pubs.acs.org/Langmuir © 2009 American Chemical Society
Packing Efficiency of Small Silica Particles on Large Latex Particles: A Facile Route to Colloidal Nanocomposites Jennifer A. Balmer, Steven P. Armes,* and Patrick W. Fowler* Dainton Building, Department of Chemistry, The University of Sheffield, Sheffield, Brook Hill, S3 7HF United Kingdom
Tibor Tarnai and Zsolt Gaspar :: Department of Structural Mechanics, Budapest University of Technology and Economics, Muegyetem rakpart 3, Budapest H-1521, Hungary
Kenneth A. Murray and Neal S. J. Williams AkzoNobel, Wexham Road, Slough, Berkshire, SL2 5DS United Kingdom Received December 17, 2008. Revised Manuscript Received February 10, 2009 The adsorption of small silica particles onto large sterically stabilized poly(2-vinylpyridine) [P2VP] latex particles in aqueous solution is assessed as a potential route to nanocomposite particles with a “core-shell” morphology. Geometric considerations allow the packing efficiency, P, to be related to the number of adsorbed silica particles per latex particle, N. Making no assumptions about the packing structure, this approach leads to a theoretical estimate for P of 86 ( 4%. Experimentally, dynamic light scattering is used to obtain a plot of hydrodynamic diameter against N, which indicates the conditions required for monolayer coverage of the latex by the silica particles. Transmission electron microscopy confirmed that, at approximately monolayer coverage, calcination of these nanocomposite particles led to the formation of well-defined hollow silica shells. This is interpreted as strong evidence for a contiguous monolayer of silica particles surrounding the latex cores. On this basis, an experimental value for P of 69 ( 4% was estimated for nanocomposite particles prepared by the heteroflocculation of a 20 nm silica sol with near-monodisperse P2VP latexes of either 463 or 616 nm diameter at approximately pH 10. X-ray photoelectron spectroscopy was used to quantify the extent of latex surface coverage by the silica particles. This technique gave good agreement with the silica packing efficiencies estimated from calcination studies.
Introduction Organic-inorganic colloidal nanocomposites, in particular those incorporating ultrafine silica particles, have attracted much interest over the past 15 years.1 There are at least four possible nanocomposite particle morphologies,2 namely, “raspberry”, “currant bun”, and two types of “core-shell” morphologies (see Figure 1). The “raspberry” morphology has a relatively silica-rich surface compared to the bulk composition.3 In contrast, the “currant bun” morphology has a surface composition that is comparable to the bulk composition, indicating that the silica particles are more or less uniformly distributed throughout such nanocomposite particles.4,5 There are a wide range of potential applications for such colloidal nanocomposite particles. Electrically conductive polypyrrole-silica and polyaniline-silica nanocomposites with “raspberry” morphologies have been evaluated for biomedical applications3b and also as synthetic mimics for *To whom correspondence should be addressed. E-mail: s.p.armes@ sheffield.ac.uk (S.P.A.) or
[email protected] (P.W.F.). (1) Bourgeat-Lami, E. J. Nanosci. Nanotechnol. 2002, 2, 1. (2) Percy, M. J.; Amalvy, J. I.; Barthet, C.; Armes, S. P.; Greaves, S. J.; Watts, J. F.; Wiese, H. J. Mater. Chem. 2002, 12, 697. (3) (a) Maeda, S.; Gill, M.; Armes, S. P.; Fletcher, I. W. Langmuir 1995, 11, 1899 (b) Pope, M. R.; Armes, S. P.; Tarcha, P. J. Bioconjugate Chem. 1996, 7, 436. (4) Barthet, C.; Hickey, A. J.; Cairns, D. B.; Armes, S. P. Adv. Mater. 1999, 11, 408. (5) Percy, M. J.; Barthet, C.; Lobb, J. C.; Khan, M. A.; Lascelles, S. F.; Vamvakaki, M.; Armes, S. P. Langmuir 2000, 16, 6913.
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cosmic dust.6 More generally, nanocomposite particles may be useful as catalysts,7 as components in electronic or photonic devices,8 as pH-responsive Pickering emulsifiers,9-11 or as sensors for volatile organic compounds.12 The incorporation of an inorganic component can also enhance the fire retardancy13 and mechanical strength of organic polymers.14 Various routes for the preparation of colloidal nanocomposite particles have been extensively reviewed.15-17 A major disadvantage for many reported syntheses in which vinyl polymerizations are conducted in the presence of ultrafine silica sols is the relatively poor silica aggregation efficiency: (6) Burchell, M. J.; Willis, M. J.; Armes, S. P.; Khan, M. A.; Percy, M. J.; Perruchot, C. Planet. Space Sci. 2002, 50, 1025. (7) Chen, C. W.; Serizawa, T.; Akashi, M. Chem. Mater. 1999, 11, 1381. (8) Mitzi, D. B. Chem. Mater. 2001, 13, 3283. (9) Read, E. S.; Fujii, S.; Amalvy, J. I.; Randall, D. P.; Armes, S. P. Langmuir 2004, 20, 7422. (10) Fujii, S.; Read, E. S.; Binks, B. P.; Armes, S. P. Adv. Mater. 2005, 17, 1014. (11) Fujii, S.; Armes, S. P.; Binks, B. P.; Murakami, R. Langmuir 2006, 22, 6818. :: (12) Vossmeyer, T.; Guse, B.; Besnard, I.; Bauer, R. E.; Mullen, K.; Yasuda, A. Adv. Mater. 2002, 14, 238. (13) Manias, E.; Touny, A.; Wu, L.; Strawhecker, K.; Lu, B.; Chung, T. C. Chem. Mater. 2001, 13, 3516. (14) Sun, T.; Garces, J. M. Adv. Mater. 2002, 14, 128. (15) Balmer, J. A.; Schmid, A.; Armes, S. P. J. Mater. Chem. 2008, 18, 5722. (16) Wang, T.; Keddie, J. L. Adv. Colloid Interface Sci. 2008, http://dx.doi. org/10.1016/j.cis.2008.06.002. (17) Zou, H.; Wu, S. S.; Shen, J. Chem. Rev. 2008, 108, 3893.
Published on Web 3/4/2009
DOI: 10.1021/la8041555
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Figure 2. Schematic representation of the adsorption of ultrafine silica particles onto a sterically stabilized latex.
Theory
Figure 1. Schematic representation of the four known morphologies for colloidal polymer-silica nanocomposite particles: (A) “raspberry”, (B) “currant bun”, (C) “core-shell” (polymer core and silica shell), and (D) inverted “core-shell” (silica core and polymer shell). a significant fraction of the original silica particles typically remains in the solution phase, rather than becoming incorporated within the nanocomposite particles.15 For example, it is known that the presence of excess silica sol can reduce the transparency of solvent-cast nanocomposite films and also result in their embrittlement.18 However, Dupin et al.19 have recently reported that the polymerization of 2-vinylpyridine (2VP) in the presence of an ultrafine silica sol results in the formation of nanocomposite particles with silica incorporation efficiencies as high as 99%. Similar results have also been reported by Schmid et al. for other vinyl polymer-silica nanocomposite particles, although in this case a glycerolfunctionalized silica sol was required.20 In principle, a more general route for the synthesis of nanocomposite particles with minimal excess silica might involve the adsorption of silica particles onto large, preformed polymer latex particles under optimized conditions such that monolayer coverage is achieved. Moreover, such controlled heteroflocculation should provide a well-defined “core-shell” nanocomposite morphology. An early example of nanocomposites prepared by heterocoagulation was reported by Bleier and Matijevıc.21 More recently, Luna-Xavier et al.22 investigated the mixing of anionic silica particles with preformed cationic poly(methyl methacrylate) latex. However, to the best of our knowledge, few experimental studies have been undertaken to investigate the number of small spherical particles that are required to fully coat larger spherical cores. The present work describes the determination of the packing efficiency of small silica particles adsorbed on the surface of relatively large sterically stabilized latexes (see Figure 2). Thus, the optimum amount of silica sol required to form “core-shell” nanocomposite particles with little or no excess silica can be calculated. (18) Schmid, A. Synthesis and characterisation of vinyl-polymer silica colloidal nanocomposite particles. Ph.D. Thesis, University of Sheffield, U. K., 2007. (19) Dupin, D.; Schmid, A.; Balmer, J. A.; Armes, S. P. Langmuir 2007, 23, 11812. (20) Schmid, A.; Tonnar, J.; Armes, S. P. Adv. Mater. 2008, 20, 3331. (21) Bleier, A.; Matijevic, E. J. Chem. Soc., Faraday Trans. I 1978, 74, 1346. (22) Luna-Xavier, J. L.; Guyot, A.; Bourgeat-Lami, E. Polym. Int. 2004, 53, 609.
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There have been various publications describing composite particles with core-shell morphologies in which the authors have attempted to estimate the packing efficiency of smaller spheres within the outer shell. For example, Ottewill et al.23 estimated the number of latex particles required to form a well-defined shell around a latex core by assuming that (i) the particles within the shell layer were hexagonally close-packed and (ii) the core diameter was significantly larger than the shell thickness and thus the latex core could be assumed to be a planar surface. Indeed, hexagonal close packing is generally assumed in most publications dealing with the packing of small particles onto larger particles.22,24-26 Alternatively, a “two-dimensional square lateral” arrangement is assumed by Bon and Colver27 for the packing of Laponite disks on polymer latex cores; curvature effects were ignored because the disk dimensions were judged to be negligible compared to the latex diameter. The present study is concerned with the coating of 463 or 616 nm diameter poly(2-vinylpyridine) [P2VP] latex with 20 nm silica particles. The following assumptions are required at this stage: (i) Both silica and latex are noninteracting, perfectly monodisperse spheres. (ii) After adsorbing the silica particles onto the latex, the former have sufficient surface mobility to obtain their maximum packing efficiency (i.e., where no more particles can be added without starting a second layer). This optimum arrangement is simply termed a “packing” in the following text. Regarding the first assumption, both P2VP latexes are nearmonodisperse as judged by dynamic light scatterning (DLS) and scanning electron microscopy (SEM), whereas the smaller silica sol has a significantly higher polydispersity (approximately 24% as judged by small-angle X-ray scattering).28 We also suspect that there may be a weak interaction between the silica particles and the poly(ethylene glycol) stabilizer located at the surface of the latex.29-32 If this is correct, the surface mobility of the adsorbed silica particles may be somewhat (23) Ottewill, R. H.; Schofield, A. B.; Waters, J. A.; Williams, N. S. J. Colloid Polym. Sci. 1997, 275, 274. (24) Hansen, F. K.; Matijevic, E. J. Chem. Soc., Faraday Trans. I 1980, 76, 1240. (25) Luckham, P.; Vincent, B.; Hart, C. A.; Tadros, T. F. Colloids Surf. 1980, 1, 281. (26) Harley, S.; Thompson, D. W.; Vincent, B. Colloids Surf. 1992, 62, 163. (27) Bon, S. A. F.; Colver, P. J. Langmuir 2007, 23, 8316. (28) Mykhaylyk, O.; Balmer, J. A.; Armes, S. P.; Ryan, A. J. Unpublished work, 2008. (29) Cosgrove, T.; Griffiths, P. C.; Lloyd, P. M. Langmuir 1995, 11, 1457. (30) Cosgrove, T.; Mears, S. J.; Obey, T.; Thompson, L.; Wesley, R. D. Colloids Surf., A 1999, 149, 329. (31) Cosgrove, T.; Mears, S. J.; Thompson, L.; Howell, I. Adsorption studies on mixed silica-polymer-surfactant systems. In Surfactant Adsorption and Surface Solubilization; ACS Symposium Series 615; American Chemical Society: Washington, DC, 1995; p 196. (32) Flood, C.; Cosgrove, T.; Howell, I.; Revell, P. Langmuir 2006, 22, 6923.
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restricted, which may reduce the final packing efficiency [see assumption (ii)]. In order to obtain realistic values of monolayer coverage for this system, it is necessary to consider alternative packing arrangements that take account of the curvature of the core particles. Clearly, full coverage of the latex surface by the silica particles is an overestimate, as 100% packing efficiency for spheres or circles cannot be achieved in two or three dimensions. The highest packing efficiency, P, that can be achieved for equal circles in the plane is in hexagonal close packing. For this scenario, a straightforward geometrical calculation shows that the silica particles would cover π/(12)1/2 or 90.7% of the latex surface. In hexagonal close packing, every circle has six neighbors. The problem of packing small monodisperse spheres on a single larger sphere maps onto the packing of circles (spherical caps) on a sphere, a problem that has many multidisciplinary applications.33 It is not possible to cover a sphere with a lattice in which all vertices have coordination number six; Euler’s theorem34 implies P that a triangulation of the sphere must obey the sum rule r(6 - r)vr = 12, where vr is the number of vertices (i.e., centers of the small spheres) with degree r. Thus, every triangulation must include some “defective” vertices of degree less than 6. This could be achieved with 4 vertices of degree 3, 6 vertices of degree 4, 12 vertices of degree 5, or 16 combinations in between.35 The highest symmetry achievable for a spherical triangulation is icosahedral (I or Ih), implying the presence of exactly 12 sites with coordination number five, if all others have coordination number six. Packings can be described quantitatively in terms of the packing radius. For each total number of small spheres, N, there is a packing radius r(N) corresponding to the maximum radius, achievable when the N spheres are optimally packed. The mapping to the unit-sphere packing problem follows from simple geometric considerations (see Figure 3). If small spheres of radius rs are packed around a larger sphere of radius rl, their centers define a sphere of radius (rl + rs). However, their mutual contacts lie on a sphere of radius (rl + rs) cos(rc) where rc is the angular radius of a spherical cap defined by the contacts of one small sphere with its neighbors in the packing, rc = arcsin[rs/(rl + rs)]. Calculation of the number of small spheres packed around the large one then reduces to finding the value of N for which r(N) = rc. The analytical form of the function r(N) is not known, but various bounds have been derived. The density (or, expressed as a percentage, the efficiency) of a packing of N spherical caps on the unit sphere is N P ¼ ð1 -cos rc Þ 2
ð1Þ
For large N and small rc, this is well approximated by P ¼
N rc Nrc 2 Nrs 2 = ð1 -cos rc Þ ¼ Nsin2 = ð2Þ 2 2 4 4ðrl þ rs Þ2
Thus, to estimate P, we require an estimate of N, which is a function of the radii rs and rl. Computer simulations have (33) Tarnai, T.; Fowler, P. W. MATCH 2007, 58, 461. (34) Barnette, D. Map Coloring Polyhedra and the Four Color Problem (Dolciani Mathematical Expositions); Mathematical Association of America: Washington, DC, 1984. (35) Grunbaum, B. Convex Polytopes (Graduate Texts in Mathematics); Springer: Berlin, 2003.
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Figure 3. Schematic representation of the geometric considerations for the packing of small spheres, of radius rs, around a large sphere, of radius rl. Their centers define a sphere of radius (rl + rs), but their mutual contacts lie on a sphere of slightly smaller radius (rl + rs) cos (rc) where rc is the angular radius of a spherical cap defined by the contacts of one small sphere with its neighbors in the packing. established values for r(N) over a wide range of N for both unconstrained and icosahedrally symmetric packings.36 For typical experimental values of rs = 10 nm and rl = 231.5 nm (see Results and Discussion), the effective radius of the spherical cap is 1 ¼ 0:0417c rc ¼ arcsin 24
ð3Þ
and this value lies between radii corresponding in Sloane’s table of icosahedrally symmetric packings to N = 1952 and N = 2012 (P = 84.8% and P = 87.3%, respectively).36 Rigorous mathematical bounds on N as a function of radius ratio follow from classical results on circle packings and do not require assumptions about the symmetry or the set of defects. The upper bound of Robinson37 is given by N
