QUANTITATIVE MICROSTRUCTURAL INVESTIGATION OF CARBON-BLACK-FILLED RUBBERS BY AFM

INTRODUCTION

Accumulation of reliable information on filled rubber morphology, filler distribution, and dispersion at micron and submicron levels is currently a topical problem.¹ The issue is complicated by active fillers, which after reaching a certain value of concentration, form spatial networks in the polymer matrix. An explicit quantitative characterization of these structures in an explicit form can be obtained from computer simulations.²

Three-dimensional transmission electron microscopy (3D-TEM) investigations of Japanese researchers^3,4 made it possible to visualize the spatial structure and determine the distances between the closest aggregates in the carbon black networks of rubber compounds; yet some important morphological characteristics of rubber compounds were disregarded in these works. Moreover, the size of the analyzed images (1 μm² × 1 μm²) gave no quantitative information concerning the state of filler distribution and microdispersion.

Different microscopy techniques for studying the microstructure of fillers, in particular carbon blacks, have been known since the 1960s.^5–7 With the advent of new experimental equipment and methods for the analysis of the fractal geometry of materials, many works related to the study of filler structures and their influence on the properties of rubber compounds have appeared.^8–13 However, most of those investigations were carried out to study single or separate filler aggregates, which rarely occurs in practice. Fillers such as carbon blacks are delivered to the rubber industry in the form of pellets (with an average granule size of 1–2 mm). In the process of mixing rubber compounds, carbon granules are broken down, which results in the formation of spatial filler networks. Because of this, the relation between the separate primary aggregate structure and the filler morphology in the final product becomes quite unclear.

Nowadays AFM became one of the most powerful and convenient tools for studying spatial surface structures of materials at micron and submicron levels. Many studies contain different results and differing interpretations of the AFMs of the structures of filled polymers, such as those for rubber–asphalt interactions¹⁴ and for elongating of filled compounds,^15–18 mixing of polymers and fillers,¹⁹ estimating agglomerate size,^20–22 studying scaling dependencies of aggregates and agglomerates in rubber by indentation,²³ and analyzing of the roughness of filled rubber in the vicinity of cracks,²⁴ among others. Most of the microstructure investigations are only qualitative (visual) examinations. Thereby, the third dimension, that is, the morphology of relief height, is often ignored, and the evaluation of AFM data is restricted to conventional two-dimensional images. To our knowledge, there are no publications concerning filled rubber compounds, which take into account the influence of the geometry of the AFM probe. As was shown for calibrating grids, the difference among features on the scanned images and the given geometrical characteristics can reach 25% in plane.²⁵ The fractal characteristics of the AFM images are also affected by the shape of the probe.^26,27

The main idea of this work is to replace continuous AFM relief with a discrete field of separate fragments. One can distinguish two major image-segmentation techniques: the watershed²⁸ and gradient methods.²⁹ In the first case, a rough surface is filled with water to a certain depth, and a continuous relief is divided into separate islands. Such an approach was used in our recent work,³⁰ which aimed to identifying agglomerates in a continuous filler network. Yet, it should be noted that information about the “bottom” part of the AFM image has been lost because the relief was flooded with water. The essence of gradient methods is to find segment boundaries by analyzing the map-height gradients. Largely, this approach is formalized, and therefore, it gives unsatisfactory results in the analysis of the topographically heterogeneous AFM scans of filled rubbers when a single region contains objects of different sizes and shapes located at different heights with no sharp borders. Based on present knowledge, we have developed an algorithm for segmenting AFM images that involves two stages: (1) identification of the local maxima (hypothetical vertices of future segments) in the relief structure, and (2) analysis of the contour lines around the vertices and decision-making about the subsequent growth of this segment or about its merging with its closest neighbors, depending on the current configuration of its base and intersections with the neighboring structures. Thus, the continuous structure of the surface of filled rubber was divided into a field of two types of separate fragments: micropellets (compact and relatively large objects) and aggregates that form secondary structures—agglomerates.

The approach developed was subsequently applied to the analysis of carbon-black-filled rubbers with different filler fractions in stretched and unstretched states. The influence of the filler volume fraction and the elongation ratio on microstructural parameters is discussed.

PREPARATION OF SAMPLES

The approach developed was used to analyze the microstructural properties of five materials: styrene–butadiene rubber (SBR) or synthetic isoprene rubber (IR) vulcanizates filled with N220 carbon black with different concentrations. The main components of these materials are given in Table I.

Table I Main Components of Materials under Study (in phr)^a

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Mixing parameters for samples 1–3 were an optimum curing time was 180 s at a temperature of 150 °C; for samples 4–5, optimum curing time was 240 s at a temperature of 143 °C. The materials for numbers 1–3 were produced at Sumitomo Rubber Industries LTD (Kobe, Japan), and, for numbers 4–5, they were produced at Vyatka State University (Kirov, Russia). In our previous studies,^30,31 we examined the microstructure of other filled rubbers using the same concept of relief segmentation.

EXPERIMENTS

The experimental studies of microstructures were performed using an Icon AFM (Bruker, Billerica, MA) in a taping mode with scan-rate of approximately 0.3 Hz. The 20 μm × 20 μm topographical AFM scans with a 1280 × 1250 dot resolution in planes were obtained for further analysis. Thus, the distance between the surface microrelief nodes was equal to approximately 15 nm, which was comparable to the tip radius of the probes (10 nm). In our experiments relatively soft cantilevers of stiffness approximately 1–3 N/m were used; rigid probes cause more artifacts, such as scratches, on the polymer surface and can cause contamination. A quantitative analysis was conducted on only the topographic scans of the relief (variation in cantilever amplitude oscillations). A phase portrait is strongly dependent on the inner scan parameters and the characteristics of the probe. Therefore, the available phase contrast of the material was used solely to assess the quality of the images.

The surfaces of fresh slices of filled rubber materials were investigated. Samples were prepared by a method similar to that described in other work³²: a sharp surgical blade is dropped onto the virgin surface of a pre-extended (10% elongation) material, cutting it into two parts. Compression of the sample during cutting impedes long-term contact between the blade and the material, thereby avoiding surface contamination and the formation of scratches. For the statistical analysis several high-quality scans were acquired for each material.

The study of samples 4 and 5 was conducted on samples in a stretched state. To that end, the samples (narrow strips 12 mm long) were prepared by the method described above, then, were mounted in the grips of a miniature tensile device and placed under the microscope scanner (Figure 1a).

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Macroscopic elongation was regulated by a central screw. To measure the micro deformations of the sample surface with an optical microscope system, a number of characteristic defect markers were found with initial distances between their centers of approximately 200 μm (A and B in Figure 1b). The area for scanning was taken from the space between those defects (at the cross in Figure 1b). Then the sample was stretched by rotating the central screw, and after the disappearance of the temporal changes in the material microstructure, the material was scanned again with respect to the initial, preset labels, which were shifted relative to each other at a certain distance (Figure 1c). In the process of stretching, surface ruptures and micropore propagation occurs (Figure 1c), so the real extension of the area between the defects is somewhat smaller (about 15% for IR/30 phr; macroscopically elongated four times) than the change in the distance between the grips of the tensile device. Further, all the measured parameters will be matched to the elongation ratio λ of the microscopic area examined between A and B, which comprises approximately 1, 2, 3, 4.

PROPOSED METHODS OF ANALYSIS

After scanning, all images were fitted to the first-order plane (to remove the macroscopic slope of the samples) and treated by partial image shape restoration to minimize the influence of the probe geometry on the micro-relief obtained. In accord with the manufacturer's data, the probe was assumed to be like a truncated cone (aspect ratio, 3:1) with a hemisphere at its end (size, 10 nm). For partial image shape restoration, we used the method suggested by Villarubia.³³ For image processing and further analysis, we developed the algorithms in MATLAB (MathWorks, Natick, MA).

Figures 2 and 3 show the AFM scans of the surface of the materials under study. The vertical bar is the height given in nanometers.

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As shown, the filled rubber relief is a complex, three-dimensional surface with many minima and maxima (Figures 2b–d and 3). The unfilled SBR vulcanizate (Figure 2a) represents a smooth relief with few large inclusions (ZnO or “microdust” particles). In the stretched microstructure (Figure 3) are chains of filler aggregates oriented along the axis of deformation. In addition, the phase images of the filled vulcanizates (not shown) revealed a distinct phase contrast between the rigid (filler) and soft (polymer) components of the rubber. Thus, we can consider the irregularities of the filled rubber surfaces to be a visible part of the filler network.

For the quantitative analysis of the microstructures, an image-processing algorithm was developed that comprises the following stages:

1. The coordinates of surface's local maxima are collected. The local surface maximum is a relief vertex around which a closed contour can be constructed, so all points of the given contour lie below a prescribed vertex. If two local maxima are located at a distance <80 nm in the xy plane and have a height difference of <10 nm (the least characteristic sizes of primary aggregates and particles of N220 carbon black), then we consider those two as one and take the maximum that lies higher. That is, the lower one is supposed to be the part of the bigger fragment with a top is defined by higher maximum and is, therefore, removed from further consideration. The obtained maxima are thereby the tops of the filler-network fragments in the material.

2. By analysis the contour lines around the maxima, the boundaries of surface fragments can be defined with an iteration procedure. Formally, any fragment is limited by the dome (the rough surface) and the flat base (a polygon). Because the spatial coordinates of all points of the AFM relief are known, there are no difficulties to calculating any geometrical characteristic of any fragment at any iteration. On each iteration step, the z-coordinates of all bases of fragments are moved down in 2-nm steps, so, the fragments grow. Figure 4 illustrates the growth process of a surface fragment.

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Obviously, when dashed line moves down, the area A of the fragment base increases. At some k-th iteration, the base boundaries “break,” and the fragment starts covering an area that does not belong to it. That leads to a sharp increase in area A in comparison with the previous iteration: A_k >> A_k−1; in this case, the fragment is returned to its previous configuration (dashed line in Figure 4), and its growth is stopped.

During the process of fragment growth, the contours of two fragments can partially intersect each other. In these cases, the contours of the fragment bases are returned to their previously higher configuration, and their further growth is stopped.

Another situation arises when one of the fragments completely overlaps (absorbs) the other(s). Treatment in such situation requires further information about the shape of the fragment bases. In the material, dense inclusions—zinc oxide particles, micro specks of dust, or partially broken filler granules—can be observed; therefore, it is important to establish correctly whether the relief irregularity is an independent structural unit or just roughness on the surface of a large-sized inclusion. To identify these objects, the compactness—the ratio between area A and perimeter P of the base is used: For the circle, c ≡ 1; more-branched shapes yield lower compactness values. If, on the k-th iteration, the fragment G₁ overlaps G₂, and the shape of the G₁ base preserves the same or greater compactness, c_1,k ≥ c_1,k−1, then, G₂ is probably not an independent fragment but a surface irregularity of the large-sized particle only, so G₂ can be excluded from further consideration (Figure 5a). In the other case (Figure 5b), when G₁ becomes more branched and occupies other fragments, G₂ and G₃, it is returned to the state of its previous iteration (dashed line in Figure 5b), and its growth is stopped.

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The analysis of the contour lines around the local maxima is repeated until all the fragments stop growing.

Thus, a continuous surface relief is decomposed into a discrete field of fragments that comprise filler in the polymer matrix. Because we have information about their geometry and relative location, we can perform a comparative analysis of the materials under study. Figure 6 presents the results obtained from the image-processing procedure—that is, silhouettes of the fragment bases obtained. The shades of gray correspond to different segment heights (the darker the color, the higher the fragment lies, that is, closer to the observer). Note that the relief fragments obtained are volumetric objects with rough surfaces and flat bases. The silhouettes are given only to facilitate the visualization procedure.

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As Figure 6 shows, there are several large, compact fragments, especially in low-loaded material (Figure 6a). By analyzing the size and shape of such objects, micropellet can be defined: a micropellet is a fragment of a relief with a size and compactness ≥300 nm and ≥0.85, respectively. The rest of the relief fragments are assumed to be filler aggregates. The size is the mean length of the line that connects two opposite points on the boundary of the base, plotted through its geometrical center as one of the points moves along the boundary with 45° angular steps, that is, the average diameter.

Visually, the resulting structure is inhomogeneous; it contains areas with high filler concentrations that gradually split into branches. So, the pieces of secondary structures—agglomerates—can be seen.

From existing experimental and theoretical studies,^34,35 we know the agglomerate formations in the material obey fractal relationships. There is a power relationship between the size of agglomerate R and the number of primary structures in agglomerate N:

where μ is a constant, and D is the mass fractal dimension. To identify agglomerates (clusters), the following algorithm is proposed:

1. Choose one of the fragments of the filler structure network that does not yet belong to any of the identified clusters.

2. Attach the relief fragments located at a distance of ≤Δ from the current segment boundaries forming the agglomerate to the growing cluster until all the accessible fragments are taken. Segmentation of the continuous relief always causes gaps to appear between the fragments (aggregates). To quantify the structure of the agglomerates, determine the maximal possible distance Δ between the neighboring fragments; fragments at a distance less than that can be considered to belong to a single secondary cluster (agglomerate). We will elaborate on the procedure of Δ estimation.

3. Start the identification of the next agglomerate; that is, return to point 1.

The surface structure, when examined, will show only the “shards” of the real three-dimensional filler clusters. The size of those visible agglomerates will vary widely. The objects used for the characteristics analysis of the clusters from the AFM scans must be sufficiently representative. If the relationship R(N) is plotted in double logarithmic coordinates (Figure 7), that there is a significant scatter, for small values of R and N, in the experimental data, which causes difficulties for approximating their line to a slope equal to D.

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Therefore, small structures with few aggregates should be eliminated from consideration and, instead, only clusters in the upper part of N(R) should be used. For all materials, minimum acceptable values can be assumed to be equal to N = 6 and R = 355 nm.

To determine the distance of Δ (below which, the aggregates belong to a single cluster) the values of the fractal dimension D(Δ) are analyzed. At large values of Δ, an overlapping of agglomerates occurs—that is, aggregates that do not belong to the current cluster join it, so the cluster becomes denser and D(Δ) increases. If the values of Δ are too small, immature clusters will be observed, that is, an essential scatter will occur in the values of N(R) and D(Δ) changes (increases or decreases). At some distance interval D(Δ) ≈ constant, that value can be thought of as the fractal dimension of filler clusters in the material. The quantitative data obtained are provided in the next section.

To identify the fractal properties of the aggregates, expressions can be used to calculate the mass of the fractal dimension D_a and the scale coefficient μ_a of the dense spatial aggregates, as derived from ref 36:

where D_p is the area-perimeter fractal dimension that relates the area A and the perimeter P of the aggregate silhouette

To analyze the character of the distribution of points (particles) on the surface examined, the Morishita index³⁷ can be used. This quantity is named after the Japanese ecologist who used this index in the analysis of the distribution of nests in large populations of birds:

The image is separated into q squares, m_i is the number of points in the i-th square, and is the total number of objects. Figure 8 presents the dependencies I_δ(q) for different characteristic distributions.³⁷

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The Morishita index demonstrates the spatial arrangement of filler particles in the material, but, like any other point statistics, does not provide complete information about the scale effects. For example, the curve I_δ(q) for the region filled with circles will not change if we increase their diameters preserving their positions, that is, increasing the filler loading.

Let us determine the scale of heterogeneity of the filler distribution in the material, that is, the smallest size of the observation window s, noting that the filler distribution throughout the material can be treated as homogeneous. To that end, the n squares of size s × s in the filler network region examined are randomly chosen, and the so-called heterogeneity index is calculated as follows:

where α_i(s) is the fraction of area occupied by the filler in the i-th square with the size, s ∈ (0.01L; 0.9L), α_L ≡ α_Lα(0.9L), the number of squares is n ∼ (0.9 L/s)², and L is the length of the image (20 μm).

The closer the value of J(s) is to unity, the more homogeneous is the distribution of the filler throughout the material for this scale. With decreasing s, the window starts to get the areas of both the high and low filler concentration. The value of s*, in which J(s) substantially deviates from unity, can be regarded as a critical scale (a mesoscopic scale); for any scale s ≥ s*, filler distribution can be considered as homogeneous. Practically, s* defines the least allowable amount of scanning in the study of these materials by various kinds of microscopy or the side length of the cube in structural modeling.

An AFM relief represents a three-dimensional surface, and the filler network fragments (Figure 5) are located relative to each other at different heights. Not all the visible fragments should be used to calculate _δ(q) and J(s), but only a few of those that are differentiated by height. To do that, distribution histograms are constructed for the heights of the fragment bases. The height h, corresponding to the maximum frequency (modal), is determined, and only the fragments with z-coordinates with a base of ∈ h ± 50 nm are chosen. Thus, a “slice” of the material is obtained that is 100 nm thick. Figure 9 shows the transformation results obtained for the images shown in Figure 6a,b. As before, the shades of gray correspond to the different segment heights.

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RESULTS AND DISCUSSION

FILLER NETWORK STRUCTURE

Figure 10 presents the plots of the heterogeneity J(s) and the Morishita index _δ(q) for SBR-filled vulcanizates.

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The structure of the materials becomes significantly anisotropic on a small observation scale (<3 μm), and then, J(s) drops and asymptotically approaches unity (Figure 10a). The presence of flash maxima indicates that the large-size fragments (micropellets) fall into the area of observation. Specifying the critical value J(s) = 1.1 (the dashed line in Figure 10a), s* can be determined, beginning with the distribution of filler in the material that is isotropic: 13, 8, and 5 μm for filler fractions 10, 30, and 50 phr, respectively.

As for the Morishita index, in all cases, the fillers are distributed throughout the material in the form of clusters [case (e) in Figure 8]. The most favorable case is the homogeneous distribution [case (a) in Figure 8]. From that viewpoint, the best filler distribution (without regard to scale effects) is that observed in the material at 50 phr, whereas the worst is in the material at 10 phr.

The heterogeneity and Morishita indexes for extended samples are presented in Figure 11.

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The heterogeneity of the filler distribution is highly dependent on the elongation ratio and the mass fraction of the filler. Strong differences between J(s) and I_δ(s) at diverse λ values at 30 phr (Figure 11a,c) indicate that during the stretching of the material at 30 phr, the structure of the filler network undergoes changes much more significant than is the case when the material is at 50 phr. This can be explained by the network rearrangement at 50 phr being hampered by the large number of contacts among the aggregates.

During stretching, the filler network is compressed in the transverse direction, and aggregates are accumulated and “stuck” around the micropellets or in dense agglomerates. Until the most pronounced maximum J(s), λ = 3 at 30 phr and λ = 2 at 50 phr correspond. Further stretching causes a partial destruction of the aggregate jam. The filler is formed in chains parallel to the axis of deformation, the graph J(s) goes lower, and the scale of heterogeneity reduces. By comparing J(s) at 50 phr and λ = 3 with λ = 4 (Figure 11b), it follows that, on a scale <6 μm, J(s, λ = 4) lies higher than does J(s, λ = 3), that is, at λ = 4, the areas of increased heterogeneity again start to form in the material. Hence it might be possible to speculate here about a periodic process: for a certain elongation ratio, the filler particles are aligned into chains in the material, and those chains approach each other so closely that they begin to form dense, inhomogeneous structures, which, in turn, are aligned into chains, until the rupture of the material. The Morishita index also testifies to the increase of maximum values, which indicates the filler particles are concentrated in specific areas of the material. That process proceeds to a certain value of λ, and then, the filler distribution becomes closer to uniform again. It is interesting that, for the material at 50 phr and λ = 1, I_δ(q) nearly coincides with the value at λ = 3 (Figure 11d), and the same can be observed for J(s). That is, these two states are equivalent with respect to filler distribution in the material.

The results of the calculated fractal dimensions of clusters as a function of the distance among the aggregates are given in Figure 12.

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In SBR/10 phr, filler particles are arranged in small groups, and therefore, it seems impossible to reliably determine D: a strong approximation error N(R) has spread through the entire interval Δ. Hence it can be concluded that representative fractal clusters in this material are not formed because of the low volume fraction of the filler. The nature of the curve for SBR/50 phr (Figure 12) points to the fact that, in this material, the branches of neighboring clusters are strong enough to penetrate each other—that is, D(Δ) does not show a plateau. For all other materials, the relationships of D(Δ) obtained produce areas where D can be counted as constant (they are bounded by dashed lines in Figure 12). Quantitative values are given in Table II. Examples of the aggregates obtained (extracted from SBR/30 phr) are shown in Figure 13.

Table II Structural Parameters of the Materials under Study

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Figure 14 presents the mean value of the distance among the closest aggregates during material elongation.

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The results have indicated that filler structures during material stretching usually move in groups—the average distance between adjacent units increases very slightly for IR/30 phr and even decreases for IR/50 phr. That is, in the latter case, a filler network shrinks rather than expands: aggregates are oriented parallel to the axis of deformation (shown below) and “slip” relative to each other, but the distance between them is not generally increased. It means that the main deformation occurs in a “free” binder located outside the concentration of agglomerates. In addition, aggregates that have risen to the material surface because of decreasing thickness of a sample during stretching can be embedded into the spaces between the originally adjacent aggregates. To illustrate these processes on the surface of the material (IR/30 phr), the same region around the characteristic dense agglomerate was scanned before and after elongation (Figure 15).

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The pictures in Figure 15 show the same area of the material, in which the aggregate groups are bounded by contours. The distance between their ingredients changes only slightly. Only a relative reorientation of structures takes place. The connecting lines indicate how the distance between the same aggregates changes.

Because the shape of extended aggregates slightly changes, and therefore new, previously invisible, fragments of the filler network appear on the surface, our attempts to construct an algorithm, which automatically determines a new position of the same aggregates on the images before and after deformation, have not met with success. Yet a “manual” image analysis (for IR/30 phr) was performed, and the distance between the same pair of aggregates was measured (approximately 50 pairs); the distribution of structural extensions parallel to the axis of deformation λ_y is shown in Figure 16.

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The results indicate (Figure 16) that the structural extension exceeds the macroscopic one only in specific cases; in general, λ_y ≤ λ.

FILLER STRUCTURE

The aggregate size distributions (Figure 17) in the materials under study can be fairly well approximated by the log-normal probability of the distribution-density law.

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The sizes of aggregates in the same polymer are shown to be dependent on a filler fraction in the material: the higher the filler content is, the smaller the mean value and dispersion of size-distributed aggregates (numeric values are given in Table II). The presence of a significant number of large-sized aggregates (micropellets and those shown below) is due to insufficient refinement of filler granules during friction in the process of mixing material components. The size distribution of aggregates remains practically unchanged during tension. That indicates that the fragments of relief that have been identified in the analysis of AFM images as aggregates are, in fact, primary, indivisible structures.

Figure 18 shows the change in the average size of aggregates in relation to their undeformed state (Figure 18a) and the degree of orientation—the ratio of the longitudinal size of aggregates (parallel to the elongation axis) to their transverse size (Figure 18b).

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For the material with 50 phr, some changes in aggregate sizes have arisen. After stretching three times, micropellets or large aggregates are separated into smaller and less-oriented fragments. During the further-elongation stage, these new fragments also begin to rotate around the axis of tension.

Fluctuations in the size of aggregates under material tension can also be associated with a change in the surface structure of the sample. Polymer partially covers the “lower” part of the aggregates shackles, making their contours more distinct and magnifying their visible sizes. The thickness of the extended sample decreases, and the vertices (at first, small-sized) of the aggregates, previously hidden in the binder, start to appear on the sample surface. Because the filler distribution throughout the sample is inhomogeneous, the occurrence of new fragments may affect the average sizes. In general, changes in the mean relative sizes of aggregates in tension can be considered to be minor: ±10% at its peak.

The calculated parameters of the filler obtained for the materials under study are summarized in Table II, along with standard deviations.

The characteristic scale s* (mesoscale) decreases with increasing volume fraction.

The fraction of micropellets is calculated as the ratio of the total area of the bases of the micropellets to the total area of the filler fragments. Investigations show that the fraction of micropellets decreases with increasing filler concentration. This is attributed to friction among the microgranules being mixed and then broken into smaller fragments. Thus both the fraction of the micropellets and their average size decrease. The fraction of micropellets and their sizes also decrease in the process of stretching the materials. For the SBR/50 phr and the stretched IR/50 phr, only a few micropellets are detected; thus, standard deviations are not given for those cases.

A similar tendency for a decrease in size is also observed for aggregates, and the difference between 10 phr and 30 phr is larger than the difference between 30 phr and 50 phr. Thus, one can say that, at some filler fraction <30 phr, the sizes of the aggregates approaches some stationary level. According to Herd et al.,⁹ the average size of aggregates of N220 in a dry state is equal to 77.3 nm, which is higher than the value obtained for SBR-vulcanizates (63 nm) and lower than that for IR-vulcanizates (93 nm). In this case, we can't expect a coincidence, because many factors related to the peculiarities of components and production technologies influence the final structure of filler aggregates. Nevertheless, a possible reason for a decrease in the results must be indicated. Because the aggregates that are partially embedded into the material surface have no sharp boundaries, and near the aggregate bases of the AFM relief and at the points of fragment contacts, there is a transitional area, where the aggregate relief gradually transfers to the binder relief. Sometimes it is impossible to accurately determine the lower boundary of the fragment. Therefore, a part of the fragments are “cut” by the computer program at a slightly larger height. The difference in these heights is 15 nm at most.

The area-perimeter fractal dimension D_p of the aggregates (not shown in the Table II) is <1.245, which, according to Herrmann et al.,²³ is typical for many carbon-black aggregates in the polymer matrix. The values of the mass fractal dimension D_a of the aggregates obtained (2.84,...,2.85) is slightly greater than the nominal values (2.43⁹), that is, their shape is almost round. These differences may be attributed to the combined action of the following factors: the irregularities of surface aggregates are filled with a polymer layer, and the finite geometry of the AFM probe restricts small-scale measurements. The influence of the latter factor can be reduced by using probes with a smaller curvature radius, which are more expensive.

In the analysis of the fractal dimensions of clusters, two types of aggregation can be defined: diffusion-limited (D ≈ 1.78) and reaction-limited (D ≈ 2.02) cluster aggregation.³⁵ We are currently unable to judge the nature of the values obtained or to show what material parameters affect the structure of clusters. However, those values do not contradict the data presented in the literature.³⁸ Moreover, it is found that, for different types of binders, the fractal dimension may vary as a function of the filler fraction or remain unchanged.³⁸

CONCLUSION

A technique was developed for studying the microstructure of filled rubber, based on image segmentation of an AFM relief. The algorithm for analysis of contour lines around the local minima of a 3D surface makes it possible to extract the fragments of a continuous relief, which can be identified both with primary filler aggregates and with micropellets (large, dense structures). Thus, the continuous AFM relief is split into separate, discrete objects. The information regarding the geometry coordinates and relative position of those fragments in the material is stored in computer memory. An algorithm to assemble the fragments obtained into secondary fractal structures—agglomerates—was also derived.

The methods developed have been used to study the microstructure of five N220 carbon-black-filled vulcanizates (SBR/10/30/50 phr, IR/30/50 phr). Two materials (IR/30/50 phr) were subjected to tensile tests, and then, the extended samples (λ = 1, 2, 3, 4) were examined.

The examination of the isotropy scale of filler distribution in the material shows that weakly filled materials appear to be the most heterogeneous (heterogeneity scale of approximately 13 μm), and highly filled materials (heterogeneity scale of approximately 5 μm)—are the least heterogeneous. The fraction and sizes of micropellets decrease with increasing filler concentration; that is, the sizes of aggregates tend toward some asymptotic value, whereas the filler fraction increases and can be approximated with the log-normal probability density law.

The analysis of secondary structures revealed two different agglomeration processes: diffusion-limited cluster aggregation for SBR/30 phr, IR/30 phr, and IR/50 phr, and reaction-limited cluster aggregation for SBR/50 phr.

The study of the filler network properties in the material undergoing stretching revealed the cyclic character of its change: during stretching, the dense structures are decomposed into aggregate chains, which, although approaching each other, combine into other dense objects that again, undergo stretching, until the break. The orientation of these aggregates changes during the extension period, whereas the average size of the aggregates remains unchanged (IR/30 phr) or changes only slightly (IR/50 phr). The analysis of a change in the distance between the neighboring aggregates indicates that the filler during stretching generally moves in groups, and the structural extension does not exceed the macroscopic extension.

The methods developed are believed to be useful techniques for comparative analysis of the microstructure of filled rubber vulcanizates. The information about the fractal properties of clusters and the morphology and distribution of filler can be used to simulate the structure and mechanical behavior of materials.