An analytic model for the field dependence of charge mobility is developed within the long-range-correlated disorder model of a dipole glass. Release of a charge carrier from a deep state is considered as hopping drift and diffusion in a quasi-Coulomb potential well. The analytic results, containing only one numerical parameter obtained from independent simulation, are in good agreement with the fit to the Monte-Carlo simulations. The developed approach justifies applicability of the concept of the effective transport level for the modeling of organic materials with large molecular dipoles.
We present a simple model of the bimolecular charge carrier recombination in polar amorphous organic semiconductors in which the dominant part of the energetic disorder is provided by permanent dipoles and show that the recombination rate constant could be much smaller than the corresponding Langevin rate constant. The reason for the strong decrease of the rate constant is the long-range spatial correlation of the random energy landscape in amorphous dipolar materials; without spatial correlation, even strong disorder does not modify the Langevin rate constant. Our study shows that the signi ﬁ cant suppression of the bimolecular recombination could take place in homogeneous amorphous organic semiconductors and does not need large-scale inhomogeneity of the material.
The incorporation of Ca(2+) into smectite minerals is well-known to have a significant effect on the swelling behavior and mechanical properties of this environmentally and technologically important group of materials. Relative to common alkali cations such as Na+, K+, and Cs+, Ca(2+) has a larger charge/ionic radius ratio and thus interacts very differently with interlayer water molecules and the oxygens of the clay basal surface. Recent (2)H and (43)Ca NMR studies of the smectite mineral, hectorite, show that the molecular scale interlayer dynamics is quite different with Ca(2+) than with alkali cations. Classical molecular dynamics (MD) simulations presented here use a newly developed hectorite model with a disordered distribution of Li+/Mg(2+) substitutions in the octahedral sheet and provide new insight into the origin of the effects of Ca(2+) on the structure, dynamics, and energetics of smectite interlayers. The computed basal spacings and thermodynamic properties suggest the potential for formation of stable monolayer hydrates that have partial and complete water contents, a bilayer hydrate, and possible expansion to higher hydration states. The system hydration energies are comparable to those previously calculated for Caâ€“montmorillonite and are more negative than for Cs+ and N+ hectorite due to the higher hydration energy of Ca(2+). The coordination environments of Ca(2+) change significantly with increasing interlayer hydration, with the extent of coordination to basal oxygens decreasing as the number of interlayer molecules increases. On external (001) surfaces, the H2O molecules closest to the surface are adsorbed at the centers of ditrigonal cavities and bridge Ca(2+) to the surface. The Ca(2+) ions on the external surface are all in outer-sphere coordination with the basal oxygens of the surface, and the proximity-restricted region with a significant number of Ca(2+) is approximately 6 Å thick. Quantification of these interactions provides a basis for understanding intercalation of Ca(2+) by organic species and smectite minerals.
In situ XRD and NMR experiments combined with molecular dynamics simulations using the grand canonical ensemble (GCMD) show that cation size, charge and solvation energy play critical roles in determining the interlayer expansion of smectite clay minerals when exposed to dry supercritical CO2 under conditions relevant to the earthâ€™s upper crust, petroleum reservoirs, and geological CO2 sequestration conditions (323 K and 90 bar). The GCMD results show that the smectite mineral, hectorite, containing interlayer alkali and alkaline earth cations with relatively small ionic radii and high solvation and hydration energies (e.g., Li+, Na+ Mg2+, and Ca2+) does not intercalate dry CO2 and that the fully collapsed interlayer structure is the energetically most stable configuration. With increasing cation size and decreasing cation solvation energy, the energy barrier to CO2 intercalation decreases. With K+, Rb+, Cs+, Sr2+, and Ba2+ the monolayer structure is the stable configuration, and CO2 should spontaneously enter the interlayer. With Cs+ there is not even an energy barrier for CO2 intercalation, in agreement with the experimental XRD and NMR results that show clay layer expansion and CO2 incorporation. The number of intercalated CO2 molecules decreases with increasing size of the alkali cation but does not vary with ion size for the alkaline earth cations. 13C NMR spectroscopy and the GCMD simulations show that the average orientation of the intercalated CO2 molecules is with their O-C-O axes parallel to the basal clay surface and that they undergo a combination of rapid rotation about an axis perpendicular to the main molecular axis and wobbling motion with respect to the basal surface. Incorporation of CO2 in the interlayer decreases the coordination of Cs+ by the oxygen atoms of the basal surfaces, which is compensated by CO2 molecules entering their solvation shell, as predicted based on previously published NMR results. The GCMD simulations show that the strength of the interaction between the exchangeable cation and the clay structure dominates the intercalation energetics in dry scCO2. With relatively small cations, the cation-clay interactions outcompete cation solvation by CO2 molecules. The computed residence times for coordination among of interlayer species are consistent with the computed energetics.
The intercalation of H2O, CO2, and other fluid species in expandable clay minerals (smectites) may play a significant role in controlling the behavior of these species in geological C-sequestration and enhanced petroleum production and has been the subject of intensive study in recent years. This paper reports the results of a computational study of the effects of the properties of the charge balancing, exchangeable cations on H2O and CO2 intercalation in the smectite mineral, hectorite, in equilibrium with an H2O-saturated supercritical CO2 fluid under reservoir conditions using Grand Canonical Molecular Dynamics (GCMD) methods. The results show that the intercalation behavior is greatly different with cations with relatively low hydration energies and high affinities for CO2 (here Cs+) than with cations with higher hydration energies (here Ca2+). With Cs+, CO2 intercalation occurs in a 1-layer structure and does not require H2O intercalation, whereas with Ca2+ the presence of a sub-monolayer of H2O is required for CO2 intercalation. The computational results provide detailed structural, dynamical and energetic insight into the differences in intercalation behavior and are in excellent agreement with in situ experimental XRD, IR, quartz crystal microbalance, and NMR results for smectite materials obtained under reservoir conditions.
Аннотация: разработана аналитическая модель, основанная на концепции транспортного уровня и эффективной температуры, для последовательного описания квази- и неравновесных режимов переноса в неполярных органических телах с гауссовским некоррелированным энергетическим расстройством. Полевые и температурные зависимости дрейфовой подвижности от неравновесного транспортного режима, относящиеся к эксперименту "времени полета", хорошо согласуются с результатами моделирования Монте-Карло в широком диапазоне полей и температур с использованием одного и того же набора параметров модели для обоих транспортных режимов.
Grand Canonical Molecular Dynamics (GCMD) simulations were performed to investigate the intercalation of CO2 and H2O molecules in the interlayers of the smectite clay, Na-hectorite, at temperatures and pressures relevant to petroleum reservoir and geological carbon sequestration conditions and in equilibrium with H2O-saturated CO2. The computed adsorption isotherms indicate that CO2 molecules enter the interlayer space of Na-hectorite only when it is hydrated with approximately three H2O molecules per unit cell. The computed immersion energies show that the bilayer hydrate structure (2WL) contains less CO2 than the monolayer structure (1WL) but that the 2WL hydrate is the most thermodynamically stable state, consistent with experimental results for a similar Na-montmorillonite smectite. Under all T and P conditions examined (323–368 K and 90–150 bar), the CO2 molecules are adsorbed at the midplane of clay interlayers for the 1WL structure and closer to one of the basal surfaces for the 2WL structure. Interlayer CO2 molecules are dynamically less restricted in the 2WL structures. The CO2 molecules are preferentially located near basal surface oxygen atoms and H2O molecules rather than in coordination with Na+ ions. Accounting for the orientation and flexibility of the structural −OH groups of the clay layer has a significant effect on the details of the computed structure and dynamics of H2O and CO2 molecules but does not affect the overall trends with changing basal spacing or the principal structural and dynamical conclusions. Temperature and pressure in the ranges examined have little effect on the principal structural and energetic conclusions, but the rates of dynamical processes increase with increasing temperature, as expected.
Adsorption and mobility of radioactive Cs+ isotopes in soil are among the most important factors affecting the long-term environmental footprint of nuclear accidents such as Chernobyl (1986) and Fukushima Daiichi (2011). In particular, Cs+ ions can be retained through their exchange with K+ naturally present in muscovite mica, one of the common soil mineral components. The ClayFF force field allowed us to realistically represent local inhomogeneities of the structure, composition, and charge on the muscovite (001) surface and to identify three structurally different types of adsorption sites. We performed molecular dynamics simulations of Cs+ and K+ adsorption at the hydrated muscovite surface and used quasi-one-dimensional site-specific potential of mean force calculations to quantify the energetics of ion exchange in this system for each individual site and for the entire muscovite surface on average. Irrespective of the type of adsorption site, both K+ and Cs+ cations are preferably adsorbed on the basal (001) muscovite surface at the centers of ditrigonal cavities as inner sphere surface complexes. The free energy difference between the most favorable and the least favorable surface sites for Cs+/K+ ion exchange amounts to 11.7 kJ/mol, with the most favorable sites occupying half of the surface and the least favorable type - 1/6 of the surface and the rest exhibiting an intermediate adsorption and ion exchange capacity. The simulation results are compared with available thermodynamic estimates based on recent X-ray reflectivity measurements.
Three new structural models of montmorillonite with differently distributed Al/Si and Mg/Al substitutions in the tetrahedral and octahedral clay layers are systematically developed and studied by means of MD simulations to quantify the possible effects of such substitutional disorder on the swelling behavior, the interlayer structure, and mobility of aqueous species. A very wide range of water content, from 0 to 700 mgwater/gclay is explored to derive the swelling properties of Cs-montmorillonite. The determined layer spacing does not differ much depending on the clay model. However, at low water contents up to 1-layer hydrate (~100 (mg water)/(g clay)) the variation of specific locations of the tetrahedral and octahedral substitutions in the two TOT clay layers slightly but noticeably affects the total hydration energy of the system. Using atom?atom radial distribution functions and the respective atomic coordination numbers we have identified for the three clay models not only the previously observed binding sites for Cs+ on the clay surface but also new ones that are correlated with the position of tetrahedral substitution in the structure. The mobility of Cs+ ions and H2O diffusion coefficients, as expected, gradually increase both with increasing water content and with increasing distance from the clay surface, but they still remain 2 to 4 times lower than the corresponding bulk values. Only small differences were observed between the three Cs-montmorillonite models, but these differences are predicted to increase in the case of higher charge density of the clay layers and/or interlayer cations.
Classical molecular dynamics simulations were performed for the smectite clay hectorite with charge-balancing Cs+ cations using a newly developed structural model with a disordered distribution of Li/Mg substitutions in the octahedral sheet and the fully flexible ClayFF force field. Calculations for systems with interlayer galleries containing 0 to 19 H2O/Cs+ suggest that the monolayer hydrate is the only stable state at all relative humidities at ambient pressure and temperature, in agreement with experimental results and previous molecular calculations. The basal spacing of this structure is also in good agreement with experimental values. In contrast to previous molecular modeling results, however, the new simulations show that interlayer Cs+ occurs on 2 different inner sphere adsorption sites: above the center of ditrigonal cavities and above Si tetrahedra. Unlike previous simulations, which employed a rigid clay model and fixed orientations of the structural âˆ’OH groups, the present results are obtained for an unconstrained clay substrate structure, where the structural âˆ’OH groups are able to assume various orientations, including being nearly parallel to the clay layers. This flexibility allows the Cs+ ions to approach the surface more closely above the centers of the hexagonal rings. In this structural arrangement, Cs+ ions are not hydrated by the H2O molecules which share the same interlayer plane, but rather by the H2O molecules coordinated to the opposite surface. In contrast, on the external basal surface, a significant fraction of H2O molecules are adsorbed above the centers of ditrigonal cavities adjacent to adsorbed Cs+ ions. For these H2O molecules, both HH2O atoms coordinate and H-bond to Ob surface oxygen atoms. The mean residence times for the Cs+ - H2O, Cs+ - Ob, and H2O - Ob coordination pairs show that Cs+ ions are more strongly coordinated with Ob atoms than H2O molecules. This result is the opposite of the behavior in Ca-hectorite, due to the much smaller hydration energy of Cs+ compared to that of Ca(2+).
This paper presents a classical molecular dynamics (MD) and metadynamics investigation of the relationships between the structure, energetics, and dynamics of Na-hydroxyhectorite and serves to provide additional, molecular-scale insight into the interlayer hydration of this mineral. The computational results support a model for interlayer H2O structure and dynamics based on 2H NMR spectroscopy and indicate that H2O molecules undergo simultaneous fast librational motions about the H2O C2 symmetry axis and site hopping with C3 symmetry with respect to the surface normal. Hydration energy minima occur at one-, one-and-one-half-, and two-water-layer hydrates, which for the composition modeled correspond to 3, 5.5, and 10 H2O/Na+, respectively. Na+ ions are coordinated by basal O atoms (OMIN) at the lowest hydration levels and by H2O molecules (OH2O) in the two-layer hydrate, and H2O molecules have an average of three H-bonds at the greatest hydration levels. The metadynamics calculations yield activation energies for site hopping of H2O molecules of ~6.0 kJ/mol for the one-layer structure and ~3.3 kJ/mol for hopping between layers in the two-layer structure. Computed diffusion coefficients for water and Na+ are substantially less than in bulk liquid water, as expected in a nanoconfined environment, and are in good agreement with previous results.
Molecular scale understanding of the structure and properties of aqueous interfaces with clays, metal (oxy-) hydroxides, layered double hydroxides, and other inorganic phases is strongly affected by significant degrees of structural and compositional disorder of the interfaces. ClayFF was originally developed as a robust and flexible force field for classical molecular simulations of such systems (Cygan, R. T.; Liang, J.-J.; Kalinichev, A. G. J. Phys. Chem. B 2004, 108, 1255-1266). However, despite its success, multiple limitations have also become evident with its use. One of the most important limitations is the difficulty to accurately model the edges of finite size nanoparticles or pores rather than infinitely layered periodic structures. Here we propose a systematic approach to solve this problem by developing specific metal-O-H (M-O-H) bending terms for ClayFF, Ebend = k (theta - theta0)**2 to better describe the structure and dynamics of singly protonated hydroxyl groups at mineral surfaces, particularly edge surfaces. On the basis of a series of DFT calculations, the optimal values of the Al-O-H and Mg-O-H parameters for Al and Mg in octahedral coordination are determined to be theta0(AlOH) = theta0(MgOH) = 110°, k(AlOH) = 15 kcal mol(-1) rad(-2) and k(MgOH) = 6 kcal mol(-1) rad(-2). Molecular dynamics simulations were performed for fully hydrated models of the basal and edge surfaces of gibbsite, Al(OH)3, and brucite, Mg(OH)2, at the DFT level of theory and at the classical level, using ClayFF with and without the M-O-H term. The addition of the new bending term leads to a much more accurate representation of the orientation of O-H groups at the basal and edge surfaces. The previously observed unrealistic desorption of OH2 groups from the particle edges within the original ClayFF model is also strongly constrained by the new modification.