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Open Access
A brief review of capillary number and its use in capillary desaturation curves
(2022) Guo, Hu; Song, Kaoping; Hilfer, R.
Capillary number, understood as the ratio of viscous force to capillary force, is one of the most important parameters in enhanced oil recovery (EOR). It continues to attract the interest of scientists and engineers, because the nature and quantification of macroscopic capillary forces remain controversial. At least 41 different capillary numbers have been collected here from the literature. The ratio of viscous and capillary force enters crucially into capillary desaturation experiments. Although the ratio is length scale dependent, not all definitions of capillary number depend on length scale, indicating potential inconsistencies between various applications and publications. Recently, new numbers have appeared and the subject continues to be actively discussed. Therefore, a short review seems appropriate and pertinent.
Open Access
Water structuring induces nonuniversal hydration repulsion between polar surfaces : quantitative comparison between molecular simulations, theory, and experiments
(2024) Schlaich, Alexander; Daldrop, Jan O.; Kowalik, Bartosz; Kanduč, Matej; Schneck, Emanuel; Netz, Roland R.
Polar surfaces in water typically repel each other at close separations, even if they are charge-neutral. This so-called hydration repulsion balances the van der Waals attraction and gives rise to a stable nanometric water layer between the polar surfaces. The resulting hydration water layer is crucial for the properties of concentrated suspensions of lipid membranes and hydrophilic particles in biology and technology, but its origin is unclear. It has been suggested that surface-induced molecular water structuring is responsible for the hydration repulsion, but a quantitative proof of this water-structuring hypothesis is missing. To gain an understanding of the mechanism causing hydration repulsion, we perform molecular simulations of different planar polar surfaces in water. Our simulated hydration forces between phospholipid bilayers agree perfectly with experiments, validating the simulation model and methods. For the comparison with theory, it is important to split the simulated total surface interaction force into a direct contribution from surface-surface molecular interactions and an indirect water-mediated contribution. We find the indirect hydration force and the structural water-ordering profiles from the simulations to be in perfect agreement with the predictions from theoretical models that account for the surface-induced water ordering, which strongly supports the water-structuring hypothesis for the hydration force. However, the comparison between the simulations for polar surfaces with different headgroup architectures reveals significantly different decay lengths of the indirect water-mediated hydration-force, which for laterally homogeneous water structuring would imply different bulk-water properties. We conclude that laterally inhomogeneous water ordering, induced by laterally inhomogeneous surface structures, shapes the hydration repulsion between polar surfaces in a decisive manner. Thus, the indirect water-mediated part of the hydration repulsion is caused by surface-induced water structuring but is surface-specific and thus nonuniversal.
Open Access
PDADMAC/PSS oligoelectrolyte multilayers : internal structure and hydration properties at early growth stages from atomistic simulations
(2020) Sánchez, Pedro A.; Vögele, Martin; Smiatek, Jens; Qiao, Baofu; Sega, Marcello; Holm, Christian
We analyze the internal structure and hydration properties of poly(diallyl dimethyl ammonium chloride)/poly(styrene sulfonate sodium salt) oligoelectrolyte multilayers at early stages of their layer-by-layer growth process. Our study is based on large-scale molecular dynamics simulations with atomistic resolution that we presented recently [Sánchez et al., Soft Matter 2019, 15, 9437], in which we produced the first four deposition cycles of a multilayer obtained by alternate exposure of a flat silica substrate to aqueous electrolyte solutions of such polymers at 0.1M of NaCl. In contrast to any previous work, here we perform a local structural analysis that allows us to determine the dependence of the multilayer properties on the distance to the substrate. We prove that the large accumulation of water and ions next to the substrate observed in previous overall measurements actually decreases the degree of intrinsic charge compensation, but this remains as the main mechanism within the interface region. We show that the range of influence of the substrate reaches approximately 3 nm, whereas the structure of the outer region is rather independent from the position. This detailed characterization is essential for the development of accurate mesoscale models able to reach length and time scales of technological interest.
Open Access
Insights into Hildebrand solubility parameters : contributions from cohesive energies or electrophilicity densities?
(2023) Miranda‐Quintana, Ramón Alain; Chen, Lexin; Smiatek, Jens
We introduce certain concepts and expressions from conceptual density functional theory (DFT) to study the properties of the Hildebrand solubility parameter. The original form of the Hildebrand solubility parameter is used to qualitatively estimate solubilities for various apolar and aprotic substances and solvents and is based on the square root of the cohesive energy density. Our results show that a revised expression allows the replacement of cohesive energy densities by electrophilicity densities, which are numerically accessible by simple DFT calculations. As an extension, the reformulated expression provides a deeper interpretation of the main contributions and, in particular, emphasizes the importance of charge transfer mechanisms. All calculated values of the Hildebrand parameters for a large number of common solvents are compared with experimental values and show good agreement for non‐ or moderately polar aprotic solvents in agreement with the original formulation of the Hildebrand solubility parameters. The observed deviations for more polar and protic solvents define robust limits from the original formulation which remain valid. Likewise, we show that the use of machine learning methods leads to only slightly better predictability.
Open Access
Theoretical insights into specific ion effects and strong‐weak acid‐base rules for ions in solution : deriving the law of matching solvent affinities from first principles
(2020) Miranda‐Quintana, Ramón Alain; Smiatek, Jens
We present a detailed study of specific ion effects, volcano plots and the law of matching solvent affinities by means of a conceptual density functional theory (DFT) approach. Our results highlight that specific ion effects and the corresponding implications on the solvation energy are mainly due to differences in the electric chemical potentials and chemical hardnesses of the ions and the solvent. Our approach can be further used to identify reliable criteria for the validity of the law of matching solvent affinities. Basic expressions are derived, which allow us to study the limiting conditions for this empirical observation with regard to matching chemical reactivity indices. Moreover, we show that chaotropic and kosmotropic concepts and their implications for the stability of ion pairs are directly related to a generalized strong and weak acids and bases (SWAB) principle for ions in solution, which is also applicable to rationalize the shape of volcano plots for different solvents. In contrast to previous assumptions, all empirical findings can be explained by the properties of local solvent‐ion complexes which dominate the specific global behavior of ion pairs in solution.
Open Access
Hybrid molecules consisting of lysine dendrons with several hydrophobic tails : a SCF study of self-assembling
(2023) Shavykin, Oleg V.; Mikhtaniuk, Sofia E.; Fatullaev, Emil I.; Neelov, Igor M.; Leermakers, Frans A. M.; Brito, Mariano E.; Holm, Christian; Borisov, Oleg V.; Darinskii, Anatoly A.
In this article, we used the numerical self-consistent field method of Scheutjens-Fleer to study the micellization of hybrid molecules consisting of one polylysine dendron with charged end groups and several linear hydrophobic tails attached to its root. The main attention was paid to spherical micelles and the determination of the range of parameters at which they can appear. A relationship has been established between the size and internal structure of the resulting spherical micelles and the length and number of hydrophobic tails, as well as the number of dendron generations. It is shown that the splitting of the same number of hydrophobic monomers from one long tail into several short tails leads to a decrease in the aggregation number and, accordingly, the number of terminal charges in micelles. At the same time, it was shown that the surface area per dendron does not depend on the number of hydrophobic monomers or tails in the hybrid molecule. The relationship between the structure of hybrid molecules and the electrostatic properties of the resulting micelles has also been studied. It is found that the charge distribution in the corona depends on the number of dendron generations G in the hybrid molecule. For a small number of generations (up to G=3), a standard double electric layer is observed. For a larger number of generations (G=4), the charges of dendrons in the corona are divided into two populations: in the first population, the charges are in the spherical layer near the boundary between the micelle core and shell, and in the second population, the charges are near the periphery of the spherical shell. As a result, a part of the counterions is localized in the wide region between them. These results are of potential interest for the use of spherical dendromicelles as nanocontainers for drug delivery.
Open Access
CO2-induced drastic decharging of dielectric surfaces in aqueous suspensions
(2024) Vogel, Peter; Beyer, David; Holm, Christian; Palberg, Thomas
We study the influence of airborne CO2 on the charge state of carboxylate stabilized polymer latex particles suspended in aqueous electrolytes. We combine conductometric experiments interpreted in terms of Hessinger's conductivity model with Poisson-Boltzmann cell (PBC) model calculations with charge regulation boundary conditions. Without CO2, a minority of the weakly acidic surface groups are dissociated and only a fraction of the total number of counter-ions actually contribute to conductivity. The remaining counter-ions exchange freely with added other ions like Na+, K+ or Cs+. From the PBC-calculations we infer a corresponding pKa of 4.26 as well as a renormalized charge in reasonably good agreement with the number of freely mobile counter-ions. Equilibration of salt- and CO2-free suspensions against ambient air leads to a drastic de-charging, which exceeds by far the expected effects of to dissolved CO2 and its dissociation products. Further, no counter-ion-exchange is observed. To reproduce the experimental findings, we have to assume an effective pKa of 6.48. This direct influence of CO2 on the state of surface group dissociation explains our recent finding of a CO2-induced decrease of the ζ-potential and supports the suggestion of an additional charge regulation caused by molecular CO2. Given the importance of charged surfaces in contact with aqueous electrolytes, we anticipate that our observations bear substantial theoretical challenges and important implications for applications ranging from desalination to bio-membranes.
Open Access
Unraveling the impact of acetylation patterns in chitosan oligomers on Cu2+ ion binding : insights from DFT calculations
(2023) Singh, Ratna; Smiatek, Jens; Moerschbacher, Bruno M.
Chitosans are partially acetylated polymers of glucosamine, structurally characterized by their degree of polymerization as well as their fraction and pattern of acetylation. These parameters strongly influence the physico-chemical properties and biological activities of chitosans, but structure-function relationships are only poorly understood. As an example, we here investigated the influence of acetylation on chitosan-copper complexation using density functional theory. We investigated the electronic structures of completely deacetylated and partially acetylated chitosan oligomers and their copper-bound complexes. Frontier molecular orbital theory revealed bonding orbitals for electrophiles and antibonding orbitals for nucleophiles in fully deacetylated glucosamine oligomers, while partially acetylated oligomers displayed bonding orbitals for both electrophiles and nucleophiles. Our calculations showed that the presence of an acetylated subunit in a chitosan oligomer affects the structural and the electronic properties of the oligomer by generating new intramolecular interactions with the free amino group of neighboring deacetylated subunits, thereby influencing its polarity. Furthermore, the band gap energy calculated from the fully and partially deacetylated oligomers indicates that the mobility of electrons in partially acetylated chitosan oligomers is higher than in fully deacetylated oligomers. In addition, fully deacetylated oligomers form more stable complexes with higher bond dissociation energies with copper than partially acetylated ones. Interestingly, in partially acetylated oligomers, the strength of copper binding was found to be dependent on the pattern of acetylation. Our study provides first insight into the influence of patterns of acetylation on the electronic and ion binding properties of chitosans. Depending on the intended application, the obtained results can serve as a guide for the selection of the optimal chitosan for a specific purpose.
Open Access
Ionic liquids in conducting nanoslits : how important is the range of the screened electrostatic interactions?
(2022) Groda, Yaroslav; Dudka, Maxym; Oshanin, Gleb; Kornyshev, Alexei A.; Kondrat, Svyatoslav
Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.
Open Access
Tuning electrode and separator sizes for enhanced performance of electrical double‐layer capacitors
(2024) Paolini, Daniele; Antony, Lintymol; Seeta Rama Raju, Ganji; Kuzmak, Andrij; Verkholyak, Taras; Kondrat, Svyatoslav
An electrical double‐layer capacitor (EDLC) comprises two porous electrodes sandwiching an electrolyte‐permeable separator, which prevents the electrodes from short‐circuiting. While previous studies have mainly focused on electrolyte and electrode properties of EDLCs, the device configuration in terms of electrode and separator sizes received less attention, with separators often simplistically modelled as infinitely large reservoirs of ions. Herein, we investigate how the relationship between electrode and separator thicknesses impacts EDLC charging. We find that the assumption of bulk reservoir holds only under specific conditions. Moreover, we identify a tradeoff between stored energy density and pressure variations within the separator, potentially jeopardizing the EDLC durability. We also explore the influence of ionic liquid additives on EDLC charging. While prior research has shown that trace amounts of uncharged additives with strong electrode affinity can significantly enhance energy storage, we observe this effect as negligible for electrodes and separators of comparable sizes. Instead, we show how to optimize EDLC performance by fine‐tuning the concentration of additives and separator‐to‐electrode size ratio to maximize stored energy density.

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