-based CRM that is being used.

Monodisperse or Polydisperse Standards
A useful distinction can be made between particle standards in which the size distribution, which is almost always unimodal, is either uniform (monodisperse) or comprises a significant range of particle sizes (polydisperse).If, as a first approximation, the size distribution is represented as a log-normal function, the degree of dispersity is given by the geometric standard deviation (crg).A perfectly mono disperse standard would have Gg of unity.However, a practical and widely accepted definition of monodispersity is given by Gg< 1.2 [28].Many CRMs/SRMs are monodisperse by this definition (Table 4).In addition, there are several sources of manufactured SSMs (Table 7), as well as a number of aerosol-based methods that can be readily implemented in the laboratory to custom-produce monodisperse particles for routine work (Table 8) [29-35].
Regardless of the choice or availability of spherical or irregular-shaped RMs, the decision whether to calibrate or verify particle size analyzer performance using monodisperse or polydisperse standards depends on the nature of the measurement technique.Polydisperse RMs are effective 'where time is of the essence, especially in instances where performance verification is all that is required.However, the presentation of the sample to the analyzer is of critical importance, if size-related bias is to be avoided.Precautions are therefore required in sample preparation [2] (especially if a sub-sample is being extracted from the bulk RM for the test), as well as in how the RM is introduced to the measurement zone of the analyzer.The latter is particularly an issue with the calibration of equipment in which a sample of the particle stream is measured, where consideration must be given to both inlet sampling bias and size-related internal losses between inlet and measurement zone [2,3,36].For these reasons, the use of monodisperse particle standards has become widespread, despite the limited availability of particle sizes, at least for CRMs/SRMs.In most cases, SSMs (Table 7) or custom-made calibrants (Table 8) are satisfactory alternatives for routine calibration activities.
Certain techniques, most notably laser diffraction, provide size measurements of the whole population of particles simultaneously in the measurement zone standards.There are a large number of aerosol particle size analyzers (impactors, centrifuges, inertial spectrometers etc. (Table 1)) that measure particle aerodynamic diameter (Dae) on the basis of some form of inertial separation process.The underlying assumption is that particle motion takes place under Stokesian motion (creeping flow), where the particle Reynolds number (Rep) is less than 1.0 [3].In this aerodynamic regime, Dae is related directly to Dv. by analogy with equation [2]: Dae Dv XPo C(Dae) [3] where PP and p 0 are the particle density and reference density (of water) respectively, and the terms C(Dv) and C(Dae) are the Cunningham slip correction factors which become significant with sub-micron sized particles.x is the particle dynamic shape factor, already discussed briefly in Section 1.2.When comparing aerodynamic particle size analysis equipment, the assumption is made that the techniques operate in similar regime of Rep.However, this assumption may not always be valid, for instance, when making comparisons of traditional equipment with the group of analyzers that determine particle size scaled in terms of Dae by time-of-flight between well-defined locations (TOF-aerodynamic particle size analyzers (Table 1)).In these instruments, Rep is significantly greater than 1 throughout their operating range, and particle motion is therefore in the ultra-Stokesian (unsteady motion) regime.A full definition of the modified Dae measured by these systems would require equation [2] to include the added mass and Basset 'history' terms that are beyond the scope of this article to define, but are attempts to describe the complex interactions between the particles and the surrounding fluid during the measurement process [37][38].These terms require assumptions to be made that effectively void the directly traceable link between Dae and Dv.The overall effect is that when the size parameter measured by such instruments is scaled in terms of Dae. they exhibit significant bias associated with both particle density [39] and shape [40][41] when compared with measurements made by more traditional methods.RMs with well-defined density, shape and size are therefore ideally required to determine the bias between modified Dae and true Dae• The development of particle size standards specifically to address variation in particle density has so far not been formalized into programs from which SRMs/ CRMs have emerged.Instead, researchers have preferred to test the performance of equipment with monodisperse, spherical particles of known density [39][40][41], often assuming bulk density values for the particles from the literature and in more rigorous studies, determining density by helium or water pyknometry if sufficient mass of calibrant is available.
The situation in connection with particle shape standards until recently was similar, and the formal process of developing SRMs/CRMs has been slow to get off the ground.Part of the problem is the complexity of defining the term 'shape'.Again, taking the case of analyzers that operate on the basis of particle motion in a fluid, the dynamic shape factor (X) appears to provide a common link to Dv in the case of instruments whose operating principle can be related to Ds 1 or Dae through the application of Stokes Law (see equations [2] and [3]).However, x varies with orientation with respect to particle motion for nonspherical particles having simple geometry, such as spheroids [6]), resulting in ambiguity in the relationship between Dv and Dst or Dae [38].The same is true for particles of more extreme geometries (e.g.disks, elongated fibers, plates having large aspect ratio with respect to their thickness or chain and branched agglomerates) in the flow.In some cases the exact value of x in the measurement zone of the analyzer being evaluated may be undefined.Under these circumstances, the concept of a shape-standard SRM/CRM with a single certified value of x may not be meaningful.The use of cluster agglomerates containing small numbers of monodisperse, micron-sized spherical polymer latex particles which have well-defined values of Xagglomerate in different orientations (Table 9) has hitherto been the nearest to standardization for establishing the behavior of agglomerated particles in particle size analyzers of this type [41][42].Although attempts have been made to define shape factors for these agglomerates that are properly descriptive under other measurement principles (e.g.light scattering [43]), this process is fraught with difficulty.
Despite the issues that have already been outlined, several individual groups have produced their own SSMs for particular purposes, mainly based on com- pact-shaped geometry.One important route to the development of these standards has been the controlled crystal growth by forced hydrolysis of simple inorganic species in accordance with procedures developed by Matijevic and co-workers (Table 1 0) [44].This has resulted in the development of several potential SSMs having a variety of well-defined shapes, such as cubes, rods, needles and ellipsoids [45][46][47].In many cases, rigorous control of particle shape to the point at which x can be evaluated, let alone determined as a function of particle orientation, has proved elusive.However, in at least one case it has been possible to grow monodisperse octahedral-shaped particles with Dv from 2 to 20 J.lm, whilst maintaining X in the range 1.19±0.06,by altering the reaction time during which particles of sodium-ferric sulfate (natrojarosite-NaFe 3 (S0 4 MOH) 6 ) are formed.In this case, values of x were reported assuming orientation independence due to similarity in profile from all directions [46].Strategies for producing SSMs based on fibers of known aspect ratio have involved a fiber extrusion process [47] and micromachining of silicon by a process widely used to mass-produce microelectronic components [48][49] (Figure 3).The latter process can be controlled with great precision and can be used to form a variety of particle shapes, in particular rod-like structures of variable 2-dimensional profile (aspect ratio) varying from 1 J.lmX 1 J.lm (square profile) to more than 30 J.lm x 1 J.lm.The chosen profile (rod or disk) is replicated millions of times by means of a mask that is used in the fabrication of the silicon dioxide particles by photolithographic etching.The etching process rounds the corners as well as slightly undercutting the profile.As a result of the latter, the thickness of the particles is limited to about 1 J.lm with current technology.Under the UK governmentsponsored Valid Analytical Measurement (VAM) pro-Fig.3 Silicon Micromachined CRM Shape Standards gram in the period 1992 to 1995, a range of 3-CRMs based on differing rectangular cross-sections was developed by AEA Technology pic in collaboration with the University of Hertfordshire [50] (Table lla).500 samples of each CRM were created, each vial containing approximately 10 6 particles.Scanning electron microscopy (SEM) was chosen as certifying method, by which an unspecified number of particles of each CRM were sized.The procedure was undertaken by a single laboratory, rather than by a consensus process, and without resort to confirmatory measurements using independent, traceable techniques.As well as providing physical dimensions, the certifying laboratory estimated indicative values of Dae from a knowledge of both particle density and extremes of orientation with respect to flow, based on the model of Oseen [6] (Table lib).
In principle, silicon micromachining offers such a degree of control over particle profile that a wide range of CRMs could be produced in order to simulate the behavior of fibers as well as acicular-shaped particles in analyzers.However, the current manufac- turing process is expensive compared with traditional particle generation methods, and only microgram quantities in terms of mass have so far been made.The development of further CRMs of this type will therefore depend very much on user demand for shape-related standards.

Mixtures of Reference Particles
It has already been mentioned (Section 3) that a limitation when using monodisperse particles is the potential number of standards having different sizes that might be required to calibrate a particle analyzer.The ability to create 'cocktails' containing more than one monodisperse RM offers the potential both to reduce the amount of work required, and perhaps more importantly, to compare the sensitivity of an instrument (in terms of the appropriate ordinate scale (number, surface area, volume or mass)) at several different sizes simultaneously.However, this argument presupposes that the 'cocktail' RM can be prepared in a traceable way based on particle concentration as well as size.
A technique has been developed for the determination of particle number concentration in suspensions of monodisperse polymer latex particles, using a TEM calibrated by a first principle method to count individual particles carefully deposited on a flat plate [51].The accuracy is claimed to be better than ±10% of the nominal particle number concentration.This procedure was used by the Japan Synthetic Rubber Co. (JSR) to certify a series of 4-CRMs each containing a equal blend by number concentration of 3monodisperse particle components as a further part of the UK VAM program [52] (Table 12).It was in-tended that these standards be used for the calibration of analyzers that determine particle size weighted by number-rather than volume or mass (Table 1).Particle size measurements for each component were also certified by TEM.The certification process, as with the shape-based CRMs from the same source, involved a single laboratory, rather than a consensus between independent laboratories.The particle concentration was chosen to be quite low (4x10 8 particles/ml aqueous suspension).At this concentration, it was predicted that each cocktail would produce a singlet to multiplet ratio close to 0.99 when the suspensions were converted to aerosol form by pneumatic nebulization with equipment capable of generating an aqueous spray with droplets having volume median diameter of 3 11m and geometric standard deviation close to 2.0 (based on Raabe [53], assuming the droplet distribution to be log-normal).

Concentration-Based Standards
The development of standards with which to evaluate the performance of particle size analyzers in terms of the distribution axis (count (number), surface area, volume (mass)) is in its infancy.By definition, particle-gas and particle-liquid systems are unstable with time, making it impossible to create a fixed RM, in the sense of the particle standards already reviewed.Nevertheless, there is a need to be able to determine the concentration-based sensitivity of analyzers as a function of particle size within their operating ranges, especially in cases where these instruments extract samples from the bulk particle suspension.In addition, there are many particle counting instruments (e.g.condensation nuclei counters, nephelometers etc.) that require calibration in terms of total particle count within a given size range.Requirements for mass concentration standards also exist for instruments that collect particulate by weighing or a massweighted technique.
The cocktail CRMs referred to in Section 4.2 were partly intended to address this issue, and were therefore formulated so that each component was present in similar number concentration.The manufacturer (JSR) indicated that they should be stable in liquid suspension at the supplied concentration for at least 3-years following their creation, provided that the samples are stored in their unopened container at temperatures between 0 and 20oC (this limit is reduced to 6-months after opening the vial containing the particles [52]).As long as the particles are kept in suspension, or re-suspended by carefully agitating the container prior to use, agglomeration is the main process that will gradually reduce particle number concentration and at the same time lead to the formation of multiplets.This process is likely to be reduced if the suspensions are further diluted with the same suspending medium prior to use.However, to the best knowledge of the author, published data on long term stability of these CRMs is lacking, making their viability as stable concentration standards uncertain.The BCR monodisperse CRMs (Table 4) could be used as an alternative particle concentration standard, and although they are not certified by particle concentration, measurements made by ESZ analyzer (Coulter counter) on 1 in 100 sample vials have provided overall coefficients of variation < ±2% of the mean particle concentration [54].The nominal particle concentration is 3 x 10 7 particles m-3 for each of the CRMs, corresponding to mass concentrations based on solids content of 0.2, 2.0 and 14.0 g L- 1 for CRMs 165, 166 and 167 respectively [13].Barfield and Bradshaw [54], in the context of establishing reference count standards for ESZ analyzers, observed that the BCR monodisperse CRMs have the smallest uncertainties of any other standard for those wanting to count particles.However, they commented that achieving concentration stability of these liquidbased suspensions is much harder to achieve than the establishment of stable and therefore certifiable particle size.Factors that have to be considered are irreversible binding of particles to the walls of containers, a process that can be offset to some extent by dilution, although the process of dilution itself introduces concerns about traceability.The accessibility to reliable particle concentration standards might be useful as a means of validating the mass integration (mass balance) method in cases where it can be applied (e.g. with ESZ analyzers).Here, the total volume, in instrument units, of the particles measured in a known volume of suspension is related to the known mass concentration and the immersed density of the particles, allowing the calibration (bias conversion) factor for the instrument to be calculated [55].
The use of monodisperse polymer latex particles as aerosol concentration standards imposes the added problem of creating the aerosol from the liquid suspension.Aerosols, by their nature are unstable systems compared with liquid suspensions because of the lower viscosity of the surrounding fluid [56].It is therefore most unlikely that creation of a particle concentration standard by a single burst of aerosol formation could provide a reference particle concentration that would remain constant during the time required for performance measurements to be made.The alternative and preferred approach is to replenish the aerosol continuously in a flow-through system.Yamamoto et al. [57] have described such an aerosol generator, which uses a purpose-built pneumatic nebulizer (Kousaka eta!. [58]) for suspending particles in the size range from 0.08 to 3.0 !!ill.They have claimed that this apparatus provides aerosols whose stability in terms of particle number concentration is < ± 10% of the mean (9.3x 10 6 particles m-3 ) during 120 min operation with particles having Dv of 0.168 !!ill.Their facility probably represents the state-of-the-art in terms of measures to control particle concentration.The aerosol was passed through a charge equilibrator to minimize electrostatic charge induced agglomeration (which can be potent with aerosols), and the particle concentration was kept low to minimize Brownian agglomeration.Furthermore, the size range of operation was chosen such that loss mechanisms to the container walls (sedimentation, inertial deposition and diffusion effects) were minimized.More recently, this system has been commercialized as the JSR-Aeromas-ter®.However, attempts to suspend two of the cocktail CRMs (AEA-1005 and AEA-1007) with this equipment resulted in a mixed outcome [52].The cocktail containing the finer particles (AEA-1005) provided highly stable aerosols over the 30-minute test period, with variability of all three components within less than 5% of the mean concentration.However, a slight, but systematic increase in concentration with elapsed time was evident with the cocktail containing the coarser particles (AEA-1007).Furthermore, the efficiency of nebulization of the 2 11m and 5 11m diameter components was lower than the expected values by factors of 5 and 100 respectively, based on the concentration of each component in the original suspension.On the basis of these data, this type of nebulizer may be unsuited for the generation of aerosol concentration standards containing particles much larger than 1 11m diameter.The gradual increase in particle concentration with time appears to be related to the volatilization of the suspending fluid in the nebulizer and can be minimized by various techniques, including operation at low ambient temperature and the use of a larger secondary reservoir attached to that of the nebulizer [59].Nevertheless, it is difficult, if not impossible to eliminate all causes of time-dependent drift in particle concentration, resulting in a gradual loss of traceability.In the end, these standards are likely to have to be used in conjunction with a validated particle concentration monitor [52].
The vibrating orifice monodisperse aerosol generator (VOMAG) is an alternative method to develop an in-house particle concentration standard for particles in the size range from about 0.5 to 50 11m volume equivalent diameter [10,29].The modal size of the particles (!lm) that are formed is related directly to variables that are both well-defined and which can be measured by directly traceable means: where Q 1 is the liquid feed rate (cm 3 min-1 ), Cr is the fractional concentration of solute in the feed liquid and Fvib (Hz) is the orifice vibration frequency.The lack of an empirical constant in this relationship makes it possible to derive the uncertainty in Dv directly from the uncertainties associated with Q~, Fvib and Cr, free from bias, although a check should always be made of particle size and sphericity by a traceable method, such as optical microscopy [35].Aerosols from the VOMAG are highly monodisperse (crg typi-cally< 1.02) and concentrations in the range 1 to 100 particles cm-3 are achievable, depending upon the configuration of the aerosol generator.The aerosol number concentration (N, particles cm-3 ) can be predicted if the particle stream emerging from the vibrating orifice is introduced without losses into a flow of carrier gas (usually air (Qcarrien L min-1 )) and thoroughly mixed without inducing losses to the walls of the mixing chamber, since: N= 0.06F Qcarrier [5] Equation [4] is not continuous (i.e.not all conditions will give rise to a monodisperse aerosol [59]).However, under conditions where monodispersity is achieved, the relationship relating the massto number-concentration of particles of size Dv (!lm) dispersed in Qc (L min-1 ) applies: M= trppmN 6 [6] where PP is the particle density (kg m-3 ) and M is the aerosol mass concentration (mg m-3 ).Strictly, this relationship only links particle number-and mass-concentration in a fully traceable manner when the particle stream is perfectly monodisperse (crg= 1.00), but in practice the error is sufficiently small that the aerosol from a VOMAG can be used both as a mass as well as a number concentration standard.Recently, Booker and Horton [59] have described a practical flow-through particle concentration source based on the VOMAG principle, in which care is taken to disperse the droplets by an air-jet sideways from the region of the vibrating orifice to reduce deposition at this location, as well as minimize losses in the aerosol sampling chamber due to sedimentation and inertial effects (Figure 4).Control of Q 1 within ±0.5% at a typical feed rate of 0.2 cm 3 min-1 was achieved using an isocratic pump, and orifice vibration frequency was stable within ±0.01% of typical operating frequency (50 kHz).The monodispersity of the aerosol stream was monitored continuously by optical means, observing the angle at which the droplet stream was dispersed (the presence of more than one stream was indicative that the particles were no longer monodisperse) 5. Future Needs: The development of particle-based standards experienced a period of rapid growth in the early 1990s, but of late has languished, probably as a result of the withdrawal of government funding for the intensive campaigns that are needed to develop adequate RMs.Probably the most pressing need at the present time is the completion of the certification of the polydisperse, spherical CRMs by the BCR (Table 6), in particular to support the performance verification of the large number of laser diffractometers in use.At the time of writing, the sub-divided powders are currently in storage at the EU Institute for Reference Materials and Measurements (IRMM-JRC-Geel, Belgium), awaiting the outcome of the call for proposals to certify them by a consensus approach, as well as characterization by a variety of non-first principle size analysis methods.In the last decade, there has also been rapid growth in capability to size sub-micron sized particulates in powder, liquid suspension and in aerosol form by techniques that involve some form of deconvolution (e.g.PCS, laser diffractometry) or whose sizerelated response requires a complex transformation of raw data to the final size distribution (e.g.TOF aerosol analyzers).In these cases, it would be beneficial if the original intent of the BCR were to be fulfilled, so that this CRM series is extended to particle sizes at least as fine as 0.1 f.!m volume equivalent diameter.

56
The production of monodisperse, spherical SRMs/ CRMs with additional certified sizes is a lower priority, since in many instances, SSMs supplied by a variety of manufacturers, as well as in-house particle generation techniques are adequate for the main use for these materials, which remains size-based calibration.Nevertheless with the emergence of nanotechnology as an important source of economic growth, there will be pressure to extend the NIST SRMs to sizes finer than 0.1 f.!m volume equivalent diameter.The twin challenges will be to develop adequate first-principle techniques to size nanometer particles, and to create them in sufficient quantity to be of use as RMs.
The future for particle shape standards remains uncertain, since it is not clear in most instances, how they can be used to provide unambiguous data especially when particle orientation with respect to the flow or interrogation technique (light beam in the case of optical-based techniques) cannot be defined.CRMs based on silicon micromachining are relatively easy to produce, although expensive relative to other material sources, and they probably have a role to play in the simulation of particles having extreme aspect ratios, such as fibers.It is unlikely, however, that impetus to develop more of these materials will arise unless there is sufficient demand for the current CRMs.As a footnote, the consensus method of certification is preferred over single laboratory certification, as there is an opportunity to quantify both interlaboratory variances as well as inter-sample variances for each CRM.
Finally, the provision of adequate standards for particle concentration is most likely to come in response to those making aerosol-based measurements.Such standards are particularly important in the fields of occupational hygiene and environmental sampling where a plethora of new techniques are in the process of development.There is a need to have an understanding of both inter-technique as well as interinstrument performance when establishing widely accepted standards, for example the PM-series for environmental particulate emission control limits in the USA.The challenge with this class of standards, is to develop systems that extend to a wide enough range of particle sizes and at the same time have minimal losses, or whose losses are accurately quantified.

Table 1
Particle Size Measured by Selected Analyzer Principles ~ diameters (D,) are defined in the text directly by several widely used techniques that employ gravitational sedimentation as the size-separating principle, where Stokes Law applies, and: U _ [pb-Ptll D2 ts-18 1]

Table 2
International Standardst Relating to Particle Size Analysis as of Jan 1, 2000 t from International Standards Organization, Geneva, Switzerland

Table 3
Selected National Standards Relating to Particle Size Analysis

Table 9
Values of Xagglommte for Clusters of Monodisperse Spherical Particles (X>mglet= 1.00), Based on Cheng et at.[ 40 I

Table 10
[42]uction of Particle Shape Standards by Controlled Crystal Growth in Accordance with Principles Described by Matijevic[42] t x based on settling under Stokesian conditions and assumed orientation independent due to similarity of profile in all orientations

Table ll (
a) Specifications of Particle Shape CRMs Developed for the UK VAM program Reference Code of Supplier: Office of Reference Materials, Laboratory of the Government Chemist, Queens Road.Teddington, Middlesex, TIV11 OLY, UK t based on reported particle density (pp) of 2.05±0.15x10' kg m-" t

Table 12 '
Cocktail' CRMs Comprising 3-Component Monodisperse ' particles ml-1 in 10 ml aqueous suspension-each component is present in similar number concentration ~Particle sizes are nominal values without tolerances quoted in the certification report.The coefficients of variation of size quoted for each component are believed to be <4% of the modal size, based on the published specification for the unblended particles