Surface phase transitions in athermal mixtures of hard rods and excluded volume polymers investigated using a density functional approach

Using fundamental measures' density functional framework based on Wertheim's first order perturbation theory [J. Chem. Phys. 87, 7323 (1987)] we study the surface phase transitions in athermal polymer-needle mixtures, which demix in bulk into the isotropic polymer-rich (rod-poor) and polymer-poor (rod-rich) phases. We find that the polymer-rich (rod-poor) phase wets the hard wall at coexistence and the wetting transition is of first order. In the partial wetting regime we find a sequence of layerings but these transitions are gradually suppressed as the chain length increases. For long enough chains we detect the prewetting line. Rods exhibit pronounced ordering at the wall in the polymer-rich phases. Our results imply that experiments on the (isotropic) wetting transition for colloidal rod-polymer mixtures should be easier to carry out than those for the colloidal rod-sphere mixtures because the wetting transition occurs at lower rod densities. On the other hand, layerings in sphere-needle mixtures may turn out to be difficult to observe experimentally because some of them will be metastable with respect to the freezing transition, whereas the remaining ones are located very close to the binodal.     

Integral equation theory for athermal solutions of linear polymers

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.     

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.     

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.     

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.     

Polydisperse telechelic polymers at interfaces: analytic results and density functional theory

We use a recently developed continuum theory to expand on an exact treatment of the interfacial properties of telechelic polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. A new surface adsorption transition is identified for ideal telechelic chains, wherein the central block is an equilibrium polymer. This transition occurs in the limit of strong end adsorption. Additionally, closed expressions are derived for the ideal continuum telechelic chain in contact with two large spheres, using the Derjaguin approximation. We analyze the interactions between colloids as a function of polydispersity and molecular weight, and the results are compared with polymer density functional theory in the dilute limit. Significant variations in polymer mediated forces are observed as a function of polydispersity, molecuar weight, and chain stiffness.     

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.     

Magnetizability tensors from auxiliary density functional theory

The working equations for the calculation of the magnetizability tensor in the framework of auxiliary density functional theory with gauge including atomic orbitals (ADFT-GIAO) are derived. Unlike in the corresponding conventional density functional theory implementations the numerical integration of the GIAOs is avoided in ADFT-GIAO. Our validation shows that this simplification has no effect on the accuracy of the methodology. As a result, a reliable and efficient implementation for the calculation of magnetizabilities of systems with more than 1000 atoms and 14 000 basis functions is presented.     

Spin-multiplet energies from time-dependent density functional theory

Starting from a formally exact density-functional representation of the frequency-dependent linear density response and exploiting the fact that the latter has poles at the true excitation energies, we develop a density-functional method for the calculation of excitation energies. Simple additive corrections to the Kohn-Sham single-particle transition energies are derived whose actual computation only requires the ordinary static Kohn-Sham orbitals and the corresponding eigenvalues. Numerical results are presented for spin-singlet and triplet energies. © 1996 John Wiley & Sons, Inc.     

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He(+) scattering.     

Excitation energies from range-separated time-dependent density and density matrix functional theory

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.     

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.     

Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures

Free energies and correlation functions of liquid and solid hard-sphere (HS) mixtures are calculated using the fundamental measure density functional theory. Using the thermodynamic perturbation theory the free energies of solid and liquid Lennard-Jones (LJ) mixtures are obtained from correlation functions of HS systems within a single theoretical approach. The resulting azeotrope- and spindle-type solid-liquid phase diagrams of HS and LJ binary mixtures are in good agreement with the corresponding ones from computer simulations.     

NMR shielding tensors from auxiliary density functional theory

The working equations for the calculation of NMR shielding tensors in the framework of auxiliary density functional theory are derived. It is shown that in this approach the numerical integration over gauge-including atomic orbitals can be avoided without the loss of accuracy. New integral recurrence relations for the required analytic electric-field-type integrals are derived. The computational performance of the resulting formalism permits shielding tensor calculations of systems with more than 1000 atoms and 15,000 basis functions.     

Molecular binding energies from partition density functional theory

Approximate molecular calculations via standard Kohn-Sham density functional theory are exactly reproduced by performing self-consistent calculations on isolated fragments via partition density functional theory [P. Elliott, K. Burke, M. H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010)]. We illustrate this with the binding curves of small diatomic molecules. We find that partition energies are in all cases qualitatively similar and numerically close to actual binding energies. We discuss qualitative features of the associated partition potentials.     

Intermolecular dispersion energies from time-dependent density functional theory

Non-expanded dispersion energies are calculated from time-dependent coupled-perturbed density functional theory (DFT) employing various non-hybrid and hybrid exchange-correlation potentials and suitable adiabatic local density approximations for the exchange-correlation kernel. Considering the dimer systems He₂, Ne₂, Ar₂, NeAr, NeHF, ArHF, (H₂)₂, (HF)₂, and (H₂O)₂ it is shown that the effects of intramonomer electron correlation on the dispersion energy are accurately reproduced with the PBE0AC exchange-correlation potential. In contrast, the uncoupled sum-over-states approximation yields inacceptable errors. These are mainly due to neglect of the Coulomb and exchange-correlation kernels and therefore, not substantially improved through an asymptotic correction of the exchange-correlation potential.     

Virial coefficients and demixing of athermal nonadditive mixtures

We compute the fourth virial coefficient of a binary nonadditive, hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a y expansion (Barboy, B.; Gelbart, W. N. J. Chem. Phys. 1979, 71, 3053) in order to trace the fluid-fluid coexistence lines, which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modeling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.     

Theoretical Auger electron spectra of polymers by density functional theory calculations using model dimers

We propose a new approach for analysis of Auger electron spectra (AES) of polymers by density functional theory (DFT) calculations with the Slater's transition-state concept. Simulated AES and X-ray photoelectron spectra (XPS) of four polymers [(CH2CH2)n (PE), (CH2CH(CH3))n (PP), (CH2CH(OCH3))n (PVME), and (CH2CH(COCH3))n (PVMK)] by DFT calculations using model dimers are in a good accordance with the experimental ones. The experimental AES of the polymers can be classified in each range of 1s-2p2p, 1s-2s2p, and 1s-2s2s transitions for C KVV and O KVV spectra, and in individual contributions of the functional groups from the theoretical analysis.