Critical Polymer Blend Research Articles

Temperature-induced composition changes in a critical polymer blend.

Temperature-induced composition changes in a critical polymer blend.

Casimir force between colloidal particles immersed in a critical polymer blend

We consider here a low-density assembly of spherical colloids immersed in a mixture of two incompatible polymers A and B. We assume that, near the consolute point Tc of the host mixture, colloids adsorb preferentially A polymer. The preferential adsorption has as a consequence that particles aggregate in the nonpreferred B phase. We aim at the computation of the induced force F(r), responsible for this aggregation, as a function of the interparticle distance r. To achieve this, use is made of a field-theoretical approach based on ψ4 theory, where the field ψ is simply the composition fluctuation (order parameter). Combining this approach with the standard cumulants method, we first demonstrate that the effective pair potential is proportional to the two-point correlation function of the host mixture. Second, very close to the critical point, we find that the effective force is universal and decays with interparticle distance r>d0 according to: F(r)/kBTc=−(64π2/27)Nd02/r3, where N is the common polymerization degree of polymers and d0 is the particle diameter. Incidentally, this force is similar to the van der Waals one between two parallel plates.

3D-ising and lifshitz critical behavior in a mixture of a polymer blend and a corresponding diblock copolymer

Thermal composition fluctuations and the associated crossover from the 3D-Ising to the isotropic Lifshitz universality class have been studied in a three-component mixture made of a critical polymer blend and the corresponding diblock copolymer. The rather complex phase diagram and the critical exponents of the isotropic Lifshitz universality class will be presented.

Crossover from 3D Ising to Isotropic Lifshitz Critical Behavior in a Mixture of a Homopolymer Blend and Diblock Copolymer

Thermal composition fluctuations and the associated crossover from the 3D Ising to the isotropic Lifshitz universality class have been studied in a three component mixture made of a critical polymer blend and the corresponding diblock copolymer. The critical exponents were found to be appreciably larger than those of the 3D Ising, in agreement with expectations from the larger upper critical dimension. Very near the critical temperature a crossover to a renormalized Lifshitz critical behavior was observed possibly caused by fluctuation induced rearrangements of the diblock copolymers.

Depolarized light scattering from critical polymer blends

Depolarized light scattering of binary polymer blends in disordered state near the demixing critical point is considered both theoretically and experimentally. It is shown that the depolarized scattering in such systems is predominantly due to double scattering processes induced by composition fluctuations. For long enough polymer chains, this scattering is stronger than the contribution from intrinsic anisotropy fluctuations. The general equation for the static and dynamic double scattering function is obtained in terms of the system structure factor. The scattering functions are calculated both analytically and numerically (dynamic part) for polymer blends. We found that the depolarized intensity depends on the polymerization degree N and the relative distance from the critical point τ = 1 – χ*/χ (where χ is the Flory-Huggins interaction parameter and χ* its critical value) as Ivh ∼︁ N2/τ2, which is in good agreement with the experimental data. It is also shown that the dynamic scattering function is decaying non-exponentially. We calculate the relaxation rate and the non-exponentiality parameter as functions of the scattering angle and τ. These theoretical predictions are compared with experimental data for three chemically different blends.

Depolarized light scattering from critical polymer blends

Depolarized light scattering from critical polymer blends

Droplet Breakup and Shear-Induced Mixing in Critical Polymer Blends

Phase-contrast microscopy, small-angle light scattering, and fluorescence microscopy have been combined in situ to study domain deformation, breakup, and homogenization in unstable mixtures of polystyrene (PS) and polybutadiene (PB) under shear flow. Close to the critical point, mixing of the two components toward a single homogeneous phase occurs via repeated deformation and fragmentation of minority-phase droplets, and the data are in good agreement with the mode-coupling renormalization-group (MCRG) theory of a simple binary mixture under shear flow. Well into the two-phase region of diluted high-molecular-weight PS/PB blends, however, the data suggest a tendency for Tc(γ) to saturate at very high shear rates.

Phase separation of polymer blends under shear field

AbstractThe effect of shear flow on phase separation in critical polymer blends has been studied. For a low‐molecular‐weight blend, the response is in good agreement with the theoretical predictions of Onuki and Kawasaki. The breakup of large‐scale critical fluctuations by the flow leads to a drop in the temperature Tc at which phase separation begins. For a high‐molecular‐weight blend, the data suggest that the mode‐coupling contribution to the decay rate of composition fluctuations is significant in both the miscible and immiscible phases. However, the lack of change of structure factor in the vorticity direction implies that there is no apparent shear induced shift in Tc.

SHEAR-INDUCED MIXING IN POLYMER BLENDS

The effect of shear flow on phase separation in critical polymer blends is reviewed. For a low-molecular-weight blend, the response is in good agreement with the theoretical predictions of Onuki and Kawasaki. The break-up of large-scale critical fluctuations by the flow leads to a drop in the temperature T c at which phase separation begins. For a high-molecular-weight blend, the data suggest that the mode-coupling contribution to the decay rate of composition fluctuations is significant in both the miscible and immiscible phases. No shear-induced shift in T c is apparent at any temperature in the one-phase region away from the equilibrium critical point, consistent with mean-field statics.

Monte Carlo study of phase separation in critical polymer blends.

Dynamics of phase separation in a polymer blend of critical composition is studied by Monte Carlo simulation of a microscopic lattice model. We find that dynamical scaling is obeyed by both the correlation function and the structure factor at late enough times, and that the asymptotic domain growth exponent is given by a modified Lifshitz-Slyozov law. We also compare the shape of the scaling function to the one previously obtained in a numerical study using a phenomenological Flory\char21{}Huggins\char21{}de Gennes free-energy functional.

Crossover to strong shear in a low-molecular-weight critical polymer blend.

Small-angle neutron scattering has been used to measure the influence of shear flow on a low-molecule-weight polymer blend near the critical point. When combined with light scattering measurements of the equilibrium (\ensuremath{\gamma}\ifmmode \dot{}\else \.{}\fi{}=0) critical dynamics, these measurements reveal that the long-range critical fluctuations begin to break apart when the shear rate becomes comparable to the characteristic relaxation rate ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{\mathrm{\ensuremath{-}}1}$, where ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$ is the equilibrium lifetime of the critical fluctuations. This effect is directly related to the decrease in the critical temperature caused by the flow, and the data are found to be in very good agreement with the theoretical predictions of Onuki and Kawasaki.

Deviation from mean-field behavior in a low molecular weight critical polymer blend

A deviation from mean-field behavior is observed in the static susceptibility and correlation length measured with small angle neutron scattering as a function of temperature near the phase boundary of a relatively low molecular weight critical polymer mixture. The possibility of a fluctuation influenced crossover from mean-field to nonmean-field behavior is considered.