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Research Papers

Quantifying Dispersion of Nanoparticles in Polymer Nanocomposites Through Transmission Electron Microscopy Micrographs

[+] Author and Article Information
Xiaodong Li

NCMIS,
Academy of Mathematics and Systems Science,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: xli@amss.ac.cn

Hui Zhang

National Center for Nanoscience and Technology,
Beijing 100190, China
e-mail: zhangh@nanoctr.cn

Jionghua Jin

Department of Industrial and
Operations Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: jhjin@umich.edu

Dawei Huang

Academy of Mathematics and Systems Science,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: dwwong1217@gmail.com

Xiaoying Qi

National Center for Nanoscience and Technology,
Beijing 100190, China
e-mail: qixy@nanoctr.cn

Zhong Zhang

National Center for Nanoscience and Technology,
Beijing 100190, China
e-mail: zhong.zhang@nanoctr.cn

Dan Yu

NCMIS,
Academy of Mathematics and Systems Science,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: dyu@amss.ac.cn

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received September 4, 2013; final manuscript received March 19, 2014; published online April 23, 2014. Assoc. Editor: Don A. Lucca.

J. Micro Nano-Manuf 2(2), 021008 (Apr 23, 2014) (11 pages) Paper No: JMNM-13-1068; doi: 10.1115/1.4027339 History: Received September 04, 2013; Revised March 19, 2014

The property of nanocomposites is crucially affected by nanoparticle dispersion. Transmission electron microscopy (TEM) is the “golden standard” in nanoparticle dispersion characterization. A TEM Micrograph is a two-dimensional (2D) projection of a three-dimensional (3D) ultra-thin specimen (50–100 nm thick) along the optic axis. Existing dispersion quantification methods assume complete spatial randomness (CSR) or equivalently the homogeneous Poisson process as the distribution of the centroids of nanoparticles under which nanoparticles are randomly distributed. Under the CSR assumption, absolute magnitudes of dispersion quantification metrics are used to compare the dispersion quality across samples. However, as hard nanoparticles do not overlap in 3D, centroids of nanoparticles cannot be completely randomly distributed. In this paper, we propose to use the projection of the exact 3D hardcore process, instead of assuming CSR in 2D, to firstly account for the projection effect of a hardcore process in TEM micrographs. By employing the exact 3D hardcore process, the thickness of the ultra-thin specimen, overlooked in previous research, is identified as an important factor that quantifies how far the assumption of Poisson process in 2D deviates from the projection of a hardcore process. The paper shows that the Poisson process can only be seen as the limit of the hardcore process as the specimen thickness tends to infinity. As a result, blindly using the Poisson process with limited specimen thickness may generate misleading results. Moreover, because the specimen thickness is difficult to be accurately measured, the paper also provides robust analysis of various dispersion metrics to the error of the claimed specimen thickness. It is found that the quadrat skewness and the K-function are relatively more robust to the misspecification of the specimen thickness than other metrics. Furthermore, analysis of detection power against various clustering degrees is also conducted for these two selected robust dispersion metrics. We find that dispersion metrics based on the K-function is relatively more powerful than the quadrat skewness. Finally, an application to real TEM micrographs is used to illustrate the implementation procedures and the effectiveness of the method.

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Figures

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Fig. 1

Illustration of the projection view of TEM micrographs

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Fig. 2

Illustrative example of the impact of h on dispersion metrics

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Fig. 3

Point patterns with clustering

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Fig. 4

(a) Mean RoI for nanoparticles. (b) Mean RoI for aggregates. (c) Difference between the K-function curve and its reference curve under the hardcore process at a content of 10% and 13% when R = 2.

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Fig. 5

Flowchart for the proposed analysis procedures

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Fig. 6

Real TEM micrographs and aggregate boundary detection

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