Copolymer Melts Research Articles

Microphase separation in polydisperse rod-rod diblock copolymer melt

The stability limits of the isotropic state of melt of rod-rod AB polydisperse diblock copolymer have been studied within weak segregation theory. The number of units in A block is assumed to be a random variable distributed by the Schulz-Zimm distribution. Inspection of the spinodal curves shows that the copolymer melt with polydisperse rigid blocks is less stable with respect to formation of the nematic and microphase separated states than the monodisperse melt. The values of ratios between strengths of isotropic and anisotropic interactions in the system strongly influences the forms of isotropic-nematic boundary curves.

Structural response of a prealigned cylindrical block copolymer melt to extensional flow

We report in situ small-angle x-ray scattering studies of a prealigned cylindrically ordered styrene-ethylene butylene-styrene block copolymer melt subjected to extensional flow. Samples are prepared via lubricated planar extensional flow and tested using two initial conditions: “parallel” with cylindrical microdomains oriented along the extensional flow direction and “perpendicular” with domains aligned transverse to the flow direction. The experiments employ a counter-rotating drum extensional flow fixture housed in an oven designed for in situ synchrotron access. The impacts of initial condition, extension rate, and final Hencky strain on the melt structure are analyzed both during and following flow. Stress and flow kinematics are strongly influenced by the initial sample orientation. While parallel samples exhibit uniaxial deformation, perpendicular samples exhibit planar extensional kinematics, attributed to susceptibility to compression along the cylindrical microdomain axis due to a microscopic buckling instability. Scattering data reveal both anisotropic deformation of microdomain spacing and reorientation induced by the flow. Persistence of higher order reflections confirms hexagonal packing throughout the flow process, and strong alignment along the stretching direction is attained for both initial conditions. Flow-induced deformation of microdomain spacing and mechanical stress relax on similar time scales upon flow cessation, while negligible relaxation of orientation is observed.

Controlling effective interactions and spatial dispersion of nanoparticles in multiblock copolymer melts

ABSTRACTThe microscopic Polymer Reference Interaction Site Model theory is employed to study, for the first time, the effective interactions, spatial organization, and miscibility of dilute spherical nanoparticles in non‐microphase separating, chemically heterogeneous, compositionally symmetric AB multiblock copolymer melts of varying monomer sequence or architecture. The dependence of nanoparticle wettability on copolymer sequence and chemistry results in interparticle potentials‐of‐mean force that are qualitatively different from homopolymers. An important prediction is the ability to improve nanoparticle dispersion via judicious choice of block length and monomer adsorption‐strengths which control both local surface segregation and chain connectivity induced packing constraints and frustration. The degree of dispersion also depends strongly on nanoparticle diameter relative to the block contour length. Small particles in copolymers with longer block lengths experience a more homopolymer‐like environment which renders them relatively insensitive to copolymer chemical heterogeneity and hinders dispersion. Larger particles (sufficiently larger than the monomer diameter) in copolymers of relatively short block lengths provide better dispersion than either a homopolymer or random copolymer. The theory also predicts a novel widening of the miscibility window for large particles upon increasing the overall molecular weight of copolymers composed of relatively long blocks. The influence of a positive chi‐parameter in the pure copolymer melt is briefly studied. Quantitative application to fullerenes in specific copolymers of experimental interest is performed, and miscibility predictions are made. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1098–1111

Triblock Copolymers Based on Monohydroxy Polystyrene with Crystallizable Amide Segments: Synthesis and Characterization

ABSTRACTFour series of triblock copolymers are studied, which are synthesized by reacting monofunctionalized polystyrene with crystallizable amide segments such as diamide (TΦT and T6T) and tetraamide (T6T6T and T6A6T). The difunctional amide segment consists of two terephthalic groups at the outside (T). The length of the soft segment changed from 1000 to 8000 g/mol using difunctionalized polystyrene (PSt) and thereby the concentration of the hard segment is varied from 35 to 4 wt%. The molecular weight of the triblock copolymer is determined by the inherent viscosity measurement method. The FT‐IR results reveal that the degree of crystallinity of the amide segments in the copolymer is high 79%. The differential scanning calorimetry shows the Tg for amorphous polystyrene and Tm for crystallizable hard segments. Depending on the amide concentration in the copolymer, the diamide and tetraamide melting temperature ranged between 125 to 280°C. All the thermogravimetric data reveal that the polymer shows single‐stage decomposition temperature centered around 410°C. The solvent resistivity of these materials is very high even at a low concentration of (4%) amide content. All the copolymers show low water absorption.

Chirality Transfer in Block Copolymer Melts: Emerging Concepts.

Chirality transfer from molecule to assembly is a ubiquitous process, occurring in every class of self-assembling materials, from liquid crystals to biological matter. Yet, a basic understanding of the influence of molecular chirality on the mesoscopic assembly of block copolymers lags decades behind nearly all other aspects of their structure (e.g., chain composition, topology, stiffness, interactions). This Viewpoint highlights recent experimental and theoretical studies of mesochiral assemblies of chiral block copolymers that are beginning to shed light onto the necessary conditions for and principle outcomes of chirality transfer in block copolymer melts.

Effect of Level of Crystallinity on Melt Memory Above the Equilibrium Melting Temperature in a Random Ethylene 1-Butene Copolymer

A strong memory effect of crystallization has been observed in melts of random ethylene copolymers even above the equilibrium melting temperature. Melt memory is correlated with self-seeds that increase the crystallization rate of ethylene copolymers. The seeds are associated with molten ethylene sequences from the initial crystals that remain in close proximity and are unable to diffuse quickly to the randomized melt state. Fast diffusion is restricted by topological chain constraints (loops, knots, and other entanglements) that build in the intercrystalline region during crystallization. The effect of topological constraints on melt memory, or on number of remaining self-seeds in the melt, is analyzed studying the melting and subsequent crystallization of a model ethylene 1-butene copolymer with 2.2 mol% ethyl branches prepared with different levels of crystallinity. There is a critical threshold level of crystallinity of 6–12% to observe the effect of melt memory on the subsequent crystallization rate of this copolymer. A faster development of the initial crystallinity may more efficiently trap knots and loops around the crystallites, leading to a lower crystallinity threshold than for slow or isothermally crystallized copolymers.

Dynamics versus energetics in phase separation

Phase separation may be driven by the minimization of a suitable free energy . This is the case, e.g., for diblock copolymer melts, where is minimized by a steady periodic pattern whose wavelength λGS depends on the segregation strength α−1. It has long been known that in one spatial dimension λGS ≃ α−1/3. Here we study in detail the dynamics of the system in 1D for different initial conditions and by varying α by five orders of magnitude. We find that, depending on the initial state, the final configuration may have a wavelength λD with λmin(α)<λD < λmax(α), where λmin ≈ ln(1/α) and λmax ≈ α−1/2. In particular, if the initial state is homogeneous, the system exhibits a logarithmic coarsening process which is arrested whenever λD ≈ λmin.

Morphology of Form I′ crystals of polybutene-1 formed on melt-crystallization

It is known that presence of both constitutional chain defects and stereodefects in butene-1 macromolecules may lead to the formation of the trigonal Form-I′ crystal polymorph on cooling the melt. In this study, Form I′ crystals were prepared by slow cooling of the melt of a specific random copolymer of butene-1 containing about 18 mol% propylene, and analyzed for the first time regarding their morphology by atomic force microscopy. It has been found that Form I′ crystals which develop on slow cooling of the isotropic melt exhibit a lamellar crystal shape, with a thickness and lateral width of less than 10 and 500 nm, respectively. In addition, there was proven that at the particular crystallization conditions the lamellae form stacks. Though crystallization seems non-spherulitic, the irregularly oriented stacks of lamellae are then also detected by polarizing optical microscopy.

Direct Comparisons of X-ray Scattering and Atomistic Molecular Dynamics Simulations for Precise Acid Copolymers and Ionomers

Designing acid- and ion-containing polymers for optimal proton, ion, or water transport would benefit profoundly from predictive models or theories that relate polymer structures with ionomer morphologies. Recently, atomistic molecular dynamics (MD) simulations were performed to study the morphologies of precise poly(ethylene-co-acrylic acid) copolymer and ionomer melts. Here, we present the first direct comparisons between scattering profiles, I(q), calculated from these atomistic MD simulations and experimental X-ray data for 11 materials. This set of precise polymers has spacers of exactly 9, 15, or 21 carbons between acid groups and has been partially neutralized with Li, Na, Cs, or Zn. In these polymers, the simulations at 120 °C reveal ionic aggregates with a range of morphologies, from compact, isolated aggregates (type 1) to branched, stringy aggregates (type 2) to branched, stringy aggregates that percolate through the simulation box (type 3). Excellent agreement is found between the simulated an...

Phase diagram of selectively cross-linked block copolymers shows chemically microstructured gel.

We study analytically the intricate phase behavior of cross-linked AB diblock copolymer melts, which can undergo two main phase transitions due to quenched random constraints. Gelation, i.e., spatially random localisation of polymers forming a system-spanning cluster, is driven by increasing the number parameter μ of irreversible, type-selective cross-links between random pairs of A blocks. Self-assembly into a periodic pattern of A/B-rich microdomains (microphase separation) is controlled by the AB incompatibility χ inversely proportional to temperature. Our model aims to capture the system's essential microscopic features, including an ensemble of random networks that reflects spatial correlations at the instant of cross-linking. We identify suitable order parameters and derive a free-energy functional in the spirit of Landau theory that allows us to trace a phase diagram in the plane of μ and χ. Selective cross-links promote microphase separation at higher critical temperatures than in uncross-linked diblock copolymer melts. Microphase separation in the liquid state facilitates gelation, giving rise to a novel gel state whose chemical composition density mirrors the periodic AB pattern.

Minimality via second variation for microphase separation of diblock copolymer melts

Abstract We consider a non-local isoperimetric problem arising as the sharp interface limit of the Ohta–Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the problem. Moreover, we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the L 1 {L^{1}} -topology.

Dual modes of self-assembly in superstrongly segregated bicomponent triblock copolymer melts.

While ABC triblock copolymers are known to form a plethora of dual-mode (i.e., order-on-order) nanostructures, bicomponent ABA triblock copolymers normally self-assemble into single morphologies at thermodynamic incompatibility levels up to the strong-segregation regime. In this study, we employ on-lattice Monte Carlo simulations to examine the phase behavior of molecularly asymmetric A(1)BA(2) copolymers possessing chemically identical endblocks differing significantly in length. In the limit of superstrong segregation, interstitial micelles composed of the minority A(2) endblock are observed to arrange into two-dimensional hexagonal arrays along the midplane of B-rich lamellae in compositionally symmetric (50:50 A:B) copolymers. Simulations performed here establish the coupled molecular-asymmetry and incompatibility conditions under which such micelles form, as well as the temperature dependence of their aggregation number. Beyond an optimal length of the A(2) endblock, the propensity for interstitial micelles to develop decreases, and the likelihood for colocation of both endblocks in the A(1)-rich lamellae increases. Interestingly, the strong-segregation theory of Semenov developed to explain the formation of free micelles by diblock copolymers accurately predicts the onset of interstitial micelles confined at nanoscale dimensions between parallel lamellae.

Microphase separation induced in the melt of Pluronic copolymers by blending with a hydrogen bonding urea-urethane end-capped supramolecular polymer.

Blending with a hydrogen-bonding supramolecular polymer is shown to be a successful novel strategy to induce microphase-separation in the melt of a Pluronic polyether block copolymer. The supramolecular polymer is a polybutadiene derivative with urea-urethane end caps. Microphase separation is analysed using small-angle X-ray scattering and its influence on the macroscopic rheological properties is analysed. FTIR spectroscopy provides a detailed picture of the inter-molecular interactions between the polymer chains that induces conformational changes leading to microphase separation.

Analysis of a Mixed Finite Element Method for a Cahn--Hilliard--Darcy--Stokes System

In this paper we devise and analyze a mixed finite element method for a modified Cahn--Hilliard equation coupled with a nonsteady Darcy--Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock copolymer melts. The time discretization is based on a convex splitting of the energy of the equation. We prove that our scheme is unconditionally energy stable with respect to a spatially discrete analogue of the continuous free energy of the system and unconditionally uniquely solvable. We prove that the discrete phase variable is bounded in $L^\infty \left(0,T;L^\infty\right)$ and the discrete chemical potential is bounded in $L^\infty \left(0,T;L^2\right)$, for any time and space step sizes, in two and three dimensions, and for any finite final time $T$. We subsequently prove that these variables converge with optimal rates in the appropriate energy norms in both two and three dimensions.

Dissipative particle dynamics of triblock copolymer melts: a midblock conformational study at moderate segregation.

As thermoplastic elastomers, triblock copolymers constitute an immensely important class of shape-memory soft materials due to their unique ability to form molecular networks stabilized by physical, rather than chemical, cross-links. The extent to which such networks develop in triblock and higher-order multiblock copolymers is sensitive to the formation of midblock bridges, which serve to connect neighboring microdomains. In addition to bridges, copolymer molecules can likewise form loops and dangling ends upon microphase separation or they can remain unsegregated. While prior theoretical and simulation studies have elucidated the midblock bridging fraction in triblock copolymer melts, most have only considered strongly segregated systems wherein dangling ends and unsegregated chains become relatively insignificant. In this study, simulations based on dissipative particle dynamics are performed to examine the self-assembly and networkability of moderately segregated triblock copolymers. Utilizing a density-based cluster-recognition algorithm, we demonstrate how the simulations can be analyzed to extract information about microdomain formation and permit explicit quantitation of the midblock bridging, looping, dangling, and unsegregated fractions for linear triblock copolymers varying in chain length, molecular composition, and segregation level. We show that midblock conformations can be sensitive to variations in chain length, molecular composition, and bead repulsion, and that a systematic investigation can be used to identify the onset of strong segregation where the presence of dangling and unsegregated fractions are minimal. In addition, because this clustering approach is robust, it can be used with any particle-based simulation method to quantify network formation of different morphologies for a wide range of triblock and higher-order multiblock copolymer systems.

Coarse-graining in simulations of multicomponent polymer systems.

We investigate the mapping required between the interaction parameters of two different coarse-grained simulation models to ensure a match of the long-range structural characteristics of multicomponent polymeric system. The basis for our studies is the recent work of Morse and workers, which demonstrated the existence of a mapping between the interaction parameters of different coarse-grained simulation models which allow for a matching of the peak of the disordered state structure factor in symmetric diblock copolymers. We investigate the extensibility of their results to other polymeric systems by studying a variety of systems, including, asymmetric diblock copolymers, symmetric triblock copolymers, and diblock copolymer-solvent mixtures. By using the mapping deduced in the context of symmetric diblock copolymers, we observe excellent agreement for peak in the inverse structure between both two popular coarse grained models for all sets of polymeric melt systems investigated, thus showing that the mapping function proposed for diblock copolymer melts is transferable to other polymer melts irrespective of the blockiness or overall composition. Interestingly, for the limited parameter range of polymer-solvent systems investigated in this article, the mapping functions developed for polymer melts are shown to be equally effective in mapping the structure factor of the coarse-grained simulation models. We use our findings to propose a methodology to create ordered morphologies in simulations involving hard repulsive potentials in a computationally efficient manner. We demonstrate the outcomes of methodology by creating lamellar and cylindrical phases of diblock copolymers of long chains in the popularly used Kremer-Grest simulation model.

In Situ SAXS Studies of Structural Relaxation of an Ordered Block Copolymer Melt Following Cessation of Uniaxial Extensional Flow

A hexagonally ordered styrene–ethylene-co-butylene–styrene triblock copolymer melt is studied during and immediately following uniaxial extensional flow using small-angle X-ray scattering. Strips of polymer melt are stretched between counter-rotating drums inside an oven designed for in situ synchrotron studies. Previous study of this sample demonstrated deformation and reorientation of PS microdomains and identified a critical Hencky strain ∼0.2 at which the structure is dramatically disrupted. To further probe microstructural dynamics, we study relaxation behavior of structure and stress in samples stretched in the melt to various Hencky strains. Upon cessation of stretching below the critical strain, structural relaxation is strongly retarded; stretching to higher strain leads to more rapid relaxation. At all strains, microdomain orientation relaxation following flow is slower than relaxation of flow-induced deformation and mechanical stress. The extension rate dependence of the sample’s response is also explored; higher rates result in faster relaxation of both stress and structure.

Monte Carlo simulations on thermodynamic and conformational properties of catenated double-ring copolymers

The thermodynamic and conformational properties of catenated double-ring A-B copolymer melts are investigated through lattice Monte Carlo simulations. The topological constraint on the catenated copolymers is shown to suppress demixing of A and B monomers. This action results in their order-to-disorder transition (ODT) at an increased segregation level and the lamellae below ODT with reduced order, when compared to diblock copolymers of linear or single-ring topology. The A and B rings are pulled closer by catenation in the copolymer, which leads to its smaller gyration radius, lamellar domain spacing, and distance between mass centers of the two rings than for the diblock copolymers. With increasing segregation tendencies, the gyration radii of the A rings of the catenated copolymers stretch along the direction normal to lamellae, while the A-block conformations of the single-ring copolymers change their shapes from ellipsoid to sphere.

Generation of Well-Relaxed All-Atom Models of Large Molecular Weight Polymer Melts: A Hybrid Particle-Continuum Approach Based on Particle-Field Molecular Dynamics Simulations.

A procedure based on Molecular Dynamics (MD) simulations employing soft potentials derived from self-consistent field (SCF) theory (named MD-SCF) able to generate well-relaxed all-atom structures of polymer melts is proposed. All-atom structures having structural correlations indistinguishable from ones obtained by long MD relaxations have been obtained for poly(methyl methacrylate) (PMMA) and poly(ethylene oxide) (PEO) melts. The proposed procedure leads to computational costs mainly related on system size rather than to the chain length. Several advantages of the proposed procedure over current coarse-graining/reverse mapping strategies are apparent. No parametrization is needed to generate relaxed structures of different polymers at different scales or resolutions. There is no need for special algorithms or back-mapping schemes to change the resolution of the models. This characteristic makes the procedure general and its extension to other polymer architectures straightforward. A similar procedure can be easily extended to the generation of all-atom structures of block copolymer melts and polymer nanocomposites.

Shear-Induced Ordering in Thin Films of Diblock Copolymer Melts.

By means of molecular dynamics simulations we investigate the response of thin, symmetric diblock copolymer melts under shear in the limit of strong segregation with nonselective substrates, where vertically oriented lamellae form. Under small shear perpendicular to the lamellar orientation, we observe an inclination of the lamellar layers. At a critical shear rate, the lamellar layers become distorted and, for very large shear, recombine with a new orientation along the direction of shear. Our simulations are accompanied by a novel, easily understandable theoretical approach to predict the critical shear rate, at which the interfaces become distorted and shear-induced reorientation sets in. This allows one to calculate quantities such as the inclination angle or the pair interaction energy as a function of applied shear rate. Our results are relevant for many technical applications, where defect-free, long-range ordered structures are needed.