Studies on coarsening of microdomains in binary polymer mixtures by Lattice Boltzmann methods

An improved free energy approach Lattice Boltzmann model(LBM) is proposed by introducing a forcing term instead of the pressure tensor. This model can reach the proper thermodynamic equilibrium after enough simulation time. On the basis of this model, the phase separation in binary polymer mixtures is studied by applying a Flory-Huggins-type free energy. The numerical results show good agreement with the analytic coexistence curve. This model can also be used to study the coarsening of microdomains in binary polymer mixtures at the early and intermediate stages.

What has brought on the effects of number-average molecular weight on the spinodals in polymer mixtures?

On the basis of the thermodynamics of Gibbs, the spinodal for the quasibinary system was derived in the framework of the Sanchez-Lacombe lattice fluid theory. All of the spinodals were calculated based on a model polydisperse polymer mixture, where each polymer contains three different molecular weight subcomponents. According to our calculations, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights, whereas that of the z-average molecular weight is invisible. Moreover, the extreme of the spinodal decreases when the polydispersity index (eta = (M) over bar (w)/(M) over bar (n)) of the polymer increases. The effect of polydispersity on the spinodal decreases when the molecular weight gets larger and can be negligible at a certain large molecular weight. It is well-known that the influence of polydispersity on the phase equilibrium (coexisting curve, cloud point curves) is much more pronounced than on the spinodal. The effect of M, on the spinodal is discussed as it results from the infuluence of composition temperatures, molecular weight, and the latter's distribution on free volume. An approximate expression, which is in the assumptions of v* v(1)* = v(2)* and 1/r --> 0 for both of the polymers, was also derived for simplification. It can be used in high molecular weight, although it failed to make visible the effect of number-average molecular weight on the spinodal.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER MIXTURES

A statistical thermodynamics theory of polydisperse polymer blends based on a lattice model description of a fluid is formulated. Characterization of a binary polydisperse polymer mixture requires a knowledge of the pure polymer system and the interaction energy. It is assumed that the intrinsic and interactive properties of polymer (for example, T*, P*, rho*, and epsilon(ij)*) are independent of molecular size. Thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid polymer parameters and the binary interaction energies. Thermodynamic stability criteria for the phase transitions of a binary mixture are shown. The binodal and spinodal of general binary systems and of special binary systems are discussed.

DYNAMIC SCALING AND FRACTAL BEHAVIOR OF SPINODAL PHASE-SEPARATION IN POLYMER MIXTURES OF POLY(METHYL METHACRYLATE) WITH POLY(STYRENE-CO-ACRYLONITRILE)

Dynamic scaling and fractal behaviour of spinodal phase separation is studied in a binary polymer mixture of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN). In the later stages of spinodal phase separation, a simple dynamic scaling law was found for the scattering function S(q,t):S(q,t) approximately q(m)-3S approximately (q/q(m)). The possibility of using fractal theory to describe the complex morphology of spinodal phase separation is discussed. In phase separation, morphology exhibits strong self-similarity. The two-dimensional image obtained by optical microscopy can be analysed within the framework of fractal concepts. The results give a fractal dimension of 1.64. This implies that the fractal structure may be the reason for the dynamic scaling behaviour of the structure function.

Phase separation of PS/PVME blend films induced by capillary force

The phase behavior of a miscible PS/PVME (80/20, w/w) blend film in a confined geometry has been investigated at the annealing temperature much lower than the low critical solution temperature (LCST) of the blend. When the annealing temperature (52degreesC) is near the glass transition temperature of the blend (51.2degreesC), PVME-rich phase at the air-film surface under a microchannel forms smaller protrusion. When the annealing temperature is increased to 70degreesC, the protruding stripes, which are almost developed, are mainly composed of the mobile PVME-rich phase. These results reveal that the capillary force lead to the enrichment of PVME-rich phase at the air-polymer interface of a PDMS microchannel, that is, the capillary force lithography (CFL) can induce the phase separation of PS/PVME blend films.

Thermodynamical study on pressure-induced compatibility in UCST polymer-containing mixtures

The present calculations were performed on the basis of the Sanchez-Lacombe lattice fluid theory and the new combinatorial rules for block copolymer according to the experimental results on the pressure-induced compatibility in poly(ethylene oxide) (PEO) and poly(ethylene oxide-b-dimethylsiloxane) (P(EO-b-DMS)) mixtures with UCST behavior. The study on enthalpy, combinatorial entropy, vacancy entropy and Gibbs energy upon mixture shows that Sanchez-Lacombe fluid theory and the new combinatorial rules could describe the pressure-induced compatibility (PIC) of polymer mixtures with UCST behavior well.

Effects of molecular weight and interaction parameter on the glass transition temperature of polystyrene mixtures and its blends with polystyrene/poly(2,6-dimethyl-p-phenylene oxide)

The glass transition temperature (T-g) of mixtures of polystyrene (PS) with different molecular weight and of blends of poly(2,6-dimethyl-p-phenylene oxide) (PPO) and polystyrene with different molecular weight (DMWPS) was studied by a DSC method. For the whole range of composition, the curves of T-g vs composition obtained by experiment were compared with predictions from the Fox, Gordon-Taylor, Couchman and Lu-Weiss, equations. It was found that the experimental results were not in agreement with those from the Fox, Gordon-TayIor and Couchman equations for the binary mixtures of DMWPS, where the interaction parameter chi was approximately zero. However, for the blends PPO/DMWPS (chi < 0), with an increase of molecular weight of PS, it was shown that the experimental results fitted well with those obtained from the Couchman, Gordon-Taylor and Fox equations, respectively. Furthermore, the Gordon-Taylor equation was nearly identical to the Lu-Weiss equation when \chi\ was not very large. Further, the dependence of the change of heat capacity associated with the glass transition (Delta C-p) on the molecular weight of PS was investigated and an empirical equation was presented. (C) 1997 Elsevier Science Ltd.

Thermodynamics of phase behavior in PEO/P(EO-b-DMS) homopolymer and block co-oligomer mixtures under pressure

The cloud-point temperatures (T-cl's) of poly(ethylene oxide) (PEO) and poly(ethylene oxide)-block-polydimethylsiloxane (P(EO-b-DMS)) homopolymer and block-oligomer mixtures were determined by turbidity measurements over a range of temperatures (105 to 130degrees), pressures (1 to 800 bar), and compositions (10-40 wt.-% PEO). The system phase separates upon cooling and T-cl was found to decrease with an increase in pressure for a constant composition. In the absence of special effects, this finding indicates negative excess volumes. Special attention was paid to the demixing temperatures as a function of the pressure for the different polymer mixtures and the plots in the T-phi plane (where phi signifies volume fractions). The cloud-point curves of the polymer mixture under pressures were observed for different compositions. The Sanchez-Lacombe (SL) lattice fluid theory was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalphy of mixing, and the volume changes of mixing. The calculated results show that modified P(EO-b-DMS) scaling parameters with the new combining rules can describe the thermodynamics of the PEO/P(EO-b-DMS) system well with the SL theory.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

Effect of polydispersity on the self-assembly structure of diblock copolymers under various confined states: A Monte Carlo study

We studied the self-assembly of polydisperse diblock copolymers under various confined states by Monte Carlo simulation. When the copolymers were confined within two parallel walls, it was found that the ordered strip structures appeared alternately with the increase in wall width. Moreover, the wall width at which the ordered structure appeared tended to increase with an increase in the polydispersity index (PDI). On the other hand, the simulation results showed that the copolymers were likely to form ordered concentric strip structures when they were confined within a circle wall.

Monte Carlo simulation of the compatibility of graft copolymer compatibilized two incompatible homopolymer blends: Effect of graft structure

Compatibility of graft copolymer compatibilized two incompatible homopolymer A and B blends was simulated by using Monte Carlo method in a two-dimensional lattice model. The copolymers with various graft structures were introduced in order to study the effect of graft structure on the compatibility. Simulation results showed that incorporation of both A-g-B (A was backbone) and B-g-A (B was backbone) copolymers could much improve the compatibility of the blends. However, A-g-B copolymer was more effective to compatibilize the blend if homopolymer A formed dispersed phase. Furthermore, simulation results indicated that A-g-B copolymers tended to locate at the interface and anchor two immiscible components when the side chain is relatively long. However, most of A-g-B copolymers were likely to be dispersed into the dispersed homopolymer A phase domains if the side chains were relatively short. On the other hand, B-g-A copolymers tended to be dispersed into the matrix formed by homopolymer B. Moreover, it was found that more and more B-g-A copolymers were likely to form thin layers at the phase interface with decreasing the length of side chain.

Crystallization and phase behavior of crystalline syndiotactic 1,2-polybutadiene/isotactic polypropylene blends in solution-cast thin films

Crystallization and phase behavior in solution-cast thin films of crystalline syndiotactic 1,2-polybutadiene (s-1,2-PB) and isotactic polypropylene (i-PP) blends have been investigated by transmission electron microscopy (TEM), atomic force microscopy (AFM) and field-emission scanning electron microscopy (FESEM) techniques. Thin films of pure s-1,2-PB consist of parallel lamellae with the c-axis perpendicular to the film plane and the lateral scale in micrometer size, while those of i-PP are composed of cross-hatched and single-crystal-like lamellae. For the blends, TEM and AFM observations show that with addition of i-PP, the s-1,2-PB long lamellae become bended and i-PP itself tends to form dispersed convex regions oil a continuous s-1,2-PB phase even when i-PP is the predominant component, which indicates a strong phase separation between the two polymers during film formation. FESEM micrographs of both lower and upper surfaces of the films reveal that the s-1,2-PB lamellae pass through i-PPconvex regions from the bottom, i.e. the dispersed i-PP regions lie on the continuous s-1,2-PB phase. The structural development is attributed to an interplay of crystallization and phase separation of the blends in the film forming process.

Surface morphology evolution of thin triblock copolymer films during spin coating

The surface morphology evolution of thin poly(styrene-block-ethylene/butylenes-block-styrene) (SEBS) triblock copolymer films as a function of the copolymer concentration was investigated by means of dynamic mode atomic force microscopy. At a relatively low copolymer concentration (0.025% w/v), the periodically orientated stripes were observed. This kind of surface patterning produced in the spin-coating process has not been reported in the literature before. It has been shown by our experiment that a shearing and stretching field can cause flexible polymer coils or aggregates to orientate during the spin coatings At a copolymer concentration of 0.05% w/v, SEBS molecule aggregates form network structures in the whole film. With further increase of the copolymer concentration, a continuous film with a microphase-separated structure was visualized.

MISCIBILITY STUDIES OF POLY(ETHYLENE OXIDE)-POLY(VINYL ACETATE) BLENDS BY VISCOMETRY METHODS

The intrinsic viscosities of poly(ethylene oxide)-poly(vinyl acetate) blends (PEO-PVA) have been measured in chloroform as a function of molecular weights of blend components and compositions. The interaction parameters Delta b obtained from the modified Krigbaum and Wall theory and the differences between the intrinsic viscosities of polymer mixtures and the weight-average intrinsic viscosities of the two blend components were both used to characterize the extent of miscibility of the blend mixtures. (C) 1995 John Wiley and Sons, Inc.