Spin-Free quantum chemistry. XXII. Multiconfiguration self-consistent field theory

Second order MCSCF theory is presented in a unitary group formulation for any multiplicity without spin projection. Its reduction to lower order theory is discussed, as well as its extension through the use of effective Hamiltonians.     

Spin-free quantum chemistry. XV Spin-only neutron diffraction

The cross section for elastic neutron diffraction is analyzed for the spin-only case, in which the orbital contributions to the magnetic moment density are negligible. For systems specified by spin-free Hamiltonians, we show that the magnetic moment density is calculated from the unpaired electron density, a spin-free quantity, which is equivalent to the spin density. The computation of the unpaired electron density is outlined and examples are discussed. The scattering cross section for an infinite interaction range Heisenberg model exhibits a temperature dependence which parallels that of the spontaneous magnetization. With a knowledge of the unpaired electron density one may determine the magnetic space group symmetry.     

Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance μ∝L^-1 from the substrate, where L is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance ξ∝L^-1/3. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.     

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.     

RPA and the linear hubbard model

The accuracy of RPA is tested semi-empirically by comparison with full Cl.     

Scaling behavior of a brush-homopolymer interface in the limit of high grafting density

The interface between a polymer brush and a chemically equivalent homopolymer is examined using self-consistent field theory (SCFT). Focusing on ultrahigh grafting densities, we extract how the properties scale with the brush thickness, L, and compare with predictions based on strong-stretching theory (SST). Although the scaling exponents are consistent, the overall agreement is poor. We attribute this to the inaccurate way the SST-based calculation treats chain fluctuations at the extremity of the brush. This accounts for a previous disagreement between SCFT and SST in regards to autophobic dewetting, and brings into question a number of other SST predictions. Our conclusion is that SST requires a more sophisticated treatment of finite-stretching corrections, along the lines of that proposed by Likhtman and Semenov [Europhys. Lett. 51, 307 (2000)].     

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using lattice-based Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.     

Optimal information acquisition for a linear quadratic control problem

This paper develops a generalization of the linear quadratic control problem with partial information. As in the standard partial information setting, it is assumed that the state variable is only observed with noise. The idea in this paper is that the information level may be chosen optimally. In real life information is costly to acquire. It is therefore a trade off between the costs of getting detailed information and the increased value this information gives. We believe that the technique we present should have potential for application within both economics and engineering.     

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.