Macromolecules 2011, 44, 191–193
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DOI: 10.1021/ma1019818
Polymer Tracer Diffusion Exhibits a Minimum in Nanocomposites Containing Spherical Nanoparticles Minfang Mu,† Michelle E. Seitz,† Nigel Clarke,‡ Russell J. Composto,† and Karen I. Winey*,† †
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6272, United States, and ‡Department of Chemistry, Durham University, Durham DH1 3LE, England Received August 26, 2010 Revised Manuscript Received October 25, 2010 Introduction. In previous work,1,2 we reported that a minimum in tracer diffusion coefficient with nanotube loading is observed in polystyrene (PS) composites with single wall carbon nanotubes (SWCNT) and multiwall carbon nanotubes (MWCNT) if the radius of gyration (Rg) of the tracer is larger than the radius of the nanotube bundles.1 Here we extend this work to include C60/PS composites to determine if the minimum in diffusion coefficient will be observed for spherical nanoparticles or if it arises from the cylindrical geometry of the nanotube bundles. Comparing PS composites with SWCNT, MWCNT, and C60 allows particle geometry and size to vary while minimizing differences in enthalphic interactions between the particles and the matrix. Experimental Details. Fullerene C60 was purchased from SES Research. Polystyrene and deuterated polystyrene with molecular weights of 76.9 and 478.7 kg/mol were purchased from Polymer Source and Pressure Chemical and will be denoted 75k dPS and 480k PS, respectively. Both polymers have PDIs of 1.03 and were used as received. Composites were prepared by first stirring 10 wt % 480k PS in toluene overnight. The C60 was dissolved in toluene at a concentration of 3 mg/mL by sonicating for 3 h. The C60 solution is purple and transparent indicating that no aggregates were observed. The C60 diameter in solution as measured with a Malvern Nano S particle size analyzer is 0.7 nm, and this agrees with reported C60 molecule size,3 indicating that it is fully dispersed. The C60 and PS solutions were combined to achieve the desired C60 concentrations of 0.01-2 wt % C60 in the dried films (C60/(C60 þ PS)). To convert to volume fractions, densities of 1.05 and 1.65 g/cm3 were used for PS and C60, respectively. The resulting solutions were spin-coated at 1000 rpm for 60 s onto cleaned silicon wafers. Previous work has suggested that C60 may segregate to the silicon substrates during spin-casting.4-7 However, the solutions used in this work have high solids loadings ((C60 þ PS)/(C60 þ PS þ toluene) = 6-10 wt % versus 2 wt %4) and the PS molecular weight is large (480k versus 1.8k4 or 76k7), both of which will lead to increased solution viscosity and mitigation of C60 segregation. Additionally, this work focuses on very low C60 loadings. Estimates from the literature indicate C60 to be stable against aggregation in bulk PS to concentrations of ∼1-2 wt % (0.64-1.27 vol %).8,9 Spin-coating was selected as the sample preparation method because quiescent solvent evaporation led to C60 crystallization (as detected by X-ray scattering). *Corresponding author. E-mail:
[email protected]. r 2010 American Chemical Society
Five or fewer spin-coated films were floated and stacked (keeping their original orientation) to obtain thick nanocomposite films (>1 μm) which were then dried in a hood for 3 days. For a sample with 1.3 vol % C60, no C60 crystalline reflections were detected with wide-angle X-ray scattering even after thermal annealing for 18 h at 150 °C (twice the annealing time used in our diffusion experiments). This suggests that C60 does not aggregate and form crystals (which due to its monodisperse size and shape C60 readily forms when aggregated) either during spin-casting or throughout the diffusion anneal. No evidence of dewetting (e.g., changes in sample appearance) was observed after annealing. Diffusion bilayers were made by picking up a floated ∼20 nm spin-cast film of 75k dPS with the C60/480k PS nanocomposite films. The bilayers were dried before annealing for 9 h in vacuum at 150 °C. Concentration profiles for 75k dPS in the C60/480k PS nanocomposites were measured by elastic recoil detection10 using a 3 MeV He2þ beam at 15° glancing angle with a spot size of ∼5 5 mm2. The sampling depth is ∼800 nm with a resolution of ∼80 nm. Diffusion coefficients were obtained by fitting the dPS volume fraction profiles to the solution to Fick’s second law convoluted with instrument resolution.10 Additionally, excellent agreement between the experimental diffusion data and the fits to Fick’s second law was obtained, suggesting diffusion into a homogeneous medium; stable layers of interfacially segregated C60 would lead to deviation from Fick’s second law solution. Results and Discussion. Figure 1 shows the measured 75k dPS volume fraction as a function of depth for a composite with 1.3 vol % C60 after annealing for 9 h at 150 °C. It is in good agreement with Fick’s second law10 using a diffusion coefficient of 8.85 10-15 cm2/s. These data are representative of results for other C60 concentrations. Figure 2 shows the tracer diffusion coefficients, D, for 75k dPS as a function of C60 concentration in C60/480k PS nanocomposites. The diffusion coefficient initially decreases rapidly with increasing C60 concentration followed by a slower increase at concentrations above a critical volume fraction, φcrit, where the minimum D is observed. This behavior is qualitatively similar to the behavior of 480k PS nanocomposites with either SWCNTs2 or MWCNTs1 when the tracer 2Rg is larger than the diameter of the nanotube bundles. For C60/480k PS composites, the diffusion coefficient is reduced by ∼80% at the critical C60 loading of 0.064 vol %. This critical C60 loading is much smaller than the percolation threshold (∼30 vol % C60 as determined by electrical conductivity11); thus, percolation of the filler is not required for a diffusion coefficient minimum to be observed. Neat 480k PS and C60/ 480k PS with critical C60 loading of 0.064 vol % have indistinguishable glass transition temperatures (107 °C, determined via second heat DSC). This is consistent with the literature8 that suggests at most a few degree increase in Tg with C60 loadings below 1.3 vol % for well dispersed composites. Therefore, the dramatic decrease in diffusion cannot be attributed to a shift in Tg. Additionally, C60 loadings below 0.63 vol % have been shown to be stable against agglomeration even after high-temperature annealing,8 indicating that the minimum in diffusion is not related to a change in the spatial distribution of the nanoparticles. Figure 3 compares the reduced diffusion (D/D0 where D0 is the diffusion coefficient in pure PS) coefficient of 75k dPS in Published on Web 12/20/2010
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Figure 1. Volume fraction of 75k dPS as a function of depth in a 1.3 vol % C60/480k PS nanocomposite after annealing for 9 h at 150 °C. The red line is the model fit using Fick’s second law with D = 8.85 10-15 cm2/s.
Figure 2. Tracer diffusion coefficient for 75k dPS in C60/480k PS nanocomposites as a function of C60 loading.
480k PS nanocomposites containing SWCNTs or C60 as a function of the particle volume fraction normalized by the critical volume fraction. The SWCNT/PS composites contain nanotube bundles with a mean diameter of ∼9.6 nm and a mean aspect ratio of ∼35, and the minimum in D occurs at 0.4 vol % SWCNT. It should be noted that both the tracer and matrix polymers are identical in these samples; they differ only in nanoparticle type and loading. The magnitude of reduction in tracer diffusion is comparable for both systems. However, the diffusion coefficient recovers differently for the two systems as the particle loading increases. In SWCNT nanocomposites, D increases above φcrit until its value becomes similar to that in pure 480k PS at a nanoparticle concentration of ∼10φcrit. In contrast, D recovers more slowly in C60 nanocomposites and does not regain the D observed in the neat matrix even at φ > 20φcrit. That PS nanocomposites with vastly different particle geometry and size should show such similar diffusion behavior is striking. The nanotube network within the CNT/PS nanocomposites is assumed to be relatively immobile during the diffusion experiments compared to the diffusing polymer chains. In comparison to nanotube bundles, C60 is more mobile, and this could complicate the interpretation of our results. As a first approximation, we use the equation for Brownian motion to estimate the diffusion coefficient of the C60 in the matrix (DC60= kBT/6πηr) where r is the particle radius of the diffusing particle and η is the viscosity of the matrix. Using r = 0.35 nm for C60, that is assuming no aggregation, and η = 8 104 Pa s for the 480k PS matrix
Communication
Figure 3. Reduced diffusion coefficients (D/D0 where D0 is the diffusion coefficient in pure PS) of 75k dPS in 480k PS nanocomposites containing SWCNTs (from ref 2) and C60 as a function of normalized nanoparticle loading. The diffusion coefficient recovery in nanocomposites with C60 is much slower for those with SWCNTs.
(determined from oscillatory shear rheology at 200 °C and shifted to 150 °C using the WLF equation with parameters c1=-6.8, c2 = 98) yields DC60= 5.6 10-16 cm2/s at 150 °C. Thus, even the slowest diffusing tracer molecules are still diffusing nearly an order of magnitude faster than the C60. Moreover, there have been reports that the addition of C60 to PS reduces the nanocomposite viscosity relative to the neat PS;12 this implies that we have overestimated η. In order for C60 to have a diffusion coefficient that is comparable to the slowest tracer polymers, the viscosity would have to be reduced by a factor of ∼9. However, at loadings of 1 wt % C60 the reported viscosity reduction12 is only a factor of 3, indicating that the tracer molecules are the most rapidly moving component in our study. Any aggregation or clustering of the C60 would presumably decrease its mobility. Thus, we conclude that although C60 is more mobile during the diffusion experiments than SWCNT and MWCNT bundles, the dPS tracer molecules are still the faster species. Assuming that the mobility of C60 can be tuned by the matrix molecular weight, an intriguing future study would be tracer diffusion in C60/PS nanocomposites as a function of matrix molecular weight. Our previous work demonstrated that the tracer molecule must be larger than the diameter of the nanotube bundles (e.g., 2Rg > d) for a diffusion minimum to occur. This study demonstrates that cylindrical fillers are not required for a minimum in tracer diffusion to be observed. The minimum in the tracer diffusion coefficient that we observed arises, at least in part, from accessing the new size regime made available by the synthesis of particles that are smaller than the polymer radius of gyration and provides a new challenge for the fundamental understanding of polymer melt diffusion. Further studies using a variety of nanofillers, polymers, and temperature to better understand how enthalpic interactions and geometric considerations contribute to the origin of the diffusion minimum are underway. While the effect of C60 on glass formation in PS has received attention recently,8,13,14 this study highlights that very small nanoparticle loadings can also significantly alter polymer dynamics at longer time scales which has implications for permeability and mechanical properties. Acknowledgment. This research was funded by the National Science Foundation Materials World Network DMR-0908449 (K.I.W., R.J.C., N.C.), MRSEC-DMR05-20020 (K.I.W., R.J.C.), and Polymer Programs DMR05-49307 (R.J.C.). N.C. gratefully acknowledges the award of an EPSRC Overseas Travel Grant,
Communication EP/E050794/1. We thank Prof. Shu Yang at the University of Pennsylvania for use of the size exclusion chromatograph.
References and Notes (1) Mu, M. F.; Composto, R. J.; Clarke, N.; Winey, K. I. Macromolecules 2009, 42 (21), 8365–8369. (2) Mu, M. F.; Clarke, N.; Composto, R. J.; Winey, K. I. Macromolecules 2009, 42 (18), 7091–7097. (3) Hedberg, K.; Hedberg, L.; Bethune, D. S.; Brown, C. A.; Dorn, H. C.; Johnson, R. D.; Devries, M. Science 1991, 254 (5030), 410–412. (4) Barnes, K. A.; Karim, A.; Douglas, J. F.; Nakatani, A. I.; Gruell, H.; Amis, E. J. Macromolecules 2000, 33 (11), 4177–4185. (5) Han, J. T.; Lee, G. W.; Kim, S.; Lee, H. J.; Douglas, J. F.; Karim, A. Nanotechnology 2009, 20 (10), 105705. (6) Holmes, M. A.; Mackay, M. E.; Giunta, R. K. J. Nanopart. Res. 2007, 9 (5), 753–763.
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