Nanomechanics of Biocompatible Hollow Thin-Shell Polymer

Apr 20, 2009 - Institute for Materials and Processes, School of Engineering, Centre for ... W. Norman McDicken, Carmel M. Moran, Stephen D. Pye, James...
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Nanomechanics of Biocompatible Hollow Thin-Shell Polymer Microspheres Emmanouil Glynos† and Vasileios Koutsos* Institute for Materials and Processes, School of Engineering, Centre for Materials Science and Engineering, The University of Edinburgh, Edinburgh, United Kingdom

W. Norman McDicken, Carmel M. Moran, Stephen D. Pye, James A. Ross, and Vassilis Sboros Medical School, Royal Infirmary of Edinburgh, The University of Edinburgh, Edinburgh, United Kingdom. † Present address: Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109 Received January 24, 2009. Revised Manuscript Received March 10, 2009 The nanomechanical properties of biocompatible thin-shell hollow polymer microspheres with approximately constant ratio of shell thickness to microsphere diameter were measured by nanocompression tests in aqueous conditions. These microspheres encapsulate an inert gas and are used as ultrasound contrast agents by releasing free microbubbles in the presence of an ultrasound field as a result of free gas leakage from the shell. The tests were performed using an atomic force microscope (AFM) employing the force-distance curve technique. An optical microscope, on which the AFM was mounted, was used to guide the positioning of tipless cantilevers on top of individual microspheres. We performed a systematic study using several cantilevers with spring constants varying from 0.08 to 2.3 N/m on a population of microspheres with diameters from about 2 to 6 μm. The use of several cantilevers with various spring constants allowed a systematic study of the mechanical properties of the microsphere thin shell at different regimes of force and deformation. Using thin-shell mechanics theory for small deformations, the Young’s modulus of the thin wall material was estimated and was shown to exhibit a strong size effect: it increased as the shell became thinner. The Young’s modulus of thicker microsphere shells converged to the expected value for the macroscopic bulk material. For high applied forces, the force-deformation profiles showed a reversible and/or irreversible nonlinear behavior including “steps” and “jumps” which were attributed to mechanical instabilities such as buckling events.

Introduction Stable, hemodynamically inert hollow micrometer-size spheres1,2 composed of a thin biocompatible shell which encapsulates an inert gas are used as ultrasound contrast agents (UCAs) and are normally referred to as microbubbles (MBs).3,4 They also have great potential as carriers for ultrasound-triggered targeted drug/ gene delivery.5 They are smaller than the smallest blood vessel of a human body to allow improved visualization of the vascular bed,6,7 and differentiate vascular patterns of tumors noninvasively. It is important to appreciate that the UCAs are different from all other medical imaging contrast media in that they have a very complex interaction with ultrasound. As they are highly compressible in the presence of a mechanical wave, like ultrasound, *To whom correspondence should be addressed. E-mail: [email protected]. (1) Keller, M. W.; Segal, S. S.; Kaul, S.; Duling, B. Circ. Res. 1989, 65(2), 458– 467. (2) Skyba, D. M.; Camarano, G.; Goodman, N. C.; Price, R. J.; Skalak, T. C.; Kaul, S. J. Am. Coll. Cardiol. 1996, 28(5), 1292–1300. (3) Sboros, V. Adv. Drug Delivery Rev. 2008, 60(10), 1117–1136. (4) Stride, E.; Edirisinghe, M. Soft Matter 2008, 4(12), 2350–2359. (5) Hernot, S.; Klibanov, A. L. Adv. Drug Delivery Rev. 2008, 60(10), 1153– 1166. (6) Burns, P. N.; Becher, H. Handbook of Contrast Echocardiography; Springer: Berlin, 2000. (7) Goldberg, B. B.; Raichlen, J. S.; Forsberg, F. Ultrasound Contrast Agents: Basic Principles and Clinical Applications; Dunitz Martin Ltd: London, 2001. (8) van der Meer, S. M.; Dollet, B.; Voormolen, M. M.; Chin, C. T.; Bouakaz, A.; de Jong, N.; Versluis, M.; Lohse, D. J. Acoust. Soc. Am. 2007, 121(1), 648–656. (9) Emmer, M.; van Wamel, A.; Goertz, D. E.; de Jong, N. Ultrasound Med. Biol. 2007, 33(6), 941–949.

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they respond with mechanical motion that at small amplitudes can be spherical, resonant, and yet nonlinear,8,9 and provide strong acoustic scatter. At larger ultrasound pressures, MBs coalesce,10 jet,11 or fragment12 in the presence of an ultrasound field and as a result emit the ultrasound with pulsed or variable spectral and energy characteristics. Acoustical experimental procedures are limited in inferring the properties of MBs;13 at best, single MB experiments have provided accurate measurements of the spectral and temporal content of MB scatter.14-17 The introduction of optical microscopy supported with high speed camera acquisition, above 10 MHz frame rate, provided unprecedented direct information on the MB motion.9,11,12,18 However, the MB shell dimensions are below the limits of the optical microscopy resolution, and its properties and contribution to (10) Postema, M.; Bouakaz, A.; Versluis, M.; de Jong, N. IEEE Trans. Ultrason., Ferroelect., Frequency Control 2005, 52(6), 1035–1041. (11) Postema, M.; van Wamel, A.; ten Cate, F. J.; de Jong, N. Med. Phys. 2005, 32(12), 3707–3711. (12) Chomas, J. E.; Dayton, P. A.; May, D.; Allen, J.; Klibanov, A.; Ferrara, K. Appl. Phys. Lett. 2000, 77(7), 1056–1058. (13) Sboros, V.; Ramnarine, K. V.; Moran, C. M.; Pye, S. D.; McDicken, W. N. Phys. Med. Biol. 2002, 47(23), 4287–4299. (14) Sboros, V.; Moran, C. M.; Pye, S. D.; McDicken, W. N. Ultrasound Med. Biol. 2003, 29(5), 687–694. (15) Sboros, V.; Pye, S. D.; MacDonald, C. A.; Gomatam, J.; Moran, C. M.; McDicken, W. N. Ultrasound Med. Biol. 2005, 31(8), 1063–1072. (16) Sboros, V.; Moran, C. M.; Pye, S. D.; McDicken, W. N. Phys. Med. Biol. 2004, 49(1), 159–173. (17) Sboros, V.; Pye, S. D.; Anderson, T. A.; Moran, C. M.; McDicken, W. N. Appl. Phys. Lett. 2007, 90(12), 123902. (18) Postema, M.; Marmottant, P.; Lancee, C. T.; Hilgenfeldt, S.; de Jong, N. Ultrasound Med. Biol. 2004, 30(10), 1337–1344.

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the mechanical behavior remain speculative. Microbubble theoretical models often fit data to the assumed shell mechanical properties,8,19-23 but no direct information on elasticity, plasticity, or other mechanical properties has ever been obtained systematically. As a result, these models have not gained wide acceptance and are not regarded as being predictive of the MB behavior. The lack of experimental data on the mechanical properties of the thin shell is central to this problem. In the literature, MBs are generally referred to as the entities that perform shell oscillations in the presence of ultrasound. Here, we investigate spherical rigid shelled microobjects that provide efficient scatter when they release a free gas microbubble out of the shell.10,14,24,25 We will thus refer to these entities as microspheres (MSs) to distinguish them from MBs that are usually identified as the bodies which oscillate in response to ultrasound and have been theoretically treated as such.26 Motivated by the fact that the atomic force microscope (AFM) has been proven to be not only a tool capable of imaging the topography of solid objects at high resolution but also a tool capable of probing the local nanomechanical material properties of various similar systems such as microcapsules,27-35 hollow faceted polyhedrons,36 ultrathin polyelectrolyte films,37 viscoelastic latex particles,38 protein nanotubes,39 collagen fibrils,40 thin virus shells,41 and cells,42 we applied the AFM force-distance curves technique to assess the mechanical properties of individual hollow microspheres. We have already shown that AFM is capable of probing the morphology of the outer surface of the microsphere shell at the (19) Marsh, J. N.; Hughes, M. S.; Hall, C. S.; Lewis, S. H.; Trousil, R. L.; Brandenburger, G. H.; Levene, H.; Miller, J. G. J. Acoust. Soc. Am. 1998, 104(3 I), 1654–1666. (20) Hoff, L.; Sontum, P. C.; Hovem, J. M. J. Acoust. Soc. Am. 2000, 107(4), 2272–2280. (21) Morgan, K. E.; Allen, J. S.; Dayton, P. A.; Chomas, J. E.; Klibanov, A. L.; Ferrara, K. W. IEEE Trans. Ultrason., Ferroelect., Frequency Control 2000, 47(6), 1494–1509. (22) Church, C. C. J. Acoust. Soc. Am. 1995, 97(3), 1510–1521. (23) Marmottant, P.; van der Meer, S.; Emmer, M.; Versluis, M.; de Jong, N.; Hilgenfeldt, S.; Lohse, D. J. Acoust. Soc. Am. 2005, 118(6), 3499–3505. (24) Bouakaz, A.; Versluis, M.; de Jong, N. Ultrasound Med. Biol. 2005, 31(3), 391–399. (25) Chin, C. T.; Burns, P. N. IEEE Trans. Ultrason., Ferroelect., Frequency Control 2004, 51(3), 286–292. (26) Stride, E.; Saffari, N. Proc. Inst. Mech. Eng., Part H 2003, 217(H6), 429– 447. :: (27) Mueller, R.; Kohler, K.; Weinkamer, R.; Sukhorukov, G.; Fery, A. Macromolecules 2005, 38(23), 9766–9771. (28) Vinogradova, O. I. J. Phys.: Condens. Matter 2004, 16(32), R1105–R1134. (29) Dubreuil, F.; Elsner, N.; Fery, A. Eur. Phys. J. E 2003, 12(2), 215–221. (30) Heuvingh, J.; Zappa, M.; Fery, A. Langmuir 2005, 21(7), 3165–3171. (31) Elsner, N.; Dubreuil, F.; Weinkamer, R.; Wasicek, M.; Fischer, F. D.; Fery, A. Prog. Colloid Polym. Sci. 2006, 132, 117–123. (32) Elsner, N.; Kozlovskaya, V.; Sukhishvili, S. A.; Fery, A. Soft Matter 2006, 2 (11), 966–972. (33) Lulevich, V. V.; Andrienko, D.; Vinogradova, O. I. J. Chem. Phys. 2004, 120(8), 3822–3826. (34) Lulevich, V. V.; Radtchenko, I. L.; Sukhorukov, G. B.; Vinogradova, O. I. Macromolecules 2003, 36(8), 2832–2837. (35) Lulevich, V. V.; Radtchenko, I. L.; Sukhorukov, G. B.; Vinogradova, O. I. J. Phys. Chem. B 2003, 107(12), 2735–2740. (36) Delorme, N.; Dubois, M.; Garnier, S.; Laschewsky, A.; Weinkamer, R.; Zemb, T.; Fery, A. J. Phys. Chem. B 2006, 110(4), 1752–1758. (37) Schoeler, B.; Delorme, N.; Doench, I.; Sukhorukov, G. B.; Fery, A.; Glinel, K. Biomacromolecules 2006, 7(6), 2065–2071. (38) Portigliatti, M.; Koutsos, V.; Hervet, H.; Leger, L. Langmuir 2000, 16(16), 6374–6376. (39) Graveland-Bikker, J. F.; Schaap, I. A. T.; Schmidt, C. F.; De Kruif, C. G. Nano Lett. 2006, 6(4), 616–621. (40) Colin, A. G.; David, J. B.; Sheena, E. R.; Neil, H. T. Appl. Phys. Lett. 2008, 92(23), 233902. (41) Ivanovska, I. L.; De Pablo, P. J.; Ibarra, B.; Sgalari, G.; MacKintosh, F. C.; Carrascosa, J. L.; Schmidt, C. F.; Wuite, G. J. L. Proc. Natl. Acad. Sci. U.S.A. 2004, 101(20), 7600–7605. (42) Lulevich, V.; Zink, T.; Chen, H.-Y.; Liu, F.-T.; Liu, G.-Y. Langmuir 2006, 22(19), 8151–8155.

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nanometer scale and has the capacity to probe their elastic and adhesive properties.43,44 In this Article, we present a systematic study of the overall mechanical properties of MSs at both low and high forces and deformations using nanocompression testing with tipless cantilevers, a technique based on AFM force-distance curves methodology. We have used in situ optical microscopy to guide the AFM tipless cantilevers on top of individual MSs to perform the testing and also to measure their sizes. Employing a variety of different spring constant cantilevers, the mechanical properties of the MSs were probed with high force resolution and sensitivity and in a systematic way for a wide range of MS sizes and shell thicknesses.

Experimental Section Materials. We investigated the biSphere microspheres (Point Biomedical Corp, San Carlos, CA) with sizes (diameters) ranging between ∼2 and ∼6 μm. These UCAs consist of a thin shell of the stiff structural biodegradable polymer polylactide (to encapsulate the microbubble) surrounded by a cross-linked albumin outer layer to make the MS harmless to the human body. They encapsulate nitrogen gas at atmospheric pressure. The Young’s modulus of the material constituting the structural rigid shell has a value in the range of approximately 1.42.8 GPa. The outer layer thickness is in the range of ∼10 nm and is constant across the MS size range. The thickness of the structural polymer shell is in the range of ∼30 nm for a MS with 4 μm diameter and varies approximately linearly with MS size; that is, the ratio of the shell thickness to the MS diameter is substantially constant for all MS sizes.45 This introduces an increase of the MS shell thickness with increasing MS diameter of ∼7.5 nm/μm. BiSphere is very stable and performs only very small shell oscillations in the presence of ultrasound; normally, the acoustic response occurs when gas escapes due to a crack on its shell followed by a free bubble oscillation in the vicinity of the shell.24 This behavior classifies it in the hard shelled microbubbles compared to the lipid shelled ones that are soft.3 Sample Preparation. The AFM experiments require the MSs to be immobilized on a solid substrate, and for this reason they were attached to Petri dishes coated with poly-L-lysine (Sigma-Aldrich Co. St. Louis, MO). The coating was formed by using a 1:10 v/v solution of poly-L-lysine in ultrapure deionized water (resistivity 18.2 MΩ 3 cm). As the MSs are gas-filled, they are buoyant and float at the water-air interface of a water suspension. Their attachment to a solid surface was achieved by bringing floating MSs into contact with a coated Petri dish inverted on top of a MS suspension. All AFM measurements were conducted with MSs attached to the bottom of Petri dishes within deionized water. Atomic Force Microscopy (AFM). In order to investigate the nanomechanical properties of the MSs, we used an AFM which is dedicated to precise and well-controlled force measurements: the Molecular Force Probe (MFP) 1D (Asylum Research, Santa Barbara, CA), mounted on an inverted optical microscope, Nikon TE2000U (Nikon UK Limited, Surrey, U. K.). This setup allows the placement of the MS below the cantilever before the force measurements (Figure 1a and b) and in situ MS sizing (Figure 1c). A digital camera (Orca-ER C4742-80, Hamamatsu Photonics, Hamamatsu, Japan) attached on the optical microscope was used to capture optical (43) Sboros, V.; Glynos, E.; Pye, S. D.; Moran, C. M.; Butler, M.; Ross, J.; McDicken, W. N.; Koutsos, V. Ultrasonics 2007, 46, 349–354. (44) Sboros, V.; Glynos, E.; Pye, S. D.; Moran, C. M.; Butler, M.; Ross, J.; Short, R.; McDicken, W. N.; Koutsos, V. Ultrasound Med. Biol. 2006, 32(4), 579– 585. (45) Ottoboni, T. B.; Tickner, E. G.; Short, R. E.; Yamamoto, R. K. Hollow Microspheres with Controlled Fragility for Medical Use. U.S. Patent US 6776761 B2, 2004.

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Figure 1. (a) Optical microscopy image of the cantilever placed in the vicinity of a MS and (b) the cantilever placed on top of the MS. (c) Typical optical microscopy image showing three microbubbles within the field of view, captured for the determination of their sizes. White scale bar at the right bottom of the images corresponds to 15 μm. images which were processed by image analysis software, IPLab v3.7 (BD Bioscience Bioimaging, Rockville, MD), in the PC that was connected to the camera. We measured the MS diameter (d) with an accuracy ∼0.5 μm using a 60 objective lens. The MSs were compressed with force-distance curves using tipless cantilevers, NSC-12 and CSC-12 (MikroMacsh, Talin, Estonia), with aluminum back coating and typical spring constant (kc) ranging from 0.08 to 2.3 N/m. We applied the force as close to the poles of the MS as possible. Before the onset of measurements, the spring constant of each cantilever was determined using a routine available within the instrument. It is based on a method proposed by Hutter and Bechhoefer46 and involves the (46) Hutter, J. L.; Bechhoefer, J. Rev. Sci. Instrum. 1993, 64(7), 1868–1873.

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Glynos et al. measurement of the intensity of the thermal noise.47 The raw data obtained from the MFP-1D represented the deflection Δ of the cantilever versus the position of the piezocrystal scanner during loading (trace or approach) and unloading (retrace or retraction). The force f is the product of Δ with kc of the respective cantilever. The cantilever sensitivity during the measurements was determined from a reference curve on a hard surface before and after the MS experiments to ensure reproducibility of the measurements. The separation, s, between the cantilever and the sample surface was calculated as the difference between the position of the piezocrystal scanner and the deflection of the cantilever measured on a hard surface. The onset (zero) of separation was taken at the point of the first measurable force (point of contact of the tip with the MS). Separations after the point of contact (i.e., larger than zero) are equal to the MS deformation due to compression. Each force-distance curve was transformed to a force-deformation (fs) curve; all force curves presented and discussed in this study are fs curves. Experimental tests on filled (not hollow) silica microspheres (MO-SCI Specialty Products, L.L.C, Rolla, MO 65401) and on glass slides were performed in water in order to check for possible effects/artifacts of our experiment geometry (tipless cantilever on a spherical object). In this case, hard spheres (made of silica) were used in order to avoid deformation during contact and have a direct comparison with the AFM data on a flat hard surface. Relatively stiff cantilevers (kc = 1.26 N/m) were used to reach high applied forces on both colloidal particles and flat surfaces. The curves had the same behavior for both spheres and flat surfaces. No detectable movements of the spherical particles were observed during compression. The small hysteresis (of the order of few nm) observed between the trace (loading) and retrace (unloading) can be attributed to small deviations from the vertical motion of the order of few nm and to related frictional forces; in addition, since all measurements have been performed in water, hydrodynamic effects cannot be excluded. For the measurements reported here, the cantilever started its motion several hundreds of nanometers away from the sample; the total piezocrystal scan size (approach and retraction) was kept at ∼6-7 μm for all measurements, and the force curves were taken at a frequency of 1 Hz, and thus, the probe speed was kept constant at ∼6-7 μm/s. We did not observe any significant variations in the slope of force curves with the probe frequency within the range of ∼0.3-3 Hz. More than two thousand force curves on more than 150 biSphere MSs were acquired. A large number of force curves were acquired for each MS in order to assess the reproducibility and variability of the measurements. An important aspect of the quantitative analysis of all the force-deformation (fs) curves is a linear region near the beginning of the curve. We associated the slope of this part of the curve with an effective MS shell stiffness keff. The minimum number of required measurements to acquire a reliable average value of the effective shell stiffness on each MS was determined by plotting the slope average of the linear part of N consecutive curves against the number of force curves N. A typical example is given in Figure 2. It was concluded consistently that the errors associated with the measurements were random and after the sixth curve the average slope converged to the slope distribution average. When stiffer cantilevers were used and after a number of consecutive force curves, there were cases where the characteristics of the fs curves changed, indicating, as it will be presented and extensively discussed later on, a permanent deformation of the MS shell. In these cases, more than 10 compressions were performed and the effective stiffness of the MS shell was determined from the first curves, and before the initiation of the MS permanent deformation. Many of the acquired forcedeformation curves on MSs exhibited a wave pattern in both trace and retrace. The oscillation amplitude varied across the (47) Butt, H.-J.; Jaschke, M. Nanotechnology 1995, 6(1), 1–7.

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Figure 2. Average slope of the linear part of N force curves on a MS against the number of force curves N.

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Figure 4. Typical force curves using a cantilever of kc = 0.12 N/m taken on two different MSs with sizes d = 4.8 μm (red circles) and d = 2.5 μm (blue squares).

Figure 3. Frequency of MS oscillation versus the effective MS shell stiffness. curve (from some A˚ to a few nm), and its frequency increased with the keff (Figure 3), suggesting vibration of the microsphere shell. The characteristics of the vibration depended on the probe speed indicating a hydrodynamics origin as the cantilever moves in the water-filled Petri dish.

Results Figure 4 shows two typical force curves obtained using a cantilever with kc = 0.12 N/m. The plots reveal an initial nonlinear region of gradually higher force up to about 10 nm followed by a more extended linear part. Similar behavior was observed for cantilevers with spring constants of 0.08 and 0.45 N/m (results not shown). The force-separation curves on the same MS were reproduced consistently with consecutive compressions, and no force curve variability on the same MS was observed. For cantilevers with higher spring constants, kc of 0.61 and 1.14 N/m, we explored different force-deformation regimes and two different types of force curves were observed. The first type of behavior can be seen in Figure 5a. The curves start again with a soft repulsive force part followed by a linear region which develops into a nonlinear behavior with progressively lower slope. Figure 5b shows the second type of behavior: in the beginning of the curve, the behavior is similar, and there is a soft repulsive force part followed by a linear region which gradually becomes nonlinear with a progressively lower slope which develops into an “inflection point’’ with almost zero slope or in some cases even negative slope, indicating an instability (we will refer to this area of the curve as instability area). After a certain deformation, the slope obtains again constant positive values similar to the initial linear part. For the case of kc = 0.61 N/m, 12% of the tested MSs exhibited an instability, while in the case of kc = 1.14 N/m the Langmuir 2009, 25(13), 7514–7522

Figure 5. (a) Typical force curves (with kc = 1.14 N/m) taken on

three MSs with sizes d = 2.6 μm (black squares), d = 3.5 μm (red circles), and d = 4.1 μm (blue triangles). (b) Typical force curves (with kc = 1.14 N/m) exhibiting an instability area on five MSs with d = 3.2 μm (dark yellow diamonds), d = 3.1 μm (black squares), d = 4.0 μm (red circles), d = 4.9 μm (blue up triangles), and d = 5.5 μm (green down triangles).

percentage of the MSs which underwent an instability was increased to 54%. For kc = 0.61 N/m, all the force curves on a particular MS, with or without an instability area, show no variability, remaining essentially the same with consecutive compressions, indicating that no permanent deformation was inflicted on the MSs which would have altered the measured MS properties and introduce variability in consecutive force curves. For kc = 1.14 N/m, most of the force curves (64%) show no variability (Figure 6a) but there were several cases (36%, Figure 6b) where the characteristics of the force curve changed after consecutive loadings. This variability appeared only within a subset of the MSs exhibiting instability, and it is associated with a pronounced hysteresis DOI: 10.1021/la900317d

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Figure 6. (a) Sequence of measurements on a MS of d = 5.5 μm (kc =1.14 N/m) and (b) sequence of curves an a MS of d = 3.8 μm (kc = 1.14 N/m).

between the trace and retrace; a typical hysteretic behavior is shown in Figure 7c. Nevertheless, the presence of an instability is not always associated with a permanent deformation of the MS. For a cantilever with kc = 1.14 N/m, although 54% of the tested MSs exhibited an instability, only 67% of them showed variability at consecutive loadings (36% of all the MSs tested with this cantilever). In Figure 7, we present some typical force-relative deformation (ε = s/h) curves for both loading and unloading for three types of force curves. Figure 7a presents a force curve without an instability area for a MS which showed no variability on consecutive compressions. The loading and unloading exhibits relatively small hysteresis; this level of hysteresis of a few nanometers can be at least partly attributed to small deviations from vertical motion and the associated friction as it was observed also on solid surfaces. Figure 7b presents a force curve with an instability area for a MS which showed no variability on consecutive loadings. We also observe small hysteresis. Finally, Figure 7c presents a force curve with an instability area for a MS which showed variable force curves on consecutive compressions. In this case, the loading and unloading exhibit significant hysteresis: it is clear that the retrace curve takes a path very different from the trace and drops to zero at the separation associated with the instability in the trace, indicating an extensive permanent deformation of the MS. The linear part extends up to about ε ≈ 2, 1, and 1.5; that is, in all cases the linear part lasts for deformations of the order of the shell thickness. For all MSs tested using a cantilever with an even higher spring constant, kc = 2.3 N/m, we observed compression curves with instability areas and wide variability (Figure 8). There were cases when the force associated with the instability area was decreasing with consecutively acquired curves and cases where, after a number of acquired curves, the shape of the curve changed dramatically, becoming eventually invariable, indicating a permanently deformed stable state (Figure 8b). 7518 DOI: 10.1021/la900317d

Figure 7. Force-relative deformation trace (loading) and retrace

(unloading) for a MS (a) without instability (d = 4.7 μm, h ≈ 35 nm, keff = 2.2 N/m), (b) with an instability area without variability (d = 4.9 μm, h ≈ 37 nm, keff = 3.0 N/m) on consecutive nanocompression tests, and (c) with an instability area and variability on consecutive tests (d = 4.1 μm, h ≈ 31 nm, keff = 7.7 N/m) for kc = 1.14 N/m. The relative deformation is defined as the ratio of the actual deformation, s, of the spherical shell over the thickness, h, of the shell.

Table 1 provides statistics on the presence of instability and variability with consecutive loadings on the same MS for the different cantilevers used in our study. The number of the MSs exhibiting instability and variability increased with the cantilever spring constant. As we have seen, all compression curves included a linear part that can be associated with an effective shell stiffness keff for each MS. Figure 9 shows the plot of the keff against the MS diameter for all cantilevers used in this study. The value of keff is generally a function of both the MS size and the cantilever spring constant. For the most compliant cantilever (kc = 0.08 N/m), the measured effective MS shell stiffness was about 1.25 N/m and appeared independent of its size. For the cantilever with kc = 0.12 N/m, we found a gentle increase of keff with the MS size. For kc = 0.45 N/m, the MS shells became stiffer and their effective stiffness decreased with their size. For all cantilevers with kc g 0.61 N/m, the MS shells appeared with higher effective stiffness independent of the Langmuir 2009, 25(13), 7514–7522

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stiffness, keff, on MS diameter, d, converges to the same functional relationship (decreasing function) for all cantilevers with kc g 0.61 N/m. The fact that, for a specific MS size, the effective shell stiffness reaches a characteristic and constant (for this size) value keff as the cantilever spring constant increases can be clearly seen in Figure 10. In order to examine the nature of the instability area observed in the force-separation curves, we performed a series of additional tests, an example of which is shown in Figure 11. On a MS where no buckling event was observed when the cantilever was placed properly on top of the MS (Figure 11a), we moved the cantilever to a position shown in Figure 11b. In this position, the MS is at the very edge of the cantilever. The MS is compressed from only one side, and we expect a concentration of stress at the edge. We expect this geometry to lead easily to a buckling type of instability. Indeed, the force curve showed an instability area. We repeated this test several times and for different MSs, and a similar behavior was observed.

Figure 8. (a) Typical force curves taken with a cantilever with kc = 2.3 N/m on four different MSs with sizes d = 3.0 μm (black squares), d = 3.6 μm (red circles), d = 4.4 μm (blue triangles), and d = 4.9 μm (green triangles). (b) Series of force curves (kc = 2.3 N/m) on the same MS (d = 3.7 μm): the sequence of curves shows that the testing produced a permanent deformation. Table 1. Statistics of MS Mechanical Behaviora kc (N/m)

instability

variability

0.08 0% 0% 0.12 0% 0% 0.45 0% 0% 0.61 12% 0% 1.14 54% 36% (67% of MS exhibiting instability) 2.3 100% 100% a Percentages correspond to the whole MS population tested for each cantilever unless otherwise stated in parentheses.

Figure 9. Effective stiffness against the MS diameter for the different cantilevers used in this study. Open symbols in each case correspond to the MS with (at least one) instability.

cantilever spring constant and with a strong dependence on their size. In other words, the dependence of the effective MS shell Langmuir 2009, 25(13), 7514–7522

Discussion Our systematic study involves the mechanical response of the MS shell for a range of applied forces and deformations. Compliant cantilevers were used to probe the response of individual MSs to low forces with high accuracy and high force resolution. By employing cantilevers with low spring constant, that is, kc = 0.08 N/m and kc = 0.12 N/m, we probed the response of the MS for forces up to approximately 70 nN. The magnitude of the applied force on the MS was gradually increased by using stiffer cantilevers (kc = 0.45 N/m, kc = 0.61 N/m, kc = 1.14 N/m, and kc = 2.3 N/m), and the MSs were probed with forces up to approximately 150, 200, 400, and 800 nN, respectively. The discussion section has two parts. (i) Small deformations: we discuss the behavior of the MS for small deformations (of the order of the thin shell and much smaller than the MS diameter) where the relation of the applied force with the deformation of the MS shell was linear. (ii) Higher deformations: we focus on the area of the force-separation curve which departs from the linear behavior and leads to nonlinear behavior and instabilities. (i) Small Deformations. Using low-spring-constant cantilevers (i.e., kc e 0.12 N/m), we applied a maximum force and deformation of ∼70 nN and ∼50 nm, respectively, on individual MSs. The gentle repulsion observed and the associated low keff measured for such compliant cantilevers can be associated with the compression of the biocompatible hydrogel outer layer which was swollen and extended in aqueous conditions. Furthermore, in a previous work,44 we had measured the root-meansquare roughness Sp of the MS surface in water to be 85 nm and the roughness average Sa to be 64 nm; this type of roughness can be associated with the structural rigid inner shell. Due to the gentle progressive compression using compliant cantilevers, the initial increase of the contact area between the flat cantilever plane and the rough shell surface can also contribute to the force profile. In any case, the applied force was not high enough to bend the shell, and since we actually probed the outer softer and rougher parts of the thin wall, we acquired low effective shell stiffness values in the range of 1-2 N/m with no significant variation with the MS size. For the case of the cantilever with kc = 0.12 N/m, some MSs with larger sizes (about 5 μm) appeared slightly stiffer with keff around 2.3 N/m. For large MSs, similar keff values were measured when stiffer cantilevers were used; consequently, we conclude that using this cantilever (kc = 0.12 N/m) we started gently to bend the shell of the larger and overall more compliant MSs. DOI: 10.1021/la900317d

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Figure 10. Effective MS shell stiffness against the cantilever spring constant for MSs of different diameters. MSs of specific size are characterized by a single value of keff for sufficiently large values of kc.

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variations in the MS shell structural characteristics and possibly small differences in the loading geometry among different tests, for kc g 0.61 N/m, there is a clear overall functional relationship between the MS keff and size. Thin shell mechanics predicts a linear elasticity for the deformation of a homogeneous spherical shell as long as the displacements are smaller or of the order of the shell thickness.48 A linear part on the force curve for small deformations was observed (and used to estimate the elastic constants) in nanocompression experiments for several systems; polyelectrolyte multilayer microcapsules,27,29-31 thin virus shells,41 and hollow faceted polyhedrons formed from catanionic surfactant mixtures.36 Furthermore, Elsner and co-workers31 performed finite elements modeling to elucidate the force-deformation behavior of polyelectrolyte microcapsules compressed by AFM colloidal probes of large radii (several times larger than the microcapsules). They showed that the Reissner analytical solution49,50 was a reliable approximation for the force-deformation relationship of a thin spherical shell even if the load is not pointlike and the contact area is extensive. Reissner predicts the following relationship for the shell stiffness, k: 4 h2 k ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E 3ð1 -ν2 Þ R

ð1Þ

where ν is the Poisson ratio, E is the Young’s modulus of the shell material, R is the radius of the spherical shell, and h is the shell thickness. In our study, the shell stiffness k corresponds to keff measured with stiff cantilevers (kc g 0.61 N/m). The MS shell thickness is around 30 nm for a MS with diameter 4 μm and changes approximately linearly with the diameter size at 7.5 nm/μm, which introduces the following (approximate) correlation of h with R (= d/2): h ¼ 1:5  10 -2 R

ð2Þ

By substituting eq 2 in eq 1 and for ν = 0.42, we obtain k ¼ 5:73  10 -4 ER

Figure 11. Optical images of a tipless cantilever placed (a) on top of the MS and (b) at the very edge of the MS (the scale bar at the bottom right of each image corresponds to 15 μm).

For a cantilever with kc = 0.45 N/m, the MSs appeared stiffer. The keff was found to distinctly depend on the MS diameter, decreasing with size from 4.5 N/m for MSs with d = 3 μm down to 2 N/m for MSs with a size of d = 5 μm (Figure 9). Further increase in keff was measured for a cantilever with kc = 0.61 N/m, especially for small MSs, revealing clearly that keff is a decreasing function of MS size; values ranged from about 11 N/m for MSs with a size of 2.5 μm down to about 3 N/m for MSs with a size of 5.5 μm. Using even stiffer cantilevers, that is, kc = 1.14 and 2.3 N/m, the measured keff values did not change significantly. This indicates that cantilevers with kc g 0.61 N/m were stiff enough to apply large forces to deform the inner structural shell significantly (albeit still on the nanoscale). As it can be clearly seen in Figures 9 and 10, despite the dispersion of the measured keff values for MSs with similar size, indicating 7520 DOI: 10.1021/la900317d

ð3Þ

Equation 3 shows that, for E independent of the MS size (as one would expect from classical elasticity theory), the MS shell stiffness increases with the MS radius. This is in contradiction with our main experimental finding where the MS shell stiffness decreased with the MS size (or the MS shell thickness). However, if we relax the assumption for a constant Young’s modulus, that is, if we allow for a size-dependent E, we can use eqs 2 and 3 in combination with our measurements of k = k(R) to plot E as a function of h. This plot is depicted in Figure 12 and shows that E increases as the shell thickness decreases and approaches the nanometer scale; it varies from approximately 18 GPa for a MS with h ≈ 17 nm (d = 2.3 μm) to approximately 2 GPa for a MS with h ≈ 42 nm (d = 5.6 μm). Hence, thicker shells possess a Young’s modulus within the range of the corresponding value of the bulk macroscopic material (1.4-2.8 GPa), while thinner shells are characterized by a much higher E. This nonlinear and dramatic increase of the elastic modulus as the wall thickness tends to very (48) Landau, L. D.; Lifshitz, E. M. Theory of Elasticity (Course of Theoretical Physics), 3rd ed.; Butterworth-Heinemann: Oxford, 1997; Vol. 7. (49) Reissner, E. J. Math. Phys. 1946, 25, 279–300. (50) Reissner, E. J. Math. Phys. 1946, 25, 80–85.

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small values is very similar to what has been previously measured using a resonant-contact atomic force microscopy technique in other nanosystems such as polypyrrole nanotubes and metallic nanowires.51-53 In addition, a recent study of the elastic moduli of hollow thin-shell poly(methyl methacrylate) (PMMA) capsules by Brillouin light scattering also found values exceeding the bulk PMMA values.54 The increase of the elastic constants at the nanoscale can be attributed to morphological and molecular restructuring and ordering that can occur due to confinement at thinner shells such as orientation of the polymer chains at tangential to the surface directions and decreased levels of defects (such as nanoporosity). Moreover, it has to be noted that surface effects can have a profound influence on materials properties as their dimensions approach the nanoscale; surface tension53 and/or gradient elasticity55 contributions cannot be excluded as a possible explanation of the increased effective elastic modulus when the surface to volume ratio increases. (ii) Higher Deformations. Above a certain deformation, the linear relationship with the force ceased and in some cases instability areas were observed. As it is clear from Table 1, the percentage of the MSs where at least one instability area was observed increased with the spring constant of the used cantilevers, reaching a value of 100% for kc = 2.3 N/m. The instabilities tended to appear at a higher frequency as the applied force increased. Figure 13 shows that the applied force which was necessary for an instability to occur increased with the effective stiffness of the MS. For stiff MS shells, that is, keff > 7 N/m, the applied force for the instability can be higher than 400 nN, reaching a value of 700 nN for the stiffest MSs tested. Figure 14 shows the normalized frequency count of MSs with and without an instability area in the force curve for the two cantilevers where a mixed behavior was observed. As the cantilever spring constant increases, the population of MSs with an instability area increases and the peak of the distribution moves to smaller (stiffer) MSs. It is clear that there is a correlation between the applied forces, the MS shell stiffness, and the onset of instability. We conclude that the instability is more probable to occur for higher forces and for more compliant shells; moreover, it appeared consistently when we compressed the MSs using the very edge of the cantilever (Figure 11). All these observations indicate strongly that its origin is a buckling effect of the MS shell. Our observations are consistent with other studies on spherical shell systems, which showed that for deformations of the order of or slightly higher than the shell thickness the linear dependency was lost and further deformation led to buckling instabilities.29,31,56-58 Similar behavior is followed by macroscopic thin shell spheres57 such as ping-pong balls59 in which the actual shape changes can be easily observed: the linear part of (51) Cuenot, S.; Demoustier-Champagne, S.; Nysten, B. Phys. Rev. Lett. 2000, 85(8), 1690–1693. (52) Cuenot, S.; Fretigny, C.; Demoustier-Champagne, S.; Nysten, B. J. Appl. Phys. 2003, 93(9), 5650–5655. (53) Cuenot, S.; Fretigny,, C.; Demoustier-Champagne, S.; Nysten, B. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69(16), 165410. (54) Still, T.; Sainidou, R.; Retsch, M.; Jonas, U.; Spahn, P.; Hellmann, G. P.; Fytas, G. Nano Lett. 2008, 8(10), 3194–3199. (55) Altan, B. S.; Evensen, H. A.; Aifantis, E. C. Mech. Res. Commun. 1996, 23 (1), 35–40. (56) Tamura, K.; Komura, S.; Kato, T. J. Phys.: Condens. Matter 2004, 16(39), L421–L428. (57) Fery, A.; Weinkamer, R. Polymer 2007, 48(25), 7221–7235. (58) Helfer, E.; Harlepp, S.; Bourdieu, L.; Robert, J.; MacKintosh, F. C.; Chatenay, D. Phys. Rev. Lett. 2001, 87(8), 088103. (59) Pauchard, L.; Rica, S. Philos. Mag. B 1998, 78(2), 225–233.

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Figure 12. Young’s modulus of MS structural shell versus MS shell thickness.

Figure 13. Force at the instability area against the effective stiffness of the MSs.

Figure 14. Normalized frequency count of MSs exhibiting/not exhibiting instability for two cantilevers.

the force-deformation curve is the result of a flat contact between the plane and the spherical shell, while the instability is the result of the development of a trough (reversed curvature), that is, buckling and contact along a circular ridge. The formation of high curvature folds is favored energetically, since in this way thin shells confine the energetically “high-cost” shell stretching to the fold region while the “low-cost” shell bending dominates elsewhere.60 The buckling instability seems to be a universal property of both macroscale and nanoscale thin spherical shells in agreement with continuum theory where no absolute length scale enters the theoretical description.57 However, the dramatic increase of the elastic modulus we report in this Article is a distinct property of nanoscale ultrathin spherical shells. (60) Lobkovsky, A.; Gentges, S.; Li, H.; Morse, D.; Witten, T. A. Science 1995, 270(5241), 1482–1485.

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The force curves with instability appeared reproducibly for applied forces up to about 200 nN. In this case, the trace and the retrace curves followed a similar path, indicating a reversible deformation of the MS shell. For higher forces, consecutive curves on the same MS showed increased variability and the instability did not appear reproducibly; the trace and retrace followed significantly different paths indicating, an irreversible (plastic) deformation of the MS shell which suggests that the elastic limit has been exceeded possibly at the fold region of the buckling area. A permanent damage of this kind resulted in a “memory” effect and led in the buckling event to appear earlier in the following curves and for a lower applied force (see Figure 6b). The instability area at a very high exerted force (>400 nN) is associated with extended irreversible buckling which caused severe permanent deformation of the MS. In some cases after a number of consecutive force-separation curves, the shape changed dramatically and then remained the same (Figure 8b). This can be connected with a severe deformation and even a cracking of the MS shell. The scattering in the shell stiffness values for MSs of similar size (even when measured with the same cantilever) cannot be attributed solely to variations in the loading geometry, since multiple different tests on the same MS exhibit much smaller dispersion of values. Therefore, our measurements indicate variations in the structural characteristics of the shell and possibly dispersion in its thickness. To our knowledge, this is the first direct measurement of both the dispersion of the shell stiffness values and the shell stiffness dependence on the MS size for an ultrasound contrast agent MB system. Furthermore, we have shown that there is a MS size-dependence also in the probability for the appearance of instabilities at higher deformation/force which ultimately can lead to cracking and rupture. Our findings compare well with observations of sonic-induced cracking and subsequent MB gas release of hard-shelled (Quantison and biSphere) UCAs using high speed optical microphotography.10,24 The UCAs did not behave homogeneously, which was attributed to the statistical presence of tiny shell flaws10 in the MS population and also to the increased rigidity as their size decreased;24 Our study verifies the statistical variations in the mechanical/structural characteristics of the shell by direct mechanical measurements and furthermore reveals for the first time an important size-dependent Young’s modulus effect which can be the underlying physical cause for the size-dependent variations in hard-shelled UCAs sonic rupture. It has to be noted that MSs with a constant ratio of shell thickness to MS diameter are expected to exhibit a similar resistance to acoustically induced stresses and all MSs (independently of their size) should rupture at a specific threshold pressure.45 However, this is not verified in ultrasound experiments,10,24 and our measurements show for the first time that the underlying reason can be the shell material Young’s modulus increase as the shell thickness approaches to nanometer-scale dimensions. We also show that it is incorrect to assume no variation in the structural/mechanical characteristics of the MS shell as usually done for theoretical modeling

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purposes,8,19-21,23 which may be one of the reasons for the lack of predictive value of these models. In addition, in these models, the dependence of shell mechanical characteristics on size is usually not based on direct experimental measurements, increasing the number of unknown parameters, which adds to the uncertainty of the theoretical calculations. The direct mechanical measurements on individual MSs using AFM force curves can aid and guide the design of novel types of UCAs with improved and controlled properties for both acoustic and drug/ gene delivery applications.

Conclusions The mechanical properties of a population of hollow thin-shell polymer microspheres with substantially similar ratio of shell thickness to MS diameter were investigated using AFM forcedistance curves in water employing tipless cantilevers with a wide range of spring constants. The force-deformation curves exhibited a linear part which was associated with an effective stiffness of the MS shell. Generally, the measured MS shell effective stiffness values depended on the cantilever spring constant and MS size. The MS shell effective stiffness obtained by relatively compliant cantilevers (kc e 0.12 N/m) was associated with the outer soft layer and the initial increase of the contact area, since the applied forces were not high enough to bend the shell. Using cantilevers with kc g 0.61 N/m, the forces were high enough to mechanically probe the inner structural polylactide shell. The MS shell stiffness converged to kc-independent values and to a clear functional relationship with the MS diameter. Applying a simple model for the deformability of the MS thin shell, its Young’s modulus of the shell material was estimated and found to be of the order of the macroscopic value at a shell thickness of ∼42 nm (d = 5.6 μm) but increased continuously when the MS shell thickness decreased down to ∼17 nm (d = 2.3 μm). Furthermore, for higher applied forces, we observed instability areas in the force curves which were associated with buckling events of the thin shell as the deformation increased. The buckling transitions were reversible for relatively moderate forces while at higher forces acquired an irreversible character due to localized plastic deformation of the thin shell. Acknowledgment. We thank Michael Zaiser and Padraig Looney for fruitful discussions. Special thanks to Bob Short and Tom Ottoboni (Point Biomedical Corporation, San Carlos, CA) for support and for providing valuable information and guidance throughout this work. The work was funded by the Engineering and Physical Sciences Research Council (EPSRC), U.K. (Project Grant GR/T21639/01). E.G. acknowledges financial support from EPSRC DTA and the Institute for Materials and Processes, School of Engineering, The University of Edinburgh. V.K. acknowledges partial financial support from RTN/DEFINO, Contract No. HPRN-CT2002-00198. C.M.M. acknowledges funding from the British Heart Foundation.

Langmuir 2009, 25(13), 7514–7522