Nanotechnology research is accelerating innovation. For example, the number of nanoparticle patents has an exponential growth rate of >30% in recent years. Nano-objects are materials with one, two or three external dimensions on the nanoscale, nominally ranging from 1 nm to 100 nm [1]. Nanoparticles, which have all three external dimensions on the nanoscale, have performance properties that often depend on their physico-chemical characteristics, i.e. size, shape, surface structure and texture. For example, catalytic properties of nanoparticles usually depend on their crystal structures, size distributions and exposed surfaces, edges and corners. The growth rates of different crystallographic surfaces can vary, leading to asymmetric particles [2]. Toxicity can be affected by nanoparticle size [3], which makes this an important metric for risk assessment [4, 5]. Stakeholders in nanoparticle characterization include industry, academics, government agencies (and particularly, regulatory agencies), and the general public through non-governmental organizations.

There are a wide variety of analytical methods for particle size measurements, including electron microscopy, dynamic light scattering [6], centrifugal liquid sedimentation, small-angle x-ray scattering, field flow fractionation, particle tracking analysis, atomic force microscopy [7] and x-ray diffraction [8]. These methods are based on different measurands, and a comparison between methods should be made with care. Many of the measurement methods for particle sizes on the nanoscale have focused on assessing an average particle size for the sample. Performance properties of nanoparticles often depend on size and shape and few particle size distributions of commercial products are monomodal and narrow in range. In fact, the nanoparticle size distribution is important to product performance in applications, in the environment, and for health and safety and for regulations. Transmission electron microscopy (TEM) methods provide two-dimensional images of nanoparticles; these images can be used to produce number-based size distributions.

Because we are interested in more than a single point representation of the sample size, we compared appropriate reference distributions, such as the normal, lognormal and Weibull distributions, with particle size distribution data. TEM particle size data were converted directly to cumulative number-based distributions. This information is useful for both nanoparticle applications, for which the surface properties may be distinctly different below a specific length scale, and regulatory requirements, for which the fraction of particles below a length scale of 100 nm would be related to whether the sample is on the nanoscale. Size distribution reference models generally have two parameters, representing the size and the shape of the distribution. For the normal distribution, these would be the sample mean and the sample standard deviation. The number of particles needed for high-accuracy estimates of the average diameter is known to depend on the spread of the particle size distribution [9].

An important step in the process is visualizing the fitted model prediction relative to the actual data. This step helped us answer the following question: where does the model deviate from the data, i.e. over what diameter range do we know the distribution well? This has relevance for the application and regulatory communities. Because TEM can be a costly method, automated image capture, particle analysis and statistical assessment were preferred.

A metrology checklist [10], established by ISO/TC 229, was used to assess and design the protocol (appendix A). There are a variety of reference materials for characterizing nanoparticle size (see [11] for lists of reference materials [12] and their sources). RM8012, a suspension of discrete, spheroidal, gold nanoparticles with a nominal size of 30 nm (NIST), was used in this study to facilitate sample preparation, image capture, particle analysis and statistical assessment of measurement uncertainty. Appendix B provides definitions of statistical, measurands and metrology terms used in this study.

This case study is intended to provide a scientific foundation for an International Organization for Standardization (ISO; www.iso.org) standard for the measurement of particle size distributions on the nanoscale by TEM. The committee, ISO/TC 229 Nanotechnologies, was established in 2005, and now has 34 national member bodies, about 40 liaison members (other ISO TCs or international organizations), along with 11 observers. The authors of this study are members of the US Technical Advisory Group (TAG) to TC 229. Standards developed by ISO/TC 229 are intended to improve commerce and facilitate communications among buyers, sellers and regulators of raw and intermediate materials.

The case study protocol for 30 nm gold nanoparticles was based on a National Institute for Occupational Safety and Health (NIOSH) internal interlaboratory comparison [13, 14] and a generic protocol from the UK National Physical Laboratory [15]. Discrete, spheroidal nanoparticles represent one of the less-complex nanoparticle morphologies; measurands of this sample should have relatively high reproducibility, and fitted parameters modelling the distributions should have low relative standard errors (RSEs). There are many TEM instruments, and sample preparation techniques are often tuned by each operator for their system. Typically, TEM sample preparation is a major contributor to measurement uncertainty. Sample preparation was not assessed in this case study. Sample mounting and dilution guidance from previous studies of this reference material was used by one lab to prepare all samples. The major constraint on TEM instrument factors was the requirement for setting the required image resolution to >2 pixels nm⁻¹. This gave an image resolution contribution to the measurement uncertainty for a 30 nm particle of ~1.6% (<0.5 nm/30 nm). The foci for this protocol were automation of image capture and particle analysis and its control plus statistical assessment of the data, the quality of the parameters for the reference models and the reproducibility of the interlaboratory results.

ISO standards exist for the measurement of particle size distributions of powders (ISO TC/24), including representation of particle size analyses [16–20], accuracy of measurement methods [21] and image analysis methods [22]. These methods, particularly ISO 9276-3 [17], have been applied to results of this interlaboratory comparison. The interlaboratory comparison team included industry (Cabot Corporation, DuPont, Hewlett Packard and RTI), US government agencies (NIOSH, Food and Drug Administration (FDA), NIST) and a university (University of Kentucky). For purposes of confidentiality, the labs are referred to as Labs A to H. The University of Kentucky prepared all samples.

NIST RM8012 has 30 nm nominal diameter gold nanoparticles stabilized by citric acid in a water dispersion. The NIST Report of Investigation [23] provides a mean particle diameter (area-equivalent diameter) of 27.6 nm. No standard deviation of the distribution was reported. Rather, a conditional measurement uncertainty was computed for results using different ampoules of the reference material (described in appendix B). The differential particle size histogram (figure 6 of [24]) shows a size range from 15 nm to 50 nm, although these numbers were not certified. This size range was used for plotting the distributions of this study. Figure 1 shows scanning electron microscopy (SEM) and TEM images for these nanoparticles. The spheroidal particles exist as discrete entities in water solution, but are faceted with specific crystal faces. These nanoparticles are not completely spherical and, depending on how they ‘sit’ on the substrate, appear to be more or less spherical, triangular or hexagonal.

Two sample preparation objectives are as follows: disperse the nanoparticles over the 3 mm TEM sample grid so that particles do not touch (so the edges of the particles will be clearly visible in the imaging system) and uniformly distribute the nanoparticles across the sampling medium [22]. RM8012 gold nanoparticle colloidal dispersion is stable; the nanoparticles have a negative charge. Prior protocols attached this standard reference material to amine-functionalized silicon grids (Catalog # SG01-051A, Dune Sciences). The positive charge on the functionalized surface helps immobilize the negatively charged gold nanoparticles, and the silicon substrate provides a relatively uniform background for improved nanoparticle imaging [13, 14, 24]. Wafers and a RM8012 sample were generously provided by NIOSH.

The typical time required to receive the sample, acquire over 500 data points, analyse the data with ImageJ and assemble the frame-wise data into a master table for analysis exceeded 20 h. Each lab received one grid; no grids were shared between laboratories.

ISO 13322-1:2004 [22] provides guidance on electron microscope operating conditions for particle size imaging and a measurement uncertainty analysis specifically for lognormal distributions, which would be the most common reference model for nanoparticle distributions. Table 1 shows the instrument factors of each lab. Specific guidance was as follows [22]:

While no SEM instruments were used in this study for particle size determination, it is notable that a recent good practice guide [15] provides some guidance on selection of instrument parameters for use with this type of instrument for particle sizing.

Each participating lab used the loading procedure specific for their instrument to mount the TEM grid in the system. The loading procedure was to minimize the eucentric height adjustment required. The images were to be of sufficient quality such that individual particles can be resolved and their dimensions measured. Each lab analysed one wafer, measured at least 500 particles, and reported the results to the team. The specific instructions were the following.

The area-equivalent average diameters of all reported particles were used to generate number-based, cumulative particle size distributions.

Since a large number of nanoparticles are needed for a high-quality particle size distribution, the work will be facilitated when image analysis software is used. Both commercial and open source software are available. For a typical sample, an appropriate reference model for the data may not be known, the data may not be monomodal, and the sample may be contaminated with nanoparticles of different sizes and shapes. Multiple models might need to be compared with the data and multiple measurands might be needed to help screen for the desired nanoparticles. Therefore, we have used a more general analysis approach that estimates the sample mean and standard deviation from a non-linear fit of the reference model to sample population data. The minimum number of particles for analysis was set at 500 for each lab, based on the experience from prior studies.

This protocol assumed that all images were taken in digital format. ImageJ, open source software with a suite of analysis routines (http://rsbweb.nih.gov/ij/download.html), was used by all laboratories for particle analysis. The procedure steps were as follows.

There are three major applications for statistical analysis of particle size data: assessment of data robustness, fitting reference models to the size distributions and assessment of measurement uncertainty.

Although each laboratory used a different TEM instrument, the sample grids were suitable for each one. Sample preparation, a known element of variability for TEM analysis, was not varied in this study. RM8012 is known to have discrete, non-aggregated gold nanoparticles in its suspension medium. This is confirmed by its Report of Investigation, in which the average particle size by dynamic light scattering is essentially the same as the size by TEM. In general, the gold nanoparticles were well separated on the functionalized silicon TEM grid surfaces, but a number of touching particles were observed on all grids. There are at least two mechanisms by which this could occur: agglomeration, which is a general phenomenon for colloidal particles in solution and increases with particle concentrations, and random deposition of one nanoparticle near another. Touching nanoparticles were assumed to be agglomerated. For Laboratory H, a total of 672 nanoparticles were imaged. Of these, there were 530 discrete nanoparticles. Fifty-one dimer, 11 trimer and one septamer nano-objects were judged to be touching and were not counted, i.e. only 79% of the imaged nanoparticles could be used directly for the automated particle analysis. It is likely that the identification of touching particles could be automated by using shape factor or aspect ratio measurands, but this was not addressed in this interlaboratory comparison.

One lab reported a calibration error, which occurred when two different magnifications were used for particle imaging (one of these magnifications had not been properly calibrated). This type of error was easily detected by the ANOVA analysis of frame-to-frame particle diameter means. In general, the labs could achieve good contrast between nanoparticles and the background, and the sample preparation method [13] gave a reasonable number of discrete, non-touching particles on the grids.

One laboratory reported thresholding problems that resulted in a number of small particle artefacts being reported. This was detected by reviewing the cumulative particle size distribution of all the data; about 5% of the ‘particles’ were less than 6 nm, which was known not to be characteristic of this reference material. The issue was corrected by redoing the thresholding and ensuring that the despeckle and erode/dilate steps were used. The effects of the erode/dilate step can be checked directly during the particle analysis process. The artefacts also could be removed manually, but this would reduce the benefits of automated analyses.

Touching particles were not analysed in this interlaboratory comparison, although ImageJ has a tool to do so (Watershed). The Watershed tool separates touching particles by inserting a linear boundary at the ‘necks’ between particles. This approach tends to reduce the total area attributed to each particle and to lower the average area-equivalent diameter reported for the sample. Figure 2 shows residual deviations and quantile plots for the analysis of non-touching and touching particles reported by Lab E (the maximum Feret diameter was used as the measurand for these plots). The Watershed algorithm data have larger residual deviations than the non-touching particle data (figure 2(a)). On a quantile plot, the size distribution for the Watershed algorithm data is narrower and the mean value of the distribution is shifted to a lower value (figure 2(b)). The use of this algorithm could introduce a consistent bias into the sample mean data.

Other factors affecting particle analysis. Even with discrete, spheroidal particles and a good sample preparation method, the results of the automated particle size analysis can require additional operator review. Typical analysis problems were thresholding inconsistency and artefacts created by the inclusion of scale bars in the analysed images. Since gold nanoparticles are faceted, crystalline solids, different cross-sectional shapes can be present in the images and very few particles have shape factors near one (representing a circular cross-section). Although area-equivalent diameter was the preferred measurand for this study (particularly since this was the measurand investigated for RM8012), other measurands that relate to nanoparticle shape provide important information about the sample. These include the minimum and maximum Feret diameters, and the shape factor. For more complex shapes, additional measurands should be considered [20].

The protocol used for the US TAG interlaboratory comparison on gold nanoparticles provided no guidance for post-processing review of the raw data from the automated image capture and particle analysis process. Interlaboratory comparisons of the data showed that there were differences in the ranges of particle sizes reported as well as the cumulative particle size distributions. These differences appeared to be due to differences in how operators treated the data and/or set thresholding parameters.

When we evaluate the area-equivalent diameter using the normal model, we can generate the following measurement uncertainty components for the sample mean: the interlab reproducibility, the trueness and the image resolution. However, since the reference material was not certified for a lognormal reference model, it is not possible to determine the trueness of the preferred reference model parameters of this study. Rather, we computed expanded measurement uncertainties for the reference model parameters, mean and standard deviation of the interlaboratory comparison. Using coefficients of variation allowed the comparison of lognormal and normal parameters on a relative basis. The equation used was [23]

where k = 2, N = 8 (number of observations), and c_v corresponds to the appropriate value in table 6. The most interesting comparison is between the fitted parameters of the lognormal distribution (the preferred model) and the standard definition parameters of the normal distribution (RM 8012 is certified for this mean). For the fitted lognormal distribution, U_ILC,x(fit) = 1.62% and U_ILC,s(fit) = 12.6%. For the normal distribution, U_ILC,x̄ = 5.54% and U_ILC,s = 33.7%. Even though the mean area-equivalent diameter for this interlaboratory study was similar to the value assigned to RM8012 (table 3), the expanded measurement uncertainty was over 5% on a relative basis.