A.J. Ramirez-Pastor

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.

Temperature dependence of scaling laws in adsorption on bivariate surfaces

The adsorption of particles with nearest-neighbor repulsive interactions is studied through Monte Carlo simulation on bivariate surfaces characterized by patches of weak and strong adsorbing sites of size l. Patches are considered to have a square geometry and they can be either arranged in a deterministic ordered structure or in a random way. Quantities are identified which scale obeying power laws as a function of the scale length l and its dependence on the temperature is determined. Consequences of this finding are discussed for the determination of the energetic topography of the surface from adsorption measurements.

Adsorption preference reversal phenomenon from multisite-occupancy theory for two-dimensional lattices

Abstract The statistical thermodynamics of polyatomic species mixtures adsorbed on two-dimensional substrates was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the coverage and temperature dependence of the Helmholtz free energy and chemical potential are given. The formalism leads to the exact statistical thermodynamics of binary mixtures adsorbed in one dimension, provides a close approximation for two-dimensional systems accounting multisite occupancy and allows to discuss the dimensionality and lattice structure effects on the known phenomenon of adsorption preference reversal.

A simple statistical mechanical approach for studying multilayer adsorption of interacting rigid polyatomics

Abstract A simple statistical mechanical approach for studying multilayer adsorption of interacting rigid molecular chains of length k (k-mers) has been presented. The new theoretical framework has been developed on a generalization in the spirit of the lattice-gas model and the classical Bragg–Williams (BWA) and quasi-chemical (QCA) approximations. The derivation of the equilibrium equations allows the extension of the well-known Brunauer–Emmet–Teller (BET) isotherm to more complex systems. The formalism reproduces the classical theory for monomers, leads to the exact statistical thermodynamics of interacting k-mers adsorbed in one dimension, and provides a close approximation for two-dimensional systems accounting multisite occupancy and lateral interactions in the first layer. Comparisons between analytical data and Monte Carlo simulations were performed in order to test the validity of the theoretical model. The study showed that: (i) the resulting thermodynamic description obtained from QCA is significantly better than that obtained from BWA and still mathematically handable; (ii) for non-interacting k-mers, the BET equation leads to an underestimate of the true monolayer volume; (iii) attractive lateral interactions compensate the effect of the multisite occupancy and the monolayer volume predicted by BET equation agrees very well with the corresponding true value; and (iv) repulsive couplings between the ad-molecules hamper the formation of the monolayer and the BET results are not good (even worse than those obtained in the non-interacting case).

Protonation of β-lactoglobulin in the presence of strong polyelectrolyte chains: a study using Monte Carlo simulation

In this work, the molecular interaction between the protein β-lactoglobulin and strong polyelectrolyte chains was studied using Monte Carlo simulations. Different coarse-grained models were used to represent the system components. Both net charge and protonation of the isolated dimeric protein were analyzed as a function of pH. The acid-base equilibrium of each titratable group was distinctively modified by the presence of polyanion or polycation chains. The complexation on the wrong side of pI was more evident with the polycation than with the polyanion. It was mainly due to a charge regulation mechanism, where the reversion in net charge of the protein was more pronounced at the left of isoelectric point of the protein. The glutamic and aspartic groups play a key role in this charge reversion. Both polyanion and polycation were spatially adsorbed in different region on the protein surface, suggesting the importance of the surface charge distribution of the protein.

Inverse percolation by removing straight rigid rods from square lattices

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse percolation by removing straight rigid rods from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing straight rigid rods of length k (k-mers) from the surface. The central idea of this paper is based on finding the maximum concentration of occupied sites (minimum concentration of holes) for which connectivity disappears. This particular value of concentration is called the inverse percolation threshold, and determines a well-defined geometrical phase transition in the system. The results, obtained for k ranging from 2 to 256, showed a nonmonotonic size k dependence for the critical concentration, which rapidly decreases for small particle sizes (). Then, it grows for k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreases again and asymptotically converges towards a definite value for large values of k. Percolating and non-percolating phases extend to infinity in the space of the parameter k and, consequently, the model presents percolation transition in all ranges of said value. This finding contrasts with the results obtained in literature for a complementary problem, where straight rigid k-mers are randomly and irreversibly deposited on a square lattice, and the percolation transition only exists for values of k ranging between 1 and approximately . The breaking of particle-hole symmetry, a distinctive characteristic of the k-mers statistics, is the source of this asymmetric behavior. Finally, the accurate determination of critical exponents reveals that the model belongs to the same universality class as random percolation regardless of the value of k considered.

Quasi-chemical approximation for polyatomic mixtures

The statistical thermodynamics of binary mixtures of polyatomic species was developed based on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear k-mers and l-mers (species occupying k sites and l sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. This process is analyzed using the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorption of interacting polyatomic mixtures.

Site-bond percolation on simple cubic lattices: numerical simulation and analytical approach

The site-percolation problem on simple cubic lattices has been studied by means of numerical simulation and analytical calculations based on exact counting of configurations on finite cells. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as and ) have been considered. In (), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. Theoretical and numerical results, supplemented by analysis using finite-size scaling theory, were used to calculate the complete phase diagram of the system in the () space. Our study allowed us also to determine the critical exponents (and universality) characterizing the phase transition occurring in the system.

Adsorption on Heterogeneous Surfaces with Simple Topographies

The localized monolayer adsorption of interacting particles onto heterogeneous surfaces has been studied through Monte Carlo simulation in the framework of the lattice–gas model. The substrate was modelled as a collection of finite homotatic patches, each one characterized by an adsorption energy arising from a discrete energy density function. Patches were distributed spatially, either in a deterministic alternate way (ordered topography) or in a non-overlapping random way (random topography). The adsorption process was analyzed by following the behaviour of surface coverage versus chemical potential (adsorption isotherm) and the differential heat of adsorption as a function of the coverage. These quantities depend on the size of the patch as well as on the topological distribution of the patches on the surface. The consequences of these findings are discussed for the determination of the energetic topography of the surface from adsorption measurements.