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Nanoscale Compression of Polymer Microspheres by Atomic Force Microscopy Susheng Tan,* Robert L. Sherman Jr., and Warren T. Ford* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078 Received February 16, 2004. In Final Form: May 27, 2004 Atomic force microscopy (AFM) was employed to probe the mechanical properties of surface-charged polystyrene microspheres with 1-12 mol% of vinylbenzyl(trimethyl)ammonium chloride (VBTA) units. On the basis of Hertz’s theory of contact mechanics, compressive moduli between 1 and 2 GPa were measured by the analysis of force-displacement curves captured on the particles via the force-volume technique. The deformation of the top of the polystyrene particles by the AFM tip was used to calculate the surface modulus. The compressive moduli are slightly less than the moduli of polystyrene bulk materials. The modulus of the polystyrene microspheres increases with an increase of the VBTA content.
Introduction The deformation of spherical particles under an external force is important because polymer microspheres are found ubiquitously in the food, pharmaceutical, coating, and chemical industries. When polymer latexes are cast onto a surface, they form a continuous film during water evaporation and annealing. Film quality depends on the capillary and interfacial forces and the viscoelastic properties of the latex particles. At the nanometer scale, polymers may have properties different from those of bulk materials. Understanding the properties of individual particles such as interfacial forces and deformation will aid in control of the final structure and mechanical properties of the latex film. Experimental studies and theoretical analysis of film formation and deformation behavior of such microscopic spheres over a wide range of environmental conditions have been reported.1-3 In 1882, Hertz developed a theoretical model for the deformation of surfaces around a contact point for elastic spheres with smooth, rigid surfaces when an external force was applied between them.4,5 Hertz’s model is based on perfect elastic assumptions: there is a normally loaded contact between the bodies; the material behaves as a linear elastic body; the radius of contact area is small compared with the radius of the sphere; there is no friction contact between the surfaces, resulting in the transfer of only normal stresses between the contacting surfaces. Extensive work has verified the success of this model at a micrometer scale, though there are restrictions that the indentation must be monotonically increasing, and the model is valid only to about 10% strain for elastic materials.6-11 *
[email protected] (S.T.);
[email protected] (W.T.F.)
(1) Keddie, J. L. Mater. Sci. Eng. R 1997, 21, 101. (2) Steward, P. A.; Hearn, J.; Wilkinson, M. C. Adv. Colloid Interface Sci. 2000, 86, 195. (3) Sundberg, D. C.; Durant, Y. G. Polym. React. Eng. 2003, 11, 379. (4) Hertz, H. J. Reine Angew. Math. 1882, 92, 156. (5) Shull, K. R. Mater. Sci. Eng. R 2002, 36, 1. (6) Liu, K. K.; Williams, D. R.; Briscoe, B. J. J. Phys. D.: Appl. Phys. 1998, 31, 294. (7) Vakarelski, I. U.; Toritani, A.; Nakayama, M.; Higashitani, K. Langmuir 2001, 17, 4739. (8) Vakarelski, I. U.; Toritani, A.; Nakayama, M.; Higashitani, K. Langmuir 2003, 19, 110. (9) Briscoe, B. J.; Liu, K. K.; Williams, D. R. J. Colloid Interface Sci. 1998, 200, 256. (10) Lu, W.; Tung, K.; Hung, S.; Shiau, J.; Hwang, K. Powder Technol. 2001, 116, 1.
Since its invention,12 the atomic force microscope (AFM) has been employed extensively to measure the force between two surfaces in controlled environments.13-17 In most AFM force measurements, a cantilever tip or a colloidal particle glued on the cantilever end has a curved surface, and the substrate fixed on the piezo system has a flat surface. Attractive and repulsive electrostatic forces and attractive van der Waals forces between solid surfaces are characterized by the force-distance method with the AFM. Biggs and Spinks reported the first deformation measurements by AFM by pushing a 20 µm polystyrene sphere attached on the cantilever beam against a mica surface.18 To obtain a measurable deformation, they applied the load up to the elastic limit of the polystyrene particle. A significant plastic deformation likely occurred, which complicated the interpretation of their data. Nevertheless, the particle deformation is of particular interest because it gives a technique for measurement of the surface energy and for understanding the mechanism of surface contact. Tsukruk and co-workers measured the elastic properties of individual polyester dendrimer molecules and small aggregates by means of the forcevolume procedure.19,20 Separated dendrimers or very small aggregates had lower elastic moduli than the bigger aggregates with long-chain clusters. They suggested that lateral constraints caused by densely packed neighboring molecules increased the stiffness of the dentritic molecules in long-chain clusters. In the present work, we evaluated the deformation of individual polystyrene microspheres on a mica surface by measuring the force-displacement curves with an AFM cantilever tip. Hertz’s model for contact mechanics was (11) Liu, K. K.; Williams, D. R.; Briscoe, B. J. Phys. Rev. E 1996, 54, 6673. (12) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56. (13) Ho, C. C.; Khew, M. C. ACS Symp. Ser. 2001, 801, 239. (14) Noy, A.; Frisbie, C. D.; Razsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943. (15) Radmacher, M.; Fritz, M.; Cleveland, J. P.; Waltes, D. A.; Hansma, P. K. Langmuir 1994, 10, 3809. (16) Considine, R. F.; Hayes, R. A.; Horn, R. G. Langmuir 1999, 15, 1657. (17) Feiler, A.; Plunkett, M. A.; Rutland, M. W. Langmuir 2003, 19, 4173. (18) Biggs, S.; Sprinks, G. J. Adhes. Sci. Technol. 1998, 12, 461. (19) Tsukruk, V. V.; Shulha, H.; Zhai, X. Appl. Phys. Lett. 2003, 82, 907. (20) Shulha, H.; Zhai, X.; Tsukruk, V. V. Macromolecules 2003, 36, 2825.
10.1021/la049597c CCC: $27.50 © 2004 American Chemical Society Published on Web 07/21/2004
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Langmuir, Vol. 20, No. 17, 2004
Tan et al.
Table 1. Properties of Latexes N+Cl-
mol% monomera
mol% N+Clpolymerb
0.36 3.8 8.5 12.2
0.32 3.3 7.3 11.3
diameter (nm) AFMc TEM 182 ( 11 242 ( 7 295 ( 3 247 ( 4
196 264 314 271
a Calculated from moles of initial monomers. b Calculated from Cl- titration. c Standard deviations of the AFM height images of more than 50 microspheres.
employed to analyze the relationship between the load and the particle deformation and to calculate compressive moduli of the polystyrene. The deformation caused by the AFM tip on the nanometer scale is elastic, and the calculated values of the moduli are slightly less than the tensile modulus of bulk polystyrene.
Figure 1. Schematic representation of a coordinate system for the elastic particle compression. (a) The AFM tip is just brought in contact with the spherical particle, and no deformation occurs. R1 and R2 are the radii of the AFM tip and the polymer sphere. (b) The elastic particle is deformed by the AFM tip indentation.
Experimental Section
TGG01, MikroMasch). Freshly cleaved mica was used as a hard nondeformable substrate for the sensitivity calibration of the photodetector. The average diameter of more than 50 polystyrene spheres was determined from at least five 10 µm × 10 µm height images using the particle size analysis program bundled with the Nanoscope IIIa software. The experimental deflection vs height curves were transformed into load vs indentation depth curves and fit to the theoretical model with commercial software (Origin 6.0, http://www.OriginLabs.com). Mean values of the compressive moduli were obtained by fitting at least 12 approaching indentation curves obtained from different polymer microparticles. To investigate the mechanical properties of individual nanoparticles at the right location, force-volume images consisting of 32 × 32 force curves were recorded in parallel with topographic images.24 Only a few individually separated polymer microspheres were in the 3µm × 3µm or 1µm × 1µm imaging region. The sample vertical displacement, z, was controlled to obtain the same maximum vertical deflection, d, and thus the same maximum applied force for each force curve. To ensure that the deformation of polymer spheres was elastic, only a small trigthreshold of AFM tip deflection was selected. Force maps reflecting, qualitatively, the sample mechnical properties were generated by taking a slice of the force curve array at a given sample height in the contact region of the curves.
Materials. All reagents were purchased from Aldrich and Fisher. Monomers were purified by passing them down basic alumina columns before their use. Water was purified on a Barnstead 3 column e-pure system to a conductivity of
