Structure of Adsorbed Polymers on a Colloid Particle Shuang Yang and Dadong Yan* Beijing National Laboratory for Molecular Sciences (BNLMS), Joint Laboratory of Polymer Science and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, China An-Chang Shi † Department of Physics and Astronomy, McMaster UniVersity, Hamilton, Ontario L8S 4M1, Canada ReceiVed January 3, 2006; ReVised Manuscript ReceiVed April 14, 2006 ABSTRACT: The adsorption of homopolymers on spherical particles with a strong attractive potential has been studied using the self-consistent field theory. The particles are immersed in concentrated polymer solutions and the structure of the adsorbed polymer layer has been examined as a function of the particle size, focusing on the average loop and tail length at different bulk concentrations and solvent qualities. The scaling relationship between the average tail/loop length and the degree of polymerization has been investigated. It is found that the average loop length is insensitive to the particle size or surface curvature. However, the average tail length depends strongly on the particle size. In particular, tails become longer for smaller particles or larger surface curvatures. It is argued that this size effect may provide a mechanism for the excess entanglements induced by adding nanoparticles to polymer solutions. 1. Introduction Mixtures of colloid suspensions and polymers are widely used in many industrial applications. Examples include adhesion and lubrication. 1 In many cases polymers can interact strongly with the colloidal particles. If one monomer is adsorbed by the particle surface, there is an enhanced probability that many others are also adsorbed on the surface due to the chain connectivity. Therefore, polymers can be strongly attracted by the particles. The adsorbed polymer conformation can be described in terms of loops and tails. 2 There are two possible applications of the adsorption between polymers and colloids. One application is to control the stability of colloidal suspensions by adding adsorbed polymers, such as in paints or in wastewater treatment. In fact the interaction between two dispersions carrying adsorption layers is rather subtle. It depends on the precise conformation of the polymer chains on the surface, and strongly on the reversibility of the adsorption. In the restricted equilibrium regime and good solvent solutions, because of the excluded volume interactions the adsorbed polymer layers on two adjacent particles repel each other and stabilize the colloidal dispersions. If a polymer chain is long enough, it can link different particles and flocculate them through bridges. The other application is to improve the rheological and mechanical properties of the system by adding small amount of nanoparticles to polymer solutions and melts. Since loops and tails of adsorbed polymers are dangling from the surface into solutions, one chain connects several particles when bridges occur between long polymer chains and colloids. In this case, the polymer composite becomes a gel where colloids act as cross-links. 3 However, if the chains are not long enough, even if no bridge occurs, the properties of polymer composite can be affected by entangle- ments between tails and loops belonging to different particles. This entanglement mechanism is different from those appearing in bulk, which are caused by long free polymer chains. The solution can also become a large polymer gel as if it is cross- linked by those nanoparticles. The rheology of the polymer solution and melt may be affected strongly by the addition of nanoparticles. For example, the viscosity of the polymer solution can be increased greatly. The key factor is the conformation of the adsorbed polymers. One interesting question is why adding a small amount of nanoparticles has a large effect. It is obvious that the size of the particles matters in these applications. Therefore, it is of great interest to investigate the effect of particle size or surface curvature on polymer adsorption. A few studies on how curvature affects the conformation of polymer near curving surfaces have appeared in the literature. Wijmans and Zhulina investigated the curvature effect on the density profile of polymer brushes at the curved surface. 4 Aubouy and Raphael presented a scaling description for the behavior of loops and tails of polymers adsorbed on a spherical surface. 5 Also, Ji and Hone 6 and Skau and Blokhuis 7 focused on the structural properties of adsorbed polymers and took into account the weak curvature effects as a perturbation. The equilibrium structure of homopolymers reversibly ad- sorbed on flat surfaces has been investigated theoretically for many years. Early theoretical treatment of a polymer solution in the vicinity of a solid surface was a mean field theory based on the ground state dominant approximation (GSA). 8-10 In this approximation, the chain end effect is ignored and the polymer chain is treated as infinitely long. Furthermore, de Gennes proposed a scaling theory beyond the mean field theory. 8,11,12 This theory grasps the spirit of self-similar structure of adsorbed polymers and predicts the main qualitative features of adsorbed layer successfully. Eisenriegler et al. derived various scaling results and the universal amplitude ratios about polymer adsorption with excluded volume interaction using the analogy with the zero-component field theory. 13-15 Scheutjens and Fleer et al. developed a lattice model, which can be used to describe many aspects of polymer adsorption. 1,16,17 The statistical distribution of tails and loops can be enumerated easily, highlighting the influence of tails and loops on experimentally observable quantities. The tails mostly builds up the external part of adsorbed layer, whereas the loops are the main part close to the wall. Recently, Semenov et al. proposed a two-parameter theory, which is a modified version of the mean field theory * Corresponding author. E-mail: yandd@iccas.ac.cn. † E-mail: shi@mcmaster.ca. 4168 Macromolecules 2006, 39, 4168-4174 10.1021/ma060014a CCC: $33.50 © 2006 American Chemical Society Published on Web 05/19/2006