Oxidative formation of bis-N-methylquinolinone from anti-head-to-head N-methylquinolinone cyclodimer.

The light-driven formation and cleavage of cyclobutane structural motifs resulting from [2 + 2]-pericyclic reactions, as found in thymine and coumarin-type systems, is an important and intensively studied photochemical reaction. Various applications are reported utilizing these systems, among others, in cross-linked polymers, light-triggered drug release, or other technical applications. Herein coumarin is most frequently used as the photoactive group. Quite often, a poor quantum yield for dimerization and cyclobutane-cleavage and a lack of reversibility are described. In this work, we present the identification of a heterogeneous pathway of dimer cleavage found in a rarely studied coumarin analog molecule, the N-methyl-quinolinone (NMQ). The monomer was irradiated in a tube flow-reactor and the reaction process was monitored using online HPLC measurements. We found the formation of a pseudo-equilibrium between monomeric and dimeric NMQ and a continuous rise of a side product via oxidative dimer splitting and proton elimination which was identified as 3,3'-bis-NMQ. Oxidative conversion by singlet oxygen was identified to be the cause of this non-conventional cyclobutane cleavage. The addition of antioxidants suppressing singlet oxygen enables achieving a 100% photochemical conversion from NMQ to the anti-head-to-head-NMQ-dimer. Using dissolved oxygen upon light activation to singlet oxygen limits the reversibility of the photochemical [2 + 2]-cycloaddition and cycloreversion of NMQ and most likely comparable systems. Based on these findings, the development of highly efficient cycloaddition-cycloreversion systems should be enabled.

Morphology-transport relationships for SBA-15 and KIT-6 ordered mesoporous silicas.

Quantitative morphology-transport relationships are derived for ordered mesoporous silicas through direct numerical simulation of hindered diffusion in realistic geometrical models of the pore space obtained from physical reconstruction by electron tomography. We monitor accessible porosity and effective diffusion coefficients resulting from steric and hydrodynamic interactions between passive tracers and the pore space confinement as a function of λ = dtracer/dmeso (ratio of tracer diameter to mean mesopore diameter) in SBA-15 (dmeso = 9.1 nm) and KIT-6 (dmeso = 10.5 nm) silica samples. For λ = 0, the pointlike tracers reproduce the true diffusive tortuosities. For 0 ≤λ < 0.5, the derived hindrance factor quantifies the extent to which diffusion of finite-size tracers through the materials is hindered compared with free diffusion in the bulk liquid. The hindrance factor connects the transport properties of the ordered silicas to their mesopore space morphologies and enables quantitative comparison with random mesoporous silicas. Key feature of the ordered silicas is a narrow, symmetric mesopore size distribution (∼10% relative standard deviation), which engenders a sharper decline of the accessible-porosity window with increasing λ than observed for random silicas with their wide, asymmetric mesopore size distributions. As support structures, ordered mesoporous silicas should offer benefits for applications where spatial confinement effects and molecular size-selectivity are of prime importance. On the other hand, random mesoporous silicas enable higher diffusivities for λ > 0.3, because the larger pores carry most of the diffusive flux and keep pathways open when smaller pores have closed off.

Olefin Metathesis in Confined Geometries: A Biomimetic Approach toward Selective Macrocyclization.

The synthesis of macrocycles is severely impeded by concomitant oligomer formation. Here, we present a biomimetic approach that utilizes spatial confinement to increase macrocyclization selectivity in the ring-closing metathesis of various dienes at elevated substrate concentration up to 25 mM using an olefin metathesis catalyst selectively immobilized inside ordered mesoporous silicas with defined pore diameters. By this approach, the ratio between macro(mono)cyclization (MMC) product and all undesired oligomerization products (O) resulting from acyclic diene metathesis polymerization was increased from 0.55, corresponding to 35% MMC product obtained with the homogeneous catalyst, up to 1.49, corresponding to 60% MMC product. A correlation between the MMC/O ratio and the substrate-to-pore-size ratio was successfully established. Modification of the inner pore surface with dimethoxydimethylsilane allowed fine-tuning the effective pore size and reversing surface polarity, which resulted in a further increase of the MMC/O ratio up to 2.2, corresponding to >68% MMC product. Molecular-level simulations in model pore geometries help to rationalize the complex interplay between spatial confinement, specific (substrate and product) interaction with the pore surface, and diffusive transport. These effects can be synergistically adjusted for optimum selectivity by suitable surface modification.

Quantifying Morphology and Diffusion Properties of Mesoporous Carbon From High-Fidelity 3D Reconstructions.

A reliable quantitative analysis in electron tomography, which depends on the segmentation of the three-dimensional reconstruction, is challenging because of constraints during tilt-series acquisition (missing wedge) and reconstruction artifacts introduced by reconstruction algorithms such as the Simultaneous Iterative Reconstruction Technique (SIRT) and Discrete Algebraic Reconstruction Technique (DART). We have carefully evaluated the fidelity of segmented reconstructions analyzing a disordered mesoporous carbon used as support in catalysis. Using experimental scanning transmission electron microscopy (STEM) tomography data as well as realistic phantoms, we have quantitatively analyzed the effect on the morphological description as well as on diffusion properties (based on a random-walk particle-tracking simulation) to understand the role of porosity in catalysis. The morphological description of the pore structure can be obtained reliably both using SIRT and DART reconstructions even in the presence of a limited missing wedge. However, the measured pore volume is sensitive to the threshold settings, which are difficult to define globally for SIRT reconstructions. This leads to noticeable variations of the diffusion coefficients in the case of SIRT reconstructions, whereas DART reconstructions resulted in more reliable data. In addition, the anisotropy of the determined diffusion properties was evaluated, which was significant in the presence of a limited missing wedge for SIRT and strongly reduced for DART.

Morphology of Fluids Confined in Physically Reconstructed Mesoporous Silica: Experiment and Mean Field Density Functional Theory.

Three-dimensional physical reconstruction of the random mesopore network in a hierarchically structured, macroporous-mesoporous silica monolith via electron tomography has been used to generate a lattice model of amorphous, mesoporous silica. This geometrical model has subsequently been employed in mean field density functional theory (MFDFT) calculations of adsorption and desorption. Comparison of the results with experimental sorption isotherms for nitrogen at 77 K shows a good qualitative agreement, with both experiment and theory producing isotherms characterized by type H2 hysteresis. In addition to the isotherms, MFDFT provides the three-dimensional density distribution for the fluid in the porous material for each state studied. We use this information to map the phase distribution in the mesopore network in the hysteresis region. Phase distributions on the desorption boundary curve are compared to those on the adsorption boundary curve for both fixed pressure and fixed density, revealing insights into the relationship between phase distribution and hysteresis.

Single-Molecule and Ensemble Diffusivities in Individual Nanopores with Spatially Dependent Mobility.

We investigated single-molecule and ensemble diffusivities in a silica nanopore with a chemically modified surface by molecular dynamics simulations. Solutes with graded polarity (nonpolar ethylbenzene and moderately polar benzyl alcohol) were equilibrated with a 40:60 v/v water/acetonitrile solvent in a 10 nm pore, the surface of which was rendered hydrophobic by modification with alkyl chains. Simulations enable detailed sampling of spatially dependent solvent and solute mobilities, which originate from microheterogeneity induced by the surface modification. Acetonitrile is enriched near the ends of the alkyl chains and forms a high-mobility interface region between the (nonpolar) bonded phase at the surface and the (polar) bulk liquid in the center of the pore. Solvent and solute diffusivities calculated from the time average of a single molecule and from the ensemble average over all molecules, respectively, revealed excellent agreement, which implies validity of ergodicity. The molecular-simulation approach to investigate the time average of a single molecule, on the one hand, and the ensemble average over a larger number of molecules, on the other hand, is general and can be adapted for a variety of surfaces, solvents, and solute molecules by using pores with tailored geometries and surface modifications.

Morphological Properties of Methacrylate-Based Polymer Monoliths: From Gel Porosity to Macroscopic Inhomogeneities.

Shaping chemical interfaces of hard and soft matter materials into physical morphologies that guarantee excellent transport properties is of central importance for technologies relying on adsorption, separation, and reaction at the interface. Polymer monoliths with a hierarchically structured pore space, for example, are widely used in flow-driven processes, whose efficiency depends on the morphology of the support material over several length scales. Compared with alternative support structures, particularly silica monoliths, polymer monoliths yield lower efficiency, which suggests a suboptimal morphology. Based on physical reconstruction by serial block-face scanning electron microscopy we evaluate the structural features of a methacrylate-based polymer monolith from the pore scale to the column scale. The morphological data reveal a homogeneous polymer skeleton with a solute-impenetrable core-porous shell architecture and a heterogeneous macropore space that suffers from inhomogeneities at the short-range and the transcolumn scale. Although the morphology of the polymer phase is favorable to efficient mass transport, the performance of the polymer monolith is limited by severe transcolumn gradients in macroporosity and macropore size. We propose to overcome these morphological limitations by pursuing a preparation strategy that involves active rather than passive shaping of the macropore space, for example, by using silica monoliths as templating structures for polymer monolith preparation.

On the underestimated impact of the gelation temperature on macro- and mesoporosity in monolithic silica.

The preparation of monolithic SiO2 with bimodal porosity using a special sol-gel procedure ("Nakanishi process") generally shows a pronounced sensitivity towards several physico-chemical parameters of the initial solution (concentrations, precursors, pH, temperature, etc.). Thus, temporal and spatial variations of these parameters during the sol-gel reactions can affect the final meso- and macropore space with respect to the pore size distributions and homogeneity. In this study we thoroughly examine the sol-gel reaction in terms of the impact of temperature accuracy and homogeneity during the gelation and their effect on meso- and macropore space. The in-depth characterization of the macroporosity in monolithic SiO2 rods, prepared by utilizing a highly homogeneous and accurate temperature profile, shows that a decrease of only 1.5 °C during the reaction doubles the mean size of the macropores in the analyzed temperature ranges (22.0-28.0 °C and 33.5-36.5 °C). Rheological measurements of the gelation points and the viscosity of the starting solutions prove that a higher reaction rate is the main reason for this marked temperature-sensitivity. Furthermore, the mesoporosity is affected to a surprising extent by the applied small temperature differences during the gelation reaction. This phenomenon is shown to be mainly caused by the temperature-dependent differences in macropore and skeleton dimensions and an inhomogeneous distribution of mesopore sizes within the skeleton. In essence, our study reveals that the impact of temperature on the formation of meso- and macroscale dimensions during the sol-gel process has been underestimated so far. The impact of a poor temperature homogeneity during monolith synthesis is exemplarily demonstrated by the application of monolithic silica capillary columns in HPLC.

Another resolution of the configurational entropy paradox as applied to hard spheres.

Ozawa and Berthier [J. Chem. Phys. 146, 014502 (2017)] recently studied the configurational and vibrational entropies Sconf and Svib from the relation Stot = Sconf + Svib for polydisperse mixtures of spheres. They noticed that because the total entropy per particle Stot/N shall contain the mixing entropy per particle kBsmix and Svib/N shall not, the configurational entropy per particle Sconf/N shall diverge in the thermodynamic limit for continuous polydispersity due to the diverging smix. They also provided a resolution for this paradox and related problems-it relies on a careful redefining of Sconf and Svib. Here, we note that the relation Stot = Sconf + Svib is essentially a geometric relation in the phase space and shall hold without redefining Sconf and Svib. We also note that Stot/N diverges with N → ∞ with continuous polydispersity as well. The usual way to avoid this and other difficulties with Stot/N is to work with the excess entropy ΔStot (relative to the ideal gas of the same polydispersity). Speedy applied this approach to the relation above in his work [Mol. Phys. 95, 169 (1998)] and wrote this relation as ΔStot = Sconf + ΔSvib. This form has flaws as well because Svib/N does not contain the kBsmix term and the latter is introduced into ΔSvib/N instead. Here, we suggest that this relation shall actually be written as ΔStot = ΔcSconf + ΔvSvib, where Δ = Δc + Δv, while ΔcSconf = Sconf - kBNsmix and ΔvSvib=Svib-kBN1+lnVΛdN+UNkBT with N, V, T, U, d, and Λ standing for the number of particles, volume, temperature, internal energy, dimensionality, and de Broglie wavelength, respectively. In this form, all the terms per particle are always finite for N → ∞ and continuous when introducing a small polydispersity to a monodisperse system. We also suggest that the Adam-Gibbs and related relations shall in fact contain ΔcSconf/N instead of Sconf/N.

Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings.

We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number.

Chemical potential and entropy in monodisperse and polydisperse hard-sphere fluids using Widom's particle insertion method and a pore size distribution-based insertion probability.

We estimate the excess chemical potential Δµ and excess entropy per particle Δs of computer-generated, monodisperse and polydisperse, frictionless hard-sphere fluids. For this purpose, we utilize the Widom particle insertion method, which for hard-sphere systems relates Δµ to the probability to successfully (without intersections) insert a particle into a system. This insertion probability is evaluated directly for each configuration of hard spheres by extrapolating to infinity the pore radii (nearest-surface) distribution and integrating its tail. The estimates of Δµ and Δs are compared to (and comply well with) predictions from the Boublík-Mansoori-Carnahan-Starling-Leland equation of state. For polydisperse spheres, we employ log-normal particle radii distributions with polydispersities δ = 0.1, 0.2, and 0.3.

Morphological Analysis of Physically Reconstructed Silica Monoliths with Submicrometer Macropores: Effect of Decreasing Domain Size on Structural Homogeneity.

Silica monoliths are increasingly used as fixed-bed supports in separation and catalysis because their bimodal pore space architecture combines excellent mass transport properties with a large surface area. To optimize their performance, a quantitative relationship between morphology and transport characteristics has to be established, and synthesis conditions that lead to a desired morphology optimized for a targeted application must be identified. However, the effects of specific synthesis parameters on the structural properties of silica monoliths are still poorly understood. An important question is how far the macropore and domain size can be reduced without compromising the structural homogeneity. We address this question with quantitative morphological data derived for a set of eight macroporous-mesoporous silica monoliths with an average macropore size (d(macro)) of between 3.7 and 0.1 µm, prepared following an established route involving the sol-gel transition and phase separation. The macropore space of the silica monolith samples is reconstructed using focused ion beam scanning electron microscopy followed by a quantitative assessment of geometrical and topological properties based on chord length distributions (CLDs) and branch-node analysis of the pore network, respectively. We observe a significant increase in structural heterogeneity, indicated by a decrease in the parameter k derived from fitting a k-gamma function to the CLDs, when d(macro) reaches the submicrometer range. The compromised structural homogeneity of silica monoliths with submicrometer macropores could possibly originate from early structural freezing during the competitive processes of sol-gel transition and phase separation. It is therefore questionable if the common approach of reducing the morphological features of silica monoliths into the submicrometer regime by changing the point of sol-gel transition can be successful. Alternative strategies and a better understanding of the involved competitive processes should be the focus of future research.

How to predict the ideal glass transition density in polydisperse hard-sphere packings.

The formula for the entropy s of the accessible volume of the phase space for frictionless hard spheres is combined with the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state for polydisperse three-dimensional packings to obtain an analytical expression for s as a function of packing density φ. Polydisperse hard-sphere packings with log-normal, Gaussian, and Pareto particle diameter distributions are generated to estimate their ideal glass transition densities φg. The accessible entropy s at φg is almost the same for all investigated particle diameter distributions. We denote this entropy as sg and can predict φg for an arbitrary particle diameter distribution through an equation s(φ) = sg. If the BMCSL equation of state is used for s(φ), then φg is found to depend only on the first three moments of a particle diameter distribution.

Effect of adsorption on solute dispersion: a microscopic stochastic approach.

We report on results obtained with a microscopic modeling approach to Taylor-Aris dispersion in a tube coupled with adsorption-desorption processes at its inner surface. The retention factor of an adsorbed solute is constructed by independent adjustment of the adsorption probability and mean adsorption sojourn time. The presented three-dimensional modeling approach can realize any microscopic model of the adsorption kinetics based on a distribution of adsorption sojourn times expressed in analytical or numerical form. We address the impact of retention factor, adsorption probability, and distribution function for adsorption sojourn times on solute dispersion depending on the average flow velocity. The approach is general and validated at all stages (no sorption; sorption with fast interfacial mass transfer; sorption with slow interfacial mass transfer) using available analytical results for transport in Poiseuille flow through simple geometries. Our results demonstrate that the distribution function for adsorption sojourn times is a key parameter affecting dispersion and show that models of advection-diffusion-sorption cannot describe mass transport without specifying microscopic details of the sorption process. In contrast to previous one-dimensional stochastic models, the presented simulation approach can be applied as well to study systems where diffusion is a rate-controlling process for adsorption.

Morphological analysis of disordered macroporous-mesoporous solids based on physical reconstruction by nanoscale tomography.

Solids with a hierarchically structured, disordered pore space, such as macroporous-mesoporous silica monoliths, are used as fixed beds in separation and catalysis. Targeted optimization of their functional properties requires a knowledge of the relation among their synthesis, morphology, and mass transport properties. However, an accurate and comprehensive morphological description has not been available for macroporous-mesoporous silica monoliths. Here we offer a solution to this problem based on the physical reconstruction of the hierarchically structured pore space by nanoscale tomography. Relying exclusively on image analysis, we deliver a concise, accurate, and model-free description of the void volume distribution and pore coordination inside the silica monolith. Structural features are connected to key transport properties (effective diffusion, hydrodynamic dispersion) of macropore and mesopore space. The presented approach is applicable to other fixed-bed formats of disordered macroporous-mesoporous solids, such as packings of mesoporous particles and organic-polymer monoliths.

On the jamming phase diagram for frictionless hard-sphere packings.

We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10(4) particles with log-normal particle diameter distributions in a wide range of packing densities φ (for monodisperse packings φ = 0.46-0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities φ(J) for equilibrated packings with initial densities φ ≤ 0.52 are located near the random close packing limit φ(RCP); the available phase space is dominated by basins of attraction that we associate with liquid. φ(RCP) depends on the polydispersity and is ∼ 0.64 for monodisperse packings. For φ > 0.52, φ(J) increases with φ; the available phase space is dominated by basins of attraction that we associate with glass. When φ reaches the ideal glass transition density φ(g), φ(J) reaches the ideal glass density (the glass close packing limit) φ(GCP), so that the available phase space is dominated at φ(g) by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation σ = 0.1, φ(GCP) ≈ 0.655 and φ(g) ≈ 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density φ(m) and ends at the crystallization offset density φ(off). For monodisperse packings, φ(m) ≈ 0.54 and φ(off) ≈ 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for φ ≤ φ(g).

Random-close packing limits for monodisperse and polydisperse hard spheres.

We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10(4) frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky-Stillinger and force-biased algorithms are distributed in a narrow density range from φ = 0.634-0.636 to φ≈ 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to φ≈ 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret φ≈ 0.64 as the random-close packing (RCP) limit and φ≈ 0.65 as a lower bound of the glass close packing (GCP) limit, whereas φ = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density φLT. The three characteristic densities φLT, φRCP, and φGCP are determined for polydisperse packings with log-normal sphere radii distributions.

Coherent analysis of disordered mesoporous adsorbents using small angle X-ray scattering and physisorption experiments.

Characterization of mesoporous adsorbents is traditionally performed in terms of the pore size distribution with bulk methods like physisorption and mercury intrusion. But their application relies on assumptions regarding the basic pore geometry. Although novel tools have enabled the quantitative interpretation of physisorption data for adsorbents having a well-defined pore structure the analysis of disordered mesoporosity still remains challenging. Here we show that small angle X-ray scattering (SAXS) combined with chord length distribution (CLD) analysis presents a precise and convenient approach to determine the structural properties of two-phase (solid-void) systems of mesopores. Characteristic wall (solid) and pore (void) sizes as well as surface areas are extracted without the need to assume a certain pore shape. The mesoporous structure of modern, commercially available fully porous and core-shell adsorbent particles is examined by SAXS/CLD analysis. Mean pore size and surface area are compared with results obtained from nitrogen physisorption data and show excellent agreement.

Estimating angoricity and granular equations of state for monodisperse packings of frictional hard spheres in a wide range of densities.

In this paper, we study the granular equation of state (EOS) for computer-generated three-dimensional mechanically stable packings of frictional monodisperse particles over a wide range of densities (packing fractions), φ=0.56-0.72. As a statistical physics framework, we utilize the statistical ensemble for granular matter, specifically the "angoricity" ensemble, where the compressional component Σ_{p} of the force-moment tensor serves as granular energy and angoricity A_{p} is the corresponding granular "temperature." We demonstrate that the systems under study conform well to this statistical description, and the simple equation of state Σ_{p}=2.8NA_{p} holds very well, where N is the number of particles. We show that granular temperature exhibits a rapid drop around the random-close packing (RCP) limit φ≈0.64-0.65, and, hence, one can say that granular packings "freeze" at the RCP limit. We repeat these calculation for shear angoricity A_{sh} and shear component Σ_{sh} of the force-moment tensor and obtain a similar EOS, Σ_{sh}=0.85NA_{sh}. Additionally, we measure the so-called keramicity, an inverse temperature variable corresponding to the determinant of the force-moment tensor, while pressure angoricity corresponds to its trace. We show that inverse keramicity κ^{-1} and angoricity A_{p} conform to an EOS 1/A_{p}Σ_{p}/N+0.11κ(Σ_{p}/N)^{3}=1.2, whose form is predicted by mean-field theory. Finally, we demonstrate that the alternative statistical ensemble where Voronoi volumes serve as granular energy (and so-called compactivity serves as temperature) does not describe the systems under study well.

Organic-solvent ditch overlap in reversed-phase liquid chromatography: A molecular dynamics simulation study in cylindrical 6-12 nm-diameter pores.

Mass transport through the mesopore space of a reversed-phase liquid chromatography (RPLC) column depends on the properties of the chromatographic interface, particularly on the extent of the organic-solvent ditch that favors the analyte surface diffusivity. Through molecular dynamics simulations in cylindrical RPLC mesopore models with pore diameters between 6 and 12 nm we systematically trace the evolution of organic-solvent ditch overlap due to spatial confinement in the mesopore space of RPLC columns for small-molecule separations. Each pore model of a silica-based, endcapped, C18-stationary phase is equilibrated with two mobile phases of comparable elution strength, namely 70/30 (v/v) water/acetonitrile and 60/40 (v/v) water/methanol, to consider the influence of the mobile-phase composition on the onset of organic-solvent ditch overlap. The simulations show that, as the pore diameter decreases from 9 to 6 nm, the bonded-phase density extends and compacts towards the pore center, which leads to increased accumulation of organic-solvent excess and thus enhanced organic-solvent diffusivity in the ditch. Because the acetonitrile ditch is more pronounced than the methanol ditch, acetonitrile ditch overlap sets in at less severe spatial confinement than methanol ditch overlap. The pore-averaged methanol and acetonitrile diffusivities are considerably raised by ditch overlap in the 6 nm-diameter pore, but also benefit from the ditch (without overlap) in the 7 to 12 nm-diameter pores, whereby local and pore-averaged effects are generally larger for acetonitrile than methanol.