## A pproach for differentiating nanoscale materi als based on the size

criterion using number of modes by count and size, locations of modes by size, mean size count, and standard deviations centered around mean sized count. Background EPA is propos ing in its proposed 8(a) and significant new use rules to differentiate discrete nanoscale materials (NMs) based on the numeric middle of a particle size range whose resolution varies according to the width of the range (the current proposal outlines five ranges: 1

– 20 nm; 20

– 50 nm; 50

– 1000 nm; and 1000

– 10000 nm). For example, the numeric middle of a NM with 90% of the primary particle sizes falling between 55

- 65 nm is 60 nm. There are several considerations and parameters to consider beyond this specif ic approach: 1. No scientific literature has differentiated or identified NMs based on the numeric middle of the size range. 2. Extensive scientific and mathematical literature has dealt with distributions of various properties and typically identifies four pro perties to characterize a distribution, as well as the type of distribution itself: mean or average, variance 1, skewness 2, and kurtosis 3 . Common distributions include: normal, Poisson, Rayleigh, exponential, and geometric, but there are many others. 3. F igures 1
- 3 illustrate different particle size distributions that, under the proposed approach, would be considered to be the same “nanoscale material” despite scientific studies demonstrating that these substances have different environmental properties (Auffan, Rose et al. 2009) : a. Figure 1

1 Measures the “width” of the distribution around the mean. For population samples , this is expressed as

1 ) ( 2 2





 

##  N x X s i i , where Xi is the data point and x is the sample mean.
2 S kewness is a measure of the asymmetry of the probability distribution around the mean. A negative value indicates a longer tail on the left, while a positive number indicates a longer tail on the right.

3 Kurtosis is a measure of the "peakedness" of the probability distribution

. Higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations.Figure 1 illustrates a broad distribution and a narrow one that have the same “middle” of the range. The peaks

are also constructed to have the same mean of particles by count, though not by mass. The black line indicates the mean at 50nm, which is also the middle of each range, while each dashed vertical line represents two standard deviations from the mean (roughly 95% of the particle size distribution) for the respective distributions.

Figure 2 illustrates two materials have different means and skewness (there is >5nm difference between the mean s), but 95% of the particle s fall into the same size range (represented by the dashed vertical lines) . The distribution for material 1 has relatively small particles and is skewed left, while the distribution for material 2 has relatively large particles and is skewed right. Even though the majority of the particle sizes are different in each distribution, they would still be considered the same “material” under the current proposal. The mean by count for each material are represented by the solid verti cal lines. 0 10 20 30 40 50 60 70 80 90 100Frequency

Particle size in nanometers Material 1

- broad distribution Material 2

- narrow distribution

0 10 20 30 40 50 60 70 80 90 100Frequency

Particle size in nanometers Material 1

- skewed left

Material 2

- skewed rightFigure 3 illustrates a material with bimodal distribution (#1) with the same mean and

#2. Line a represents the mean for both substances, which also happens to be the median for material #2. The median for material #1 is at line b. Lines c & d are the modes for material #1.
Although the proposed approach as d understanding of and compliance with the rule parameters based on different size distributions su approach. At the same time, more complexity o would be unable to meet the requirements, because the proposed revised approach is based on statistical distrib utions science. 

### Foundations for a n alternative Although the mathematics of distributions differentiation of NMs based o n distribution or distributions , such as utilizing Student’s T There are several reasons for th 1. There are several different types of “particle” including, but not limited to: a. Primary particle b. Grain c. Aggregate d. Agglomerate No single method or protocol exists for characterizing these properties of a single material that can span orders of magnitude of size or to adjust for different conditions. 0 20Frequency

illustrates a material with bimodal distribution (#1) with the same mean and width of range as material #2. Line a represents the mean for both substances, which also happens to be the median for material #2. The median for material #1 is at line b. Lines c & d are the modes for material #1.
approach as d escribed in the current rule c ould simplify understanding of and compliance with the rule , the differences in environmental parameters based on different size distributions su pport the idea for a more rigorous approach. At the same time, more complexity o r nuance does not mean a regulated entity would be unable to meet the requirements, because the proposed revised approach is utions science. 

### n alternative approach Although the mathematics of distributions has been extensively described, a rigorous n particle size distributions utilizing a particular type of , such as utilizing Student’s T

- test, is probably not warranted. There are several reasons for th is: There are several different types of “particle” including, but not limited to:

No single method or protocol exists for characterizing these properties of a single material that can span orders of magnitude of size or to adjust for different 40 60 80 Material 1 material

Material 2 material b c d a

width of range as material #2. Line a represents the mean for both substances, which also happens to be the median for material #2. The

simplify , the differences in environmental

for a more rigorous r nuance does not mean a regulated entity would be unable to meet the requirements, because the proposed revised approach is
been extensively described, a rigorous particle size distributions utilizing a particular type of is probably not warranted. There are several different types of “particle” including, but not limited to:

No single method or protocol exists for characterizing these properties of a single material that can span orders of magnitude of size or to adjust for different100 Material 1

- bimodal

Material 2

- broad2. Under the Nanoscale Material Stewardship Program and the nanoscale notices

rec eived under the New Chemicals Program, the Agency has frequently seen particle size distributions that are bimodal size distributions typically representing aggregation and agglomeration processes. There are several other processes that might generate a b i
- or trimodal distribution including particle formation processes that occur under threshold reaction conditions (this might also lead to graininess). There may be others. 3. Different shapes will also lead to issues of defining the boundaries of distributions of critical parameters for non

- spheroid nanoscale materials like fibers, trees, etc. 4. Utilizing statistical tools, such as a Student’s t- test, to identify whether a particular size distribution is the same or different than another size distribution is a scientifically objective approach to settling the question as to whether two materials are the same from a size perspective within specified limits of statistical uncertainty. However, this would require embedding the distribution information into th e nomenclature of a discrete material. This strict approach is well outside the norm of how EPA considers distributions in Unknown Variable Composition and Biological (UVCB) substances for chemical nomenclature. Second, it would place a large burden on i ndustry to submit and EPA to assess potentially new submissions. Taking into account the above issues, and given the need to balance simplicity and taking a case - by

- case approach, the following framework is an alternative propos al for differentiating NMs from each other based on size. The other parameters outlined in the proposed rule would remain the same. 

### Alternative approach
1. The key parameters of size distributions are: a. Number of modes by count and size b. Locations of modes by size c. Mean size by count d. Two standard deviations centered around mean size by count 2. Each chemical substance that meets the definition of a nanoscale material should be evaluated as to the number of type of critical dimensions. Scale of dimensions (a, b, and c) Example

Shapes Number of

critical dimensions Dimensions Notes

ab c Spheroid,

cubes 1 Diameter Zingg’s shape: equant ab  c Irregular

shapes, cones 1 Equivalent spherical diameter Submitter

should convert volume or surface area ofNM into an equivalent spherical diameter

ab<c Fiber,

needle, rod, 2 Length and diameter ab should be

converted to equivalent circular diameter Zingg’s shape: prolate ab>c Ring,

sheet, torus 2 Depth and diameter ab should be

converted to equivalent circular diameter Zingg’s shape: oblate a<b<c Ribbons,

attached or unattached 3 Length, width, depth Zingg’s shape:

bladed Two dimensions should be considered equivalent or on the “same scale” when each dimension’s mean by count are within 3/2 of each other. This approach was developed by Zingg for use in describing 3

- dimensional objects in geology (Zingg 1935) }

. Materials that are “hollow” or that encapsulate another substance should have another critical dimension: internal volume. 3. Each critical dimension should be defined by the four parameters of the size distribution as follows:

a. Number of modes by integer number provided the distribution is statistically relevant. Hence, a bimodal distribution is different than unimodal distribution. A mixture of two normal distributions with equal standard deviations is bimodal only if their means differ by at least twice the common standard deviation (Schilling, Watkins et al. 2002) b. Locations of modes by size, mean size by count, two standard deviations centered around mean size by count by the f ollowing approaches to size resolution: i. for parameters up to 20 nm, the parameter differs from that of other materials by 2 nm or more, ii. for parameters between 20 and 50 nm, the parameter differs from that of other materials by 5 nm or more, iii. for parameters between 50 and 1000 nm, the parameter differs from that of other materials by 10 nm or more,iv. for parameters between 1000 and 10000 nm, the parameter differs from that of other materials by 100 nm or more, v. for parameters greater than 10000 nm, the parameter differs from that of other materials by 1000 nm or more 4. Nanoscale materials shall be distinguished by distributions at the primary, secondary, and tertiary structural level, e.g. primary particles, aggregates, and agglomerates. Hence, an aggregate with a mean size by count of 8 microns would be different than an aggregate with a mean size by count of 4 microns, even if the nanoscale primary particles of each substance would be considered to have the same size distribution

. Auffan, M ., J. Rose, et al. (2009). "Towards a definition of inorganic nanoparticles from an environmental, health and safety perspective." Nat Nano advance online publication

. Schilling, M. F., A. E. Watkins, et al. (2002). "Is Human Height Bimodal?" The American Statistician 56 (3): 223

- 229. Zingg, T. (1935). "Beitrag zur Schotteranalyse." Schweizerische Mineralogische und Petrographische Mitteilungen 15 : 39

– 140.