On the use of the Hill’s model as local isotherm in the interpretation of the behaviour of the adsorption energy distributions

Adsorption of hexamethyl pararosaniline chloride dye on MgO‐PbFe2O4: Experimental study and statistical physics modeling via double‐layer model

“…The mean values for C s at their ideal temperature have been calculated by changing the C 1 and C 2 values in comparison to the temperature. 53 𝜀 1 = RT ln…”

“…Two parameters refer to the adsorption energy of the two underlying layers in terms of our model expression (Equations 18 and 19). The mean values for C s at their ideal temperature have been calculated by changing the C 1 and C 2 values in comparison to the temperature 53 $$\begin{equation}{\varepsilon _1}= {\rm{RT}}\;{\rm{ln}}\left( {\frac{{{C_S}}}{{{C_1}}}} \right).\end{equation}$$ $$\begin{equation}{\varepsilon _2} = {\rm{RT}}\;{\rm{ln}}\left( {\frac{{{C_S}}}{{{C_2}}}} \right).\end{equation}$$…”

On the origin of cooperativity effects in the formation of self-assembled molecular networks at the liquid/solid interface

“…4,21,46 The main difference between the stated adsorption isotherms is the introduction of molecule-molecule interactions in the Hill and Matsuda models as opposed to the Langmuir model which is developed under the assumption of non-interacting molecules. 4,46,47 By the introduction of intermolecular interactions, a new parameter is added to the models that accounts for these interactions and is known as a cooperativity factor. For additional details of each of the models and their comparison, we direct the reader to relevant literature.…”

Quantifying the Cooperative Process of Molecular Self-Assembly on Surfaces: A Case Study of Isophthalic Acids

“…In the next section, we provide an overview of different analytical approaches to explain the experimental data trends. An empirical model very often used for analyzing cooperative processes in literature, based on the reaction of the type proposed in eq 2, can be understood as multiple (denoted by x) ligand (L) binding from solution to multiple receptors on the same protein, or in the case of adsorption, multiple surface sites (S) forming the self-assembled structure, L x S. 49 This model is known as the Hill equation (eq 3), 50 where [L] denotes the equilibrium concentration of molecules in a supernatant solution, and K denotes the equilibrium constant for the process. A major difference between the simple Langmuir model presented in eq 1 and the Hill equation is the introduction of parameter n. The Hill coefficient, n, is an indicator of cooperative interactions and can loosely be interpreted as the number of neighboring adsorbing molecules per surface site.…”