1436
Langmuir 1993,9, 1436-1438
Notes Initiation of Aggregation in Colloidal Particle Monolayers
D.J. Robinson and J. C. Earnshaw' The Department of Pure and Applied Physics, The Queen's University of Belfast, Belfast BT7 l N N , Northern Ireland Received October 29,1992. In Final Form: February 24, 1993
1. Introduction The formation of random clusters from small basic subunitaby such nonequilibriumprocesses as aggregation, coagulation,and flocculationfeatures in many important phenomena in science and technology. In particular, the aggregation of particles of colloidal dimensions is a phenomenon of longstanding interest because of ita role in natural processes and industrial pr0ducta.l Previous studies2of these nonequilibrium phenomena in three dimensions have been subject to significant experimental difficulties. In contrast two-dimensional colloidal monolayers enable the structure and dynamical properties of the system to be accessed directly: the "atomic" structure of the monolayer is readily visualized by optical microscopy while ita mechanical properties can be m e a s ~ r e d . ~In! ~some respects the direct visualization of the structure makes the system an experimental analogue of computer simulations. Such colloidal monolayers permit the exploration of such fundamental phenomena as crystallizationand melting,516diffusion limited a g g r e g a t i ~ nand , ~ ~reversible, ~ dynamical clustering and ~rdering.~ A suitable model system comprises polystyrene microspheres spread at a fluid interface to form a stable quasitwo-dimensional array,6 trapped by capill& and electrostaticlO forces orders of magnitude greater than kT.In our studies8colloidal monolayers were made to aggregate by raising the electrolyte concentration of the water substrate, the consequent electrostatic screeningallowing the attractive van der Waals forces to dominate. In practice the concentrations required to induce quite modest rates of aggregation were surprisingly large compared to colloids in bulk solution, for which rather low electrolyte concentrations (=millimolar divalent salt) induce rapid aggregationell Typically divalent salt concentrations exceeding 0.5 M were required to induce rapid aggregation.* Even more puzzlingly, some of our samples refused to aggregate at all, irrespective of the substrate (1) Jullien, R.;Botet, R. Aggregation and Fractal Aggregates; World Scientific: Singapore, 1987. (2) Vicsek,T.Fractal CrowthPhenomena;World Scientific: Singapore, 1989; p 247. (3) Earnshaw, J. C.;Robinson, D. J. J.Phys.: Condens. Matter 1990, 2,9199. (4) Garvey, M. J.; Mitchell, D.; Smith, A. L. Colloid Polym. Sci. 1979, 257, 70. (5) Pieranaki, P. Phys. Reu. Lett. 1983,45, 569. (6) Armstrong,A.J.;Mockler, R. C.;OSullivan,W. J.J.Phys: Condens. Matter 1989, I, 1707. (7) Hurd, A. J.; Schaefer, D. W. Phys. Reu. Lett. 1985,54, 1043. (8) Robinson, D.J.; Earnshaw, J. C. Phys. Rev. A 1992,46,2045,2055, 2065. (9) Onoda, G. Y. Phys. Rev. Lett. 1985,55, 226. (10) Earnshaw, J. C.J. Phys. D Appl. Phys. 1986, 19, 1863. (11) Carpineti, M.; Giglio, M. Phys. Reu. Lett. 1992, 68, 3327.
molarity. Other workers have noted the need for large concentrations.7J2 Obviously the simple ideas about screening outlined above must be inadequ& for surface colloids. In this paper we consider this problem. The following section briefly reviews some pertinent characteristics of colloidal monolayers and the ideas underpinning the conventional model. We then discuss a hypothesis which seems to resolve at least some of the observed contradictions and describe experimental investigations tending to support it. 2. Background Physics 2.1. Polystyrene Microspheres. In our experiments we used sulfonated polystyrenemicrospheres, of diameter 1.088f 0.079 pm. They have a low surface concentration of acid groups compared to certain other latex particles13 and should therefore be easily induced to aggregate by the addition of electrolyte. Also, with only one permanently bound surfacegroup present (*sod-)the surfacechemistry is simplified.13 Figure l a sketchesthe surfacechemistryof the particles. In their manufacture sodium dodecylsulfate (SDS)adsorbs at the hydrophobic"basenpolystyrene sites on the particle, leaving the sulfonate group (*SOa-) exposed to the dispersing medium. The adsorbed surfactant assists in the stabilization of the particles by increasing the surface charge and by making the particles more hydrophilic, reducing the likelihood of hydrophobic bonding. The particles are also inherently negatively charged due to the sulfate surface groups (-SO4-). The degree of ionization of both types of acid groups depends upon the pH of the medium. The surface charges should be fairly uniformly distributed.13 The particles are thus surrounded by an atmosphere of cationic counterions from the surface sulfate (K+)and sulfonate (Na+)groups. The counterions form a diffuse ion atmosphere,the second half of a double layer of charge at the surface of the c0ll0id.l~The physical extent of this layer depends upon the ionic strength and valency of the aqueous phase. A particle at the surface of a fluid has an asymmetric counterion cloud5J5(see Figure 21, leading to an effective dipole moment p = Ze/(cK)lI2 perpendicularto the interface (E is the effective dielectric constant of the medium, while K - ~ is the Debye screening length). Through the air, the particles interact with an algebraic, dipolar force law, whereas interactions propagatingthrough the water decay exponentially because of the counterion screening. The exponentially screened Coulomb law dominates at low interparticle separations (
