Session X25: Block Copolymer Phase Behavior

Molecular Simulation of Bicontinuous Phases in Diblock Copolymer Melts

Molecular simulations are used to study the stabilization of different bicontinuous phases in diblock copolymer (DBC) melts. The stabilization approach entails attempting to reduce the packing frustration inside the bicontinuous phases nodes by the addition of a ``filler'' with affinity for the A component. Two different strategies are considered: 1) addition of selective-solvent particles, and 2) addition of homopolymer. Approximate phase boundaries were found via free-energy calculations. A very dissimilar phase behavior is observed upon increasing the amount of the ``additive'' in the two different strategies. While with the first strategy (i.e., addition of selective solvent) we observed the progression Gyroid (G) $\to $ Perforated Lamella $\to $ Lamella $\to $ Reversed-Gyroid. With the second strategy (i.e., addition of homopolymer) we observed the progression of morphologies G $\to $ Cylinder $\to $ Double Diamond (DD) $\to $ Plumber's Nightmare (P). In both the DD and the P phases, the homopolymer concentrates preferentially in the nodes, suggesting the reduction of the nodes' packing frustration. In addition, a novel morphology was observed, wherein cylinders of two different diameters alternate in a tetragonal packing. The contrasting difference in the phase behavior observed for the two strategies is understood as a consequence of the difference in mixing entropy exhibited by the two additives.   

Orthorhombic \textit{Fddd} Network in Diblock Copolymer Melts

Poly(styrene-\textit{block}-polyisoprene) (S-I) diblock copolymer melts with asymmetric volume fraction are shown to form an orthorhombic \textit{Fddd} network structure, which Tyler et al. predicted with self-consistent field theory for diblock copolymer melts. The studies with small-angle X-ray scattering and transmission electron microscopy revealed that the phase diagram of the S-I diblock copolymer exhibits the sequence of transition of disorder-gyroid-\textit{ Fddd}-lamellae with decreasing temperature and \textit{Fddd} phase appears within the narrow composition and temperature range where gyroid, lamellae, and hexagonally perforated layer (HPL) phases appear. The ratio of unit cell parameters ($a$:$b$:$c)$ estimated from the peak positions of the scattering function is 1:2.00:3.51, which agrees with the result of the theoretical calculation by Tyler et al. In this orthorhombic structure with the observed unit cell parameters, the higher order reflections 022, and 004 overlaps with the reflection 111 at the first order peak.   

Fluctuation effects in block copolymers

Using recently developed techniques for locating phase transitions, we study the effects of fluctuations in a field theoretic model on block copolymer behavior. Specifically, we couple the use of complex Langevin dynamics within a field theoretic framework and thermodynamic integration techniques for the calculation of free energies of fluctuating systems to show a revised prediction of the diblock copolymer phase diagram. Further, these methods are extended into blend systems to investigate unbinding transitions and critical micelle concentrations in cylindrical phases.   

Scaling of Diblock Copolymer Lamella near the Order Disorder Transition

Our accumulated knowledge of the physics of diblock copolymer phase transitions is extensive after decades of intense interest. There are, however, several inconsistencies between experiment and current theoretical understanding. Notably, one of the simplest measurable parameters, the length-scale of microphase separation, falls significantly out of agreement with theory near the order disorder transition (ODT). This length scales as $(\chi N) ^{m}$ where $\chi$ is the Flory- Huggins interaction parameter and $N$ is the number of monomers – experiments yield $m=0.8$ while theory predicts $m = 1$. We use optical microscopy to make real space measurements of the thickness of symmetric polystyrene - block - poly (2 vinyl pyridine), which we find to scale linearly - as predicted by theory. Our experiment suggests two simple optical methods for the measurement of $\chi$.   

Self-assembly of Asymmetric Architectures: Study of the Phase Behavior of an ABAC Block Copolymer

We have investigated the bulk phase behavior of the asymmetric tetrablock poly(cyclohexylethylene-b-ethylene-b-cyclohexyethylene-b-dimethylsiloxane) (CECD) in order to elucidate the effects of asymmetry created by introducing a third chemically distinct block to the well-studied CEC triblock. These tetrablock polymers are especially attractive due to the potential of degrading the D block, leaving a mechanically robust polyolefin triblock nanoporous material. Starting with CEC triblocks that self-assemble into different morphologies (hexagonally packed cylinders and lamellae), varying amounts of D have been added, creating two series of polymers along distinct isopleths. A combination of small-angle x-ray scattering, transmission electron microscopy and dynamic mechanical spectroscopy have revealed the complex phase behavior of these asymmetric polymers. Addition of as little as nine percent D by volume drastically changes the tetrablock morphological behavior as compared to their precursor CEC triblocks. These promising results exhibit the influence of asymmetry on the self-assembly of complex architectures in block copolymers.   

Soft and Strong Thermoplastic Elastomers Through Molecular Design

Thermoplastic elastomers (TPE) that have a low linear modulus and yet are strong at large extension are of great importance in a variety of technological applications. Current TPE designs based on ABA triblock copolymers are limited in that the maximum volume fraction of the hard A blocks, which correlates with the material strength, is restricted by the constraint that the A domains be discrete while the soft B domains are continuous. In this study, we have investigated new designs of TPEs that utilize polydispersity of the hard blocks in tandem with novel block architectures to control morphology in microphase separated AB block copolymers. Self-consistent field theory calculations confirm that these designs stabilize spherical and cylindrical phases at higher volume fractions of the hard blocks, with the maximum volume fraction of the hard block in some cases approaching twice that of a conventional ABA thermoplastic elastomer.   

Influence of Soft Segment Composition on Phase Separated Microstructure of PDMS-Based Multiblock Polyurethane Copolymers.

Multiblock polyurethane (PU) copolymers with polydimethylsiloxane (PDMS) based soft segments possess intriguing microphase separation behavior and excellent biocompatibility. In this study we investigate the microphase-separated structure of PDMS-PUs with various well-defined soft segment compositions, which is closely connected to the structural and surface properties of these copolymers. The PDMS-PUs are shown to exhibit a three phase, core-shell like morphology. Intra- and intercomponent hydrogen bonding was explored using FTIR spectroscopy and quantitative analysis of hard/soft segment mixing was determined by small-angle X-ray scattering. The presentation will focus on the latest findings, particularly the role of PDMS in controlling the details of the microphase-separated texture.   

Nanoparticle-Regulated Phase Behavior and Morphological Development in an Ordered Block Copolymer

Although microphase-ordered block copolymer motifs are employed to template inorganic nanoparticles, only recently has the effect of nanoparticles on copolymer self-assembly been explored. In this work, we examine the influence of nanoparticles on the copolymer order-disorder transition (ODT) temperature. Theoretical results from a hybrid self-consistent field/density functional theory -- supported by experimental observations of a model copolymer/nanoparticle system -- confirm that judicious selection of nanoparticle size and selectivity can be used to increase the ODT temperature at constant concentration. For a given nanoparticle size and selectivity, we show that there likewise exists a critical nanoparticle concentration beyond which the ODT temperature decreases. The ability of nanoparticles to increase the ODT temperature is a unique consequence of their size and is not expected for small-molecule additives. At high concentrations, the nanoparticles form percolated colloidal networks that represent highly confined environments for the copolymer molecules.   

Effects of Lithium Salts on the Domain Size of Polyethylene Oxide Containing Block Copolymers

The morphology of block copolymers with and without lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salts are measured with small-angle x-ray scattering (SAXS). The block copolymers comprise of polyethylene oxide (PEO), a polymer with a higher dielectric constant that dissolves LiTFSI, and polystyrene (PS), a polymer with a lower dielectric constant that does not dissolve LiTFSI. Due to the hygroscopic nature of the salts, blend preparation is performed completely in a glovebox and the SAXS samples are sealed off in airtight sample holders. To ensure that moisture contamination does not affect morphology, Karl-Fischer titrations are performed after SAXS measurements. Our data will be compared with literature results that indicate a 300{\%} increase in the domain spacing of PEO-containing block copolymers spacing due to the addition of LiTFSI.   

Weak Segregation Theory of Microphase Separation in Block Copolymers: New Results and Perspectives.

The weak segregation theory (WST) of microphase separation in block copolymers (BC) is based on the vision by Landau (1937) and seminal breakthrough by Leibler (1980) into microscopic theory of as well as the Brazovskii-Fredrickson-Helfand (1975, 1987) understanding of the corresponding fluctuation effects. The WST is especially helpful in the situation when one tries to form the well reproducible ordered morphologies, for which purpose they are to be formed as smoothly as possible. Among other new results in this field, I address the following issues: $i)$ non-conventional morphologies and phase transitions in the bulk and confined ternary ABC block copolymers; \textit{ii}) the BC phase diagram control via their chemical modification involving thermoreversible association between the different blocks; \textit{iii}) the WST analysis of the non-centrosymmetric lamellar structures in the blends of the ternary and binary BC; and \textit{iv}) semidulute BC solutions as photonic crystals.   

Tunable Microphase Segregation of Gradient Copolymers: Ordering in Materials with Sinusoidal Composition Profiles

Gradient copolymers are a class of polymers that exhibit a gradual change in composition along the entire chain from mostly A-monomer to mostly B-monomer. Theoretical work has predicted that gradient copolymers organize into sinusoidal composition profiles rather than the step-like profiles seen for block copolymers. Here, small-angle x-ray scattering and rheological studies were performed to investigate the impact of gradient design and comonomer choice on this unique ordering. Samples showed a variety of non-terminal behaviors consistent with their chain architecture relative to block copolymers, indicating highly tunable microphase segregation. Scattering results also demonstrated that a range of ordering was attained, with higher order peaks visible in more microphase-segregated samples. In addition, it was demonstrated for the first time that application of high amplitude oscillatory shear induced domain shear alignment in a manner similar to block copolymers, even though gradient copolymers do not possess distinct domain boundaries.   

Polydispersity effects in block copolymer melts

We examine the effects of polydispersity on the phase behavior of diblock copolymer melts using self-consistent field theory (SCFT). The calculations are performed with an efficient spectral-based algorithm that can handle high degrees of polydispersity with only a modest increase (i.e., a factor of 2 or 3) in computational cost over that of monodisperse melts [Matsen, EPJE, {\bf 21}, 199 (2006)]. We find that even small degrees of polydispersity can have a significant effect on the domain sizes and the position of the phase boundaries. For large polydispersities, fractionation also becomes important and the phase diagram develops large two-phase coexistence regions [Matsen, PRL, {\bf 99}, 148304 (2007)]. As a consequence, the complex gyroid phase becomes unstable with respect to the coexistence of lamellae and cylinders.   

Polydispersity-Driven Morphological Transitions in ABC Triblock Terpolymers

The use of synthetic polymerization techniques (e.g., controlled radical polymerizations) that often yield polydispersity indices greater than 1.1 is becoming more widespread. Advances in these methodologies have increased the number of monomers amenable to incorporation in block copolymers and will potentially drive commercial costs down. Since many block copolymer properties are governed by the underlying mesostructure, understanding the influence of polydispersity on morphological behavior should prove vital to the success of block copolymer commercialization efforts. This presentation will focus on polydispersity-driven morphological transitions in poly(isoprene-$b$-styrene-$b$-ethylene oxide) (ISO) triblock terpolymers. ISO triblocks with polydisperse polystyrene blocks were prepared by anionic polymerization and their morphological behavior was characterized using small-angle x-ray scattering and dynamic mechanical spectroscopy. Only lamellar microstructures were identified along the f$_{I }$= f$_{S}$ isopleth for polydisperse ISO triblocks, while an orthorhombic network (O$^{70})$ was previously identified in monodisperse ISO triblocks.   

Scaling of the ODT of Block Copolymers in Compressed CO$_{2}$

It is well-known that diblock copolymers with sufficient $\chi N$ form periodic microphase-separated domains upon cooling through an order-disorder transition (ODT). We have investigated the scaling behavior of the ODT as a function of polymer volume fraction, \textit{$\phi $}, of several nearly symmetric poly(styrene-$b$-2-vinylpyridine) and poly(styrene-$b$-isoprene) diblock copolymer/diluent systems in relation to the well-known dilution approximation. Using compressed CO$_{2}$ in the place of conventional liquid diluents allowed$_{ }$the determination of the scaling parameter, \textit{$\alpha $}, for highly concentrated systems where \textit{$\phi $ }ranges from 0.85 to 1.0 at high temperatures. The scaling was determined by combining optical birefringence measurements of the ODT ($\chi _{ODT})$ with the ellipsometric swelling measurements (\textit{$\phi $}) of the constituent homopolymers at increasing CO$_{2}$ pressures. We show that sorption of small volume fractions of CO$_{2}$ results in significant reductions in the observed ODTs. Yet, \textit{$\alpha $ }was clearly shown not to be universal even for a specific diblock copolymer. For styrene-b-isoprene copolymers, it appears that \textit{$\alpha $ }is an increasing function of copolymer molecular weight. In contrast, the styrene-b-2-vinylpyridine copolymers studied show no obvious correlation with molecular weight, with \textit{$\alpha $ } taking on both positive and negative values.   

Pressure Effect on Phase Behavior of Weakly Interacting Block Copolymers by using FTIR spectroscopy

Hydrostatic pressure effect on the phase transition of polystyrene-block-poly(n-pentyl methacrylate) [PS-b-PnPMA] copolymer was investigated by FTIR spectroscopy. The size of closed-loop consisting of both the lower disordered-to-ordered transition and the upper ordered-to-disordered transition became smaller with increasing pressure. The functional groups belonging to the PnPMA block are much more sensitive to pressure compared with those belonging to the PS block. The sensitivity of the functional groups change with pressure is different from that with temperature.