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Buckling instabilities of octadecylamine functionalized carbon nanotubes embedded in epoxy
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 66 (2006) 128–136 www.elsevier.com/locate/compscitech
Buckling instabilities of octadecylamine functionalized carbon nanotubes embedded in epoxy V.G. Hadjiev
a,*
, D.C. Lagoudas b, E-S. Oh b, P. Thakre b, D. Davis b, B.S. Files c, L. Yowell c, S. Arepalli c, J.L. Bahr d, J.M. Tour d
a
d
Texas Center for Superconductivity and Advanced Materials, University of Houston, 202 Science Center, Houston, TX 77204, USA b Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA c NASA-Johnson Space Center, 2101 NASA Road One, Houston, TX 77058, USA Department of Chemistry, Department of Chemical Engineering and Material Science, and Center for Nanoscale Science and Technology, Rice University, MS222, Houston, TX 77005, USA Received 7 October 2004; accepted 18 January 2005 Available online 13 September 2005
Abstract We demonstrate effects of nanotubes buckling and debonding in octadecylamine (ODA) derivatized single wall carbon nanotubes (SWCNT)/epoxy nanocomposites under mechanical and thermal loads uniquely detected by means of Raman spectroscopy and documented by TEM imaging. It is shown that ODA functionalization of SWCNTs provides weak sidewall interactions between the nanotubes and epoxy matrix, which make axially compressed ODA-SWCNTs susceptible to buckling. The feasibility of ODA-SWCNTs buckling in epoxy matrix is also supported by the structural mechanics calculations. 2005 Elsevier Ltd. All rights reserved. Keywords: Polymer-matrix composites (PMCs); Fibre/matrix bond; Buckling; Raman spectroscopy; TEM
1. Introduction Recent studies of single wall carbon nanotubes (SWCNTs) functionalized by direct reaction with octadecylamine (ODA, H2N–C18H37) have shown stable dispersion of thus derivatized nanotubes in the organic solvents that are commonly used for preparation of SWCNT/epoxy (EP) nanocomposites [1,2]. Importantly, in one case, ODA functionalized only the semiconducting nanotubes and this selectivity was used successfully for bulk separation of semiconducting from metallic SWCNTs [2]. Part of the ODA molecules forms zwitterion groups SWCNT-COO H3N–C18H37 [1] (ionic bonding) at the defect sites. The other part of ODA is *
Corresponding author. Tel.: +1 713 743 8442; fax: +1 713 743 8201. E-mail address: [email protected] (V.G. Hadjiev). 0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.01.004
physisorbed along the SWCNT sidewalls (van der Waals attraction) [2], and facilitates to large extent the solubility of the ODA-functionalized nanotubes in organic solvents. Given the complex surface modification of the ODA functionalized nanotubes, the next natural step is one to study the interfacial and mechanical properties of ODASWCNTs embedded in polymer matrix, i.e., of the corresponding nanocomposite. In the ODA-SWCNT/EP nanocomposites, the attached ODA functional groups and physisorbed molecules on the SWCNT surface are expected to modify strongly the nanotube–epoxy interface region and thereby to change the adhesion between the nanotubes and the epoxy matrix. It has been firmly realized that the nanotubes used for preparation of nanocomposites with controlled properties have to be purified [3]. The standard purification procedures, based on acid reflux, oxidize the nanotubes
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through attachment of carboxyl (–COOH) groups at the defect sites and nanotubeÕs ends. It is well established that oxidized SWCNTs and the epoxy matrix interact with each other through two major mechanisms. These are van der Waals nanotube sidewall–epoxy interaction and the covalent bonding created by reaction of the carboxyl groups on the nanotube and the epoxy group in the matrix. The functionalization of oxidized SWCNTs with octadecylamine (ODA) substitutes the carboxyl groups for alkylamine ones and hence it is expected to modify the interface interactions in the epoxy nanocomposites. In addition, the physisorbed ODA on the nanotubeÕs sidewall may play the role of a surfactant that also change the sidewall–epoxy interaction. Among the experimental techniques used for studying of the SWCNTs nanocomposites, Raman spectroscopy has proven to be an efficient tool for probing the interfacial properties of SWCNT/EP nanocomposites. It has been shown that Raman spectroscopy can monitor the load transfer from the epoxy matrix to the nanotubes with applied mechanical [4] or thermal [5] loads. On the other hand, a complementary transmission electron macroscopy (TEM) study of the nanocomposites could reveal important information about the size of SWCNTs therein and residual distortion that may appear after loading of the nanocomposite [6]. In the present study, we utilize both experimental approaches. Loads applied on the SWCNTs result in strain of the nanotubes that can be detected as a change of the carbon vibrations frequency. The carbon vibrations that involve C–C bond-stretching motions with eigenvectors being tangential to the nanotube surface are particularly sensitive to the nanotube strain [7]. The highest frequency tangential carbon vibrations in SWCNTs give rise to a graphite-like G-band around 1500–1590 cm1 in the Raman spectra. The G-band usually exhibits a doublet structure with higher frequency component G+ corresponding to the longitudinal carbon vibrations, that is, those along the nanotube axis [8,9]. The second band in the doublet, denoted as G, involves transversal carbon vibrations. The G+-band vibrations have been studied in detail and the correspondence between the change of the vibration frequency and strain on the SWCNT is established [4,7]. SWCNTs in the nanocomposite act as unidirectional strain sensors that can be read when the incident light polarization has a component along the nanotube axis [4]. The Raman intensity of the carbon vibrations in a SWCNT, measured for parallel incident ð~ eI Þ and scattered ð~ eS Þ light polarizations, varies as IS = I0 cos4h with the angle h between the polarization vectors ~ eI k~ eS and the nanotube axis [10]. The Raman scattering technique provides sensitivity capable of detecting strain changes on SWCNTs with 0.012% resolution, thus making it suitable for certain low load measurements [11].
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In this paper, we present a study of load transfer through the complex interface in ODA functionalized SWCNT/EP nanocomposites.
2. Experimental 2.1. Sample preparation SWCNTs produced by laser ablation technique [12] were purified following the procedure described in Ref. [13]. Functionalization was performed in two steps. Firstly, the purified SWCNTs were slurred in concentrated H2SO4, 30% H2O2 was added, and the mixture was stirred at 70 C for 20 min. The slurry was poured in cold water, filtered, washed extensively, and dried under vacuum. Functionalization with ODA took place in the second step, when thus treated SWCNTs were mixed with ODA and heated at 110 C for 40 h. The mixture was then cooled, sonicated in EtOH (bath sonicator) for 1 h, filtered, sonicated in THF, filtered, and dried. The preparation of the ODA-SWNT/EP nanocomposite included the following steps: A suspension of ODASWCNTs in 70% acetone/30% toluene was mixed with epoxy resin EPIKOTE 862 [14]. The mixture was kept in a nitrogen purged beaker and stirred until most of the solvent was evaporated. In the next step, EPIKURE W curing agent [14] was added and the mixture stirred well. The blend was placed in a vacuum oven and kept for 2 h at 60 C before it was cast in a preheated at 60 C mold. The loaded mold was annealed at 80 C for 1/2 h in a vacuum oven. The curing cycle involved an annealing at 121 for 1 h and followed by another one at 175 for 2 h. Thus prepared composite samples had rectangular bar shape with size 50 · 10 · 2 mm3 and contained 0.5% ODA-SWCNT. Reference nanocomposite samples loaded with 0.5–1% non-functionalized nanotubes were prepared following the same nanocomposite preparation procedure. 2.2. Transmission electron microscopy Small pieces of the ODA-SWCNT/EP composite specimen were embedded in another epoxy block for stability during sectioning using microtomy. The supporting epoxy resin contained dodecenyl succinic anhydride (DDSA), LX-112 epoxy resin, araldite 502 (provided by Ladd research). The epoxy/anhydride ratio was 1.0:1.0 and benzyl dimethyl amine (BDMA) was used as the accelerator. The mixture was poured into block molds and left overnight in an oven at 60 C for curing. The polymer blocks were cut into thin (60– 90 nm) slices using a diamond knife (Diatome) on Leica UltracutE microtome. The slices were picked upon 3 mm diameter copper grids and examined using JEOL 1200 EX TEM operated at an accelerating voltage of
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100 kV. Kodak 4489 films were used to capture micrographs. The pictures presented in the paper were produced from negatives scanned at 600 dpi. 2.3. Raman spectroscopy Raman spectra were recorded on a Jobin Yvon S3000 spectrometer equipped with a LN-cooled charged coupled device (CCD). A long-working distance microscope objective (50·) of Olympus 45 microscope was used for both to focus the laser beam to a spot 2 lm in diameter on the sample surface and to collect the scattered light. The laser power density was kept below 104 W/ cm2 to prevent a substantial overheating of the sample at the laser spot. 2.4. Mechanical and thermal load fixtures We loaded the nanocomposite samples onto a homemade four-point bending fixture similar to that described in Ref. [15]. The geometry of the four-point bending supports can be reconfigured in a way that allows measurements of the same sample under either tensile or compressive loads. The corresponding strain in the sample was measured by strain gauges attached close to the measurement spot. It has been shown that the surface strain measured by the strain gauge deviates from the average strain within the penetration depth of the laser beam in the composite by less than 1/1000 part of it [4]. For thermal stress measurements the samples were placed in a liquid helium optical cryostat used to vary their temperature in the range 4.5–320 K. The carbon vibrations frequency of the plain ODA-functionalized SWCNTs was used as a reference from which we measured the frequency change in composites due to stress transfer. The C–C stretching frequency in SWCNTs has intrinsic temperature dependence that has been accounted for in this work.
3. Results In Figs. 1 and 2 we display selected images from the TEM examination of specimens cut from the ODASWCNT nanocomposite. Fig. 1 shows a TEM image of ODA-functionalized nanotubes embedded in the epoxy matrix. From this image alone, it is not clear whether the observed tubules are individual SWCNTs surrounded by the physisorbed ODA molecules or SWCNT bundles. The TEM image in Fig. 2, however, evidences for formation of a distinctive interface region between the nanotube and epoxy matrix that likely contains physisorbed ODA molecules. Further on we call this region the ODA-shell. The straight nanotube or thin bundle in Fig. 2 is apparently pulled-out from the epoxy matrix. The ODA functional groups are removed from
Fig. 1. TEM image of ODA-functionalized SWCNTs embedded in the epoxy matrix of 0.5% ODA-SWCNT/EP nanocomposite. The arrows indicate well separated nanotubes or bundles.
Fig. 2. A straight ODA-SWCNT or a thin bundle pulled-out from the epoxy matrix. The thickness of the nanotube/bundle surrounding shell is 2 nm.
one of the nanotubeÕs ends, revealing a thickness of 2 nm of the ODA-shell. A careful examination of the TEM images recorded in the present study shows that the ODA-SWCNTs embedded in the epoxy matrix appeared to have bent shapes with straight segments 35– 125 nm long. Next, we present the results from Raman spectroscopy measurements of the nanocomposites. In Fig. 3 we compare the Raman spectra of 0.5% ODASWCNT/ EP nanocomposite recorded at zero applied load (1), at applied compressive load that results in
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250 (2)
G
-
(4)
0.5
(3) (1)
0.0 1530
1560 1590 1620 Raman Shift (cm-1)
Fig. 3. Raman spectra of 0.5% ODA-SWCNT/EP excited with 514.5 nm laser line and measured at (1) zero applied load; (2) loaded to average strain of 0.35% and measured with incident/scattered light polarization along the load direction; (3) under the same load with light polarization perpendicular to the load direction; (4) under tensile load that introduced 0.4% strain in the composite. The inset displays the radial breathing modes (RBM) at zero applied load. The RBM frequency is given in cm1.
0.35% average strain in the composite for two directions of the incident/scattered light polarization: (2) along and (3) perpendicular to the load direction, and under tensile load that introduces 0.4% strain in the composite (4). It is clearly seen that the compressive strain causes an upward shift of the xGþ frequency only in those nanotubes that have axes along the load direction. The G+band frequency of Raman spectrum (3) in Fig. 3 remains almost unchanged. These observations are similar to those reported in Ref. [4] for non-functionalized SWCNT/EP composites. Note also that the linewidth of the 1590 cm1 mode broadens by 10% in both (2) and (3) spectra, which can be attributed to inhomogeneous broadening. Indeed, for a given incident light polarization the laser line excites nanotubes directed at different angles to the light polarization and applied load. The frequency shift of the corresponding Raman lines is different and they contribute to the overall spectrum with Raman intensity weighted according to the IS = I0 cos4h dependence. This effect should give an apparent broadening of the measured Raman line. The inset in Fig. 3 shows the Raman spectrum of the radial breathing modes (RBM) of the nanotubes in the ODA-SWCNT/EP nanocomposite. The excited RBM contribute to a single Raman peak that is centered at 189.3 cm1. Therefore, the 514.5 nm laser line used in this experiment excites the nanotubes with narrow diameter distribution, which have RBM frequencies close to 189.3 cm1. The (RBM) frequency xRBM of a given nanotube in a bundle depends on the nanotube diameter dt as xRBM (cm1) = 223.5 (cm1)/dt (nm) + 12.5 cm1 [16]. From the expression for xRBM we calculate that
0.30 0.15
+
200
0.00
+
Intensity ( arb.units)
150
1.0
the peak at 189.3 cm1 stems from nanotubes with diameters close to 1.26 nm. Thus determined average diameter of the nanotubes present and excited at this wavelength is also very close to that derived from xG ¼ xGþ 32:6 ðcm1 Þ=d 1:4 [17] with x G ¼ t 1 1 1568:5 cm and xGþ ¼ 1592:1 cm taken from Fig. 3, spectrum (1). It is well established that the 514.5 nm laser line excites only the semiconducting SWCNTs with diameters around 1.26 nm [18]. Therefore, in the present study we monitor by Raman spectroscopy exclusively the semiconducting ODA-SWCNTs in the nanocomposite. Fig. 4 presents the relative change of xGþ in ODASWCNT/EP composites under tensile and compressive load, by using the same specimen with different positioning of the supports, as shown in the sketches therein, to induce compressive or tensile stresses on the upper surface by the application of the same external load. The relative change of the G+ vibration frequency DxGþ =xGþ is proportional to the axial strain on the nanotube [11] and therefore Fig. 4 displays strain transfer from the matrix to the nanotubes at various external loads. The most striking feature in Fig. 4 is the asymmetry of the loading curves in compression and tension. Under increasing compression the strain in ODA-SWCNT/ EP composite is transferred non-monotonically (full circles), which is in contrast to the loading curve for nonfunctionalized SWCNT/EP composite presented in the same figure by the thick grey line. There are at least two intervals in which the strain transfer rate decreases to zero. They correspond to the plateau regions of the curve where further increase of the surface strain causes no change in the carbon vibrations frequency. The loading curve upon release of the load (empty circles) shows small hysteresis. The tensile loading curves are almost straight with practically no hysteresis.
∆ωG /ωG (%)
G
1.5
+
131
-0.15 -0.30
-0.4
-0.2 0.0 0.2 0.4 Surface Strain (%)
Fig. 4. Relative change of xGþ in ODA-SWCNT/EP composites under increasing (full circles) and decreasing (empty circles) tensile and compressive loads. The grey thick curve presents the compressive loading of non-functionalized SWCNT/EP composite. The thickness of the grey line is equal to the accuracy of DxGþ =xGþ measurements [11]. All the lines that connect the experimental points are guided to the eye. The configuration of the sample supports and the microscope objective used for focusing the laser beam is sketched in the figure.
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In view of the observed behavior of the ODASWCNTs under compression it is instructive to study their vibrational frequency shift upon lowering temperature of the nanocomposite sample. Cooling the nanocomposite leads to a shrinkage of the epoxy matrix and the corresponding strain in the matrix is transferred to the nanotubes. The driving force behind this process is the thermal stress applied to the nanotubes that is due to the difference in the coefficient of thermal expansion (CTE) Da = am ant 65 · 106 K1 of the matrix am [19] and the nanotubes ant [20]. The difference between the cases of applied uniaxial load shown in Fig. 4 and that upon cooling is that in the latter the matrix shrinks in all directions. The results of the thermal strain transfer in ODA-SWCNT/EP are shown in Fig. 5. The measured frequency shift at given temperature is related to the corresponding thermal strain in the EP matrix through = DaDT, where DT is the deviation of the temperature from room temperature. Expectedly, the shrinking matrix facilitates the strain transfer to overcome the first plateau at 0.15% surface strain in Fig. 4. At 0.36% thermal strain (260 K), the monotonic increase of the load transfer in ODA-SWCNT/EP with lowering temperature is interrupted and the loading curve passes through a well defined minimum at 0.5% thermal strain. Further increase of the compressive stress beyond that achieved in the uniaxial loading experiment activates again the strain transfer process. The loading curve of the ODA-SWNTs/EP nanocomposite deviates strongly from that of non-functionalized SWCNT/EP nanocomposite given in Fig. 5 with the thick grey line, in particular for thermal strains larger than 0.4%. Releasing the compressive load upon increasing temperature of the sample leads to strong hysteresis in the thermal load cycle, whereas no discernible
4. Discussion Now we discuss the processes behind the observed behavior of the ODA-SWCNT/epoxy composite under compressive loads. The predominant sidewall interaction between unpolar to slightly polar non-functionalized SWCNTs and the epoxy matrix is van der Waals interaction except for the possible sparse covalent bonding at the defect sites on oxidized carbon nanotubes. Typically, epoxy materials easily wet micron-size carbon fibers [21], which implies strong van der Waals attraction between the epoxy matrix and the carbon fibers. We anticipate similar attraction strength between the non-functionalized SWCNTs and epoxy. As mentioned above, the ODA functionalization of SWCNTs involves oxidation of the nanotubes by acid treatment followed by amination of the SWCNT-COOH
0.2
0.30 0.15
+
0.0
∆ωG /ωG (%)
∆ωG+/ωG+ (%)
0.4
hysteresis is observed in the non-functionalized SWCNT/EP sample (load release curve is not shown). The thermal load curve of the ODA-SWCNT/EP sample shown in Fig. 5 suggests that debonding of the ODA-SWCNTs in the nanocomposites might take place under high thermal loads. To check this possibility we measured the ODA-SWCNT/EP sample under compressive and tensile loads after the thermal load cycle. The loading curve obtained in this measurement is presented in Fig. 6 with crossed circles. It differs drastically from the one measured before the thermal load cycle (full circles). The carbon vibrations frequency of ODA-SWCNTs in the thermally cycled sample gives no indication for load transfer under loads that result in 0.1% to 0.3% strain in the nanocomposite. The sample also exhibits lower strain transfer at the maximum load applied than in the measurements before the cycle. We find in this behavior a clear indication for nanotubes debonding caused by the thermal load applied to the nanocomposite.
-0.6
-0.4
-0.2
0.0
Thermal Strain (%) Fig. 5. Thermal strain transfer in 0.5% ODA-SWCNT/EP under uploading (full circles) and releasing load (empty circles). The lines that connect the data points are guided to the eye. Temperature is related to the corresponding thermal strain in the EP matrix through = DaDT, where Da is the difference in the coefficient of thermal expansion of the matrix and SWCNTs and DT is the deviation of the temperature from room temperature. The uploading curve of non-functionalized SWCNT/EP nanocomposite is given for comparison (thick grey line). As in Fig. 1, the thickness of the grey line is equal to the accuracy of DxGþ =xGþ measurements.
0.00
+
-0.8
-0.15 -0.30
-0.4
-0.2
0.0
0.2
0.4
Surface Strain (%) Fig. 6. DxGþ =xGþ of ODA-SWCNT/EP composites (crossed circles) under tensile and compressive loads measured after the thermal load cycle displayed in Fig. 4. The loading curve of the same sample before the thermal cycle is also given (full circles) for comparison. The lines through the data points are guided to the eye.
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groups at the defect sites. As a result of the functionalization the ODA-SWCNTs lack the ability to covalently bond to the epoxy matrix. Instead, the relatively long ODA alkyl chains attached to the defect sites on the nanotubes are likely to keep the nanotube sidewall at a distance from the epoxy matrix thus weakening the van der Waals interaction. The ODA molecules adsorbed along the SWCNTs sidewalls further weaken the interaction between SWCNT sidewalls and epoxy matrix. Therefore, the overall effect of the ODA functional groups on the embedded in epoxy ODA-SWCNTs is that the nanotubes are separated from the epoxy matrix by a shell 2 nm thick (see, e.g., Fig. 2), we call it the ODAshell, which makes van der Waals attraction between the nanotubes and the epoxy matrix vanishingly small. We have found a discernible shell also in images of the nanotubes embedded in the epoxy matrix. A closeup of such image is shown in Fig. 7. Note that the thin bundle seen in Fig. 7 is embedded in an epoxy channel with a diameter three times larger than that of the nanotubes bundle. Bundle buckling and points of contacts of the bundle and the matrix are also seen in the image. Importantly, although the TEM-micrograph displayed in Fig. 7 presents ODA-SWCNTs in epoxy that might be buckled as a result of microtome cutting [22], it clearly shows a gap of 2–3 nm between the bundle and the epoxy matrix. Therefore, in the ODA-SWCNT/EP composite the thin bundles or individual nanotubes are strongly coupled to the matrix only at the points of mechanical interlocking, possibly reinforced by the zwitterion alkylamine chains, whereas the sidewall interactions are expected to be weak. Under weak unidirectional load, the strain transfer of up to 0.15% is close to the maximum estimated in Ref. [11]. Further increase of the load results in lack of strain transfer rate until 0.25% average strain in the nanocomposite is achieved. We suggest that for this range
133
of average strains in the nanocomposite, the nanotubes along the load direction undergo a buckling that is greatly facilitated by the weak interactions in the lateral directions. This interpretation is also supported by the lack of a plateau in the loading curve under tensile load given in Fig. 4. In the thermal load experiment, the matrix shrinks in all directions upon decreasing temperature and provides enough lateral support that prevents the first buckling. At higher thermal strains in the nanocomposite, partial debonding seems to deteriorate some of the load transfer modes most likely those associated with the ODA groups. The physisorbed ODA molecules along the sidewalls are expected to be highly mobile on the nanotubeÕs surface. Under certain high loads they may scramble and this effect could be seen as debonding. In addition, the coupling through zwitterions can be destroyed under compressive thermal loads. Releasing the stresses in the matrix leads to almost monotonic decrease in the strain on the ODA-SWCNTs consistently with the suggested interpretation of the experimental data under compressive loads. It is important to note that in these experiments we measured the Raman spectra at the same spot on the sample, with deviations of the laser spot position less than 0.5 lm. Measurements at other spots on the sample have given similar results but the coherence of the data in Figs. 4–6 is mostly due to the ‘‘same spot’’ measurements. Motivated by the chemistry of functionalization and the interactions between the SWCNT, functional moieties, and the polymer, a structural mechanics model for a limited load transfer is suggested assuming a buckling instability. In this simplified buckling model the SWCNTs or the SWCNT bundles are represented as laterally supported beams on an elastic foundation as shown in Fig. 8. Following the analysis given in Refs. [23,24], the critical stress for buckling of a nanotube on an elastic foundation with the modulus k can be written as p2 EI kl4 2 rcr ¼ m þ 2 4 ; ð1Þ m p EI Al2 where m denotes the number of half waves along the buckled nanotube, E is the YoungÕs modulus of the nanotube, l is the length of the nanotube under axial
Fig. 7. TEM image close-up of a ODA-SWCNT bundle embedded in epoxy matrix.
Fig. 8. Buckling of a SWCNT supported laterally by octadecylamineepoxy matrix.
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stress, I is the area moment of inertia, and A is the nanotube cross-sectional area. For a bundle of nanotubes, E, I, and A are generally different from those of the comprising nanotubes. In the absence of elastic foundation, the critical stress for buckling reduces to the EulerÕs buckling stress rcr = p2EI/Al2 [23]. It is worth noting that the number of half waves to which a given nanotube can be buckled under the critical stress is determined only by the value of kl4/p4EI [23,24]. This is summarized in Table 1. For particular combinations of values of k, l, E and I, as for instance kl4/p4EI = 4, the critical stresses for m = 1 and m = 2 are the same and an instability towards a transition from one to two-half waves buckling may occur. More generally, a transition from n to (n + 1)-half waves may take place at kl4/p4EI = n2(n + 1)2. Now we calculate k for the ODA-SWCNTs and bundles embedded in the epoxy matrix. Given the relation between the relative frequency shift of the tangential G+ mode and axial nanotube strain z [11], DxGþ =xGþ ¼ 1:04z , one obtains that the first plateau in Fig. 4, assigned to buckling of ODA-SWCNTs in the epoxy matrix, occurs at the axial stress of 1.08 GPa, provided the YoungÕs modulus of the nanotubes is 1 TPa. To estimate k from Eq. (1) one also needs the dimensions of the embedded nanotubes or bundles. As discussed in Section 2, the average diameter of the ODA-SWCNTs monitored by Raman spectroscopy during the loading experiments is 1.26 nm. On the other hand, the TEM images in Figs. 3 and 7 reveal thin bundles with diameter 3 nm, which is close to that of a four-nanotubes bundle [25]. The well pronounced plateaus in the loading curve in compression shown in Fig. 4 indicate for a predominant length of the straight nanotube segments in the ODA-SWCNT nanocomposite. Indeed, the segments length distribution determined from the TEM images was found to spread from 35 to 125 nm, having a notable peak at 75 nm. Further, we take into account that the SWCNT is a hollow cylinder with finite wall thickness h and radius r. Using Eq. (1), we calculate k = 0.36 MPa [26] for the ODA-shell that surrounds the individual SWCNTs with r = 0.63 nm, h = 0.066 nm [27] and the average segment length l = 75 nm buckled under stress rcr = 1.08 GPa. We also obtain k = 0.14 MPa [28] for the ODA-shell surrounding the nanotube bundles with r = 1.5 nm and l = 75 nm. Here m = 1 is chosen, since kl4/p4EI < 4 for both cases. The lower value of k for the nanotube bundles than that for isolated nanotubes could be attributed to the difference in their aspect ratio Table 1 The number of half waves m for different values of kl4/p4EI kl4/p4EI
04
4 36
(n 1)2n2 n2(n + 1)2
m
1
2
n
d, and the area moment of inertia I as follows from the model of k given in Ref. [29] or to the different surface topography of the bundles and the nanotubes. It is instructive one to estimate the equivalent effective YoungÕs modulus for the ODA-epoxy surrounding the SWCNTs, which is assumed to be isotropic. For this purpose we use the model of Lanir and Fung [29], which suggests the following relationship between the foundation modulus k and the elastic properties of an isotropic matrix: k¼
8pEm ð1 mm Þ=ð1 þ mm Þ ; ð3 4mm ÞK 0 ½mpd þ mpd=2K 1 ½mpd
ð2Þ
where Em and mm are the YoungÕs modulus and PoissonÕs ratio of the matrix, respectively, d is the ratio of the radius to the length of the column, m is the number of half waves, and both K0 and K1 are the modified Bessel functions of the second kind. Using Eq. (2), mm = 0.35 is taken equal to that of the epoxy matrix [30], and k calculated above, we obtain Em = 0.19 MPa for the ODA-epoxy that surrounds the individual nanotube and Em = 0.07 MPa for the surrounding of the nanotube bundles. These effective moduli are much lower than the YoungÕs modulus of the epoxy 2.72 GPa [14], which suggests that the ODA-shell provides very weak lateral support. Next, we analyze the second plateau in the loading curve in Fig. 4. As discussed above, once a buckling with given mode m occurs further increase of the applied stress leads to no transition to another buckling mode for the same l. Therefore, the second plateau in Fig. 4 has to be treated as a result of m = 1 buckling of the linear segments l/2 created from the buckling responsible for the first plateau. Using Eq. (1) and the k obtained from the first plateau, we estimate a critical buckling stress 1.58 GPa for a ODA-SWCNT with l/2 = 37.5 nm. On the other hand, form the experimental results shown in Fig. 4 we find that the second plateau corresponds to 1.88 GPa stress on the nanotubes, a value close to the estimated one from Eq. (1). From these estimates we conclude that the second plateau in Fig. 4 could be due to the buckling of the SWCNTs, which have been bent and are in contact with the polymer after initial loading (the first plateau). It is interesting to analyze whether the local minimum in the thermal loading curve for the ODA-SWCNT/EP nanocomposite shown in Fig. 5 and attributed to debonding processes is also associated with the nanotube buckling. From Fig. 5 we find that the turning point in the loading curve for the ODA-SWCNT/EP nanocomposite is at 2.88 GPa stress on the nanotubes. Assuming that the critical stress of buckling of ODASWCNT in the shrinking epoxy matrix is 2.88 GPa we obtain from Eq. (1) k = 1.18 MPa, a reasonable value for k that reflects an improvement of the coupling of the nanotubes to the shrunk matrix. This estimate also
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indicates that the debonding process of ODA-SWCNT in epoxy under the thermal loading might be initiated by buckling. In conclusion, the model analysis presented here fully supports the interpretation of compressive loading curves for the ODA-SWCNT/EP nanocomposites shown in Figs. 4 and 5 as due to buckling of the nanotubes at relatively low critical stresses. In a follow-up modeling it will be interesting to analyze the experimental results presented here within more realistic models [31,32] that account for microbuckling and kinking phenomena, an indication for which is seen in Fig. 7. 5. Conclusions In summary, we have presented a study of interfacial and mechanical properties of ODA-SWCNT/EP nanocomposites using both experimental (Raman spectroscopy and TEM) and theoretical approaches. The observed differences in loading of the non-functionalized and ODA-functionalized SWCNT/EP nanocomposites are attributed to the interface modification in ODASWCNT/EP nanocomposites. We have given evidence that the observed two plateaus in the strain transfer in ODA-SWCNT/EP under compression are due to buckling of the nanotubes facilitated by the very weak sidewall nanotube–epoxy interactions. Thermal loads created upon cooling the sample below 260 K lead to debonding of the nanotubes that is likely initiated by nanotubeÕs buckling. Finally, we want to emphasis the uniqueness of the combined Raman and TEM experiment because the standard mechanical stress measurements hardly could detect this peculiar behavior of tiny amount of ODA-SWCNTs under compression. Acknowledgments We thank W. Holmes for helping us with the nanocomposites preparation. This work was supported in part by the state of Texas through the Texas Center for Superconductivity and Advanced Materials, the Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles, funded by NASA Cooperative Agreement No. NCC-1-02038, and the Institute of Space Systems Operations (ISSO) at the University of Houston. References [1] Hamon MA, Chen J, Hu H, Chen Y, Itkis ME, Rao AM, et al. Dissolution of single-walled carbon nanotubes. Adv Mater 1999;11(10):834–40. [2] Chattopadhyay D, Galeska L, Papadimitrakopoulos F. A route for bulk separation of semiconducting from metallic single-wall carbon nanotubes. J Am Chem Soc 2003;125(11):3370–5.
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[3] Arepalli S, Nikolaev P, Gorelik O, Hadjiev VG, Bradlev HA, Holmes W, et al. Protocol for the characterization of single-wall carbon nanotube material quality. Carbon 2004;42(8–9):1783–91. [4] Hadjiev VG, Iliev MN, Arepalli S, Nikolaev P, Files BS. Raman scattering test of single-wall carbon nanotube composites. Appl Phys Lett 2001;78(21):3193–5. [5] Lourie O, Wagner HD. Evaluation of YoungÕs modulus of carbon nanotubes by micro-Raman spectroscopy. J Mater Res 1998;13(9):2418–22. [6] Lourie O, Cox DM, Wagner HD. Buckling and collapse of embedded carbon nanotubes. Phys Rev Lett 1998;81(8):1638–41. [7] Reich S, Jantoljak H, Thomsen C. Shear strain in carbon nanotubes under hydrostatic pressure. Phys Rev B 2000; 61(20):R13389–92. [8] Dubay O, Kresse G, Kuzmany H. Phonon softening in metallic nanotubes by a Peierls-like mechanism. Phys Rev Lett 2002; 88(23):235506-1-4. [9] Jorio A, Souza AG, Dresselhaus G, Dresselhaus MS, Swan ¨ nlu¨ MS, et al. G-band resonant Raman study of 62 AK, U isolated single-wall carbon nanotubes. Phys Rev B 2002;65(15): 155412. [10] Gommans HH, Alldredge JW, Tashiro H, Park J, Magnuson J, Rinzler AG. Fibers of aligned single-walled carbon nanotubes: polarized Raman spectroscopy. J Appl Phys 2000;88(5):2509–14. [11] Under reasonable approximation [4], the relative change in the SWCNT tangential mode frequency xGþ at 1590 cm1 is given by DxGþ =xGþ ¼ cð1 mt Þz , where z is the axial strain of the nanotube, c = 1.24 being the Gru¨neisen parameter and mt = 0.16 is the nanotubes Poisson ratio. In our experiment the typical maximum deviation in the fit position of the 1590 cm1 line within 10 consecutive measurements was 0.2 cm1. Given this experimental accuracy we find that the minimum DxGþ =xGþ we are able to resolve is 0.013%, which corresponds to 0.012% strain on the nanotube. [12] Arepalli S, Holmes WA, Nikolaev P, Hadjiev VG, Scott CD. A parametric study of single-wall carbon nanotube growth by laser ablation. J Nanosci Nanotechnol 2004;4(7):762–73. [13] Chiang IW, Brinson BE, Smalley RE, Margrave JL, Hauge RH. Purification and characterization of single-wall carbon nanotubes. J Phys Chem B 2001;105(6):1157–61. [14] Product Bulletin SC:1183-02, EPIKOTETM Resin 862/EPIKURETM Curing Agent W, Resolution Performance Products LLC, P.O. Box 4500 Houston, TX 77210-4500. [15] Young RJ, Thongpin C, Stanford JL, Lovell PA. Fragmentation analysis of glass fibres in model composites through the use of Raman spectroscopy. Composites A 2001;32(2):253–69. [16] Bachilo SM, Strano MS, Kittrell C, Hauge RH, Smalley RE, Weisman RB. Structure-assigned optical spectra of single-walled carbon nanotubes. Science 2002;298(5602):2361–6. [17] Jorio A, Pimenta MA, Souza AG, Samsonidze GG, Swan AK, ¨ nlu¨ MS, et al. Resonance Raman spectra of carbon nanotubes U by cross-polarized light. Phys Rev Lett 2003;90(10):107403. [18] Kataura H, Kumazawa Y, Maniwa Y, Umezu I, Suzuki S, Ohtsuka Y, et al. Optical properties of single-wall carbon nanotubes. Synth Met 1999;103(1–3):2555–8. [19] Mark JE, editor. Polymer data handbook. New York: Oxford University Press; 1999. [20] Maniwa Y, Fujiwara R, Kira H, Tou H, Kataura H, Suzuki S, et al. Thermal expansion of single-walled carbon nanotube (SWNT) bundles: X-ray diffraction studies. Phys Rev B 2001;64(24):241402. [21] Wagner HD. Spreading of liquid droplets on cylindrical surfaces accurate determination of contact angle. J Appl Phys 1990;67(3):1352–5. [22] Thostenson ET, Chou TW. On the elastic properties of carbon nanotube-based composites: modelling and characterization. J Phys D 2003;36(5):573–82.
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[23] Timoshenko S. Theory of elastic stability. New York: McGrawHill; 1936. [24] Chen W-F, Atsuta T. Theory of beam columns. New York: McGraw-Hill; 1976. [25] The number N of SWCNTs in a bundle is related to the number Nc of the nanotubes across the bundle diameter D as N ¼ ð3N 2c þ 2N c Þ=4, provided Nc is even, and it is the closest integer to D (nm)/1.7 (nm). [33] For a bundle diameter D 3 nm, N = 4. [26] For a hollow SWCNT cylinder with the outer radius r and the wall thickness h, the cross-sectional area and the area moment of inertia are Ant = p{r2(r h)2} and Int = p/4{r4 (r h)4}, respectively. [27] Yakobson BI, Brabec CJ, Bernholc J. Nanomechanics of carbon tubes: instabilities beyond linear response. Phys Rev Lett 1996;76(14):2511–4.
[28] The area moment of inertia of a four-nanotubes bundle is derived from that of a individual nanotube by applying the parallel axis theorem, I4nt = 4(Int + r2Ant). The cross-sectional area of the bundle is A4nt = 4Ant. [29] Lanir Y, Fung FCB. Fiber composite columns under compression. J Comp Mater 1972;6:387–401. [30] Kaw AK, Willenbring G. A software tool for mechanics of composite materials. Int J Eng Ed 1997;13(6):433–41. [31] Lagoudas DC, Tadjbakhsh I, Fares N. A new approach to microbuckling of fibrous composites. J Appl Mech 1991;58(2):473–9. [32] Lagoudas DC, Saleh AM. Compressive failure due to kinking of fibrous composites. J Comp Mater 1993;27(1):83–106. [33] Saito R, Dresselhaus G, Dresselhaus MS. Physical properties of carbon nanotubes. London: Imperial College Press; 1998.
Buckling instabilities of octadecylamine functionalized carbon nanotubes embedded in epoxy V.G. Hadjiev
a,*
, D.C. Lagoudas b, E-S. Oh b, P. Thakre b, D. Davis b, B.S. Files c, L. Yowell c, S. Arepalli c, J.L. Bahr d, J.M. Tour d
a
d
Texas Center for Superconductivity and Advanced Materials, University of Houston, 202 Science Center, Houston, TX 77204, USA b Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA c NASA-Johnson Space Center, 2101 NASA Road One, Houston, TX 77058, USA Department of Chemistry, Department of Chemical Engineering and Material Science, and Center for Nanoscale Science and Technology, Rice University, MS222, Houston, TX 77005, USA Received 7 October 2004; accepted 18 January 2005 Available online 13 September 2005
Abstract We demonstrate effects of nanotubes buckling and debonding in octadecylamine (ODA) derivatized single wall carbon nanotubes (SWCNT)/epoxy nanocomposites under mechanical and thermal loads uniquely detected by means of Raman spectroscopy and documented by TEM imaging. It is shown that ODA functionalization of SWCNTs provides weak sidewall interactions between the nanotubes and epoxy matrix, which make axially compressed ODA-SWCNTs susceptible to buckling. The feasibility of ODA-SWCNTs buckling in epoxy matrix is also supported by the structural mechanics calculations. 2005 Elsevier Ltd. All rights reserved. Keywords: Polymer-matrix composites (PMCs); Fibre/matrix bond; Buckling; Raman spectroscopy; TEM
1. Introduction Recent studies of single wall carbon nanotubes (SWCNTs) functionalized by direct reaction with octadecylamine (ODA, H2N–C18H37) have shown stable dispersion of thus derivatized nanotubes in the organic solvents that are commonly used for preparation of SWCNT/epoxy (EP) nanocomposites [1,2]. Importantly, in one case, ODA functionalized only the semiconducting nanotubes and this selectivity was used successfully for bulk separation of semiconducting from metallic SWCNTs [2]. Part of the ODA molecules forms zwitterion groups SWCNT-COO H3N–C18H37 [1] (ionic bonding) at the defect sites. The other part of ODA is *
Corresponding author. Tel.: +1 713 743 8442; fax: +1 713 743 8201. E-mail address: [email protected] (V.G. Hadjiev). 0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.01.004
physisorbed along the SWCNT sidewalls (van der Waals attraction) [2], and facilitates to large extent the solubility of the ODA-functionalized nanotubes in organic solvents. Given the complex surface modification of the ODA functionalized nanotubes, the next natural step is one to study the interfacial and mechanical properties of ODASWCNTs embedded in polymer matrix, i.e., of the corresponding nanocomposite. In the ODA-SWCNT/EP nanocomposites, the attached ODA functional groups and physisorbed molecules on the SWCNT surface are expected to modify strongly the nanotube–epoxy interface region and thereby to change the adhesion between the nanotubes and the epoxy matrix. It has been firmly realized that the nanotubes used for preparation of nanocomposites with controlled properties have to be purified [3]. The standard purification procedures, based on acid reflux, oxidize the nanotubes
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through attachment of carboxyl (–COOH) groups at the defect sites and nanotubeÕs ends. It is well established that oxidized SWCNTs and the epoxy matrix interact with each other through two major mechanisms. These are van der Waals nanotube sidewall–epoxy interaction and the covalent bonding created by reaction of the carboxyl groups on the nanotube and the epoxy group in the matrix. The functionalization of oxidized SWCNTs with octadecylamine (ODA) substitutes the carboxyl groups for alkylamine ones and hence it is expected to modify the interface interactions in the epoxy nanocomposites. In addition, the physisorbed ODA on the nanotubeÕs sidewall may play the role of a surfactant that also change the sidewall–epoxy interaction. Among the experimental techniques used for studying of the SWCNTs nanocomposites, Raman spectroscopy has proven to be an efficient tool for probing the interfacial properties of SWCNT/EP nanocomposites. It has been shown that Raman spectroscopy can monitor the load transfer from the epoxy matrix to the nanotubes with applied mechanical [4] or thermal [5] loads. On the other hand, a complementary transmission electron macroscopy (TEM) study of the nanocomposites could reveal important information about the size of SWCNTs therein and residual distortion that may appear after loading of the nanocomposite [6]. In the present study, we utilize both experimental approaches. Loads applied on the SWCNTs result in strain of the nanotubes that can be detected as a change of the carbon vibrations frequency. The carbon vibrations that involve C–C bond-stretching motions with eigenvectors being tangential to the nanotube surface are particularly sensitive to the nanotube strain [7]. The highest frequency tangential carbon vibrations in SWCNTs give rise to a graphite-like G-band around 1500–1590 cm1 in the Raman spectra. The G-band usually exhibits a doublet structure with higher frequency component G+ corresponding to the longitudinal carbon vibrations, that is, those along the nanotube axis [8,9]. The second band in the doublet, denoted as G, involves transversal carbon vibrations. The G+-band vibrations have been studied in detail and the correspondence between the change of the vibration frequency and strain on the SWCNT is established [4,7]. SWCNTs in the nanocomposite act as unidirectional strain sensors that can be read when the incident light polarization has a component along the nanotube axis [4]. The Raman intensity of the carbon vibrations in a SWCNT, measured for parallel incident ð~ eI Þ and scattered ð~ eS Þ light polarizations, varies as IS = I0 cos4h with the angle h between the polarization vectors ~ eI k~ eS and the nanotube axis [10]. The Raman scattering technique provides sensitivity capable of detecting strain changes on SWCNTs with 0.012% resolution, thus making it suitable for certain low load measurements [11].
129
In this paper, we present a study of load transfer through the complex interface in ODA functionalized SWCNT/EP nanocomposites.
2. Experimental 2.1. Sample preparation SWCNTs produced by laser ablation technique [12] were purified following the procedure described in Ref. [13]. Functionalization was performed in two steps. Firstly, the purified SWCNTs were slurred in concentrated H2SO4, 30% H2O2 was added, and the mixture was stirred at 70 C for 20 min. The slurry was poured in cold water, filtered, washed extensively, and dried under vacuum. Functionalization with ODA took place in the second step, when thus treated SWCNTs were mixed with ODA and heated at 110 C for 40 h. The mixture was then cooled, sonicated in EtOH (bath sonicator) for 1 h, filtered, sonicated in THF, filtered, and dried. The preparation of the ODA-SWNT/EP nanocomposite included the following steps: A suspension of ODASWCNTs in 70% acetone/30% toluene was mixed with epoxy resin EPIKOTE 862 [14]. The mixture was kept in a nitrogen purged beaker and stirred until most of the solvent was evaporated. In the next step, EPIKURE W curing agent [14] was added and the mixture stirred well. The blend was placed in a vacuum oven and kept for 2 h at 60 C before it was cast in a preheated at 60 C mold. The loaded mold was annealed at 80 C for 1/2 h in a vacuum oven. The curing cycle involved an annealing at 121 for 1 h and followed by another one at 175 for 2 h. Thus prepared composite samples had rectangular bar shape with size 50 · 10 · 2 mm3 and contained 0.5% ODA-SWCNT. Reference nanocomposite samples loaded with 0.5–1% non-functionalized nanotubes were prepared following the same nanocomposite preparation procedure. 2.2. Transmission electron microscopy Small pieces of the ODA-SWCNT/EP composite specimen were embedded in another epoxy block for stability during sectioning using microtomy. The supporting epoxy resin contained dodecenyl succinic anhydride (DDSA), LX-112 epoxy resin, araldite 502 (provided by Ladd research). The epoxy/anhydride ratio was 1.0:1.0 and benzyl dimethyl amine (BDMA) was used as the accelerator. The mixture was poured into block molds and left overnight in an oven at 60 C for curing. The polymer blocks were cut into thin (60– 90 nm) slices using a diamond knife (Diatome) on Leica UltracutE microtome. The slices were picked upon 3 mm diameter copper grids and examined using JEOL 1200 EX TEM operated at an accelerating voltage of
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100 kV. Kodak 4489 films were used to capture micrographs. The pictures presented in the paper were produced from negatives scanned at 600 dpi. 2.3. Raman spectroscopy Raman spectra were recorded on a Jobin Yvon S3000 spectrometer equipped with a LN-cooled charged coupled device (CCD). A long-working distance microscope objective (50·) of Olympus 45 microscope was used for both to focus the laser beam to a spot 2 lm in diameter on the sample surface and to collect the scattered light. The laser power density was kept below 104 W/ cm2 to prevent a substantial overheating of the sample at the laser spot. 2.4. Mechanical and thermal load fixtures We loaded the nanocomposite samples onto a homemade four-point bending fixture similar to that described in Ref. [15]. The geometry of the four-point bending supports can be reconfigured in a way that allows measurements of the same sample under either tensile or compressive loads. The corresponding strain in the sample was measured by strain gauges attached close to the measurement spot. It has been shown that the surface strain measured by the strain gauge deviates from the average strain within the penetration depth of the laser beam in the composite by less than 1/1000 part of it [4]. For thermal stress measurements the samples were placed in a liquid helium optical cryostat used to vary their temperature in the range 4.5–320 K. The carbon vibrations frequency of the plain ODA-functionalized SWCNTs was used as a reference from which we measured the frequency change in composites due to stress transfer. The C–C stretching frequency in SWCNTs has intrinsic temperature dependence that has been accounted for in this work.
3. Results In Figs. 1 and 2 we display selected images from the TEM examination of specimens cut from the ODASWCNT nanocomposite. Fig. 1 shows a TEM image of ODA-functionalized nanotubes embedded in the epoxy matrix. From this image alone, it is not clear whether the observed tubules are individual SWCNTs surrounded by the physisorbed ODA molecules or SWCNT bundles. The TEM image in Fig. 2, however, evidences for formation of a distinctive interface region between the nanotube and epoxy matrix that likely contains physisorbed ODA molecules. Further on we call this region the ODA-shell. The straight nanotube or thin bundle in Fig. 2 is apparently pulled-out from the epoxy matrix. The ODA functional groups are removed from
Fig. 1. TEM image of ODA-functionalized SWCNTs embedded in the epoxy matrix of 0.5% ODA-SWCNT/EP nanocomposite. The arrows indicate well separated nanotubes or bundles.
Fig. 2. A straight ODA-SWCNT or a thin bundle pulled-out from the epoxy matrix. The thickness of the nanotube/bundle surrounding shell is 2 nm.
one of the nanotubeÕs ends, revealing a thickness of 2 nm of the ODA-shell. A careful examination of the TEM images recorded in the present study shows that the ODA-SWCNTs embedded in the epoxy matrix appeared to have bent shapes with straight segments 35– 125 nm long. Next, we present the results from Raman spectroscopy measurements of the nanocomposites. In Fig. 3 we compare the Raman spectra of 0.5% ODASWCNT/ EP nanocomposite recorded at zero applied load (1), at applied compressive load that results in
V.G. Hadjiev et al. / Composites Science and Technology 66 (2006) 128–136
250 (2)
G
-
(4)
0.5
(3) (1)
0.0 1530
1560 1590 1620 Raman Shift (cm-1)
Fig. 3. Raman spectra of 0.5% ODA-SWCNT/EP excited with 514.5 nm laser line and measured at (1) zero applied load; (2) loaded to average strain of 0.35% and measured with incident/scattered light polarization along the load direction; (3) under the same load with light polarization perpendicular to the load direction; (4) under tensile load that introduced 0.4% strain in the composite. The inset displays the radial breathing modes (RBM) at zero applied load. The RBM frequency is given in cm1.
0.35% average strain in the composite for two directions of the incident/scattered light polarization: (2) along and (3) perpendicular to the load direction, and under tensile load that introduces 0.4% strain in the composite (4). It is clearly seen that the compressive strain causes an upward shift of the xGþ frequency only in those nanotubes that have axes along the load direction. The G+band frequency of Raman spectrum (3) in Fig. 3 remains almost unchanged. These observations are similar to those reported in Ref. [4] for non-functionalized SWCNT/EP composites. Note also that the linewidth of the 1590 cm1 mode broadens by 10% in both (2) and (3) spectra, which can be attributed to inhomogeneous broadening. Indeed, for a given incident light polarization the laser line excites nanotubes directed at different angles to the light polarization and applied load. The frequency shift of the corresponding Raman lines is different and they contribute to the overall spectrum with Raman intensity weighted according to the IS = I0 cos4h dependence. This effect should give an apparent broadening of the measured Raman line. The inset in Fig. 3 shows the Raman spectrum of the radial breathing modes (RBM) of the nanotubes in the ODA-SWCNT/EP nanocomposite. The excited RBM contribute to a single Raman peak that is centered at 189.3 cm1. Therefore, the 514.5 nm laser line used in this experiment excites the nanotubes with narrow diameter distribution, which have RBM frequencies close to 189.3 cm1. The (RBM) frequency xRBM of a given nanotube in a bundle depends on the nanotube diameter dt as xRBM (cm1) = 223.5 (cm1)/dt (nm) + 12.5 cm1 [16]. From the expression for xRBM we calculate that
0.30 0.15
+
200
0.00
+
Intensity ( arb.units)
150
1.0
the peak at 189.3 cm1 stems from nanotubes with diameters close to 1.26 nm. Thus determined average diameter of the nanotubes present and excited at this wavelength is also very close to that derived from xG ¼ xGþ 32:6 ðcm1 Þ=d 1:4 [17] with x G ¼ t 1 1 1568:5 cm and xGþ ¼ 1592:1 cm taken from Fig. 3, spectrum (1). It is well established that the 514.5 nm laser line excites only the semiconducting SWCNTs with diameters around 1.26 nm [18]. Therefore, in the present study we monitor by Raman spectroscopy exclusively the semiconducting ODA-SWCNTs in the nanocomposite. Fig. 4 presents the relative change of xGþ in ODASWCNT/EP composites under tensile and compressive load, by using the same specimen with different positioning of the supports, as shown in the sketches therein, to induce compressive or tensile stresses on the upper surface by the application of the same external load. The relative change of the G+ vibration frequency DxGþ =xGþ is proportional to the axial strain on the nanotube [11] and therefore Fig. 4 displays strain transfer from the matrix to the nanotubes at various external loads. The most striking feature in Fig. 4 is the asymmetry of the loading curves in compression and tension. Under increasing compression the strain in ODA-SWCNT/ EP composite is transferred non-monotonically (full circles), which is in contrast to the loading curve for nonfunctionalized SWCNT/EP composite presented in the same figure by the thick grey line. There are at least two intervals in which the strain transfer rate decreases to zero. They correspond to the plateau regions of the curve where further increase of the surface strain causes no change in the carbon vibrations frequency. The loading curve upon release of the load (empty circles) shows small hysteresis. The tensile loading curves are almost straight with practically no hysteresis.
∆ωG /ωG (%)
G
1.5
+
131
-0.15 -0.30
-0.4
-0.2 0.0 0.2 0.4 Surface Strain (%)
Fig. 4. Relative change of xGþ in ODA-SWCNT/EP composites under increasing (full circles) and decreasing (empty circles) tensile and compressive loads. The grey thick curve presents the compressive loading of non-functionalized SWCNT/EP composite. The thickness of the grey line is equal to the accuracy of DxGþ =xGþ measurements [11]. All the lines that connect the experimental points are guided to the eye. The configuration of the sample supports and the microscope objective used for focusing the laser beam is sketched in the figure.
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In view of the observed behavior of the ODASWCNTs under compression it is instructive to study their vibrational frequency shift upon lowering temperature of the nanocomposite sample. Cooling the nanocomposite leads to a shrinkage of the epoxy matrix and the corresponding strain in the matrix is transferred to the nanotubes. The driving force behind this process is the thermal stress applied to the nanotubes that is due to the difference in the coefficient of thermal expansion (CTE) Da = am ant 65 · 106 K1 of the matrix am [19] and the nanotubes ant [20]. The difference between the cases of applied uniaxial load shown in Fig. 4 and that upon cooling is that in the latter the matrix shrinks in all directions. The results of the thermal strain transfer in ODA-SWCNT/EP are shown in Fig. 5. The measured frequency shift at given temperature is related to the corresponding thermal strain in the EP matrix through = DaDT, where DT is the deviation of the temperature from room temperature. Expectedly, the shrinking matrix facilitates the strain transfer to overcome the first plateau at 0.15% surface strain in Fig. 4. At 0.36% thermal strain (260 K), the monotonic increase of the load transfer in ODA-SWCNT/EP with lowering temperature is interrupted and the loading curve passes through a well defined minimum at 0.5% thermal strain. Further increase of the compressive stress beyond that achieved in the uniaxial loading experiment activates again the strain transfer process. The loading curve of the ODA-SWNTs/EP nanocomposite deviates strongly from that of non-functionalized SWCNT/EP nanocomposite given in Fig. 5 with the thick grey line, in particular for thermal strains larger than 0.4%. Releasing the compressive load upon increasing temperature of the sample leads to strong hysteresis in the thermal load cycle, whereas no discernible
4. Discussion Now we discuss the processes behind the observed behavior of the ODA-SWCNT/epoxy composite under compressive loads. The predominant sidewall interaction between unpolar to slightly polar non-functionalized SWCNTs and the epoxy matrix is van der Waals interaction except for the possible sparse covalent bonding at the defect sites on oxidized carbon nanotubes. Typically, epoxy materials easily wet micron-size carbon fibers [21], which implies strong van der Waals attraction between the epoxy matrix and the carbon fibers. We anticipate similar attraction strength between the non-functionalized SWCNTs and epoxy. As mentioned above, the ODA functionalization of SWCNTs involves oxidation of the nanotubes by acid treatment followed by amination of the SWCNT-COOH
0.2
0.30 0.15
+
0.0
∆ωG /ωG (%)
∆ωG+/ωG+ (%)
0.4
hysteresis is observed in the non-functionalized SWCNT/EP sample (load release curve is not shown). The thermal load curve of the ODA-SWCNT/EP sample shown in Fig. 5 suggests that debonding of the ODA-SWCNTs in the nanocomposites might take place under high thermal loads. To check this possibility we measured the ODA-SWCNT/EP sample under compressive and tensile loads after the thermal load cycle. The loading curve obtained in this measurement is presented in Fig. 6 with crossed circles. It differs drastically from the one measured before the thermal load cycle (full circles). The carbon vibrations frequency of ODA-SWCNTs in the thermally cycled sample gives no indication for load transfer under loads that result in 0.1% to 0.3% strain in the nanocomposite. The sample also exhibits lower strain transfer at the maximum load applied than in the measurements before the cycle. We find in this behavior a clear indication for nanotubes debonding caused by the thermal load applied to the nanocomposite.
-0.6
-0.4
-0.2
0.0
Thermal Strain (%) Fig. 5. Thermal strain transfer in 0.5% ODA-SWCNT/EP under uploading (full circles) and releasing load (empty circles). The lines that connect the data points are guided to the eye. Temperature is related to the corresponding thermal strain in the EP matrix through = DaDT, where Da is the difference in the coefficient of thermal expansion of the matrix and SWCNTs and DT is the deviation of the temperature from room temperature. The uploading curve of non-functionalized SWCNT/EP nanocomposite is given for comparison (thick grey line). As in Fig. 1, the thickness of the grey line is equal to the accuracy of DxGþ =xGþ measurements.
0.00
+
-0.8
-0.15 -0.30
-0.4
-0.2
0.0
0.2
0.4
Surface Strain (%) Fig. 6. DxGþ =xGþ of ODA-SWCNT/EP composites (crossed circles) under tensile and compressive loads measured after the thermal load cycle displayed in Fig. 4. The loading curve of the same sample before the thermal cycle is also given (full circles) for comparison. The lines through the data points are guided to the eye.
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groups at the defect sites. As a result of the functionalization the ODA-SWCNTs lack the ability to covalently bond to the epoxy matrix. Instead, the relatively long ODA alkyl chains attached to the defect sites on the nanotubes are likely to keep the nanotube sidewall at a distance from the epoxy matrix thus weakening the van der Waals interaction. The ODA molecules adsorbed along the SWCNTs sidewalls further weaken the interaction between SWCNT sidewalls and epoxy matrix. Therefore, the overall effect of the ODA functional groups on the embedded in epoxy ODA-SWCNTs is that the nanotubes are separated from the epoxy matrix by a shell 2 nm thick (see, e.g., Fig. 2), we call it the ODAshell, which makes van der Waals attraction between the nanotubes and the epoxy matrix vanishingly small. We have found a discernible shell also in images of the nanotubes embedded in the epoxy matrix. A closeup of such image is shown in Fig. 7. Note that the thin bundle seen in Fig. 7 is embedded in an epoxy channel with a diameter three times larger than that of the nanotubes bundle. Bundle buckling and points of contacts of the bundle and the matrix are also seen in the image. Importantly, although the TEM-micrograph displayed in Fig. 7 presents ODA-SWCNTs in epoxy that might be buckled as a result of microtome cutting [22], it clearly shows a gap of 2–3 nm between the bundle and the epoxy matrix. Therefore, in the ODA-SWCNT/EP composite the thin bundles or individual nanotubes are strongly coupled to the matrix only at the points of mechanical interlocking, possibly reinforced by the zwitterion alkylamine chains, whereas the sidewall interactions are expected to be weak. Under weak unidirectional load, the strain transfer of up to 0.15% is close to the maximum estimated in Ref. [11]. Further increase of the load results in lack of strain transfer rate until 0.25% average strain in the nanocomposite is achieved. We suggest that for this range
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of average strains in the nanocomposite, the nanotubes along the load direction undergo a buckling that is greatly facilitated by the weak interactions in the lateral directions. This interpretation is also supported by the lack of a plateau in the loading curve under tensile load given in Fig. 4. In the thermal load experiment, the matrix shrinks in all directions upon decreasing temperature and provides enough lateral support that prevents the first buckling. At higher thermal strains in the nanocomposite, partial debonding seems to deteriorate some of the load transfer modes most likely those associated with the ODA groups. The physisorbed ODA molecules along the sidewalls are expected to be highly mobile on the nanotubeÕs surface. Under certain high loads they may scramble and this effect could be seen as debonding. In addition, the coupling through zwitterions can be destroyed under compressive thermal loads. Releasing the stresses in the matrix leads to almost monotonic decrease in the strain on the ODA-SWCNTs consistently with the suggested interpretation of the experimental data under compressive loads. It is important to note that in these experiments we measured the Raman spectra at the same spot on the sample, with deviations of the laser spot position less than 0.5 lm. Measurements at other spots on the sample have given similar results but the coherence of the data in Figs. 4–6 is mostly due to the ‘‘same spot’’ measurements. Motivated by the chemistry of functionalization and the interactions between the SWCNT, functional moieties, and the polymer, a structural mechanics model for a limited load transfer is suggested assuming a buckling instability. In this simplified buckling model the SWCNTs or the SWCNT bundles are represented as laterally supported beams on an elastic foundation as shown in Fig. 8. Following the analysis given in Refs. [23,24], the critical stress for buckling of a nanotube on an elastic foundation with the modulus k can be written as p2 EI kl4 2 rcr ¼ m þ 2 4 ; ð1Þ m p EI Al2 where m denotes the number of half waves along the buckled nanotube, E is the YoungÕs modulus of the nanotube, l is the length of the nanotube under axial
Fig. 7. TEM image close-up of a ODA-SWCNT bundle embedded in epoxy matrix.
Fig. 8. Buckling of a SWCNT supported laterally by octadecylamineepoxy matrix.
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stress, I is the area moment of inertia, and A is the nanotube cross-sectional area. For a bundle of nanotubes, E, I, and A are generally different from those of the comprising nanotubes. In the absence of elastic foundation, the critical stress for buckling reduces to the EulerÕs buckling stress rcr = p2EI/Al2 [23]. It is worth noting that the number of half waves to which a given nanotube can be buckled under the critical stress is determined only by the value of kl4/p4EI [23,24]. This is summarized in Table 1. For particular combinations of values of k, l, E and I, as for instance kl4/p4EI = 4, the critical stresses for m = 1 and m = 2 are the same and an instability towards a transition from one to two-half waves buckling may occur. More generally, a transition from n to (n + 1)-half waves may take place at kl4/p4EI = n2(n + 1)2. Now we calculate k for the ODA-SWCNTs and bundles embedded in the epoxy matrix. Given the relation between the relative frequency shift of the tangential G+ mode and axial nanotube strain z [11], DxGþ =xGþ ¼ 1:04z , one obtains that the first plateau in Fig. 4, assigned to buckling of ODA-SWCNTs in the epoxy matrix, occurs at the axial stress of 1.08 GPa, provided the YoungÕs modulus of the nanotubes is 1 TPa. To estimate k from Eq. (1) one also needs the dimensions of the embedded nanotubes or bundles. As discussed in Section 2, the average diameter of the ODA-SWCNTs monitored by Raman spectroscopy during the loading experiments is 1.26 nm. On the other hand, the TEM images in Figs. 3 and 7 reveal thin bundles with diameter 3 nm, which is close to that of a four-nanotubes bundle [25]. The well pronounced plateaus in the loading curve in compression shown in Fig. 4 indicate for a predominant length of the straight nanotube segments in the ODA-SWCNT nanocomposite. Indeed, the segments length distribution determined from the TEM images was found to spread from 35 to 125 nm, having a notable peak at 75 nm. Further, we take into account that the SWCNT is a hollow cylinder with finite wall thickness h and radius r. Using Eq. (1), we calculate k = 0.36 MPa [26] for the ODA-shell that surrounds the individual SWCNTs with r = 0.63 nm, h = 0.066 nm [27] and the average segment length l = 75 nm buckled under stress rcr = 1.08 GPa. We also obtain k = 0.14 MPa [28] for the ODA-shell surrounding the nanotube bundles with r = 1.5 nm and l = 75 nm. Here m = 1 is chosen, since kl4/p4EI < 4 for both cases. The lower value of k for the nanotube bundles than that for isolated nanotubes could be attributed to the difference in their aspect ratio Table 1 The number of half waves m for different values of kl4/p4EI kl4/p4EI
04
4 36
(n 1)2n2 n2(n + 1)2
m
1
2
n
d, and the area moment of inertia I as follows from the model of k given in Ref. [29] or to the different surface topography of the bundles and the nanotubes. It is instructive one to estimate the equivalent effective YoungÕs modulus for the ODA-epoxy surrounding the SWCNTs, which is assumed to be isotropic. For this purpose we use the model of Lanir and Fung [29], which suggests the following relationship between the foundation modulus k and the elastic properties of an isotropic matrix: k¼
8pEm ð1 mm Þ=ð1 þ mm Þ ; ð3 4mm ÞK 0 ½mpd þ mpd=2K 1 ½mpd
ð2Þ
where Em and mm are the YoungÕs modulus and PoissonÕs ratio of the matrix, respectively, d is the ratio of the radius to the length of the column, m is the number of half waves, and both K0 and K1 are the modified Bessel functions of the second kind. Using Eq. (2), mm = 0.35 is taken equal to that of the epoxy matrix [30], and k calculated above, we obtain Em = 0.19 MPa for the ODA-epoxy that surrounds the individual nanotube and Em = 0.07 MPa for the surrounding of the nanotube bundles. These effective moduli are much lower than the YoungÕs modulus of the epoxy 2.72 GPa [14], which suggests that the ODA-shell provides very weak lateral support. Next, we analyze the second plateau in the loading curve in Fig. 4. As discussed above, once a buckling with given mode m occurs further increase of the applied stress leads to no transition to another buckling mode for the same l. Therefore, the second plateau in Fig. 4 has to be treated as a result of m = 1 buckling of the linear segments l/2 created from the buckling responsible for the first plateau. Using Eq. (1) and the k obtained from the first plateau, we estimate a critical buckling stress 1.58 GPa for a ODA-SWCNT with l/2 = 37.5 nm. On the other hand, form the experimental results shown in Fig. 4 we find that the second plateau corresponds to 1.88 GPa stress on the nanotubes, a value close to the estimated one from Eq. (1). From these estimates we conclude that the second plateau in Fig. 4 could be due to the buckling of the SWCNTs, which have been bent and are in contact with the polymer after initial loading (the first plateau). It is interesting to analyze whether the local minimum in the thermal loading curve for the ODA-SWCNT/EP nanocomposite shown in Fig. 5 and attributed to debonding processes is also associated with the nanotube buckling. From Fig. 5 we find that the turning point in the loading curve for the ODA-SWCNT/EP nanocomposite is at 2.88 GPa stress on the nanotubes. Assuming that the critical stress of buckling of ODASWCNT in the shrinking epoxy matrix is 2.88 GPa we obtain from Eq. (1) k = 1.18 MPa, a reasonable value for k that reflects an improvement of the coupling of the nanotubes to the shrunk matrix. This estimate also
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indicates that the debonding process of ODA-SWCNT in epoxy under the thermal loading might be initiated by buckling. In conclusion, the model analysis presented here fully supports the interpretation of compressive loading curves for the ODA-SWCNT/EP nanocomposites shown in Figs. 4 and 5 as due to buckling of the nanotubes at relatively low critical stresses. In a follow-up modeling it will be interesting to analyze the experimental results presented here within more realistic models [31,32] that account for microbuckling and kinking phenomena, an indication for which is seen in Fig. 7. 5. Conclusions In summary, we have presented a study of interfacial and mechanical properties of ODA-SWCNT/EP nanocomposites using both experimental (Raman spectroscopy and TEM) and theoretical approaches. The observed differences in loading of the non-functionalized and ODA-functionalized SWCNT/EP nanocomposites are attributed to the interface modification in ODASWCNT/EP nanocomposites. We have given evidence that the observed two plateaus in the strain transfer in ODA-SWCNT/EP under compression are due to buckling of the nanotubes facilitated by the very weak sidewall nanotube–epoxy interactions. Thermal loads created upon cooling the sample below 260 K lead to debonding of the nanotubes that is likely initiated by nanotubeÕs buckling. Finally, we want to emphasis the uniqueness of the combined Raman and TEM experiment because the standard mechanical stress measurements hardly could detect this peculiar behavior of tiny amount of ODA-SWCNTs under compression. Acknowledgments We thank W. Holmes for helping us with the nanocomposites preparation. This work was supported in part by the state of Texas through the Texas Center for Superconductivity and Advanced Materials, the Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles, funded by NASA Cooperative Agreement No. NCC-1-02038, and the Institute of Space Systems Operations (ISSO) at the University of Houston. References [1] Hamon MA, Chen J, Hu H, Chen Y, Itkis ME, Rao AM, et al. Dissolution of single-walled carbon nanotubes. Adv Mater 1999;11(10):834–40. [2] Chattopadhyay D, Galeska L, Papadimitrakopoulos F. A route for bulk separation of semiconducting from metallic single-wall carbon nanotubes. J Am Chem Soc 2003;125(11):3370–5.
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