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Measurement of the Elastic Modulus of Single Bacterial Cellulose Fibers Using Atomic Force Microscopy Ganesh Guhados,†,⊥ Wankei Wan,†,‡,| and Jeffrey L. Hutter*,§,‡ Department of Chemical and Biochemical Engineering, Graduate Program in Biomedical Engineering, and Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada Received February 17, 2005. In Final Form: April 22, 2005 The ability of the atomic force microscope to measure forces with subnanonewton sensitivity at nanometerscale lateral resolutions has led to its use in the mechanical characterization of nanomaterials. Recent studies have shown that the atomic force microscope can be used to measure the elastic moduli of suspended fibers by performing a nanoscale three-point bending test, in which the center of the fiber is deflected by a known force. We extend this technique by modeling the deflection measured at several points along a suspended fiber, allowing us to obtain more accurate data, as well as to justify the mechanical model used. As a demonstration, we have measured a value of 78 ( 17 GPa for Young’s modulus of bacterial cellulose fibers with diameters ranging from 35 to 90 nm. This value is considerably higher than previous estimates, obtained by less direct means, of the mechanical strength of individual cellulose fibers.
Introduction The development of scanning probe microscopies has enabled studies of a variety of physical-chemical properties of materials at the micro- and nanoscale. In particular, the atomic force microscope (AFM) has permitted the exploration of electrically insulating materials such as biomolecules and polymers.1 The sensitivity of the AFM to subnanonewton forces has led to its use in the characterization of surface and material properties such as friction,2 adhesion,3,4 and elastic modulus.5 The lateral resolution of the AFM allows mechanical properties to be determined in samples of nanometer size, for which conventional macroscopic testing is impossible. A few such studies have been previously performed on materials such as carbon nanotubes,6,7 polypyrrole nanotubes,8 and poly(L-lactic acid)9 by means of a three-point bending test: i.e., an AFM cantilever was used to apply a known force on a fiber bridging a gap. In those studies, * Corresponding author. Address for correspondence: Department of Physics and Astronomy, The University of Western Ontario, London, ON N6A 3K7, Canada. E-mail:
[email protected]. Telephone: (519) 661-2111 x86719. Fax: 519-661-2033. † Department of Chemical and Biochemical Engineering, The University of Western Ontario. ‡ Graduate Program in Biomedical Engineering, The University of Western Ontario. § Department of Physics and Astronomy, The University of Western Ontario. ⊥ E-mail:
[email protected]. | E-mail:
[email protected]. (1) Samorı`, P. J. Mater. Chem. 2004, 14, 1353. (2) Carpick, R. W.; Salmeron, M. Chem. Rev. 1997, 97, 1163. (3) Weisenhorn, A. L.; Maivald, P.; Butt, H.; Hansma, P. K. Phys. Rev. B. 1992, 45, 11226. (4) Hoh, J.; Cleveland, J. P.; Prater, C. B.; Revel, J.-P.; Hansma, P. K. J. Am. Chem. Soc. 1992, 114, 4917. (5) Radmacher, M.; Fritz, M.; Hansma, P. K. Biophys. J. 1995, 69, 264. (6) Salvetat, J.-P.; Briggs, G. A. D.; Bonard, J. M.; Bacsa, R. R.; Kulik, A. J.; Sto¨ckli, T.; Burnham, N. A.; Forro´, L. Phys. Rev. Lett. 1999, 82, 944. (7) Yu, M.-F.; Bradley, S. F.; Arepalli, S.; Ruoff, R. S. Phys. Rev. Lett. 2000, 84, 5552. (8) Cuenot, S.; Sophie, D.-C.; Nysten, B. Phys. Rev. Lett. 2000, 85, 1690. (9) Tan, E. P. S.; Lim, C. T. Appl. Phys. Lett. 2004, 84, 1603.
forces were applied at only a single location near the center of the fiber, and the elastic modulus determined through an assumed elastic model. However, not only does this approach exclude the possibility of confirming the model used to describe the data, it also makes it difficult to verify the position along the fiber at which the force is applied. In this study, we have chosen to measure the mechanical properties of bacterial cellulose, a polymer of glucose units linked together by β-(1-4)-glycosidic linkages, that is produced by the gram-negative bacteria Acetobacter xylinum BPR2001. Bacterial cellulose has a high degree of crystallinity and is produced in the form of fibers of diameter less than 50 nm10,11 and a degree of polymerization of between 2000 and 6000.12 The morphology, crystallinity, and conformational structures of bacterial cellulose have been characterized by electron microscopy,13 AFM,14 X-ray diffraction,13,15 nuclear magnetic resonance spectroscopy,16 and Fourier transform infrared spectroscopy.17,18 Because of the difficulty of isolating individual fibers, the mechanical properties of bacterial cellulose have been explored only in bulk samples, for instance by using longitudinal oscillation testing.19 In such an approach, only the average properties of meshes of bacterial cellulose bundles can be determined. Bacterial cellulose has been utilized for numerous applications, such as wound dressings,20 as acoustic diaphragms,21 as micro blood vessels,22,23 and as a scaffold material for tissue engineering of (10) Brown, R. M., Jr.; Willison, J. H.; Richardson, C. L. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 4565. (11) Ohad, I.; Danon, I. O.; Hestrin, S. J. Cell. Biol. 1962, 12, 31-46. (12) Iguchi, M.; Yamanaka, S.; Budhiono, A. J. Mater. Sci. 2000, 35, 261. (13) Krystynowicz, A.; Czaja, W.; Wiktorowska-Jezierska, A.; Goncalves-Miskiewicz, M.; Turkiewicz, M.; Bielecki, S. J. Ind. Microbiol. Biotechnol. 2002, 29, 189. (14) Hirai, A.; Tsujii, Y.; Tsujii, M.; Horii, F. Biomacromolecules 2004, 5, 2079. (15) Eichhorn, S.; Young, R. J. Cellulose 2001, 8, 197. (16) Masuda, K.; Adachi, M.; Hirai, A.; Yamamoto, H.; Kaji, H.; Horii, F. Solid State Nucl. Magn. 2003, 23, 198. (17) Kacurakova, M.; Smith, C. A.; Gidley, J. M.; Wilson, H. R. Carbohyd. Res. 2002, 337, 1145. (18) Joseph, G. A. M.E.Sc Thesis, The University of Western Ontario, 2001. (19) Kunihiko, W.; Mari, T.; Tasushi, M.; Fumihiro, Y. Cellulose 1998, 5, 187.
10.1021/la0504311 CCC: $30.25 © 2005 American Chemical Society Published on Web 05/27/2005
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cartilage.22 Its hydrophilic nature, coupled with its native dimensions, makes bacterial cellulose an ideal material for the preparation of hydrophilic, biocompatible nanocomposites with controlled mechanical properties for replacement medical devices.24 Therefore, it is essential to study the structural and mechanical properties of these fibers. Here, we report the study of mechanical properties of bacterial cellulose fibers by atomic force microscopy. We show that making a series of measurements along the fiber allows us to verify the elastic model used and provides elastic modulus measurements more accurately than previously possible. Materials and Methods Bacterial Cellulose. Bacterial cellulose was produced in a Biostat M Bioreactor (B. Braun Biotech, Inc.) using a fructosebased medium by A. xylinum BPR 2001 (ATCC #700178) at an optimum pH of 5.0 and temperature of 28 °C. This results in cellulose production as long, bundled fibers, rather than in the form of beads in shake flasks.25 They were treated with 1% (w/w) of NaOH in a bath of boiling water for 30 min and washed repeatedly with deionized water to ensure complete removal of the bacteria. The product fiber was stored in deionized water at 4 °C in a refrigerator. Sample Preparation. A 1 mL sample of 0.36 wt % bacterial cellulose suspension was dispersed by sonication for 2 h at room temperature. Then 50 µL of the sonicated sample was placed on a silicon-nitride-coated silicon grating (NanoAndMore, Germany) with a pitch of 3.0 µm and nominal step height of 1000 nm. The sample was spin-coated to obtain a uniform submonolayer of evenly dispersed fibers suspended over the grooves. X-ray Diffractometry. Samples were analyzed using a Rigaku DMX-2 X-ray diffractometer, equipped with Cu KR radiation. Data were collected from 5 to 40° at an increment of 0.05° and a counting time of 2 s. The sample was dried in a drying oven for 1 h at 60 °C. It was then cooled to room temperature before the scan. The degree of crystallinity was calculated according to Eichhorn et al.15 and Horii et al. 26 Atomic Force Microscopy. All atomic force microscope (AFM) experiments were performed using a Multimode AFM with a Nanoscope IIIa controller (Digital Instruments). Samples were imaged in air using Si3N4 cantilevers with a nominal spring constant of 0.5 N/m (MLCT Microlever F, Veeco Instruments), chosen because their compliance approximately matched that expected of the suspended fibers. Using the thermal noise technique,27 we measured an actual spring constant of 1.03 ( 0.05 N/m. Because of the discrepancy with the nominal value, we verified the spring constant with the added-mass method28 (after experiments were complete since this technique is potentially destructive), by which we obtained a value of 1.23 ( 0.14 N/m. We chose to use the spring constant measured by the (20) Fontana, J. D.; de Souza, A. M.; Fontana, C. K.; Torriani, I. L.; Moreschi, J. C.; Gallotti, B. J.; de Souza, S. J.; Narcisco, G. P.; Bichara, J. A.; Farah, L. F. Appl. Biochem. Biotechnol. 1990, 24-25, 253. (21) Asrar, J.; Hill, J. C. J. Appl. Polym. Sci. 2002, 83, 457. (22) Svensson, A.; Nicklasson, E.; Harrah, T.; Panilaitis, B.; Kaplan, D. L.; Brittberg, M.; Gatenholm, P. Biomaterials 2005, 26, 419. (23) Klemm, D.; Schumann, D.; Udhardt, U.; Marsch, S. Prog. Polym. Sci. 2001, 26, 1561. (24) Stacy, A.; Hutchens, J. W.; Evans, B. R.; O’Neill, H. M. US Patent Appl. Publ. 2004, 20040096509. (25) Joseph, G.; Rowe, G. E.; Margaritis, A.; Wan, W. J. Chem. Technol. Biot. 2003, 78, 964. (26) Horii, F.; Hirai, A.; Kitamaru, R. Polym. Bull. (Berlin)1982, 8, 162. (27) Hutter, J. L.; Bechhoefer, J. Rev. Sci. Instrum. 1993, 64, 1868, with corrections pointed out by: Butt, H.-J.; Jaschke, M. Nanotech. 1995, 6, 1. Walters, D. A.; Cleveland, J. P.; Thomson, N. H.; Hansma, P. K.; Wendman, M. A.; Gurley, G.; Elings, V. Rev. Sci. Instrum. 1996, 67, 3583. (28) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403, with corrections for the position of the added mass relative to the tip pointed out by: Sader, J. E.; Larson, I.; Mulvaney, P.; White, L. R. Rev. Sci. Instrum. 1995, 66, 3789.
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Figure 1. Model for the shape of a fiber clamped to supports a distance L apart while being deformed by a vertical force F applied at a distance a from one end of the fiber. thermal noise technique in our calculations since we checked it periodically throughout the experiments. The sample was imaged in contact mode to locate isolated fibers that spanned the gap. Once identified, such fibers were imaged at higher resolution (typically with scan sizes of 2.4-3.2 µm) to determine their dimensions. Fibers of diameter less than 100 nm were chosen for mechanical testing. Nanomechanical Testing. Mechanical testing was performed using the force-volume mode, in which cantilever deflection is recorded as a function of vertical sample displacements i.e., force spectra are obtainedsfor an array of positions arranged in a square grid. We chose a grid resolution high enough (usually 32 × 32 or 64 × 64 pixels) to ensure that force spectra were obtained at several locations on each suspended fiber. A vertical ramp of size 500 nm and ramp rate of 1 Hz were used; we verified that this was slow enough to avoid viscoelastic effects. The maximum applied force was limited to 90 nN via a trigger threshold. The map of piezo height required to achieve this threshold for each grid point also serves as a low-resolution topographical image of the sample. For the majority of points in a force-volume image, the AFM tip encounters the rigid surface of the grating, resulting in a cantilever deflection ∆y that is equal to the vertical sample displacement ∆z after contact is made. Since the sensitivity of the cantilever deflection signal (“A-B”) is initially unknown, such points serve to calibrate the detector sensitivity. For those points in which the tip encounters a suspended fiber, deflection of the fiber results in a value of ∆y < ∆z. Thus, force spectra corresponding to such points display shallower slopes in the contact regime. In this case, ∆z ) ∆y + δ, where δ is the deflection of the fiber. In principle, the deflection of the fiber is due to tensile, compressive and shear deformations. However, when the ratio of the length of fiber that bridges the gap to the diameter is more than 16, shear can be neglected.29 This condition was met for all fibers characterized in this study. In general, the deflection of a suspended beam depends on the applied forces and the boundary conditions at its edges. The latter determines the choice of model for deducing the elastic modulus. In our case, the fibers remained stationary after repeated imaging, suggesting that they were strongly adhered to the substrate; thus, a clamped configuration in which both end deflections and end slopes are fixed at zero was assumed. Data Analysis and Young’s Modulus Determination. For a clamped, suspended beam of length L subjected to a concentrated load F applied at a point a relative to one end, the expected deflection δ(x) for all points x along the beam is given by
{
F [(L + 2a)x - 3La](L - a)2x2 0 < x < a 6EIL3 δ(x) ) F [(L + 2x)a - 3Lx](L - x)2a2 a < x < L 6EIL3
(1)
where I is the area moment of inertia of the beam and E is its Young’s modulus. This shape is illustrated in Figure 1. In the case of an AFM experiment, the beam deflection is measured at the single point where the force is applied, so x ) a. As the AFM tip is scanned across the beam, the measured deflection is then expected to be29
δ(a) )
[
]
F a(L - a) 3EI L
3
(2)
(29) Timoshenko, S.; Gere, J. M. Mechanics of Materials, 4th ed.; PWS Publishing Co.: Boston, MA, 1997.
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for positions a distance a from the end of the beam. In the special case of a force applied at the center of the beam, a ) L/2, the deflection becomes δ ) FL3/192EI. This expression has been used in previous AFM studies of suspended beams. Since the applied force is, in this case, due to the AFM cantilever, it is given by F ) k∆y, where k is the spring constant of the cantilever and ∆y the deflection of the cantilever from its equilibrium position. The condition that ∆z ) ∆y + δ(x) then becomes
[
∆z ) ∆y 1 +
(
)]
k a(L - a) 3EI L
3
(3)
so that the measured slope of the contact portions of the force spectra is expected to be
(
[
)]
dy k a(L - a) ) 1+ dz 3EI L
3 -1
(4)
Figure 2. AFM height image of cellulose fibers suspended over gaps of 1.5 µm width.
for positions along the suspended fiber. The dimensions of the fiber can be estimated from contactmode images. The suspended fiber length, L, is accurately determined by the gap and orientation of the fiber. We measured the width and height of the fibers in the region immediately adjacent to the trench using a cross-section perpendicular to the fiber. In most cases, bundles of a few bacterial cellulose fibers spanned the gap; we approximated the cross-section as an ellipse and took the maximum measured height h and the width w (corrected for tip convolution) to be its principal axes. The area moment of inertia for this geometry is calculated as
I)
πwh3 64
(5)
The functional form for dy/dz then depends on a single undetermined parameter E, the Young’s modulus of the fiber, which can be obtained from a fit of the functional form of eq 4 to the slopes dy/dz measured at a series of locations along a suspended fiber. The procedure we followed in practice was to collect a forcevolume image of the region containing the fiber and use a custom analysis routine implemented in the Igor Pro software package (Wavemetrics) to measure the slope dy/dz of the contact region for each force spectrum in the image. A histogram of the (uncalibrated) slopes thus measured typically reveals a peak corresponding to the majority of positions, in which the AFM tip contacts either the rigid substrate or fibers supported by the rigid substrate. Since the theoretical slope for such positions is dy/dz ) 1, all slopes are normalized to the mean value of slope measurements contained in that peak, thus calibrating the y sensitivity. We then selected those points closest to the midline of the fiber (easily identified from the topographical image or an image map of the measured slopes) and plotted their (normalized) values as a function of distance a from the end of the fiber. The values of these slopes were then fitted to the functional form of eq 4 using the Levenberg-Marquardt30 nonlinear least-squares fitting algorithm (also implemented in Igor Pro) to determine the Young’s modulus of the fiber.
Results An AFM height image of several bacterial cellulose fibers on the grating surface is shown in Figure 2. Isolated fibers spanning trenches on the grating surface were chosen for further study by force volume imaging. Secure anchoring of fibers on the grating surface is indicated by the results shown in Figure 3, in which a scan direction perpendicular to the fiber axis was chosen. It can be seen that despite significant lateral motion of the suspended portion of the fiber, the remainder remained firmly anchored on the substrate. This confirms that the clamped model il(30) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recpies in Fortran77; Cambridge University Press: Cambridge, U.K., 1986.
Figure 3. Two AFM height images (trace and retrace) of a cellulose fiber suspended over a 1.5 µm gap. Note the significant lateral motion of the suspended portion while the portion of the fiber on the substrate remains firmly anchored. Images are 3.2 µm square with the gray scale spanning a vertical height range of 400 nm.
lustrated by Figure 1 can be applied to our experimental results. It should be noted that after the image obtained in Figure 3b was obtained, the fiber broke; thus, we recommend lateral imaging of suspended fibers only after force volume data are obtained. Typical individual force curves measured in a region such as that illustrated in Figure 2 are shown in Figure 4 for a position on the rigid substrate (Figure 4a) and a position at the center of a suspended fiber (Figure 4b). Comparing the force curves obtained on the bare substrate with those on the fiber shows that the fiber is soft enough to respond to the force applied, allowing its elastic modulus to be measured. The coincidence of the loading (approach) and unloading (retraction) curves indicates that the fibers
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Figure 6. Slope of force spectra for positions along a suspended fiber. For positions where the fiber is not supported, the slope is smaller than for positions where the fiber is backed by the rigid substrate. The solid curve is the best fit to the expected values for a clamped-beam configuration. In this case, the fiber had a suspended length of 1.62 µm.
Figure 4. Force spectra obtained on (a) the bare substrate and (b) near the middle of a suspended fiber. The shallow slope in part b indicates sample deformation, allowing the mechanical strength of the fiber to be measured. (Solid curve: approach. Dashed curve: retraction.)
geometric correction factor by assuming an elliptical crosssection for the fiber bundle and a pyramidal AFM tip with 35° sidewalls terminated by a spherical cap of 20 nm radius, according to the manufacturer’s specifications. For the case shown in Figure 6, we estimated I ) (6.5 ( 0.6) × 10-31 m4, leading to a value of E ) 117 ( 19 GPa, where the uncertainty includes the uncertainties in I, the fit, and the spring constant calibration. The elasticity data were obtained for fibers with heights ranging from 27 to 88 nm. We note no significant variation in Young’s modulus with fiber diameter, consistent with the expectation that internal shear is unimportant in this measurement. On the basis of these measurements, we determine an average Young’s modulus of 78 ( 13 ( 4 GPa for bacterial cellulose fibers, where the random error of (13 GPa is based on the standard deviation of results for the 10 fibers measured, and the systematic error of (4 GPa is due to the uncertainty in the spring constant calibration, which is not reduced by repeated measurements. Discussion
Figure 5. Force spectra obtained at a position 150 nm from that of Figure 4b, offset from the fiber axis. Note that the slope of the approach curve in the region immediately after contact (i.e., piezo positions decreasing from ∼200 to ∼100 nm) is much shallower than that in Figure 4b. (Solid curve: approach. Dashed curve: retraction.)
behave in an elastic manner. In cases where the probed position is laterally offset from the midline of the fiber, hysteresis in cantilever deflection between the approach and retractions curves is seen. This is likely due to slipping of the fiber along the side of the tip. An example is shown in Figure 5. More importantly, a lower slope (dz/dy) is measured, probably because the force between the tip and fiber is no longer vertical. As a consequence, the value of Young’s modulus estimated from such a force curve would be incorrect. The force-curve slopes for a particular suspended fiber as a function of position along its length are plotted in Figure 6. As expected, maximum compliance occurs near the center of the fiber. Indicated is a single-parameter fit of eq 4 to these data. To use this fit to estimate Young’s modulus of the fiber, its area moment of inertia, I, must be determined. We use cross sections of the height images of fibers (obtained prior to force volume imaging) on both sides of the gap to estimate their height and width. The height is easily and accurately obtained by the AFM. However, the measured width is an overestimate due to convolution of the tip with the fiber profile. We apply a
Mechanical properties are important in determining a material’s functionality and its possible applications. For bulk materials, elastic moduli can be determined using standard mechanical testing procedures. However, for nanomaterials, direct determination of Young’s modulus becomes more difficult. The use of the AFM for direct Young’s modulus determinations of nanofibers was first reported in 1999. Results on polypyrrole nanotubes8 and carbon nanotubes6 indicated a strong dependence on fiber size. On the other hand, recent results for poly(L-lactic acid) fibers9 showed a much smaller size dependence. In the present study, we have determined that over a fiber diameter range of 27-88 nm, the elastic modulus of bacterial cellulose has a constant value of 78 ( 17 GPa. In previous AFM studies of the mechanical properties of nanofibers,6-9 elastic moduli were calculated from deflection measurements at a single point near the center of a suspended fiber and an assumed elastic model. Such an approach provides no means of distinguishing between alternate models, such as clamped vs simply supported configurations, from which very different elastic moduli would be inferred, or of weighing the importance of additional terms, such as deflection due to shear. In our approach, we measure the fiber compliance at several points along its suspended portion and obtain the elastic modulus from a fit to a model. Validation is supplied by the agreement between the experimental data and the model prediction. An additional advantage over a singlepoint measurement is that elastic moduli are based on more data, leading to a smaller uncertainty. Moreover, a
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single-point measurement is unduly reliant on scanner calibration and microscope controller stability, each of which affects the ability to choose a position located precisely at the fiber center. In our study, justification of the clamped-beam model is provided by the AFM micrographs shown in Figure 3, in which two AFM height images (trace and retrace) of a cellulose fiber suspended over a 1.5 µm gap are shown. It can be seen that despite significant lateral motion of the suspended portion, the portion of the fiber on the substrate remains firmly anchored. Further validation is provided by Figure 6, in which slopes of force spectra are plotted as a function of position along a suspended fiber. The fit to the clamped-beam model indicated by the solid curve follows the data well, though some deviation from the expected compliance can be seen near the ends of the fiber. In other cases (not shown) slight asymmetry is evident, possibly indicating a change in fiber cross-section across the gap due to rearrangements such as twisting of fiber bundles. A single-point measurement made at the center of a fiber will yield the same Young’s modulus as determined by our approach, albeit with a larger uncertainty, if the elasticity model is justified. However, the effects of positioning error on elastic moduli derived from a singlepoint measurement can be large. From eq 4, it can be shown that an error δa in the position a along the fiber will lead to an error δE = 12E(δa/L)2 in the reported value of Young’s modulus. For example, for a fiber suspended across a 1.5 µm gap, a position error of δa ) 150 nm (10% of L, in this case) will result in a 12% overestimate of Young’s modulus. The consequences of measurements off the fiber axis are more difficult to estimate theoretically. For the data shown in Figure 5, a point offset laterally from the fiber center by 150 nm was chosen. An estimate of Young’s modulus based on these data (with the erroneous assumption that they were acquired at the fiber center) would be 40% too low. Theoretical studies have placed an upper limit on the mechanical strength of cellulose in the range of 130-170 GPa.31-33 However, the actual value is a function of the degree of crystallinity of the cellulose sample.15 Experimentally, for sheets of bacterial cellulose with 80% crystallinity derived from wet pellicles prepared in a static culture, a Young’s modulus of 33.3 GPa has been reported. For sheets derived from bacterial cellulose prepared in agitated culture, the corresponding value for crystallinity is 72% and Young’s modulus is 28.3 GPa.19 These values are significantly lower than our result of 78 ( 17 GPa for single nanofibers. We have determined the crystallinity of our bacterial cellulose sample to be about 60% using X-ray diffraction, following the method of Horii et al.26 and Eichhorn et al.15 The discrepancy in mechanical strength with previous studies of bacterial cellulose is most likely due to a difference in the physical state of the samples. Dried bacterial cellulose pellicles and sheets prepared from agitated culture fibers are nonwoven materials consisting of tangled webs of randomly oriented fibers. Our results are derived from direct measurements of single fibers, or aligned bundles of a few fibers. (31) Marho¨fer R. J.; Reiling, S.; Brickmann, J. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 1350. (32) Sakurada, I.; Nukushina, Y.; Ito, T. J. Polym. Sci. 1962, 57, 651. (33) Tashiro, K.; Kobayashi, M. Polym. Bull. (Berlin)1985, 14, 213.
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Young’s modulus of microcrystalline cellulose with 48.5% crystallinity has been reported to be 25 ( 4 GPa. For flax and hemp fibers with crystallinity of 64.3% and 59.7%, Young’s moduli of 36 ( 7 and 40 ( 4 GPa, respectively, have been reported.15 These results were obtained by embedding the micrometer size fibers into an epoxy matrix and measuring the Raman band shift by subjecting the composite to bending stress. The dependence of Young’s modulus of cellulose fibers on crystallinity has been modeled by considering the fiber as a composite material consisting of a crystalline phase and an amorphous phase. Two limiting models, depending on the parallel (Voigt model) or series (Reuss model) arrangement of the crystalline phase, can be derived for the range of Young’s moduli possible.34 On the basis of these models and an assumption of Young’s moduli of amorphous (5 GPa) and crystalline cellulose (128 GPa), Eichhorn et al. developed a relationship between Young’s modulus and the percent crystallinity of the cellulose sample.15 They determined that for microcrystalline cellulose, flax and hemp, Young’s moduli fall within the limits of these two models and are best described by a model proposed by Ganster et al.,35 which takes into account the aspect ratio of the crystallites. The Eichhorn relationship predicted that for a cellulose sample with 60% crystallinity, as the case with our bacterial cellulose sample, Young’s modulus should be within the range of 12 GPa (Reuss model) and 74 GPa (Voigt model). The value of 78 ( 17 GPa we have determined is thus consistent with the Voigt model, implying that the crystalline regions in the bacterial cellulose fibers are mostly aligned in a parallel arrangement, and represents one of the highest values measured for cellulose at this level of crystallinity. This parallel arrangement of the crystalline regions in bacterial cellulose microfibrils was experimentally demonstrated by Koyama et al. using electron microdiffraction at precisely controlled tilt angles, with the chain directionality determined by staining the reducing ends.36 Conclusions In summary, we have developed a technique to accurately measure the elastic modulus of nanofibers using atomic force microscopy. Rather than the nanoscale threepoint bending test employed in previous studies, we systematically measure deflection across a suspended fiber, allowing us to obtain more accurate data and justify the mechanical model we use. In the present study, we measured the mechanical properties of single fibers of bacterial cellulose, and determined a Young’s modulus of 78 ( 17 GPa. No dependence on diameter was observed, indicating that shear forces are unimportant and that the fiber therefore behaves mechanically like a homogeneous material. Acknowledgment. We thank Dr. Charles Wu for collecting the XRD data. We also thank the Canada Foundation for Innovation for funding of the atomic force microscope infrastructure and NSERC (Canada) for operational support. G.G. thanks the University of Western Ontario for an IGSS scholarship. LA0504311 (34) Harris, B. Engineering Composite Materials; IOM Communications Ltd.: London, 1999. (35) Ganster, J.; Fink, H.-P.; Fraatz, J.; Nywlt, M. Acta Polym. 1994, 45, 312. (36) Koyama, M.; Helbert, W.; Imai, T.; Sugiyama, J.; Henrissat, B. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 9091.
