Analysis of Morphology and Transport Characteristics of Mesoporous Materials
Today, mesoporous silica are employed in a wide field of applications. They are used for example as packing materials in chromatography, as support materials for the transport of medical agents within and through the human body, in catalysis or as nanoparticles in nanomedicine. In particular, the mo...
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|Today, mesoporous silica are employed in a wide field of applications. They are used for example as packing materials in chromatography, as support materials for the transport of medical agents within and through the human body, in catalysis or as nanoparticles in nanomedicine. In particular, the mobility of guest molecules within the mesopore system, which is spatially confined by the solid silica framework, is a central aspect in all fields of application. The diffusive transport within and through the mesopores is directly connected to the pore morphology: Due to the spatial confinement of the pore volume and the resulting steric interactions of the guest molecules with the solid silica walls the transport of the molecules is hindered compared to diffusion within free space. This hindrance of diffusion is quantitatively expressed by the effective diffusion coefficient. To make predictions about the transport properties of different individual silica, the formulation of quantitative expressions that describe the relationship between their morphological features and the resulting transport properties is necessary. The pore morphology of the investigated material is often just roughly described by using simplified geometrical models. However, by using simplified geometrical models, individual morphological aspects like constrictions, irregularities or other defects like dead-ends within the pore system, which have a significant influence on the transport properties of an individual material, are not taken into account, often leading to defective and inaccurate results in investigations of morphology-transport relationships. By means of electron tomography (ET), the real three-dimensional (3D) structure of a material can be reconstructed, uncovering morphological details on the nanoscale and making a most accurate investigation of the morphology possible. In this work, the reconstructions are subsequently employed as geometrical models for numerical simulations of hindered diffusion within and through the mesopore system for different tracer sizes. The resulting tracer size dependent functions for the accessible porosity and for the corresponding diffusion coefficients then accurately reflect the morphology-induced hindrance of diffusion for the underlying individual pore system. In the present work, this approach is employed for the investigation of various silica with fundamentally different morphology by means of hindered diffusive transport within and through the mesopores of the correspondent silica framework. The goal of this work is the formulation of general expressions, which enable accurate predictions about the performance of the investigated material for a certain field of application, using only a few material-specific parameters and avoiding the need of an underlying simplified geometrical model.
In the first chapter a chromatographic column packed with mesoporous silica particles is investigated in terms of its inter- and intraparticle morphology and its influence on separation characteristics in size exclusion chromatography (SEC). The work is focused on a 2.1 mm I.D. column packed with fully porous ethylene-bridged-hybride-(BEH)particles (1.7 µm particle diameter). The goals of the study include (i) the investigation of morphology-transport/retention relationships for SEC-columns, (ii) the determination of optimal experimental conditions to either maximize peak capacity or assure a constant rate of peak capacity over the whole separation window, (iii) the prediction and comparison of SEC-performance of core-shell particles (nonporous core, porous shell) possessing the same mesopore morphology in their shell as fully porous BEH particles, and (iv) the discussion about possible advantages if the presented reconstruction-simulation approach is employed in order to accelerate method development in SEC. First, the packing microstructure is reconstructed by means of focused ion beam scanning electron microscopy (FIB-SEM) in order to compare the packing characteristics of sections close to the wall of the column with those in the column center. By means of macropore-scale lattice-Boltzmann method (LBM) simulations of the flow profile the influence of the packing microstructure on the flux velocity can be investigated. A clear radial heterogeneity of the packing density is observed, causing an obvious dependence of the flux velocity (obtained from LBM simulations) on the radial position within the column. The flux close to the column walls is much weaker than in the center of the column, where the flux velocity is equal the velocity within unrestricted bulk volume. This radial variation of the flux velocity can be explained by the similar shape of the pressure profile that results from the packing procedure. While single silica particle close to the solid column wall experience an enhanced compressive stress, the pressure is more distributed over the rather flexible particles located in the bulk volume of the column center. Furthermore, the 3D reconstruction of the packing material in the column center obtained by FIB-SEM proofs the existence of a random sphere packing in this area of the column. From the reconstruction, an external (interparticle) porosity of the column of εe = 0.39 is determined. By means of ET, the mesopore volume inside the BEH particles is reconstructed and subsequently employed as geometrical model for diffusion simulations. Numerical simulations of hindered diffusion are conducted within the mesopore volume based on the random-walk particle-tracking-(RWPT-)technique, and the intraparticle porosity ε as well as the local diffusive hindrance factor Kd can be obtained as functions of λ, the ratio of mean mesopore size and tracer diameter. For pointtracers, an accessible intraparticle porosity of ε0 = 0.49 is obtained with this technique. The derived porosity function is compared to the accessible porosity when assuming a cylindrical or a spherical pore geometry, demonstrating a particularly high discrepancy in case of a cylindrical pore model. Furthermore, the analogy between the obtained function for the local diffusive hindrance factor and the well-known RENKIN model is certified. Here, a significant deviance is observed especially for large λ. For pointtracers, an intraparticle tortuosity value of τ0 = 1.95 is furthermore determined from the effective diffusion coefficient at λ = 0. The reconstructed bulk stack (based on FIB-SEM) and the 3D reconstruction of the intraparticle mesopore volume (based on ET) are subsequently employed as geometrical models for diffusion simulations using the hierarchical diffusion model, where tracers of different sizes move through both the macropore volume between the BEH particles and the intraparticle mesopore space, providing tracer size dependent values for the effective diffusivity Dbed. The effective bed diffusivity reflects the interplay of the inter- and intraparticle tracer diffusivities, resulting in a parabolic behavior of Dbed as function of λ. First, small tracers have access to both inter- and intraparticle porosity, causing Dbed to decrease with increasing tracer sizes until at a certain λ, Dbed starts to increase again since the accessible intraparticle porosity becomes significant smaller than the accessible interparticle volume and the diffusion is mainly controlled by the external (interparticle) diffusion. The observed morphology-transport relationships are furthermore used to make presumptions about the performance of SEC-experiments under certain experimental conditions. It is shown that optimal experimental conditions can easily be diagnosed with help of the precedent findings, so that central parameters limiting the performance of SEC-experiments, for example the global peak capacity or the rate of peak capacity, can be controlled. Under certain conditions it is then possible to determine the optimal flow rate for a given temperature and mean pore size in order to maximize the global peak capacity. Additionally, the influence of core-shell particles as packing material on the rate of peak capacity is investigated for different ρ (ratio between the diameter of the nonporous core to the diameter of the whole particle). Here, an increasing peak capacity is found for increasing ρ, though meanwhile a more rapidly closing separation window is observed. This means in praxis that the application of core-shell particles in SEC-experiments is advantageous, if simple analyte mixtures as well as a small amount of high molecular mass analytes are present in the experiment.
In the second chapter morphology-transport relationships of two mesoporous silica with ordered pore systems, SBA-15 and KIT-6, are investigated. SBA-15 exhibits a 1D primary pore system, which is composed of hexagonally arranged cylindrical pores, as well as a secondary pore system, where the pores are located at random positions within the amorphous silica walls around the primary pores and therefore allow for diffusive transport in all directions through the ordered pore system. The 3D primary pore system of KIT-6, in contrast, is built of two interpenetrating networks of cylindrical pores, while the secondary pores (mostly micro- and small mesopores) are located like in SBA-15 within the silica walls and therefore provide for a high interconnectivity of the primary pores. First, the structural parameters of both materials are examined by means of X-Ray diffraction analysis (XRD) and nitrogen physisorption analysis. 3D reconstructions of the pore spaces of SBA-15 and KIT-6 obtained from ET are subsequently employed as geometrical models for numerical simulations of diffusive transport through the materials. By means of the RWPT-technique the accessible porosity for pointtracers and the corresponding effective diffusion coefficients can be determined and shown as functions of λ. For pointtracers (λ = 0), accessible porosities of ε0 = 0.69 und ε0 = 0.70 are obtained for SBA-15 and KIT-6, respectively. The diffusive tortuosity can be directly determined for both systems from the respective diffusion coefficient (SBA-15: τ0 = 1.41; KIT-6: τ0 = 1.31). Furthermore, the relationship between the porosity and the corresponding tortuosity as functions of λ are investigated in more detail by considering ε(λ) as a function of τ(λ). It is shown that the global and local diffusion coefficient for hindered diffusion can be evaluated by ARCHIE`s law for small tracer sizes (small λ), while for larger tracers (large λ) the WEISSBERG equation is more appropriate for this purpose. This approach is found to be an equally good alternative to the reconstruction-simulation-approach for the determination of the global and the local diffusion coefficient. With the use of previous findings about ordered silica from this study, the morphology-transport relationships are compared with those found for unordered silica. It is shown that ordered silica give better results in terms of higher selectivities than observed for unordered silica. This comes from the narrower pore size distribution of KIT-6 and SBA-15, which leads to a faster decline of the diffusion with increasing tracer sizes than it is the case for unordered silica. However, the transport efficiency through and within ordered materials is not significantly better than for unordered silica, even in case of a highly interconnected ordered 3D pore structure. Additionally, a narrower pore size distribution causes an enhanced sensitivity against constrictions or other irregularities within the pore system of ordered silica, so that no clear advantage of using ordered silica rather than unordered silica as packing materials in chromatography or as support structures can be pointed out in this study.
The third chapter deals with the analysis of morphology-transport relationships for two unordered mesoporous silica of different mean pore sizes, Si60 with a mean pore size of dmeso = 5.9 nm and Si100 with dmeso = 13.0 nm. By means of ET, the pore volumes of Si60 and Si100 are reconstructed and subsequently employed as geometrical models for RWPT-simulations within the mesopores. Similarly to the second chapter, the main aspect of this study is the determination of the accessible porosities as well as the effective diffusion coefficients experienced by passive tracers of different sizes due to the steric and hydrodynamic interaction with the solid silica walls during their diffusion through the mesopore space of each material. With this technique, diffusive tortuosities can be directly determined from the inverse diffusion coefficients for pointtracers (λ = 0). The investigation of the accessible porosities and the diffusion coefficients of both materials as functions of λ shows a stronger hindrance of the tracer diffusion with increasing tracer sizes for Si60 than observed for Si100 for similar tracer sizes. As a result, the access to the mesopores of Si60 can be assumed to be more selective to different tracer sizes, which is of highest interest when it comes to the immobilization or transport of key molecules or the size selective formation of new species within the mesopores, for example. This study is focused on the ring-closing metathesis of a α,ω-diene to the macro(mono)-cyclization (MMC) product and to the oligomer by means of a Hoveyda-Grubbs-catalysator of the second generation, which is immobilized inside the mesopores. Via diffusion ordered nuclear magnetic resonance spectroscopy (DOSY-NMR) the hydrodynamic diameters of the relevant species (MMC product, oligomer, substrate, and catalyst) can be determined and inserted into the previously obtained tracer size dependent functions of the porosities and the diffusion coefficients to allow for accurate predictions about the accessibility of the mesopores for the correspondent species as well as its mobility within the pore system. It is shown that already the first size selective step, the immobilization of the catalyst within the pores, lets assume a significantly smaller catalyst uptake (at similar reaction time) for Si60 than for Si100 due to the substantial spatial confinement and therefore much slower diffusion of the catalyst within and through the pore space of Si60. Because of the larger oligomer size in contrast to the smaller MMC product as well as the smaller substrate, the formation of the MMC product is preferred over that of the oligomer for both materials, which is more pronounced for Si60 than for Si100. With the observed higher selectivity of Si60 comes along a strongly reduced mobility of the species within the mesopores, which may cause a smaller reaction efficiency and yield. The presented approach towards the quantification of transport properties of mesoporous silica is generally applicable to most different micro-reaction systems with various catalysts, substrates and reaction products, to determine the correspondent selectivities and efficiencies of the considered systems. Together with the obtained information and complementary experimental data, it is possible to uncover complex reaction paths and to enable a better understanding of mechanisms within olefin metathesis.
The fourth chapter is focused on the investigation of the radial dependence of the morphology within dendritic mesoporous silica nanoparticles (DMSNs). Four different DMSNs are compared, which were all synthesized in a typical microemulsion system with slightly modified reaction parameters. For synthesis, the primary aspect was the independent adjustment of the particle size and the pore size distribution, enabling a pairwise investigation of the four DMSNs: Two of the DMSNs exhibit a comparable pore size distribution, but different particle sizes (i), while the other two DMSNs possess shifted PSDs at similar particle size (ii). By means of ET, 3D reconstructions of the four DMSNs are obtained, serving as geometrical models for the radial analysis of essential morphology-specific descriptors. For radial investigation, concentric hollow spheres with defined radius and coat thickness are cut from the center point of the DMSNs and the segment porosity as well as the chord length distribution (CLD) within the segment mesopore space is determined for different radii. The porosity and the mean chord length (i.e., the mean distance between two opposite silica walls) can then be considered as functions of the outer segment radius. For all DMSNs, a significant porosity loss is observed at the surface of the particles, which is assumed to result from the calcination step during synthesis, leading to a partial melting of the particle surface. The smaller porosity at the particle surface has massive influence on the accessibility of the intraparticle mesopore space for molecules coming from the outside as well as their exit velocity from inside the DMSNs, which needs to be taken into account when considering the applicability and efficiency of DMSNs as drug carriers and for controlled drug release in the human body. Furthermore, the investigation of the mean chord length as a function of the radius reveals a broadening of the pore diameter within increasing radius of the considered segment for one of the DMSNs. Such conical pore shape is particularly convenient, for example if especially large molecules (e.g., DNA or RNA) should have access to the intraparticle mesopore space.
In summary, the present work shows that with the underlying approach, i.e., the employment of 3D reconstructions as geometrical models for subsequent diffusion simulations as well as the quantitative investigation of morphological features and the resulting transport properties of an individual material, most different silica materials can be analyzed by means of various problems: The investigation of the effect of synthesis parameters on morphological features, the influence of the pore arrangement and geometries on the efficiency or performance of a material in chromatography or catalysis, for instance, or the radial investigation of the intraparticle pore morphology, to name just a few examples. It is shown that by means of simplified geometric models (e.g., cylindrical or spherical pore models) in most cases the very individual pore structure of mesoporous silica cannot be adequately described. In this work an approach is presented, which enables the quantification of morphology and transport properties for individual materials in a simple way, so that in the next step highly accurate general expressions can be formulated for different classes of silica materials.