Hybrid density functional theory for homopolymer mixtures confined in a selective nanoslit

By integrating polymer density function theory (DFT) and single-chain molecular simulation, a hybrid DFT is developed for homopolymer mixtures confined in a selective nanoslit. Two weighting functions are adopted separately in the polymer DFT for repulsive and attractive contributions to the excess free energy functional. The theoretical results agree well with simulation data for the density profiles, configurations (tail, loop and train), adsorption amounts, layer thicknesses, and partition coefficients. The polymer-slit interaction is found to have a large effect on the density profiles and partition coefficients but is found to have a small effect on the average sizes and percentages of the configurations. Nearly half of the polymer segments form tails, and the other half form trains. In addition, bridges are observed to form for sufficiently long polymer chains. As the length difference between two polymers increases, the effect of chain connectivity becomes increasingly important.     

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.     

Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.     

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.     

Density functional theory of realistic models of polyethylene liquids in slit pores: comparison with monte carlo simulations

Density functional theory is applied to study properties of fully detailed, realistic models of polyethylene liquids near surfaces and compared to results from Monte Carlo simulations. When the direct correlation functions from polymer reference interaction site model (PRISM) theory are used as input, the theory somewhat underpredicts the density oscillations near the surface. However, good agreement with simulation is obtained with empirical scaling of the PRISM-predicted direct correlation functions. Effects of attractive interactions are treated using the random-phase approximation. The results of theoretical predictions for the attractive system are also in reasonable agreement with simulation results. In general, the theory performs best when the wall-polymer interaction strength is comparable to polymer-polymer interactions.     

Density functional theory of adsorption of mixtures of charged chain particles and spherical counterions

We propose a microscopic density functional theory to describe nonuniform ionic fluids composed of chain molecules with charged "heads" and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is based on the approach of Yu and Wu [J. Chem. Phys. 117, 2368 (2002)] of adsorption of chain molecules and on theory of adsorption of electrolytes [O. Pizio, A. Patrykiejew, and S. Sokolowski, J. Chem. Phys. 121, 11957 (2004)]. As an application of the proposed formalism we investigate the structure and adsorption of fluids containing segments of different length in a slitlike pore.     

Macromorphology of polypropylene homopolymer tacticity mixtures

The macromorphology of isotactic/atactic (iPP/aPP) and isotactic/syndiotactic (iPP/sPP) polypropylene mixtures is examined by optical microscopy. The spherulitic macrostructure of equimolecular weight [weight‐average molecular weight (M_w) = 200k] iPP/aPP blends is volume‐filling to very high aPP concentrations when the crystallization temperature is 130 °C. Similar spherulitic macrostructures (spherulite size and volume‐filling nature) are observed for iPP homopolymer and a 50/50 iPP/aPP blend at low crystallization temperatures (115–135 °C). At higher crystallization temperatures (140–145 °C), a equimolecular weight (M_w = 200k) 50/50 iPP/aPP blend exhibits nodular texture that blurs the spherulitic boundaries. Double temperature jump experiments show that the nodular texture is due to melt phase separation that develops prior to crystallization. The upper critical solution temperature (UCST) of a 50/50 iPP/aPP blend (M_w = 200k) lies below 155 °C, and the blend is miscible at conventional melt processing temperatures. The UCST behavior is controlled by the blend molecular weight and aPP microstructure. aPP microstructures containing increased isospecific sequencing (although still noncrystalline) exhibit a reduced tendency for phase separation in 50/50 mixtures (M_w = 200k) and the absence of nodular texture at low undercoolings (140–145 °C). Equimolecular weight (M_w = 200k) 50/50 iPP/sPP mixtures exhibit phase‐separated texture at all crystallization temperatures. The size scale of the phase‐separated texture decreases with decreasing crystallization temperature because of a competition between crystallization and phase separation from a melt initially well mixed from the initial solution blending process. Extended melt annealing experiments show that the 50/50 iPP/sPP mixture (M_w = 200k) is immiscible in the melt at conventional melt processing temperatures. The iPP/sPP pair shows a much stronger tendency for phase separation than the iPP/aPP polymer pair. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1947–1964, 2000     

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.     

Density functional theory investigation of decamethyldizincocene

A density functional investigation into the structure and vibrational properties of the recently synthesized, novel, Zn(I)-containing species decamethyldizincocene has been performed. Our analysis is in agreement with the general structural properties of the experimental results. We have corroborated the experimental geometry as a true minimum on the global molecular energy surface, confirmed the experimental hypothesis that the Zn atoms are in a Zn(I) state, and provided a detailed analysis of the experimentally undefined Zn-dominant IR and Raman spectral bands of this unusual Zn(I) species.     

Density functional theory: Approximating quasiparticle density functional

A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn–Sham quasiparticle concept and the Levy–Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems.     

Density functional theory for Yukawa fluids

We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.     

Density functional theory and molecular clusters

Density functional theory (DFT) methods, including nonlocal density gradient terms in the exchange and correlation energy functionals, were applied to various types of molecular clusters: H-bonded, ionic, electrostatic, and London. Reliable results on the structure and stabilization energy were obtained for the first two types of cluster as long as Becke3LYP and Becke3P86 functionals and basis sets of at least DZ + P quality were used. DFT methods with currently available functionals failed completely, however, for London-type clusters, for which no minimum was found on the potential energy surfaces. DFT interaction energy exhibits the same basis set extension dependence as the Hartree-Fock (HF) interaction energy. Therefore, the Boys-Bernardi function counterpoise procedure should be employed for elimination of the DFT basis set superposition error. © 1995 John Wiley & Sons, Inc.     

Density functional theory for triplet superconductors

The density functional theory of superconductivity is extended to triplet superconductors and superfluid helium 3. We prove a Hohenberg-Kohn-type theorem for these systems and derive effective single-particle equations. The latter include exchange and correlations in a formally exact way and allow the treatment of both electronic and phonon-induced superconductivity. The relation of this approach to the Bogolubov-de Gennes mean-field theory and to phenomenological theories based on Ginzburg-Landau functionals is discussed. © 1997 John Wiley & Sons, Inc.     

Density functional theory on phase space

Forty‐five years after the point de départ [Hohenberg and Kohn, Phys Rev, 1964, 136, B864] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the electron density still eludes us—and possibly will do so forever [Schuch and Verstraete, Nat Phys, 2009, 5, 732]. In what follows we examine a formulation in the same spirit with phase space variables. The validity of Hohenberg–Kohn–Levy‐type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation‐exchange functionals on phase space. A new proof of the overbinding property of the Müller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the Thomas–Fermi model. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Density functional theory for excited states

In this article, we justify the use of standard Kohn-Sham (KS ) band structure theory for the calculation of the low-energy spectrum of metals and the density of states. For the higher spectrum, one can start the KS excited-state calculations by using as the first-order approximation the spin orbitals of the ground state. We next deal with the problem of degenerate states by using the subspace theory minimum principle. © 1995 John Wiley & Sons, Inc.     

Density functional theory study of formaldehyde oligomers

Hydrogen‐bonded formaldehyde oligomers (dimer to pentamer) are studied using density functional theory (DFT), the B3LYP method, and the 6‐311+G* basis set. Many‐body interaction energies are obtained to study the contribution of many‐body terms to binding energy. The basis set superposition error (BSSE)‐corrected total energies are ?229.08170, ?343.61410, ?458.16660, and ?572.70901 hartrees for dimer, trimer, tetramer, and pentamer, respectively, with corresponding binding energies ?2.55, ?4.86, ?6.99, and ?9.49 kcal/mol. Two‐body energies have been found to contribute significantly to the total binding energy in dimer to pentamer, whereas higher‐order interaction energies are negligible. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Density functional theory study of BnC clusters

B_nC clusters (n = 3–10) were studied at the density functional theory (DFT) (B3LYP)/6‐311G** level of theory. The calculations predicted that the most stable configurations of the B_nC clusters are the (n + 1)‐membered cyclic structures. For boron–carbon clusters, the configurations containing greater numbers of three‐membered boron rings are more favorable, except for the B₇C and B₉C clusters. Through molecular orbital analysis of these B_nC clusters, we have concluded that π‐electron delocalization plays a crucial role in the stability of n + 1‐membered cyclic structures. In this paper, the relative stability of each cluster is discussed based on their single atomic‐binding energies. The capability of clusters to obtain or lose an electron was also discussed, based on their vertical electron detachment energies (VDEs), adiabatic electron detachment energies (ADEs), vertical electron affinities (VEAs) and adiabatic electron affinities (AEAs). Copyright © 2011 John Wiley & Sons, Ltd.     

Density functional theory of field theoretical systems

The field theoretical background of relativistic density functional theory is emphasized and its consequences for relativistic Kohn-Sham equations are shown. The local density approximation for the exchange energy functional is reviewed and the importance of relativistic corrections for an accurate representation of the exchange functional is demonstrated. © 1995 John Wiley & Sons, Inc.