Phase Behavior Of Block Copolymers Research Articles

Side chain effect on the self-assembly of coil-comb copolymer by self-consistent field theory in two dimensions

The phase behavior of coil-comb copolymers A–(Bm+1Cm) (side chain number m = 1–5) is investigated by real-space self-consistent field theory (SCFT). Depending on the copolymer composition and architecture, eight two-dimensional ordered phases are observed, including two-color lamellae (LAM2), three-color lamellae (LAM3), hexagonal cylinders (HEX), core–shell hexagonal phase (CSH), hexagon outside hexagonal phase (HEX2), two interpenetrating tetragonal phase (TET2), lamellae with beads inside (LAM + BD), and lamellae with core–shell beads (LAM3 + CSB). When the volume fractions are comparable, i.e., fA ≈ fB ≈ fC, LAM_3 phase is found to be stable for m = 1 while the hexagonal phases (core–shell hexagonal phase CSH or hexagon outside hexagonal phase HEX2) are stable if m > 1. The phase region of the hexagonal phases HEX, CSH or HEX2 enlarges with increasing m. For short coil length, such as fA = 0.1, the phase diagram is complex, especially when m = 1. For longer coil length, the lamellae become the dominant phase. The phase transition from lamellar phase to hexagonal phase is observed with the increase of the side chain length when the side chain number m is large, which is in agreement with the experimental results. Our results give a good way to tailor the phase behavior of block copolymer and are very useful to further study the hierarchical structure of the coil-comb block copolymer.

Computational modeling of block‐copolymer directed self‐assembly

ABSTRACTDirected self‐assembly (DSA) is a potentially promising method of writing lithographic patterns on a sub‐40 nm length‐scale. While the utility of DSA has been demonstrated in principle, there are many challenges that need to be solved before its wide adoption in the semiconductor industry. Computational modeling is crucial in addressing many of those challenges, for example, optimizing polymer formulations, producing a better pattern, or predicting the defect density. In particular, the use of mesoscale approaches such as Self‐Consistent Field Theory (SCFT), coarse‐grained Monte Carlo, coarse‐grained Molecular Dynamics, and Dynamic Density Functional Theory (DDFT) to describe polymer morphology—both bulk and in confinement—is now widespread. These models are used to predict phase behavior of block copolymers in thin films (undirected self‐assembly), as well as in cases of chemo‐ and graphoepitaxy (DSA). In the near future, modeling is expected to be an integral part of formulation design and screening process. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 90–95

Shear‐Induced Orientation of Gyroid PS‐b‐P4VP(PDP) Supramolecules

The phase behavior of block copolymer based supramolecular complexes polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) and amphiphilic pentadecylphenol (PDP) molecules resembles the phase behavior of conventional block copolymers. Several PS-b-P4VP(PDP) complexes are found to self-assemble into gyroid nanostructures. Typically, the grains are randomly oriented with a maximal size of several micrometers. Here, the orientation of a gyroid PS-b-P4VP(PDP) complex upon shearing is reported. It is found that the (111) gyroid lattice direction orients parallel to the shear direction after only several seconds of large amplitude oscillatory shearing. Oriented gyroid complexes can be used as templates for the preparation of metal nanofoams with improved ordering with potentially superior properties.

A Strategy to Explore Stable and Metastable Ordered Phases of Block Copolymers

Block copolymers with their rich phase behavior and ordering transitions have become a paradigm for the study of structured soft materials. A major challenge in the study of the phase behavior of block copolymers is to obtain different stable and metastable phases of the system. A strategy to discover complex ordered phases of block copolymers within the self-consistent field theory framework is developed by a combination of fast algorithms and novel initialization procedures. This strategy allows the generation of a large number of candidate structures, which can then be used to construct phase diagrams. Application of the strategy is illustrated using ABC star triblock copolymers as an example. A large number of candidate structures, including many three-dimensionally ordered phases, of the system are obtained and categorized. A phase diagram is constructed for symmetrically interacting ABC star triblock copolymers.

Features of the phase behavior of block copolymers related to their polydispersity

To calculate cloud points of a melt of block copolymers, at which its microphase separation occurs, for the first time in the theory of polymers, a spectral method is used in a model that takes into account the compressibility of the melt and the polydispersity of its macromolecules. A particular case of this calculation for a copolymer whose macromolecules consist of two blocks is described, and the polydispersity of each of them is defined through the exponential Flory distribution.

One-Pot Synthesis of Block Copolymers in Supercritical Carbon Dioxide: A Simple Versatile Route to Nanostructured Microparticles

We present a one-pot synthesis for well-defined nanostructured polymeric microparticles formed from block copolymers that could easily be adapted to commercial scale. We have utilized reversible addition-fragmentation chain transfer (RAFT) polymerization to prepare block copolymers in a dispersion polymerization in supercritical carbon dioxide, an efficient process which uses no additional solvents and hence is environmentally acceptable. We demonstrate that a wide range of monomer types, including methacrylates, acrylamides, and styrenics, can be utilized leading to block copolymer materials that are amphiphilic (e.g., poly(methyl methacrylate)-b-poly(N,N-dimethylacrylamide)) and/or mechanically diverse (e.g., poly(methyl methacrylate)-b-poly(N,N-dimethylaminoethylmethacrylate)). Interrogation of the internal structure of the microparticles reveals an array of nanoscale morphologies, including multilayered, curved cylindrical, and spherical domains. Surprisingly, control can also be exerted by changing the chemical nature of the constituent blocks and it is clear that selective CO(2) sorption must strongly influence the block copolymer phase behavior, resulting in kinetically trapped morphologies that are different from those conventionally observed for block copolymer thin films formed in absence of CO(2).

Unexpected Consequences of Block Polydispersity on the Self-Assembly of ABA Triblock Copolymers

Controlled/"living" polymerizations and tandem polymerization methodologies offer enticing opportunities to enchain a wide variety of monomers into new, functional block copolymer materials with unusual physical properties. However, the use of these synthetic methods often introduces nontrivial molecular weight polydispersities, a type of chain length heterogeneity, into one or more of the copolymer blocks. While the self-assembly behavior of monodisperse AB diblock and ABA triblock copolymers is both experimentally and theoretically well understood, the effects of broadening the copolymer molecular weight distribution on block copolymer phase behavior are less well-explored. We report the melt-phase self-assembly behavior of SBS triblock copolymers (S = poly(styrene) and B = poly(1,4-butadiene)) comprised of a broad polydispersity B block (M(w)/M(n) = 1.73-2.00) flanked by relatively narrow dispersity S blocks (M(w)/M(n) = 1.09-1.36), in order to identify the effects of chain length heterogeneity on block copolymer self-assembly. Based on synchrotron small-angle X-ray scattering and transmission electron microscopy analyses of seventeen SBS triblock copolymers with poly(1,4-butadiene) volume fractions 0.27 ≤ f(B) ≤ 0.82, we demonstrate that polydisperse SBS triblock copolymers self-assemble into periodic structures with unexpectedly enhanced stabilities that greatly exceed those of equivalent monodisperse copolymers. The unprecedented stabilities of these polydisperse microphase separated melts are discussed in the context of a complete morphology diagram for this system, which demonstrates that narrow dispersity copolymers are not required for periodic nanoscale assembly.

Controlling the phase behavior of block copolymers via sequential block growth

Block copolymers remain one of the most extensively investigated classes of polymers due to their abilities to self-organize into various nanostructures and modify polymer/polymer interfaces. Despite fundamental and technological interest in these materials, only a handful of experimental phase diagrams exist due to the laborious task of preparing such diagrams. In this work, two copolymer series are each synthesized from a single macromolecule via sequential living anionic polymerization to yield molecularly asymmetric diblock and triblock copolymers systematically varying in composition. The phase behavior and morphology of these copolymers are experimentally interrogated and quantitatively compared with predictions from mean-field theories, which probe copolymer phase behavior beyond current experimental conditions.

Thermodynamic Properties of Block Copolymer Electrolytes Containing Imidazolium and Lithium Salts

We report on the thermal properties, phase behavior, and thermodynamics of a series of polystyrene-block-poly(ethylene oxide) copolymers (SEO) mixed with the ionic species Li[N(SO2CF3)2] (LiTFSI), imidazolium TFSI (ImTFSI), and an equimolar mixture of LiTFSI and ImTFSI (Mix). Differential scanning calorimetric scans reveal similar thermal behavior of SEO/LiTFSI and SEO/ImTFSI at the same salt concentrations. Phase behavior and thermodynamics were determined using a combination of small-angle X-ray scattering and birefringence. The thermodynamics of our mixtures can be mapped on to the theory of neat block copolymer phase behavior provided the Flory−Huggins interaction parameter, χ, between the blocks is replaced by an effective χ (χeff) that increases linearly with salt concentration. The phase behavior and the value of m, the slope of the χeff versus salt concentration data, were similar for SEO/LiTFSI, SEO/ImTFSI, and SEO/Mix blends. The theory developed by Wang [J. Phys. Chem. B. 2008, 41, 16205] provides a basis for understanding the fundamental underpinnings of the measured value of m. We compare our experimental results with the predictions of this theory with no adjustable parameters.

Effect of an Ionic Liquid Solvent on the Phase Behavior of Block Copolymers

The phase behavior of concentrated mixtures of block copolymers with an ionic liquid has been studied using a large series of block copolymers with varying molecular weight and volume fraction to gain a thorough understanding of the thermodynamics of self-assembly. The lyotropic phase behavior of mixtures of poly(styrene-block-2-vinylpyridine) (S2VP) copolymers with the ionic liquid imidazolium bis(trifluoromethane)sulfonimide ([Im][TFSI]) is reminiscent of block copolymer/selective molecular solvent mixtures, and ordered microstructures corresponding to lamellae, hexagonally close-packed cylinders, body-centered cubic, and face-centered cubic oriented micelles are observed. Scaling analysis reveals that, in contrast to observations of block copolymer/molecular solvent mixtures, the interfacial area occupied by each S2VP chain decreases upon the addition of [Im][TFSI], indicating a considerable increase in the effective segregation strength of the S2VP copolymer with ionic liquid addition.

Tuning block copolymer phase behavior with a selectively associating homopolymer additive

AbstractWe use polymer random phase approximation (RPA) theory to calculate the microphase separation transition (MST) spinodal for an AB + C diblock copolymer–homopolymer blend where the C homopolymers are strongly attracted to the A segment of the copolymers. Our calculations indicate that one can shift the MST spinodal value of the A − B segmental interaction parameter (χABN)S to significantly lower values [i.e., (χABN)S < 10.5] upon the addition of a selectively attractive C homopolymer. For a sufficiently attractive C homopolymer, (χABN)S can be pushed to negative values, indicating microphase separation in what would appear to be a completely miscible diblock copolymer. Furthermore, we show that microphase separation can occur in diblock copolymer–homopolymer blends where the segmental interactions between all polymer constituents are attractive. By tuning the value of (χABN)S with a homopolymer additive, one is therefore able to tune the effective copolymer segregation strength and thus dramatically affect the blend phase behavior. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2083–2090, 2009

Determining basic thermodynamic properties for some poly(n-alkyl methacrylates)

Polymethacrylates have been known to belong to an intermediate class of materials between commodity and engineering plastics. Those materials are used mainly for glass and molding compounds, and also for dispersions, adhesives, additives, and binders.1 In addition, block copolymers from polymethacrylates and polystyrene are widely used as passive electronic materials and as templates.2–4 Therefore, there is a need for studying the bulk thermodynamic properties of those polymethacrylates and also the phase behavior of block copolymers from them. Basic thermodynamic data such as volumetric properties for the methacrylate polymers are then essential to suffice the need. Once the volume data for given polymeric materials are given, other thermodynamic properties of the materials can be obtained by various thermodynamic relations.

New characterization methods for block copolymers and their phase behaviors

In this feature article, we briefly review the new methods we have utilized recently in the investigation of morphology and phase behavior of block copolymers. We first describe the chromatographic fractionation method to purify block copolymers from their side products of mainly homopolymers or block copolymer precursors inadvertently terminated upon addition of the next monomer in the sequential anionic polymerization. The chromatographic method is extended to the fractionation of the individual block of diblock copolymers which can yield the diblock copolymer fractions of different composition and molecular weight, which also have narrower distributions in both molecular weight and composition. A more detailed phase diagram could be constructed from the set of block copolymer fractions without the need of acquiring many block copolymers each prepared by anionic polymerization. The fractions with narrow distribution in both molecular weight and composition exhibit better long-range ordering and sharper phase transition. Next, epitaxial relationships between two ordered structures in block copolymer thin film is discussed. We employed the direct visualization method, transmission electron microtomography (TEMT) to scrutinize the grain boundary structure.

Self-assembled block copolymers: Bulk to thin film

Block copolymers that two or more polymer chains are covalently linked have drawn much attention due to self-assembly into nanometer-sized morphology such as lamellae, cylinders, spheres, and gyroids. In this article, we first summarize the phase behavior of block copolymers in bulk and thin films and some applications for new functional nanomaterials. Then, future perspectives on block copolymers are described.

Phase Behavior of Symmetric Sulfonated Block Copolymers

Phase behavior of poly(styrenesulfonate-methylbutylene) (PSS-PMB) block copolymers was studied by varying molecular weight, sulfonation level, and temperature. Molecular weights of the copolymers range from 2.9 to 117 kg/mol. Ordered lamellar, gyroid, hexagonally perforated lamellae, and hexagonally packed cylinder phases were observed in spite of the fact that the copolymers are nearly symmetric with PSS volume fractions between 0.45 and 0.50. The wide variety of morphologies seen in our copolymers is inconsistent with current theories on block copolymer phase behavior such as self-consistent field theory. Low molecular weight PSS-PMB copolymers (<6.2 kg/mol) show order−order and order–disorder phase transitions as a function of temperature. In contrast, the phase behavior of high molecular weight PSS-PMB copolymers (>7.7 kg/mol) is independent of temperature. Due to the large value of Flory–Huggins interaction parameter, χ, between the sulfonated and non-sulfonated blocks, PSS-PMB copolymers with PSS and PMB molecular weights of 1.8 and 1.4 kg/mol, respectively, show the presence of an ordered gyroid phase with a 2.5 nm diameter PSS network. A variety of methods are used to estimate χ between PSS and PMB chains as a function of sulfonation level. Some aspects of the observed phase behavior of PSS-PMB copolymers can be rationalized using χ.

Effect of solvents on closed-loop phase behavior of block copolymers

We studied the effect of solvent selectivity on the closed-loop phase behavior of a polystyrene- block-poly( n-pentyl methacrylate) copolymer. It was found that the lower disorder-to-order transition temperature (LDOT) and upper order-to-disorder transition temperature (UODT) consisting of the closed-loop were very sensitive to the selectivity of the solvent. With the addition of very small amounts of non-selective solvents such as di- n-octyl phthalate and dimethyl phthalate, the LDOT increased rapidly, whereas the UODT decreased dramatically; thus, the immiscibility loop was shrunk greatly. On the other hand, both the LDOT and UODT decreased with increasing amount of dodecanol, a highly selective solvent to poly( n-pentyl methacrylate) block. However, the decrease in the LDOT was greater than that of the UODT, leading to an increased immiscibility loop.

Influence of Carbon Dioxide Swelling on the Closed-Loop Phase Behavior of Block Copolymers

The influence of carbon dioxide sorption on the closed-loop phase diagram of polystyrene-block-poly(n-pentyl methacrylate) copolymers, PS-b-PnPMA, was investigated. Differential dilation of the constituent blocks was used to induce microphase separation of the PS-b-PnPMA. With increasing carbon dioxide loading an appreciable expansion in the size of the closed loop was found. At a carbon dioxide activity of 0.1 the upper order-to-disorder transition temperature (UODT) was elevated by more than 20 °C, whereas the lower disorder-to-order transition temperature (LDOT) was depressed by the same magnitude. This arises from the entropic nature of the closed-loop miscibility gap in this weakly interacting system, where microphase separation is driven by disparity in free volumes between dissimilar segments of the chain.

Effect of Dispersion of Inorganic Nanoparticles on the Phase Behavior of Block Copolymers in a Selective Solvent

Effect of Dispersion of Inorganic Nanoparticles on the Phase Behavior of Block Copolymers in a Selective Solvent

A Simple Field-Theoretic Simulation Method for Compressible Block Copolymer Systems

A simple field-theoretic simulation method based on a compressible random-phase approximation (RPA) theory has been suggested to understand the self-assembly behavior and its pressure responses of compressible block copolymer systems. Finite compressibility is incorporated in the free energy functional for the dissipative dynamics through effective RPA interactions that account for the excluded volume and the attractive nonbonded interactions. It was shown that basic equation-of-state parameters completely characterizing given block components readily yield stable and metastable morphologies without any presumed symmetry over a wide range of temperature−pressure−composition space for copolymer melts in unconfined or confined geometry. It was demonstrated that the simulation tool is capable of predicting in a unified way block copolymer phase behavior, not only exhibiting nanoscale ordering either upon cooling or reversely upon heating, but also revealing barotropicity and baroplasticity.

Structure and Phase Behavior of Block Copolymer Melts near the Sphere−Cylinder Boundary

The phase behavior of a poly(styrene-block-isoprene) copolymer (SI) with styrene volume fraction f = 0.18 was studied by small-angle X-ray scattering (SAXS), optical birefringence, and rheology conducted under quiescent conditions and under the influence of shear flow. This sample is located at the border between ordered spheres and ordered cylinders. Near the order−disorder transition, SI block copolymers with f 0.18 form ordered cylinders. Our sample exhibits a phase transition from ordered cylinders to disordered micelles at 70 ± 2 °C. The cylinder phase obtained by a quiescent quench is highly defective and thus cannot be detected using birefringence. However, birefringence measurements made in the presence of shear flow and high-resolution SAXS measurements on both quiescent and sheared samples confirm the presence of ordered cylinders. The data obtained from our sample differs qualitatively from all previously published data on SI copolymers with f = ...