In Couette flow, the liquid atoms adjacent to a solid substrate may have a finite average tangential velocity relative to the substrate. This so-called slip has been observed frequently. However, the particular molecular-level mechanisms that give rise to liquid slip are poorly understood. It is often assumed that liquid slip occurs by surface diffusion whereby atoms independently move from one substrate equilibrium site to another. We show that under certain conditions, liquid slip is due not to singular independent molecular motion, but to localized nonlinear waves that propagate at speeds that are orders of magnitude greater than the slip velocity at the liquid–solid interface. Using non-equilibrium molecular dynamics simulations, we find the properties of these waves and the conditions under which they are to be expected as the main progenitors of slip. We also provide a theoretical guide to the properties of these nonlinear waves by using an augmented Frenkel–Kontorova model. The new understanding provided by our results may lead to enhanced capabilities of the liquid–solid interface, for heat transfer, mixing, and surface-mediated catalysis.

Conceptual models of smectite hydration include planar (flat) clay layers that undergo stepwise expansion as successive monolayers of water molecules fill the interlayer regions. However, X-ray diffraction (XRD) studies indicate the presence of interstratified hydration states, suggesting non-uniform interlayer hydration in smectites. Additionally, recent theoretical studies have shown that clay layers can adopt bent configurations over nanometer-scale lateral dimensions with minimal effect on mechanical properties. Therefore, in this study we used molecular simulations to evaluate structural properties and water adsorption isotherms for montmorillonite models composed of bent clay layers in mixed hydration states. Results are compared with models consisting of planar clay layers with interstratified hydration states (e.g. 1W–2W). The small degree of bending in these models (up to 1.5 Å of vertical displacement over a 1.3 nm lateral dimension) had little or no effect on bond lengths and angle distributions within the clay layers. Except for models that included dry states, porosities and simulated water adsorption isotherms were nearly identical for bent or flat clay layers with the same averaged layer spacing. Similar agreement was seen with Na- and Ca-exchanged clays. While the small bent models did not retain their configurations during unconstrained molecular dynamics simulation with flexible clay layers, we show that bent structures are stable at much larger length scales by simulating a 41.6×7.1 nm2 system that included dehydrated and hydrated regions in the same interlayer.

Molecular dynamics computer simulations were used to study methanol molecules confined between the layers of 2:1 phyllosilicates. The model systems are based on natural Ca- and Na-rich montmorillonites. Data from the literature and determined by fitting the calculated layer spacing to experimental values were employed to obtain interactions between the charged 2:1 layers and the solvent molecules. The montmorillonite surface atoms were held rigid and the methyl group in the methanol molecule was represented by a soft Lennard-Jones sphere. Electrostatic interactions were determined by the Ewald sum method, whereas the van der Waals interactions were described by a Lennard-Jones potential. Comparison of our results with diffraction data indicates a good reproduction of the layer spacing. After the initial solvent layer forms, additional solvent layers form only after previous layers are complete. Each Ca2+ and Na+ ion in the monolayer has four and two methanol molecules, respectively, in the first solvation shell, whereas the solvation shell in the multilayer contains six and four methanol molecules, respectively. This agrees well with experimental data.

Organo-clays represent a special challenge for molecular simulations because they require accurate representation of the clay and the organic/aqueous sections of the model system and accurate representation of the interactions between them. Due to the broad range of force-field models available, an important question to ask is which sets of parameters will best suit the molecular modeling of the organo-intercalated smectites? To answer this question, the structure of the ethylene glycol (EG)-smectite complex is used here as a testing model because the intercalation of EG in smectites provides a stable interlayer complex with relatively constant basal spacing.

Three smectite samples with substantially different layer charge and charge localization were selected for X-ray diffraction (XRD) measurements. Their molecular models were built and molecular-dynamics simulations performed using various combinations of the organic force fields (CGenFF, GAFF, CVFF, and OPLS-aa) with ClayFF and INTERFACE force fields used to describe smectites. The simulations covered a range of different EG and water contents. For every structure, the density distribution of interlayer species along the direction perpendicular to the layer plane was calculated and then used to optimize the XRD patterns for these simulated models.

A comparison of these results with experimental XRD patterns shows very large discrepancies in the structures and basal spacings obtained for different layer charges as well as for different force fields and their combinations. The most significant factor affecting the accuracy of the calculated XRD patterns was the selection of the clay-mineral force-field parameters. The second important conclusion is that a slight modification of the basal oxygen parameters for non-electrostatic interactions (increase of their effective atomic diameters) may be a simple and straightforward way to improve significantly the agreement between the modeled XRD patterns with experiments, especially for high-charge smectites. Generally, among organic force fields, the least accurate results were obtained with CGenFF. For unmodified ClayFF, its combination with GAFF gave the best results, while the two other sets (OPLS-aa and CVFF) gave the best results in combination with ClayFFmod. The INTERFACE and INTERFACEmod produced much better results for low-charge montmorillonite than for high-charge smectites.

The aqueous chemistry of water films confined between clay mineral surfaces remains an important unknown in predictions of radioelement migration from radioactive waste repositories. This issue is particularly important in the case of long-lived anionic radioisotopes (129I-, 99TcO4-, 36Cl-) which interact with clay minerals primarily by anion exclusion. For example, models of ion migration in clayey media do not agree as to whether anions are completely or partially excluded from clay interlayer nanopores. In the present study, this key issue was addressed for Cl- using MD simulations for a range of nanopore widths (6 to 15 Å) overlapping the range of average pore widths that exists in engineered clay barriers. The MD simulation results were compared with the predictions of a thermodynamic model (Donnan Equilibrium model) and two pore-scale models based on the Poisson-Boltzmann equation under the assumption that interlayer water behaves as bulk liquid water. The simulations confirmed that anion exclusion from clay interlayers is greater than predicted by the pore-scale models, particularly at the smallest pore size examined. This greater anion exclusion stems from Cl- being more weakly solvated in nano-confined water than it is in bulk liquid water. Anion exclusion predictions based on the Poisson-Boltzmann equation were consistent with the MD simulation results, however, if the predictions included an ion closest approach distance to the clay mineral surface on the order of 2.0 ± 0.8 Å. These findings suggest that clay interlayers approach a state of complete anion exclusion (hence, ideal semi-permeable membrane properties) at a pore width of 4.2 ± 1.5 Å.

We performed Monte Carlo and molecular dynamics simulations to investigate the interlayer structure of a uranyl-substituted smectite clay. Our clay model is a dioctahedral montmorillonite with negative charge sites in the octahedral sheet only. We simulated a wide range of interlayer water content (0 mg H2O/g clay — 260 mg H2O/g clay), but we were particularly interested in the two-layer hydrate that has been the focus of recent X-ray absorption experiments. Our simulation results for the two-layer hydrate of uranyl-montmorillonite yield a water content of 160 mg H2O/g clay and a layer spacing of 14.66 Å. Except at extremely low water content, uranyl cations are oriented nearly parallel to the surface normal in an outer-sphere complex. The first coordination shell consists of five water molecules with an average U-O distance of 2.45 Å, in good agreement with experimental data. At low water content, the cations can assume a perpendicular orientation to include surface oxygen atoms in the first coordination shell. Our molecular dynamics results show that ${\text{UO}}_2{\left({\text{H}}_2\text{O}\right)}_5^{2+}$ complexes translate within the clay pore through a jump diffusion process, and that first-shell water molecules are exchangeable and interchangeable.

Many important properties of clay minerals are defined by the species of charge-balancing cation. Phenomena such as clay swelling and cation exchange depend on the cation species present, and understanding how the cations bind with the mineral surface at a fundamental level is important. In the present study the binding affinities of several different charge-balancing cations with the basal surface of the smectite mineral, montmorillonite, have been calculated using molecular dynamics in conjunction with the well-tempered metadynamics algorithm. The results follow a Hofmeister series of preferred ion adsorption to the smectite basal surfaces of the form:

K+ > Na+ > Ca2+ > Cs+ > Ba2+

The results also revealed the energetically favorable position of the ions above the clay basal surfaces. Key features of the free-energy profiles are illustrated by Boltzmann population inversions and analyses of the water structures surrounding the ion and clay surface. The results show that weakly hydrated cations (K+ and Cs+) preferentially form inner-sphere surface complexes (ISSC) above the ditrigonal siloxane cavities of the clay, while the more strongly hydrated cations (Na+) are able to form ISSCs above the basal O atoms of the clay surface. The strongly hydrated cations (Na+, Ca2+, and Ba2+), however, preferentially form outer-sphere surface complexes. The results provide insight into the adsorption mechanisms of several ionic species on montmorillonite and are relevant to many phenomena thought to be affected by cation exchange, such as nuclear waste disposal, herbicide/pesticide-soil interactions, and enhanced oil recovery.

In order to understand the microscopic properties of alkylammonium-intercalated vermiculites, molecular dynamics simulations employing the clayff-CVFF force field were performed to obtain the interlayer structures and dynamics. The layering behavior of alkyl chains was uncovered. With the model used in the present study (1.2 e per unit cell), the alkyl chains formed monolayers with carbon-chain lengths of C6, bilayers from C7 to C10, and pseudo-trimolecular layers from C15 to C18. Intermediate states also existed between bilayer and pseudo-trimolecular layer states from C11 to C14. The ammonium groups had two locations: most ammonium groups were located over the six-member rings (~90%), and the rest above the substitution sites (~10%). The ammonium groups interacted with the vermiculite surface through H bonds between ammonium H atoms and surface O atoms. The ammonium groups were fixed firmly on surfaces and, therefore, had very low mobility. The alkyl chains were slightly more mobile. The similarities and differences between alkylammonium-intercalated vermiculites and smectites were revealed. The layering behaviors of alkyl chains were similar in alkylammonium-intercalated vermiculites and smectites: the alkyl chain behavior was controlled by both the amount of layer charge and the carbon chain length. The distributions of ammonium groups, however, were different, caused by the layer-charge distribution in vermiculites being different from that in smectites. The atomic-level results derived in the present study will be useful for future research into and the applications of organo-vermiculites.

The resistance–nodulation–division efflux machinery confers antimicrobial resistance to Gram-negative bacteria by actively pumping antibiotics out of the cell. The protein complex is powered by proton motive force; however, the proton transfer mechanism itself and indeed even its stoichiometry is still unclear. Here we review computational studies from the last decade that focus on elucidating the number of protons transferred per conformational cycle of the pump. Given the difficulties in studying proton movement using even state-of-the-art structural biology methods, the contributions from computational studies have been invaluable from a mechanistic perspective.

The state and dynamics of water and cations in pure and mixed Na-Cs-montmorillonite as a function of the interlayer water content were investigated in the present study, using Monte Carlo and classical, molecular-dynamics methods. While highly idealized, the simulations showed that the swelling behavior of hetero-ionic Na-Cs-montmorillonite is comparable to the swelling of a homo-ionic Na- or Cs-montmorillonite. The mixed Na-Cs-montmorillonite is characterized by intermediate interlayer distances compared to homo-ionic Na- and Cs-montmorillonites. Dry, hetero-ionic Na-Cs-montmorillonite is characterized by a symmetric sheet configuration, as is homo-ionic Cs-montmorillonite.

We found that at low degrees of hydration the absolute diffusion coefficient of Cs+ is less than for Na+, whereas at greater hydration states the diffusion coefficient of Cs+ is greaterthan for Na+. An analysis of the relative diffusion coefficients (the ratio between the diffusion coefficient of an ion in the interlayer and its diffusion coefficient in bulk water) revealed that water and Na+ are always less retarded than Cs+. With large interlayer water contents, tetralayer or more, Na+ ions preferentially form outer-sphere complexes. The mobility perpendicular to the clay surface is limited and the diffusion is equivalent to two-dimensional diffusion in bulk water. In contrast, Cs+ ions preferentially form ‘inner-sphere complexes’ at all hydration states and their two-dimensional diffusion coefficient is less than in bulk water.

The question remains unanswered as to why experimentally derived relative diffusion coefficients of Cs+ in the interlayer of clays are about 20 times less than those we obtained by classical molecular dynamics studies.

A hybrid of montmorillonite (Mnt) and rifampicin (RIF) was synthesized and the structure and stability of the drug carrier system clarified. Density functional theory calculations involving dispersion corrections (DFT-D3) were performed to characterize interactions acting in the interlayer space of montmorillonite intercalated with rifampicin. The structure and stability of the RIF-Mnt intercalated complex were determined. Calculations revealed the deformation of the molecular structure of rifampicin after intercalation into the Mnt interlayer space due to the clay environment. The ansa chain of RIF was bent in the interlayer space compared with the structure of the RIF molecule in the monocrystal. RIF was keyed into the Mnt surface by means of numerous hydrogen bonds of weak to moderate strength. The calculated vibrational spectrum from ab initio molecular dynamics (AIMD) was in good agreement with the FTIR measured spectra and helped to analyze the overlapped vibrational bands. Based on analysis of structural stability, theoretical calculations revealed that Mnt is a suitable drug carrier for delayed release of the RIF drug. Batch adsorption experiments showed the large adsorption capacity of montmorillonite for RIF.

Molecular dynamics (MD) simulations provide an accurate description of the mineral–fluid interface from the perspective of the atomistic level taking into account all atom interactions. This simulation approach is computationally expensive if applied to large molecular systems. Classical Fluid Density Functional Theory (f-DFT) delivers structural and thermodynamic information at comparatively small computational costs. Numerous applications of f-DFT for electrolytes neglect an explicit consideration of solvent. In this work, an unrestricted three-component model (3CM) of f-DFT was applied, which incorporates Lennard-Jones (LJ) attractions for the description of the short-range interactions of fluid–fluid and fluid–wall rather than the hard sphere repulsions, named DFT/LJ-3CM. The DFT/LJ-3CM model considers ions as charged LJ particles and treats solvent molecules as neutral LJ particles. To validate the performance of the DFT/LJ-3CM, the f-DFT calculations were compared with atomistic simulations for montmorillonite (Mnt) with various hydrated states in electrolyte solutions. This benchmarking was used to assess critically the advantages and limitations of the f-DFT model. The calibrated DFT/LJ-3CM model for Na and Ca Mnt was applied to calculate cation selectivity for the ion exchange equilibrium with effective ion radius and swelling behavior of Mnt. The predictions of the DFT/LJ-3CM model were found to be in good agreement with the atomistic simulations and experimental data under a wide range of conditions. At the same time, the DFT calculations were 3–4 orders of magnitude faster than conventional MD simulations. Thus, the DFT/LJ-3CM model can be a computationally effective alternative to atomistic simulation in providing structural and thermodynamic properties of fluid–clay mineral interfaces. The DFT/LJ-3CM model provides a robust approach, which can be used for upscaling in reactive transport simulators and modeling ion migration taking place under more complex thermo-chemo-hydro-mechanical conditions.

Experimental studies have shown that a sharp, high-frequency IR band at ~3615 cm-1 (in H2O form) and at ~2685 cm-1 (in D2O form) is a common feature for all smectites, and its position correlates with layer charge. In order to explain the molecular origin of this band in terms of total layer charge, charge localization, as well as nature of interlayer cations influencing the position and intensity of this peak, a series of classical molecular dynamics (MD) simulations was performed for several smectite models. The smectite layers were described using a modified CLAYFF force field, where the intramolecular vibrations of H2O were described more accurately by the Toukan-Rahman potential. The power spectra of molecular vibrations of hydrogens were calculated for selected sub-sets of interlayer H2O to analyze quantitatively their contribution to the observed spectral features. The statistics of hydrogen bonds in the smectite interlayers were also analyzed to support the spectral calculations.

The simulation results demonstrated clearly that only the H2O molecules in close proximity to the smectite surface are responsible for the sharp vibrational band observed. Other hypotheses for the possible origins of this band were considered carefully and eventually rejected. Two orientations of H2O molecules donating one or two H bonds to the basal oxygens of the smectite surface (monodentate and bidentate orientations, respectively) were observed. In both orientations, these H bonds are quite weak, pointing to a generally hydrophobic character of the smectite surface. Both orientations contributed to the high-frequency band, but the monodentate orientation provided the predominant contribution because surface H2O molecules in this orientation were much more abundant. In good agreement with experiment, only a small difference in the peak position was observed between smectites with different charge localization. The effect of the total layer charge, i.e. the red-shift for higher-charge smectites, was also confirmed. This shift arose from the decrease in the H-bonding distances of H2O in monodentate and bidentate orientation.

Pyrophyllite is the precursor to other smectite-group minerals which exhibit swelling. The mineral structure of pyrophyllite can lead to other minerals in the smectite group, including montmorillonite, through appropriate isomorphous substitutions. In this work, an atomic model of the pyrophyllite interlayer was constructed. The response of the interlayer was evaluated using steered molecular dynamics simulations. In steered molecular dynamics, external forces were applied to individual atoms to study the response of the model to applied forces. In this work, forces are applied to the surface clay atoms to evaluate the displacement vs. applied stress in the interlayer between clay layers. This paper describes the construction of the model, the simulation procedure, and the results of the simulations which show that under the applied loading, deformation occurs mainly in the interlayer. The clay layers show relatively little deformation. The results show that the relationship between applied stress and displacement of the interlayer is linear. The stress-deformation relationship for the interlayer is presented.

A better understanding of the thermodynamics of radioactive cesium uptake at the surfaces of phyllosilicate minerals is needed to understand the mechanisms of selective adsorption and help guide the development of practical and inexpensive decontamination techniques. In this work, molecular dynamics simulations were carried out to determine the thermodynamics of Cs+ adsorption at the basal surface of six 2:1 phyllosilicate minerals, namely pyrophyllite, illite, muscovite, phlogopite, celadonite, and margarite. These minerals were selected to isolate the effects of the magnitude of the permanent layer charge (⩽2), its location (tetrahedral vs. octahedral sheet), and the octahedral sheet structure (dioctahedral vs. trioctahedral). Good agreement was obtained with the experiments in terms of the hydration free energy of Cs+ and the structure and thermodynamics of Cs+ adsorption at the muscovite basal surface, for which published data were available for comparison. With the exception of pyrophyllite, which did not exhibit an inner-sphere free energy minimum, all phyllosilicate minerals showed similar behavior with respect to Cs+ adsorption; notably, Cs+ adsorption was predominantly inner-sphere, whereas outer-sphere adsorption was very weak with the simulations predicting the formation of an extended outer-sphere complex. For a given location of the layer charge, the free energy of adsorption as an inner-sphere complex varied linearly with the magnitude of the layer charge. For a given layer charge location and magnitude, adsorption at phlogopite (trioctahedral sheet structure) was much less favorable than at muscovite (dioctahedral sheet structure) due to electrostatic repulsion between adsorbed Cs+ and the H atom of the OH- ion directly below the six-membered siloxane ring cavity. For a given layer charge magnitude and octahedral sheet structure, adsorption to celadonite (octahedral sheet layer charge) was favored over adsorption to muscovite (tetrahedral sheet layer charge) due to the increased distance to the surface K+ ions and the decreased distance to the O atom of the OH- ion directly below the surface cavity.

We propose a constitutive equation for flows of gases in high-rate regimes where the Navier–Stokes theory breaks down. The model generalizes the Navier–Stokes relation and agrees well with that model in all lower rate flows examined. Our proposed constitutive relation is calibrated with the method of objective molecular dynamics (OMD) using families of compressible and incompressible flows of Lennard-Jones argon. The constitutive relation makes use of the higher-order objective strain rates due to Rivlin and Ericksen (J. Rat. Mech. Anal., vol. 4, 1955, pp. 323–425). The constitutive relation is fully frame-indifferent, and the macroscopic flows corresponding to the OMD simulations are exact solutions for the proposed model. The model is shown to agree with atomistic results much better than the Navier–Stokes equations in the transition regime. The success of our model indicates that it is not higher gradients that become important in the high-rate regime, but rather higher rates of change of the strain rate tensor. While somewhat more complicated to implement than the Navier–Stokes relation, the proposed model is expected to be compatible with existing methods of computational fluid dynamics and may extend those methods to higher rate regimes, while preserving their ability to handle large spatial scales.

Engineering flow systems operating under low pressures and/or at the micro/nano scale generally include a physically adsorbed gas layer next to the surface. In this paper, we develop a scattering kernel that accounts for the effect of adsorption, arising from van der Waals interactions, on the dynamics of molecules impinging on solid smooth surfaces. In the limit of low bulk density, surface adsorption becomes negligible and the scattering kernel recovers consistently the Cercignani–Lampis model, which best describes molecular collisions with a clean, smooth surface. In the limit of high bulk density, a dense adsorbed molecular layer forms next to the surface and its presence is picked up by the Maxwell model with complete diffuse reflection, which better captures the multiple collisions suffered by molecules. A weight coefficient based on the Langmuir adsorption isotherm is incorporated into the modelling to handle the transition between these two limiting conditions of low and high densities. The proposed model is validated against high-fidelity molecular dynamics simulations that are performed for a variety of gas–surface combinations and adsorbed molecular layers with different densities. It is shown that the proposed model very well captures the scattering patterns of beams of gas molecules at different velocities impinging on surfaces, as well as momentum and energy accommodation coefficients in the entire range of explored conditions.

This paper presents systematic molecular dynamics modelling of Na-montmorillonite subjected to uniaxial compression and unidirectional shearing. An initial 3D model of a single-cell Na-montmorillonite structure is established using the Build Crystal module. The space group is C2/m, and COMPASS force fields are applied. Hydration analysis of Na-montmorillonite has been performed to validate the simulation procedures, where the number of absorbed water molecules varied with respect to the various lattice parameters. A series of uniaxial compression stress σzz and unidirectional shear stress τxy values are applied to the Na-montmorillonite structure. It is shown that the lattice parameter and hydration degree exhibit significant influence on the stress–strain relationship of Na-montmorillonite. The ultimate strain increases with increases in the lattice parameter but decreases in the number of water molecules. For saturated Na-montmorillonite, more water molecules result in a stiffer clay mineral under uniaxial compression and unidirectional shearing.