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.     

Monomer density profiles for polymer chains in confined geometries: massive field theory approach

Taking into account the well known correspondence between the field theoretical ?(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.     

A density-functional theory study of the confined soft ellipsoid fluid

A system of soft ellipsoid molecules confined between two planar walls is studied using classical density-functional theory. Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different Ans?tze and the intermolecular interaction is incorporated using two different direct correlation functions (DCF's). The first is a numerical DCF obtained from simulations of bulk soft ellipsoid fluids and the second is taken from the Parsons-Lee theory. In both the isotropic and nematic phases the numerical DCF gives density and order parameter profiles in reasonable agreement with simulation. The Parsons-Lee DCF also gives reasonable agreement in the isotropic phase but poor agreement in the nematic phase.     

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.     

Structure of flexible and semiflexible polyelectrolyte chains in confined spaces of slit micro/nanochannels

Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

Structure and conformation properties of 1-alkyl-3-methylimidazolium halide ionic liquids: a density-functional theory study

The structures and conformational properties of 1-alkyl-3-methylimidazolium halide ionic liquids have been studied with a Becke's 3 Parameter functional method. The interaction mechanisms between the cation and the anion in 1-ethyl-3-methylimidazolium (Emim+) halide and 1-butyl-3-methylimidazolium (Bmim+) halide ionic liquids were investigated using 6-31G*, 6-31++G**, and 6-311++G** basis sets. Forty structures of different ion pairs were optimized and geometrical parameters of them have been discussed in details. Halide ions (Cl- or Br-) have been gradually placed in different regions around imidazolium cation and the interaction energies between the anion and the cation have been calculated. Theoretical results indicate that there are four activity regions in the vicinity of the imidazolium cations, in these regions the imidazolium cations and the halide anions formed stable ion pairs. Imidazolium cations can form hydrogen bond interactions with one, two or three but no more than three nearest halide anions. The halide ions are situated in hydrogen bond positions rather than at random.     

Study on the coil–globule transition and dynamics of polymer chain confined in slit

The coil–globule transition and dynamics of a lattice self‐avoiding bond fluctuation polymer chain confined in slit are studied by Monte Carlo simulations. The coil–globule transition temperature of polymer chain is increased at intermediate slit height H (H ∼ R_G0 with R_G0 the radius of gyration of polymer in dilute solution) due to the squeeze of the polymer in the repulsive slit, but it is decreased by surface attraction as the polymer is extended along the surface. We have compared the difference between the rotational relaxation time τ_R for the reorientation of end‐to‐end vector and the relaxation time τ for the polymer diffusing over a distance of the size of polymer. We find that τ_R is clearly distinct from τ as they have different scaling exponents in their slit height‐dependent behaviors and for the polymer in the extended coil state, that is, α_R > α. And both exponents increase with an increase in the intrapolymer attraction and surface attraction. However, these scaling relations are destroyed by strong surface attraction when the polymer is adsorbed on surfaces. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1053–1062     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Atomic volumes and polarizabilities in density-functional theory

Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H-Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.     

First hyperpolarizability of a sesquifulvalene transition metal complex by time-dependent density-functional theory

The first hyperpolarizability and electronic excitation spectrum of sesquifulvalene and a sesquifulvalene ruthenium complex have been computed and analyzed with use of time-dependent density-functional theory. A new orbital decomposition scheme is introduced that allows the computed first hyperpolarizability to be related to the electronic structure of complex molecules. The analysis shows that the first hyperpolarizability of sesquifulvalene is not associated with the first intense absorption, with HOMO-1 --> LUMO+1 character, but is dominated by the lowest energy transition, with HOMO --> LUMO character, despite its very low intensity. In the ruthenium complex, the analysis reveals that the strong enhancement of the nonlinear optical response compared to free sesquifulvalene should not be attributed to the effect of complexation on the hyperpolarizability of sesquifulvalene. The strong hyperpolarizability originates from MLCT transitions from ruthenium d-orbitals to an empty orbital located at the seven ring of sesquifulvalene, transitions that have no analogue in free sequifulvalene.     

Calculating thermodynamic properties from perturbation theory: Part III. The mixtures of square-well chain fluid

A completely analytic perturbation theory has been developed to calculate the Helmholtz energy, compressibility factor, internal energy and constant-volume heat capacity for square-well chain fluid mixtures. This theory is based on the improved Barker–Henderson macroscopic compressibility (mc) approximation proposed by Zhang, the first-order perturbation theory of Wertheim in which Zhang’s analytic monomer radial distribution function as the function of temperature and monomer density is used, and a simple mixing rule similar to that of Hino–Prausnitz. The validity of the perturbation theory is evaluated by comparing the calculated compressibility factor, internal energy and constant-volume heat capacity for the freely jointed square-well chain mixtures from the theory to MC simulation data. The results show that the theory predicts results in good agreement with simulation results.     

Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory

We present a simple and efficient embedding scheme for the wave-function based calculation of the energies of local excitations in large systems. By introducing an embedding potential obtained from density-functional theory (DFT) it is possible to describe the effect of an environment on local excitations of an embedded system in wave-function theory (WFT) calculations of the excitation energies. We outline the implementation of such a WFT-in-DFT embedding procedure employing the ADF, Dalton and DIRAC codes, where the embedded subsystem is treated with coupled cluster methods. We then evaluate this procedure in the calculation of the solvatochromic shift of acetone in water and of the f-f spectrum of NpO(2)(2+) embedded in a Cs(2)UO(2)Cl(4) crystal and find that our scheme does effectively incorporate the environment effect in both cases. A particularly interesting finding is that with our embedding scheme we can model the equatorial Cl(-) ligands in NpO(2)Cl(4)(2-) quite accurately, compared to a fully wavefunction-based calculation, and this opens up the possibility of modeling the interaction of different ligands to actinyl species with relatively high accuracy but at a much reduced computational cost.     

Calculation of nonadiabatic couplings in density-functional theory

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.     

Orientational orders of small anisotropic molecules confined in slit pores

Based on a constant-pressure Monte Carlo molecular simulation, we have studied orientationally ordered transitions of small anisotropic molecules confined in two parallel hard walls. These molecules are modeled by the hard Gaussian overlap model. The molecular elongations of the chosen molecules are so small that the molecules cannot form stable liquid-crystal (LC) phases in the bulk. But in the slit pores, we found, while the distance between two walls of the pores decreases to the molecular scale, an orientationally ordered phase can form. It shows that even hard confining surfaces favor the alignment of the small anisotropic molecules. Thus we conclude that the required molecular elongation for forming LC phases will decrease in confinement. Our results indicate that some non-LC small molecules may form stable LC phases due to the inducement of confining surfaces.     

Structure and stability of Al-doped boron clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Bn and AlBn clusters, up to n=12, have been systematically investigated by using the density-functional approach. The results of Bn clusters are in good agreement with previous conclusions. When the Al atom is doped in Bn clusters, the lowest-energy structures of the AlBn clusters favor two-dimensional and can be obtained by adding one Al atom on the peripheral site of the stable Bn when n相似文献   

Monte Carlo simulations of chains confined inside a cube

Self-avoiding walks (SAWs) and random-flight walks (RFWs) of various lengths embedded on a simple cubic lattice have been computer generated inside cubes of varying side. If B is the side of the confining cube, we define the reduced cube side size B₀ as B₀ = (B − 1)/<r²>^1/2, where <r²>^1/2 is the root-mean-square end-to-end distance of the non-confined chains. Dimensionless diagrams are then given of the Monte Carlo estimates for the dimensions, the entropy, and the compressibility parameter PV/(kT) of the confined chains as a function of B₀. The comparative behaviour of the confined SAWs and RFWs is established, scaling properties are examined, and the Monte Carlo estimates compared with theory when such theory is available.