Aljaž Godec

Understanding controlled drug release from mesoporous silicates: theory and experiment.

Based on the results of carefully designed experiments upgraded with appropriate theoretical modeling, we present clear evidence that the release curves from mesoporous materials are significantly affected by drug-matrix interactions. In experimental curves, these interactions are manifested as a non-convergence at long times and an inverse dependence of release kinetics on pore size. Neither of these phenomena is expected in non-interacting systems. Although both phenomena have, rather sporadically, been observed in previous research, they have not been explained in terms of a general and consistent theoretical model. The concept is demonstrated on a model drug indomethacin embedded into SBA-15 and MCM-41 porous silicates. The experimental release curves agree exceptionally well with theoretical predictions in the case of significant drug-wall attractions. The latter are described using a 2D Fokker-Planck equation. One could say that the interactions affect the relative cross-section of pores where the local flux has a non-vanishing axial component and in turn control the effective transfer of drug into bulk solution. Finally, we identify the critical parameters determining the pore size dependence of release kinetics and construct a dynamic phase diagram of the various resulting transport regimes.

Modus operandi of controlled release from mesoporous matrices: a theoretical perspective.

The ability to alter the rate at which molecules are released from pores by manipulating structural and surface properties of mesoporous materials was demonstrated consistently in numerous studies. Yet an understanding of the role of pore size, attraction to pore walls and of the release mechanism in general has still been elusive. Here we address these issues by means of a simple 2-dimensional (2D) model of ordered porous matrices with various pore sizes and strengths of molecule-wall attractions. The system dynamics are described with a 2D Fokker-Planck equation which is solved numerically for various cases of initial concentration distribution. We show that the interactions with walls play an essential and fundamental role in controlled release from mesoporous materials, regardless of whether they are additionally functionalized or not. They affect the relative cross-section where the local flux has a non-vanishing axial component and accordingly the effective transfer rate into bulk solution. Furthermore the inclusion of molecule-wall attractions into the theoretical description turns out to be the missing piece of the puzzle that explains the origin of the experimentally observed dependence of release kinetics on the pore size. Our results enable us to reinterpret existing experimental findings and provide a revised view of the mechanism of controlled release from ordered porous matrices.

The phase (trans)formation and physical state of a model drug in mesoscopic confinement

Compounds embedded into mesoporous or even microporous matrices are interesting for many emerging applications, such as novel catalysts, sensors, batteries, hydrogen storage materials or modern drug delivery devices. We report on two unexpected phenomena regarding the structural and dynamic properties of a model drug substance (indomethacin) when confined in mesoscopic matrices. Firstly, we show that the confinement directs the crystallization of the drug into a stable polymorph that is not otherwise formed at all; its relative amount depends on the pore size. This phenomenon is also explained theoretically using a modified classical heterogeneous nucleation theory. Secondly, we demonstrate that--even at relatively low volume fractions--the confined drug forms a condensed phase in a way that obstructs the passage of the pore channels. This may have far-reaching consequences for understanding the mechanisms of drug release from porous matrices.

Guest-host van der Waals interactions decisively affect the molecular transport in mesoporous media.

We present clear evidence that the global (macroscopic) transport from/to mesoporous materials is significantly affected by the interactions between the mesoporous host and the guest molecules. The problem is considered in a most general way so the solutions apply for a variety of cases such as the release of a guest from porous matrices, catalysis occurring in porous materials or processes taking place in separation techniques. The concept is proved on the experimentally determined release profiles of a model drug (indomethacin) from accurately designed SBA-15 and MCM-41 mesoporous silicates. In order to allow for a full quantitative analysis, a very high frequency of sampling was carried out at short release times. The agreement between the experimentally determined and the theoretically predicted curves is excellent not only in shape but also in all major trends. In the broadest sense, one might say that the host–guest interactions change the effective cross-section of pores through which the transport of guest occurs. In addition, the interactions lower the efficiency of utilization of the guest. In drug release this is observed as a decrease of released matter at long times, in catalysis this would correspond to a decrease of global turnover efficiency etc. However, it is not only the final outcome that is affected but also the transport pattern (e.g. the shape of release curves) during a wide range of timescales. Our finding might have a profound influence on the design of various devices based on meso- or macroporous materials.

Quantifying non-ergodicity of anomalous diffusion with higher order moments

Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.

Diffusion of finite-size particles in two-dimensional channels with random wall configurations

Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-sized particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. With the application of diffusing pathogens in hydrogels in mind, we consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].

Suspensions of modified TiO2 nanoparticles with supreme UV filtering ability.

TiO2nanoparticles (20–23 nm in size) were coated with a silica layer onto which lauric acid was strongly bound. The strong (probably covalent) bonding was proved using detailed comparative thermal analysis. The functionalized TiO2nanoparticles exhibited significantly reduced agglomeration, both in dry and in dispersed states (in oily media). The reduced tendency towards agglomeration was consistent with contact angle measurements which showed an increased hydrophobicity of functionalized TiO2. The strong (covalent) bonding also greatly improved the stability of the nanoparticulate sample in suspensions. Finally, the UV filtering efficiency of functionalized samples was much improved when compared to non-functionalized or those functionalized using conventional stabilizers based on adsorption. This effect was consistent with our theoretical prediction in which we correlated the particle size and the UV filtering ability.

Nonlinear diffusion in two-dimensional ordered porous media based on a free volume theory.

A continuum nonlinear diffusion model is developed to describe molecular transport in ordered porous media. An existing generic van der Waals equation of state based free volume theory of binary diffusion coefficients is modified and introduced into the two-dimensional diffusion equation. The resulting diffusion equation is solved numerically with the alternating-direction fully implicit method under Neumann boundary conditions. Two types of pore structure symmetries are considered, hexagonal and cubic. The former is modeled as parallel channels while in case of the latter equal-sized channels are placed perpendicularly thus creating an interconnected network. First, general features of transport in both systems are explored, followed by the analysis of the impact of molecular properties on diffusion inside and out of the porous matrix. The influence of pore size on the diffusion-controlled release kinetics is assessed and the findings used to comment recent experimental studies of drug release profiles from ordered mesoporous silicates.

Inversion of pore size dependence of solute transport kinetics from increasingly attractive ordered porous matrix

The problem of solute transport in interacting ordered porous media is addressed by numerically solving the 2D Fokker-Planck equation using 4-step operator splitting. The subtle interplay between drift and diffusion is shown to result in a nontrivial dependence of solute transport kinetics on pore size. Depending on the strength of attraction to pore walls distinct regimes of pore size dependence of transport kinetics are found. The results suggest a decoupling of local dynamics from large-scale transport.

Ion-size effect within the aqueous solution interface at the Pt(111) surface: molecular dynamics studies

All-atom classical force-field based molecular dynamics simulations have been employed to investigate the structure and dynamics of interfacial water in systems of pure water, 1 M LiOH and 1 M KOH aqueous solutions at an uncharged Pt(111) surface. Results indicate that the ordering of water molecules is affected as far as 9 Å from the Pt surface, corresponding to three layers of water molecules. Specific packing geometries of water in electrolyte solutions depend on the ionic radius, and both Li(+) and K(+) ions are found to adsorb directly onto the Pt surface. Significantly higher values of the water-dipole autocorrelation function in the adlayer are found for the system with Li(+) ions compared to the systems with K(+) ions or pure water. Also strongly reduced translational motion is observed in the case of Li(+), both in-plane and perpendicular to the surface. This result suggests a strong stabilizing role of Li(+) ions on water molecules. Decreased mobility of the water adlayer makes it difficult for other compounds in the aqueous solution to access the Pt surface. This implies that the reason for the reduced catalytic activity of Pt(111) surface in the presence of LiOH is due to the freezing effect Li(+) ions have on water.