STATISTICAL-MECHANICS OF SELF-ASSEMBLED MONOLAYERS

A simple model is presented for self-assembled monolayers such as alkylthiols irreversibly adsorbed on a gold surface. It involves an assembly of cylindrical molecules; one end of each cylinder is bound on the surface atom and the other end is highly oriented toward the solution. It has the following assumptions: planar arrangement of adsorption sites with identical spacing on the surface, saturation of the sites with the adsorbates, possibility of free rotation of the adsorbate around the site, interaction between the adsorbate and solvent, and interaction among the adsorbates having a harmonic potential. With these assumptions, a classical Hamiltonian is obtained, including three-dimensional rotation energy and potential energy due to the two interactions. A canonical partition function is derived from the Hamiltonian in an integral form. It depends mainly on the adsorbate-adsorbate interactions, the length and the diameter of the adsorbate, and the spacing of the sites. It is expressed by an approximate equation valid for a long adsorbate and low temperatures. The Helmholtz energy and the average value of the tilt angle are estimated from numerical integration of the partition function. The Helmholtz energy decreases almost linearly with an increase in the length of the adsorbate. The chain tilts more than the angle predicted from the geometry of the packed chains. The larger the tilt angle, the more blocked is the ion penetration through the film.