Cluster approximation applied to multisite-occupancy adsorption: configurational entropy of the adsorbed phase for dimers and trimers on triangular lattices.

The adsorption of dimers and trimers on triangular lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations. The thermodynamic process is analyzed through the behavior of the configurational entropy per site of the adsorbed phase as a function of the coverage. MC calculations, supplemented by the thermodynamic integration method, are performed in the grand canonical ensemble. The theoretical model used in the present study is called Cluster Approximation (CA), and it is based on exact calculation of states on finite cells. An efficient algorithm allows us to determine the detailed structure of the configuration space for m = l1 × l2 cells. From there, the thermodynamic properties can be obtained. Five systems are investigated, according to the size and shape of the molecule in the adsorbed state: (i) dimers, (ii) linear trimers, (iii) triangular trimers, (iv) 60°-angular trimers and (v) 120°-angular trimers on triangular lattices. Dimer and trimer are the simplest cases of a polyatomic adsorbate, containing all the properties of the multisite-occupancy adsorption and can be used to model several experimental systems. CA solutions are tested by comparison with MC simulations and previous data in the literature. Special interest is devoted to the calculation of the configurational entropy per site in the limit case of θ → 1 (full coverage), where some exact results are available. The theoretical formalism is also applied to model CH4 and CO2 clathrate hydrates. In these systems, a triangular lattice is used to simulate the substrate, and methane(carbon dioxide) molecules can be well represented by triangular(linear) trimers. The good qualitative agreement between simulation and analytical data supports the validity of the CA scheme to predict the behavior of a wide variety of multisite-adsorption models, for which theoretical solutions are very difficult to obtain.

CO2-CH4 Exchange Process in Structure I Clathrate Hydrates: Calculations of the Thermodynamic Functions Using a Flexible 2D Lattice-Gas Model and Monte Carlo Simulations.

A two-dimensional lattice-gas model, supplemented by Monte Carlo simulations in the grand canonical ensemble, is applied to study the CO2/CH4 exchange process in sI clathrate hydrates. The coverage dependence of the Helmholtz free energy, chemical potential, entropy, and degree of deformation of the sI structure is given. Two different situations are considered according to the value of the intra- and inter-species' interactions. First, lateral interactions between the guest species and water molecules are introduced by following the well-known Lorentz-Berthelot mixing rules. Second, the study is restricted to an ideal clathrate hydrate, where the lateral interactions are neglected and entropy governs the exchange of CH4 by CO2. In the case of real clathrate hydrates (non-zero lateral interactions), the displacement phenomenon is clearly observed from the behavior of the chemical potential and Helmholtz free energy as functions of coverage. The guest species CO2 has an occupation of more than 80% of the cavities, and therefore displaces the CH4 species. Only 13 to 15% of CH4 remains stagnant in the sI structure. With respect to the degree of deformation, a direct relationship between cell distortion and cell occupancy is observed. Finally, the detailed analysis carried out for the ideal clathrate hydrate allows us to interpret the physical mechanism underlying the exchange process: it is entropy, not energy, that drives the displacement of CH4 by CO2 in sI clathrate hydrates.

Interaction between ß-Lactoglobuline and Weak Polyelectrolyte Chains: A Study Using Monte Carlo Simulation.

Complexation between the ß-lactoglobulin and a weak acid polyelectrolyte (PE) has been studied using Monte Carlo simulations. Different coarse-grained models were used to represent the system, and two different acidic constants were used on the PE model. The protein-PE interaction is quantified considering the average PE monomers adsorbed on the protein as a function of pH. A maximum in the interaction between macromolecules was found, which is explained as a function of the titration behavior of the ß-lactoglobuline and weak PE. We also found that there was a direct relation between the pH range of monomers adsorbed and the change on dissociation profile of the protein and weak PE compared to isolated conditions. The complexation of protein-PE increased both the dissociation degree of the PE chain and the protein net charge. This benefits the monomer adsorption on the protein surface.

Multiple Exclusion Statistics.

A new distribution for systems of particles in equilibrium obeying the exclusion of correlated states is presented following Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. Haldane's statistics and Wu's distribution are recovered in the limit of noncorrelated states of the multiple exclusion statistics. In addition, an exclusion spectrum function G(n) is introduced to account for the dependence of the state exclusion on the occupation number n. The results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size k (k-mers) where the multiple exclusion occurs. Remarkable agreement is found with grand-canonical Monte Carlo simulations from k=2 to 10 where the multiple exclusion dominates as k increases.

Adsorption of three-domain antifreeze proteins on ice: a study using LGMMAS theory and Monte Carlo simulations.

In the present work, the adsorption of three-domain antifreeze proteins on ice is studied by combining a statistical thermodynamics based theory and Monte Carlo simulations. The three-domain protein is modeled by a trimer, and the ice surface is represented by a lattice of adsorption sites. The statistical theory, obtained from the exact partition function of non-interacting trimers adsorbed in one dimension and its extension to two dimensions, includes the configuration of the molecule in the adsorbed state, and allows the existence of multiple adsorption states for the protein. We called this theory "lattice-gas model of molecules with multiple adsorption states" (LGMMAS). The main thermodynamics functions (partial and total adsorption isotherms, Helmholtz free energy and configurational entropy) are obtained by solving a non-linear system of j equations, where j is the total number of possible adsorption states of the protein. The theoretical results are contrasted with Monte Carlo simulations, and a modified Langmuir model (MLM) where the arrangement of the adsorption sites in space is immaterial. The formalism introduced here provides exact results in one-dimensional lattices, and offers a very accurate description in two dimensions (2D). In addition, the scheme is capable of predicting the proportion between coverage degrees corresponding to different conformations in the same energetic state. In contrast, the MLM does not distinguish between different adsorption states, and shows severe discrepancies with the 2D simulation results. These findings indicate that the adsorbate structure and the lattice geometry play fundamental roles in determining the statistics of multistate adsorbed molecules, and consequently, must be included in the theory.

Adsorption thermodynamics of two-domain antifreeze proteins: theory and Monte Carlo simulations.

In this paper we develop the statistical thermodynamics of two-domain antifreeze proteins adsorbed on ice. We use a coarse-grained model and a lattice network in order to represent the protein and ice, respectively. The theory is obtained by combining the exact analytical expression for the partition function of non-interacting linear k-mers adsorbed in one dimension, and its extension to higher dimensions. The total and partial adsorption isotherms, and the coverage and temperature dependence of the Helmholtz free energy and configurational entropy are given. The formalism reproduces the classical Langmuir equation, leads to the exact statistical thermodynamics of molecules adsorbed in one dimension, and provides a close approximation for two-dimensional systems. Comparisons with analytical data obtained using the modified Langmuir model (MLM) and Monte Carlo simulations in the grand canonical ensemble were performed in order to test the validity of the theoretical predictions. In the MC calculations, the different mechanisms proposed in the literature to describe the adsorption of two-domain antifreeze proteins on ice were analyzed. Indistinguishable results were obtained in all cases, which verifies the thermodynamic equivalence of these mechanisms and allows the choice of the most suitable mechanism for theoretical studies of equilibrium properties. Even though a good qualitative agreement is obtained between MLM and MC data, it is found that the new theoretical framework offers a more accurate description of the phenomenon of adsorption of two-domain antifreeze proteins.

Screening of bio-compatible metal-organic frameworks as potential drug carriers using Monte Carlo simulations.

A series of bio-compatible metal-organic frameworks (MOFs) have been studied as potential carriers for drug delivery applications. Grand canonical Monte Carlo (GCMC) simulations were performed to study the adsorption of the model drug ibuprofen. Simulations were first validated with available experimental data for ibuprofen adsorption and release in MIL-53, MIL-100 and MIL-101. In the second stage, the study was extended to three additional MOFs with interesting properties in terms of bio-compatibility and porosity: CDMOF-1, based on edible precursors; MOF-74 containing a highly biocompatible metal (Mg); and BioMOF-100, a mesoporous MOF with extremely high pore volume. By comparing with experimental data, we show how GCMC simulation is able to predict the macroscopic performance of new porous MOFs in drug delivery applications, providing useful molecular-level insights and giving thermodynamic and structural details of the process. Adsorption isotherms, snapshots, energy of adsorption and radial distribution functions were used to analyse the drug delivery process.