A three stage model for adsorption of non ionic surfactants

The adsorption of nonionic surfactants onto both hydrophilic and hydrophobic surfaces has been extensively researched from the point of view of physical chemistry.i,2 In these studies nonionic surfactants were assumed to interact with both the surface and each other. The resultant adsorption isotherms were then explained in terms of interaction strength and surfactant orientation. A five stage model for adsorption has been postulatedi,3 in which interaction was favored with the surface by a specific part of the molecule (see Fig. 1). This model contains three different adsorption sequences, denoted by A, B, and C. The adsorption sequence is determined by the surfactant's interactions with the surface. In sequences A and C a vertically orientated monolayer is formed in stage V, but sequence B halts at stage III. The processes corresponding to these stages are as follows. (I) The molecule is adsorbed onto a surface mainly due to van der Waal's interaction. Some other interaction may be present, but this will be surfactant/surface dependent. The molecule lies flat on the surface as a result of positive adsorption along its length. This may be caused by van der Waal's forces or hydrophobic/hydrophilic interactions with the surface. (II) More surfactants are adsorbed onto the surface and are held flat against the surface until a horizontal monolayer is built up. (III A) If the hydrophilic group is only weakly adsorbed it may be displaced from the surface by the alkyl chains of adjacent molecules. (III B) If there is no favored type of displacement for the molecules then the adsorbate remains flat on the surface. This may be due to low concentration levels which do not give rise to significant surfactant-solute interactions. (III C) If there is a strong interaction between the hydrophilic group and the surface the alkyl chains are displaced and surfactant-solute interactions become significant. (IV A) and (IV C) As the surfactant concentration in the bulk solution approaches the critical micelle concentration the molecules on the surface change orientation, becoming vertically orientated and reveal more vacant sites on the surface. This results in a significant increase in the adsorption rate. (V A) and (V C) Virtually all sites are full and a saturation limit is reached. After (V C) micelle production may take place on the surface. In stages III and IV, for cases A and C in Fig. 1, the change in surfactant orientation from horizontal to vertical is fundamental to the explanation of the isotherm profile. Without it the secondary adsorption process cannot be explained in terms of the number of sites onto which adsorption can take place. The isotherms corresponding to each of the three adsorption sequences is given in Fig. 2. The different stages are marked on the graphs. Note that the graphs are of surfactant adsorbed against concentration. In this paper we propose a new three stage model based upon the process of random sequential adsorption. This is the process by which particles are placed on a surface or line in an irreversible, random manner. At each time step a random position and orientation is chosen for the particle. If a particle can be placed in this position without overlapping with any previously placed particle then it is deposited onto the line or surface. This subject is much studied, the review by Bartelt and Privman provides an up to date list of references. Most problems have been solved exactly in one dimension either on the lattice, where k-mers are deposited,5,6 or in the continuum, where lines of length 1 are deposited. In the continuum the problem is better known as the random car parking problem. In two dimensions various numerical studies have been performed. In all these models the surface becomes covered with particles as time evolves. When the surface is full, in the t= 00 limit, no further deposition is possible and the surface is said to be jammed. The proportion of the surface covered in this limit is called the jamming coverage.