Theoretical model of adsorption in a templated porous material

The Use of Computational Methods for the Development of Molecularly Imprinted Polymers

Recent years have witnessed a dramatic increase in the use of theoretical and computational approaches in the study and development of molecular imprinting systems. These tools are being used to either improve understanding of the mechanisms underlying the function of molecular imprinting systems or for the design of new systems. Here, we present an overview of the literature describing the application of theoretical and computational techniques to the different stages of the molecular imprinting process (pre-polymerization mixture, polymerization process and ligand-molecularly imprinted polymer rebinding), along with an analysis of trends within and the current status of this aspect of the molecular imprinting field.

Fluids in porous media. IV. Quench effect on chemical potential

It appears to be a common sense to measure the crowdedness of a fluid system by the densities of the species constituting it. In the present work, we show that this ceases to be valid for confined fluids under some conditions. A quite thorough investigation is made for a hard sphere (HS) fluid adsorbed in a hard sphere matrix (a quench-annealed system) and its corresponding equilibrium binary mixture. When fluid particles are larger than matrix particles, the quench-annealed system can appear much more crowded than its corresponding equilibrium binary mixture, i.e., having a much higher fluid chemical potential, even when the density of each species is strictly the same in both systems, respectively. We believe that the insight gained from this study should be useful for the design of functionalized porous materials.

Mode-coupling theory predictions for the dynamical transitions of partly pinned fluid systems

The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system. The only significant qualitative difference lies in the shape of the diffusion-localization lines at high matrix densities, with a reentry phenomenon for the PP system but not for the QA model, in full agreement with recent computer simulation results. This finding clearly lends support to the predictive power of the MCT for fluid-matrix systems. In addition, the predictions of the MCT are shown to be in stark contrast with those of the random first-order transition theory. The PP systems are thus confirmed as very promising models for differentiating tests of theories of the glass transition.

Statistical mechanics of homogeneous partly pinned fluid systems

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.

A computational study of electrolyte adsorption in a simple model for intercalated clays

A pillared interlayered clay is represented by a two-dimensional quenched charged disordered medium, in which the pillar configuration is produced by the quench of a two-dimensional electrolyte and the subsequent removal of the anions (that act as a template). The cation charge is counterbalanced by a neutralizing background that is an ideal representation of the layer's negative charge in the experimental system. In this paper we investigate the adsorption of electrolyte particles in this charged disordered medium resorting both to the use of the replica Ornstein-Zernike equation in the hypernetted chain approximation and grand canonical Monte Carlo simulations. The theoretical approach qualitatively reproduces the simulated behavior of the adsorbed fluids. Theoretical estimates of the material porosities obtained for various types of pillar distributions are in good agreement with the simulation. We investigate the influence of the matrix on correlation functions and adsorption isotherms.

Topological considerations on microporous adsorption processes in simple models for pillared interlayered clays

The microporous structure of pillared interlayered clays is determined by their interlayer separation and the distribution of the pillars that separate their layers. The pillars provide stability to these quasi-two-dimensional high surface area materials. In this work we present a topological analysis of available and accessible volumes within various simple models of pillared interlayered clays. Each model is characterized by a distribution of pillars. Both fully ordered structures and disordered pillar distributions with either attractive or repulsive interpillar correlations are considered. Particular attention is paid to the problem of accessibility. In systems with similar degrees of porosity, even when cavities within each model might be able to host the same adsorbate molecules, their accessibility will strongly depend on the pillar distribution. The theoretical analysis presented in this work may facilitate the interpretation of experimental results, pointing out those quantities that are key to describe the texture of the porous material.

Computer simulation of volatile organic compound adsorption in atomistic models of molecularly imprinted polymers

Molecularly imprinted polymers (MIPs) offer a unique opportunity to significantly advance volatile organic compound (VOC) sensing technologies and a number of other applications. However, the development of these applications using MIPs has been hindered by poor understanding of the microstructure of MIPs, geometry of binding sites, and the details of molecular recognition processes in these materials. This is further complicated by the vast number of optimization parameters such as building components and processing conditions. Computer simulations and molecular modeling can help us understand adsorption and binding phenomena in MIPs on the molecular level and thus provide a route to more efficient MIP design strategies. So far, molecular models have been either oversimplified or severely limited in length scale, essentially focusing on a single binding site. Here, we propose a more general, atomistically detailed model that describes the microstructure of MIPs. We apply this model to investigate adsorption of pyridine, benzene, and toluene in MIPs and demonstrate that it is able to capture a number of essential experimental features. Therefore, this model can serve as a starting point in computational design and optimization of MIPs.

Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.

Fluids in porous media. I. A hard sponge model

The morphology of many porous materials is spongelike. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum. We found an analytical expression for describing the interaction potential between fluid particles and the spongelike porous matrix. The diagrammatic expansions of different correlation functions are derived as well as that of grand potential. We derived also the Ornstein-Zernike (OZ) equations for this model. In contrast to Madden-Glandt model of random porous media [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the OZ equations for a fluid confined in our hard sponge model have some similarity to the OZ equations of a three-component fluid mixture. We show also how the replica method can be extended to study our sponge model and that the same OZ equations can be derived also from the extended replica method.

Chemical potential of a hard sphere fluid adsorbed in model disordered polydisperse matrices

We consider a model for adsorption of a simple fluid in disordered polydisperse adsorbents. The fluid consists of hard sphere particles. On the other hand, the adsorbents of this study are modeled as a collection of hard spheres with their diameter obeying a certain distribution function. Our focus is in the evaluation of the chemical potential of the fluid immersed in such a polydisperse material. It permits us to obtain porosity and pore size distribution for the adsorbent, as well as a set of adsorption isotherms. The latter have been calculated theoretically and by grand canonical Monte Carlo simulations. We observe that the width of assumed polydispersity distribution affects all the properties of the system. Nevertheless, the effect of matrix packing is dominant in determining adsorption for this class of models. We are convinced that the matrix structures generated via more sophisticated algorithms would exhibit stronger effects of polydispersity on the entire set of properties of adsorbed simple fluids.

Replica Ornstein-Zernike theory of adsorption in a templated porous material: Interaction site systems

Molecular templating offers the possibility of porous materials whose selectivity rivals the molecular recognition observed in nature. The design of templated materials requires a molecular understanding of the templating effect on the material structure and performance. We present here a theoretical description of adsorption in a model templated porous material. Our model material is a quenched, equilibrated mixture of template and matrix molecular species where the template component has been subsequently removed. We propose a set of site-site [i.e., reference interaction site model (RISM)] replica Ornstein-Zernike equations relating the correlation functions of template, matrix, and adsorbing fluid molecules. To test this approach, we focus here on systems interacting via hard-sphere site-site potentials and employ a Percus-Yevick closure. We consider chain and cluster species composed of up to five spheres and observe a range of effects associated with template structure, including higher affinity toward, and enhanced templating by, compact cluster molecules. We assess these effects by grand canonical Monte Carlo simulation and discuss their implication to the design of templated molecular recognition materials.

Vapor-liquid transitions of dipolar fluids in disordered porous media: Performance of angle-averaged potentials

Using replica integral equations in the reference hypernetted-chain (RHNC) approximation we calculate vapor-liquid spinodals, chemical potentials, and compressibilities of fluids with angle-averaged dipolar interactions adsorbed to various disordered porous media. Comparison with previous RHNC results for systems with true angle-dependent Stockmayer (dipolar plus Lennard-Jones) interactions indicate that, for a dilute hard sphere matrix, the angle-averaged fluid-fluid (ff) potential is a reasonable alternative for reduced fluid dipole moments m( *2)=mu(2)/(epsilon(0)sigma(3))< or =2.0. This range is comparable to that estimated in bulk fluids, for which RHNC results are presented as well. Finally, results for weakly polar matrices suggest that angle-averaged fluid-matrix (fm) interactions can reproduce main features observed for true dipolar (fm) interactions such as the shift of the vapor-liquid spinodals towards lower temperatures and higher densities. However, the effective attraction induced by dipolar (fm) interaction is underestimated rather than overestimated as in the case of angle-averaged ff interactions.

Integral equation study of a Stockmayer fluid adsorbed in polar disordered matrices

Based on replica integral equations in the (reference) hypernetted chain approximation we investigate the structural features and phase properties of a dipolar Stockmayer fluid confined to a disordered dipolar matrix. The integral equations are applied to the homogeneous high-temperature phase where the system is globally isotropic. At low densities we find the influence of dipolar interactions between fluid (f) and matrix (m) particles to be surprisingly similar to the previously investigated effect of attractive isotropic (fm) interactions: the critical temperature of the vapor-liquid transition decreases with increasing (fm) coupling, while the critical density increases. The anisotropic nature of the dipolar (fm) interactions turns out to play a more dominant role at high fluid densities where we observe a pronounced sensitivity in the dielectric constant and a strong degree of local orientational ordering of the fluid particles along the local fields generated by the matrix. Moreover, an instability of the dielectric constant, which is a precursor of ferroelectric ordering occurring both in bulk Stockmayer fluids and in fluids in nonpolar matrices, is observed only for very small dipolar (fm) couplings.

Effect of templated quenched disorder on fluid phase equilibrium

Templating offers a means to direct the structure of quenched disorder. We show here that changes in phase equilibrium due to the presence of quenched disorder can themselves be altered by templating. We calculate the phase diagram of a fluid in a collection of template-directed, quenched particles by solving a set of replica Ornstein-Zernike equations within the mean spherical approximation and show templating to enhance phase behavior, that is, shift the phase envelope upward from its location for a nontemplated system of identical available volume. This enhancement is due to an augmented number of fluid-fluid interactions.