Mnp r pdf

To quantify the distinctiveness of the two classes, we evaluate the average cross entropy from information theory, where the average cross entropy between two distributions p and q is defined as , where N is the number of elements in distribution p , and p i and q i represent the likelihood of the i th element of distribution p predicted by distribution p and q , respectively.

H p , q quantifies the distinctiveness between distribution p and distribution q : the larger H p , q , the more distinct p is from q. Using this measure, the two classes identified from the triangular prism sample are found to be much less distinct than the nanorod case. This can be seen quantitatively by comparing the average cross entropy with respect to the bulk distribution Table S3.

We hypothesize that the distinctions between the triangular particles and rod-shaped impurities were so large that the possible presence of intraclass variations among the triangular particles were weighted to a lesser degree and thus not identified by the algorithm. Compared to the 2-class scenario triangles and rod-shaped impurities in the first iteration of classification, classifying the particles into four classes triangles, symmetrically truncated triangles, asymmetrically truncated triangles, and rod-shaped impurities in the second iteration significantly improved log-likelihood from 6.

Upon applying more iterations of classification, the log-likelihood did not improve further, suggesting that there is no more significant intraclass variation to capture and that the algorithm has converged. Applying further iterations of classification on the class of rod-shaped impurities also did not improve the log-likelihood, suggesting that the class has little intraclass variation. In this case, the averaged cross entropy between subclasses are now sufficiently large such that these subclasses are quantifiably distinct from each other.

However, by taking into account all four descriptors the algorithm was able to make a clear distinction between the three subclasses. This demonstrates the importance of using high-dimensional features for the classification of shapes.

Further classification of the Au triangular prisms class. Distributions and relative population of particles in each class red pure triangles, cyan symmetrically truncated triangles, yellow asymmetrically truncated triangles. These information can potentially be used to interpret kinetically controlled formation mechanisms and relative speed of growth of different facets during the formation of Au nanoparticles by, for example, helping to illuminate the shape transition from 3-fold symmetrical triangular particles to 6-fold symmetrical hexagonal particles Figure S4.

The existence of these potential interpretations of the classification results demonstrated that AutoDetect-mNP is capable of more than just arbitrary assigning NPs to classes but also potentially helping to unveil the underlying physical processes governing the distribution of NP shapes. In future studies, a kinetic growth model, potentially similar to the one previously reported by Handwerk et al. These NP systems have been widely studied in literature for a variety of applications.

The most significant challenge of extending to NP systems beyond Au NPs is the decrease in image contrasts. As a heavy metal with large nuclear mass and high lattice packing efficiency, Au interacts strongly with incoming electron beams, and thus showing very high contrasts when imaged in TEM. CdSe and Pd, however, interact with electrons much more weakly and, therefore, show much lower contrasts under TEM.

Because of the reduced image contrasts, K -means image segmentation no longer showed satisfactory performances on these NPs. Therefore, we instead employed the image segmentation method reported by Powers et al, which is designed to analyze images with low contrasts. The algorithm identifies two shape classes in the data set: nanocubes and irregularly shaped impurities. Irregularly shaped impurities only took a small part of the entire population, showing that the reaction has good shape control.

Upon applying more iterations of classification on the data set, it can be seen that the algorithm further broke down the class of cubes into smaller subclasses based on the nuanced differences among the cubes Figure S6. In this way, the algorithm is again shown to be capable of providing information on the shape distributions of NPs at different levels of details, from quantifying the yield of the nanocubes to characterizing the nuanced variations in the shapes of the nanocubes.

However, the algorithm was still found to be capable of analyzing the shapes of these NPs with relatively high accuracy Figure S7. A total of 25 images of the QDs were analyzed. However, the image segmentation algorithm failed to achieve satisfactory performance on seven of the images, and therefore all analysis was done based on the 18 images successfully segmented, which contain NPs. Therefore, we relied on the log-likelihood metric to determine the optimum number of classes through iterative classifications.

Log-likelihood converged to From visual inspection of the shapes of NPs in each class Figure S7 , it can be seen that the classification intuitively makes sense, with NPs in different classes showing different symmetries. In this work, we developed an unsupervised machine learning algorithm, AutoDetect-mNP, that classifies Au NPs in TEM images based on extracted morphological information without human intervention.

AutoDetect-mNP automatically decides the optimal number of classes for clustering based on intra- and interclass feature similarities and provides more relevant statistical distributions of the features for each class generated by the algorithm. The use of classes as a way of characterizing the shape distributions of nanoparticles can also be quantified with a cross-entropy measure post defacto to distinguish it from a more featureless continuum.

By comparing the analysis results on the composition of Au nanorod mixtures with different aspect ratios with human labeling and other existing algorithms, we demonstrated that our method is quantitatively reliable while being much more efficient.

Applying the algorithm to the characterization of shape distributions of synthesized Au triangular prisms, the algorithm identified rod-shaped impurities from the triangular main products. Furthermore, running the algorithm iteratively on identified classes can organize the shapes of the particles hierarchically.

It is hoped that the quantitative shape distributions provided by the algorithm can potentially help to provide insights into the mechanism of the formation of the nanoparticles. It was shown that, by using different particle detection methods, the algorithm can be applied to much broader categories of NPs. We can imagine future studies using AutoDetect-mNP to answer scientific questions such as optimizing reaction conditions for a high-throughput experimental setup, modeling the reaction mechanism with real-time analysis of particle shapes captured by TEM videos, or studying the self-assembly of NPs with different shapes.

NaBH 4 powder was stored in an argon glovebox. Cadmium oxide CdO All the glassware used for the synthesis of Au NPs was thoroughly cleaned using freshly prepared aqua regia volume ratio of HCl and HNO 3 , respectively followed by fully rinsing with copious amounts of DI-water. All chemicals were of reagent grade and used without further purification unless specified otherwise. Two types of AuNRs were synthesized by a facile seed-mediated growth involving a binary surfactant mixture.

The seed solution was prepared as follows: 10 mL of 0. Upon the addition of NaBH 4 , the color of the seed solution turned yellow-brownish. The growth solution was obtained by first mixing 3. The solution was heated with occasional agitation until all the CTAB was dissolved. The yellowish color of the growth solution turned to colorless. A certain amount of HCl Table 2 was added to the solution, and the mixture was stirred at rpm for 15 min.

A 40 mL portion of the final products were isolated by centrifugation at rpm for 15 min followed by careful removal of the supernatant.

A 10 mL portion of DI-water was added to the pellet, and the mixture was sonicated briefly to disperse the pellet. Homogeneous gold triangular prisms were also synthesized by seed-mediated method. For the growing process, the UV—vis spectra of the seed solution were taken using 1 cm quartz cuvette to determine the concentration of the seed. The extinction coefficient of the seed solution is 9. In order to synthesize the triangular prism with edge length in 80 nm, the final concentration of the seed in the growth solution should be Prior to preparing the growth solution, the stock mixture of 0.

Finally, a certain amount of seed solution was added under vigorous stirring. For the purification process of Au nanoprisms, 0. The mixture was left undisturbed for 4 h and centrifuged twice at rpm for 15 s. The supernatant was carefully removed, and 0. Palladium nanocubes were synthesized with a method similar to a previous report. A 50 mL aqueous growth solution was prepared in a mL round-bottom flask containing The solution turned into a dark brown color during the growth process.

The final products were cooled to room temperature and isolated by centrifugation at rpm for 15 min followed by removal of the supernatant. The resulting pellet was dispersed in 5 mL of water by sonication. CdSe cores were synthesized using a modified version of a previously published procedure. The reaction was stopped after approximately 4 min and quickly cooled. The QDs were purified from free ligand and excess precursors via precipitation with acetone and redispersion in hexanes several times.

Sizing and concentrations were determined using previously established calibration curves. Samples were prepared according to the work of Ondry et al. Finally the nanocrystals were centrifuged at rpm in hexanes to remove any remaining insoluble impurities. In order to calculate the concentration of Au nanorods, we referred to the theoretical extinction coefficient of the AuNR reported by Park et al.

The optical density of the solution was collected using a Shimadzu UV UV—vis spectrophotometer with 1 nm resolution. The path length of the cuvette was 1 cm. To make a ratio of short and long AuNRs, the concentration of each sample was fixed to 90 pM. The sample was fully dried in a vacuum desiccator before being imaged. The well was covered with a glass slide to slow solvent evaporation and was allowed to sit for at least 8 h.

The samples were transferred via scooping from below to an amorphous carbon coated TEM grid for microscopy. All images were recorded under kV accelerating voltage. Drift correction feature of the imaging software was enabled during the acquisition of all images. Experimental parameters during the imaging process can impact the performance of the algorithm. The efficiency of particle detection can depend on the resolutions and contrasts of the TEM images.

Therefore, optimizing experimental parameters during imaging to improve image resolution and contrast is recommended. We observed that magnification and camera exposure time are two of the most important imaging parameters to fine-tune. Matlab codes for real-time image analysis during imaging are included in the Github repository for AutoDetect-mNP to help the users optimize experimental parameters during imaging.

Imsegkmeans segments the image by performing a K -means clustering on the pixel intensities of each image. Shape descriptors for each particles were calculated by the regionprops function in Matlab. Each convex-shaped marker obtained at the end of UECS iterations was then dilated for the same number of times as it has been eroded to recover its original shape. K -means clustering and naive Bayes classifier used for unsupervised classification are well established clustering algorithms and are implemented in Matlab.

Of note, particles resolved by UECS were excluded during the automated classification process to avoid skewing of classification results by potential artifacts generated by UECS. Instead, these particles were assigned classes after the normal particles are clustered into different classes.

Unsupervised clustering of extracted features and selection of optimal number of clusters K , using circularity of Au nanorods as an example. Many users have provided feedback on the class, which is reflected in all of the different demonstrations shown in this document. All authors contributed insights and discussed and edited the manuscript. National Center for Biotechnology Information , U. JACS Au. Published online Feb Jakob C. Justin C. Paul Alivisatos. Author information Article notes Copyright and License information Disclaimer.

Corresponding author. Received Sep Published by American Chemical Society. This article has been cited by other articles in PMC. Keywords: transmission electron microscopy, nanoparticles, machine learning, unsupervised learning, image analysis.

Open in a separate window. Figure 1. Results and Discussion AutoDetect-mNP Algorithm Our goal is to develop an unsupervised algorithm capable of achieving four tasks in an automated manner for mNP particle classification. Figure 2. Figure 3.

Au Triangular Prisms After validating the performance of the algorithm on an artificially constructed data set, we demonstrate the potential of AutoDetect-mNP for characterizing and quantifying mNPs for a synthesis of Au triangular prisms as reported by Jones et al.

Figure 4. Figure 5. Conclusions In this work, we developed an unsupervised machine learning algorithm, AutoDetect-mNP, that classifies Au NPs in TEM images based on extracted morphological information without human intervention. Synthesis of Gold Nanorods Two types of AuNRs were synthesized by a facile seed-mediated growth involving a binary surfactant mixture.

Synthesis of Gold Triangular Prisms Homogeneous gold triangular prisms were also synthesized by seed-mediated method. Synthesis of Pd Nanocubes Palladium nanocubes were synthesized with a method similar to a previous report. Figure 6. Acknowledgments X. Author Contributions X. Notes The authors declare no competing financial interest. References Noguez C. Surface plasmons on metal nanoparticles: The influence of shape and physical environment.

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