pubs.acs.org/Langmuir © 2009 American Chemical Society
Effect of Surface Properties of Elastomer Colloids on Their Coalescence and Aggregation Kinetics Cornelius Gauer, Hua Wu, and Massimo Morbidelli* Institute for Chemical and Bioengineering, Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland Received May 13, 2009. Revised Manuscript Received July 1, 2009 We study the aggregation kinetics of two elastomer colloids with similar bulk polymer properties but with different surface charge groups in order to understand the role of the surface properties in particle coalescence during aggregation. It is confirmed that clusters of the elastomer particles stabilized purely by ionic surfactants coalesce in both reaction-limited and diffusion-limited aggregation (RLCA and DLCA) regimes and that the coalescence is independent of the coagulant type. On the other hand, clusters formed by elastomer particles stabilized by charged polymer end groups, which are fixed on the particle surface, are fractal objects with a fractal dimension of 1.7 in the DLCA and 2.1 in the RLCA regime. This indicates insignificant cluster coalescence during aggregation, most likely due to a hindrance effect of the fixed charges.
1. Introduction Aggregation of small, colloidal particles to form large clusters is a phenomenon that either can be exploited e.g. in solid-liquid separation or has to be avoided e.g. during particle synthesis. Since many processes of practical interest (e.g., industrial, environmental, medical) deal with dispersions of fine particles (colloids), it is important to understand the mechanism and kinetics of colloidal aggregation and the structure of the formed clusters. Various experimental and theoretical studies during the past decades have revealed that clusters obtained through aggregation of colloidal particles are typical fractal objects of ramified topology, which can be well represented by the mass fractal dimension, Df, which is the exponent describing the scaling between mass and size (M LDf).1-4 Although precise topological information is not contained in Df, its knowledge allows one to calculate important properties (e.g., density, surface area, hydrodynamic size, etc.) of clusters. It has been well established5-7 that most colloidal aggregation processes are universal with respect to aggregation kinetics and cluster structure. Two limiting aggregation regimes are typically classified: the diffusion-limited clustercluster aggregation (DLCA) and the reaction-limited clustercluster aggregation (RLCA). The former is associated with a power-law growth of the average cluster size and Df ≈ 1.7-1.8 *To whom correspondence should be addressed: e-mail morbidelli@chem. ethz.ch; Tel 0041-44-6323034. (1) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: New York, 1982. (2) Jullien, R.; Botet, R. Aggregation and Fractal Aggregates; World Scientific: Singapore, 1987. (3) Meakin, P. Adv. Colloid Interface Sci. 1988, 28, 249–331. (4) The Fractal Approach to Heterogeneous Chemistry; Avnir, D., Ed.; Wiley: Chichester, UK, 1989. (5) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature (London) 1989, 339, 360–362. (6) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Phys. Rev. A 1990, 41, 2005–2020. (7) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Klein, R.; Ball, R. C.; Meakin, P. J. Phys.: Condens. Matter 1990, 2, 3093–3113. (8) Forrest, S. R.; Witten, T. A. J. Phys. A: Math. Gen. 1979, 12, L109–L117. (9) Weitz, D. A.; Oliveria, M. Phys. Rev. Lett. 1984, 52, 1433–1436. (10) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. Rev. Lett. 1984, 53, 1657–1660.
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and the latter with an exponential growth kinetics and Df ≈ 2.02.1. These results have been proven in numerous studies3,5-28 on gold, silica, polystyrene, and other particles that can be considered as rigid, nondeformable spheres. Aggregation of soft particles can deviate considerably from the above universal picture. Their deformability often promotes colloidal interaction in a shallow minimum, therefore allowing restructuring, as has been observed for microgel particles29,30 or liposomes.31-33 Moreover, soft particles may have the chance to coalesce or fuse. As has been demonstrated recently,34 upon (11) Aubert, C.; Cannell, D. S. Phys. Rev. Lett. 1986, 56, 738–741. (12) Bolle, G.; Cametti, C.; Codastefano, P.; Tartaglia, P. Phys. Rev. A 1987, 35, 837–841. (13) Wiltzius, P. Phys. Rev. Lett. 1987, 58, 710–713. (14) Martin, J. E. Phys. Rev. A 1987, 36, 3415–3426. (15) Martin, J. E.; Wilcoxon, J. P.; Schaefer, D.; Odinek, J. Phys. Rev. A 1990, 41, 4379–4391. (16) Midmore, B. R. J. Chem. Soc., Faraday Trans. 1990, 86, 3763–3768. (17) Carpineti, M.; Ferri, F.; Giglio, M.; Paganini, E.; Perini, U. Phys. Rev. A 1990, 42, 7347–7354. (18) Shih, W. Y.; Liu, J.; Shih, W.-H.; Aksay, I. A. J. Stat. Phys. 1991, 62, 961– 984. (19) Zhou, Z.; Chu, B. J. Colloid Interface Sci. 1991, 143, 356–365. (20) Burns, J. L.; Yan, Y. D.; Jameson, G. J.; Biggs, S. Langmuir 1997, 13, 6413– 6420. (21) Axford, S. D. T. J. Chem. Soc., Faraday Trans. 1997, 93, 303–311. (22) Tirado-Miranda, M.; Schmitt, A.; Callejas-Fernandez, J.; FernandezBarbero, A. Langmuir 1999, 15, 3437–3444. (23) Tirado-Miranda, M.; Schmitt, A.; Callejas-Fernandez, J.; FernandezBarbero, A. Phys. Rev. E 2003, 67, 011402. (24) Lattuada, M.; Sandkuhler, P.; Wu, H.; Sefcik, J.; Morbidelli, M. Adv. Colloid Interface Sci. 2003, 103, 33–56. (25) Wu, H.; Lattuada, M.; Sandkuhler, P.; Sefcik, J.; Morbidelli, M. Langmuir 2003, 19, 10710–10718. (26) Sandkuhler, P.; Sefcik, J.; Morbidelli, M. Adv. Colloid Interface Sci. 2004, 108, 133–143. (27) Berka, M.; Rice, J. A. Langmuir 2005, 21, 1223–1229. (28) Jia, Z.; Wu, H.; Xie, J. J.; Morbidelli, M. Langmuir 2007, 23, 10323–10332. (29) Fernandez-Nieves, A.; Fernandez-Barbero, A.; Vincent, B.; de las Nieves, F. J. Langmuir 2001, 17, 1841–1846. (30) Cheng, H.; Wu, C.; Winnik, M. A. Macromolecules 2004, 37, 5127–5129. (31) Roldan-Vargas, S.; Martin-Molina, A.; Quesada-Perez, M.; BarnadasRodriguez, R.; Estelrich, J.; Callejas-Fernandez, J. Phys. Rev. E 2007, 75, 021912. (32) Roldan-Vargas, S.; Barnadas-Rodriguez, R.; Martin-Molina, A.; QuesadaPerez, M.; Estelrich, J.; Callejas-Fernandez, J. Phys. Rev. E 2008, 78, 010902. (33) Roldan-Vargas, S.; Barnadas-Rodriguez, R.; Quesada-Perez, M.; Estelrich, J.; Callejas-Fernandez, J. Phys. Rev. E 2009, 79, 011905. (34) Gauer, C.; Jia, Z.; Wu, H.; Morbidelli, M. Langmuir 2009, Article ASAP, DOI: 10.1021/la900963f.
Published on Web 07/20/2009
DOI: 10.1021/la901702s
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physical contact elastomer particles may coalesce (fuse completely) as a result of polymer chain interdiffusion or viscous flow.35,36 This effect is basically known from the film formation of latex paints and other types of coatings.37 Moreover, functional surface groups or surfactants can play a crucial role in various aspects of film formation such as colloidal stability, particle ordering, degree of polymer interdiffusion across particleparticle boundaries, etc.36 The range of interests may well exceed obvious problems such as in film healing or overcoming the processing difficulties of natural or synthetic rubber particles. However, to our knowledge, detailed investigations on how the properties of surface charge groups (e.g., fixed or mobile) of elastomer particles affect the coalescence and aggregation behaviors are missing in the literature. Therefore, in this work we study the aggregation kinetics and cluster structure of two types of latices with similar material properties (e.g., the same polymer composition and glass transition temperature) of the elastomer particles but different surface charge group properties. In particular, one is stabilized purely by adsorbed ionic surfactants while the other purely by fixed charges originating from ionic polymer chain-end groups in the absence of surfactants. The aggregation experiments are conducted under both DLCA and RLCA conditions in quiescent fluid. Light scattering techniques have been employed to measure particle size and cluster structure, and for additional support cryogenic scanning electron microscopy (cryo-SEM) has also been used. Simulations of the time evolutions of the average cluster sizes, based on population balance equations (PBE) and appropriate scattering functions, return the physical parameters of the aggregation kinetics. It will be demonstrated that the nature of the particle surface groups controls cluster coalescence, leading to distinct differences for the aggregation kinetics under DLCA and RLCA conditions. The paper is organized as follows: In the Experiments section, we describe the relevant properties of the two colloids and how the aggregation experiments were carried out, including details about the applied light scattering and cryo-SEM techniques, as well as how to quantify the initial aggregation kinetics. Then, in the Modeling section, we elucidate the PBE model and its characteristics as well as how to construct the measured average radii with the PBE simulations. In the section Results and Discussion are included two parts: part 1 compares and discusses the results in aggregation kinetics and cluster structure for the two colloids under DLCA conditions, while part 2 is devoted to RLCA results. Finally, we summarize our findings in the Conclusions section.
2. Experiments 2.1. Aggregation
Experiments.
Colloidal
Systems.
Two types of latices, supplied by Solvay Solexis (Italy), have been used, both of which are aqueous dispersions of fluorinated elastomer particles with the same polymer composition (copolymerization of vinylidene fluoride and hexafluoropropylene) and glass transition temperature (Tg ≈ -20 C). One of the two latices was produced by emulsion polymerization, and based on the supplier, the obtained particles are bare of charges and their stability against aggregation is achieved by adsorbed carboxylic charges (acc) from a mixture of perfluoropolyetherbased surfactants, the details of which can be found elsewhere.34 This latex is referred to in the following as acc-latex. It is rather (35) Mazur, S. Coalescence of Polymer Particles. In Polymer Powder Technology; Narkis, M., Rosenzweig, N., Eds.; Wiley: Chichester, UK, 1995; Chapter 8, pp 157-216. (36) Keddie, J. L. Mater. Sci. Eng. R 1997, 21, 101–170. (37) Fitch, R. M. Polymer Colloids; Academic Press: San Diego, 1997. (38) Kerker, M. The Scattering of Light; Academic Press: New York, 1969.
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monodisperse, and the radius of the primary particles measured by both dynamic and static light scattering is Rp=60 nm. Another latex was produced by emulsion-free polymerization, and the obtained particles are solely stabilized by fixed charges (fc), which are negative and originate from dissociation of polymer chain-end groups. This second one is called fc-latex. Unlike the acc-latex, the fc-latex is somewhat polydisperse, which is indicated by the deviation of the ratio between the radius of gyration measured by static light scattering (Rg,0 =120 nm) and the hydrodynamic radius measured by dynamic light scattering at 90 (Rh,0 = 125 nm) from the value of (3/5)1/2, characteristic of monodisperse spheres.38 To better understand the polydispersity, we have measured the particle size distribution (PSD) obtained from image analysis of the cryo-SEM pictures of the original latex, as presented in the Supporting Information (SI-Figure 1). The number-average of the primary particle radii is 115 nm, which is considered as initial particle radius Rp for the simulation. On the basis of the light scattering theory,38,39 using the measured PSD, we can well reproduce the measured values of Rg,0 and Rh,0 as well as the average form factor, ÆP(q)æ (see Supporting Information, SI-Figure 2). The refractive index and density of the polymer are 1.37 and 1.8 kg/L, respectively. DLCA Experiments. The fast or diffusion-limited aggregation (DLCA) experiments were conducted at T=25 C and at a particle volume fraction of φ=3.0 10-5 for the acc-latex and φ= 5.0 10-5 for the fc-latex. Both systems were destabilized by introducing analytical grade nitric acid (HNO3), sodium chloride (NaCl), or magnesium sulfate (MgSO4). Deionized water used for the preparation was purified through a Millipore Simpak 2 column and further filtered through 0.1 μm Acrodisc syringe filters (Pall, UK) to remove any potential dust. The experiments were started by pouring 4 parts prediluted coagulant into 1 part prediluted colloid, followed by a quick and gentle hand shaking. After few seconds equilibrium, the experimental volume (50 mL) was portioned into two glass vials, one of which was used for particle size measurement by dynamic light scatting and the second was stored upside down. Every 10-20 min the vials were turned and exchanged for the measurement to avoid sedimentation. The experiments were conducted at different coagulant concentrations, which allows determination of the critical coagulant concentration, CCC,40 above which the aggregation kinetics does not increase anymore with the coagulant concentration, thus reaching the DLCA regime. The obtained CCC values for different salts are listed in Table 1. For each latex and coagulant type, the DLCA kinetics reported here is an average from at least three runs above CCC. RLCA Experiments. All aggregation experiments in the slow or reaction-limited (RLCA) regime were carried out also at T= 25 C, but at larger particle volume fraction, φ = 5.0 10-3. Coagulant concentrations were chosen sufficiently below CCC, in order to have an aggregation rate that was slow enough to allow direct measurement of the initial aggregation rates or colloidal stability. The prediluted coagulant was added as 9 parts to 1 part prediluted latex to minimize the effect of local excess coagulant concentrations. For the measurements of cluster evolution by light scattering, small volumes of samples were taken from the aggregating system and diluted to φ=5.0 10-5. Sedimentation of clusters was prevented by slowly turning the reaction container every couple of hours. Note that for both DLCA and RLCA experiments no stirrer has been used to avoid sedimentation during the aggregation, since the effect of the shear force of the stirrer on the aggregation (39) Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter; Lindner, P., Zemb, T., Eds.; Elsevier: Amsterdam, 2002. (40) Hackley, V. A.; Ferraris, C. F. The Use of Nomenclature in Dispersion Science and Technology; Special Publication 960-3; National Institute of Standards and Technology: Washington, DC, 2001.
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Table 1. Experimentally Obtained CCC Values of Different Types of Coagulant for the acc- and fc-Latices
CCCH2SO4/mol L-1 CCCHNO3/mol L-1 CCCNaCl/mol L-1 CCCMgSO4/mol L-1
dropping mode
DLCA experiment
acc-latex φ=0.14
acc-latex fc-latex φ=3.0 10-5 φ=5.0 10-5
0.4 0.5 1.4 0.6
0.3 0.9 0.4
1.1 1.3 0.2
rate and cluster structure would complicate our explanation of the experimental results. 2.2. Colloid Characterization. Light Scattering. Along aggregation, both cluster size and cluster mass distribution (CMD) evolve with time. Direct measurement of the CMD is usually not available or rather laborious, and therefore average quantities are measured. Light scattering techniques provide very reliable measures in the form of the average hydrodynamic and gyration radii, ÆRhæ and ÆRgæ, which represent two independent moments of the CMD. The dynamic light scattering (DLS) measurements were performed at a fixed angle of θ = 90 in a BI-200SM goniometer (Brookhaven Instruments). Inserted samples were illuminated by a laser beam of λ0=532 nm wavelength, emitted from a solid-state laser, Ventus LP532 (Laser Quantum, UK). It quantifies the socalled autocorrelation function through a digital correlator, BI-9000AT (Brookhaven Instruments), from which the average translational diffusion coefficient, ÆDæ, can be estimated. Then, the average hydrodynamic radius, ÆRhæ, can be calculated via the Stokes-Einstein relation:39,41,42 kT ð1Þ ÆRh æ ¼ 6πμl ÆDæ where kT is the thermal energy and μl is the dynamic viscosity of the dispersion medium. Most of the static light scattering (SLS) measurements were carried out, using the same setup described above, in the angle range from θ=16 to 150. The average radius of gyration, ÆRgæ (= ÆRg2æ1/2), was estimated from the normalized intensity curve of the scattered light, I(q)/I(0), by applying the Guinier plot:39,43 "
IðqÞ -ln Ið0Þ
# ¼
q2 2 ÆRg æ 3
ð2Þ
within the so-called Guinier regime, defined as qÆRgæ < 1. The corresponding magnitude of the scattering vector is defined by 4πn0 θ q ¼ sin ð3Þ λ0 2 with n0 representing the refractive index of the dispersion medium. For samples containing sufficiently large fractal clusters, a small-angle static light scattering (SASLS) instrument, Mastersizer 2000 (Malvern, UK), was used, which allows to estimate not only ÆRgæ but also the fractal dimension, Df. This is based on the fact that the average structure factor, ÆS(q)æ (= I(q)/[I(0)P(q)]), where P(q) is the measured form factor of the primary particles, versus q exhibits the so-called power law regime in 1/ÆRgæ
