3D Dispersion of Spherical Silica Nanoparticles in Polymer

Article pubs.acs.org/Macromolecules

3D Dispersion of Spherical Silica Nanoparticles in Polymer Nanocomposites: A Quantitative Study by Electron Tomography Florent Dalmas,*,† Nicolas Genevaz,‡ Matthias Roth,† Jacques Jestin,‡ and Eric Leroy† †

ICMPE (Institut de Chimie et des Matériaux Paris-Est), UMR 7182, CNRS/Université Paris-Est Créteil, 2-8 rue Henri Dunant, 94320 Thiais, France ‡ LLB (Laboratoire Léon Brillouin), CEA Saclay, 91191 Gif-sur-Yvette, Cedex, France ABSTRACT: A simple methodology is proposed to quantitatively discuss the quality of the 3D dispersion of grafted silica nanoparticles (NPs) mixed with free chains in nanocomposites. 3D observations of NPs are obtained by transmission electron tomography (TEMT). The NPs are individualized from the tomograms by segmentation and watershed processing. Equivalent dispersions of spherical objects are then generated. By computing 3D Voronoi tessellation from the spheres, the local environment is investigated for each NP through geometrical measurements. Two types of populations of NP can be extracted: either densely packed or isolated. As the length of the free chains decreases, when the length of the free chains are close to the ones of the grafted chains, this second population becomes predominant and the quality of the dispersion gradually increases. The width of the local volume fraction distribution surrounding each NP can be considered as a quantitative parameter indicative of the homogeneity of the microstructure. It becomes narrower as the quality of the dispersion increases.

1. INTRODUCTION Nowadays, polymer-based nanocomposites are widely used in designed products for mechanical, optical, thermal, or electrolytic applications. Such macroscopic properties are known to be driven by one specific feature, the huge interfacial area developed by nanofillers which appears to be strongly related to two main effects: a structural effect (shape, dispersion, and organization of the nanofillers within the material) and an interfacial effect (nature and strength of the filler−filler and filler−matrix interactions).1−5 Despite the numerous studies that investigated the influence of specific parameters on the behavior of nanocomposites, it is still difficult to determine the respective role of these two effects.2,6 As a consequence, one of the key challenging points is the development of meaningful and effective tools for multiscale morphological characterization and quantification at the nanoscale. Although the first paper using tomography techniques in TEM in order to study polymeric materials was published as early as 1988 by Spontak et al.,7 electron tomography recently emerged as an efficient tool to get a detailed and realistic description of nanostructured polymeric systems.8−15 Conventional TEM only provides two-dimensional (2D) projections of a three-dimensional (3D) sample of a given thickness. As a consequence of these limitations, the interpretation of such images is not unambiguous. On the contrary, TEM tomography (TEMT) generates 3D images with a nanometer scale resolution from tilt series of 2D projections.16 For instance, substantial further progresses on the microstructural analysis of block copolymers17,18 or polymeric nanocomposites8,10,13,14,19 have been achieved during the past decade by this technique. Nevertheless, the © 2014 American Chemical Society

resolution in TEMT reconstructed volumes is very often limited by the “missing wedge” in tilt series acquisition16 which induces a loss of resolution in the direction parallel to the electron beam, i.e., the z direction. The precise quantification of the observed 3D microstructure is then strongly limited. Different strategies have been recently considered to solve this issue. From an experimental point of view, needle-like TEM samples have been, for instance, processed by focused ion beam (FIB) technique, allowing a complete rotation of the sample and avoiding any missing angular observation.20,21 Multiple-axis tomography has also been developed.22 By acquiring several tilt series at various tilt axes, it reduces the “missing wedge” to a “missing cone” which decreases the elongation in the z direction in reconstructed volumes. On the other hand, several teams have developed new reconstruction algorithms in order to improve the reliability of the reconstruction. Generally speaking, these algorithms are based on the knowledge of prior information on the reconstructed objects.23−27 For instance, the discrete algebric reconstruction technique (DART) assumes that the volume consists in discrete objects that match one gray level.23 The “compressed sensing” numerical method extended by Leary et al.26 for TEMT is based on the reconstruction of a signal “sparse” in known small domains. More reliable reconstructed volume with minimized artifacts usually observed in TEMT (streaking, object blurring, or elongation) can be thus obtained from such numerical approaches since the raw tilt series consist in Received: January 10, 2014 Revised: February 18, 2014 Published: March 5, 2014 2044

dx.doi.org/10.1021/ma500075s | Macromolecules 2014, 47, 2044−2051

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neutron scattering (SANS), either hydrogenated (H) or deuterated polystyrene (PS) chains were used as grafted chains or matrix. Since the H/D nature of the polystyrene does not change the material microstructure, we will indifferently discuss both systems in the present work. An aqueous colloidal suspension of silica nanoparticles were purchased from Aldrich (Ludox TM40). The silica beads were first transferred in dimethylacetamide (DMAc) by dilution and water evaporation. Then, the preparation of the grafted nanoparticles followed a protocol previously described by Chevigny et al.1 Briefly, this method is based on nitroxide-mediated polymerization (NMP) and consists of binding covalently the alkoxyamine (which acts as an initiator and controlling agent) to the surface of the silica nanoparticles in two steps and then polymerize from the alkoxyamine-functionalized surface of the particles (“grafting from” method). Using this method, we synthesized two batches of particles grafted with D PS chains, Mn,grafted = 32 800 g mol−1, PDI = 1.2, and with H PS chains, Mn,grafted = 26 400 g mol−1, PDI = 1.4, with comparable grafting density of around 0.2 mol nm−2. Two types of D polystyrene (Mn = 169 000 g mol−1, PDI = 3 and Mn = 111 300 g mol−1, PDI = 1.12) were purchased from Polymer Source and use as received. Lower mass H polystyrene matrices were also synthesized by classical radical polymerization (Mn = 61 300 g mol−1, PDI = 2.8) and controlled radical polymerization via NMP (Mn = 23 000 g mol−1, PDI = 1.6 and Mn = 26 400 g mol−1, PDI = 1.4). The preparation of nanocomposites followed the method developed in the laboratory as described by Jouault et al.3 A suspension of grafted nanoparticles in DMAc was mixed with a concentrated solution of PS (10 vol %, also in DMAc) at particle volume fractions ranging from 2.7 to 4.1 vol % (determined by thermogravimetric analysis). The mixtures were stirred (using a magnetic rod) for 2 h. Then, they were casted into aluminum molds (2 cm radius) and evaporated in an oven at constant temperature, Tcast = 130 °C, for 8 days. This method of preparation enabled us to obtain stable films whose local structure does not evolve with time. The final dispersion of the particle inside the polymer matrix is then only depending of the grafted to matrix chain length ratio R. The final macroscopic silica volume fractions in the nanocomposites were measured by TGA (thermogravimetric analysis). Table 1 summarizes the different nanocomposites prepared in the present study. 2.2. Transmission Electron Tomography. Nanocomposite films were microtomed at room temperature using a Leica Ultracut UCT microtome with a diamond knife at a cutting speed of 0.2 mm s−1. The thin sections, of about 250 nm thick, were floated onto deionized water and collected on a 300-mesh copper grid. Tilt series were acquired by conventional TEM bright field imaging using a FEI Tecnai F20 field emission gun transmission electron microscope operating at an accelerating voltage of 200 kV. 121 images were recorded at magnification ×28 000 with tilt angles ranging from −60° to +60° with an increment of 1°, using a GIF CCD Camera from Gatan. The pixel size of the projections is 0.95 nm. The exposure time for each projection was set to 0.4 s. Tilt series were acquired using the

sufficiently contrasted well-defined objects with a discrete gray level range. 3D image analysis is the next important step for a complete quantification of the material microstructure. It is thus of importance to develop numerical tools in order to extract relevant microstructural parameters from 3D observations. Several studies focus on the quantification of shape, size, and spatial distribution of objects in segmented volumes.28−32 For example, Thiedmann et al. recently proposed a method to measure, from TEMT images, size and coordination of densely packed CdSe nanoparticles in nanocomposites for solar cell application.31 By assuming a spherical shape for the particles, they analyzed the interconnected conductive pathway within the volume for a given electron hopping distance. In all these studies, the main critical point is the segmentation step of the volume allowing individualizing the objects of interest (e.g., pores, particles, or aggregates) with the best signal-to-noise ratio. In the present work we propose a simple approach, based on the analysis of TEMT reconstructions, in order to quantify the dispersion of spherical nanoparticles, whose size dispersion is well-known, in a polymer matrix. In a first step, an equivalent model microstructure consisting of an assembly of polydisperse spheres is built from 3D observations of nanocomposite materials (polystyrene matrix filled with grafted silica nanoparticles). Then, from a 3D Voronoi tesselation, characteristic microstructural parameters are calculated in order to describe the nanoparticle local environment (number of close neighbors, interparticle distance, and local volume fraction), and their relevance in the particle dispersion quantification is discussed considering the material properties.

2. EXPERIMENTAL SECTION 2.1. Materials. Note that in order to investigate in future works the conformation and the dynamical properties of the chains by small-angle

Table 1. Composition of the Synthesized Nanocomposites grafted chains silica volume fraction (vol %) 4.5 4.5 4.5 4.3 2.6

H Mn or D (g mol−1) H H H H D

26 400 26 400 23 000 23 000 32 800

matrix

PDI 1.4 1.4 1.6 1.6 1.2

H Mn or D (g mol−1) D D H H H

169 000 111 300 61 300 23 000 26 400

PDI

R

3 1.12 2.8 1.6 1.4

0.16 0.24 0.38 1 1.2

Figure 1. Electron tomography observation of agglomerated nanoparticles: 3D rendering and corresponding orthogonal slices of (a) the reconstructed volume and (b) the volume after watershed treatment and segmentation. (c) Equivalent 3D dispersion of polydisperse spheres. 2045


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Table 2. Results of the 3D Image Analysis for Nanocomposites with Various R Ratios and Silica Contents, ΦSiO2: Average Value and Standard Deviation Extracted from the Gaussian Laws Fitted on the Nfaces, Φlocal, and Interparticle Distance Distributionsa R

ΦSiO2 (vol %)

0.16

4.5

0.24

4.5

0.38

4.5

1 1.2

4.3 2.7

Nfaces 13 ± 2 (63%) 16 ± 2 (37%) 11 ± 1 (26%) 12 ± 7 (74%) 11 ± 2 (21%) 12 ± 5 (79%) 12 ± 4 11 ± 5

Φlocal (vol %)

interparticle (center to center) distance (nm)

8.2 ± 7.3

50 ± 28

4.6 ± 6.7

46 ± 25 (69%) 81 ± 61 (31%) 51 ± 24 (56%) 76 ± 44 (44%) 77 ± 50 80 ± 70

3.2 ± 3 2.3 ± 1.1 1.6 ± 1.3

The relative distribution weight is indicated in parentheses for fits with two populations.

a

Figure 3. Nanoparticle size distribution (radius, RNP, in nm) extracted from the 3D image analyzes of all obtained tomograms. between a high spatial resolution in the reconstructed volume and computation time.33 In TEM images silica nanoparticles appear darker than the polymer matrix because of the mass/thickness contrast. Nevertheless, before any image treatment, the contrast was inverted in the tomograms and nanoparticles correspond to bright regions in the following figures. 2.3. Image Processing. The obtained tomograms were treated using the 3D tools of the ImageJ software.34 In a first step, in order to reduce noise in the image and to enhance the edge of the objects, a 3D median filter (size of the structuring object 2 × 2 × 2 nm3) was applied, followed by a 2D background subtraction (rolling ball radius of 25 pixels). Then, a watershed filter was applied in order to individualize the silica nanoparticles. Figure 1a shows a reconstructed volume of agglomerated nanoparticles. One can observe the elongation artifact in the z direction (corresponding to the sample thickness) induced by the missing wedge in the tilt series acquisition.16 An artificial merging of the particles in the z direction occurs, preventing the segmentation of individual particles with a simple gray level thresholding in the tomogram. Thus, after binarization of the volume (the threshold is calculated from the image histogram using a maximum entropy method), a 3D minimum filter was first applied with a radius of 5 pixels. Such a filter results in an erosion of the particles (i.e., the maximum intensity areas) over a thickness of 5 pixels. As the particle mean radius is 13 ± 2.5 nm, i.e. 14 ± 3 pixels, this first step allows isolating the center of each particle and reducing the noise in the tomograms. Then, the coordinates of the particle centroids can be easily found by using the “3D object counter” plug-in35 from ImageJ after segmentation of the volume. Using these centroid positions as seeds in the watershed process, the nanoparticles are individualized

Figure 2. Local environment of spheres within a 3D dispersion of polydisperse particles: (a) considered particles, (b) Voronoi cells tessellated from each sphere, and (c) close neighbor identification. Digital Micrograph software (from Gatan), which allows for an automated acquisition with drift and focus correction (by crosscorrelation) between each projection. Alignment and reconstruction were performed using the DigiECT software from DigiSENS. Alignment of the tilt series was realized with the seed-tracking procedure implemented in DigiECT. About 100 contrasted seeds, consisting in well-defined details from the sample microstructure (i.e., nanoparticles), were automatically detected and tracked over the entire tilt series. In addition to the projection alignment, this procedure allows for the positioning of the tilt axis in the series. The SIRT (simultaneous iterative reconstruction technique) reconstruction algorithm was used, with 20 iterations which is a good compromise 2046


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Figure 4. (a) TEM image at tilt angle 0°, (b) 3D rendering of the segmented volume after watershed treatment, and (c) computed equivalent dispersion of polydisperse spheres for nanocomposites with R = 0.16, 0.38, and 1. the grafted polymer shell), VNP, and the volume of its computed surrounding cell, Vcell. Three reconstructed volumes were acquired and analyzed for each material to ensure a representative statistic. This corresponds to a total number of analyzed particles ranging from 200 to 1000 for materials with R = 1 and R = 0.16, respectively.

and separated in the segmented volume. Figure 1b illustrates the resulting volume. By taking into account the connectivity of the objects in the 3 directions, the “3D object counter” plug-in calculates the volume of each nanoparticle, VNP. In a final step, an equivalent model microstructure is generated from the measured nanoparticle volume and coordinates. To do so, a dispersion of spheres with a radius of RNP = (3/4VNP/π)1/3 is created (see Figure 1c). In order to describe the particle local environment, a Voronoi tessellation is then computed by using the open source software library, VORO++, developed by Rycroft.36 This software extends the Voronoi tessellation to a 3D polydisperse spherical particle system. It creates nonoverlapping convex polyhedra (called Voronoi cells), each containing one particle. In this algorithm, the face of a polyhedron is defined as the assembly of points with equal tangential distance between two neighbor spheres. Each face is thus outside the particle and cannot intercept any other particle. Figure 2a,b illustrates the computed Voronoi cells for given particles within a 3D dispersion. Each Voronoi cell is characterized by its number of faces, Nfaces (equivalent to the number of neighbors for the particle, i.e., its coordination number), its volume, Vcell, and its close neighbors, i.e., the cells with common faces. Only cells that do not share any face with one of the box side are taken into account in the calculations in order to avoid boundary effect on the measurements. We can then calculate the interparticle (center to center) distance, i.e., the distance between close neighbor particles (see Figure 2c) and the local particle volume fraction, Φlocal, defined by the ratio between the nanoparticle volume (without considering

3. RESULTS AND DISCUSSION For more clarity, we will only detail in this section the results obtained for the nanocomposites with R = 0.16, 0.38, and 1 (R being the grafted to matrix chain length ratio). The global trends can be discussed regarding these systems and the whole results of quantification obtained for all the five samples are summarized in Table 2. First of all, the particle size distribution was extracted from all the analyzed volumes, whatever the nanocomposite (since the same type of silica nanoparticles are used as fillers in all materials). A normal distribution was found for the nanoparticle radius, RNP = 13.2 ± 2.7 nm (see Figure 3). This is in complete agreement with the value of 13.0 ± 2.5 nm previously obtained for RNP by small-angle X-ray scattering analysis (SAXS) on the same nanoparticles.4 This hence ensures the reliability of the proposed TEM tomogram segmentation and watershed and of the 3D geometrical measurements. 2047


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Figure 4 displays, for each nanocomposite, a TEM image acquired at a tilt angle of 0°, the corresponding segmented tomogram and the generated equivalent dispersion of spheres. This figure obviously shows the influence of the R ratio on the nanoparticle dispersion within the polystyrene matrix. Voronoi tessellation subdivides the volume in different cells around the particles. This computational approach is an important tool for quantitative geometric description. Each cell characterizes the region of immediate influence for each particle. This allows defining the local environment of each particle by identifying the nearest-neighbor particles. We thus apply our computational approach, described in the Experimental Section, to the different nanocomposites. Distributions have been fitted by one or two Gaussian populations represented by lines on the following histograms. Table 2 summarizes the parameters used for the Gaussian law fits that are discussed in the following. Figure 5 displays the distribution of the particle coordination number (face number of the cells, Nfaces). This parameter can be

Figure 5. Distribution of the number of faces, Nfaces, per Voronoi cell in nanocomposites with R = 0.16, 0.38, and 1.

Figure 6. 3D representation of distance between close neighbor spheres (Voronoi cells that share a face with one box edge were not taken into account).

discussed as the number of closest neighbors of each nanoparticle. For R = 0.16, the distribution can be fitted by two Gaussian populations. Two kinds of particles are highlighted, depending on their coordination number: either 13 or 16 in average. As R increases, it can be first observed that the population of particles with a high number of neighbors

decreases and for R = 1 only one population is observed with Nfaces = 12 ± 4. Using the same approach, Yi et al.32 observed, for simulated ternary sphere packing, that the face number of the Voronoi cells is related to the particle diameter (14 for larger ones). Since the silica nanoparticles utilized in the present work have shown a strictly monodisperse size distribution (Figure 3), each observed population in Figure 5 can be attributed to one specific local environment of the particles (the size dispersity being only responsible, here, for the overall width of each population). As a result, this indicates for low R values the existence of two types of local environment for the nanoparticles and can be directly related to the degree of dispersion in the volume. Indeed, the heterogeneous spatial distribution of particles observed in Figure 4 for R = 0.16 and 0.38 leads to a local environment for the particles which depends on their location either within dense aggregates (numerous close neighbor particles) or in the matrix region with lower particle concentration (fewer and more distant neighbors). The distance between closest neighbors was also calculated. Figure 6 highlights the neighboring particles in the equivalent structure of the three considered nanocomposites. It allows appreciating qualitatively the evolution of the interparticle distance (value and heterogeneity) with the R ratio: the heterogeneity in the interparticle distance appears to decrease as R increases. The corresponding distributions are presented in Figure 7. Here again,

Figure 8. Distribution of the number of the local volume fraction, Φlocal, in nanocomposites with R = 0.16, 0.38, and 1.

this parameter allows for a precise quantification of the dispersion quality of spheres within the volume. Indeed, the higher the R ratio, the narrower the distribution. Furthermore, as shown in Table 2, the average volume fraction tends toward the value of the macroscopic one as R increases. One has to remind that the volume fraction determined by our method is a local value that included only the first neighbors’ particles that enables us to discuss both individual and aggregates dispersion with the same parameter. Since a limited volume is observed by TEMT

Figure 7. Distribution of the interparticle (center to center) distance (nm) in nanocomposites with R = 0.16, 0.38, and 1.

two type of populations, whose relative contribution depends on the R ratio and therefore on the dispersion, can be discussed. For R = 0.16, very large aggregates of densely packed particles are observed in Figure 4. Accordingly, a monodisperse interparticle distance 2049


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(typically of about 0.2 μm3), this is not necessary the total number of particles per aggregates. The relationship between the local volume fraction deduced from our presented method and the effective volume fraction that can be determined by TGA or SAXS will be the scope of a future publication currently under redaction. These results suggest that the width of the local volume fraction distribution in the whole volume can be considered as an indirect dispersion quality indicator. Indeed, the plot of the full width at half-maximum (fwhm) of the fitted Φlocal normal distributions (Figure 9) highlights the microstructural transition

50 nm. The second population comes from nanoparticles located outside the aggregates that are surrounded by a more diluted local environment with less (around 12) and more distant neighbors (average interparticle distance of about 77 nm). As R increases, this second population becomes more and more predominant. The aggregated phase gradually disappears and shows a decrease in the aggregate density as R increases (coordination decreasing from 16 to 13). On the other hand, the overall distribution of local volume fraction becomes more and more narrow, and its mean value tends to the macroscopical silica volume fraction.

4. CONCLUSION The dispersion of polystyrene (PS) grafted spherical silica nanoparticles in a polystyrene (PS) matrix was investigated by transmission electron tomography. Depending on the R ratio between the molar mass of the grafted PS chains and the matrix ones, various microstructures were observed. A procedure for the segmentation of the tomograms was optimized in order to isolate the nanoparticles within the volume. The elongation artifact inherent to the TEM tomography can be avoided by generating equivalent dispersions of spheres from the experimental reconstructed volumes. Then, a quantitative image analysis approach was developed based on a 3D Voronoi tessellation computed from the spherical objects. A precise analysis of the nanoparticle local environment was extracted from this method through the identification of the closest neighbors of each particle. The quality of the dispersion could quantitatively be discussed from statistical measurements of the interparticle distance, the number of closest neighbors, and the local density. As R increases, the microstructure was shown to gradually evolve from a densely aggregated structure to a homogeneous dispersion of individual particles. The quality of the dispersion can be quantitatively described by the fwhm of the local volume fraction distribution. Nevertheless, for analysis at larger scale (e.g., the scale of the agglomerates), other tomographical techniques such as focused ion beam (FIB) coupled with scanning electron microscopy (SEM) have to be considered for the 3D microstructural characterization. The versatile method proposed in the present work opens up several prospects for investigating more deeply the structure− mechanical properties relationships in polymer nanocomposites. For instance, the same methodology could be applied to the same stretched materials and the local deformation (spatial rearrangement of the nanoparticles) could be investigated as a function of the macroscopic elongation. The critical issue of the modification of the polymer matrix mechanical properties in the vicinity of the nanoparticles could then be addressed.

Figure 9. Evolution of the full width at half-maximum (fwhm) of the local volume fraction distribution with the R ratio (dashed line is a plot of the power law fit y = aR−1 as a guide for the eye).

from densely aggregated nanoparticles to a homogeneous random dispersion as R increases. The case where R = 0.38 being a critical point in this transition. The fwhm almost follow an R−1 decrease from 17 vol % (i.e., a wide distribution revealing a large scale heterogeneous dispersion) to 2−3 vol % for randomly distributed particles. All these results have to be compared to what was previously obtained on similar materials by SAXS and SANS (small-angle neutron scattering) by Chevigny et al.1,37 The R ratio was discussed as the relevant parameter in nanoparticle dispersion, and by analyzing the interparticle structure factor, similar results were obtained with a critical value of about R = 0.24 for the dispersion transition. In this study, the thickness of the grafted shell onto nanoparticles was extracted from the fitted structure factor or from SANS measurements combined with neutron contrast variation.37 For low R values the aggregation of the particle was related to a collapse of the grafted chains resulting from the entropic expulsion of the free polystyrene chains from the smaller grafted ones. In other words, the cluster formation is the result of a depletion process induced by an unfavorable mixing entropy contribution resulting from the difference of molecular mass between the grafted (short) and the free chains (long). For R > 0.24, the free chains can swell the grafted ones creating then repulsive interparticle interactions and favoring the particle dispersion. The methodology proposed in the present paper allows going further the morphological description of this mechanism by giving rise to a statistical analysis of the local environment of the nanoparticles. Indeed, the present study highlighted, at very low R value, the coexistence of two kinds of nanoparticles. One corresponds to densely packed nanoparticles within agglomerates and is characterized by a high coordination number (around 16) and an interparticle mean distance of about

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AUTHOR INFORMATION

Corresponding Author

*Fax +33 4 72 43 85 28, Tel +33 4 72 43 72 58, e-mail florent. [email protected] (F.D.). Present Address

F.D.: MATEIS (Matériaux: Ingénierie et Science), UMR 5510 CNRS/INSA de Lyon, Bât. B. Pascal, 7 Avenue Jean Capelle, 69621Villeurbanne cedex, France. Notes

The authors declare no competing financial interest. 2050


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(33) Heidari Mezerji, H.; Van den Broek, W.; Bals, S. Ultramicroscopy 2011, 111 (5), 330−336. (34) ImageJ homepage: http://rsbweb.nih.gov/ij/. (35) Bolte, S.; Cordelières, F. P. J. Microsc. (Oxford, U. K.) 2006, 224 (3), 213−232. (36) Rycroft, C. H. CHAOS 2009, 19, 041111. (37) Chevigny, C.; Jestin, J.; Gigmes, D.; Schweins, R.; Di-Cola, E.; Dalmas, F.; Bertin, D.; Boué, F. Macromolecules 2010, 43 (11), 4833− 4837.

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3D Dispersion of Spherical Silica Nanoparticles in Polymer

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