Copolymer Melts Research Articles

Phase diagrams of polymer-containing liquid mixtures with a theory-embedded neural network

We develop a deep neural network (DNN) that accounts for the phase behaviors of polymer-containing liquid mixtures. The key component in the DNN consists of a theory-embedded layer that captures the characteristic features of the phase behavior via coarse-grained mean-field theory and scaling laws and substantially enhances the accuracy of the DNN. Moreover, this layer enables us to reduce the size of the DNN for the phase diagrams of the mixtures. This study also presents the predictive power of the DNN for the phase behaviors of polymer solutions and salt-free and salt-doped diblock copolymer melts.

Enhanced sampling of cylindrical microphase separation via a shell-averaged bond-orientational order parameter.

The formation of a hexagonal phase from disordered phase is one of the typical order-disorder transitions (ODTs) observed in asymmetric diblock copolymer systems. In order to drive this transition in a particle-based simulation, we introduce a shell-based bond-orientational order parameter that selectively responds to the mesoscopic order of the hexagonal cylinder phase. From metadynamics simulations in a bond-free particle model system, the characteristic pathway involved with the underlying free energy surface is deduced for the disordered-to-hexagonal transition. It is shown consecutively that the transition pathway and the metastable state are reproduced in dissipative particle dynamics simulations for the corresponding transition in a bulk asymmetric block copolymer melt system. These agreements suggest that efficient strategies for enhanced sampling with particle-based simulations of block copolymer systems can be devised using coarse-grained pictures of the mesoscopic order.

Multifunctional nonwoven materials, produced by electrospinning of a heated solution and melt of ethylene-octene copolymer

Nonwoven materials with an average fiber diameter of 4.7 μm and 3.9 μm were prepared by electrospinning of a heated solution and melt of the thermoplastic polyolefin elastomer – ethylene-octene copolymer. The materials prepared from the melt have fibers with a smooth surface, while materials produced from a heated solution have “shish-kebab” morphology with highly extended surface. X-ray diffraction analysis data demonstrates increasing of the mesophase content in the fibers prepared from the melt and the orthorhombic crystalline phase – for a heated solution. The produced nonwovens show superhydrophobic and oleophilic properties, high sorption capacity (up to 109 g/g for motor oil) and can be used for various applications, e.g. oil removal from water surface and matrices in tissue engineering.

Dynamics and Viscoelasticity of Disordered Melts of Symmetric Diblock Copolymers

Simulations of coarse-grained models are used to study relationships among chain motion, composition fluctuations, and stress relaxation in unentangled melts of symmetric diblock copolymers. Measurements of the dynamic structure factor S(q,t) are reported as a function of wavenumber q, time t, and χN, where χ is the Flory–Huggins interaction parameter and N is degree of polymerization. The function S(q,t) is found to be a nearly exponential function of time, S(q,t) ∝ e–t/τ(q), for wavenumbers similar to or less than the wavenumber q* at which the static structure factor S(q) ≡ S(q,t=0) is maximum. The relationship between the decay time τ(q) and S(q) is used to define an effective wavenumber-dependent diffusivity D(q) for fluctuations of wavenumber q. The function D(q) is shown to change very little with changes in χN and to be a monotonically decreasing function of the nondimensional wavenumber qRg, where Rg is polymer radius of gyration. The linear shear stress relaxation modulus G(t) is inferred from measurements of the shear stress autocorrelation function. At low values of χN, far from the order–disorder transition (ODT), the modulus G(t) agrees with predictions of the Rouse model. Near the ODT, G(t) develops an additional slowly decaying feature arising from slow decay of composition fluctuations with q ∼ q*. The behavior of G(t) near the ODT is predicted nearly quantitatively by a modified version of the model of Fredrickson and Larson (FL), in which the prediction of the FL theory for the slowly decaying component is added to the prediction of the Rouse theory for contributions arising from single-chain relaxation, using the independently measured behavior of S(q,t) as an input to the theory.

Equilibrium Field Theoretic Study of Nanoparticle Interactions in Diblock Copolymer Melts.

Block copolymer matrices are often used to control nanoparticle (NP) dispersion behavior, but the effects of diblock domain interfaces on particle-particle interactions have not been well characterized. In this paper, polymer field theoretic simulations are used to quantify interactions between both bare and grafted spherical NPs in microphase-separated A-B diblock copolymers. It is shown that for bare NPs that have an athermal interaction with and a diameter similar to the B domain, the presence of an A-B interface leads to an effective interaction between the particles with multiple minima separated by a free energy barrier. It is further shown that these effects primarily result from chain stretching and compression near the A-B interface induced by particle-particle interactions as opposed to increases in A-B contact at the interfaces. Grafted chains largely prevent these effects and reduce particle-particle interaction strength. When confined by diblock domain interfaces, grafted chains have a reduced extension compared to what is expected for de-wetted brush chains, as commonly described in homopolymer results. Finally, these studies indicate a new route toward linking spherical NPs in a controlled fashion, allowing for tunable plasmonic properties in the case of metallic NPs.

Theory of Microphase Segregation in the Melts of Copolymers with Dendritically Branched, Bottlebrush, or Cycled Blocks.

Theory of microphase segregation in the melt of diblock copolymers comprising two strongly incompatible blocks of similar or different topologies is developed. The spectrum of considered architectures include copolymers with arbitrary combinations of bottlebrush-like, dendritic, cycled blocks, and so on. Our theory provides quantitative predictions of how the morphology of the microphase segregated structures can be controlled not only by the volume fractions of the incompatible blocks, but also by their architecture. These predictions open perspectives for developing new materials, for example, photonic crystals, with independently adjustable volume fractions and morphology of the domains.

Understanding the effects of dipolar interactions on the thermodynamics of diblock copolymer melts

We present results highlighting the roles of dipolar interactions in affecting thermodynamics of diblock copolymer melts. Field theoretic methods and coarse-grained molecular dynamics (MD) simulations are used to understand the effects of dipolar interactions among copolymer segments. In particular, the effects of dipolar interactions on disorder-lamellar transition and domain spacing of the lamellar morphology are studied. It is shown that dipolar interactions stabilize the lamellar morphology over the disordered phase. Furthermore, the domain spacing for the lamellar morphology is predicted to increase with an increase in disparity between dipole moments of two kinds of monomers in the diblock or equivalently a mismatch in the dielectric constant of homopolymers forming the diblock. MD simulations reveal that additional orientational effects resulting from the anisotropic nature of the dipolar interaction potential are significant for highly polar monomers. In contrast, the field theoretic models based on orientationally averaged dipolar interaction potentials, such as those used in this work, fail to capture the effects of orientational correlations.

Rheology of symmetric diblock copolymers

Using large-scale simulations with the graphics processing unit (GPU) accelerated Highly Optimized Object-oriented Many-particle Dynamics (HOOMD)-blue software we investigate the anisotropic, dynamic-mechanical properties of lamellae-forming diblock copolymer melts. Both, the shear-stress autocorrelation function in equilibrium as well as stress-controlled simulations of shear flow are considered. The latter are implemented in (HOOMD)-blue via reverse nonequilibrium molecular dynamics simulation (RNEMDS).We find that copolymer lamellae that are perpendicularly oriented to the shear flow have similar rheological properties than unstructured homopolymer melts. Copolymer lamellae with the metastable parallel and the unstable transverse orientation exhibit similar dynamic-mechanical behavior in the linear regime. Most notably, they are characterized by a high dissipation.(RNEMDS) enables the study of oscillatory shear flow as well as the investigation of nonlinear rheology. Our simulation results for a soft, coarse-grained model at very high frequencies indicate that the finite speed of stress propagation has to be accounted for in the quantitative analysis, and we devise an analytic prediction for the nonlinear velocity and spatially varying stress profiles as a function of the loss and storage moduli.

Correction to Optimized Phase Field Model for Diblock Copolymer Melts

Correction to Optimized Phase Field Model for Diblock Copolymer Melts

Stability of the A15 phase in diblock copolymer melts

The self-assembly of block polymers into well-ordered nanostructures underpins their utility across fundamental and applied polymer science, yet only a handful of equilibrium morphologies are known with the simplest AB-type materials. Here, we report the discovery of the A15 sphere phase in single-component diblock copolymer melts comprising poly(dodecyl acrylate)-block-poly(lactide). A systematic exploration of phase space revealed that A15 forms across a substantial range of minority lactide block volume fractions (fL = 0.25 - 0.33) situated between the σ-sphere phase and hexagonally close-packed cylinders. Self-consistent field theory rationalizes the thermodynamic stability of A15 as a consequence of extreme conformational asymmetry. The experimentally observed A15-disorder phase transition is not captured using mean-field approximations but instead arises due to composition fluctuations as evidenced by fully fluctuating field-theoretic simulations. This combination of experiments and field-theoretic simulations provides rational design rules that can be used to generate unique, polymer-based mesophases through self-assembly.

Calibration of a lattice model for high-molecular-weight block copolymer melts.

The Morse calibration is applied to a lattice model designed for efficient simulations of two-component polymer melts of high molecular weight. The model allows multiple occupancy per site, which results in high invariant polymerization indices, and interactions are limited to monomers within the same site, which enhances the computational speed. The calibration maps the interaction parameter of the lattice model, α, onto the Flory-Huggins χ parameter of the standard Gaussian-chain model, by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. The quantitative accuracy of the calibration is tested by comparing the order-disorder transition of symmetric diblock copolymer melts to the universal prediction obtained from previous simulations. The model is then used to confirm the universality of fluctuation corrections to the critical point of symmetric binary homopolymer blends.

High-pressure neutron scattering and random-phase approximation analysis of a molten Baroplastic diblock copolymer

Through high-pressure, small-angle neutron scattering (SANS) and a random-phase approximation (RPA) theory based on a molecular model, we investigate the origin of the pressure responsiveness of a phase-segregating deuterated polystyrene-block-poly (2-ethyl hexyl acrylate) (dPS-b-PEHA) copolymer melt for use as a material for low-energy processing. The SANS intensities for the copolymer were measured over a temperature range at applied pressures between 0.1 and ∼83 MPa. The copolymer exhibited an order-disorder transition (ODT) and revealed baroplasticity, where its ODT was suppressed upon pressurization as ΔTODT/ΔP≈ -15.8 K/100 MPa to ease subsequent processing. Theory predicts that a disparity in the self interactions εjj’s (Δεjj=εPS−εPEHA) or a disparity in the compressibilities between blocks precisely yields the observed ΔTODT/ΔP. The effective Flory-Huggins χ is argued to consist of the conventional enthalpic χH and entropic χS coming from Δεjj mediated by the copolymer bulk modulus. Pressure strengthens χH due to densification, whereas the augmented bulk modulus reduces χS. The diminution of χS is shown to be the source of baroplasticity.

Optimized Phase Field Model for Diblock Copolymer Melts

Self-consistent field theory (SCFT) is a versatile framework for investigating self-assembly and thermodynamic properties in broad classes of polymer systems. Nonetheless, it is expensive to implement in higher space dimensions d as propagator fields of d + 1 dimensions must be resolved in a numerical SCFT simulation. In principle, SCFT can be exactly reduced to a phase field (or density functional) theory involving only d-dimensional species density fields, but the density functional of the reduced theory is not known analytically. Although asymptotic approximations to the functional are available in the literature, e.g., the Ohta–Kawasaki (OK) model for diblock copolymers, these functionals tend to produce inaccurate and unreliable predictions. Here, we present a phase field mapping technique adapted from force-matching concepts in the particle coarse-graining literature to best-fit coefficients in a trial density functional using data obtained from low-dimensional SCFT simulations. Such a mapping schem...

Generalizing the effects of chirality on block copolymer assembly

We explore the generality of the influence of segment chirality on the self-assembled structure of achiral-chiral diblock copolymers. Poly(cyclohexylglycolide) (PCG)-based chiral block copolymers (BCPs*), poly(benzyl methacrylate)-b-poly(d-cyclohexylglycolide) (PBnMA-PDCG) and PBnMA-b-poly(l-cyclohexyl glycolide) (PBnMA-PLCG), were synthesized for purposes of systematic comparison with polylactide (PLA)-based BCPs*, previously shown to exhibit chirality transfer from monomeric unit to the multichain domain morphology. Opposite-handed PCG helical chains in the enantiomeric BCPs* were identified by the vibrational circular dichroism (VCD) studies revealing transfer from chiral monomers to chiral intrachain conformation. We report further VCD evidence of chiral interchain interactions, consistent with some amounts of handed skew configurations of PCG segments in a melt state packing. Finally, we show by electron tomography [3D transmission electron microscope tomography (3D TEM)] that chirality at the monomeric and intrachain level ultimately manifests in the symmetry of microphase-separated, multichain morphologies: a helical phase (H*) of hexagonally, ordered, helically shaped tubular domains whose handedness agrees with the respective monomeric chirality. Critically, unlike previous PLA-based BCP*s, the lack of a competing crystalline state of the chiral PCGs allowed determination that H* is an equilibrium phase of chiral PBnMA-PCG. We compared different measures of chirality at the monomer scale for PLA and PCG, and argued, on the basis of comparison with mean-field theory results for chiral diblock copolymer melts, that the enhanced thermodynamic stability of the mesochiral H* morphology may be attributed to the relatively stronger chiral intersegment forces, ultimately tracing from the effects of a bulkier chiral side group on its main chain.

Self‐Consistent Field Theory of Inhomogeneous Polymeric Systems: A Variational Derivation

AbstractThe self‐consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many‐body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric systems such as polymer blends and block copolymer melts. The polymeric SCFT is commonly derived using field‐theoretical techniques. Here, an alternative derivation of the SCFT equations and SCFT free energy functional using a variational principle is provided. Numerical methods of solving the SCFT equations and applications of the SCFT are also briefly introduced.

Defect-free hexagonal patterns formed by AB diblock copolymers under triangular confinement

The self-assembly of a hexagonal cylinder-forming diblock copolymer melt under the hexagonal confinement provides a useful method for the fabrication of defect-free hexagonal patterns. However, the validity of this method depends on the commensurability of the hexagonal size to the domain spacing. Here we turn to another lateral confinement whose shape adapts to the hexagonal lattice, i.e. the regular triangle. First, we attempted to verify that the perfect hexagonal patterns are exclusively the thermodynamic stable morphologies in the triangles with whatever sizes using the self-consistent field theory (SCFT). Then, we simulate the annealing kinetics of the confined melt using the SCFT iteration process. We find that a small number of defects are usually formed in a large triangle even with a commensurate size to the domain spacing. Finally, we propose a multi-step annealing process, where the perfect hexagonal patterns are yielded via a heterogenous nucleation process. Importantly, the achievement of the perfect hexagonal patterns does not exhibit a size-incommensurability issue with the triangles, and thus could become a promising nanolithography scheme.

Formation of homochiral helical nanostructures in diblock copolymers under the confinement of nanopores.

The control of the homochirality of helical structures formed in achiral systems is of great interest as it is helpful for understanding the origin of homochirality in life. In this work, we introduce a spiral arrangement of patches into the inner surface of a nanopore to guide the self-assembly of a cylinder-forming AB diblock copolymer melt into a homochiral single helix. We calculate the free energy of the single-helical structures with different handedness using self-consistent field theory (SCFT). Moreover, we simulate the self-assembly process using an iterative process of SCFT solution starting from a disordered state, and count the formation probability of different helical structures. We find that the formation probability of the homochiral helix with favorable free energy increases rapidly, leading to the conclusion that a minuscule difference of 0.5-1.0 × 10-4kBT per chain is enough to obtain the homochiral helix by suppressing its counterpart of a higher free energy. However, for a stronger chiral guiding field, other homochiral helical structures with unfavorable handedness and thus increasingly higher free energy become more likely to be formed. Morphological snapshots during the self-assembly process reveal that the formation of these metastable helical structures is induced by their kinetic pathways, which are altered to be favorable by the strong chiral field of the patch pattern. Therefore, our work suggests that both thermodynamics and kinetics are important for controlling the chirality of helical structures.

Self-Organization of Triblock Copolymer Melt Chains Physisorbed on Non-neutral Surfaces.

We here report the self-organization process of poly(styrene-b-ethylene/butadiene-b-styrene) (SEBS) triblock copolymer chains physically adsorbed on a non-neutral surface. Spin-cast SEBS thin films were prepared on silicon (Si) substrates and then annealed at a high temperature far above the bulk glass transition temperatures of the two constituent blocks. To reveal the buried interfacial structure, we utilized solvent rinsing processes and a suite of surface-sensitive techniques including ellipsometry, X-ray reflectivity, atomic force microscopy, and grazing incidence small angle X-ray scattering. We revealed that the SEBS chains form two different chain structures on the substrate simultaneously: (i) “flattened chains” with the average height of 2.5 nm but without forming microdomain structures; (ii) “loosely adsorbed chains” with the average height of 11.0 nm and the formation of perpendicularly oriented cylindrical microdomains to the substrate surface. In addition, the kinetics to form the perpendicular-oriented cylinder was sluggish (∼200 h) and proceeded via multistep processes toward the equilibrium state. We also found that the lateral microdomain structures were distorted, and the characteristic lengths of the microdomains were slightly different from the bulk even after reaching “quasiequilibrium” state within the observed time window. Furthermore, we highlight the vital role of the adsorbed chains in the self-assembling process of the entire SEBS thin film: a long-range perturbation associated with the adsorbed chains propagates into the film interior, overwhelming the free surface effect associated with surface segregation of the lower surface tension of polystyrene blocks.

A new framework for X-ray photon correlation spectroscopy analysis from polycrystalline materials.

We report a new analytical framework for interpreting data from X-ray photon correlation spectroscopy measurements on polycrystalline materials characterized by strong scattering intensity variations at fixed wavevector magnitude (i.e., anisotropic scattering). Currently, no analytical method exists for the interpretation of the time-dependent anisotropic scattering from such materials. The framework is applied to interrogate the dynamics of a spherical micelle-forming diblock copolymer melt below the order-disorder transition, wherein finite size grains of a micellar body-centered cubic structure produce anisotropic scattering. A wealth of analytical information is recovered from a simple measurement, including distributions of relaxation times and speeds associated with micelles within grains. The findings of this study demonstrate the efficacy of this new analytical method, which may be readily adapted for application to a variety of materials and systems.

Tuning Arm Architecture Leads to Unusual Phase Behaviors in a (BAB)5 Star Copolymer Melt

The self-assembly behavior of (B1AB2)5 star copolymers, composed of five asymmetric BAB-triblock arms joined at the end of B2-blocks, has been investigated using the self-consistent field theory. T...