Reversible Aggregation of Soft Particles A. Ferna ´ ndez-Nieves, † A. Ferna ´ ndez-Barbero, † B. Vincent, ‡ and F. J. de las Nieves* ,† Group of Complex Fluids Physics, Department of Applied Physics, University of Almerı ´a, 04120 Almerı ´a, Spain, and School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, U.K. Received September 20, 2000. In Final Form: November 30, 2000 In this work, the aggregation of microgel particles has been investigated, paying special attention to the structure of the clusters formed in the process. In particular, the aggregates’ fractal dimension was determined by static light scattering. The results indicate that the aggregates are more compact than expected for diffusive aggregation. A reversible aggregation mechanism is proposed on the basis of the competition between osmotic and elastic contributions arising from the soft character of the particles. Aggregation proceeds in an energy minimum of restricted depth, giving rise to the formation of more compact clusters than expected. Finally, the process reversibility is tested, confirming the secondary minimum controlled aggregation. Introduction In the past decade, models have developed describing the structure that results from the union of subunits. The aggregation of colloidal particles is a good model for describing this phenomenon. Both theory and experiments have shown a universal behavior, independent of the particle nature, when the aggregation of clusters is diffusion-limited (DLCA) or reaction-limited (RLCA). 1 DLCA occurs when every collision between clusters results in the formation of an irreversible bond. This regime gives rise to the formation of branched clusters, with a typical fractal dimension of 1.7-1.8. RLCA occurs when a small fraction of collisions leads to cluster formation. In this case, the aggregates are more compact than those formed in a DLCA process, with a fractal dimension of around 2.1. DLCA and RLCA are limited to certain ideal condi- tions. In particular, clusters have to be randomly dis- tributed in space, with no position correlation at any time. Additionally, the aggregation must occur in a deep energy minimum that guarantees a Brownian path for every cluster. Intermediate aggregation modes between DLCA and RLCA have also been reported both, theoretically and experimentally. 2,3 In addition, the formation of more compact structures than expected for RLCA processes has been encountered and explained in terms of reaction reversibility. 4-6 In this case, the contact between particles is considered to be reversible so that they can loosen and re-form repeatedly after collision. This reversible mode of aggregation has been related to the finiteness of the energy well that holds the particles together. 7,8 In this work, the aggregation of mesoscopic gellike particles (i.e. soft particles) is studied. In particular, we have studied the structure of the aggregates formed under high salt conditions (far above the critical coagulation concentration of the colloidal system). The clusters present a more compact structure than expected for DLCA, which could be related to the soft character of these colloids, that are able to swell or deswell, depending on the environmental conditions. This feature not only modifies the particle structure and overall size but also gives rise to the appearance of new contributions to the total interaction potential between particles. Osmotic and elastic effects due to surface interpenetration are taken into account, yielding a finite energy minimum where aggregation takes place. This model supports the obtained cluster structures. Finally, the aggregation reversibility is experimentally tested, confirming the presented sce- nario. Monitoring Cluster Structure Cluster Morphology. It is well-known that colloidal clusters exhibit a fractal structure, characterized by a fractal dimension d f , which is directly related to the cluster compactness. Cluster growth is such that its mass, M, increases slower than its volume. Mathematically, M(R) ∼ R df with d f < 3 (in a three-dimensional space) and R the radius of the aggregate. 9 This description implies that the pair correlation function of primary particles within a fractal aggregate scales as 10 corresponding to a decay of the local density as the length scale increases. This power law is usually employed for obtaining the fractal dimension of growing mesoscopic clusters. Static Light Scattering. In a static light scattering experiment, the measured mean scattered intensity, I, * To whom correspondence should be addressed (e-mail: fjnieves@filabres.ual.es). † University of Almerı ´a. ‡ University of Bristol. (1) Carpineti, M.; Giglio, M. Adv. Colloid Interface Sci. 1993, 46, 73. (2) Kolb, M.; Botet, R.; Jullien, R. Phys. Rev. Lett. 1983, 51, 1123. (3) Asnaghi, D.; Carpineti, M.; Giglio, M.; Sozzi, M. Phys. Rev. A 1992, 45, 1018. (4) Aubert, C.; Cannell, D. S. Phys. Rev. Lett. 1986, 56, 738. (5) Dimon, P.; Sinha, S. K.; Weitz, D. A.; Safinya, C. R.; Smith, G. S.; Varaday, W. A.; Lindsay, H. M. Phys. Rev. Lett. 1986, 57, 595. (6) Jullien, R. CCACAA 1992, 65, 2, 215. (7) Shih, W. Y.; Aksay, I. A.; Kikuchi, R. Phys. Rev. A 1987, 36, 10, 5015. (8) Lin, J.; Shih, W. Y.; Sarikaya, M.; Aksay, I. A. Phys. Rev. A 1990, 41, 6, 3206. (9) de Guzman, M.; Martı ´n, M. A.; Mora ´ n, M.; Reyes, M. Estructuras fractales y sus aplicaciones; Labor SA: Madrid, 1993. (10) Vicsek, T. Fractal growth phenomena; World Scientific: Singa- pore, 1992. g(r) ∼ r df-3 (1) 1841 Langmuir 2001, 17, 1841-1846 10.1021/la001351u CCC: $20.00 © 2001 American Chemical Society Published on Web 02/13/2001