Density functional theory of homopolymer mixtures confined in a slit

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.     

Density functional theory for copolymers confined in a nanoslit

A density functional theory is developed for copolymers confined in a nanoslit on the basis of our previous work for homopolymers. The theory accurately captures the structural characteristics for diblock and alternating copolymers composed of hard-sphere or square-well segments. Satisfactory agreement is obtained between the theoretical predictions and simulation results in segment density profiles, segment fractions, and partition coefficients. Structures under confinement strongly depend on the substituent segment sizes for the hard-sphere copolymers and also on the segment-wall attractions for the square-well copolymers. Alternating copolymers are found to behave as homopolymers with effective segment size, and effective segment-segment and segment-wall interactions.     

Adsorption of copolymers in a selective nanoslit: a hybrid density functional theory

A hybrid density functional theory (DFT) is developed for adsorption of copolymers in a selective nanoslit. The DFT incorporates a single-chain simulation for the ideal-gas free energy functional with two weighted density approximations for the residual free energy functional. The theory is found to be insensitive to the width parameter used in the weighted density. Theoretical predictions are in excellent agreement with simulation results in the segment density profiles and the adsorption configurations including tail, loop, and train for copolymers with various sequences over a wide range of surface affinity. The bridge conformation is also observed in multiblock copolymers. Ordered assembly is facilitated in copolymers with longer chain/block and at stronger attraction between segment B and the slit wall. While diblock copolymer shows the longest tail, alternating copolymer has the shortest. As the attraction between segment B and the slit wall increases, the average size and fraction decrease for tail, but increase for loop and train.     

Comparison of random-walk density functional theory to simulation for bead-spring homopolymer melts

Density profiles for a homopolymer melt near a surface are calculated using a random-walk polymeric density functional theory, and compared to results from molecular dynamics simulations. All interactions are of a Lennard-Jones form, for both monomer-monomer interactions and surface-monomer interactions, rather than the hard core interactions which have been most investigated in the literature. For repulsive systems, the theory somewhat overpredicts the density oscillations near a surface. Nevertheless, near quantitative agreement with simulation can be obtained with an empirical scaling of the direct correlation function. Use of the random phase approximation to treat attractive interactions between polymer chains gives reasonable agreement with simulation of dense liquids near neutral and attractive surfaces.     

Adsorption isoterms and capillary condensation in a nanoslit with rough walls: a density functional theory

Adsorption isoterms and capillary condensation in an open slit with walls decorated with arrays of pillars are examined using the density functional theory. Compared with the main substrate, the pillars can have the same or different parameters in the Lennard-Jones interaction potential between them and the fluid in the slit. The roughness of the solid surface, defined as the ratio between the area of the actual surface and the area of the surface free of pillars, is controlled by the height of the pillars. It is shown that the capillary condensation pressure first increases with increasing roughness, passes through a maximum, and then decreases. The amount of adsorbed fluid at constant volume of the slit has, in general, a nonmonotonic dependence on roughness. These features of adsorption and capillary condensation are results of increased surface area and changes in the fluid-solid potential energy due to changes in roughness.     

Hybrid density functional theory band structure engineering in hematite

We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.     

Interactions between colloidal particles in amphiphilic mixtures: a density functional theory study

We present a density functional theory study of interactions between spherical colloidal particles in amphiphile solutions. Theory is found to be in good agreement with previously published molecular dynamics simulations. It is used to analyze the effect of the amphiphile solution bulk density, the chain length, and the solvent mole fraction on the potential of mean force between the particles. The general features of the potential of mean force are rationalized in terms of formation of layers and bilayers of amphiphilic molecules in the intercolloidal gap. Theory yields the same general trends as observed in simulations and in experiments. In particular, the computed mean force changes its character from repulsive to attractive and back to repulsive as the solvent mole fraction is gradually increased.     

Structure of Lennard-Jones fluids confined in square nanoscale channels from density functional theory

The density distribution of Lennard-Jones fluids confined in square nanoscale channels with Lennard-Jones walls has been studied using the nonlocal density functional theory (DFT) based on the Tarazona model. The effect of channel lengths on the density profiles with various chemical potentials was discussed. It was found that there is an apparent layering phenomenon for the confined fluids due to the combining influences of the enhancing solid-fluid interaction and the excluded volume effect. The pronounced density peaks were observed at the corners of square channels due to the strong fluid-solid interactions. The grand canonical ensemble Monte Carlo simulation (GCEMC) was applied to test the nonlocal DFT results. The DFT calculations are in relatively good agreement with the GCEMC simulations. The adsorption isotherms in a series of square channels were evaluated based on the obtained density distributions. The adsorption mechanism within the square pores was investigated. A comparison between the adsorptions of the square pores with those of the corresponding slit-size pores has been given.     

Hybrid density functional theory investigation of a series of alloxan-based thiosemicarbazones and semicarbazones

Recently, the synthesis and the NMR characterization of a series of eight alloxan-based thiosemicarbazones and semicarbazones were reported. These compounds exhibit a strongly hydrogenbonded hydrazinic proton that is a part of a characteristic six-membered ring. This proton is highly deshielded and resonates far downfield in the proton NMR spectra. In this report, mPW1PW91/6-31+G(d,p) calculations have been used to investigate the structure and other molecular properties of this series of eight compounds. The relationship between the ¹H and ¹³C NMR chemical shifts and various geometric parameters was investigated, and linear relationships for proton peaks that are involved in hydrogen-bond interactions were found.     

Microstructure of inhomogeneous polyatomic mixtures from a density functional formalism for atomic mixtures

A free energy density functional theory (DFT) for inhomogeneous polymeric mixtures is developed by treating the polyatomic system as a strongly associating atomic fluid mixture. The theory, derived in terms of segment density, retains the simple form of the DFTs for atomic fluids. Invoking the complete bonding limit of a stoichiometric mixture in the association free energy functional yields a computationally simple and accurate functional for the polyatomic system. Comparisons of theory calculations with molecular simulations are presented for inhomogeneous solutions and blends of linear and branched chains, demonstrating the capability of the theory to accurately capture the entropic and enthalpic effects governing the microstructure.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Structures and correlation functions of multicomponent and polydisperse hard-sphere mixtures from a density functional theory

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld [Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state [Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. Chem. Phys. 54, 1523 (1971)]. The theoretical predictions agreed very well with the molecular simulations for the overall density profiles, the local compositions, and the radial distribution functions of uniform as well as inhomogeneous hard-sphere mixtures. The density functional theory was further extended to represent the structure of a polydisperse hard-sphere fluid near a hard wall. Excellent agreement was also achieved between theory and Monte Carlo simulations. The density functional theory predicted oscillatory size segregations near a hard wall for a polydisperse hard-sphere fluid of a uniform size distribution.     

Exact-exchange density functional theory for hyperpolarizabilities

Time-dependent density functional theory (TDDFT) employing the exact-exchange functional (TDDFTx) has been formulated using the optimized effective potential method for the beta static hyperpolarizabilities, where it reduces to coupled-perturbed Kohn-Sham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the beta static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exact-exchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the self-interaction error in standard DFT methods and has the correct long-range behavior, provides results close to those of time-dependent Hartree-Fock in the static limit.     

Promoters in the hydrogenation of alkynes in mixtures: insights from density functional theory

Hydrogenation of alkyne-alkene mixtures of small sized hydrocarbons has been traditionally performed with Pd-based catalysts modified by a second metal. Over the last few years, this hydrogenation process has become a thriving field to understand selective processes that might be applicable to more complex molecules, for instance those derived from biomass. We summarize here the large body of experimental and open industrial documents to show the properties of different catalytic formulations, we concentrated on the role of the secondary metals employed. We compare these results to theoretical work performed over the last few years and to our new results based on Density Functional Theory. With this insight, we illustrate how secondary compounds behave under typical reaction conditions and how the reaction conditions might affect the stability of the catalyst.     

Excitonic effects in a time-dependent density functional theory

Excited state properties of one-dimensional molecular materials are dominated by many-body interactions resulting in strongly bound confined excitons. These effects cannot be neglected or treated as a small perturbation and should be appropriately accounted for by electronic structure methodologies. We use adiabatic time-dependent density functional theory to investigate the electronic structure of one-dimensional organic semiconductors, conjugated polymers. Various commonly used functionals are applied to calculate the lowest singlet and triplet state energies and oscillator strengths of the poly(phenylenevinylene) and ladder-type (poly)(para-phenylene) oligomers. Local density approximations and gradient-corrected functionals cannot describe bound excitonic states due to lack of an effective attractive Coulomb interaction between photoexcited electrons and holes. In contrast, hybrid density functionals, which include long-range nonlocal and nonadiabatic corrections in a form of a fraction of Hartree-Fock exchange, are able to reproduce the excitonic effects. The resulting finite exciton sizes are strongly dependent on the amount of the orbital exchange included in the functional.     

Fluid density profile transitions and symmetry breaking in a closed nanoslit

The density profiles in a fluid interacting with the two identical solid walls of a closed long slit were calculated for wide ranges of the number of fluid molecules in the slit and temperature by employing density functional theory in the local density approximation. Two potentials, the van der Waals and the Lennard-Jones, were considered for the fluid-fluid and the fluid-walls interactions. It was shown that the density profile corresponding to the stable state of the fluid considerably changes its shape with increasing average density (rhoav) of the fluid inside the slit, the details of changes being dependent on the selected potential. For the van der Waals potential, a single temperature-dependent critical value rhosb of rhoav was identified, such that for rhoav < rhosb the stable state of the system is described by a symmetric density profile, whereas for rhoav >/= rhosb it is described by an asymmetric one. This transition constitutes a spontaneous symmetry breaking of the fluid density distribution in a closed slit with identical walls. For rhoav >/= rhosb, a metastable state, described by a symmetric density profile, was present in addition to the stable asymmetric one. The shape of the symmetric profile changed suddenly at a value rhoc-h > rhosb of the average density, the density rhoc-h being almost independent of temperature. Because of the shapes of the profiles before and after the transformation, this transition was named cup-hill transformation. At the transition point, the density of the fluid near the walls decreased suddenly from a liquid-like value becoming comparable with the density of a gaseous phase, and the density in the middle of the slit increased suddenly from a gaseous-like value becoming on the order of the density of a liquid phase. For the Lennard-Jones potential, there are two temperature-dependent critical densities, rhosb1 and rhosb2, such that the stable density profile is asymmetric (symmetry breaking occurs) for rhosb1 相似文献   

Density functional theory for a primitive model of nanoparticle-block copolymer mixtures

Amphiphilic block copolymers provide useful templates for fabrication of nanostructured materials that are appealing for a wide variety of applications. The preparation of polymer-particle hybrid materials requires a good understanding of the chemical nature and topology of the amphiphilic molecules as well as their interactions with the embedded nanoparticles. This article reports a density functional theory (DFT) for a coarse-grained model of block copolymer-nanoparticle mixtures that is able to account for the properties of particles and copolymers within a self-consistent framework. It predicts various well-organized structures that can be effectively controlled by adjusting the polymer chain length and polymer-particle interactions. Illustrative examples based on relatively short chains suggest that, in qualitative agreement with experiments, large particles tend to be excluded from a polymer brush near a solid substrate, whereas smaller particles may be dissolved. The DFT is able to capture the dispersion of large particles in the microdomain of block copolymer that is energetically favorable, but localization of smaller particles at the microdomain interfaces.