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Langmuir 2009, 25, 3108-3114
Determination of Cross-Link Density in Ion-Irradiated Polystyrene Surfaces from Rippling Yogesh Karade,‡ Sascha A. Pihan,† Wilhelm H. Brünger,§ Andreas Dietzel,‡ Rüdiger Berger,† and Karlheinz Graf*,†,| Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany, EindhoVen UniVersity of Technology, Den Dolech 2, 5600 MB EindhoVen, The Netherlands, and Fraunhofer Institute for Silicon Technology, Fraunhoferstrasse 1, D-25524 Itzehoe, Germany ReceiVed July 22, 2008. ReVised Manuscript ReceiVed October 23, 2008 The irradiation of polymer surfaces with ion beams leads to pronounced chemical and physical modifications when the ions are scattered at the atoms in the polymer chain. In this way, different products of decomposition occur. Here we show that by changing the ion fluence and the mass of the ion the local mechanical properties as Young’s modulus of a polystyrene surface layer can be tailored. By annealing prestretched irradiated PS near the glass transition, surface rippling occurs in the irradiated areas only, which can be described with an elastic model. The moduli obtained from rippling periodicities and elastic model assumptions are in the range between 8 and 800 MPa at the glass transition and characterize the irradiated PS as rubberlike. From these values the network density and the molar mass of entanglement are quantified. The obtained network density equals the density of hydrogen vacancies generated through the scattered ions, as confirmed by simulations of the atomic scattering and displacement processes. The obtained molar mass of entanglement reveals that the PS locally was densely cross-linked. Our results show that even for nondiscrete layered polymer systems relevant polymer parameters can be derived from the well-known surface rippling without the need for costly chemical analysis.
Introduction Topologically structured polymer surfaces are utilized for directed cell growth,1,2 as stamps in charged printing,3 for highthroughput screening,4 and in integrated microfluidic systems.5 Micro- and nanovessels on polymer surfaces can be used to study physicochemical, medical, and biological processes and reactions.6 Beside conventional lithography techniques, significant progress has been reported on polymer surface structuring by nonconventional methods such as those provided by buckling instability.7-10 This type of surface structuring was suggested to be useful for diffraction gratings, for optical sensors, and for the roughening of textile fibers. Additionally, it was demonstrated to work as a testing platform to determine the mechanical properties of polymeric thin films without the need for expensive test equipment. * Corresponding author. E-mail:
[email protected]. ‡ Eindhoven University of Technology. † Max Planck Institute for Polymer Research. § Fraunhofer Institute for Silicon Technology. | Current address: University of Siegen, Physical Chemistry, AdolfReichwein-Str., D-57068 Siegen, Germany. (1) Detrait, E.; Lhoest, J.-B.; Knoops, B.; Bertrand, P.; van den Bosch de Aguilar, Ph. J. Neurosci. Methods 1998, 84, 193–204. (2) Hendrick, V.; Muniz, E.; Geuskens, G.; Werenne, J. Cytotechnology 2001, 36, 49–53. (3) Cao, T. B.; Xu, Q. B.; Winkleman, A.; Whitesides, G. M. Small 2005, 1, 1191–1195. (4) Senkan, S. M. Nature 1998, 394, 350–353. (5) Takano, N.; Doeswijk, L. M.; van den Boogaart, M. A. F.; Auerswald, J.; Knapp, H. F.; Dubochet, O.; Hessler, T.; Brugger, J. J. Micromech. Microeng. 2006, 16, 1606–1613. (6) Barton, J. E.; Odom, T. W. Nano Lett. 2004, 4, 1525–1528. (7) Bowden, N.; Huck, W. T. S.; Paul, K. E.; Whitesides, G. M. Appl. Phys. Lett. 1999, 75, 2557–2559. (8) Stafford, C. M.; Harrison, C.; Beers, K. L.; Karim, A.; Amis, E. J.; Vanlandingham, M. R.; Kim, H.-C.; Volksen, W.; Miller, R. D.; Simonyi, E. E. Nat. Mater. 2004, 3, 545–550. (9) Volynskii, A. L.; Bazhenov, S.; Lebedeva, O. V.; Bakeev, N. F. J. Mater. Sci. 2000, 35, 547–554. (10) Knittel, D.; Kesting, W.; Schollmeyer, E. Polym. Int. 1997, 43, 231–239.
The phenomena of buckling instability for an elastic surface can be explained as follows. If a compressive force parallel to the surface on the skin layer/bulk material composite exceeds a critical value, then ripples appear on the skin. The ripple periodicity depends on the material properties of the skin and the bulk material (their Poisson ratio and Young modulus) and the thickness of the skin but is independent of the applied stress and strain.11 The quantitative relationship between the measured ripple periodicity, Rp, induced by the buckling instability and the Young modulus of the buckled layer in the surface (Es) is given by12
Es ) 3Eb
( )
1 - ν2s Rp 1 - ν2 2πh b
3
(1)
where νb and Eb are the Poisson ratio and Young modulus of the bulk substrate and νs and h are the Poisson ratio and thickness of the rippled surface layer, respectively. The buckling instability phenomenon has been widely used in the development of complex patterns on different systems (e.g., thin metal film deposited on a polydimethylsiloxane (PDMS) substrate13 and plasma-treated PDMS film on untreated PDMS bulk14,15). The Young modulus of thin PS films deposited on PDMS substrates has been calculated by exploiting the relationship among the periodicities of the ripples on the thin PS films and the film thickness, the Poisson ratios of the film and PDMS, and the Young modulus of the PDMS.8,16 Recently, the rippling (11) Genzer, J.; Groenewold, J. Soft Matter 2006, 2, 310–323. (12) Brush, D. O.; Almroth, B. O. Buckling of Bars, Plates and Shells; McGrawHill: New York, 1975. (13) Bowden, N.; Brittain, S.; Evans, A. G.; Hutchinson, J. W.; Whitesides, G. M. Nature 1998, 393, 146–149. (14) Katzenberg, F. Macromol. Mater. Eng. 2001, 286, 26–29. (15) Katzenberg, F. Nanotechnology 2003, 14, 1019–1022. (16) Harrison, C.; Stafford, C. M.; Zhang, W. H.; Karim, A. Appl. Phys. Lett. 2004, 85, 4016–4018.
10.1021/la802363v CCC: $40.75 2009 American Chemical Society Published on Web 02/09/2009
Cross-Link Density in Polystyrene Surfaces
concept was used to determine the mechanical properties of a polyelectrolyte multilayer.17-19 Here, we explore the concept of buckling instability on polymer surface layers, which were locally irradiated by ions, to estimate their Young modulus. Understanding the mechanical properties of these locally cross-linked polymers is important because they find applications in improving the local roughness for improved adhesion20 or commercial water-treatment membranes.21 In addition to the local mechanical properties, we investigate how polymer structure parameters such as the cross-link density and the molar mass between the cross-links can be determined from ripple periodicities. In this way, we link the determination of the mechanical properties of polymeric thin films with that of the molecular properties of the network. Compared to similar approaches in the literature,22 our analysis shows that a uniform energy deposition along the ion path is not required to get an average cross-link density in the irradiated PS surface. Ion projection direct cross-linking (IPDC)23 was used to locally cross-link skin layers of stretched polymer substrates on the submicrometer scale.24 The ion projector allows a vertical irradiation of substrate surfaces with a lateral resolution down to 50 nm.25 In our experiments, we irradiated square-shaped areas with 32 µm side lengths within the substrate surface with a separation of 12 µm. The thickness of the cross-linked layers was controlled by using different ion species, viz., xenon (Xe+), argon (Ar+), and helium (He+). The cross-linking densities were varied by varying the ion fluence. After IPDC, annealing the polymer substrate above the glass-transition temperature, Tg, resulted in the relaxation of the orientated polymer chains in the non-cross-linked volumes. In the cross-linked layer, rippling occurred.
Experimental Section Fabrication of Polymer Substrates. Polystyrene (PS) powder (Mw ) 2.6 × 105 g mol-1, PDI ) 1.07) was synthesized in-house by anionic polymerization and annealed in a 60 mm × 10 mm pressing mold (PW 40 EH Paul-Otto Weber Maschinen and Apparatebau GmbH, Germany). Two Kepton foils of the same dimensions were placed on both sides of the mold cavity to avoid direct contact of the molten PS with the metal surfaces of the mold. In this way, smooth polymer surfaces with a root-mean-square (rms) roughness of ∼2 nm were obtained. The PS powder was annealed at 160 °C (Tg ≈ 100 °C) in air for 1 h. After that, the molten PS was pressed at 20 kN into substrates and then cooled to room temperature in 90 min. PS substrates with different thicknesses varying from 2 to 4 mm were obtained by varying the amount of the PS powder. Afterward, each substrate was fixed with a clamp in an extensometer (Instron 6022, Instron Deutschland GmbH, Germany) and heated to 100 °C, the glass-transition temperature of PS. After that, the PS substrate was clipped with a second clamp 3 cm below the first one and stretched at a constant speed of 0.5 mm min-1 to the desired stretching ratio of 200% () length of the substrate after stretching, divided by its original length in %). After being (17) Lu, C. H.; Dönch, I.; Nolte, M.; Fery, A. Chem. Mater. 2006, 18, 6204– 6210. (18) Lu, C. H.; Mohwald, H.; Fery, A. Soft Matter 2007, 3, 1530–1536. (19) Nolte, A. J.; Rubner, M. F.; Cohen, R. E. Macromolecules 2005, 38, 5367–5370. (20) Carbone, G.; Mangialardi, L. J. Mech. Phys. Solids 2004, 52, 1267–1287. (21) Chennamsetty, R.; Escobar, I.; Xu, X. L. Desalination 2006, 188, 203– 212. (22) Herden, V.; Klaumünzer, S.; Schnabel, W. Nucl. Instrum. Methods Phys. Res. B 1998, 146, 491–495. (23) Bu¨scher, K.; Berger, R.; Bru¨nger, W.; Graf, K. Microelectron. Eng. 2006, 83, 819–822. (24) Martinez-Pardo, M. E.; Cardoso, J.; Vazquez, H.; Aguilar, M.; Rickards, J.; Andrade, E. Nucl. Instrum. Methods Phys. Res. B 1997, 131, 219–225. (25) Bru¨nger, W. H.; Torkler, M.; Leung, K. N.; Lee, Y.; Williams, M. D.; Loeschner, H.; Stengl, G.; Fallmann, W.; Paschke, F.; Stangl, G.; Rangelow, I. W.; Hudek, P. Microelectron. Eng. 1999, 46, 477–480.
Langmuir, Vol. 25, No. 5, 2009 3109 stretched, the clamped substrate was slowly cooled in air to 50 °C in 2 h and then to room temperature within 1 min. Such a substrate was divided into smaller pieces of 10 mm × 6 to 7 mm. Here, only those pieces from the central areas of the stretched substrate were used. The rms roughness values for the substrates were ∼6.3 nm. Ion Beam Irradiation. The surfaces of the polymer substrates were modified by means of ion projection direct cross-linking within locally defined areas at a lateral resolution of less than 100 nm.26 A grid mask with an array of square-shaped openings of 250 µm × 250 µm was inserted into the beam. Ions passing through the mask openings were projected perpendicularly27 onto the target surface with a demagnification of approx. 8.3 at 73 keV. Thus, the stretched PS substrates were irradiated as an array of square-shaped areas of 32 µm × 32 µm each. Different ion species (He+, Ar+, and Xe+) were used. The ion current was kept constant with a Faraday cup within an error of ∼5%, and the ion fluence was varied from 1013 to 2.0 × 1015 ions cm-2 for exposure times between 5 s and about 34 min. Afterward, the irradiated PS substrates were annealed in vacuum (
