Symmetric Diblock Copolymers Research Articles

Ion transport properties of mechanically stable symmetric ABCBA pentablock copolymers with quaternary ammonium functionalized midblock

ABSTRACTAnion exchange membranes (AEMs) are a promising class of materials for applications that require selective ion transport, such as fuel cells, water purification, and electrolysis devices. Studies of structure–morphology–property relationships of ion‐exchange membranes revealed that block copolymers exhibit improved ion conductivity and mechanical properties due to their microphase‐separated morphologies with well‐defined ionic domains. While most studies focused on symmetric diblock or triblock copolymers, here, the first example of a midblock quaternized pentablock AEM is presented. A symmetric ABCBA pentablock copolymer was functionalized to obtain a midblock brominated polymer. Solution cast films were then quaternized to obtain AEMs with resulting ion exchange capacities (IEC) ranging from 0.4 to 0.9 mmol/g. Despite the relatively low IEC, the polymers were highly conductive (up to 60 mS/cm Br− at 90 °C and 95%RH) with low water absorption (<25 wt %) and maintained adequate mechanical properties in both dry and hydrated conditions. X‐ray scattering and transmission electron microscopy (TEM) revealed formation of cylindrical non‐ionic domains in a connected ionic phase. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 612–622

Phase transition of a symmetric diblock copolymer induced by nanorods with different surface chemistry.

We investigate the phase transition of a symmetric diblock copolymer induced by nanorods with different surface chemistry. The results demonstrate that the system occurs the phase transition from a disordered structure to ordered parallel lamellae and then to the tilted layered structure as the number of rods increases. The dynamic evolution of the domain size and the order parameter of the microstructure are also examined. Furthermore, the influence of rod property, rod-phase interaction, rod-rod interaction, rod length, and polymerization degree on the behavior of the polymer system is also investigated systematically. Moreover, longer amphiphilic nanorods tend to make the polymer system form the hexagonal structure. It transforms into a perpendicular lamellar structure as the polymerization degree increases. Our simulations provide an efficient method for determining how to obtain the ordered structure on the nanometer scales and design the functional materials with optical, electronic, and magnetic properties.

Ordering block copolymers with structured electrodes.

We study the kinetics of alignment and registration of block copolymers in an inhomogeneous electric field by computer simulations of a soft, coarse-grained model. The two blocks of the symmetric diblock copolymers are characterized by different dielectric constants. First, we demonstrate that a combination of graphoepitaxy and a homogeneous electric field extends the maximal distance between the topographical guiding patterns that result in defect-free ordering compared to graphoepitaxy alone. In a second study, the electric field in the thin block copolymer film is fabricated by spatially structured electrodes on an isolating substrate arranged in a one-dimensional periodic array; no additional topographical guiding patterns are applied. The dielectrophoretic effect induces long-range orientational order of the lamellae and, additionally, registers the lamellar structure with the electrodes due to the field inhomogeneities at the edges of the structured electrodes. Thus, orientational and translational order is established by the inhomogeneous electric field. The simulations identify a process protocol of time-dependent electric potentials that suppresses defect formation by initially forming a sandwich-like structure and subsequently reorienting these lying into standing lamellae that are registered with the structure of the electrodes. This process-directed self-assembly results in large defect-free arrays of aligned and registered lamellae using electrodes with a saw-tooth period of 4 lamellar periodicities, L0, and a spacing of 10L0.

A surface interaction model for self-assembly of block copolymers under soft confinement.

The surface interaction between substrates and block copolymers is one of the most important factors that control the alignment of self-assembled domains under thin film confinement. Most previous studies simply modeled substrates modified by grafting polymers as a hard wall with a specified surface energy, leading to an incomplete understanding of the role of grafted polymers. In this study, we propose a general model of surface interactions where the role of grafted polymers is decomposed into two independent contributions: the surface preference and the surface softness. Based on this model, we perform a numerical analysis of the stability competition between perpendicular and parallel lamellae of symmetric diblock copolymers on substrates modified by homopolymers using self-consistent field theory. The effects of the surface preference and the surface softness on the alignment of lamellar domains are carefully examined. A phase diagram of the alignment in the plane of the surface preference parameter and the surface softness parameter is constructed, which reveals a considerable parameter window for preparing stable perpendicular lamellae even on highly preferential substrates.

Phase Behavior of Diblock Copolymer–Homopolymer Ternary Blends: Congruent First-Order Lamellar–Disorder Transition

We have established the existence of a line of congruent first-order lamellar-to-disorder (LAM–DIS) transitions when appropriate amounts of poly(cyclohexylethylene) (C) and poly(ethylene) (E) homopolymers are mixed with a corresponding compositionally symmetric CE diblock copolymer. The line of congruent transitions, or the congruent isopleth, terminates at the bicontinuous microemulsion (BμE) channel, and its trajectory appears to be influenced by the critical composition of the C/E binary homopolymer blend. Blends satisfying congruency undergo a direct LAM–DIS transition without passing through a two-phase region. We present complementary optical transmission, small-angle X-ray scattering (SAXS), transmission electron microscopy (TEM), and dynamic mechanical spectroscopy (DMS) results that establish the phase behavior at constant copolymer volume fraction and varying C/E homopolymer volume ratios. Adjacent to the congruent composition at constant copolymer volume fraction, the lamellar and disordered ph...

INTERRELATIONS BETWEEN MORPHOLOGY AND SOFTENING BEHAVIOR IN SELF-ASSEMBLED POLY (BUTADIENE-BLOCK-(STYRENE-STAT-BUTADIENE)) COPOLYMERS

ABSTRACTTwo series of poly(butadiene-block-(styrene-stat-butadiene) (PB-SBR) diblock copolymers were synthesized to study interrelations between microphase-separated state and relaxation dynamics. Series I consists of six symmetric PB-SBR samples (ΦSBR ∼ 0.50) with different styrene contents in the random SBR block (21 mol% ≤ xS,SBR ≤ 52 mol%). Series II contains six asymmetric PB-SBR diblock copolymers with almost constant styrene content in the SBR block (xS,SBR = 32 ± 4 mol%) and SBR volume fractions in the range of 0.20 ≤ ΦSBR ≤ 0.69. All PB-SBR diblock copolymers have a total molecular weight of about 200 kg/mol with 1,2-vinyl content of about 8.5 and 15.8 mol% in the soft PB and in the hard SBR block, respectively. A novel synthesis route has been developed so as to maintain low 1,2-vinyl contents in both blocks and a random distribution of the styrene units in the SBR block. The softening behavior of non–cross-linked PB-SBR diblocks was investigated by differential scanning calorimetry, providing first information about miscibility. The morphology of cross-linked PB-SBR diblock copolymers, which have been vulcanized with sulfur at 150 °C using standard procedures, was studied by atomic force microscopy. Dynamic shear measurements aimed at understanding the influence of morphological changes on the segmental dynamics of both phases, αPB and αSBR, were performed on vulcanized samples. Atomic force microscopy results and shear data indicate that symmetric diblock copolymers with styrene content higher than 27 mol% in the SBR block are well microphase separated. Strongly segregated states are also observed for asymmetric diblock copolymers with volume fractions 0.28 ≤ ΦSBR ≤ 0.60 showing cylindrical and lamellar morphologies. The origin of changes in the αPB and αSBR dynamics depending on morphology and segregation strengths is considered. Implications for the use of rubbery PB-SBR block copolymers in composites for tire treads are discussed.

Effect of wall potential on morphology of symmetric diblock copolymers in nanotrench

We have investigated the morphology of symmetric poly(styrene-b-methyl methacrylate) (PS-b-PMMA) diblock copolymers in narrow trenches by performing Monte Carlo (MC) simulations. We considered two types of interactions between the PMMA-attractive trench walls and the PS-b-PMMA. First, an exponential-type wall potential was applied to the PMMA segments to attract them to the wall, which has been widely used for the coarse-grained MC model. In the second case, only the PMMA blocks initially located near the trench wall were adsorbed to the wall. In both cases, the number of the PMMA lamellae was step-wisely increased each time the trench was widened by ∼1.0L0 (L0: lamellae period in the bulk). However, due to its considerably thin PMMA layer, the trench width in the second case had ∼0.7L0 offset from that in the first case. These results imply the importance of interfacial characterization between the diblock copolymers and the trench walls.

Confinement effects on the miscibility of block copolymer blends.

Thin films of long and short symmetric AB diblock copolymers are examined using self-consistent field theory (SCFT). We focus on hard confining walls with a preference for the A component, such that the lamellar domains orient parallel to the film with an even number ν of monolayers. For neat melts, confinement causes the lamellar period, D, to deviate from its bulk value, Db, in order to be commensurate with the film thickness, i.e., L = νD/2. For blends, however, the melt also has the option of macrophase separating into ν(l) large and ν((s)) small monolayers so as to provide a better fit, where L = ν(l)D(l)/2 + ν(s)D((s))/2. In addition to performing full SCFT calculations of the entire film, we develop a semi-analytical calculation for the coexistence of thick and thin monolayers that helps explain the complicated interplay between miscibility and commensurability.

Research Update: Triblock copolymers as templates to synthesize inorganic nanoporous materials

This review focuses on the application of triblock copolymers as designed templates to synthesize nanoporous materials with various compositions. Asymmetric triblock copolymers have several advantages compared with symmetric triblock copolymers and diblock copolymers, because the presence of three distinct domains can provide more functional features to direct the resultant nanoporous materials. Here we clearly describe significant contributions of asymmetric triblock copolymers, especially polystyrene-block-poly(2-vinylpyridine)-block-poly(ethylene oxide) (abbreviated as PS-b-P2VP-b-PEO).

Influence of substrate interaction and confinement on electric-field-induced transition in symmetric block-copolymer thin films.

In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.

Self-assembly of symmetric rod-coil diblock copolymers in cylindrical nanopore

Self-assembly of rod-coil (RC) symmetric diblock copolymers (DBCs) in a cylindrical nanopore is investigated by performing dissipative particle dynamics simulation.

Tuning phase structures of a symmetrical diblock copolymer with a patterned electric field.

Electric fields can induce the orientation of the phase interfaces of block copolymers and provide a potential method to tune polymer phase structures for nanomaterial manufacture. In this work, we applied self-consistent field theory to study the self-assembly of a diblock copolymer confined between two parallel neutral substrates on which a set of electrodes was imposed to form a patterned electric field. The results showed that an alternatively distributed electric field can induce the formation of a parallel lamellar phase structure, which exists stably only in the system with selective substrates. The phase structure was proved to be sensitive to the characteristics of the electric field distribution, such as the strength of the electric field, the size and position of the electrodes, and the corresponding phase diagram was calculated in detail. The transition pathway of the phase structure from the perpendicular layered phase to the parallel layered phase was further analysed using the minimum energy path method. It is shown that the path and the active energy barrier of the phase transition depend on the electric field strength. Compound electric field patterns that can be designed to control the formation of novel and complex microphase structures were also examined.

On the order-disorder transition of compressible diblock copolymer melts.

We performed both the fast off-lattice Monte Carlo simulations of symmetric diblock copolymers (DBC) in an isothermal-isobaric ensemble and the self-consistent field calculations of asymmetric DBC to properly determine the order-disorder transition (ODT) of a model system of compressible DBC melts used in the literature when it is a first-order phase transition, and studied for the first time the co-existence of the two phases at ODT. We found that the co-existing region is quite small and decreases as the system becomes less compressible, which justifies the previous ODT results obtained by equating the Helmholtz free energy per chain of the two phases. We also found that for the most compressible system where there is no repulsion between the same type of segments, the self-consistent field theory predicts that ODT is a second-order phase transition even for asymmetric DBC melts due to its mean-field approximation.

Boundary Tension Between Coexisting Phases of a Block Copolymer Blend

Self-consistent field theory (SCFT) is used to evaluate the excess free energy per unit area (i.e., tension) of different boundaries (or interfaces) between the coexisting phases of a block copolymer blend. In this first study of its kind, we focus on the boundaries separating the short- and long-period lamellar phases that form in mixtures of small and large symmetric diblock copolymers of polymerizations Ns and Nl, respectively, when Ns ≪ Nl. According to strong-segregation theory (SST), the tension is minimized when both sets of lamellae orient parallel to the boundary, but experiments [Hashimoto, , Macromolecules 1994, 27, 1562] tend to observe kink boundaries instead, where the domains of one lamellar phase evolve continuously into those of the other lamellar phase. Our more refined SCFT calculations, on the other hand, do predict a lower tension for the kink boundary consistent with the experimental observations. For completeness, we also examine the boundaries that form when the short-period lamellar phase disorders, and again the SCFT results are in agreement with experiment.

Self-assembly of lamella-forming diblock copolymers confined in nanochannels: Effect of confinement geometry**Project supported by the National Natural Science Foundation of China (Grant Nos. 11204215, 51302187, 20990234, 20925414, 21204040, and 91227121), the Natural Science Foundation of Tianjin City, China (Grant Nos. 12JCYBJC32500 and 14JCZDJC32100), the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (Grant No. IRT1257), and the

The self-assembly of symmetric diblock copolymers confined in the channels of variously shaped cross sections (regular triangles, squares, and ellipses) is investigated using a simulated annealing technique. In the bulk, the studied symmetric diblock copolymers form a lamellar structure with period LL. The geometry and surface property of the confining channels have a large effect on the self-assembled structures and the orientation of the lamellar structures. Stacked perpendicular lamellae with period LL are observed for neutral surfaces regardless of the channel shape and size, but each lamella is in the shape of the corresponding channel's cross section. In the case of triangle-shaped cross sections, stacked parallel lamellae are the majority morphologies for weakly selective surfaces, while morphologies including a triangular-prism-shaped B-cylinder and multiple tridentate lamellae are obtained for strongly selective surfaces. In the cases of square-shaped and ellipse-shaped cross sections, concentric lamellae are the signature morphology for strongly selective surfaces, whereas for weakly selective surfaces, stacked parallel lamellae, and several types of folding lamellae are obtained in the case of square-shaped cross sections, and stacked parallel lamellae are the majority morphologies in the case of ellipse-shaped cross sections when the length of the minor axis is commensurate with the bulk lamellar period. The mean-square end-to-end distance, the average contact number between different species and the surface concentration of the A-monomers are computed to elucidate the mechanisms of the formation of the different morphologies. It is found that the resulting morphology is a consequence of competition among the chain stretching, interfacial energy, and surface energy. Our results suggest that the self-assembled morphology and the orientation of lamellae can be manipulated by the shape, the size, and the surface property of the confining channels.

Influence of Composition Fluctuations on the Linear Viscoelastic Properties of Symmetric Diblock Copolymers near the Order-Disorder Transition.

Rheological evidence of composition fluctuations in disordered diblock copolymers near the order-disorder transition (ODT) has been documented in the literature over the past three decades, characterized by a failure of time-temperature superposition (tTS) to reduce linear dynamic mechanical spectroscopy (DMS) data in the terminal viscoelastic regime to a temperature-independent form. However, for some materials, most notably poly(styrene-b-isoprene) (PS-PI), no signature of these rheological features has been found. We present small-angle X-ray scattering (SAXS) results on symmetric poly(cyclohexylethylene-b-ethylene) (PCHE-PE) diblock copolymers that confirm the presence of fluctuations in the disordered state and DMS measurements that also show no sign of the features ascribed to composition fluctuations. Assessment of DMS results published on five different diblock copolymer systems leads us to conclude that the effects of composition fluctuations can be masked by highly asymmetric block dynamics, thereby resolving a long-standing disagreement in the literature and reinforcing the importance of mechanical contrast in understanding the dynamics of ordered and disordered block polymers.

Universal Phenomenology of Symmetric Diblock Copolymers near the Order–Disorder Transition

We present a simulation study of how properties of symmetric diblock copolymers depend on the invariant degree of polymerization N̅, focusing on the vicinity of the order–disorder transition (ODT). Results from several coarse-grained simulation models are combined to cover a range of N̅ ≃ 200–8000 that includes most of the experimentally relevant range. Results are presented for the free energy per chain, the value of χeN at the ODT, the latent heat of transition, the layer spacing, the composition profile, and compression modulus in the ordered phase. Universality (i.e., model independence) is demonstrated by showing that equivalent results for all properties are obtained from corresponding thermodynamic states of different simulation models. Corresponding states of symmetric copolymers are states with equal values of the parameters χeN and N̅, where χe is an effective Flory–Huggins interaction parameter and N is a degree of polymerization. The underlying universality becomes apparent, however, only if data are analyzed using an adequate estimate of χe, which we obtain by fitting the structure factor in the disordered state to recent theoretical predictions. The results show that behavior near the ODT exhibits a different character at moderate and high values of N̅, with a crossover near N̅ ≃ 104. Within the range N̅ ≲ 104 studied here, the ordered and disordered phases near the ODT both contain strongly segregated domains of nearly pure A and B, in contrast to the assumption of weak segregation underlying the Fredrickson–Helfand (FH) theory. In this regime, the FH theory is inaccurate and substantially underestimates the value of χeN at the ODT. Results for the highest values of N̅ studied here agree reasonably well with FH predictions, suggesting that the theory may be accurate for N̅ ≳ 104. Self-consistent field theory (SCFT) grossly underestimates (χeN)ODT for modest N̅ because it cannot describe strong correlations in the disordered phase. SCFT is found, however, to yield accurate predictions for several properties of the ordered lamellar phase.

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.

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.

Defect removal in the course of directed self-assembly is facilitated in the vicinity of the order-disorder transition.

The stability of prototypical defect morphologies in thin films of symmetric diblock copolymers on chemically patterned substrates is investigated by self-consistent field theory. The excess free energy of defects and barriers of defect-removal mechanisms are obtained by computing the minimum free-energy path. Distinct defect-removal mechanisms are illustrated demonstrating that (i) defects will become unstable at a characteristic value of incompatibility χN* above the order-disorder transition and (ii) the kinetics is accelerated at weak segregation. Numerical findings are placed in the context of physical mechanisms, and implications for directed self-assembly are discussed.