Quantitative Analysis of Montmorillonite Platelet Size by Atomic Force

Ind. Eng. Chem. Res. 2006, 45, 7025-7034

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Quantitative Analysis of Montmorillonite Platelet Size by Atomic Force Microscopy Harry J. Ploehn* and Chunyan Liu Department of Chemical Engineering and the USC NanoCenter, UniVersity of South Carolina, Columbia, South Carolina 29208

This work focuses on the use of atomic force microscopy (AFM) for quantitative analysis of the size of suspended, exfoliated platelet materials. In particular, we study a model materialsmontmorillonite (MMT) claysand use tapping-mode AFM with image analysis software to quantify the distributions of MMT platelet thickness and aspect ratio. X-ray diffraction (XRD), transmission electron microscopy (TEM), and AFM confirm that, upon dispersion in water, MMT particles exfoliate into stable platelet suspensions, as is wellknown. We use dry weight analysis, dynamic light scattering (DLS), and AFM to assess the impact of sample preparation procedures for exfoliation and obtaining high-quality AFM images. Unexfoliated MMT and other contaminant particles can be removed by low-speed centrifugation; however, large exfoliated platelets are increasingly removed as centrifugal acceleration increases. Dilution of MMT suspensions with acetone prior to deposition onto mica leads to high-quality AFM images with many isolated platelets. Quantitative analysis of the data from many AFM images shows that the distribution of MMT platelet thickness is narrow and centered near 1.0 nm. The distribution of platelet aspect ratio closely follows a log-normal distribution, which has not been previously reported in the literature for MMT. We find that the average aspect ratio measured by AFM correlates linearly with the effective spherical particle diameter measured by DLS. 1. Introduction Polymer nanocomposites containing layered silicate nanoparticles have attracted much attention from both industry and academia. The addition of relatively small amounts of clay to a polymer matrix can lead to marked improvements in mechanical properties1-11 (modulus, strength, toughness), thermal stability,12-16 gas barrier,17-23 and so on. To a large extent, the enhanced performance of nanocomposites depends on the ability to exfoliate clay particles into individual, high aspect ratio platelets, and to disperse them (and perhaps orient them) in the polymer matrix (e.g., ref 24). Layered silicate clays such as montmorillonite (MMT) consist of stacks of platelets, with each platelet having a thickness (Z) of ∼1 nm. The specific surface area (Sˆ ) of a stack of n platelets is given by

Sˆ )

2 FnZ

(1)

assuming that the platelets are “neatly” stacked and neglecting the surface area of edges. Equation 1 shows that decreasing the average number of platelets in each stack maximizes Sˆ . Complete exfoliation of MMT (e.g., FM ) 2.86 g/cm3 for Cloisite Na+) into individual platelets (n ) 1) leads to a remarkably high specific surface area of Sˆ ) 700 m2/g. In other words, complete exfoliation maximizes the area of the internal phase interface between the polymer and platelet phases. A simple scaling argument shows why platelet exfoliation is critical to creating a true polymer nanocomposite. The presence of the platelet changes the energy and entropy of polymer molecules located in the “interphase” near the platelet surface. For simplicity, assume that the average thickness of the interphase (L) scales with a characteristic molecular dimension of the polymer, and that the density of the polymer in the * To whom correspondence should be addressed. E-mail address: [email protected].

interphase equals that in the bulk (FP). The interphase volume (per unit mass of polymer) is

Vˆ i )

wM LSˆ 1 - wM

(2)

where wM is the mass fraction of platelets in the polymer-platelet composite. Hence, the fraction of the polymer volume consisting of a polymer “interphase” is

φi ) FPVˆ i )

( )( )

wM wM 2L FP LSˆ FP ) 1 - wM 1 - wM nZ FM

(3)

For composites containing unexfoliated platelet stacks, 2L/(nZ) , 1, and, therefore, the volume fraction of polymer in the interphase is negligible. A true “nanocomposite” has much larger values of φi, meaning that a significant fraction of the polymer is “interfacial”. All of the polymer becomes “interfacial” (φ{int} ) 1) at the critical platelet mass fraction, which is given by

wM,crit )

( )( )

1 Z FM ≈n 1 + LSˆ FP 2L FP

(4)

For MMT that has been completely exfoliated in poly(ethylene terephthalate) (PET, FP ≈ 1.397 g/cm3, and assuming25 L ≈ 20 nm), the critical platelet loading is ∼5.0 wt %. To achieve the greatest performance enhancement per unit mass of layered filler particles, they should be completely exfoliated into individual platelets (to a minimum of n ) 1, if possible). Moreover, the thickness of the individual platelets should be much smaller than the characteristic interphase thickness ([Z/L] , 1). The presence of exfoliated platelets leads to the formation of a polymer (inter)phase with properties unlike those of the bulk polymer. Interfacial polymer may have altered free volume, a different spectrum of molecular relaxation processes, and suppressed or promoted crystallinity. If we are fortunate, these

10.1021/ie051392r CCC: $33.50 © 2006 American Chemical Society Published on Web 03/01/2006

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characteristics may improve the material’s mechanical properties, flame retardancy, or other performance metrics. The platelet aspect ratio (R) is also important for developing polymer nanocomposites with improved gas barrier performance. Various forms of the “tortuous path” model26-29 all propose that platelets increase that diffusion path length for transport of penetrant molecules through a composite. These models all predict that gas permeability decreases as R increases. The aspect ratio R is defined as the ratio of a characteristic lateral dimension to the platelet thickness. For platelets having irregular shapes, the square root of the area (A) of the platelet face provides a convenient lateral dimension. Thus the aspect ratio can be defined as

R)

xA Z

(5)

for individual platelets (n ) 1). In reality, platelets have a distribution of face areas and, thus, a distribution of aspect ratios. One recent tortuous path model29 predicts a disproportionate effect of larger platelets on barrier performance, so measurement of the aspect ratio distribution has merit. Despite the importance of platelet exfoliation for the synthesis of successful polymer nanocomposites, very little work has been done to directly quantify all of their physical characteristics (n, Z, R) in a consistent and statistically significant way. Exfoliation can often be achieved in a suitable solvent, typically followed by dynamic light scattering (DLS) or transmission electron microscopy (TEM) to measure platelet size. DLS provides a fast, convenient means of measuring an “effective spherical” particle diameter, but its relationship to platelet aspect ratio is not straightforward. Moreover, DLS cannot measure the degree of exfoliation. TEM permits direct visualization of the lateral dimensions of platelets deposited on a surface; however, we still cannot discern whether platelets are fully exfoliated from TEM images. Atomic force microscopy (AFM) has also become an important technique for the characterization of nanoparticles. Unlike TEM, AFM can provide size characterization in all three spatial dimensions, because it provides direct information about the height as well as lateral dimensions of nanoparticles on surfaces. AFM has been used to characterize various types of exfoliated clay platelets.30-38 For the most part, these previous studies focused on descriptive, qualitative aspects of platelet characterization. Recent work on MMT32 shows the remarkable compliance of exfoliated platelets and the care that must be taken in sample preparation. Balnois et al.33 used AFM to perform a detailed quantitative analysis of the dimensions of laponite, finding that the characteristic lateral dimension of the platelets followed a log-normal distribution. Very recently, Cadene et al.38 used AFM to quantify distributions of height, length, and width of MMT platelets. Our work goes further in this direction. Here, we combine results from XRD, TEM, DLS, and especially AFM into a quantitative picture of platelet exfoliation and size distributions, including thickness and aspect ratio. This paper features results for MMT as a model system, emphasizing sample preparation issues and basic elements of quantitative analysis. 2. Experimental Section 2.1. Materials and Sample Preparation. The MMT used in our work was sodium montmorillonite (Cloisite Na+) from Southern Clay Products, Inc. Suspensions that contained 1.0 wt % MMT were prepared by dispersing the as-received MMT

powder in deionized water (18 MΩ cm resistivity, Barnstead Nanopure), sonication for up to 2 h (VWR, model 75HT), and stirring (stir plate with magnetic stir bar) for 12 h. The suspensions were then centrifuged (Eppendorf model 5403, Brinkmann) for 60 min. We used various rotational speeds (up to 7000 rpm), but our standard procedure used a speed of 4000 rpm. Rotational speed (rpm) may be converted to centrifugal acceleration (“g-number”, expressed as multiples of the standard gravitational acceleration, g ) 9.8 m/s2) using the relation

g-number )

[

]

2π(rpm)2 r 60 g

(6)

where r is the centrifugal radius (a parameter that is dependent on the specific rotor model and tube inserts used). For our rotor and tubes, r ) 0.112 m. After centrifugation, the supernatant solution was decanted and retained for analysis. Multiple samples of the supernatant solution were weighed, dried, and re-weighed to determine the MMT mass concentration. The concentration of cleaned stock MMT suspension was typically ∼0.7 wt %. We used dialysis to remove dissolved solutes from one suspension sample. Cellulose membrane dialysis tubing (Aldrich, product D9277) has a nominal molecular weight cutoff of 12 400 daltons, according to the vendor. Prior to use, the dialysis tubing was washed by soaking in deionized water overnight, followed by copious rinsing. The sample was sealed in tubing and immersed in a large bath of deionized water (1800 mL bath water per 10 mL sample). The bath water was changed at least eight times over a period of 24 h. Muscovite mica for AFM imaging was obtained as 9.5 mm disks of grade V-4 (Structure Probe, Inc., West Chester, PA) and freshly cleaved prior to use. TEM grids were 200 mesh carbon-coated copper grids (Structure Probe, Inc.). 2.2. Dynamic Light Scattering (DLS). For the analysis of particle size using DLS, the platelet suspension was first diluted to 10-4-10-5 g/L. DLS measurements were performed using a Brookhaven light scattering system, including a model BI200 goniometer, model BI-9000AT correlator, and a Lexel model 95 argon ion laser operated at a wavelength of 514.5 nm. The scattering angle was fixed at 90°, and the measurements were conducted at room temperature. Light scattering theory and methods for data analysis may be found in classic texts39 and monographs on the subject.40,41 We used the method of cumulants to extract the decay constant (Γ) and polydispersity indices from the autocorrelation function. Despite the fact that the particles are highly anisotropic platelets, we use D ) Γ/q2 to compute the particle diffusivity, where q ) (4πn/λ) sin(θ/2) is the magnitude of the scattering vector, n the refractive index of the suspending liquid, θ the scattering angle, and λ the wavelength of the incident light in a vacuum. From D, the mean hydrodynamic diameter of the particles (dh) can be calculated from the Stokes-Einstein equation.39 All of this analysis assumes that the particles are monodisperse spheres. Thus, the particle diameter that we report from DLS is the effective hydrodynamic diameter of an equivalent sphere. Although this is not an exact measurement of the platelet lateral dimension, it is useful for comparative purposes. 2.3. Atomic Force Microscopy (AFM). For AFM imaging, the samples were diluted with acetone to a solids concentration of ∼10-5 g/L. A small amount of platelet suspension was dropped onto a freshly cleaved mica sheet (∼2.5 µL/cm2). The mica sheet then was dried in air for at least 4 h. The images were recorded in ambient atmosphere at room temperature with a PicoPlus AFM system (Molecular Imaging) that was operated

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Figure 1. (a) X-ray diffractogram of montmorillonite (MMT) powder, and (b) a typical transmission electron microscopy (TEM) image of a single MMT platelet.

in the acoustically driven, intermittent contact (“tapping”) mode. The probes were commercially available silicon AFM tips (Mikromasch Ultrasharp NSC12/3), with a cantilever spring constants of 2.5-8.5 N/m and resonance frequencies of 120190 kHz. AFM images were analyzed using the Scanning Probe Image Processor (SPIP) image analysis software (Image Metrology). The vertical step resolution of the Z piezoelectric transducer is approximately (0.01 nm, and the accuracy of the measurement is approximately (0.1 nm, because of calibration issues. The resolution in the lateral dimension is ∼5-10 nm, because of tip convolution. 2.4. Transmission Electron Microscopy (TEM). Samples for TEM were prepared by first diluting the platelet suspension to ∼10-3 g/L. A drop of the diluted suspension was placed onto the carbon-coated TEM grid and allowed to air-dry. TEM images were acquired on the Hitachi model H-8000 TEM system at an accelerating voltage of 200 kV. 2.5. X-ray Diffraction (XRD). X-ray diffraction (XRD) data were collected on dry powder samples using an X-ray diffractometer (Rigaku, model D-MAX-2100). 3. Results and Discussion 3.1. Confirmation of Platelet Structure. An X-ray diffractogram (Figure 1a) of the as-received MMT powder manifests diffraction peaks that are characteristic of scattering from platelet stacks. The sharp peak at the lowest angle indicates that the interlayer spacing between MMT platelets is 1.16 nm. The theoretical thickness of a single MMT platelet42 is ∼1.0 nm. Hydrated interlayer cations probably account for the difference between the measured interlayer spacing and the theoretical platelet thickness. As expected, the as-received MMT powder consists of agglomerated particles that are composed of stacked platelets, each having a thickness close to the theoretical value for MMT. The MMT powder was dispersed in water, sonicated, and centrifuged as described previously, giving a stable suspension of platelets. A sample was diluted and deposited on a carbon grid for TEM imaging. A typical TEM image of an MMT

particle (Figure 1b) clearly shows what appears to be a platelet. However, we cannot conclude from this (or any) TEM image that the observed particles are individual platelets, as opposed to stacks of two or more platelets. We could use image analysis software to compile (from many TEM images) a distribution of the particle lateral areas. However, TEM does not give us the thicknesses of the observed particles; therefore, we cannot obtain the aspect ratio distribution in this way. Figure 2 shows two typical AFM images of diluted MMT suspension deposited onto mica, obtained from different locations on the same specimen. The “features” appear to be platelets. Cross-sectional analysis (Figure 2c and 2d) shows that many of the platelets have a uniform thickness, ∼1.1 nm, which corresponds to the interlayer spacing from XRD (Figure 1a) and the theoretical MMT platelet thickness.42 The images show that MMT platelets are not at all regularly shaped, and the “width” (loosely defined here) is in the range of 10-1000 nm. For now, we have established that AFM can identify exfoliated MMT platelets, and that their dimensions are in accord with theoretical expectations, TEM images, and XRD results. These qualitative findings are similar to those reported in previous studies.32 Our ultimate objective here (vide infra) is to show how sophisticated image analysis software can be used for quantitative analysis of AFM image data. 3.2. Sample Preparation Conditions. Quantitative analysis of the platelet size dictates that we gather many AFM images for each sample, so that the results are accurate and statistically valid. Before proceeding, we first report various results assessing the impact of sample preparation steps on dispersion, exfoliation, and the quality of AFM images. We routinely use sonication to promote mixing and centrifugation to remove unexfoliated particles from stock suspensions. One suspension was also dialyzed to assess the impact on AFM imaging. AFM specimens are prepared by diluting the stock suspension and depositing a sample onto the mica substrate. All of these steps may have some impact on quantitative analysis of platelets. We have not performed an exhaustive AFM analysis of every sample because of time constraints. Instead, we use DLS as a screening tool to give us an indication of the average particle size and the breadth of the size distribution. Although DLS provides only the effective diameter of an equivalent sphere, we obtain results quickly. We rely on AFM to gather more quantitative size information only for selected sets of samples. 3.2.1. Sonication. After MMT powder and water had been mixed, some particles had a tendency to settle rather than disperse. Sonication helps keep the particles suspended, but it could result in an undesired reduction of the platelet size. Results from DLS (see Table S1 in the Supporting Information) show that sonication time (up to 140 min) has no significant effect on the effective particle diameter and polydispersity index. MMT particles in the “as-dispersed” and sonicated suspensions have the same effective diameter (∼400 nm) and the same polydispersity index (∼25%).43 Sonication apparently does not break down the platelets, nor does it seem to promote exfoliation. Nonetheless, we routinely sonicate MMT suspensions to help promote good mixing and dispersion. 3.2.2. Dialysis. One experiment used dialysis to remove excess salts from a MMT suspension, to identify any effect on exfoliation. In using the term “excess salt”, we mean any ionic solutes beyond the counterions necessary to balance the MMT surface and edge charges. Dialysis would decrease the ionic strength, increase the electrostatic repulsion between the platelets, and possibly lead to greater exfoliation. Figure 3 shows typical AFM images of the MMT suspension before and after

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Figure 2. (a and b) Typical atomic force microscopy (AFM) topography images of MMT suspensions deposited onto mica. (c and d) Cross-sectional plots showing the vertical dimension along the horizontal and vertical lines shown in images a and b, respectively. The height difference between points 1 and 2 in panel c is 1.08 nm, and the lateral distance between points 1 and 2 in panel d is ∼914 nm.

Figure 3. AFM images of MMT suspensions deposited on mica: (a) undialyzed suspension and (b) dialyzed suspension. The boxed region in panel b shows an example of a mineral contaminant particle that is excluded from any quantitative analysis.

dialysis. The image of the dialyzed sample has far fewer small particles than the image of the undialyzed sample. However, the smallest particles in the image of the undialyzed sample are too large to have escaped through the dialysis membrane. Thus, we speculate that the smaller particles may be crystals of residual salts in the suspension. Dialysis would remove excess

dissolved salt from the suspension while retaining essentially all particulates. This could account for the large reduction in the number of smaller particles seen in the image of the dialyzed sample. The presence of excess dissolved salts would also account for the impurities that Piner et al.32 observed in their MMT


Figure 4. AFM images of MMT suspensions deposited onto mica from (a) water and (b) acetone solutions.

samples and studied extensively via AFM. They prepared MMT suspensions by dispersion and sedimentation only, without washing (repeated centrifugation and re-dispersion in DI water) or dialysis. They determined that their impurities (i) were found in all clay samples; (ii) consisted mainly of sodium, magnesium, and fluorine; (iii) were impossible to separate from clay using sedimentation, simple filtration, or electrophoresis; (iv) were mobile on graphite and thus hydrophilic; and (v) could be removed from mica by rinsing. All of these observations are consistent with identification of the impurities as salt crystals. In the recent work of Cadene et al.,38 MMT samples for AFM were prepared by diluting stock MMT suspension with 1.0 mM NaCl solution. They observed two distinct particle populations: larger particles that were clearly MMT platelets, and much smaller cylindrical or elliptical platelets. The heights of the smaller particles differed little from those of the MMT platelets. However, considering the relatively high salt concentration, one cannot exclude the possibility that the smaller particles are salt crystals. We have previously shown44 that dialysis is effective, and sometimes critical, for the removal of excess dissolved salts prior to AFM imaging of nanoparticles on surfaces. However, in this work, we normally did not dialyze our MMT suspensions, because the platelets seemed to be much bigger and more numerous than the smaller particles that we believe are salt crystals. Salt crystals could be problematic for quantitative analysis of clays with smaller platelet size, or samples made from suspensions with higher concentrations of excess salt. This point needs to be addressed through characterization of MMT samples with more carefully controlled surface chemistry. This would entail ion exchange to control the counterion identity, as well as exhaustive dialysis to minimize excess salt. Based on visual inspection of the images, we do not believe that dialysis has a significant effect on the degree of MMT exfoliation. However, we have not conducted any further quantitative analysis using the image analysis tools discussed below. Further work is needed to gather additional images and perform quantitative analysis to prove whether dialysis has a significant impact on degree of exfoliation. At this point, we cannot exclude the possibility that the dialysis of MMT suspensions may lead to greater platelet exfoliation. 3.2.3. Solvent. Figure 4 shows AFM images of MMT suspensions diluted with water (Figure 4a) or acetone (Figure 4b) just before deposition onto the mica. When water was used

as the diluent, the deposited MMT particles seem to be aggregated on the mica surface. In contrast, when acetone was used as the diluent, the MMT particles seem to be spread more evenly over the mica surface. The apparent particle aggregation for deposition from water may be caused by its high surface tension (72 dyne/cm), leading to strong capillary forces between the MMT particles during the drying process. The surface tension of acetone is only 22.6 dyne/cm, so the capillary force between the particles would be smaller in this case. Moreover, acetone has a much higher vapor pressure than water, so this sample would dry much more quickly, perhaps minimizing aggregation. Generally, all samples are diluted with acetone prior to deposition on mica for AFM imaging. 3.2.4. MMT Concentration. Although the platelets observed in Figure 4b seem to be evenly dispersed, close examination reveals a high incidence of randomly overlapping platelets. This makes it difficult to identify individual platelets and measure their aspect ratio accurately, especially if we want to use automated image analysis algorithms. The ability to resolve individual MMT platelets is strongly dependent on the suspension concentration. Figure 5 shows AFM images of MMT platelets deposited from suspensions of higher and lower concentrations. The image made from the more concentrated suspension (Figure 5a) shows evidence of platelet overlap and (perhaps) re-aggregation. The image made from the lessconcentrated suspension (Figure 5b) reveals greater numbers of what seem to be well-separated, individual platelets. For all images to be used for quantitative analysis, we dilute the stock MMT suspensions at least by a factor of 800 (preferably by 1200) prior to deposition onto the mica. Unfortunately, the use of dilute suspensions means that each AFM image will include fewer particles. Hence, we must collect more images to have enough particles for a reliable measure of the particle size distributions. 3.3. Quantitative Analysis. In this section, we turn to more quantitative analysis of AFM images of MMT platelets deposited on mica. Except as noted, all samples for quantitative analysis were prepared using a standard protocol including suspension sonication, centrifugation for 1 h at 4000 rpm (2003g), 1200-fold dilution with acetone, deposition onto freshly cleaved mica, and drying in a covered dish. 3.3.1. Degree of Exfoliation. Typical AFM images for samples prepared by the standard protocol are shown in Figure 5b (and Figure S2 in the Supporting Information). The platelets

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Figure 5. AFM images of MMT platelets deposited onto mica from suspensions of differing concentration: (a) 3.48 × 10-3 wt % and (b) 5.83 × 10-4 wt %.

are well-separated on the mica surface, so we must use a large scan area (7.5 µm × 7.5 µm) and gather many images to have enough platelets for an accurate measure of the distribution. We use image analysis software (SPIP, published by Image Metrology) to discriminate MMT particles from mica and to gather height, lateral dimensions, and area for every platelet. Beginning with a “raw” image, we first apply a plane correction by selecting “average profile fit”, and then we set the bearing height to zero under “Z-offset.” We then used the threshold function to set the detection level to 0.6 nm; this eliminates features with heights less than this value. The distributions do not include particles with lateral areas less than 1000 nm2. We do not attempt to exclude any features that seem to be overlapping platelets. However, we do occasionally observe particles that are obviously much too tall to be platelets (e.g., the highlighted particle in Figure 3b, presumably residual mineral contamination), and so we exclude these from the analysis. For every particle, we obtain the average vertical dimension, or mean height, of that individual particle, relative to the mean height of the mica background. Figure 6a gives the distribution of the mean height of MMT particles in this sample, compiled from 49 different AFM images. The distribution shows that the average mean height is 0.97 nm with a standard deviation of (0.25 nm (N ) 1141). The median value of the mean feature height is 0.91 nm. The main peak in this distribution (the tallest six bars in Figure 6a) contains ∼87% of all of the features. The mean height of the MMT particles from AFM agrees with the theoretical thickness of MMT platelets42 and is consistent with the interlayer spacing from XRD (see Figure 1a). These results demonstrate that the large majority of the particles in these images are individual, exfoliated MMT platelets. It is also interesting to consider the distribution of maximal heights (Figure 6b), representing the highest point associated with every particle. The distribution indicates an average maximal height of 1.38 nm, a median value of 1.20 nm, and a mode (most-common value) of 1.1 nm. The existence of a dominant peak at 1.1 nm supports the conclusion that the large majority of the particles are single, isolated, exfoliated MMT platelets. We also observe a secondary peak between 1.9 nm and 2 nm, and possibly even a third peak at 3.1 nm. These peaks represent short stacks of two or three platelets, or large platelets with smaller fragments on top. Examples of the latter can be seen in Figures 2a, 2b (upper left quadrant), and 3b. From their

Figure 6. Distribution of (a) mean heights and (b) maximal heights of MMT platelets on mica.

qualitative appearance, these seem to be doublets that did not completely exfoliate. However, we cannot rule out the possibility of random stacking of exfoliated platelets as the suspension dries on the mica surface. Because we are able to identify individual platelets, we can readily measure the true distribution of the platelet aspect ratio. For each platelet, we know its mean height as well as its lateral area. The platelet’s area divided by its mean height equals the aspect ratio of that particular platelet. Compiling the aspect ratios of all of the platelets in several images produces an aspect ratio distribution. The distribution for our standard MMT sample (Figure 7a) is rather broad, ranging from ∼60 to 500, with most of the platelets having aspect ratios in the range of 80-300. From this distribution, we find that the mean aspect ratio is 166, the standard deviation is 86, and the median value is 147 (N ) 1141).


Figure 8. (9) Concentration (right axis) and (b) effective spherical particle diameter (left axis) of MMT particles remaining in suspension as functions of centrifugal acceleration (expressed as multiples of unit gravity, g).

Figure 7. Aspect-ratio distributions for MMT platelets deposited on mica: (a) all platelets (N ) 1141) from 49 different AFM images; (b) a subset of platelets with thicknesses in the range of 0.80-1.20 nm (N ) 749); and (c) all platelets (N ) 247) from six different AFM images, 250fold dilution. Solid curves are log-normal distributions based on the measured mean and standard deviation.

Remarkably, the aspect ratio follows a log-normal distribution that is parametrized by the mean and standard deviation of log R, as computed from the measured distribution (see the solid curve in Figure 7a). To our knowledge, this finding has been previously reported only once, for laponite.33 Log-normal particle size distributions are commonly found for dispersions produced by grinding or comminution.45 Moreover, log-normal particle size distributions are commonly encountered in the soil physics literature. Thus, it may not be surprising that MMT platelets have a log-normal distribution of aspect ratio. The distribution of average platelet thickness (see Figure 6a), although centered at ∼1.0 nm, is not perfectly uniform. Thus,

it may not be appropriate to include all of the particles in the aspect ratio distribution. If we include only particles that have mean thicknesses of 0.80-1.20 nm, the aspect ratio follows the log-normal distribution even more closely (see Figure 7b). The mean aspect ratio has a somewhat larger value, 180 ( 91, with a median value of 160 (N ) 749). These values are somewhat greater than those given previously (for the distribution in Figure 7a), because most of the excluded particles have higher mean thicknesses and correspondingly lower aspect ratios. Could we have measured the aspect ratio distribution using more concentrated (less dilute) suspensions, thus reducing the required number of AFM images? Using all platelets found in six images, such as that shown in Figure 5a (250-fold dilution), we find the distribution shown in Figure 7c. The mean thickness for these platelets is 1.13 ( 0.19 nm, and the mean aspect ratio is 123 ( 48 (N ) 247). Not only is the mean aspect ratio lower than that previously reported, but the distribution is more narrow. Several factors could account for the difference between the distributions in Figures 7a and 7c, including (i) random error due to the small sample size in Figure 7c, (ii) systematic error in measurement of the lateral area or platelet thickness, and (iii) natural bias toward higher platelet thickness due to the higher concentration. Because the mean height here (1.13 nm) is 17% higher than that for the more-dilute sample (0.97 nm, Figure 6a), correcting the mean aspect ratio upward by 17% gives a value of 143, which is not that much less than the value of 166 for the distribution in Figure 7a. We conclude that one can estimate the mean aspect ratio from fewer images made from higher-concentration samples, but the values will naturally be more subject to bias, because of the smaller sample size and lower incidence of isolated, “clean” platelets. 3.3.2. Differential Settling by Centrifugation. Centrifugation removes particles that may not be fully exfoliated, as well as nonlayered quartz particles that are present in natural clays as contaminants. However, prolonged, higher-speed centrifugation may also remove fully exfoliated platelets with the largest aspect ratios. The largest exfoliated platelets would have the greatest impact on barrier performance in a polymer nanocomposite. For these reasons, we have studied the effect of centrifugation speed on the MMT particle size using DLS and AFM with quantitative analysis. A suspension that contained 1.0 wt % MMT powder was centrifuged at different rotational speeds for 1 h and diluted 250-fold with acetone. All other aspects of sample preparation followed the standard protocol. Figure 8 shows the concentration of MMT remaining in the suspension (prior to dilution), as well as the effective spherical particle diameter (from DLS), each as functions of the centrifugal acceleration. Values are given in

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Table S2 in the Supporting Information and the effective diameter is plotted as a function of centrifuge rotational speed in Figure S3 (also given in the Supporting Information). First, the MMT concentration in the as-prepared, uncentrifuged (0 rpm) sample is only 0.87 wt %. This is due to the fact that some of the MMT particles settle out of solution without any imposed centrifugation. From this, we infer that at least 13% of the starting MMT is not exfoliated at all. For centrifugal accelerations increasing up to 125g, the residual MMT concentration decreases slightly (down to 0.83 wt %). Over the same range, the effective particle diameter (Figure 8) and polydispersity index43 (see Table S2 in the Supporting Information) remain almost unchanged. Low-speed centrifugation leads to some additional particle settling, but these particles do not contribute much to the scattering of light. These observations are consistent with the removal of smaller, morespherical unexfoliated particles, leaving behind mostly exfoliated platelets with larger effective size and higher Stokes drag. We have not analyzed the structure of the particles removed by lowspeed centrifugation to confirm this hypothesis. For accelerations greater than 125g (Figure 8), increasing the centrifugal acceleration causes significant decreases in both the concentration of MMT that remains suspended and the effective particle diameter. Over the same range, the polydispersity index seems to decrease slightly (see Table S2 in the Supporting Information), although this trend may not be statistically significant. Higher-speed centrifugation clearly removes the largest particles in the distribution, which we know are large exfoliated platelets. These results suggest that, for our MMT powder and centrifuge, centrifugation at 1000 rpm (∼125g) for 1 h is optimal for removing contaminant particles while minimizing the loss of exfoliated platelets. Dry weight analysis does not discriminate between aggregates and platelets, and DLS gives only an effective spherical particle diameter. Quantitative analysis of AFM images can tell us more about the shape and dimensions of the particles remaining in suspension, as a function of centrifugal acceleration. Typical AFM images of the MMT suspension samples centrifuged at various rotational speeds (0-7000 rpm) can be seen in Figure S4 in the Supporting Information. The images show that MMT particles spread evenly on the mica with, in some cases, smaller particles deposited on top of the bigger platelets. Visual examination of the images does not show any obvious relationship between the particle size and the rotational speed. Comparisons based on quantitative analysis of the AFM images are more revealing. For MMT samples centrifuged at varying rotational speeds, image analysis leads to log-normal aspect ratio distributions (e.g., Figure 7c for the sample centrifuged at 4000 rpm). Figure 9 shows the average aspect ratio of MMT platelets remaining in suspension, as a function of centrifugal acceleration. Figure S3 in the Supporting Information shows the same data, plotted as a function of the rotational speed of the centrifuge. The data in Figure 9 suggest that low-speed centrifugation (500 rpm or 31g) leads to a significant increase in mean aspect ratio for the platelets that remain in suspension. Two factors may be responsible. First, low-speed centrifugation may remove nonplatelet contaminant particles and unexfoliated MMT having low aspect ratios, leaving platelets in suspension with a higher average aspect ratio. Second, the removal of contaminant particles may result in “cleaner” MMT platelets after they are deposited on the mica surface. To test this idea, Figure 9 also shows the average platelet “width”, which is equal to the square

Figure 9. Lateral dimensions of MMT particles remaining in suspension as a function of centrifugal acceleration: (b) average aspect ratio and (9) average “width” equal to the square root of platelet lateral area.

Figure 10. Correlation between the mean aspect ratio measured by AFM with the effective particle diameter measured by dynamic light scattering (DLS).

root of the lateral area. This measure is not subject to any bias introduced by the deposition of contaminant particles on top of platelets, or by random error in measurement of the mean thickness. Compared to that for no centrifugation, the average platelet width is higher for platelets that remain in suspension after low-speed centrifugation. For increasing levels of centrifugal acceleration, the trends in the average aspect ratio and platelet width (Figure 9) agree with that observed in the DLS data (Figure 8). For accelerations greater than ∼100g, the average aspect ratio and width of platelets remaining in suspension decrease as the acceleration increases. This decrease is consistent with that observed in the effective particle diameter, as measured by DLS, as well as with the decrease in MMT concentration observed in the dry weight analysis. Physically, these trends are explained by the removal of more of the exfoliated platelets as the centrifugal acceleration increases. At lower speeds, mostly large-aspect-ratio platelets are removed, but higher speeds lead to the removal of increasing numbers of smaller platelets. The trends observed in the DLS and AFM data for varying centrifugal acceleration yield a useful correlation, shown in Figure 10. The effective spherical particle diameter, as measured by DLS (Figure 8), correlates linearly with the average aspect ratio, as measured by AFM (Figure 9). We have excluded the data point for the uncentrifuged sample (0 rpm), based on the assumption that it contains a significant amount of unexfoliated MMT particles. The correlation seems to be linear with a good correlation coefficient. The polydispersity index from DLS (Table S2 in the Supporting Information) is independent of centrifugation speed (∼25%), as is the standard deviation of the aspect ratio (∼45%, if expressed as a percentage of the average). Thus, it seems reasonable to estimate the standard


deviation of the aspect ratio to be ∼1.8 times the polydispersity index that was measured by DLS. If this correlation is accurate, the effective particle diameter and polydispersity from DLS can be used to predict the mean aspect ratio and its standard deviation that would be obtained from AFM. This would save a great deal of time for routine analysis of platelet suspensions. Careful AFM measurements require many hours and much skill to prepare samples and gather enough images, whereas DLS measurements require only sample dilution and yield results in a few minutes. 4. Conclusion This work focuses on the characterization of a model platelet material, montmorillonite (MMT), by transmission electron microscopy (TEM), X-ray diffractometry (XRD), dynamic light scattering (DLS), and atomic force microscopy (AFM). In particular, this work attempts to provide a starting point for the development of AFM as a tool for quantitative analysis of the size distributions of particles with platelet morphology. Some materials, such as MMT, are easily dispersed in water and give stable suspensions. However, proving that the particles are exfoliated, and quantifying the degree of exfoliation, can be an unexpected challenge. Neither DLS nor TEM can discriminate between single platelets and “short stacks” of a few platelets. Moreover, we are not aware of any previous efforts to quantify the distribution of platelet aspect ratio. AFM provides an ideal tool for these purposes; however, one must be careful, with regard to sample preparation and data analysis. Sonication promotes dispersion of the powder in water but has little impact on exfoliation. Dialysis removes dissolved salts that would otherwise produce small particles that appear in images of undialyzed MMT. However, we have not yet quantified the effect of dialysis on MMT exfoliation. Dilution with acetone seems to help greatly in dispersing the platelets on the mica surface. The samples must be diluted enough so that the large majority of platelets are isolated. However, with increasing dilution, one must gather more AFM images to ensure that enough particles are sampled for an accurate measure of the thickness and aspect ratio distributions. If one gathers data for a sufficient number of particles, one can then explore the impact of excluding certain populations from the sample, such as overlapped platelets. One can also begin to explore, in a quantitative way, the effect of processing variables (such as centrifugation speed) on the degree of exfoliation, platelet aspect ratio, and other relevant engineering variables. Acknowledgment H.J.P. gratefully acknowledges Prof. William B. Russel for his exceptional ability as a mentor, teacher, scholar, and leader of the chemical engineering profession. We also acknowledge the financial support of the University of South Carolina NanoCenter and the Voridian Division of Eastman Chemical Company. Supporting Information Available: Data tables and figures showing the effects of sonication and centrifugation on effective particle size and average aspect ratio; typical AFM images for an MMT suspension diluted 1200-fold with acetone; and typical AFM images for MMT suspensions centrifuged at different speeds (PDF). This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Usuki, A.; Kawasumi, M.; Kojima, Y.; Okada, A.; Kurauchi, T.; Kamigaito, O. Swelling Behavior of Montmorillonite Cation Exchanged for ω-Amino Acids by ω-Caprolactam. J. Mater. Res. 1993, 8, 1174.

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ReceiVed for reView December 13, 2005 ReVised manuscript receiVed January 29, 2006 Accepted January 29, 2006 IE051392R

Quantitative Analysis of Montmorillonite Platelet Size by Atomic Force

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