Lattice Boltzmann study of hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

By incorporating self-consistent field theory with lattice Boltzmann method, a model for polymer melts is proposed. Compared with models based on Ginzburg-Landau free energy, our model does not employ phenomenological free energies to describe systems and can consider the chain topological details of polymers. We use this model to study the effects of hydrodynamic interactions on the dynamics of microphase separation for block copolymers. In the early stage of phase separation, an exponential growth predicted by Cahn-Hilliard treatment is found. Simulation results also show that the effect of hydrodynamic interactions can be neglected in the early stage.

STUDY OF COARSENING OF MICRODOMAINS IN BLOCK COPOLYMERS BY LATTICE BOLTZMANN METHODS

In order to understand the coarsening of microdomains in symmetric diblock copolymers at the late stage, a model for block copolymers is proposed. By incorporating the self consistent field theory with the free energy approach Lattice Boltzmann model, hydrodynamic interactions can be considered. Compared with models based on Ginzburg-Landau free energy, this model does not employ phenomenological free energies to describe systems. The model is verified by comparing the simulation results obtained using this method with those of a dynamical version of the self consistent mean field theory. After that,the growth exponents of the characteristic domain size for symmetric block copolymers at late stage are studied. It is found that the viscosity of the system affects the growth exponents greatly, although the growth exponents are all less than 1/3 Furthermore, the relations between the growth exponent, the interaction parameter and the chain length are studied.

Active site structure of NO decomposition on perovskite(-like) oxides: An investigation from experiment and density functional theory

Active site structure for NO decomposition carried out on perovskite-like oxides were discussed based on the N-2 yield measured from LaSrNi1-x,AlxO4 with different B-site cations and from La2-ySryCuO4 with different crystal phases. Results show that the active site contains two oxygen vacancies, two transition metals, and one lattice-oxygen, with the oxygen vacancy locating on the apex of MO6 octahedron, and the lattice oxygen locating between the two transition metals (i.e., M-O-M plane). Density functional theory (DFT) analysis to the structure shows that this new active site is the most active structure for NO adsorbing, and hence, for NO decomposition. The similar trend of the relative energies that are required for the formation of oxygen vacancies with f form (calculated from DFT), the amount of oxygen vacancies, and the activities (N-2 yield) certifies this result further.

A self-consistent field theory study on the morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers

By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.

Lattice energy estimation for inorganic ionic crystals

An empirical method based on chemical bond theory for the estimation of the lattice energy for ionic crystals has been proposed. The lattice energy contributions have been partitioned into bond dependent terms. For an individual bond, the lattice energy contribution made by it has been separated into ionic and covalent parts. Our calculated values of lattice energies agree well with available experimental and theoretical values for diverse ionic crystals. This method, which requires detailed crystallographic information and elaborate computation, might be extended and possibly yield further insights with respect to bond properties of materials.

Theoretical estimation of thermodynamic properties of the system PS/PPO on the basis of modified combining rule of Sanchez-Lacombe lattice fluid model

The three scaling parameters described in Sanchez-Lacombe lattice fluid theory (SLLFT), T*, P* and rho* of pure polystyrene (PS), pure poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and their mixtures are obtained by fitting corresponding experimental pressure volume-temperature data with equation-of-state of SLLFT. A modified combining rule in SLLFT used to match the volume per mer, v* of the PS/PPO mixtures was advanced and the enthalpy of mixing and Flory-Huggins (FH) interaction parameter were calculated using the new rule. It is found that the difference between the new rule and the old one presented by Sanchez and Lacombe is quite small in the calculation of the enthalpy of mixing and FH interaction parameter and the effect of volume-combining rule on the calculation of thermodynamic properties is much smaller than that of energy-combining rule. But the relative value of interaction parameter changes much due to the new volume-based combining rule. This effect can affect the position of phase diagram very much, which is reported elsewhere [Macromolecules 34 (2001) 6291]

Self-assembly of star block copolymers by dynamic density functional theory

The dynamic mean-field density functional method, driven from the generalized time-dependent Ginzburg-Landau equation, was applied to the mesoscopic dynamics of the multi-arms star block copolymer melts in two-dimensional lattice model. The implicit Gaussian density functional expression of a multi-arms star block copolymer chain for the intrinsic chemical potentials was constructed for the first time. Extension of this calculation strategy to more complex systems, such as hyperbranched copolymer or dendrimer, should be straightforward. The original application of this method to 3-arms block copolymer melts in our present works led to some novel ordered microphase patterns, such as hexagonal (HEX) honeycomb lattice, core-shell HEX lattice, knitting pattern, etc. The observed core-shell HEX lattice ordered structure is qualitatively in agreement with the experiment of Thomas [Macromolecules 31, 5272 (1998)].

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory (SLLFT). For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights of the polydisperse polymer, but the z-average molecular weight ((M) over bar (z)) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of (M) over bar (n) on the spinodal. Moreover, it has been found that the effect of changing (M) over bar (w) on the spinodal is much bigger than that of changing (M) over bar (n) and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature (UCST). However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of upsilon(*)=upsilon(1)(*)=upsilon(2)(*) and (1/r(1)(0))-(1/r(2i)(0))-->(1/r(1)(0)).

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .1. POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION

The Gibbs free energies and equations of state of polymers with special molar mass distributions, e.g., Flory distribution, uniform distribution and Schulz distribution, are derived based on a lattice fluid model. The influence of the polydispersity (or t

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .2. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION

In this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .3. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION WITH STRONG-INTERACTIONS

For a binary mixture of polydisperse polymers with strong interactions, the free energy, the equation of state, the chemical potentials and the spinodal are formulated on the basis of the lattice fluid model. Further, the spinodal curves for the system wi

STATISTICAL THERMODYNAMICS OF A LATTICE FLUID - PURE POLYMER

A statistical thermodynamics theory of a polydisperse polymer based on a lattice model of a fluid is formulated. The pure polydisperse polymer is completely characterized by three scale factors and the distribution law of the system. The equation of state does not satisfy a simple corresponding state principle, except for the polymer fluid with sufficiently high molecular weight.