Unsupervised Analysis of Optical Imaging Data for the Discovery of Reactivity Patterns in Metal Alloy

Operando wide‐field optical microscopy imaging yields a wealth of information about the reactivity of metal interfaces, yet the data are often unstructured and challenging to process. In this study, the power of unsupervised machine learning (ML) algorithms is harnessed to analyze chemical reactivity images obtained dynamically by reflectivity microscopy in combination with ex situ scanning electron microscopy to identify and cluster the chemical reactivity of particles in Al alloy. The ML analysis uncovers three distinct clusters of reactivity from unlabeled datasets. A detailed examination of representative reactivity patterns confirms the chemical communication of generated OH− fluxes within particles, as supported by statistical analysis of size distribution and finite element modelling (FEM). The ML procedures also reveal statistically significant patterns of reactivity under dynamic conditions, such as pH acidification. The results align well with a numerical model of chemical communication, underscoring the synergy between data‐driven ML and physics‐driven FEM approaches.


Introduction
[4][5] Image analysis is typically done using a supervised method, which involves manually labeling training data. [6]However, this approach DOI: 10.1002/smtd.202300214 can be costly and time-consuming and can introduce bias from the training data.An alternative approach, which is less commonly used but gaining popularity, is to apply unsupervised ML methods that do not require manual input. [7,8]The majority of the practical examples in science of unsupervised image analysis often come from biology and related bioinformatics fields, [9][10][11][12] while other fields are barely considered and still waited to be explored.This work showcases a practical application of unsupervised ML in surface science, leveraging the analysis of optical datasets from an operando reflection-based microscope (RM).The ability to predict material reactivity through such methods can have significant socio-economic implications for improving material durability and increasing energy efficiency. [13]30] RM has high temporal and spatial resolution, allowing for measurements with a resolution of ≈200 nm and acquisition rates up to kHz in a wide field (mm) range. [14,25]However, the generation of large optical datasets also poses significant challenges in processing feature-rich optical images.][33][34] While these methods are automated, they can be subject to human bias and may require fine-tuning of empirical parameters.In this study, we propose an efficient unsupervised machine learning framework for fully automated analysis of reflective videos obtained from the operando monitoring of the local electrochemical degradation by aqueous solution of Al alloy of 6061 series as a model system.
[37] When exposed to an electrolytic solution, these particles initiate multiple localized electrochemical reactions across a large surface area, making Al alloys a suitable model system for the development of pattern recognition algorithms.In our recent study, [38] Figure 1.Correlative microscopy approach used in this study (further details can be found in Section S1 in the Supporting Information).a) The setup for operando optical observation of the mirror-polished (<40 nm roughness [38] ) Al6061 interface exposed to 5 × 10 −3 m NaCl is depicted.b) A diagram of the optical signal generation during OH − production (from ORR and HER) over a Si-rich particle is induced by galvanic coupling between the particle embedded in the anodically active Al matrix.Incident light (E i ) is focused on the metal surface.The collected light includes the contributions of reflected light (E r ) from the surface film and the metal.Their interference forms the basis for the quantification of local surface thickness changes via the Fresnel equations.c) On the left, an example of operando optical movie from RM is shown, correlated with ex situ SEM and EDX analysis.The evolution of normalized (to t = 0 s) light reflectivities (1+∆R/R) in areas (1, marked as blue square) and (2, marked as red square) are depicted in the figure on the right top.1+∆R/R values are converted to relative film thickness, depicted on the right y-axis.The slopes of curves (1-blue) and (2-red) define rates of film evolution.The bottom right presents a diagram of Al(III) stability as a function of pH calculated in HydroMeduza software [44] (soluble species taken into account: Al 3+  utilizing correlative techniques such as optical (reflectivity, fluorescence) microscopies, scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDX), we observed that all particles within an Al6061 alloy drive pH basification through the reduction of oxygen (ORR) and evolution of hydrogen (HER), leading to localized dissolution and precipitation of films.[41][42][43] In contrast to previous work, this study demonstrates that increasing the average distance between particles and incorporating Cl − into the conductive electrolyte results in accelerated film dissolution and enhanced chemical communication, but now within individual micrometric particles, i.e., showing intraparticle reactivity patterns.Complementary finite element modeling (FEM) was also employed to provide further insight.This research offers a case study of unsupervised ML applied to the field of surface science and highlights the synergistic relationship between data-driven and physics-driven approaches.

Quantification of Film Evolution over Particles
The investigation of intraparticle communication within individual micrometric particles requires using a correlative microscopy approach using sub-micrometer spatial resolution imaging techniques, i.e., sub-particle resolution imaging (Figure 1, see also Section S1 in the Supporting Information for experimental details).The surface of a mirror polished Al6061 sample was initially analyzed using SEM and EDX.The sample was then placed in a corrosive electrolyte of 5 × 10 −3 m NaCl (neutral pH) in the optical setup (Figure 1a).Note, no external electrochemical perturbations were imposed on the system.Instead, the sample was allowed to freely corrode, forming localized galvanic cells around the particles within the Al matrix (Figure 1b).The sample underwent primary oxidation, forming a 10 nm surface film of Al oxides/hydroxides (denoted as Al(OH) 3 for simplicity in Figure 1b).This process was monitored dynamically and operando by RM, by illuminating the sample surface with a blue light (490 nm wavelength) through a ×40 water immersion objective and recording maps (at 5 Hz) of the dynamic changes in light reflected by the sample surface and collected onto a CCD camera.In this section, we conducted a manual analysis of a small fraction (8.5 × 6 μm 2 ) of the optically screened region.In the subsequent section, we will expound on an automated analysis of the entire wide-field optical footage (187 × 180 μm 2 ).
The presence of particles is visible in both optical and SEM images (Figure 1c) as regions of dark contrast compared to the surrounding Al matrix.EDX analysis shows that the particles are rich in Si and are composed of the SiO 2 phase, as reported in our previous work. [38]It should be noted that Fe-rich particles were also observed in some areas of the sample (Section S2, Supporting Information).However, since there was no significant evolution of surface films over Fe-rich particles within the time frame of the experiment (as shown in Section S2 in the Supporting Information and previous work [38] ), only the reactivity over Si-rich particles will be discussed in the main text.
Si-rich particles are galvanically coupled to the less noble Al matrix and serve as centers for the generation of OH − due to ORR and HER (Figure 1b) (as reported [38] using fluorescence microscopy).The pH gradients control the dynamics of surface film evolution, as illustrated from the Al(III)-pH diagram in Figure 1c (bottom right).Experimentally, the in situ transformation of surface films is quantified from optical movies of reflectivity changes (Figure 1c, top left), taken at a 5 Hz acquisition rate over 20 s in this work.Example curves of normalized reflectivity changes in Figure 1c (top right) demonstrate a linear change in light intensity, which was converted into relative thickness of the surface film based on the Fresnel equation (as detailed in Section S1 in the Supporting Information).An increase in the thickness of surface films was attributed to the precipitation of Al(OH) 3 films (pathway 1 in Figure 1c), while a decrease was attributed to the formation of soluble Al(OH) 4 − (pathway 2 in Figure 1c).The rate of surface film evolution was defined as the slope of the film relative thickness evolution and optical movies were converted into maps of rates of film evolution (Figure 1d).
The blue regions in Figure 1d correspond to areas of Al(OH) 3 precipitation, the red regions correspond to film dissolution, and the white regions indicate that the film is unchanged during the whole experiment, with the extent of film dissolution ranging from −0.3 to 0.3 nm s −1 .Overall, the dominating color in the map of film evolution is light red, indicating the gradual dissolution of surface films over the Al matrix.][47] The corrosive effect of Cl − ions can promote the release of Al 3+ , which can subsequently result in local acidification of the pH due to Al 3+ hydrolysis and ultimately, the dissolution of the surface film.Areas over particles are visible as blue regions, mostly within the edge of the particles, with regions of intense red areas located in the center of the particles.Such difference in behavior within different regions of the particle surface are likely related to the pH gradients over a single particle.In the following sections, we will discuss this phenomenon in detail, providing an unsupervised statistical analysis of particle reactivities.
It is worth noting that scratches from polishing and small defects, visible as dark lines and spots in both optical and SEM images (Figure 1c), are also evident in the map of film evolution as different shades of blue (Figure 1d).This indicates that precipitation of surface films occurs in these areas, more likely due to the generation of OH − over these regions (observed with fluorescence microscopy in our previous work [38] ) that should compensate for local pH acidification due to hydrolysis of Al 3+ ions.

Unsupervised Clustering of Particle Activities
The wide-field videos contain a large amount of unstructured but valuable information that cannot be efficiently treated with conventional data processing algorithms.In this section, we describe a novel pipeline for automated analysis of the complete wide-field image (187 × 180 μm 2 ) with the aim of identifying patterns of reactivity across particle areas.The routine extensively utilizes unsupervised machine learning algorithms, such as K-means and principal component analysis (PCA), as well as OpenCV libraries (Figure 2).
In the first step (Figure 2), a single frame of the optical video was used to find coordinates and extract images of individual particles.This was done through automated image segmentation and image thresholding, which allowed for the extraction of the positions of all 155 particles on the Al interface.Then, the local optical intensities within the images of individual particles were normalized and converted to local rates of surface film conversion with the aid of the Fresnel equation, as described in Figure 1.
In the second step, we flattened the image matrix into a 1D array and performed dimensionality reduction using PCA to visualize our 155 images in 2D.Prior to flattening, we interpolated the images of each individual particle to a uniform size of 30×30 pixels to exclude particle size as a criterion for clustering.To identify different patterns present in our data, we used K-means clustering for the original reactivity images.Using the elbow method, we determined the optimal number of clusters to be 3, as shown in Figure 2 (step 2).For each cluster, we identified its representative pattern corresponding to the cluster centroid, which is formed by the mean values for all pixels.We observed that centroids 2 and 3 represented similar reactivity images of particles, with a blue region on the particle periphery and a red area in the center.Based on this similarity, we merged clusters 2 and 3 into a single category (labeled as category 2 in Figure 2).In contrast, the reactivity pattern observed for centroid 1 was markedly distinct, with a blue region present across almost the entire surface of the particle.We attributed this to a separate category labeled as 1.
It is important to note that some images in category 1 (Figure 2, step 3) display a light red color in the middle of the particle area.However, the intensity and area coverage of this red region are significantly lower compared to those of the red region in the middle of the particles from category 2. Our approach utilizes an automated ML algorithm for the assignment of particle type, which ensures that the process is unbiased and based solely on the automated score.Upon manual verification, the percentage of falsely identified images in categories 1 and 2 was found to be 8% and 6%, respectively, demonstrating satisfactory accuracy.All images of the presented categories and technical details of the pipeline routine can be found in Section S3 (Supporting Information), along with a reference to the original python code.

Role of the Particle Size in Intraparticle Communication
For a majority of particles, clustered in category 2, the reactivity maps shown in Figure 2 reveal regions of opposite reactivity within the same particle, with a preferred precipitation behavior along the edge of the particle and preferred dissolution at the center of the particle (blue vs red areas).The aim of this section is to discuss the physical origin of such opposite reactivities.This is analyzed through a typical example of particle detailed in Figure 3.A first comparison is made, in Figure 3a, between the initial optical image of the particle and its reactivity map.The inset of Figure 3a presents the spatial distribution of the reflectivity and reactivity along the same cross-section of the particle.The position of the particle in the optical image is marked by a decrease in reflectivity, which is attributed to the lower reflection of the SiO 2 surface in comparison to the surrounding Al surface.If some local changes in reflectivity are detected along the particle image, the reflectivity steadily decreases along the cross-section.On the contrary the reactivity shows stronger local variations, with apparently no correlation between rate of film evolution and local reflectivity.
Remarkably, the dissolution of the surface film is observed not only within the particle but also in its immediate vicinity (red region surrounding the particle in Figure 3a), extending up to <1 μm to the Al surface with an absolute value of approximately −0.1 nm s −1 .This phenomenon, known as trenching in corrosion science, [17,36,45,48] occurs due to the preferential dissolution of the Al matrix resulting from regions of stronger galvanic coupling (higher local current density) to a more noble particle. [17,36,45,48,49]The spatial extent of trenching is in agreement with previous studies, while the absolute value of the film dissolution provides new information that is not directly accessible under typical corrosion conditions.Considering the local equivalence of anodic and cathodic current densities for the galvanic cell generated by a single particle, it is reasonable to anticipate that the spatial range of trenching will be similar to that of film precipitation over the particle.This suggests that the particle's size, and hence its geometry, may contribute to the local reactivity observed across its surface.
To corroborate on such hypothesis, Figure 3b presents the size distribution of particles for both categories of particles.A comparison of the size of the two distributions shows that category 1 is limited to the smallest particles, approximately < 2 μm 2 , while category 2 shows a much wider distribution of particle sizes which can be as large as ca.6 μm 2 .This suggests that a necessary (but not sufficient) condition for belonging to category 1 (no communication) is a surface area < 2 μm 2 implying a size threshold for particle to present surface film dissolution (marked as red in our notation).We recall that the entire area of the particle is cathodically active, producing OH − fluxes that control the surface film evolution according to the Al(III)-pH diagram (Figure 1c).Under the assumption of a constant normalized flux of OH − on the particle surface, the unique feature of larger particles is that they always possess higher pH values with the maximum located at the particle center.This is due to the higher degree of overlapping of OH − diffusion fields generated on larger surface areas, referred as intraparticle communication in this work.This provides a qualitative chemical explanation of the observed pattern of surface film evolution for particles in category 2.
Note that in contrast to our previous work where the interparticle communication was observed, [38] in this work, the averaged distance between particles was increased from ≈2 to ≈6 μm that should be responsible in the transposition of inter-to intraparticle communication, observed herein (Section S4, Supporting Information).In order to test the hypothesis of the influence of particle size on the pattern of surface evolution, a finite element model (FEM) was developed using COMSOL Multiphysics 5.5 software.The model considered circular disks of varying sizes generating identical normalized fluxes of OH − while the bulk pH was equal to 7. Additionally, the model assumed that the particles were covered with an Al(OH) 3 film that could either precipitate or dissolve as a function of local pH.Technical details of the numerical calculations can be found in Section S5 in the Supporting Information.The absolute value of the OH − flux kinetics of the Al(OH) 3 was not measured in this work, but values were chosen within the range reported in the literature and summarized. [38]in order to qualitatively match the observed phenomenon.
The results of the simulations are given in Figure 3c.Starting from the edge of the particle a film deposition is observed.The film deposition is homogeneous for particle size up to 1.5 μm in diameter (<2 μm 2 surface area).When the particle size increases from 1.5 to 2.5 μm in diameter (from 1.8 to 4.9 μm 2 area), the film deposition is localized on the edge of the particle while towards the center of the particle the deposition rate decreases towards either no deposition or a (red) region of slight film dissolution.Further increase in particle size from 2.5 to 2.7 μm results in an increase in the size of the red area as well as the absolute values of dissolution rates.These simulated data are in good qualitative agreement with the distribution of particle sizes in categories 1 and 2 as shown in Figure 3b.A detailed analysis of the proposed model (Section S5, Supporting Information) reveals that the extent of the dissolution region depends on the bulk pH for a given particle size.In the following section, we further investigate this dependence experimentally and numerically to provide more evidence for the mechanism of intraparticle communication.

Impact of pH Acidification on Intraparticle Communication
After observing the reactivity of particles at neutral pH in 5 × 10 −3 m NaCl using wide-field optical technique, a few drops of concentrated H 2 SO 4 were added to create a 10 × 10 −3 m H 2 SO 4 solution.After adjusting the focus for ≈5 s, another optical movie was recorded for a duration of 20 s.The images of individual particles were then extracted and converted into maps showing the rate of surface film evolution, using the same procedure as outlined in step 1 of Figure 2. The output data includes two images of surface film evolution at both neutral and acidic bulk pH for the same 155 particles (as shown in Figure 4, step 1).
The aim of this section was to identify descriptors that could indicate the extent of change between the two images and then cluster these descriptors accordingly.To achieve this, we computed the pixel-wise values of the local rates of surface transformation under both neutral and acidic pH conditions and generated a correlation matrix of the results (as shown in Figure 4, step 1, with some technical details provided in Section S3 in the Supporting Information).In brief, we began by segmenting the squared image of the particle, including its surroundings (Figure 4, step 1).To accomplish this, an automated unsupervised ML technique was employed to partition the image, which had a continuous range of values, into a segmented image consisting of 5 of the most representative mean values.The middle value corresponded to "no surface evolution" with a rate of 0, while two values represented high and moderate dissolution situations with rates less than 0, and two other values represented precipitation situations with rates greater than 0. We then plotted these mean values on the x-axis taken from the image at neutral pH and on the y-axis taken from the image at acid pH, creating a 5 by 5 matrix.We subsequently determined the number of pixels belonging to each distribution of mean values, normalized it by the total number of pixels, and placed it in the corresponding square of the correlation matrix.
We discuss briefly, with few examples, how to read and interpret the correlation matrix.The initial observation concerns the range of dissolution and precipitation rates on each axis which are distinct.For instance, the most negative value on the y-axis (acid pH) was −0.48 nm s −1 , while on the x-axis (neutral pH) it was −0.45 nm s −1 .The cell of the matrix with the coordinates (−0.45, −0.48) nm s −1 corresponds then to pixels of the segmented images having the highest dissolution rates in both neutral and acid pH.It indicates that these areas are subject to the same type of reaction (a dissolution) but with higher dissolution rates in acid than in neutral pH, as expected.Similarly, the opposite corner cell of the matrix with coordinates (0.26, 0.14) nm s −1 reflects regions with the highest precipitation rates.Again, this cell indicates that the pixels subjected to precipitation in neutral pH are also subjected to precipitation in acid pH but with a lower precipitation rate, also consistent with higher solubility of the Al surface films in more acidic environment (Figure 1c).All diagonal cells of the matrix can be analyzed similarly.They correspond to areas of the segmented image showing identical behavior between neutral and acid pH.The diagonal cells include 61% of the pixels, meaning that 61% of the particle image show similar trend in neutral and acid pH.
The second key observation pertains to matrix cells that lie outside the matrix diagonal, as these cells represent regions showing varying reactivity between neutral and acid pH.As the most pertinent example, we describe and interpret the 2nd column from the left, corresponding to regions of moderate dissolution of −0.27 nm s −1 at neutral pH.A significant number of pixels (12%) in the 2nd column belong to the high dissolution rate of −0.48 nm s −1 at acid pH revealing the expansion of the surface film dissolution over Al matrix upon acidification.The 3 cells below the diagonal ((−0.27,0), (−0.27, 0.02), and (−0.27, 0.14) nm s −1 ) account for 7% of pixels, and they indicate the areas of an opposite effect, namely favorable precipitation (or disfavored dissolution) at acid pH.The 3rd and 4th columns from the left, which represent no surface evolution and moderate precipitation, respectively, also show a similar effect, as can be seen from the important filling of the cells of the matrix below the diagonal.The overall trend of higher filling of the cells below the diagonal is consistent with the reactivity maps, which show a decrease in the extent of the red color within the particle as it transitions from neutral to acid pH.
In summary, the correlation matrix is a valuable tool as it reflects the degree of reactivity change between neutral and acid pH in a precise and quantitative manner.It can be used to quantify and cluster reactivity transitions.Furthermore, the overall shape of the matrix can reveal apparently counter-intuitive conclusions, such as the fact that while more acidic conditions may yield an overall dissolution of the substrate, the particles may actually be more prone to precipitation.
In the second step (Figure 4, step 2), we visualize pattern changes upon acidification by using dimensionality reduction with PCA on the correlation matrices described above.We then perform clustering using the K-means algorithm with the number of clusters equal to 2, as identified by the elbow method, similarly to Figure 2. Figure 4 (step 2) shows the images that are closest to the centroids of the defined clusters.We use this approximation because the true centroids are correlation matrices that cannot be converted back to images of reactivity.The ML analysis of the data indicates that the (pseudo) centroids 1 and 2 display a similar pattern of reactivity, in which the red region inside the particle decreases in size and intensity at acidic pH values.
To confirm the suggested trend, using the same kinetic formalism for Al hydroxides formations, the simulation of the particle reactivity pattern has been recomputed and compared for neutral and acid pH solutions (Figure 4, step 3).The decrease in the extent of dissolution (red) regions in the particle center is consistent with the numerical model (Figure 4, step 3) developed in the previous section.We also provide the comparison between simulated and experimental 2D profiles to confirm that acidification leads consistently to an increase in the rate of film formation (Section S6, Supporting Information).The decrease in bulk pH results in a decrease in pH over the center of the particle, which in turn disfavors the formation of soluble Al(OH) 4 − (pathway 2 in Figure 1c) and favors the formation of Al(OH) 3 film (pathway 1 in Figure 1c).
In conclusion, chemical communication between particles can exhibit varying behavior based on experimental conditions and particle distribution.The intensity of diffusive fluxes between particles decreases with increasing distance, leading to a decline in interparticle communication.Our studies on Al6061 alloy (herein and ref. [38]) showed that a distance increase from 2 to 6 μm was sufficient to inhibit interparticle communication and promote intraparticle communication.Automated image analysis was crucial in detecting this trend, as it may have gone unnoticed using traditional manual methods.

Conclusion
In this study, we adapted unsupervised ML algorithms to analyze the reactivity patterns from wide-field reflection-based optical microscopy of individual Si-rich particles during the immersion of Al6061 alloy interface in 5 × 10 −3 m NaCl.The analysis uncovered two distinct patterns: (1) homogeneous precipitation of a surface film over the particles and (2) the presence of an area in the particle center where the surface film was dissolving.The largest particles consistently displayed pattern 2, which was attributed to higher pH values in the particle center as a result of overlapping generated OH − diffusion fields within a single particle.This phenomenon, known as intraparticle chemical communication, is sensitive to bulk pH and was less pronounced after pH acidification.The experimental results of unsupervised ML clustering were rationalized through FEM simulations, highlighting the synergy of the two approaches in extracting knowledge from data-rich experimental datasets.This novel approach offers invaluable insights into microscale reactivity patterns, advancing materials selection and design, and paving the way for enhanced durability and energy efficiency across various applications.
Figure 1.Correlative microscopy approach used in this study (further details can be found in Section S1 in the Supporting Information).a) The setup for operando optical observation of the mirror-polished (<40 nm roughness[38] ) Al6061 interface exposed to 5 × 10 −3 m NaCl is depicted.b) A diagram of the optical signal generation during OH − production (from ORR and HER) over a Si-rich particle is induced by galvanic coupling between the particle embedded in the anodically active Al matrix.Incident light (E i ) is focused on the metal surface.The collected light includes the contributions of reflected light (E r ) from the surface film and the metal.Their interference forms the basis for the quantification of local surface thickness changes via the Fresnel equations.c) On the left, an example of operando optical movie from RM is shown, correlated with ex situ SEM and EDX analysis.The evolution of normalized (to t = 0 s) light reflectivities (1+∆R/R) in areas (1, marked as blue square) and (2, marked as red square) are depicted in the figure on the right top.1+∆R/R values are converted to relative film thickness, depicted on the right y-axis.The slopes of curves (1-blue) and (2-red) define rates of film evolution.The bottom right presents a diagram of Al(III) stability as a function of pH calculated in HydroMeduza software[44] (soluble species taken into account: Al 3+ , Al(OH) 2 + , Al(OH) 3 , Al(OH) 4 − , Al 13 O 4 (OH) 24 7+ , Al 2 (OH) 2 4+ , Al 3 (OH) 4 5+ , AlOH 2 + ; solid species: Al(OH) 3 (s), AlOOH(s), Al 2 O 3 (s)).Pathway (1) corresponds to the film precipitation and pathway (2) to the film dissolution observed in the related regions in the optical movies.d) A reconstructed map of rates of local film evolution deduced from the optical movie is presented.The scale bars are 2 μm.

Figure 2 .
Figure 2. Automated pipeline for reactivity pattern recognition (Section S3, Supporting Information).Step 1: The positions of all individual particles (155 in total) were extracted from a wide-field optical movie (187 × 180 μm 2 with a resolution of 200 nm) and converted into maps of rates of film evolution.Step 2: PCA projection of 155 maps of rates colored according to the results of clustering.The centroid image (see definition in text) of each cluster is represented in the figure.Step 3: Cluster 1 was placed in category 1 (47 particles, 30% of the whole population).Cluster 2 and cluster 3 both demonstrate the presence of intraparticle communication and were therefore merged to form a single category (labeled as category 2) of 108 particles (70% of the whole population).The scale bars of individual particles are 1 μm.

Figure 3 .
Figure 3. Size effect on intraparticle communication.a) Comparison over a single particle of (left side) the map of the rate of film evolution, and (right side) the first optical reflectivity image of the same area.The scale bars are 1 μm.The insets at the bottom of the figure display the values along the dotted line in the center of each image.b) Histogram of particle size distribution depending on the category it belongs: category 1 (red, no communication) and category 2 (blue, intraparticle communication).c) Numerical simulations of the rate of film evolution (details in text) over single disk particles for particle diameter of 1.5, 2.5, and 2.7 μm.

Figure 4 .
Figure 4. Pipeline for the analysis of the evolution of particle reactivity upon acidification.(Section S3, Supporting Information).Step 1: The rates of film evolution over all 155 individual particles are correlated pixel-by-pixel before and after pH acidification (via the addition of H 2 SO 4 to a pH neutral solution of 5 × 10 −3 m NaCl).The outcome is presented as a correlation matrix (unique for each particle) where every cell represents the total number of pixels (shown in each cell in %) that possesses a given rate of film evolution at neutral pH (read on the x-axis) and a given rate at acid pH (read on the y-axis).Step 2: Results of the dimensionality reduction by PCA for correlation matrices of each particle colored according to clustering results.The particle at neutral and acid pH closest to the centroid of each cluster is shown and marked as (pseudo) centroid.Step 3: Numerical simulations are undertaken on the example of a particle with a diameter of 2.6 μm to reproduce the pattern extracted from clustering.The scale bars are 1 μm.