Calculating the equation of state parameters and predicting the spinodal curve of isotactic polypropylene/poly(ethylene-co-octene) blend by molecular dynamics simulations combined with Sanchez-Lacombe lattice fluid theory

Molecular dynamics simulations are adopted to calculate the equation of state characteristic parameters P*, rho*, and T* of isotactic polypropylene (iPP) and poly(ethylene-co-octene) (PEOC), which can be further used in the Sanchez-Lacombe lattice fluid theory (SLLFT) to describe the respective physical properties. The calculated T* is a function of the temperature, which was also found in the literature. To solve this problem, we propose a Boltzmann fitting of the data and obtain T* at the high-temperature limit. With these characteristic parameters, the pressure-volume-temperature (PVT) data of iPP and PEOC are predicted by the SLLFT equation of state. To justify the correctness of our results, we also obtain the PVT data for iPP and PEOC by experiments. Good agreement is found between the two sets of data. By integrating the Euler-Lagrange equation and the Cahn-Hilliard relation, we predict the density profiles and the surface tensions for iPP and PEOC, respectively. Furthermore, a recursive method is proposed to obtain the characteristic interaction energy parameter between iPP and PEOC. This method, which does not require fitting to the experimental phase equilibrium data, suggests an alternative way to predict the phase diagrams that are not easily obtained in experiments.

Colloidal photonic crystals with a graded lattice-constant distribution

In this work, a gradient polystyrene colloidal photonic crystal was fabricated by annealing in a graded temperature field. The lattice constant of the gradient crystal gradually varied along the temperature-gradient direction. The positional bandgap wavelength as well as the attenuation of the bandgap wavelength could be tuned dependent on the position of the gradient colloidal crystal along the gradient direction because of the lattice-constant variation.

Effects of chain flexibility on polymer conformation in dilute solution studied by lattice Monte Carlo simulation

Effects of chain flexibility on the conformation of homopolymers in good solvents have been investigated by Monte Carlo simulation. Bond angle constraint coupled with persistence length of polymer chains has been introduced in the modified eight-site bond fluctuation simulation model. The study about the effects of chain flexibility on polymer sizes reveals that the orientation of polymer chains under confinement is driven by the loss of conformation entropy. The conformation of polymer chains undergoing a gradual change from spherical iso-diametric ellipsoid to rodlike iso-diametric ellipsoid with the decrease of polymer chain flexibility in a wide region has been clearly illustrated from several aspects. Furthermore, a comparison of the freely jointed chain (FJC) model and the wormlike chain (WLC) model has also been made to describe the polymer sizes in terms of chain flexibility and quasi-quantitative boundary toward the suitability of the models.

A novel self-consistent-field lattice model for block copolymers

We develop a self-consistent-field lattice model for block copolymers and propose a novel and general method to solve the self-consistent-field equations. The approach involves describing the polymer chains in a lattice and employing a two-stage relaxation procedure to evolve a system as rapidly as possible to a free-energy minimum. In order to test the validity of this approach, we use the method to study the microphases of rod-coil diblock copolymers. In addition to the lamellar and cylindrical morphologies, micellar, perforated lamellar, gyroid, and zigzag structures have been identified without any prior assumption of the microphase symmetry. Furthermore, this approach can also give the possible orientation of the rods in different structures.

Estimation thermal expansion coefficient from lattice energy for inorganic crystals

By using the study of the lattice energy and the structural parameters of binary inorganic crystals, a new parameter reflecting the thermal expansion property has been found, the relation between the linear expansion coefficient and new parameter has been established. A semiempirical method for evaluation of linear expansion coefficient from the lattice energy is presented, and developed to the complex crystals. The estimated values of the linear expansion coefficients of both simple and complex crystals are in good agreement with the experimental values.

Pressure effects on the thermodynamics of trans-decahydronaphthalene/polystyrene polymer solutions: Application of the Sanchez-Lacombe lattice fluid theory

The cloud-point temperatures (T-cl's) of trans-decahydronaphthalene(TD)/polystyrene (PS, (M) over bar (w) = 270 000) solutions were determined by light scattering measurements over a range of temperatures (1-16degreesC), pressures (100-900 bar), and compositions (4.2-21.6 vol.-% polymer). The system phase separates upon cooling and T-cl was found to increase with rising pressure for constant composition. In the absence of special effects, this finding indicates positive excess volume for the mixing. Special attention was paid to the demixing temperatures as a function of pressure for different polymer solutions and the plots in the T-phi plane (where phi signifies volume fractions). The cloud-point curves of polymer solutions under different pressures were observed for different compositions, which demonstrated that pressure has a greater effect on the TD/PS solutions when far from the critical point as opposed to near the critical point. The Sanchez-Lacombe lattice fluid theory (SLLFT) was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalpy of mixing, and the volume changes of mixing. The calculated results show that modified PS scaling parameters can describe the thermodynamics of the TD/PS system well. Moreover the SLLFT describes the experimental results well.

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]

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)).

Crystal growth and structural analysis of PrMnO3 and TbMnO3

Single crystals of PrMnO3 and TbMnO3 were grown by floating zone method and the crystal structure was determined by single crystal X-ray diffractometry. The structure of these compounds belongs to the orthorhombic system (space group is Pnma, No. 62) with the lattice parameters alpha approximate to root (.) - a(p), b approximate to 2 (.) a(p) , c approximate to root 2.a(p) and Z = 4, where a(p) is ideal cubic perovskite cell parameter.

Thermodynamics of blends of PEO with PVAc: application of the Sanchez-Lacombe lattice-fluid theory

Sanchez-Lacombe (SL) lattice-fluid theory was used to predict the miscibility of the PEO/PVAc blending system. Integral interaction parameters, g of this polymer pair were calculated by using SL theory. And the effect of the temperature, composition of blends and molecular weight of PVAc on the extent of their miscibility has been discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

Thermodynamics of PMMA/SAN blends: Application of the Sanchez-Lacombe lattice fluid theory

Polymer blends of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN) with an acrylonitrile content of about 30 wt % were prepared by means of solution-casting and characterized by virtue of pressure-volume-temperature (PVT) dilatometry. The Sanchez-Lacombe (SL) lattice fluid theory was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalpy of the mixing, the volume change of the mixing, and the combinatorial and vacancy entropies of the mixing for the PMMA/SAN system. A new volume-combining rule was used to evaluate the close-packed volume per mer, upsilon*, of the PMMA/SAN blends. The calculated results showed that the new and the original volume-combining rules had a slight influence on the FH interaction parameter, the enthalpy of the mixing, and the combinatorial entropy of the mixing. Moreover, the spinodals and the binodals calculated with the SL theory by means of the new volume-combining rule could coincide with the measured data for the PMMA/SAN system with a lower critical solution temperature, whereas those obtained by means of the original one could not.