Predicting the phases of a two-dimensional hard-rod system with real-space self-consistent field theory

Molecular Bonding in an Orbital-Free-Related Density Functional Theory

A density functional theory based on polymer self-consistent field theory is applied to systems of two atoms in order to show that this approach is capable of predicted molecular bonding. Periodic table elements from hydrogen up to neon are examined and homonuclear diatomic molecules are found to form for H₂, N₂, O₂, and F₂, in agreement with known results. The heteronuclear molecules CO and HF, which are known to exist under ambient conditions, are also found to be stable. Bond lengths for most of these molecules agree with experimental results to within less than 8%, with the exception of O₂ and F₂ which deviate more significantly. The bonding energy for H₂ is given and is within 16% of the known value, but fundamental vibrational frequencies do not agree well with experiment. The main approximations of the theory are very simple and include a Fermi-Amaldi correction to the electron-electron interaction to account for self-interactions and a basic expression for the Pauli potential to account for the exclusion principle. The self-consistent equations are solved in terms of basis functions that encode the cylindrical symmetry of diatomic molecules. Since orbitals are not used, the approach is related to orbital-free density functional theory.

The self-assembly of particles with isotropic interactions

A generic field-theoretic model for the self-assembly of particles with isotropic interactions, motivated by ideas in DNA-mediated colloidal assembly, is presented. A simplest possible system of colloids in explicit solvent is examined to determine the ability of non-connected particles to form complex nanometre or micron scale equilibrium structures in the absence of confounding kinetic effects. It is found that non-trivial morphologies are possible and that, for this effectively one component system, these parallel the phases of diblock copolymer melts for certain parameter choices, despite the absence of connectivity or packing frustration in the model. An explanation for the morphological similarity between these architecturally disparate systems is given. For other parameter choices, it is found that meta-stable and defected phases become more common, and that similarity with block copolymer morphologies decreases.

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean-field equations are iterated with Anderson mixing. The different methods are tested on the triply periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

Deuteron spectra, spin-lattice relaxation, and stimulated echoes in ice II

(2)H NMR spectra, spin-lattice relaxation, and stimulated echoes have been measured in polycrystalline ice II in the temperature range of 84-145 K at ambient pressure. From the spectra we obtain the quadrupole coupling constant in ice II, e(2)qQ/h = (225.7+/-1.2) kHz, and the asymmetry parameter, eta = 0.118+/-0.006. At 145 K, a phase transition of ice II into ice I(c) is observed by a change of both, its spectral and relaxation behavior. The spin-lattice relaxation in ice II is bimodal, showing two components of approximately the same weight. The fast relaxing part of the recovery curve progresses monoexponentially and the temperature dependence of its mean relaxation time corresponds to an unusually low activation energy of 2.3 kJ mol(-1). The slowly relaxing part, displaying average relaxation times of about 4000 s, is significantly stretched with a Kohlrausch parameter of 0.6 and shows no temperature dependence. The stimulated echo experiments show a temperature independent correlation decay. The analysis of intermediate states indicates that no small-angle motions are involved in the underlying process. Both findings exclude an interpretation in terms of molecular motion. Instead, spin diffusion in the deuteron system has to be considered as the origin of the phenomena observed in the stimulated echo experiments.

Two-dimensional fluid with competing interactions exhibiting microphase separation: theory for bulk and interfacial properties

Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems with isotropic pair potentials between the particles, due to the fact that the pair interaction between the colloids has competing attraction and repulsion over different length scales. Here we present a simple density functional theory for a model of such a two-dimensional fluid. The theory predicts a bulk phase diagram exhibiting cluster, stripe, and bubble modulated phases, in addition to homogeneous fluid phases. Comparing with simulation results for this model from the literature, we find that the theory is qualitatively reliable. The model allows for a detailed investigation of the structure of the fluid and we are able to obtain simple approximate expressions for the static structure factor and for the length scale characterizing the modulations in the microphase separated phases. We also investigate the behavior of the system under confinement between two parallel hard walls. We find that the confined fluid phase behavior can be rather complex.