A MULTILAYER THEORY FOR INTERFACIAL PROPERTIES OF SYSTEMS CONTAINING HYDROGEN-BONDING MOLECULES

We propose a generalized, lattice-based statistical thermodynamic theo ry for understanding the interfacial phenomena in systems containing h ydrogen bonding molecules (often termed as associating molecules), suc h as water: amphiphiles, block copolymers and associating solid surfac es. The basic assumption is that the configurational partition functio n (Q) can be factored into two parts: (i) one term [Q((phys))] arising from the presence of nonassociating, or the ''physical,'' interaction s, for which we adopt the self-consistent-field theory [Scheutjens and Fleer, J. Phys. Chem. 84, 178 (1980)], (ii) the other term [Q((hbond) )] arising from the presence of hydrogen bond interactions, for which we propose a new association theory. The focus of the proposed associa tion theory is on the correct counting of the number of II bonds that are formed between various types of donor and acceptor sites that sati sfy the proximity and orientational requirements for bond formation. T he expression for Q((hbond)) is evaluated by accounting for the entrop ic loss and energy released upon the formation of each hydrogen bond, and the transient nature of hydrogen bonds. The equilibrium criteria f or H bonding is satisfied by minimizing the free energy of the system with respect to the number of H bonds formed between each type of dono r site present in each layer z and each type of acceptor site present in each layer z', where z' = z, or z +/- 1. It turns out that the fina l expression for Q((hbond)) , at equilibrium, depends only on the frac tion of unbonded association sites of all types that are located at va rious distances from the interface, which are themselves related to th e equilibrium constant of formation of H bond between various donor-ac ceptor pairs, temperature of the fluid and the concentration profile i n the interfacial region. For systems containing pure, spherical, asso ciating molecules in the fluid phase, our expression for Q((hbond)) is found to;be identical to that of the density functional theory [Segur a et al., Mel. Phys. 90, 759 (1997)], except for the inherent differen ces existing between continuum and lattice treatments. We present the results of the proposed theory in two parts. First, we verify the ther modynamic consistency of our approach with the Gibbs adsorption rule. Second, to clearly elucidate the role of hydrogen bonding on interfaci al properties, we provide results for systems containing a binary flui d mixture, which comprises of an associating monomeric solvent and an amphiphilic, di-block, chain molecule, against an associating solid su rface. (C) 1998 American Institute of Physics. [S0021-9606(98)50137-7] .