Solute Sorption, Diffusion, and Advection in Macro–Mesoporous Materials: Toward a Realistic Bottom-Up Simulation Strategy

Abstract

We present a general bottom-up strategy to simulate solute transport through macro–mesoporous adsorbents with functionalized surfaces. The strategy is illustrated for conditions in reversed-phase liquid chromatography, for which realistic representations of the solute interaction with the functionalized, solid–liquid interface (interfacial dynamics) as well as geometrical models of the fluid-filled, macro–mesoporous adsorbent are available from experiments. Interfacial dynamics are modeled at the single-mesopore level using molecular dynamics simulations. Effective mesopore diffusion is addressed by Brownian dynamics simulations. Fluid flow and the engendered hydrodynamic dispersion (advection–diffusion problem) are resolved via lattice-Boltzmann and Brownian dynamics simulations. The hallmarks of the simulation approach are efficient linker schemes that guarantee the integration of the detailed, molecular-level, interfacial dynamics information into the complex hierarchical porosity, and multiscale transport models. The proposed simulation strategy promises an in-depth understanding of how the interfacial dynamics affect macroscale transport depending on the fluid flow velocity through the adsorbent.

Mobile-Phase Contributions to Organic-Solvent Excess Adsorption and Surface Diffusion in Reversed-Phase Liquid Chromatography

“…The OS density profiles show four solvent layers of different widths in the solvated stationary phase (Figure 5). The small density peaks closer to the silica surface (at z < 0.825 and <0.925 nm, respectively, in the MeOH and ACN density profiles) represent solvent layers associated with the bondedphase region, which contains the silica surface and the less flexible bonded-phase groups of the first and second chain segment (CH 2 (1)−CH 2 (12)). 31 Accordingly, the function of OS presence in the bonded-phase region comprises the coordination of residual OH groups at the silica surface through HB formation (first OS density peak), the coordination of surface-adsorbed W and OS molecules (second and third OS density peak, respectively), and solvation of bonded-phase groups (third OS density peak).…”

“…But analyte molecules spend the majority of their time in the RPLC column in contact with the bonded phase and thus within a narrow layer referred to as the chromatographic (solid–liquid) interface. The inclusion of the interfacial dynamics in multiscale simulations of mass transport through a chromatographic bed is a recent achievement − and was preceded by two decades of dedicated molecular simulation studies of the RPLC interface. − …”

Axial Diffusion in Liquid-Saturated Cylindrical Silica Pore Models

“…Alkanes such as n -heptane or cyclohexane are often used as probe molecules to measure the tortuosity by pulsed field gradient NMR. , However, for pore sizes below 6 nm, the tortuosity values start to depend on the pore size and thus deviate from a purely structural definition. ,, For molecular heterogeneous catalysis in confined geometries, pore diameters around 6 nm are expected to engender spatial confinement effects . Being able to separate tortuosity from surface interaction effects is therefore an important step when developing predictive (multiscale) models. , While various theoretical or empirical tortuosity–porosity relations have been proposed, random walk particle tracking simulations of inert tracer molecules inside physical reconstructions of real porous materials give a more direct access to these relations . For a straight cylindrical mesopore of constant diameter, the tortuosity is by (the structural) definition equal to 1.…”

Confinement Effects on Distribution and Transport of Neutral Solutes in a Small Hydrophobic Nanopore

“…In recent years, molecular simulations have become a highly attractive approach to analyze coupled transports in single nanopores and nanoporous materials with respect to their constituent contributions. − Because molecular simulations offer unprecedented insights into the interfacial dynamics resulting from the solute–solvent–surface interactions, they are key to unravel the fundamentals of separation and transport processes and to shape and refine the design principles for nanofiltration membranes, supercapacitors, catalysts, and stationary phases for liquid chromatography . The derived molecular-level picture can be subsequently embedded into multiscale simulation approaches that reproduce and even predict macroscopic behavior (e.g., the process performance). − If combined with physical reconstruction of the pore space morphology by tomographic methods, multiscale simulation approaches enable an unusually detailed and accurate unterstanding of the interplay between morphological properties, interfacial dynamics, and solute transport …”