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Notes: We apply statistical mechanical principles to derive simple expressions relating the hydrogen bond thermodynamic properties to the static dielectric constant of water. The approach followed by us was to develop an expression for the Kirkwood's structure factor (g) of water, taking into account the dipolar correlations between a central molecule and H-bonded neighbors present in infinite number of shells surrounding the central molecule. The number of H-bonded neighbors in a specific shell was related to the probability P for the various donor/acceptor sites of any given water molecule to be associated. Neglecting cooperativity effects, we evaluated P by focusing only on the correct counting of H-bonds formed between various association sites rather than on the oligomer distribution. The theory yielded an extremely simple expression for the structure factor (g) of the fluid at any given temperature in terms of the enthalpy (H) and entropy (S) changes associated with bond formation. The proposed theory was then combined with the Kirkwood–Frohlich theory for evaluating the dielectric constant (ε0). We have demonstrated that the theory correctly predicts the dielectric constant of ice-I without the use of any adjustable parameters. We have then deduced estimates for H-bond thermodynamic properties (H=−5.58 kcal/mole of H-bonds; S=−8.89 cal/deg⋅mole of H-bonds) by fitting the theoretical results for ε0 of liquid water to available experimental data over temperatures ranging from 0 °C to the critical point of water. The error in the theoretical values was found to be within 1% of the corresponding experimental values over the entire range of temperatures studied. To further test the theory, we have demonstrated that the temperature variation of the average number of H-bonds per water molecule, calculated using the proposed theory with the above mentioned values for H and S, compares quite well with those estimated from various available spectroscopic and molecular simulation studies. © 2000 American Institute of Physics.

Notes: We propose a generalized, lattice-based statistical thermodynamic theory for understanding the interfacial phenomena in systems containing hydrogen bonding molecules (often termed as associating molecules), such as water, amphiphiles, block copolymers and associating solid surfaces. The basic assumption is that the configurational partition function (Q) can be factored into two parts: (i) one term [Q(phys)] arising from the presence of nonassociating, or the "physical," interactions, 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 association theory is on the correct counting of the number of H bonds that are formed between various types of donor and acceptor sites that satisfy the proximity and orientational requirements for bond formation. The expression for Q(hbond) is evaluated by accounting for the entropic loss and energy released upon the formation of each hydrogen bond, and the transient nature of hydrogen bonds. The equilibrium criteria for 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 donor 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 final expression for Q(hbond), at equilibrium, depends only on the fraction of unbonded association sites of all types that are located at various distances from the interface, which are themselves related to the equilibrium constant of formation of H bond between various donor-acceptor pairs, temperature of the fluid and the concentration profile in the interfacial region. For systems containing pure, spherical, associating molecules in the fluid phase, our expression for Q(hbond) is found to be identical to that of the density functional theory [Segura et al., Mol. Phys. 90, 759 (1997)], except for the inherent differences existing between continuum and lattice treatments. We present the results of the proposed theory in two parts. First, we verify the thermodynamic consistency of our approach with the Gibbs adsorption rule. Second, to clearly elucidate the role of hydrogen bonding on interfacial properties, we provide results for systems containing a binary fluid mixture, which comprises of an associating monomeric solvent and an amphiphilic, di-block, chain molecule, against an associating solid surface. © 1998 American Institute of Physics.

Notes: We present, in this note, a simple, highly computationally efficient, and yet exact set of expressions to accurately account for H-bond interactions among molecules in any multilayer theory of interfaces. We also demonstrate that these expressions, derived using the bond-counting approach, are entirely consistent with concepts inherent in the reaction equilibrium approach proposed by F. Z. Dolezalek [Phys. Chem. 64, 727 (1908)]. © 1999 American Institute of Physics.

Notes: We apply principles of statistical mechanics to derive simple expressions relating the hydrogen bond thermodynamic properties to the static dielectric constant of aqueous solutions. The approach followed by us was to develop an expression for the dipolar correlations between a centrally fixed molecule of a given type and its neighbors present in the surrounding shells, in terms of bonding probabilities, and combine the resulting expression with the Kirkwood–Frohlich equation. We considered only those neighboring molecules which are a part of the H-bonded cluster containing the central molecule. The bonding probabilities were evaluated by assuming a reaction equilibrium model, in which the formation of clusters between different association sites was represented by a series of chemical reactions. To demonstrate the utility of the theory, we provide comparison of the results for the temperature and composition variation of dielectric constant and H-bond stoichiometry of three model systems, methanol+water, ethanol+water, and acetone+water mixtures, against available experimental/simulation data. © 2002 American Institute of Physics.