Copolymer Melts Research Articles

Polymerization-Induced Microphase Separation with Long-Range Order in Melts of Gradient Copolymers.

In this work, we studied the question of whether it is possible to develop a one-step approach for the creation of microphase-separated materials with long-range order with the help of spontaneous gradient copolymers, i.e., formed during controlled copolymerization solely due to the large difference in the reactivity ratios. To that end, we studied the polymerization-induced microphase separation in bulk on the example of a monomer pair with realistic parameters based on styrene (S) and vinylpirrolydone (VP) by means of computer simulation. We showed that for experimentally reasonable chain lengths, the structures with long-range order start to appear at the conversion degree as low as 76%; a full phase diagram in coordinates (fraction of VP—conversion degree) was constructed. Rather rich phase behavior was obtained; moreover, at some VP fractions, order–order transitions were observed. Finally, we studied how the conversion degree at which the order–disorder transition occurs changes upon varying the maximum average chain length in the system.

Impact of Thin-Film Confinement on the Packing of Low-Coordinate Spheres in Bulk

The self-assembly of a purposely designed AB-type multiblock copolymer melt under the confinement of thin film with two identical surfaces attractive to minority A-blocks is investigated using self...

Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts.

The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In a recent study, one of us and coworkers have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: at early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials.

Correlation between linear and nonlinear material functions under large amplitude oscillatory shear

Fourier transform rheology is the most frequently used method to interpret the nonlinear rheological behavior of complex fluids under large amplitude oscillatory shear (LAOS). However, the unclear relationship between the higher harmonics and the fundamental harmonic obscures the physical meaning of the nonlinear functions. Here, we hypothesize that all the nonlinear oscillatory shear functions and normal stress functions can be expressed as linear combinations of linear viscoelastic functions or their derivatives at different frequencies under both strain-controlled LAOS (LAOStrain) and stress-controlled LAOS (LAOStress). We check this hypothesis using the time-strain separable Wagner model, Giesekus model, and modified Leonov model. We find such correlations between the nonlinear material functions and the linear material functions are intrinsic for viscoelastic liquids under LAOStrain, and for viscoelastic solids under LAOStress. Finally, these correlations are justified by a viscoelastic standard polydimethylsiloxane, an ethylene–octene multiblock copolymer melt, and a typical simple yield stress material (0.25 wt. % Carbopol).

Simulation of diblock copolymer surfactants. III. Equilibrium interfacial adsorption.

Monte Carlo simulations are used to study adsorption of highly asymmetric diblock copolymers to a polymer-polymer interface, and the results compared to self-consistent field theory (SCFT) predictions. The simulation model used here is a bead-spring model that has been used previously to study equilibrium and kinetic properties of spherical micelles [J. A. Mysona et al., Phys. Rev. E 100, 012602 (2019)2470-004510.1103/PhysRevE.100.012602; Phys. Rev. E 100, 012603 (2019)10.1103/PhysRevE.100.012603; Phys. Rev. Lett. 123, 038003 (2019)10.1103/PhysRevLett.123.038003]. Interfacial copolymer concentration Γ and interfacial tension γ are measured as functions of bulk copolymer concentration at concentrations up to the critical micelle concentration over a range of values of the Flory-Huggins χ parameter. The dependence of interfacial pressure Π = γ_{0}-γ on Γ (where γ_{0} is the interfacial tension in the absence of copolymer) is found to be almost independent of χ and to be accurately predicted by SCFT. The bare interfacial tension γ_{0} and total interfacial tension γ(Γ) can also be accurately predicted by SCFT using an estimate of χ obtained from independent analysis of properties of symmetric diblock copolymer melts. SCFT predictions obtained with this estimate of χ do not, however, adequately describe the thermodynamics of the coexisting bulk copolymer solution, as a result of contraction of the strongly interacting core block of dissolved copolymers. Accurate predictions of the relationship between bulk and interfacial properties can thus only be obtained for this system by combining SCFT predictions of the interfacial equation of state with a fit to the measured equation of state for the bulk solution.

Toward all stereocomplex-type polylactide with outstanding melt stability and crystallizability via solid-state transesterification between enantiomeric poly(l-lactide) and poly(d-lactide)

Stereoblock copolymerization is regarded an appealing strategy to substantially enhance the melt stability (i.e., the survival ability of the intermolecular collaboration between poly(l-lactide) (PLLA) and poly(d-lactide) (PDLA) upon melting) of high-molecular-weight (high-MW) stereocomplex-type polylactide (SC-PLA), however it usually suffers from complicated synthetic procedures and even impaired sustainability. Herein, solid-state transesterification (SST) has been devised as a facile and robust route to prepare unique multi-stereoblock PLA copolymers with outstanding melt stability and unexpectedly strong crystallizability from commercial available linear high-MW PLLA/PDLA (50/50) blends. The SST was performed through low-temperature (i.e., 180 °C) melt-blending of PLLA and PDLA in the presence of trace amounts (0.03–0.035 wt%) of catalysts, where the enantiomeric PLA chains could rapidly co-crystallize into solid-state SC crystallites upon melting and subsequently the hetero-chain transesterification reaction occurs exclusively in the mobile amorphous phase of the pre-formed SC crystallites. As a result, multiblock-like PLLA-b-PDLLA-b-PDLA copolymers with long crystallizable PLLA and PDLA blocks are in-situ generated. The results show that high-content SC crystallites can be exclusively formed in the melt-crystallization of the copolymers even at high cooling rates (e.g., 40 °C/min) and low temperatures (e.g., 140 °C). More interestingly, the presence of the non-crystallizable PDLLA blocks not only does not disturb the SC crystallizability of the enantiomeric PLA blocks, as evidenced by the same high crystallinity and melting temperature as those of starting PLLA/PDLA blends, but also increase the crystallization rate by stabilizing the clusters of ordered PLLA/PDLA segments in the copolymer melt. Overall, these findings could open a new pathway to develop melt-processible all SC-PLA for engineering applications.

Efficient numerical scheme for a new hydrodynamically-coupled conserved Allen–Cahn type Ohta–Kawaski phase-field model for diblock copolymer melt

In this work, we first propose a new hydrodynamically-coupled phase-field model for the diblock copolymer melt that is derived based on the Allen–Cahn dynamics where the volume fraction of two composing monomers is conserved by using a nonlocal Lagrange multiplier. Formally, the system is a highly nonlinear system that consists of the incompressible Navier–Stokes equations and a nonlocal-type Allen–Cahn type equation. Then, to solve the model, we develop a linear and second-order time-marching scheme via the Invariant Energy Quadratization approach with the stabilization technique for the nonlinear potentials, as well as the projection method for the Navier–Stokes equations. The unconditional energy stability of the numerical method is proved, and several experiments of 2D and 3D are performed to validate the accuracy and energy stability of the developed numerical scheme.

Self-assembly of a triply periodic continuous mesophase with Fddd symmetry in simple one-component liquids.

Triply periodic continuous morphologies (networks) arising as a result of the microphase separation in block copolymer melts have so far never been observed self-assembled in systems of particles with spherically symmetric interaction. We report a molecular dynamics simulation where two simple one-component liquids form upon cooling an equilibrium network with the Fddd space group symmetry. This complexity reduction in the liquid network formation in terms of the particle geometry and the number of components evidences the generic nature of this class of phase transition, suggesting opportunities for producing these structures in a variety of new systems.

Bottom-up Construction of Dynamic Density Functional Theories for Inhomogeneous Polymer Systems from Microscopic Simulations

We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of the mobility coefficient, $\Lambda(r,r')$, which relates the thermodynamic driving force on monomers at position $r'$ to the motion of monomers at position $r$. A first approach based on the Green-Kubo formalism turns out to be impractical because of a severe plateau problem. Instead, we propose to extract the mobility coefficient from an effective characteristic relaxation time of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblock copolymer melts. The DDFT results are in very good agreement with the data from corresponding fine-grained simulations.

Block Copolymer–Nanorod Co-assembly in Thin Films: Effects of Rod–Rod Interaction and Confinement

Simulations and experiments of nanorods (NRs) show that co-assembly with block copolymer (BCP) melts leads to the formation of a superstructure of side-to-side NRs perpendicular to the lamellar axis. A mesoscopic model is validated against scanning electron microscopy (SEM) images of CdSe NRs mixed with polystyrene-block-poly(methyl methacrylate). It is then used to study the co-assembly of anisotropic nanoparticles (NPs) with a length in the same order of magnitude as the lamellar spacing. The phase diagram of BCP/NP is explored as well as the time evolution of the NR. NRs that are slightly larger than the lamellar spacing are found to rotate and organise side-to-side with a tilted orientation with respect to the interface. Strongly interacting NPs are found to dominate the co-assembly while weakly interacting nanoparticles are less prone to form aggregates and tend to form well-ordered configurations.

Microphase Segregation in the Melts of Bottlebrush Block Copolymers

We present an analytical theory of microphase separation in the melt of bottlebrush and comblike block copolymers in the strong segregation limit. The constructed phase diagram predicts morphologie...

A new insight into multi-tier structure tailoring: Synchronous utilization of particle migration and incompatible interface separation under shear flow

In this work, polyethylene (PE)/silica microsphere composite melt is used to penetrate the ethylene-α-octene block copolymer (OBC) melt in multi-melt multi-injection molding (M3IM) process. Due to the viscosity difference between PE/silica composite melt and OBC melt, a disturbed flow interface of these two melts formed. Thanks to the “shear-induced migration” theory in suspended balance model (SB model) and the unique flow field in M3IM, silica microspheres can be designed to migrate from high shear rate layer to low shear rate layer in PE/silica core melt, further to intaglio micro-pits on the interface of PE/silica core and OBC skin melt. As a result, the migrated silica microspheres can be intuitively observed by peeling off the OBC layer, as well as a “lotus seedpod”-like structure consisting of quantity-adjustable asperities and micro-pits can be constructed on the peeled surface of OBC layer. This work sheds lights to rapidly fabricate multi-tier structures by polymer melt processing strategies, aiming to manufacture functional devices on a large scale.

Thermal behavior of ethylene copolymers with di- and tri-alkenylsilsesquioxane comonomers synthesized by post-metallocene catalysts

This paper reported thermal properties of ethylene copolymers with di- and tri-alkenylsilsesquioxanes (POSS) synthesized by bis(phenoxy-imine) Ti, Zr, V, and V salen-type complexes. Ethylene copolymers with multi-alkenyl POSS obtained by such complexes contain multi-alkenyl POSS incorporated into the polymer chain as a side group. They were characterized by different thermal behavior depending on the kind of multi-alkenyl POSS comonomer, and type of the catalyst used, as well as polymerization conditions and thus the structure of the copolymer chain. Ethylene/POSS copolymers differed in incorporation of POSS into the polymer chain, content of specific unsaturation groups, and molecular weight, as well as heterogeneity of polymer chain compositions. The incorporation of multi-alkenyl POSS into the polymer chain affected melting and crystallization processes of copolymers in different ways. The POSS units could act as a nucleating agent of macromolecules. The increasing POSS content in E/POSS copolymers resulted in increasing thermal stability of obtained products, regardless of the kind of multi-alkenylsilsesquioxanes used. Thermal stability of such copolymers increased with decreasing content of trisubstituted vinylene groups (internal saturations) as well. The highest improvement of thermal stability over 85 °C in comparison with PE was observed in case of E/POSS copolymers synthesized by bis(phenoxy-imine) zirconium catalyst. The composition heterogeneity of E/POSS copolymers was found to affect markedly thermal stability of E/POSS copolymers.

Simulation Study of Process-Controlled Supramolecular Block Copolymer Phase Separation with Reversible Reaction Algorithm.

A supramolecular diblock copolymer formed by reversible bonds between the two blocks shows a rich microphase separation behavior and has great application potential in stimuli-responsive materials. We propose a novel method to describe supramolecular reactions in dissipative particle dynamics, which includes a reversible reaction to accurately reproduce the strength, saturation, and dynamic properties of the reversible bonds in the simulations. The thermodynamic properties and dynamic processes of the supramolecular diblock copolymer melts in both equilibrium and non-equilibrium states were studied using this method. The simulation results show that the method can faithfully characterize phase behaviors and dynamic properties of supramolecular diblock copolymer melts, especially in a non-equilibrium state, which provides a novel tool to unveil self-assembly mechanism and describe the properties of supramolecular block copolymers.

Synthesis and Self-Assembly of ABn Miktoarm Star Polymers

The stability of tetrahedrally close-packed (TCP) phases in block copolymer melts is predicted by theory to depend on molecular architecture, yet no experimental studies to date have probed its effect. Motivated by this open question, here we report an efficient synthesis of asymmetric ABn miktoarm star polymers using functionalized sugars as cores for orthogonal grafting-from block copolymerizations. A combination of ring-opening and atom transfer radical polymerization produced model low dispersity materials comprising a single A = poly(lactide) (L) and multiple B = poly(dodecyl acrylate) (D) arms that amplify "conformational asymmetry" through two concerted effects: the mikto architecture and disparate block statistical segment lengths. Analyzing the self-assembly of LD2 and LD3 samples resulted in the discovery of two TCP phases, σ and A15, that remained stable to significantly higher A-block volume fractions as the number of B arms increased. These results experimentally establish the importance of conformational asymmetry and molecular architecture as powerful design tools for the self-assembly of block copolymers into nonclassical phases.

A rigorous derivation of mean-field models describing 2D micro phase separation

We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction rho such that the micro phase separation results in an ensemble of small disks of one component. We consider the two dimensional case in this paper, whereas the three dimensional case was already considered in Niethammer and Oshita (Calc Var PDE 39:273–305, 2010). Starting from the free boundary problem restricted to disks we rigorously derive the heterogeneous mean-field equations on a time scale of the order of {mathcal {R}}^{3}ln (1/rho ), where {mathcal {R}} is the mean radius of disks. On this time scale, the evolution is dominated by coarsening and stabilization of the radii of the disks, whereas migration of disks becomes only relevant on a larger time scale.

A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends.

A renewed focus on the phase behavior of nominally single-component, compositionally asymmetric diblock copolymers has revealed a host of previously unanticipated Frank-Kasper (FK) and quasicrystalline phases. However, these periodic and aperiodic particle packings have thus far only been reported in low molecular weight, highly conformationally asymmetric diblock copolymers, leaving researchers with a relatively small library of polymers in which these phases can be studied. In this work, we report on a simple approach to access these morphologies: blending two diblock copolymers with the same corona block length and varied core block lengths. Compositionally symmetric and asymmetric polystyrene-b-1,4-polybutadiene (SB) diblock copolymers with constant corona block lengths were blended together and shown via small-angle X-ray scattering and transmission electron microscopy to order into the FK A15 and σ phases, as well as a dodecagonal quasicrystal, providing a route to various particle packings in high molecular weight diblock copolymer melts.

Tuning the thermal properties of poly(ethylene)‐like poly(esters) by copolymerization of ε‐caprolactone with macrolactones, in the presence of a pyridylamidozinc(II) complex

ABSTRACTLinear aliphatic poly(ester)s, as thermoplastic materials, are more and more envisaged as the potential “green” alternative to traditional plastics. Aliphatic polyesters having long methylene chain behave as “polyethylene‐like” materials and can be prepared by ring‐opening polymerization (ROP) of macrolactones. A pyridylamidozinc(II) complex was used for the ROP of ε‐caprolactone (CL) and of two large ring size lactones, the ω‐6‐hexadecenlactone (6HDL) and the ω‐pentadecalactone (PDL). High turnover frequencies were observed for the CL polymerization, while for the macrolactones, an entropy‐driven behavior was recognized. Random copolymerizations of the PDL with 6HDL and of the macrolactones with CL were successfully achieved, and the copolymer microstructure was ascertained by NMR and MALDI analyses. The copolymer melting temperatures, measured by DSC, and the thermal degradation behavior, studied by TGA in nitrogen and air atmosphere, were dependent on the copolymer's composition. © 2020 Wiley Periodicals, Inc. J. Polym. Sci.2020,58, 528–539

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.