J. Phys. Chem. C 2007, 111, 17923-17927
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Improved Load Transfer in Nanotube/Polymer Composites with Increased Polymer Molecular Weight† Minfang Mu and Karen I. Winey* Department of Materials Science and Engineering, UniVersity of PennsylVania, 3231 Walnut Street, Philadelphia, PennsylVania 19104-6272 ReceiVed: February 25, 2007; In Final Form: June 18, 2007
Mechanical interactions between amorphous polymers and nanofillers were probed by measuring the tensile moduli of nanocomposite fibers with aligned single wall carbon nanotubes (SWNT) and carbon nanofibers (CNF). Polymer chains provide better load transfer and thereby higher tensile moduli when the polymer size is large relative to the diameter of the filler. The specific interfacial area of the filler is not sufficient to explain this observed increase in elastic modulus. The effective modulus of SWNT bundles was ∼250 GPa, as calculated using a short fiber model.
Introduction Single wall carbon nanotubes (SWNT) have exceptional mechanical properties as illustrated by a tensile modulus as high as 1 TPa,1 which makes them particularly attractive as reinforcing nanoscale fillers in polymers. Given that the mechanical properties of composites depend critically on the load transfer efficiency at the filler/polymer interface,2,3 chemical functionalization methods have been used to improve the load transfer efficiency at nanotube/polymer interfaces.4-6 However, SWNT functionalization adds numerous chemical steps to composite fabrication and introduces defects on the nanotube surface that compromise their electrical and thermal properties.7,8 An alternative way to improve the interfacial load transfer is to strengthen noncovalent bonding between carbon nanotubes and polymers by introducing specific interactions such as π-π interactions8 and CH-π interactions.9 With these specific interactions, polymer wrapping of SWNT has been widely observed experimentally10-13 and by simulation14 when the polymer is a single strand of DNA or has specific functional groups such as phenylenevinylene. DNA-SWNT or conjugated polymer-SWNT complexes have proven useful in separating SWNT by type15 but are not applicable to composites. In the absence of specific interactions, it is unlikely that polymer chains uniformly wrap SWNT and, even so, how does tight polymer wrapping of SWNT improve load transfer? Another important issue for load transfer is the interfacial area between filler and polymer, as reported by Cadek et al.16 They observed a linear dependence of tensile modulus on the interfacial area per unit volume in carbon nanotube/semicrystalline polymer composites. In this study, we probe the load transfer at the nanotube/ polymer interface in amorphous polymer composites. We measured the mechanical properties of poly(methyl methacrylate) (PMMA) nanocomposite fibers containing well-aligned SWNT or carbon nanofibers (CNF) as a function of polymer molecular weight. In these systems, there is no covalent bonding or specific interactions beyond the weak van der Waals force between the fillers and the PMMA matrix. Fibers with aligned fillers provide insight into load transfer at filler/polymer interfaces, because the filler-filler interactions are minimized. We found that longer polymer chains more effectively transfer mechanical load to SWNT bundles, even without specific †
Part of the special issue “Richard E. Smalley Memorial Issue”. * Corresponding author. E-mail:
[email protected]. Phone: 215898-0593. Fax: 215-573-2128.
interactions and at a fixed filler/polymer interfacial area. When the radius of gyration, Rg, of a nonassociating amorphous polymer is greater than the diameter of a high aspect ratio filler, the tensile modulus increases substantially. Experimental Section SWNT were synthesized by a high-pressure carbon monoxide conversion (HiPco) method. Raw SWNT was purified by thermal oxidization, followed by a HCl treatment.17 The residual metal is less than 5 wt %, as measured by scanning thermogravimetric analysis (TGA). CNF was purified by the same method. PMMA was purchased from Polysciences and used as received. The molecular weights are 25 kg/mol and 100 kg/ mol (denoted as 25 k and 100 k), and the polydispersity indices for the two polymers are ∼1.7, as measured by size exclusion chromatography (SEC). SWNT/PMMA and CNF/PMMA nanocomposites were prepared by a coagulation method.18 The SWNT/N,N-dimethylformamide (DMF) suspension was sonicated for 24 h to exfoliate SWNT aggregates into small bundles or isolated tubes and then mixed with the PMMA/DMF solution under sonication. This SWNT/PMMA/DMF solution was poured into excess water, and the nanocomposite rapidly precipitated. The resulting composites were dried in vacuum oven at 130 °C for 24 h. Prior to coagulation, a substrate submerged into the SWNT suspension and dried for atomic force microscopy (AFM) to characterize the SWNT bundle size.19 The mean diameter of these SWNT bundles is ∼9.6 nm and the mean aspect ratio of SWNT is ∼35. Coagulation is sufficiently rapid as to avoid agglomeration of the SWNT bundles. Raman microspectroscopy was used to evaluate the spatial distribution of SWNT in nanocomposites. The nanocomposites prepared by coagulation were hot pressed into ∼30 µm films at 150 °C. The Raman intensity of the nanocomposite film was collected at a wavenumber of 1590 cm-1 (D band of SWNT) using Ar ion laser excitation at 514.5 nm. The Raman imaging scans were 10 × 10 µm2 with a step size of 0.5 µm, and multiple regions were imaged on each sample. The Raman intensities were scaled, so that the average intensity for each image was 100 au. The standard deviation of the intensity provides a measure of the spatial uniformity of SWNT in the nanocomposites.18 The nanocomposites were spun into fibers from the melt state using a DACA SpinLine at ∼200 °C. The diameter of the spinneret was 0.5 mm, the extrusion speed was 1.0 mm/min,
10.1021/jp0715530 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/31/2007
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Figure 1. (a) Raman mapping image (10 × 10 µm) collected at 1590 cm-1 from a 1.0 wt % SWNT/100 k PMMA composite film. Standard deviation of the normalized intensity is less than 4/100, indicating a uniform SWNT distribution. (b) The fwhm, as measured by SAXS, indicating the alignment of SWNT bundles in 1.0 wt % SWNT/PMMA composite fibers as a function of the fiber diameter. Similar SWNT alignment was observed in composites with 25 k and 100 k PMMA.
and the winder speeds were 6, 11, 16, or 21 m/min to make fibers with various diameters (50-120 µm) and extents of filler alignment. The degree of filler alignment was characterized by small-angle X-ray scattering (SAXS) for SWNT/PMMA composite fiber, where the scattering arises from the form factor scattering from SWNT bundles.20 The d002 spacing of graphite in wide-angle X-ray scattering (WAXS) is used to characterize the degree of CNF alignment. The intensity was integrated in a q range of 0.015 to 0.15 Å-1 for SWNT composites and 1.7 to 2.0 Å-1 for CNF nanocomposites. The scattering intensity as a function of azimuthal angle was fit using a Lorentzian function, and the full width at half-maximum (fwhm) corresponds to the degree of alignment: 0° is perfectly aligned, 180° is isotropic. The tensile modulus of the nanocomposite fibers was measured using an Instron Model 5564 table mounted materials testing system at room temperature at a crosshead speed of 1.0 mm/min and a gauge length of 2.54 cm. Results and Discusions The SWNT bundles were observed to be uniformly dispersed at a length scale of one micron according to Raman mapping, Figure 1a, as previously demonstrated with our coagulation method.18 The 1.0 wt % SWNT nanocomposites with either 25 k or 100 k PMMA have standard deviations of the normalized
Figure 2. Tensile moduli of composite fibers with different filler loadings as a function of fiber diameter. (a) SWNT/100 k PMMA composites. (b) SWNT/25 k PMMA composites. (c) CNF/100 k PMMA composites. Only the SWNT/100 k PMMA composites exhibit an increase in tensile modulus with loading.
Raman intensity < 4/100, indicating that the dispersion of SWNT in the composite is very good and has not been significantly affected by the matrix molecular weight. Figure 1b shows the degree of SWNT alignment in the nanocomposite fibers. The alignment of SWNT increases somewhat with decreasing fiber diameter, but all of the fwhm values are small (∼7-11°), indicating a good alignment of SWNT bundles. The molecular weight of the polymer matrix does not effect SWNT alignment. Figure 2a shows the tensile moduli of the 100 k PMMA composite fibers with 0, 1.0, and 2.0 wt % SWNT as a function of fiber diameter. The tensile moduli of PMMA fibers (Em) increased from ∼3000 MPa to ∼4500 MPa as the diameter of the fiber decreased from 120 to 50 µm. Decreasing fiber diameter correlates with extending the polymer conformation,
Load Transfer in Nanotube/Polymer Composites
J. Phys. Chem. C, Vol. 111, No. 48, 2007 17925
TABLE 1: Relative Elastic Moduli (Ec/Em) of Various Nanocomposite Fibers along with Their Relative Filler Size (2Rg/D), Specific Interfacial Area (r), and Filler-Filler Separation (a-D) composite
2Rg/D
R (µm-1)
[a-D] (nm)
Ec/Ema (MPa)
1.0 SWNT wt %/100 k 2.0 SWNT wt %/100 k 1.0 SWNT wt %/25 k 2.0 SWNT wt %/25 k 6.4 CNF wt %/100 k 17.7 CNF wt %/100 k
1.79 1.79 0.90 0.90 0.22 0.22
3.33 6.66 3.33 6.66 3.33 9.19
85.5 57.7 85.5 57.8 192.7 85.5
1.25 1.53 1 1 1 1
a Obtained Ec for 50 µm diameter fibers by fitting the experimental data in Figure 2; used a fiber diameter of 110 mm for 17.7 CNF wt %/100 K.
between 25 k PMMA and SWNT bundles provides poor load transfer efficiency and no increase in moduli (Figure 2b). When PMMA chains encompass the SWNT bundles, the composites have higher load transfer efficiency and higher tensile modulus. Longer polymer chains provide better load transfer efficiency between the polymer matrix and the SWNT, but total load transfer at the filler/polymer interface might also depend on the specific interfacial area.16,27 Because the SWNT bundles are well-aligned in the fiber, a simple construct can be applied to calculate their interfacial area. By assuming that the composite fibers are composed of tetragonal unit cells with one cylindrical filler in each cell, we find the weight fraction of the fillers, c, can be expressed as:28
c)
Ffπ(D/2)2L Fma2L
(1)
where Ff and Fm are the densities of fillers and matrix, respectively; D is the diameter of filler, L is the filler length, which is the same as the unit cell length, and a is the width of the unit cell. By rearranging eq 1, the interfacial area per unit volume R is given by:
R) Figure 3. Schematic of the interactions between polymers and fillers, showing the importance of size. Note the lengths of the fillers are considerably longer than shown here.
which explains the increase in the tensile modulus relative to bulk PMMA (∼2000 MPa).21 The tensile moduli also increased with the addition of SWNT (Figure 2a), which is consistent with our previous work.22 In 50 µm diameter fibers, the increases in modulus relative to PMMA are 25% and 53% for 1.0 wt % and 2.0 wt % SWNT nanocomposites, respectively (Table 1). The tensile moduli of the SWNT/25 k PMMA composite fibers (Ec) also increase with decreasing fiber diameter, Figure 2b. However, in contrast to SWNT/100 k PMMA fibers, the moduli do not change with 1.0 wt % or 2.0 wt % SWNT indicating poor load transfer efficiency at the SWNT-polymer interface. In nanocomposites with isotropic distributions of SWNT, nanotube-nanotube interactions with attraction energies of ∼40kBT obscure the SWNT-polymer interactions.23 During melt fiber spinning, high extensional forces align the nanotube bundles and thereby reduce nanotube-nanotube interactions.24 Du et al. observed a significant decrease in the electrical conductivity of fibers with increased SWNT alignment,25 which also originates from the reduced number of tube-tube contacts. The decrease in tube-tube contact strongly suppresses the load transfer through tube-tube interactions in the SWNT/PMMA fibers. Therefore, the contribution of the SWNT to the tensile moduli of these aligned composites relies predominantly on the SWNT/polymer interaction, which is the interfacial load transfer. Our results indicate that the SWNT/polymer interactions become stronger and improve the composite fiber modulus (Ec) as the PMMA molecular weight increases. The radius of gyration (Rg) is ∼8.6 nm for 100 k PMMA and ∼4.3 nm for 25 k PMMA.26 In 100 k PMMA composites, the ratio of 2Rg to the SWNT bundle diameter (DSWNT) is 1.79 (Table 1) indicating a high probability that one high molecular weight polymer can surround a SWNT bundle (Figure 3). In contrast, 2Rg/DSWNT for 25 k PMMA composites is 0.90, so that the SWNT bundles are larger than the polymer coil. The limited entanglement
πDL 4Fmc ) FfD a2L
(2)
With FSWNT ) 1.5 g/cm3 (ref 29) and FPMMA ) 1.2 g/cm3, the interfacial area per unit volume or specific interfacial area of the 1.0 wt % SWNT composite is 3.3 µm-1 (Table 1). This value is independent of the molecular weight of the polymer and only depends on the density ratio (matrix/filler), filler diameter, and loading. In these well-aligned SWNT/PMMA fiber composites, increasing R by increasing the filler concentration (c) does not increase the observed Ec when the molecular weight of the matrix is only 25 k. This observation points toward the importance of 2Rg/D for interfacial load transfer. We further evaluate the relative importance of specific interfacial area (R) and the relative filler size (2Rg/D) by using another carbon nanofiller, namely, carbon nanofiber (CNF), having a graphene-like surface. The tensile modulus of the CNF is in the range of 100-600 GPa,30 which is comparable with the tensile modulus of SWNT bundles.31 The CNF diameter of ∼77 nm is much larger than the radius of gyration of 100 k PMMA, so it is difficult for CNF to be embedded within a single polymer chain coil. A 6.4 wt % CNF/PMMA composite has the same specific interfacial area (R) value as the 1.0 wt % SWNT/PMMA composites; the density of CNF is 1.2 g/cm3. Cadek et al.16 have reported that the tensile moduli increase linearly with the specific interfacial area in nanotube/polymer composites with various nanotubes. However, we observed that the tensile modulus of the 6.4 wt % CNF/100 k PMMA composite fiber is the same as pure PMMA (Figure 2c). This suggests that the load transfer at such CNF/100 k PMMA interfaces is poor. The larger CNF is not surrounded by individual PMMA coils (2Rg/D ) 0.22), which leads to a very low load transfer efficiency and inhibits the reinforcing effect of the filler. Naturally, the comparison of 1.0 wt % SWNT/100 k PMMA and 6.4 wt % CNF/100 k PMMA composites fibers is complicated by possible differences in the weak van der Waals forces due to the details of the graphene structures of the fillers. Nonetheless, both composites have comparable filler moduli and the same matrix and specific interfacial area, but only the system with a large 2Rg/D value exhibits an improved modulus, thereby
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suggesting that the specific interfacial area alone is insufficient in predicting the mechanical properties in these polymer nanocomposites. Indirect filler-filler interactions that might arise when a polymer spans the distance between fillers could also influence the mechanical properties. Based on eq 1, the average interfaceto-interface distance [a-D] between the nearest SWNT bundles in 1.0 wt % SWNT/PMMA composite fibers is 85.5 nm, which is 9 times larger than the gyration of radius of 100 k PMMA. Thus, the probability that one polymer chain will bridge two fillers is very low. In 6.4 wt % CNF/PMMA composites, [a-D] is 192.7 nm (Table 1). If the CNF-CNF separation is reduced to be the same as in 1.0 wt % SWNT nanocomposites, which corresponds to a CNF loading 17.7 wt %, the specific interfacial area is almost 3 times larger than that in the 1.0 wt % SWNT composites. The dispersion of 17.7 wt % CNF in PMMA is still good at this high loading and the azimuthal fwhm value for a 120 µm diameter fiber is ∼70°, on the basis of the d002 reflection. Though the alignment of CNF is not as good as the SWNT in the composite fibers, indicating a relatively high filler-filler contact interaction, the tensile modulus of 17.7 wt % CNF/PMMA composite fibers remains the same as the PMMA fibers (Figure 2c). (Fibers with diameters less than 100 µm were not obtained because of the brittleness of the 17.7 wt % CNF/PMMA composite.) We conclude that physical entanglements between nanoscale fillers and polymer chains play an important role in load transfer efficiency in polymer nanocomposites. Of the three parameters considered in this study (2Rg/D, R, [a-D]), the parameter most strongly correlated with modulus in these nanocomposites is 2Rg/D, the relative size of the amorphous polymer to the rodlike filler. When the filler diameter is larger than ∼2Rg of the matrix polymer, the polymer does not surround the high aspect ratio filler, and the load transfer efficiency at the filler/polymer interface is poor (Figure 3). Consequently, the tensile moduli of the composites are equal to the modulus of the 25 k PMMA, even when R is as large as 6.66 µm-1 in 2.0 wt % SWNT composite. When the polymer size is larger than the filler diameter (2Rg/DSWNT ) 1.79 for the SWNT/100 k PMMA composites), the entanglement between polymer and filler effectively transfers the load, and the tensile modulus increases. A short fiber model was used to calculate the effective modulus of SWNT bundles (Ef) in the composites.32 The short fiber model assumes different strains on the filler and the polymer matrix and an inhomogeneous load on the filler. Using this model, the tensile modulus of the composite fiber (Ec) can be calculated by the following equation:
Ec ) VmEm + VfEf{1 - tan h(ns)/ns}
(3)
where Em and Ef are the tensile moduli of the polymer matrix and filler, Vm and Vf are the volume fractions, s is the aspect ratio of filler, and n is a dimensionless parameter given by n2 ) 2Em/[Ef(1 + νm) ln(Pf/Vf)] , where νm is the Poisson’s ratio of PMMA and Pf is the filler packing factor. We approximate our fibers by assuming that all of the SWNT bundles have the same size and are square packed, perfectly aligned, and uniformly dispersed. Thus, the composite was divided into tetragonal unit cells with one cylindrical filler in each cell, consistent with eq 1, and ln(Pf/Vf) ) ln(π/Vf). The calculated effective moduli of the SWNT bundles in 100 K PMMA composites is ∼250 GPa (Table 2). This bundle modulus is smaller than the published value of one individual SWNT tube, 1 TPa, but is comparable to the tensile modulus of SWNT bundles with ∼10 nm diameter.31 The slight difference
TABLE 2: Effective Moduli of SWNT Bundles, Ef, Calculated by Applying a Short, Aligned Fiber Model to the SWNT/PMMA Nanocomposite Fibers composite (SWNT/PMMA) 1.0 wt %/25 k 2.0 wt %/25 k 1.0 wt %/100 k 2.0 wt %/100 k
Eca (MPa)
Efb (GPa)
5000 5000 5600 6900
5.32 5.30 246 262
a
Experimental data for fibers from Figure 2 with 50 µm diameter where the highest degree of SWNT alignment was obtained in our experiments. b Calculated from eq 3 using Em(100 k) ) 4500 MPa, Em(25 k) ) 5000 MPa, FSWNT ) 1.5 g/cm3, FPMMA ) 1.2 g/cm3, νm ∼ 0.4, and s ) ∼ 35, as observed by AFM. The 1.0 wt % and 2.0 wt % composites correspond to 0.8 vol % and 1.6 vol %, respectively.
between the effective bundle modulus in the 1.0 wt % and 2.0 wt % SWNT composite might come from the increased tubetube interactions at the higher SWNT loading. In contrast the effective bundle modulus is only ∼5 GPa in the SWNT/25 k PMMA composite fibers. This low effective modulus indicates low load transfer efficiency. The reinforcing effect of SWNT bundles on a polymer matrix evidently requires SWNTpolymer entanglement. An alternative interpretation is suggested by earlier studies of melt extruded PMMA fibers, in which the modulus increases from 1500 to 3500 MPa at different draw velocities and processing temperatures.33 The authors attributed this increase in modulus to extended chain conformations of the PMMA. In the nanocomposites studied here, the presence of cylindrical fillers might promote polymer elongation during melt fibers spinning because of increased viscosity and might also retard polymer relaxations prior to cooling below the glass transition temperature. We attempted to account for polymer elongation in this study by (1) plotting the modulus as a function of fiber diameter, which corresponds to the strength of the melt extrusion process, and (2) reporting relative increases in modulus at fixed fiber diameters. Future studies should probe the extent of polymer anisotropy in nanocomposite fibers but are likely to be complicated by the alignment of the cylindrical fillers. Whether the molecular weight effect we report here is rooted in interfacial load transfer or in chain conformation, the molecular weight of the matrix polymer is critical for maximizing the mechanical properties of nanocomposite fiber. In summary, while the molecular weight of an amorphous polymer matrix has no significant effect on SWNT dispersion and alignment in SWNT/PMMA composite fibers, the molecular weight plays a crucial role in mechanical load transfer. The relative size of the polymer, 2Rg/D, where Rg is the polymer radius of gyration and D is the diameter of the cylindrical filler, must be greater than one to improve load transfer at the fillerpolymer interface and increase the elastic moduli of the composite. In contrast, the specific interfacial area did not correlate with composite moduli in these nanocomposites with an amorphous polymer matrix. Small filler sizes (D) and suitable polymer molecular weight (Rg) are critical requirements for high load transfer in nanocomposite through filler-polymer entanglements. Acknowledgment. This research was funded by the National Science Foundation MRSEC-DMR05-20020. We thank Dr. Fangming Du and Dr. Reto Haggenmueller for valuable discussions. We are grateful to Professor Shu Yang of our department for access to the SEC.
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