Structure and Ordering in Localized Adsorption of Particles Z. ADAMCZYK, 1 M. ZEMBALA, B. SIWEK, AND P. WARSZYlqSKI Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, 30-239 Krak6w, Poland Received October 27, 1989; accepted March 20, 1990 Localized, sequential adsorption of colloid particles interacting via screened Coulomb potential was analyzed theoretically and experimentally. The two-dimensional (2D) pair correlation functions were simulated by using the Monte Carlo technique for various surface concentrations 0 and for various screening length parameters Ka, characterizing the "softness" of the particle-particle interaction potential. For Ka >> 1 the hard-disk limiting behavior was confirmed (maximum surface concentration 0rex = 55% ). The 0rex for soft disks, which is generally much smaller than the above value, was also determined as a function of the Ka parameter. A distinctive tendency toward a short-range ordering, analogous to the 3D results obtaining previously for colloid suspensions, was found for surface concentration close to the 0~x value. Theoretical predictions were tested by applying the direct experimental method based on microscope observations of particle adsorption. A monodisperse polystyrene suspension was used (particle size 0.90 #m) and the adsorbing surface was made of mica sheets. Experimental results proved to be in good agreement with Monte Carlo simulations illustrating well the tendency towards structurization (2D quasi-liquid phase formation) for surface concentrations close to the predicted 0rexvalues. © 1990 Academic Press,Inc. INTRODUCTION The importance of the understanding of structurization and ordering phenomena oc- curring in dispersions of colloid particles was recognized long ago. These systems, whose in- tereaction energy is dominated by repulsive double-layer (DL) forces originating from the screened Coulomb potential, can be used for testing recent statistical-mechanical theories of the fluid phase. This is so because the particle- particle correlation functions (or structure facctors) are relatively easily accessible from X-ray or light scattering experiments. Struc- ture formation in dilute colloid dispersions was studied by means of the Monte Carlo (MC) simulation technique in (1-3). On the other hand, closed analytical solutions of the Orn- stein-Zernicke equation based on the mean spherical approximation (MSA) were reported in (4, 5 ) for colloid dispersions interacting via the screened Coulomb potential. This approx- l To whom correspondence should be addressed. imation fails, however, for lower volume con- centration of suspensions. This deficiency was overcome by the modified, rescaled MSA method (6). An approximate analytical so- lution of this problem based on a perturbation analysis was derived in (7). More recently, ex- tensive MC simulations were applied for a quantitative characterization of the two-par- ticle radial distribution function (pair corre- lation function) g12 and for calculation of the structure factor of dilute colloid dispersions (8-10). It should be mentioned, however, that in these works an inaccurate formula was used to describe the DL interactions. The equation used is valid for thin double layers and low surface potentials, presumably smaller than +50 mV, whereas the fitting values of the sur- face potential assumed in ( 1, 2, 5, 6) were in the range of- 150 to -250 mV, i.e, well above this limit. The problem of deriving appropriate expressions for the particle DL interactions shall be addressed to in the next section. 123 Journalof Colloid and InterfaceScience, Vol. 140,No. 1, November1990 0021-9797/90 $3.00 Copyright © 1990 by Academic Press,Inc. All rights of reproduction in any formreserved.