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The structure of the solvation shell of the aqueous Fe3+ ion has been a subject of controversy due to discrepancies between experiments and different levels of theory. We address this issue by performing simulations for a wide range of ion concentrations, using various potential energy functions, supplemented by density functional theory calculations of selected configurations. The solvation shell undergoes abrupt transitions between two states: a hexacoordinated octahedral (OH) state and a capped trigonal prism (CTP) state with 7-fold coordination. The lifetime of these states is dependent on concentration. In dilute FeCl3 solutions, the lifetimes of both are similar (≈1 ns). However, the lifetime of the OH state increases with ion concentration, while that of the CTP state decreases slightly. When a uniform negative background charge is used instead of explicit counterions, the lifetime of the OH state is greatly overestimated. These findings underscore the need for further experimental measurements and higher-level simulations.
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We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.
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From studies via molecular dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. All interactions in the fully passive limit are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus-like structure: nearly one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics approximately a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, magnitude of which depends upon the strength of activity, but only weakly.
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Using extensive molecular dynamics simulation of a coarse-grained model, we demonstrate the possibility of sustained unidirectional motion (durotaxis) of droplets without external energy supply when placed on a polymer brush substrate with stiffness gradient in a certain direction. The governing key parameters for the specific substrate design studied, which determine the durotaxis efficiency, are found to be the grafting density of the brush and the droplet adhesion to the brush surface, whereas the strength of the stiffness gradient, the viscosity of the droplet, or the length of the polymer chains of the brush have only a minor effect on the process. It is shown that this durotaxial motion is driven by the steady increase of the interfacial energy between droplet and brush as the droplet moves from softer to stiffer parts of the substrate whereby the mean driving force gradually declines with decreasing roughness of the brush surface. We anticipate that our findings indicate further possibilities in the area of nanoscale motion without external energy supply.
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A Density Functional Theory is employed to study depletion interactions between nanoparticles mediated by semiflexible polymers. The four key parameters are the chain contour length and the persistence length of the polymeric depletant, its radius of gyration, and the nanoparticle radius. In the Density Functional Theory calculation of the depletion interaction between the nanoparticles mediated by semiflexible polymers, the polymer gyration radius is kept constant by varying the contour length and the persistence length simultaneously. This makes it possible to study the effect of the chain stiffness on the depletion potential of mean force between the nanoparticles for a given depletant size. It is found that the depletion attraction becomes stronger for stiffer polymer chains and larger colloids. The depletion potential of mean force is used as input to compute the phase diagram for an effective one-component colloidal system.
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In this paper we report the classification of all the 81 magnetic line group families into seven spin splitting prototypes, in analogy to the similar classification previously reported for the 1651 magnetic space groups, 528 magnetic layer groups, and 394 magnetic rod groups. According to this classification, electrically induced (Pekar-Rashba) spin splitting is possible in the antiferromagnetic structures described by magnetic line groups of type I (no anti-unitary operations) and III, both in the presence and in the absence of the space inversion operation. As a specific example, a group theoretical analysis of spin splitting in CoO (8, 8) nanotube is carried out and its predictions are confirmed byab initiodensity functional theory calculations.
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Wetting and drying phenomena are studied for flexible and semiflexible polymer solutions via coarse-grained molecular dynamics simulations and density functional theory calculations. This study is based on the use of Young's equation for the contact angle, determining all relevant surface tensions from the anisotropy of the pressure tensor. The solvent quality (or effective temperature, equivalently) is varied systematically, while all other interactions remain unaltered. For flexible polymers, the wetting transition temperature Tw increases monotonically with chain length N, while the contact angle at temperatures far below Tw is independent of N. For semiflexible polymer solutions, Tw varies non-monotonically with the persistence length: Initially, Tw increases with increasing chain stiffness and reaches a maximum, but then a sudden drop of Tw is observed, which is associated with the isotropic-nematic transition of the system.
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A Density Functional Theory study is performed to analyze both bulk and interfacial properties of solvent-polymer binary mixtures. The effects of increasing polymer chain length on the bulk phase diagram morphology and interfacial tension are presented and compared to the prior simulation results. Good agreement between simulation and Density Functional Theory is found, including its ability to reproduce the density inversion phenomenon for highly asymmetric solvent-polymer binary mixtures. The data on the interfacial tensions is used to compute contact angles of the mixture at a planar wall, with particular focus on the wetting transition. The dependence of the wetting temperature on the polymer chain length and the mixture composition is analyzed in detail.
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Mode-coupling theory is developed and employed to compute the nanoparticle diffusion coefficient in polymer solutions. Theoretical results are compared with molecular dynamics simulation data for a similar model. The theory properly reproduces the simulated effects of the nanoparticle size, mass, and concentration on the nanoparticle diffusion coefficient. Within the mode-coupling theory framework, a microscopic interpretation of the nonmonotonic dependence of the diffusion coefficient on the nanoparticle concentration is given in terms of structural and dynamic effects. Both the size dependence and mass dependence of the diffusion coefficient indicate a pronounced breakdown of the Stokes-Einstein relation for the present model.
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Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several cases of bending stiffness κ (the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e., NA=16, NB=32 or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (N=32) and large stiffness disparity (κB/κA=4.9 to 8), both isotropic-nematic and nematic-nematic unmixing occur. It is found that the phase diagrams may exhibit a triple point or a nematic-nematic critical point, and that coexisting phases differ appreciably in their monomer densities. The properties of the two types of chains (nematic order parameters, chain radii, etc.) in the various phases are studied in detail, and predictions on the (anisotropic) critical behavior near the critical point of nematic-nematic unmixing are made.
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Density Functional Theory is employed to study structural properties and interactions between solvent-free polymer-grafted nanoparticles. Both monodisperse and bidisperse polymer brushes with variable chain stiffness are considered. The three major control parameters are the grafting density, the grafted chain length, and its stiffness. The effect of these parameters on the brush-brush overlap and attractive interaction strength is analyzed. The Density Functional Theory results are compared with the available simulation data, and good quantitative agreement is found.
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The Asakura-Oosawa (AO) model of colloid-polymer mixtures has been extensively studied over the past several decades both via computer simulations and Density Functional Theory (DFT). At this point, its structural and thermodynamic properties both in the bulk and in contact with flat structureless walls are well understood. At the same time, the phase behavior of AO mixtures in spherical cavities and cylindrical pores, while thoroughly investigated by simulations, has not received a comparably detailed DFT treatment. In this paper, we use the DFT results for the AO model in the bulk and under planar confinement as a point of reference for studying its thermodynamic and structural properties in cavities and pores. The accuracy of the DFT approach is assessed by comparing its predictions with the available extensive simulation data; good overall agreement is generally found with some notable exceptions in the vicinity of wetting and drying transitions. The deviations of the phase behavior in confinement from the bulk phase diagram are analyzed using the Kelvin equation, which is seen to work reasonably well under moderate confinement, i.e., for sufficiently large radii of confining cavities and pores.
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We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.
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In this Letter we report on the colossal spin splitting (on the order of several electronvolts) in the collinear antiferromagnetic (AFM) MnF2 (110) monolayer, which we obtained from first-principles calculations and explain in terms of group-theoretical analysis. This Pekar-Rashba AFM-induced spin splitting with a magnetic mechanism does not require the presence of spin-orbit coupling such as with a traditional Rashba-Dresselhaus electric mechanism. Furthermore, it was observed for all wave vectors, including high-symmetry points of the two-dimensional (2D) Brillouin zone. This is in contrast to recently reported AFM-induced spin splitting in the bulk structure of MnF2, which was both smaller by at least an order of magnitude and required to vanish by symmetry at several high-symmetry points and directions of the three-dimensional Brillouin zone. The crucial part of our group-theoretical analysis is the determination of the magnetic layer group for the monolayer structure for which we propose a simple and generic procedure.
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The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As the difference in bending stiffness is increased, the two chain types separate into two coexisting nematic phases. The phase behavior is rationalized by considering the chemical potentials of the two components and the Gibbs excess free energy. The geometric properties of the chain conformations under the various conditions are also discussed.
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In this work, we report a Density Functional Theory based study of phase behavior of lyotropic liquid-crystalline polymers under both good and varying solvent conditions in the presence of external electric or magnetic field. Our microscopic model for the good solvent case is based on the tangent hard-sphere chain with bond-bending potential to account for the chain stiffness; the variable solvent quality is modeled by adding attractive monomer-monomer interactions. The phase diagrams are constructed in three intensive variables (temperature, pressure, and field strength), and are characterized by the presence of critical and triple lines, which originate from the critical and triple points of the corresponding zero-field case. The merging of critical and triple lines results in the appearance of the "double critical" and "critical triple" points, already known from the earlier studies of the phase behavior of spin fluids in magnetic fields. The important difference of the present model from the spin fluids is due to the finite stiffness of the polymer chains (characterized by their persistence length), which adds an additional parameter controlling the morphology of the phase diagrams.
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Nanoparticle diffusion in polymer melts is studied by the combination of Molecular Dynamics (MD) simulations and Mode-Coupling Theory (MCT). In accord with earlier experimental, simulation, and theoretical studies, we find that the Stokes-Einstein (SE) hydrodynamic relation Dn â¼ 1/Rn holds when the nanoparticle radius Rn is greater than the polymer gyration radius Rg, while in the opposite regime, the measured nanoparticle diffusion coefficient Dn exceeds the SE value by as much as an order of magnitude. The MCT values of Dn are found to be consistently higher than the MD simulation values. The observed discrepancy is attributed to the approximations involved in constructing the microscopic friction as well as to the approximate forms for dynamic structure factors used in MCT. In a thorough test of underlying MCT assumptions and approximations, various structural and dynamical quantities required as input for MCT are obtained directly from MD simulations. We present the improved MCT approach, which involves splitting of the microscopic time-dependent friction into two terms: binary (originating from short-time dynamics) and collective (due to long-time dynamics). Using MD data as input in MCT, we demonstrate that the total friction is largely dominated by its binary short-time term, which, if neglected, leads to severe overestimation of Dn. As a result, the revised version of MCT, in agreement with the present MD data, predicts 1/Rn 2 scaling of the probe diffusion coefficient in a non-hydrodynamic regime when Rn < Rg. If the total friction is dominated by the collective long-time component, one would observe 1/Rn 3 scaling of Dn in accordance with previous studies.
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The contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor rw), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form zwall(y) = Δ cos(2πy/λ), for a potential of short range σw acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change in the wall-vapor surface tension can be computed exactly, and corrections to Wenzel's equation are typically of the order σwΔ/λ2. For fixed rw and fixed σw, the approach to Wenzel's result with increasing λ may be nonmonotonic and this limit often is only reached for λ/σw > 30. For a non-additive binary mixture, density functional theory is used to work out the density profiles of both coexisting phases for planar and corrugated walls as well as the corresponding surface tensions. Again, deviations from Wenzel's results of similar magnitude as in the above ideal gas case are predicted. Finally, a crudely simplified description based on the interface Hamiltonian concept is used to interpret the corresponding simulation results along similar lines. Wenzel's approach is found to generally hold when λ/σw â« 1 and Δ/λ < 1 and under conditions avoiding proximity of wetting or filling transitions.
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Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.
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The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained models, with a bond-angle potential to control chain stiffness, for chain lengths comparable to the persistence length of the chains. We varied both the density of the monomeric units and the effective temperature that controls the quality of the implicit solvent. For very stiff chains, only a single transition from an isotropic fluid to a nematic is found, with a phase diagram of "swan-neck" topology. For less stiff chains, however, also unmixing between isotropic fluids of different concentration, ending in a critical point, occurs for temperatures above a triple point. The associated critical behavior is examined in the MD simulations and found compatible with Ising universality. Apart from this critical behavior, DFT calculations agree qualitatively with the MD simulations.