Symmetric Polymer Blends Research Articles

Modeling the competition between phase separation and polymerization under explicit polydispersity.

The dynamics of phase separation for polymer blends is important in determining the final morphology and properties of polymer materials; in practical applications, this phase separation can be controlled by coupling to polymerization reaction kinetics via a process called 'polymerization-induced phase separation'. We develop a phase-field model for a polymer melt blend using a polymerizing Cahn-Hilliard (pCH) formalism to understand the fundamental processes underlying phase separation behavior of a mixture of two species independently undergoing linear step-growth polymerization. In our method, we explicitly model polydispersity in these systems to consider different molecular-weight components that will diffuse at different rates. We first show that this pCH model predicts results consistent with the Carothers predictions for step-growth polymerization kinetics, the Flory-Huggins theory of polymer mixing, and the classical predictions of spinodal decomposition in symmetric polymer blends. The model is then used to characterize (i) the competition between phase separation dynamics and polymerization kinetics, and (ii) the effect of unequal reaction rates between species. For large incompatibility between the species (i.e. high χ), our pCH model demonstrates that the strength for phase separation directly corresponds to the kinetics of phase separation. We find that increasing the reaction rate k̃, first induces faster phase separation but this trend reverses as we further increase k̃ due to the competition between molecular diffusion and polymerization. In this case, phase separation is delayed for faster polymerization rates due to the rapid accumulation of slow-moving, high molecular weight components.

Composite entanglement topology and extensional rheology of symmetric ring-linear polymer blends

Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction ϕR. Chains with degree of entanglement Z≈14 are mixed to produce 10 well-entangled systems with ϕR varying from neat linear to neat ring melts. Z is large enough that except for very large ϕR, the rings are threaded by multiple linear chains in equilibrium. Primitive path analysis is used to visualize and quantify the structure of the composite ring-linear entanglement network. We measure the quantity of ring-linear threading and linear-linear entanglement as a function of ϕR and identify with simple arguments a ring fraction ϕR≈0.4 where the topological constraints of the composite entanglement network are maximized. These topological analyses are used to rationalize the ϕR-dependence of ring and linear chain dynamics, conformations, and rheology. Simulations of startup uniaxial elongation flows demonstrate the extensional stress overshoot observed in recent filament stretching experiments and characterize how it depends on the blend composition and entanglement topology. The overshoot is driven by an overstretching and recoil of ring polymers due to the convective unthreading of rings from linear chains.

Stereocomplex and individual crystallization behavior of symmetric or enantiomeric substituted Poly(lactic acid)s random copolymers with high crystallizabilities

Stereocomplex (SC) crystallization is reported for the first time for the enantiomeric blends of random copolymers of l-configured poly(l-2-hydroxybutanoic acid-co-l-2-hydroxy-3-methylbutanoic acid) [P(L-2HB-co-L-2H3MB)] (49/51) and d-configured poly(d-2-hydroxybutanoic acid-co-d-2-hydroxy-3-methylbutanoic acid) [P(D-2HB-co-D-2H3MB)] (47/53) with high individual crystallizabilities. Unblended l-configured P(L-2HB-co-L-2H3MB) and d-configured P(D-2HB-co-D-2H3MB) formed individual crystallites through purification, solvent evaporation, and melt crystallization. Three types of individual crystallites (provisionally named as α-, β-, and γ-forms) were observed in the unblended copolymers depending on the crystallization methods. SC crystallites were formed in the blends through solvent evaporation and melt crystallization method. All types of monomer units cocrystallized in the individual and SC crystallites. The melting and equilibrium-melting temperatures of SC crystallites in the blends were 192.5–203.7 °C and 205.2 °C, respectively, which were significantly higher than the melting temperatures of individual crystallites in the unblended copolymers (61.6–133.1 °C). The maximum radial growth rate of SC crystallites (13.5 μm min−1) was 10 and 27 times higher than those of individual crystallites of the unblended copolymers (1.4 and 0.5 μm min−1), indicating that SC crystallization increased the crystallization rate. SC crystallization proceeded via regimes II and III. The copolymer crystallizability, monomer cocrystallizability, and crystallization rate of P(L-2HB-co-L-2H3MB) (49/51) and P(D-2HB-co-D-2H3MB) (47/53) are compared with those reported for the series of symmetric or enantiomeric polymer blends of poly(l-lactic acid-co-l-2-hydroxybutanoic acid) (56/44) and poly(d-lactic acid-co-d-2-hydroxybutanoic acid) (52/48) with lowindividualcrystallizabilities and poly(l-lactic acid-co-l-2-hydroxy-3-methylbutanoic acid) (47/53) and poly(d-lactic acid-co-d-2-hydroxy-3-methylbutanoic acid) (47/53) with noindividualcrystallizability.

Stress relaxation in symmetric ring-linear polymer blends at low ring fractions.

We combine linear viscoelastic measurements and modelling in order to explore the dynamics of blends of the same-molecular-weight ring and linear polymers in the regime of the low volume fraction (0.3 or lower) of the ring component. The stress relaxation modulus is affected by the constraint release (CR) of both rings and linear components due to the motion of linear chains. We develop a CR-based model of ring-linear blends that predicts the stress relaxation function in the low fraction regime of ring component in excellent agreement with experiments. Rings trapped by their entanglements with linear chains can only relax by linear-chain-induced constraint release, resulting in much slower relaxation of rings than of linear chains. The relative viscosity of the blend with respect to the linear melt viscosity η L at ring overlap volume fraction increases proportionally to the square root of ring molecular weight . Our experimental results clearly demonstrate that it is possible to enhance the viscosity and simultaneously the structural relaxation time of linear polymer melts by adding a small fraction of ring polymers. These results not only provide fundamental insights into the physics of the CR process but also suggest ways to fine-tune the flow properties of linear polymers by means of adding rings.

Monte Carlo Simulation of Strain-Enhanced Stereocomplex Polymer Crystallization.

We performed dynamic Monte Carlo simulations to investigate strain-induced polymer crystallization under separate enhancements of the driving forces for homocomponent and stereocomplex crystallization in the half-half symmetric racemic polymer blends. The results showed that the polymer strain significantly enhances the stereocomplex crystallization, in comparison to the parallel cases of template-induced crystal growth without any strain in the previous simulations. We attributed the results to the strain-induced polymer crystallization favoring intermolecular crystal nucleation at high temperatures, which benefits the stereocomplex crystallization. Our observations provided a molecular-level interpretation to the strain- or shear-enhanced stereocomplex crystallization in the racemic polylactide blends.

Effective interaction between nanoparticles mediated by a symmetric polymer blend.

We analytically study the polymer-mediated (PM) interactions between spherical particles immersed in a symmetric polymer blend. By making use of standard methods of the liquid state theory we have found out a nonconventional mechanism of the PM interactions caused by nonuniformities in the local composition of the polymer blend induced by the particles. The relative significance of the contributions to the PM interaction potential due to the finite compressibility of the polymer blend and its compositional nonuniformity is found to drastically depend on the polymer-to-particle size ratio. In the protein limit of relatively small particles, the mechanism due to the compositional nonuniformity, specific to polymer blends, is shown to play a dominant role in the PM interactions.

Equilibrating high-molecular-weight symmetric and miscible polymer blends with hierarchical back-mapping

Understanding properties of polymer alloys with computer simulations frequently requires equilibration of samples comprised of microscopically described long molecules. We present the extension of an efficient hierarchical backmapping strategy, initially developed for homopolymer melts, to equilibrate high-molecular-weight binary blends. These mixtures present significant interest for practical applications and fundamental polymer physics. In our approach, the blend is coarse-grained into models representing polymers as chains of soft blobs. Each blob stands for a subchain with Nb microscopic monomers. A hierarchy of blob-based models with different resolution is obtained by varying Nb. First the model with the largest Nb is used to obtain an equilibrated blend. This configuration is sequentially fine-grained, reinserting at each step the degrees of freedom of the next in the hierarchy blob-based model. Once the blob-based description is sufficiently detailed, the microscopic monomers are reinserted. The hard excluded volume is recovered through a push-off procedure and the sample is re-equilibrated with molecular dynamics (MD), requiring relaxation on the order of the entanglement time. For the initial method development we focus on miscible blends described on microscopic level through a generic bead-spring model, which reproduces hard excluded volume, strong covalent bonds, and realistic liquid density. The blended homopolymers are symmetric with respect to molecular architecture and liquid structure. To parameterize the blob-based models and validate equilibration of backmapped samples, we obtain reference data from independent hybrid simulations combining MD and identity exchange Monte Carlo moves, taking advantage of the symmetry of the blends. The potential of the backmapping strategy is demonstrated by equilibrating blend samples with different degree of miscibility, containing 500 chains with 1000 monomers each. Equilibration is verified by comparing chain conformations and liquid structure in backmapped blends with the reference data. Possible directions for further methodological developments are discussed.

Unravelling the surface composition of symmetric linear-cyclic polymer blends

We perform molecular dynamics computer simulations of free-standing films of symmetric binary linear-cyclic polymer mixtures at equimolar composition. We show that the density of linear polymers at the free-surface is enhanced with respect to the bulk value for short chains, but it is depleted for long chains. Our findings suggest that the enhancement of the composition of linear chains reported for polystyrene polymer blends might hold in a more extended composition range than the one considered in previous experiments at the free surface. Focusing on the equimolar regime of the two polymer species with the identical chain length allows us to safely conclude that the observed surface deviations from the bulk are driven by the topological differences between the two polymer species, and rule out any role played by the different concentration of the two polymer species.

Phase separation and crystallization in double crystalline symmetric binary polymer blends

Blending of two or more pure polymers is an effective way to produce composites with tunable properties. In this paper, we report dynamic Monte Carlo simulation results on the crystallization of crystalline/crystalline (A/B) symmetric binary polymer blend, wherein the melting temperature of A-polymer is higher than B-polymer. We study the effect of segregation strength (arises from the immiscibility between A- and B-polymers) on crystallization and morphological development. Crystallization of A-polymer precedes the crystallization of B-polymer upon cooling from a homogeneous melt. Simulation results reveal that the morphological development is controlled by the interplay between crystallization driving force (viz., attractive interaction) and de-mixing energy (viz., repulsive interaction between two polymers). With increasing segregation strength, the interface becomes more rigid and restricts the development of crystalline structures. Mean square radius of gyration shows a decreasing trend with increasing segregation strength, reflecting the increased repulsive interaction between A- and B-polymers. As a consequence, a large number of smaller size crystals form with lesser crystallinity. Isothermal crystallization reveals that the transition pathways strongly depend on segregation strength. We also observe a path-dependent crystallization behavior in isothermal crystallization: two-step (sequential) isothermal crystallization yields superior crystalline structure in both A- and B-polymers than one-step (coincident) crystallization.

Surface roughening in polymer blend thin films by lateral phase separation: A thermodynamic mechanism

We use a phase portrait approach to study the phase equilibria of a symmetric binary polymer blend confined between an attracting wall and a neutral wall. We find multiple solutions for this wall regime where only one solution exists for antisymmetric walls. We also argue that, when one wall is a free surface, roughening of the free surface upon lateral phase separation is expected, since thermodynamics alone implies that the coexisting phases should exist at different heights to minimise energy. We focus on the graphical insight provided by this phase portrait approach.

The Spatial-Temporal Lamellar Structures in the Confined Ideal Polymer Blends

We consider the formation of self-organized spatial-temporal oscillating structures in symmetric binary polymer blends confined by two flat walls. An influence of these walls on the formation of the oscillating volume structures is studied. This phenomenon is simulated by an initial boundary-value problem for the conserved order parameter (or the concentration of one of the components in a binary mixture). Under a special choice the dynamical Puri-Binder’s boundary conditions these structures look like the lamellar structures. The behavior of the order parameter is described by the modified Cahn-Hilliard equation which models so-called the non-Fickian diffusion in the symmetric binary polymer blends. The nonlinear dynamical boundary conditions correspond to the process of adsorption-desorption on the walls. As a result, these nonlinear surface processes induce into the volume the spatial-temporal asymptotically periodic structures of relaxation, pre-turbulent or turbulent type with finite, countable or non-countable points of discontinuities on the period correspondingly. The frequency of oscillations on the period follows a power-law for the relaxation type and increases exponentially in the other cases.

Measurement of geometrical parameters in cocontinuous polymer blends: 3D versus 2D image analysis

Formulae of stereology are used to estimate 3D geometrical parameters of cocontinuous structures measured from 2D micrographs of polymer blends. 3D images of symmetric and nonsymmetric polymer blends made of fluorescently labelled polystyrene and styrene-ran-acrylonitrile copolymer were obtained with laser scanning confocal microscopy. Geometrical parameters of the blend interface, specifically volume fraction, surface area per unit volume (S (V) ) and average of local mean curvature were measured directly from the 3D images and compared to the values estimated from analysis of a number of 2D slices combined with stereological relations. When the total length of phase boundary considered in the analysis of the 2D slices (L(Tot) ) was at least 6000 times bigger than the characteristic length of the microstructure (S(-1) (V) ), the standard deviation for all the parameters measured became negligible. However, considerable discrepancies between the average values computed from 3D and 2D images were observed for any value of L(Tot) . The mean curvature distribution was also measured from both the 3D images and the 2D slices. The distribution was estimated from the 2D slices but with a width about 2.4 times that of the true value obtained from the 3D images.

Equilibrium Phases for Thin Films of Polymer Blend Solutions

We investigate the structure of thin films of polymer blend solutions at equilibrium, taking into account the influence of the solvent concentration. Concentration profiles are obtained by numerical integration of the Hamiltonian flow associated with the mean-field Flory―Huggins―de Gennes theory supplemented by appropriate boundary terms. We focus, in particular, on the case of symmetric polymer blend solutions confined between walls that are antisymmetric with respect to both polymers and symmetric with respect to the solvent. It is shown that, as the system evolves from the one-phase region to the two-phase region, the equilibrium structure of the film undergoes a transition from a monolayer to a bilayer type of structure. Then, depending on whether T is, respectively, greater or smaller than the wetting transition temperature of the solvent free polymer blend, the equilibrium configuration either remains a bilayer or becomes a laterally phase separated structure as solvent is removed from the film. We finally uncover a complete family of new unstable solutions having no analogues in the solvent free case and exhibiting a possibly chaotic behavior of the system.

On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends

The self-consistent field (SCF) approach to the thermodynamics of dense polymer liquids is based on the idea that short-range correlations in a polymer liquid are almost independent of how monomers are connected into polymers over larger scales. Some limits of this idea are explored in the context of a perturbation theory for symmetric polymer blends. We consider mixtures of two structurally identical polymers, A and B, in which the AB monomer pair interaction differs slightly from the AA and BB interactions by an amount proportional to a parameter alpha. An expansion of the free energy to first order in alpha yields an excess free energy of mixing per monomer of the form alphaz(N)phi(A)phi(B) in both lattice and continuum models, where z(N) is a measure of the number of intermolecular near neighbors per monomer in a one-component (alpha=0) reference liquid with chains of length N. The quantity z(N) decreases slightly with increasing N because the concentration of intramolecular near neighbors is slightly higher for longer chains, creating a slightly deeper intermolecular correlation hole. We predict that z(N)=z(infinity)[1+betaN(-1/2)], where N is an invariant degree of polymerization and beta=(6/pi)(3/2) is a universal coefficient. This and related predictions about the slight N dependence of local correlations are confirmed by comparison to simulations of a continuum bead-spring model and to published lattice Monte Carlo simulations. We show that a renormalized one-loop theory for blends correctly describes this N dependence of local liquid structure. We also propose a way to estimate the effective interaction parameter appropriate for comparisons of simulation data to SCF theory and to coarse-grained theories of corrections to SCF theory, which is based on an extrapolation of perturbation theory to the limit N-->infinity.

Thermal Induced Periodic Phase Separation in Polymer Blends

Simulations were carried out for studying the periodic phase separation of a symmetric binary polymer blend on the basis of Cahn-Hilliard-Cook theory. The time dependent interaction parameter () was assumed to undergo a step-wise oscillation. The hierarchic structures composed of both large and small domains were obtained. The mechanism of the periodic formation of hierarchic structures was also demonstrated.

Morphology of multi-component polymer systems: single chain in mean field simulation studies.

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies reconstruction on patterned substrates.

Morphology control in symmetric polymer blends using two-step phase separation

This paper studied through modeling and computer simulation the two-step thermal-induced phase separation phenomenon in a symmetric polymer blend via spinodal decomposition. The two-step phase separation phenomenon involves the two-step process where the initial quench is allowed to phase separate for a certain period of time before the second quench takes place into the unstable region. The second quench occurs at the transition between the early and intermediate stages of spinodal decomposition, which is the time frame when functional polymeric materials with predefined material properties are fabricated. The one-dimensional model consisted of the Cahn–Hilliard theory for spinodal decomposition, and incorporated the Flory–Huggins–deGennes free energy equation, the slow mode mobility theory and reptation model for polymer diffusion. The numerical results replicated frequently reported experimental observations published in the literature. This includes the observation that secondary phase separation occurs only if the second quench is sufficiently deep. Furthermore, the numerical results indicate that a dimensionless diffusion coefficient may be used as a parameter to control the formation and evolution of the phase-separated regions during spinodal decomposition as a means to tailor-make functional polymeric materials with predefined material properties.

Morphology control in symmetric polymer blends using spinodal decomposition

This paper studied, through modeling and computer simulation, the thermal-induced phase separation phenomenon in a symmetric polymer blend via spinodal decomposition. The one-dimensional model consisted of the Cahn–Hilliard theory for spinodal decomposition, and incorporated the Flory–Huggins–deGennes free energy equation, the slow mode mobility theory and reptation model for polymer diffusion. The numerical results replicated frequently reported experimental observations published in the literature for the early and intermediate stages of spinodal decomposition for symmetric polymer blends. Furthermore, the numerical results indicate that a dimensionless diffusion coefficient may be used as a parameter to control the formation and evolution of the phase-separated regions during spinodal decomposition as a means to customize functional polymeric materials with predefined material properties.

Phase behaviors of symmetric polymer blend systems

AbstractThe modified double‐lattice model is extended to polymer blend systems. We redefine Cγ as a new universal function of interaction energy to reduce the mathematical defects that originate from the truncation of higher order interaction energy terms. We correlate Cγ with Ryu et al.'s numerical results for symmetric polymer blends with various chain lengths (r1 = r2 = 8, 20, 50, or 100). In addition, oriented interactions between polymer segments are considered with respect to the secondary lattice concept. The proposed model shows a good agreement with the experimental data. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1532–1538, 2004

Dynamic Density Functional Theory for Sheared Polymeric Systems

AbstractSummary: Details of the dynamic density functional theory for sheared polymer systems are presented. The method is illustrated on polymer blends with and without compatibilizers. Shearing slows down coarsening of structures at later stages of phase separation, trapping the system in kineticly driven metastable states. Under certain conditions the system is found trapped in a metastable multiple sphere morphology, while under other conditions a sphere‐to‐string transition is observed. The results are sensitive to the (block co)polymer architecture.The morphology of a symmetric polymer blend in a 32 × 32 box.imageThe morphology of a symmetric polymer blend in a 32 × 32 box.