Structure and mobility of solvents and solutes at solid-liquid interfaces in mesopore models with different pore geometries obtained from molecular dynamics simulations

Computer simulations contribute significantly to the understanding of chemical processes at the molecular level and are used in many areas of chemistry. In high performance liquid chromatography (HPLC), theoretical models and calculations are essential to characterize occurring interactions at the solid-liquid interface of porous materials and develop improvements for this separation technique. This work deals with the molecular-level picture of single mesopores present in stationary phases for reversed phase liquid chromatography (RPLC). RPLC is the most commonly used HPLC method for the separation of nonpolar to moderately polar analytes using a hydrophobically modified stationary phase and an aqueous-organic mobile phase. Retention factors of analytes are calculated from their retention time relative to the retention of dead time markers; small, inert molecules that ideally do not interact with the stationary phase. In the first part of this work, two common dead-time marker molecules are investigated regarding their interactions with the chromatographic interface using molecular dynamics (MD) simulations of slit pore models. From the obtained data, a theoretical model for the prediction of retention factors is developed and compared with experimental measurements. Preliminary MD simulations of analyte molecules in single mespores were already able to characterize the origin and properties of surface diffusion, which plays a crucial role for transport through the chromatographic fixed bed, as it is responsible for relatively high diffusion coefficients of analytes in RPLC. With a multiscale simulation approach, the effective macroscopic diffusion coefficient of analyte molecules are calculated in the macro-mesoporous space of the chromatographic bed. The second part of this work deals with MD simulations of model mesopores with different pore geometry to investigate the influence of curvature on the structure of the chromatographic interface and characterize the distribution and mobility of different species in the simulation systems. In Chapter 1, MD simulations of the dead time markers acetone and uracil in an RPLC slit pore model are used to elucidate their interactions with the chromatographic interface. Water (W) and acetonitrile (ACN) are used as mobile phase in the range of 80/20 to 10/90 (v/v) W/ACN. The pore model is a 10-nm silica slit pore modified with 3.11 μmol m–² dimethyl octadecylsilyl (C18) and 0.93 μmol m–² trimethyl silyl (C1) groups on the surface, representing an RPLC pore with column-averaged surface geometry. In this study, the density distribution, orientation, hydrogen bonding, and diffusivity of acetone and uracil are investigated to compare their behavior to solvent molecules and true analyte molecules. The density profiles of both solutes show a clear enrichment in the interface at low ACN content of the mobile phase (up to 70-80 vol %-ACN), indicating that they are not completely inert molecules. The calculated data of acetone are compared with ACN and acetophenone based on similarities in solvent properties and molecular structure, respectively. Regarding surface attachment and orientation in the corresponding surface peaks, acetone resembles ACN. In the interfacial region, orientation as well as the mobility gain relative to the bulk liquid region of acetone resembles acetophenone due to the similarity in their hydrogen bonding (HB) pattern. The simulated data of uracil are mostly compared to acetone because it differs from typical RPLC solutes regarding its hydrophilic molecular structure. In general, the interaction of uracil with the bonded phase is weaker than that of acetone, reflecting a shorter dead time than acetone. Orientation and HB analysis show that uracil does not require a particular orientation to maximize its HB coordination in the interfacial region, which prevents uracil from exhibiting a higher diffusive mobility there. In contrast to analyte molecules in the chromatographic interface, the dead time markers prefer HB to solvent molecules over bonded-phase contacts. Overall, this study provides insights into the advantages and disadvantages of the two dead time markers and shows that their suitability depends on the retention type. In Chapter 2, the influence of surface curvature on the chromatographic interface is investigated with MD simulations of a cylindrical mesopore model. The simulation box contains a silica block with a carved out cylinder of 9 nm in length, representing a mesopore in an RPLC column of average pore size. Adjacent to both sides of the cylinder pore are two solvent reservoirs with a length of 5.53 nm, resulting in a cylindrical-inside-a-slitpore model and allowing a direct comparison of the competition between planar and curved surface regarding distribution and mobility of solvent and analyte molecules. The inner cylindrical and outer planar surface are modified with C18 groups of similar occupancy (2.89 µmol m–2 inside and 2.96 µmol m–2 outside), preventing hydrophilic interaction liquid chromatography (HILIC) retention at the pore entrances. A bonded-phase coverage of 54% in total was achieved by endcapping with C1 groups (1.71 µmol m–2 inside and 1.32 µmol m–2 outside). The apolar ethylbenzene and moderately polar acetophenone are simulated in a 70/30 (v/v) W/ACN mobile phase. A W-rich mobile phase was chosen because of the expected high local ACN excess and surface diffusion effects observed in previous simulated slit pore systems. The results show that the cylinder pore geometry leads to more stretched C18 chains which shift the interfacial region further towards the bulk region. Due to the higher local density of the bonded phase inside the pore, ACN enrichment in the so-called ACN ditch is higher than at the planar surface, increasing the local ACN excess in the ACN density maximum from 32 vol% (outside) to 39 vol% (inside). The increased ACN excess is accompanied by an increase in ACN mobility: 2.46 ± 0.10 10–9 m2 s–1 (inside) vs 2.16 ± 0.08 10–9 m2 s–1 (outside). This affects the analyte molecules in the same way, since a mobility increase for both molecules is observed in the interfacial region of the cylindrical pore. Regarding analyte distribution, the data show a strong preference of ethylbenzene for the inner curved surface (because of the higher hydrophobcitiy) whereas acetophenone distributes equally between inner curved and outer planar surface, because the increased bonded-phase contacts at the curved surface do not compensate for a loss of W contacts. The cylindrical pore geometry therefore enhances the local pore-scale selectivity of the stationary phase for apolar analytes. In Chapter 3, the confinement effect of a small 6-nm RPLC cylindrical pore on solvent and analyte behavior is compared to MD simulations of the 10-nm slit pore from Chapter 1. The pore surface bears 2.87 µmol m–2 C18 and 1.77 µmol m–2 C1 groups and MD simulations for ethylbenzene and acetophenone were carried out for four mobile phases in the range between 70/30 and 10/90 (v/v) W/ACN. The data show that, due to the small pore diameter, no bulk liquid region is formed inside the cylindrical pore and as a consequence, the ACN-ditch region forms an overlap in the pore lumen. The strong surface curvature leads to a greater extension of the C18 chains compared to the planar surface (and also more than in the 9-nm cylindrical pore) and, consequently, to a higher local bonded-phase density at the chain ends, preventing the solvation by ACN molecules. Therefore, the interface region shifts further into the pore interior. Due to the ACN ditch overlap phenomenon, the local averaged solvent composition of the entire cylindrical pore region is much richer in ACN compared to the slit pore and only matches at 90 vol % ACN. This affects surface diffusion in a positive way: The mobility maximum of the ACN diffusion coefficient D||,ACN,max in the cylindrical pore is higher than in the slit pore for all solvent compositions (from 12% increase at 90 vol % ACN to 38% increase at 50 vol % ACN). The data show further, that the increased hydrophobicity inside the cylindrical pore enhances polarity-dependent differences between analyte molecules. In the slit pore, analyte distribution between the chromatographic interface and the bulk liquid region strongly varies with the solvent composition: the more W the mobile phase contains (strong retention), the more analyte is found inside the bonded phase and interface region, which is more pronounced for apolar molecules. In the cylindrical pore, differences of analyte density intensities are smaller, which is explained with the confinement effect of the small cylindrical pore volume. The apolar ethylbenzene is more distributed into the C18 chains than acetophenone, the latter one showing a broader, asymmetric adsorption peak weighted toward the interfacial region. This directly influences the pore-averaged analyte mobility : although surface diffusion D||,analyte inside the cylindrical pore is increased for both analytes, only is higher than in the slit pore (except for 10/90 (v/v) W/ACN, where the difference becomes insignificant); ethylbenzene is slowed down because of the lower mobility inside the bonded-phase region. In Chapter 4, a theoretical approach is developed using previously simulated slit pore data to predict retention factors a priori. In general, the retention factor k is the ratio of the difference between the retained analyte and a non-retained molecule (dead time marker) to the total amount of dead time marker in the column (assuming an equal concentration of both compounds in the bulk volume). Direct calculation of retention factors based on the slit pore simulation is not possible because of the unknown number of dead time marker molecules in the interparticle space. Therefore, normalized density profiles of the analytes ethylbenzene, benzene, acetophenone, and benzyl alcohol, as well as the dead time marker uracil simulated from 80/20 to 10/90 (v/v) W/ACN in the 10-nm slit pore are used to calculate the respective analyte surface excess by subtracting uracil from the analyte density values. In addition, the same solute set is measured on a 5 µm C18 High Strength Silica (HSS) column to investigate if the measured retention factors are in a linear relationship to the calculated surface excesses. This proportionality constant should further scale with the retention time of uracil. The data show that, for all measured compositions a linear relationship between calculated surface excess and corresponding retention factor is obtained (R2 > 0.98), confirming the first assumption. The slope obtained from the linear fit functions does not show a visible linear relationship (R2 = 0.29), so that the second assumption cannot be verified with the results. The obtained plot, however, resembles the experimentally observed U-shaped elution curve of uracil. The approach established in this chapter is well suited for predicting retention factors from existing MD simulations for small, neutral analytes in RPLC. The accuracy, however, is limited to < 1% as a relative error, which is mainly due to the following assumptions made in this study: i) the entire mesopore network morphology of a particle is neglected by using the averaged slit pore geometry, ii) the actual pore size distribution within a mesoporous particle is reduced to a constant size of 10 nm, and iii) the surface modification on the used HSS-C18 column differs by 13% from the slit pore (2.70 µmol m–2 vs 3.11 µmol m–2). In Chapter 5, the influence of length and ligand density of surface-attached alkyl groups in RPLC pore spaces on effective mesopore and fixed-bed diffusion coefficients is investigated using a hierarchical simulation approach. For this purpose, the density and diffusion profiles of analyte molecules in the RPLC slit pore obtained from MD simulations discussed in Chapter 1 are first implemented for Brownian dynamics simulations in a mesopore space physically reconstructed using scanning transmission electron microscopy to ensure detailed, spatially-dependent information in the interfacial region at the molecular level. For the comparison of chain length and ligand densities, MD simulations of C18, C8, as well as high density (hd)-C8 modified slit pores are chosen. A modified random walk particle tracking (RWPT) approach is then carried out to calculate the effective diffusion coefficients Dmeso of the analytes. At the largest of length scale, the mass transfer of analyte molecules between mesopore and macropore space is simulated. This is achieved by determining the effective diffusion coefficient in the chromatographic bed (Dbed) for which a macropore space reconstructed by focused ion-beam scanning electron microscopy is used. The data show that in the slit pore, and thus at the level of a single mesopore, analyte retention properties and surface modification dominate: the longer and higher the density of the alkyl chains, the higher are surface diffusion coefficients of the analyte molcules. In the mesopore space, analyte mobility is reduced by surface tortuosity; analyte diffusion coefficients in the C18 phase are also lower compared to the C8 phases. Using a 2D distance map of the mesopore space reconstruction shows that opposite pore walls can approach each other closely, resulting in an overlap of the interfacial regions. Consequently, high mobility regions cannot fully develop, disfavoring the C18 phase due to its chain length and the associated shift of the interface region towards the bulk liquid (compared to shorter chain lengths). In the macropore space, the calculated bed diffusion coefficients of the analytes show that Dbed depend strongly on the analyte-specific retention but rather little on surface properties (chain length and ligand density).