Compression of polymer brushes: quantitative comparison of self-consistent field theory with experiment

The self-consistent field theory (SCFT) prediction for the compression force between two semi-dilute polymer brushes is compared to the benchmark experiments of Taunton et al. [Nature, 1988, 332, 712]. The comparison is done with previously established parameters, and without any fitting parameters whatsoever. The SCFT provides a significant quantitative improvement over the classical strong-stretching theory (SST), yielding excellent quantitative agreement with the experiment. Contrary to earlier suggestions, chain fluctuations cannot be ignored for normal experimental conditions. Although the analytical expressions of SST provide invaluable aids to understanding the qualitative behavior of polymeric brushes, the numerical SCFT is necessary in order to provide quantitatively accurate predictions.

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Calculation of converged rovibrational energies and partition function for methane using vibrational-rotational configuration interaction

The rovibration partition function of CH4 was calculated in the temperature range of 100-1000 K using well-converged energy levels that were calculated by vibrational-rotational configuration interaction using the Watson Hamiltonian for total angular momenta J=0-50 and the MULTIMODE computer program. The configuration state functions are products of ground-state occupied and virtual modals obtained using the vibrational self-consistent field method. The Gilbert and Jordan potential energy surface was used for the calculations. The resulting partition function was used to test the harmonic oscillator approximation and the separable-rotation approximation. The harmonic oscillator, rigid-rotator approximation is in error by a factor of 2.3 at 300 K, but we also propose a separable-rotation approximation that is accurate within 2% from 100 to 1000 K. (C) 2004 American Institute of Physics.

Unit-cell approximation for diblock−copolymer brushes grafted to spherical particles

This paper examines the equilibrium phase behavior of thin diblock-copolymer films tethered to a spherical core, using numerical self-consistent field theory (SCFT). The computational cost of the calculation is greatly reduced by implementing the unit-cell approximation (UCA) routinely used in the study of bulk systems. This provides a tremendous reduction in computational time, permitting us to map out the phase behavior more extensively and allowing us to consider far larger particles. The main consequence of the UCA is that it omits packing frustration, but evidently the effect is minor for large particles. On the other hand, when the particles are small, the UCA calculation can be readily followed up with the full SCFT, the comparison to which conveniently allows one to quantitatively assess the effect of packing frustration.

A hydrogen-1 nuclear magnetic resonance, mass spectral and extended Hückel study of some olefin complexes of rhodium(I) and iridium(I) and the crystal and molecular structure of η4-2,4-dimethylpenta-1,4-diene(η5-formylcyclopentadienyl)rhodium(I)

A 1H NMR study of monosubstituted η-cyclopentadienyl-rhodium(I) complexes of type LLRh(C5H4X) and -iridium(I) complexes of type L2Ir(C5H4X) (L = ethene, LL = 1,3- or 1,5-diolefin; X = C(C6H5)3, CHO, or COOCH3) has been carried out. For complexes of both metals in which the neutral ligand is ethene or a non-conjugated diolefin the NMR spectra of the cyclopentadienyl protons are unusual in that H(2), H(5) resonate to high field either at room temperature or below. The corresponding NMR spectra for the cyclopentadienyl ring protons of complexes where the neutral ligand is a conjugated diene are, with one exception, normal. A single crystal X-ray structural analysis of (η4-2,4-dimethylpenta-1,4-diene)(η5-formylcyclopentadienyl)rhodium(I) (which exhibits an abnormal 1H NMR spectrum) reveals substantial localisation of electron density in the C(3)C(4) Cp ring bond (1.283(33) Å) which may be consistent with a contribution from an ‘allyl-ene’ rotamer to the ring—metal bonding scheme. An extended Hückel calculation with self consistent charge iteration was performed on this complex. The results predict a greater Mulliken overlap population for the C(3)C(4) bond in the cyclopentadienyl ring and show that the localisation is dependent on both the Cp ring substituent and the nature of the diolefin. The mass spectral fragmentation patterns of some representative diene complexes of iridium(I) and rhodium(I) are presented.

Spin-polarized electronic-structure of MnBiAl

The self-consistent spin-polarized band-structure calculation of ferromagnetic compound MnBiAl in its low-temperature phase has been performed. In this paper the calculation results are given. Comparison with the results of MnBi is performed in order to find the effect on electronic structure by doping with Al.

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 $\mu \propto L^{-1}$ 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 $\xi \propto L^{-1/3}$. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.

Polydispersity-induced macrophase separation in diblock copolymer melts

The effect of A-block polydispersity on the phase behavior of AB diblock copolymer melts is examined using a complete self-consistent field theory treatment that allows for fractionation of the parent molecular-weight distribution. In addition to observing the established shift in phase boundaries, we find the emergence of significant two-phase coexistence regions causing, for instance, the disappearance of the complex phase window. Furthermore, we find evidence that polydispersity relieves packing frustration, which will reduce the tendency for long-range order.

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.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.