Abstract 
The ability to simulate transport properties like diffusion and hydrodynamic dispersion
coefficients as well as performance factors (e.g., retention and selectivity) in hierarchically
porous materials is a key challenge and of paramount importance to the understanding and design of
functional devices. This addresses continuousflow reactors, desalination membranes, battery
electrodes, as well as fixedbed adsorption and separation columns.
^{1}
We resolve this issue by porescale simulations of advection, diffusion, sorption and
partitioning using a multiscale reconstruction approach that provides realistic models for surface
chemistry (and resulting liquidphase organization on the singlepore level) as well as for the 3D
morphology of mesopore and macropore spaces in hierarchical (macromesoporous) materials. In
particular, molecular dynamics simulations take account for the pore shape, surface
functionalization, liquid phase composition, and solute structure and quantify solvent/solute
distribution and mobility on the single mesopore level.
^{2,3} In the next step, the mesopore network is reconstructed by electron tomography to
serve as model for simulations of hindered diffusion of (finitesize) solutes using a randomwalk
approach.
^{4} This leads to very accurate hindrance factor expressions for diffusion that
substantially improve expressions based on an idealized singlepore geometry.
^{5} The combination of the molecular dynamics and randomwalk simulations offers access to
longtime diffusion coefficients covering the impact of surface chemistry, solvent composition, and
solute structure, as well as the entire mesopore space morphology resulting from a specific
material preparation route.
The effective mesopore scale dynamics (revealing diffusion, retention, and selectivity) is
subsequently coupled with the advectiondiffusion dynamics in the macropore space of the
hierarchically structured materials, e.g., the interstitial macropores in a packing of particles or
the flowthrough macropores of a monolith. Fluid flow is simulated using the latticeBoltzmann
method6 and care is taken for solvent and solute exchange between the stagnant pools in the
mesopores and flowing fluid in the macropores of the material.
^{7} In this way, diffusion, sorption and partitioning in the mesopores is connected to the
fluid flow dynamics in the macropores, which allows to calculate effective dispersion coefficients
for solvent and solutes in the longtime limit. These coefficients can be studied systematically as
a function of the average velocity
^{7,8} with explicit variation of surface modification, solvent composition, solute
structure as well as mesopore space and macropore space characteristics (e.g., porosity, pore size
distribution, order vs. disorder) through finetuned experimental synthesis or
computergeneration.
In this approach, the simulations do not just corroborate experimental findings but take the
lead in the targeted design of bed morphologies and surface functionalization for boosted material
performance in demanding applications.
(1) C. P. Haas, T. Müllner, R. Kohns, D. Enke & U. Tallarek (2017) Highperformance
monoliths in heterogeneous catalysis with singlephase liquid flow. React. Chem. Eng. 121:8416–8
426.
(2) S. M. Melnikov, A. Höltzel, A. SeidelMorgenstern & U. Tallarek (2013) How ternary
mobile phases allow tuning of analyte retention in hydrophilic interaction liquid chromatography.
Anal. Chem. 85:8850–8856.
(3) J. Rybka, J. Kärger & U. Tallarek (2017) Singlemolecule and ensemble diffusivities in
individual nanopores with spatially dependent mobility. ChemPhysChem 18:7416–7426.
(4) D. Hlushkou, A. Svidrytski & U. Tallarek (2017) Tracersizedependent pore space
accessibility and longtime diffusion coefficient in amorphous, mesoporous silica. J. Phys. Chem. C
121:8416–8426.
(5) S.J. Reich, A. Svidrytski, D. Hlushkou, D. Stoeckel, C. Kübel, A. Höltzel & U. Tallarek
(2018) Hindrance factor expression for diffusion in random mesoporous adsorbents obtained from
porescale simulations in physical reconstructions. Ind. Eng. Chem. Res. 57:3031–3042.
(6) S. Khirevich, I. Ginzburg & U. Tallarek (2015) Coarse and finegrid numerical behavior
of MRT/TRT latticeBoltzmann schemes in regular and random sphere packings. J. Comput. Phys.
281:708–742.
(7) A. Daneyko, D. Hlushkou, V. Baranau, S. Khirevich, A. SeidelMorgenstern & U. Tallarek
(2015) Computational investigation of longitudinal diffusion, eddy dispersion, and transparticle
mass transfer in bulk, random packings of core–shell particles with varied shell thickness and
shell diffusion coefficient. J. Chromatogr. A 1407:139–156.
(8) U. M. Scheven, S. Khirevich, A. Daneyko & U. Tallarek (2014) Longitudinal and transverse
dispersion in flow through random packings of spheres: A quantitative comparison of experiments,
simulations, and models. Phys. Rev. E 89:053023.
