Nanoscale Indentation of Polymer and Composite Polymer−Silica

Langmuir 2007, 23, 2007-2014

2007

Nanoscale Indentation of Polymer and Composite Polymer-Silica Core-Shell Submicrometer Particles by Atomic Force Microscopy Silvia Armini,*,†,‡ Ivan U. Vakarelski,§ Caroline M. Whelan,† Karen Maex,†,‡ and Ko Higashitani§ IMEC, SPDT/ADRT DiVision, Kapeldreef 75, B-3001 LeuVen, Belgium, Department of Electrical Engineering, Katholieke UniVersiteit LeuVen, Kasteelpark Arenberg 1, B-3001 HeVerlee, Belgium, and Department of Chemical Engineering, Kyoto UniVersity-Katsura, Nishikyo-ku, Kyoto 615-8510, Japan ReceiVed August 1, 2006. In Final Form: NoVember 14, 2006 Atomic force microscopy was employed to probe the mechanical properties of surface-charged polymethylmethacrylate (PMMA)-based terpolymer and composite terpolymer core-silica shell particles in air and water media. The composite particles were achieved with two different approaches: using a silane coupling agent (composite A) or attractive electrostatic interactions (composite B) between the core and the shell. Young’s moduli (E) of 4.3 ( 0.7, 11.1 ( 1.7, and 8.4 ( 1.7 GPa were measured in air for the PMMA-based terpolymer, composite A, and composite B, respectively. In water, E decreases to 1.6 ( 0.2 GPa for the terpolymer; it shows a slight decrease to 8.0 ( 1.2 GPa for composite A, while it decreases to 2.9 ( 0.6 GPa for composite B. This trend is explained by considering a 50% swelling of the polymer in water confirmed by dynamic light scattering. Close agreement is found between the absolute values of elastic moduli determined by nanoindentation and known values for the corresponding bulk materials. The thickness of the silica coating affects the mechanical properties of composite A. In the case of composite B, because the silica shell consists of separate particles free to move in the longitudinal direction that do not individually deform when the entire composite deforms, the elastic properties of the composites are determined exclusively by the properties of the polymer core. These results provide a basis for tailoring the mechanical properties of polymer and composite particles in air and in solution, essential in the design of next-generation abrasive schemes for several technological applications.

Introduction In recent years, there has been an increasing interest in the design and fabrication of functional colloidal particles for application in catalysis, biotechnology, medicine, ecology, and other areas.1-4 In this respect, an important role is played by composite particles that consist of either organic or inorganic colloidal cores, coated with shells of different chemical composition.5 They are attractive from both a scientific and a technological point of view because their properties can be substantially different from those of the individual template core or shell materials.6 By tailoring the different component parts, it is possible to combine several advantageous properties in one structure.7 Our study focuses on composite structures comprising polymer particles coated by silica achieved by either creating chemical bonds using silane coupling agents or tuning the pH in order to form electrostatic attractive interactions between the core and the shell. The major advantage of the silica coating is that it can * Corresponding author. Phone: +32 (0) 16 28 86 17. Fax: +32 (0) 16 28 13 15. E-mail: [email protected]. † IMEC. ‡ Katholieke Universiteit Leuven. § Kyoto University-Katsura. (1) Zhang, S. W.; Zhou, S. X.; Weng, Y. M.; Wu, L. M. Langmuir 2005, 21, 2124. (2) Steigerwald, J.; Murarka, S.; Gutmann, R. Chemical-Mechanical Planarization of Microelectronic Materials; John Wiley & Sons: New York, 1997. (3) Singh, R. K.; Lee, S.-M.; Choi, K.-S.; Basim, G. B.; Choi, W.-S.; Moudgil, B. M.; Chen, Z. MRS Bull. 2002, 27 (10), 752-760. (4) Basim, G. B.; Brown, S.; Vakarelski, I.; Moudgil, B. J. Dispersion Sci. Technol. 2003, 24, 499-515. (5) Amalvy, J. I.; Percy, M. J.; Armes, S. P.; Leite, C. A. P.; Galembeck, F. Langmuir 2005, 21, 1175. (6) Caruso, F.; Caruso, R. A.; Mo¨hwald, H. Science 1998, 282, 1111. (7) Dudnik, V.; Sukhorukov, G. B.; Radtchenko, I. L.; Mo¨hwald, H. Macromolecules 2001, 34, 2329.

be easily modified creating specific interactions with the help of stabilizers, surfactants, and silane coupling agents.8 While the surface chemistry and structure of such colloids has been extensively studied, their mechanical properties, which at the nanometer scale may be different from those of bulk materials, deserve more attention. The deformation of spherical particles under an external force, the focus of this work, is interesting for their ubiquitous applications in the food, pharmaceutical, coating, chemical, and microelectronic industry. In the field of microelectronics, one of the major applications of submicrometer colloidal particles, as abrasives in a slurry chemical composition, is in the chemical mechanical polishing (CMP) process that is used to achieve planarization, i.e., smoothing the uneven topography of nonplanar thin films of metals/dielectrics. A CMP system, comprising a polishing pad, appropriate slurry, and a wafer surface, is influenced by many variables including tool process parameters, waferto-wafer variables, fluid dynamics, and slurry variables, such as hardness, roughness, and elastic modulus. In particular, the composite particles are aimed at improving the CMP process of softer materials such as Cu or dielectrics. Many advantages are expected from the elasticity of the polymer core, such as reduced mechanical damage, e.g., scratching, high polishing rate, and improved planarity. The soft polymer core behaves as a cushion preventing scratching by agglomerates and foreign material. The higher removal rate with respect to the small silica particles alone is attributed to an increased filling factor, due to the higher number of silica particles that interact with the polished surface.9 Furthermore, assisted by the spring-like effect (mechanical (8) Graf, C.; Vossen, D. L. J.; Imhof, A.; Van Blaaderen, A. Langmuir 2003, 19, 6693. (9) Yano, H.; Matsui, Y.; Minamihaba, G.; Kawahashi, N.; Hattori, M. Mater. Res. Soc. Symp. Proc. 2001, 671, M2.4.1.

10.1021/la062271e CCC: $37.00 © 2007 American Chemical Society Published on Web 01/06/2007

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Figure 1. Schematic of the CMP polishing mechanism with composite polymer core-silica shell particles.

compliance) coming from the elastic polymer core, the recessed Cu regime should be protected and polished at a lower removal rate, as sketched in Figure 1. On the convex area, higher pressure is applied and transferred through the elastic polymer material to the silica in the shell. As a result, the removal rate is higher at the convex area with respect to the concave region where pressure is not applied to the particles. The result of this mechanism is enhanced planarity. Therefore, the mechanical properties of the polymer core are of paramount importance in CMP. Better control of the process demands a detailed understanding of the role played by each of the relevant parameters and the subtle interactions between them.2-4 While considerable progress has been made in identifying the role of the slurry chemistry,10 evaluation of the role of mechanical abrasion is complicated by the difficulty in establishing the relationship between the mechanical characteristics, such as hardness (H) and elastic modulus (E), of the abrasives and of the films being planarized.11 In fact, while there has been significant progress in the quantification of the mechanical properties of glass12 and polymer13 coatings and surface layers in the nanometer regime using both AFM and nanoindentation,14 the issue of relevant mechanical properties of submicrometer-sized abrasives remains vague. In the past, Steiniz15 determined particle microhardness through microindentation, but the indented particle areas were of the order of 100 µm2 with a minimum indenter size of 20 µm2. Smaller particles could be sintered or pressed together for ease of indentation, but heating or stressing both polymeric and glass particles is expected to change their mechanical properties.15 Shorey et al.16 measured the nanohardness of magnetic and nonmagnetic abrasives used in magnetorheological finishing with a minimum average size of 5 µm. Their research has demonstrated the capability of using nanoindentation to characterize the hardness of micrometer-sized abrasives in forms that are actually used in polishing, such as particle agglomerates. Both the nanohardness and the elastic modulus can be calculated by means of the load-displacement curves. This requires that the particle be constrained from displacement resulting from the indenter’s loading from the top. For this reason, Shorey et al. rigidly fixed the magnetic particles to a glass substrate by embedding them in an epoxy matrix, while the nonmagnetic particles were cast in a polymer substrate. The hardness of smaller silicon spheres in a size range from 40 to 100 nm was measured by Gerberich et al. by squeezing individual particles between a (10) Steigerwald, J. M. A Fundamental Study of Chemical-Mechanical Polishing of Copper Thin Films. Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY, 1995. (11) Ramarajan, S.; Hariharaputhiran, M.; Her, Y. S.; Babu, S. V. Surf. Eng. 1999, 15 (4), 324. (12) Oliver, W. C.; Pharr, G. M. J. Mater. Res. 1992, 7 (6), 1564. (13) VanLandingham, M. R.; Villarubia, J. S.; Guthrie, W. F.; Meyers, G. F. Macromol. Symp. 2001, 167, 15. (14) Baker, S. P. Thin Solid Films 1997, 308-309, 289. (15) Steiniz, R. Met. Alloys 1943, 17, 1183. (16) Shorey, A. B.; Kwong, K. M.; Johnson, K. M.; Jacobs, S. D. Appl. Opt. 2000, 39 (28), 5194.

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diamond-tipped probe and sapphire.17 Furthermore, Babu et al. claim that for nanometer-sized particles, porosity may offer an indirect measure of hardness that can be correlated with the trend in removal rates observed in the CMP process.18 The ability of AFM to probe local surface topography, elastic properties, and adhesive forces makes this technique ideal for detecting nanomechanical properties in the case of both the polymer and the composite polymer core-silica shell particles investigated in our work.19-21 In this contribution we report the results of our experiments aimed at understanding the relation between the mechanical properties of polymer and composite particles and their size and composition in air, water, and different pH solutions. Experimental Section Materials. Methyl methacrylate (99% purity, Aldrich), methoxypolyethylene glycol methacrylate (average molecular weight 454, Aldrich), 4-vinylpyridine (95% purity, Aldrich), 2,2′-azobis (2-methylpropionamidine) dihydrochloride (97%, Sigma-Aldrich), (chloromethyl)trimethylsilane (98%, Aldrich), vinyltriethoxysilane (g98%, Fluka), and tetraethoxysilane (99+%, Alfa Aesar) were used as received. pH solutions were prepared using analytical grade HCl (37%, Air Products, Italy), NaOH (5 N, Merck KGaA, Germany), and NaCl (Wako Chemical Co.) as background electrolytes. The 30 nm (determined by SEARS titration) colloidal silica (Levasil 100/30%) used to make the composite particles was kindly provided by H. C. Starck. Preparation of Polymer Particles. Poly-(methylmethacrylate) (PMMA)-based spheres were synthesized by a surfactant-free radical free polymerization, using a modification of the procedure described by Nishimoto et al.22 Our polymerization conditions and characterization of the products are reported in detail elsewhere.23 A typical polymerization procedure was as follows: methyl methacrylate (MMA), methoxypolyethylene glycol methacrylate (MPEGMA), and ion-exchanged water (DIW) were charged in a round-bottomed three-necked flask. In order to prevent aggregation of the particles, a third comonomer, 4-vinylpyridine (4-ViPy), was added to the system. This solution was heated to 343 K while stirring. The azatype polymerization initiator 2,2′-azobis(2-methylpropionamidine) dihydrochloride (predissolved in water) (APDH) was then added to the reaction mixture. Before the process was initiated, i.e., monomer is added, the solution was purged with nitrogen, and the reaction was carried out under nitrogen gas atmosphere until the conversion exceeded 80-90%, as determined thermogravimetrically. Finally, the system was quenched in a cold water bath to discontinue the reaction. The final size of the polymer particles was 367 ( 15 nm in the dry state as determined by scanning electron microscopy (SEM) from an average of 100 measurements and 494 ( 59 nm in water as determined by dynamic light scattering (DLS) at a constant ionic strength (I) ) 10-3 M. For the SEM analysis, a drop of colloidal dispersion was dried in air. The dispersions resulting from the synthesis were centrifuged, the supernatant solutions discarded, and the particles resuspended in deionized water using ultrasonic treatment. This postsynthesis treatment process was repeated 3 times. (17) Gerberich, W. W.; Mook, W. M.; Perrey, C. R.; Carter, C. B.; Baskes, M. I.; Mukherjee, R.; Gidwani, A.; Heberlein, J.; McMurry, P. H.; Girshick, S. L. J. Mech. Phys. Solids 2003, 51, 979. (18) Babu, S. V.; Hariharaputhiran, M.; Ramarajan, S.; Her, Y. S.; Mayton M. M. The role of particulate properties in the CMP of copper. CMP-MIC Conference Proceedings, February 19-20, 1998; p 121. (19) Vanlandingham, M. R.; McKnight, S. H.; Palmese, G. R.; Ellings, J. R.; Huang, X.; Bogetti, T. A.; Eduljee, R. F.; Gillespie, J. W. J. Adhes. 1997, 64, 31. (20) Chizhik, S. A.; Huang, Z.; Gorbunov, V. V.; Myshkin, N. K.; Tsukruk, V. V. Langmuir 1998, 14, 2606. (21) Vakarelski, I. U.; Toritani, A.; Nakayama, M.; Higashitani, K. Langmuir 2003, 19, 110. (22) Nishimoto, K.; Hattori, M.; Kawahashi, N. U.S. Patent 6,582,761, November 21, 2000. (23) Armini, S.; Whelan, C. M.; Smet, M.; Eslava, S.; Maex, K. Polymer J. 2006, 38, 786.

Polymer-Silica Core-Shell Submicrometer Particles The treatment gave PMMA nanoparticles with positive surface charge (ζ-potential ∼ +4 mV, at a constant I ) 10-3 M). Preparation of Composite A: Silane Coupling Agent between Core and Shell. An aqueous dispersion containing the PMMAbased particles previously synthesized was charged in a roundbottomed three-necked flask, (chloromethyl)trimethylsilane was added, and the mixture was stirred at pH 2-3. This first step allowed us to obtain an aqueous dispersion of silanized PMMA-based particles that could be added to a colloidal silica particle suspension, to obtain a dispersion of particles in which silica particles had adhered to the polymer ones. To achieve this, an aqueous dispersion containing the colloidal silica particles (pH 8) was added to the former solution. The polymer particles are kept at low pH in order to increase the ionization degree of the amino groups at the surface. In this way, the colloid stability is increased. The silica particles are kept at basic pH for the same reason. Vinyltriethoxysilane was added to this aqueous dispersion, the mixture was stirred, and then tetraethoxysilane (TEOS) was added, heated to 333 K, stirred, and then cooled in a cold water bath. Thus, an aqueous dispersion containing composite particle A was obtained. The final pH after mixing is around neutrality. The final size of composite A particles, where the shell is made by 30 nm diameter silica particles, was 550 ( 27 nm as determined by SEM and 554 ( 67 nm as determined by DLS at a constant I ) 10-3 M. Preparation of Composite B: Electrostatic Attraction Forces between Core and Shell. An aqueous dispersion (pH 2) containing the PMMA-based particles was mixed with an aqueous dispersion containing the colloidal silica, to obtain an aqueous dispersion (pH 5). The mixture was stirred to obtain an aqueous dispersion containing composite B particles. In this synthesis, the pH of the final solution after mixing is crucial to obtain electrostatic attraction between the core and the shell. As seen in the previous case, the initial pH of the polymer is low for stability reasons, while the final pH is adjusted to 5 because at that pH the silica is negatively charged (isoelectric point (iep) around 2) and the terpolymer is positively charged (iep around 7) due to the presence of amino groups on the surface. The final size of composite B particles, where the shell is made by 30 nm diameter silica particles, was 440 ( 18 nm as determined by SEM and 567 ( 64 nm as determined by DLS at a constant I ) 10-3 M. From the measured sizes of the polymer and composite particles, it was possible to estimate the average number of silica nanoparticles in the shell of the composites. Under the assumption of continuous monolayer coverage, for 30 nm silica particles this number is 540. Characterization. Layers of particles were deposited on welldefined, atomically smooth, freshly cleaved mica substrates in air and in solution. The freshly cleaved mica substrate is negatively charged in water24 while the polymer particles are positively charged, due to the presence of surface amino groups from the initiator and the 4-ViPy. A drop of solution containing the polymer nanoparticles was slowly dried under vacuum, and a homogeneous layer of hexagonally packed spheres was formed, as shown in Figure 2. The size of the particles as determined by SEM, as an average of 100 measurements, was 367 ( 15 nm. The diameters of the polymer and composite particles measured by DLS were larger than those determined by SEM since the former technique determines the diameter of solvent-swollen particles, whereas the latter measures particles in the dry state. For the polymer particles we measured ca. 50% swelling in water, while for the composites A and B the percentage decreases to 35% and 38%, respectively. This swelling is acceptable considering the presence of hydrophilic groups such as 4-ViPy and MPEGMA in the terpolymer. The polymer particles stayed firmly attached to the surface in water, as revealed by SEM investigation after 10 min dipping. For the composite particles, the same technique was used. Even though both the mica- and the silica-covered composites are negatively charged, as revealed by electrophoretic light scattering, for the composite the negative value is an average, and the unavoidable (24) Ananthapadmanabhan, K. P.; Mao, G. Z.; Goddard, E. D.; Tirrell, M. Colloids Surf. 1991, 61, 167.

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Figure 2. (a) SEM image of the polymer particle layer deposited on a newly cleaved mica substrate. (b) AFM 3D image registered in tapping mode AFM in air. presence of even small uncovered areas of positively charged polymer core leads to an electrostatic attraction with the negative mica surface. Analysis of the composite particles’ behavior relies on knowledge of their coating quality. The SEM investigation shown in Figure 3, parts a and b, reveals the different morphology of composites A and B, respectively. In the presence of silane coupling agents, the silica particles on the surface of the polymer core are prone to form a continuous layer. The thin silica coating from TEOS hydrolysis can be distinguished bridging the silica particles in the shell. The electrostatically coated polymer cores show a more regular spherical shape due to a less dense coverage. Normal interaction force measurements were carried out with a Digital Instruments (DI, Santa Barbara, CA) Nanoscope III atomic force microscope. A fused silica liquid cell was used for measurements in water. All measurements were performed using commercial silicon rectangular cantilevers coated with Si3N4 (MikroMasch) with an approximate tip radius of 10 nm, measured after the AFM experiment by SEM. We selected the shortest cantilever with a normal spring constant of KN ) (10.0 ( 0.3) N/m, which was determined by the frequency method.25 The other cantilevers on the same chip were broken to minimize unwanted interactions with the sample. Before use, the cantilevers were plasma-treated for 1 min in an argonwater moisture atmosphere of 80 Pa, using a plasma kit (Kit-BP1, Samco Co., Kyoto) combined with a 1.0 W radio frequency plasma generator (ENI ACG 98, 13.6 MHz).26 Forces normal to the particle layers were measured following the method of Ducker et al.27 Small normal loads ensured an absence of permanent indentation marks and kept the deformations in the elastic regime. The experimental deflection versus height curves were transformed into load versus indentation depth curves. To evaluate the nanomechanical properties, we analyzed at least 10 force-distance curves measured on three to six randomly selected (25) Cleveland, J. P.; Manne, S.; Bocker, D.; Hansma, P. K. ReV. Sci. Instrum. 1993, 64, 403. (26) Donose, B. D.; Vakarelski, I. U.; Higashitani, K. Langmuir 2005, 21, 1834. (27) Ducker, W. A.; Senden, T. J.; Pasheley, R. M. Langmuir 1992, 8, 1831.

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Figure 4. Force curves showing the cantilever deflection vs piezo displacement for the terpolymer particles in air (a) and water (b). The insets show the same curves from the bare mica substrate.

particles, but the force curves analyses were always centered on the particle. The elastic properties of the particles in aqueous media were probed by scanning in water from a Millipore filtration system, with an internal specific resistance no less than 17.6 MΩ/cm and pH of 5.6 ( 0.5.26 In water the capillary forces, originating in ambient pressure from the formation of a liquid meniscus between probing tip and sample, were not present. Furthermore, when the speed of the piezo was varied in the range of 0.1-10 µm/s, no difference was observed, which allowed us to interpret the data in terms of pure elastic response (no viscoelasticity effects).

piezo displacement for the terpolymer particles in air (a) and in water (b). The insets show the same curves on the bare mica substrate. It is evident that in the case of mica, the slope of the deflection versus sample height curve was taken as a reference because it is an infinitely stiff surface compared to the cantilever stiffness. Therefore, this slope was used to calibrate the sensitivity of the position-sensitive photodiode, i.e., to convert the voltage into cantilever vertical deflection with the assumption that the tip follows the sample displacement.31 On the softer terpolymer surface, the tip indented the sample surface and the cantilever deflection was smaller than the sample vertical displacement, leading to z deflection versus z displacement curves with a slope lower than in the case of mica. The difference between the sample height or cantilever deflection that would be measured on a hard surface and the deflection measured on a soft surface is equal to the indentation depth of the tip into the surface, δ

Results and Discussion

δ)z-d

Figure 3. SEM image of (a) composite A, and (b) composite B (inset: composite B after 30 min of dipping in a solution at pH 3).

Data Processing: Force versus Indentation Curves. To quantitatively assess the elasticity of the polymer and composite particles, the force curves were converted into force versus indentation curves. A brief description is given below. The detailed procedure to obtain AFM force curves is given elsewhere.27-30 A mica plate was attached to the piezo system that moved vertically with a constant scan rate of 1 Hz. The cantilever deflection was detected by the voltage change of the split photodiode onto which the laser beam reflected at the rear of the cantilever was focused. The deflection was then converted into the interaction force F between surfaces, using the spring constant of the cantilever, KN, using Hooke’s law

F ) K Nd

(1)

The force curves in Figure 4 show the cantilever deflection versus (28) Vakarelski, I. U.; Toritani, A.; Nakayama, M.; Higashitani, K. Langmuir 2001, 17, 4739. (29) Touhami, A.; Nysten, B.; Dufreˆne, Y. F. Langmuir 2003, 19, 4539. (30) Tan, S.; Sherman, R. L.; Ford, W. T. Langmuir 2004, 20, 7015.

(2)

Taking into account the deflection offset value, d0, measured for the cantilever away from the sample surface, eq 1 becomes

F ) KN(d - d0)

(3)

Similarly, taking into account the height offset z0 where the tip first contacts the sample surface, eq 2 becomes

δ ) (z - z0) - (d - d0)

(4)

In Figure 4a, during the approach phase of the tip to the surface (A) there is no contact between the tip and the sample. Only at point B does the tip jump into contact with the sample surface due to attractive van der Waals and electrostatic forces.24 The cantilever deflects further under increasing force at the linear part of the force curve between B and C. At C the maximum load is reached. From C to B the piezo scan retracts; the tip stays in contact with the surface even in the absence of applied load due (31) D’Costa, N. P.; Hoh, J. H. ReV. Sci. Instrum. 1995, 66, 5096.

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to capillary forces present in the high-humidity atmosphere. This adhesion force disappears in water. The maximum adhesive force is reached in D, corresponding to a negative deflection of the cantilever compared with the deflection in B. The cantilever then breaks free from the surface and returns to its starting deflection (A). Modeling Tip-Particle Contact. Figure 5, parts a and b, shows a schematic representation of polymer spheres compressed between an AFM tip and a rigid substrate by an applied normal external load F. To quantitatively extract values of Young’s modulus from the force-indentation curves, we applied the classical Hertzian contact models from the continuum mechanics of contacts.32,33 Adhesion or long-range forces are not considered in the Hertzian theory; therefore, the contact area between nonconforming elastic solids falls to zero when the load is removed.34,35 By the repetition of force-distance measurements at different locations, we tested the reproducibility of local measurements. Measurements taken not exactly on top of the particles or when the particles moved during indentation resulting in atypical force curves were ignored in our analysis. The reproducibility observed in the indentation experiment is a strong indication that we remained in the limit of the elastic deformation of the particles. We estimated a standard deviation for E of about 20% for the polymer and 30% for the composites. Hence, plastic deformation theories36,37 are not included in the data analysis. Furthermore, forces due to the van der Waals attraction and electrostatic repulsion were not detected in the approaching force curve and their contributions were regarded as negligible compared with the force due to particle deformation. Hertzian models describe the indentation of the nondeformable silicon nitride tip (E1 ) 130-160 GPa, ν1 ) 0.27)38,39 into the sample surface. The tip shape can generally be modeled by two geometries: a conical or a paraboloid indenter is considered.29 The load versus indentation depth becomes

Fcone ) 2/π tan R E*δ2

(5)

Fparaboloid ) 4/3E*R*1/2δ3/2

(6)

where R is the half-opening angle of the conical tip (value given by the manufacturer ) 15°), R* ) R1R2/(R1 + R2), where R1 and R2 are, respectively, the radius of curvature of the spherical or paraboloid indenter and of the indented particles, and 1/E* ) (1 - ν12)/E1 + (1 - ν22)/E2, where E1 and E2 are the surface elastic modulus and ν1 and ν2 are the Poisson ratios of the tip and of the sample, respectively. Because the Poisson ratios of the PMMA-based terpolymer and the composites are not known, the Poisson ratio of bulk PMMA (ν2 ) 0.38)40 was used in the calculations. From eqs 5 and 6, if a quasi-quadratic relation is observed between F and δ, the conical model should be applied, while if the relation is close to a δ3/2 variation, the spherical or paraboloid model should be used. The latter model resulted in (32) Hertz, H. J. Reine Angew. Math. 1882, 92, 156. (33) Sneddon, I. N. Int. J. Eng. Sci. 1965, 3, 47. (34) Johnson, K. L. Contact Mechanics; Cambridge University Press: Cambridge, 1985. (35) Note: Johnson, Kendal, and Roberts considered in a continuum model (JKR model) the aspect of adhesion in the elastic contact regime. (a) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. A 1971, 324, 301. By considering a long-range potential outside the contact zone and thus avoiding the edge infinities, the DMT (Derjaguin-Muller-Toporov) was developed. (b) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314. (36) Maugis, D.; Pollock, H. M. Acta Metall. 1984, 32, 1323. (37) Biggs, S.; Spinks, G. J. Adhes. Sci. Technol. 1998, 12 (5), 461. (38) Yaralioglu, G. G.; Degertekin, F. L.; Crozier, K. B.; Quate, C. F. J. Appl. Phys. 2000, 87, 7491. (39) Kracke, B.; Damaschke, B. Appl. Phys Lett. 2000, 77, 361. (40) Lorriot, T. Eng. Fract. Mech. 2000, 65, 703.

Figure 5. Schematic drawing for relative positions of the tip and the particle before (a) and after (b) the load is applied. In (a) the AFM tip is 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, respectively. (b) The elastic particle is deformed by the AFM tip indentation. The modulus of the sample can be evaluated from the slope of the loading region of the curve.

good fitting of the experimental data for polymer and composite particles in air and water. In Figure 6, the fitting for the F versus δ curves for the PMMA-based terpolymer in air and water are shown. The fitting for a conical geometry of the indenter is shown for comparison. For the systems considered here, we assume Etip . Epolymer/composite and, therefore, E ) Epolymer/composite. Therefore, under the assumptions discussed above, the deformation of the particle is

δ3 ) 9F2(R1 + R2)(1 - ν22)2/16R1R2E22

(7)

The compressive modulus is

E2 ) [3F(1 - ν22)/4δ3/2][(R1 + R2)/R1R2]1/2

(8)

Hertzian models are accurate for relevantly small values of d or when δ , R1, R2. Alternatively, we can treat the data extracted from the force curves with Sneddon’s equation for a parabolic indenter,41 which can be a better approximation for larger values of δ.

E2 )

∆zdefl,i,i-1 (1 - ν22)KN xδ∆δi,i-1 2xR1β 1

where β ) Acros/A, Acros is the cross-sectional area at the indentation depth δ from the apex, A is the area at the apex, β is equal to 2 for elastic deformation of a sphere,42 and i and i-1 refer to the adjacent tip displacements. Air versus Water and Polymer Particles versus Composites. In Figure 7, the force versus indentation depth curves in air (a) and water (b) are shown for PMMA-based terpolymer particles (1), composite A (2), composite B (3), and the bare mica substrate (4). A qualitative trend for the hardness and elastic modulus of the particles is already revealed. Applying the same load, the indentation depths increase from the mica substrate to the relatively soft polymer. In both air and water, the mechanical properties of the particles follow the same trend. We find that the difference between the curves for composites A and B is not significant and falls within the spread of the experimental data estimated from the difference between five force curves registered in different locations on the sample. Therefore, in air the contribution of the silica shell to the mechanical properties of both composites is similar. This is not observed in water, where the different percentage of swelling of the composites (22% and 29% for composites A and B, respectively) results in a lower E for composite B. (41) Tsukruk, V. V.; Everson, M.; Lander, L.; Brittain, W. Langmuir 1996, 12, 3905. (42) Stierman, I. Y. Contact Problems in Elastic Theory; Gostex-isdat: Leningrad, 1952.

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Figure 6. Typical force vs indentation depth curves for the PMMAbased terpolymer in air (a) and water (b). The curves were fitted with the Hertz model (solid line ) cone indenter; dashed line ) paraboloid indenter).

In Figure 8, we compared the Hertzian and Sneddon’s approaches to extract from the force curves the elastic modulus of the polymer particles in air at different penetration depths and we achieved similar results: E ) 4.3 ( 0.8 GPa using Hertzian and E ) 2.4 ( 0.5 GPa using Sneddon’s approach. A similar analysis done by Chizhik et al.20 has shown that both approaches give consistent and reliable results for the elastic modulus calculation. For further calculations we selected the Hertzian model, which is relatively simple, gives reliable results, and does not require additional assumptions. The E values were calculated for a force range between 0.5 and 1.3 µN. The data in Figure 8 show that the modulus does not depend on δ which also means that the elastic deformation was reversible. Therefore, we safely assumed a constant value of E in the experimental curve fitting. Results for the different systems studied are presented in Table 1 and are in good agreement with the Young’s modulus measured for bulk materials in air. From our measurements, for the terpolymer particles we found E ) 4.3 GPa in air. For comparison, Briscoe et al., using the contact compliance method43 for the PMMA system, reported an E value of about 4 GPa. We also compared the values of Young’s modulus achieved for the composites (11.1 and 10.3 GPa, respectively, for composites A and B) with the values of 10-16 GPa reported in the literature44 for PMMA reinforced with colloidal silica (in the size range of 0.04-15 µm with filler concentrations in the range of 33-78 wt %). Nevertheless, the AFM technique measures the elastic properties of the materials at the nanometer scale, and this makes it extremely sensitive to any phase (43) Briscoe, B. J.; Fiori, L.; Pelillo, E. J. Phys. D: Appl. Phys. 1998, 31, 2395. (44) Cannon, M. L. Composite Resins. In Encyclopaedia of Dental DeVices and Instrumentation; Webster, J. G., Ed.; Wiley: New York, 1988.

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Figure 7. Force vs indentation depth curves in air (a) and water (b) for PMMA-based terpolymer particles (1), composite B (2), composite A (3), and the bare mica substrate (4).

Figure 8. Compressive modulus vs deformation for the terpolymer particles in air. Two different elastic models to calculate E were evaluated (Sneddon’s model, solid squares; Hertz model, open squares). The bar demonstrates the range of elastic bulk modulus variation for the specific material.

separation. The composite particles in the present article are heterogeneous for the AFM. Therefore, the comparison of E for silica-reinforced polymer materials, for which the AFM does not give reproducible results,45 and that calculated by AFM for the composite core-shell particles may not be appropriate. Because the silica shells consist of separate particles and do not individually deform when the entire composite deforms, as evident in Figure 1, the elastic properties of the composites are determined by the properties of the polymer core. When the tip approaches the (45) Mammeri, F.; Rozes, L.; Le Bourhis, E.; Sanchez, C. J. Eur. Ceram. Soc. 2006, 26 (3), 267.

Polymer-Silica Core-Shell Submicrometer Particles

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Table 1. Compressive Modulus for Polymer and Composites in Air, Water, and Different pH Solutions Calculated by Applying the Hertz Theorya E (GPa) sample

sizeSEM (nm)

sizeDLS (nm)

swelling %

air

water

pH 3

pH 9

pH 12

polymer composite A composite Aa composite B composite Ba

367 ( 15 453 ( 35 453 ( 35 440 ( 25 440 ( 25

550 ( 60 554 ( 70 554 ( 70 567 ( 68 567 ( 68

50 35 35 38 38

4.3 ( 0.7 11.1 ( 1.7 9.1 ( 1.4 10.3 ( 1.5 8.4 ( 1.7

1.6 ( 0.2 8.0 ( 1.2 6.5 ( 1.0 3.6 ( 0.5 2.9 ( 0.6

0.5 ( 0.1 5.3 ( 0.8 4.4 ( 0.7 2.0 ( 0.3 1.6 ( 0.3

1.3 ( 0.1 6.4 ( 1.0 5.3 ( 0.8 5.5 ( 0.8 4.5 ( 0.9

2.8 ( 0.3 5.3 ( 0.8 4.4 ( 0.7 5.5 ( 0.8 4.5 ( 0.9

a

E value for R1 ) radius of the silica particle in the shell.

composite particle it touches and pushes a hard silica sphere without penetration at this point. When the tip transfers the force to the silica particle it is the latter that penetrates into the polymer core. This mechanism should be taken into account in the calculation of E since the size of the indenter is now larger than the tip radius. With the use of the radius of the silica, the calculated values for E are lower. The difference in E between the two composites can be attributed to the presence of a continuous silica layer in composite A. In this case we may assume that it is the tip that penetrates into the silica layer. For both composites, the values calculated for E with R1 ) 10 nm and R1 ) 30 nm are reported in Table 1. The E estimated for the PMMA-based terpolymer in air is in the same order of magnitude as the modulus reported by other authors for polystyrene measured in air by the same technique and compared with bulk measurements.20 In this respect, we should mention the average values of compressive moduli from 1 to 2 GPa reported by Tan et al. for polystyrene extracted from the force-displacement curves captured from single particles via the time-consuming force-volume technique.30 Influence of pH. The size and calculated elastic modulus for the polymer and composite particles are reported in Table 1. The values refer to measurements in air, water, and pH 3, 9, and 12. The concentration of NaCl as a background electrolyte was 10-3 M. The amino groups on the surface of the polymer particles have been confirmed by several characterization techniques such as conductometric titration, Fourier transform infrared spectroscopy, and electrophoretic light scattering.23 They have been attributed mainly to fragments arising from dissociation of the aza-initiator. Also, the methoxypolyethylene glycol chains contribute to impart hydrophilicity to the terpolymer that results in considerable swelling in solution. The swelling behavior is strongly pH-dependent due to the ionization/deionization of the amino groups. Binks et al. studied nanocomposite poly(4vinylpyridine)-based microgel particles. They found that the particles became increasingly cationic upon lowering the pH of the aqueous dispersion and, more importantly, they also became much more hydrophilic and swollen with water. At around pH 3.4 (which corresponds approximately to the pKa value of the poly(4-vinylpyridine) chains) the diameter increases dramatically with decreasing pH (from 250 nm at pH 8.8 to 630 nm at pH 2.7).46 Dynamic light scattering sizing technique allowed for the quantification of the swelling of the terpolymer at different pH. At pH 3 the swelling percentage is about 75%. At low pH, less than 9, the amino groups are protonated to the NH3+ form. The pH value in water, for example, ensures the protonation of more than 90% of the amino groups.47 The polymer swells due to the electrostatic repulsion between charged groups, ion hydration, and the osmotic pressure exerted by mobile counterions. The (46) Binks, B. P.; Murakami, R.; Armes, S. P.; Fujii, S. Langmuir 2006, 22, 2050. (47) Dejugnat, C.; Sukhorukov, G. B. Langmuir 2004, 20, 7265.

Table 2. Compressive Modulus for Composite B with Different Silica Shell Thicknesses Calculated by Applying the Hertz Theorya E (GPa)a

E (GPa)

composite B silica shell thickness (nm)

air

water

air

water

15 30 45 85

3.9 ( 0.6 10.3 ( 1.5 8.2 ( 1.2 12.2 ( 1.8

1.9 ( 0.3 3.6 ( 0.5 2.2 ( 0.3 12.4 ( 1.9

4.5 ( 0.7 8.4 ( 1.7 5.7 ( 0.9 6.0 ( 0.9

2.2 ( 0.3 2.9 ( 0.6 1.5 ( 0.2 6.0 ( 0.9

a

E value for R1 ) radius of the silica particle in the shell.

degree of swelling in an aqueous medium is a function of two counteracting forces, the hydrophilic force due to the ionization and the attractive hydrophobic force between alkyl groups.48 The global decrease in elastic modulus with increased swelling was experimentally confirmed since the polymer particles show an increase in E with pH. Even if we consider that E may also depend on reorganization of the different parts of the terpolymer in solution, the most reasonable explanation for this phenomenon is that there is a direct proportionality between the E of the swollen polymer and the volume ratio of unswollen to swollen polymer. Furthermore, the presence of water molecules inside the particles leads to a decrease in the value of E.49 It is more complex to interpret the trend in the value of E as a function of pH for the composites. Due to the coating with a thin continuous shell of silica, composite A is stable and the value of E is not affected by pH variations. Composite B shows a smaller E value at lower pH. Since pH 3 is close to the isoelectric point of silica, a likely explanation is the occurrence of a nonhomogeneous silica coating of the polymer core. This hypothesis has been confirmed by SEM analysis of composite B after dipping in a solution at pH 3, as evident from the inset in Figure 3. Influence of Silica Shell Thickness. From the data presented in Table 2, the effect of the diameter of the silica particles forming the shell (from 15 to 85 nm) on E for composite B in air and water is shown. If we consider as a size of the indenter the size of the tip, the calculated Young’s modulus shows a linear dependence on the silica coating thickness in air, while in water it is constant for silica diameters of 15 and 45 nm and it increases dramatically for 85 nm. This behavior could be related to the effect of the swelling and softening of the polymer core. In this case, a correlation between mechanical properties, size, and efficiency of the coating and strength of the adhesion between the core and the shell would have been experimentally found.50 (48) Cai, Q. Y.; Grimes, C. A. Sens. Actuators, B 2000, 71, 112. (49) Johnson, B.; Niedermaier, D. J.; Crone, W. C.; Moorthy, J.; Beebe, D. Mechanical Properties of a pH Sensitive Hydrogel. Session on Biologically Inspired Synthesis and Properties; Proceedings of the SEM Annual Conference on Experimental Mechanics, Milwaukee, WI, June 10-12, 2002. (50) Nguyen, T. 28th Annual Meeting of The Adhesion Society Proceedings, Mobile, AL, February 13-16, 2005; p 205.

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Nevertheless, if we consider as the size of the indenter the size of the silica particles in the shell, in air the new calculated E values for 15, 30, 45, and 85 nm silica diameter are approximately 4.5, 8.4, 5.7, and 6.0 GPa, respectively. The values are in reasonable agreement considering a 20-30% experimental error for the composites with silica 15, 45, and 85 nm and a 30-40% error for the 30 nm silica shell. In this case, as already mentioned, the elastic properties of the composites appear to be determined exclusively by the properties of the polymer core. This is especially true for composite B with different coatings in water where the calculated E values are close to the value found for the terpolymer core in water. It was not possible to measure E for the composites with a silica diameter of 85 nm due to the lack of adhesion between the composite and the mica substrate in water. In order to have an idea of the uncertainty of the results, a more detailed discussion on the systematic error is necessary, and our estimates are reasonably close to those reported for this technique by other authors.51 If we sum all the systematic errors, 20% for the piezo calibration, 20% for the KN calibration, 25% for the apparent variability in the data sets, we have a combined error of around 50%. This is a conservative estimate, and the actual accuracy can be much better (20%). Regardless, our main interest was to detect relative changes in mechanical properties rather than focusing on absolute values.

Conclusions By combining optimal cantilever parameters and experimental conditions, we have obtained reliable force-indentation data appropriate for further contact mechanics analysis for both polymer and composite polymer core-silica shell particles with and without silane coupling agents at the interface between core and shell (composite A and B, respectively). Both Sneddon’s and Hertzian models of elastic contact gave consistent results in the range of indentation depths up to 80 nm, as demonstrated by the reproducibility of the experimental data. The simpler Hertzian theory was applied to fit the experimental force-indentation curves and to extract the elastic modulus values for polymer and composites in air, water, pH solutions, and to investigate the effect of the silica shell thickness. In water medium, the polymer particles soften, which is attributed to the swelling of the PMMA-based terpolymer containing hydrophilic groups such as amino and methoxypoly(51) Radmacher, M.; Fritz, M.; Cleveland, J. P.; Walters, D. A.; Hansma, P. K. Langmuir 1994, 10, 3809.

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ethylene glycol and the penetration of the solvent molecules into the entangled network of chains. It can also be concluded that as the polymer particles dry under ambient conditions, most of the ionic repeat units recede to the interior of the particles and are replaced on the surface by nonpolar methacrylate repeat units. Thus, the surface in air has a modulus similar to that of bulk PMMA. The silica coating enhances the mechanical properties of composite A in air and water. This effect is questionable in the case of composite B. The main difference between the composites is the presence of a continuous silica layer reinforcing the shell structure for composite A. In the case of composite B, because the silica shell consists of separate particles free to move in the longitudinal direction that do not individually deform when the entire composite deforms, the elastic properties of the composites are determined by the properties of the polymer core. When the tip approaches the composite particle it touches and pushes a hard silica sphere without penetration at this point. When the tip transfers the force to the silica particle it is the latter than penetrates into the polymer core. This mechanism should be taken into account in the calculation of the E value since the size of the indenter is now larger than the tip radius. The difference in E between composite A and B in air falls within the spread of the experimental data. Changes in pH affect the swelling of the PMMA related to the observed increase in E with increasing pH. The value of E for composite A is independent of pH, whereas for composite B softening at pH 3 can be explained by the presence of uncovered areas on the polymer core and a further reorganization of the terpolymer making interpretation of the results more complex. For composite B in air and water, if we consider the silica particle radius as the size of the indenter, E does not depend on the diameter of the silica in the coating. It is determined exclusively by the elastic properties of the polymer core. This study provides a basis for tailoring the mechanical properties of polymer and composite particles in air and solution, essential in the design of next-generation abrasive schemes for several technological applications. Acknowledgment. The author is grateful to all the members of the Professor Higashitani’s Laboratory in the Department of Chemical Engineering of Kyoto University for their help and fruitful discussions. Particular thanks to B. C. Donose, E. Taran, and T. Yamamoto. This work has been carried out within IMEC’s Advanced Interconnect Industrial Affiliation Program. LA062271E