Compression of polyelectrolyte brushes in a salt-free theta solvent

This paper examines the normal force between two opposing polyelectrolyte brushes and the interpenetration of their chains that is responsible for sliding friction. It focuses on the special case of semi-dilute brushes in a salt-free theta solvent, for which Zhulina and Borisov (J. Chem. Phys. 107, 5952 (1997)) have derived analytical predictions using the classical strong-stretching theory (SST). Interestingly, SST predicts that the brushes contract as they are compressed together maintaining a polymer-free gap, which provides an explanation for the ultra-low frictional forces observed in experiment. We examine the degree to which the SST predictions are affected by chain fluctuations by employing self-consistent field theory (SCFT). While the normal force is relatively unaffected, fluctuations are found to have a strong impact on brush interpenetration. Even still, the contraction of the brushes does significantly prolong the onset of interpenetration, implying that a sizeable normal force can be achieved before the sliding friction becomes significant.     

Reversible sphere-to-lamellar wetting transition at the interface of a diblock copolymer system

We use ellipsometry to investigate a transition in the morphology of a sphere-forming diblock copolymer thin-film system. At an interface the diblock morphology may differ from the bulk when the interfacial tension favours wetting of the minority domain, thereby inducing a sphere-to-lamella transition. In a small, favourable window in energetics, one may observe this transition simply by adjusting the temperature. Ellipsometry is ideally suited to the study of the transition because the additional interface created by the wetting layer affects the polarisation of light reflected from the sample. Here we study thin films of poly(butadiene-ethylene oxide) (PB-PEO), which order to form PEO minority spheres in a PB matrix. As temperature is varied, the reversible transition from a partially wetting layer of PEO spheres to a full wetting layer at the substrate is investigated.     

Monte Carlo phase diagram for diblock copolymer melts

The phase diagram for diblock copolymer melts is evaluated from lattice-based Monte Carlo simulations using parallel tempering, improving upon earlier simulations that used sequential temperature scans. This new approach locates the order-disorder transition (ODT) far more accurately by the occurrence of a sharp spike in the heat capacity. The present study also performs a more thorough investigation of finite-size effects, which reveals that the gyroid (G) morphology spontaneously forms in place of the perforated-lamellar (PL) phase identified in the earlier study. Nevertheless, there still remains a small region where the PL phase appears to be stable. Interestingly, the lamellar (L) phase next to this region exhibits a small population of transient perforations, which may explain previous scattering experiments suggesting a modulated-lamellar (ML) phase.     

The freeonN-electron procedure and the Hubbard connection

The Hubbard connection correlates Hückel molecular orbital and valence bond states by means of the Hilckel-Hubbard Hamiltonian. The connection is greatly simplified through the use of the freeonN-electron procedure. The present paper reviews the mathematical background for the procedure and shows how it applies to the Hubbard connection. The allyl radical is taken as an example.     

Spin-free quantum chemistry. XXIV. Freeon many-body theory

We present the freeon, singlet, unitary group formulation of many-body theory as an alternative to the particle-number-conserving, spin-projected, fermion, second-quantized formulation. It is based on the generator-state-approach (GSA ) developed in part 23 of this series. We develop C1, perturbation, coupled-cluster, and random-phase theories.     

Spin-free quantum theory. XXV. The unitary-group formulation of fermion many-body theory

The fermion unitary group formulation (UGF ) of many-body theory is based on the unitary group U(2n) where n is the number of freeon orbitals. This formulation, which conserves particle-number but not spin, is isomorphic to the particle-number-conserving, second-quantized formulation (SQF ). In UGF we derive the familiar diagrammatic algorithm for matrix elements, M(Y) = (?1)^H+L where H and L denote the numbers of hole lines and loops in the diagram D(Y) of M(Y). The unitary group derivation is considerably simpler than is the conventional, second-quantized derivation that employs time-dependence, Wick's theorem, normal-order, and contractions. In neither fermion UGF nor SQF is spin conserved. We carry out in UGF the spin-projection (symmetry adaptation to SU (2)) of the fermion vectors and obtain with a spin-free Hamiltonian the same matrix elements as with the freeon UGF (part 24 of this series). The fermion unitary group formulation for a spin-free Hamiltonian should be regarded as an alternate path to spin-free quantum chemistry.     

The freeon theory of magnetism. I. The Heisenberg interaction

The freeon theory of magnetism is a viable alternative to the well-known Heisenberg theory. In particular, the freeon-exchange theory provides a deeper insight into the nature of the magnetic interaction than does the spin-exchange theory. In addition, it avoids the superfluous M_S quantum number in zero-field splitting, the overcounting of spin states, the spin frustration, and the spin paradigm. The freeon-exchange theory employs the algebra of the symmetric group and/or the unitary group in place of the spin algebra. The basis vectors of freeon theory are the Gel'fand states which are uniquely labeled by Gel'fand diagrams; the latter provide both the electron configuration and the spin quantum number. Both the spin and the freeon formulations support the Landé interval rule. In this article, we apply freeon theory to transition-metal dimers, trimers, and tetramers; these are examples of molecular magnets which have applications to microcircuitry. The freeon theory follows the permutation-group principle laid down by Herman Weyl over one-half a century ago. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 287–297, 1997     

The Ising free-energy functional

We show that the Ising free-energy functional f(T, X) yields a second-order phase transition. The value of X, a generalized order parameter, which minimizes the functional is the real-order parameter, Ω = tanh[Ω(T_C/T)] where T_c = J/(2k) and J is the Ising coupling constant. The Ising theory is applicable to the second-order phase transitions in ferromagnets, ferroelectrics, and superconductors. The constant temperature slices of f(T, X) yields the Ising functional which is valid over the entire range of T and which is identical to the Landau functional for T/T_C close to unity. © 1996 John Wiley & Sons, Inc.