Phase Behavior Of Diblock Copolymers Research Articles

Cylindrically confined assembly of diblock copolymer under oscillatory shear flow

Manipulating the self-assembly nanostructures with combined different control measures is emerging as a promising route for numerous applications to generate templates and scaffolds for nanostructured materials. Here, the two different control measures are a cylindrical confinement and an oscillatory shear flow. We study the phase behavior of diblock copolymer confined in nanopore under oscillatory shear by considering different $D/L_0$ ($D$ is the diameter of the cylindrical nanopore, $L_0$ is the domain spacing) and different shears via Cell Dynamics Simulation. Under different $D/L_0$, in the system occurs different morphology evolution and phase transition with the changing of amplitude and frequency. Meanwhile, it forms a series of novel morphologies. For each $D/L_0$, we construct a phase diagram of different forms and analyze the reason why the phase transition occurs. We find that although the morphologies are different under different $D/L_0$, the reason of the phase transition with the changing of amplitude and frequency is roughly the same, all caused by the interplay of the field effect and confinement effect. These results can guide an experimentalist to an easy method of creating the ordered, defect-free nanostructured materials using a combination of the cylindrical confinement and oscillatory shear flow.

Thermosensitive copolymer synthesized by controlled living radical polymerization: Phase behavior of diblock copolymers of poly(N‐isopropyl acrylamide) families

ABSTRACTIn this study, we prepared a series of thermosensitive polymers with low polydispersity index (PDI) values by nitroxide‐mediated controlled radical polymerization (NMRP) with 2,2,6,6‐tetramethyl‐1‐piperdinyloxy nitroxide (TEMPO) as a stable nitroxide‐free radical. Poly(N‐isopropyl acrylamide) (PNIPAAm)‐block‐poly(N‐tert‐butyl acrylamide) (PNTBA) was successfully synthesized, first, through polymerization with N‐isopropyl acrylamide to obtain the reactive polymer PNIPAAm‐TEMPO and, second, through polymerization by the addition of N‐tert‐butyl acrylamide (NTBA). The added molar fraction of NTBA during the second polymerization was adjusted accordingly to obtain the final polymerization product, a thermosensitive polymer (PNIPAAm‐block‐PNTBA), which had a targeted lower critical solution temperature (LCST). The result shows that the synthesis method used in this study effectively controlled the formation of the polymer to obtain a low PDI. The thermosensitive block copolymer, PNIPAAm‐b‐PNTBA (molar ratio = 9:1), with LCSTs in the range 27.7–39.8°C, was obtained through controlled living radical polymerization with PNIPAAm–TEMPO. Specifically, the 5 wt % aqueous solution of PNIPAAm‐b‐PNTBA (molar ratio = 9:1) had an LCST of 37.4°C; this was close to body temperature, 37°C. The 5 wt % aqueous solution of PNIPAAm‐b‐PNTBA (molar ratio = 9:1) showed potential for use in biomedical applications. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43224.

Effect of curvature on properties of diblock copolymers confined between two coaxial cylinders: 2. Domain adjustment in a curved bilayer

We study the phase behavior of diblock copolymers in a curved bilayer. Three aspects are discussed in detail: domain size distributions of the two adjacent monolayers within the film, optimal film thickness for a bilayer, and structural transition from a monolayer to a bilayer. One major finding is the determination of transition point in film thickness where the layer-type structure goes from monolayer to bilayer. At high confinement, the transition point increases as the curvature increases regardless of the symmetry of diblock copolymers. At low confinement, the transition point might increase or decrease, depending on the symmetry of diblock copolymers.

Nanoscale Phase Separation in Sequence-Defined Peptoid Diblock Copolymers

Microphase-separated block copolymer materials have a wide array of potential applications ranging from nanoscale lithography to energy storage. Our understanding of the factors that govern the morphology of these systems is based on comparisons between theory and experiment. The theories generally assume that the chains are perfectly monodisperse; however, typical experimental copolymer preparations have polydispersity indices (PDIs) ranging from 1.01 to 1.10. In contrast, we present a systematic study of the relationship between chemical structure and morphology in the solid state using peptoid diblock copolymers with PDIs of ≤1.00013. A series of comb-like peptoid block copolymers, poly(N-2-(2-(2-methoxyethoxy)ethoxy)ethylglycine)-block-poly(N-(2-ethylhexyl)glycine) (pNte-b-pNeh), were obtained by solid-phase synthesis. The number of monomers per chain was held fixed at 36, while the volume fraction of the Nte block (ϕNte) was varied from 0.11 to 0.65. The experimentally determined order-disorder transition temperature exhibited a maximum at ϕNte = 0.24, not ϕNte = 0.5 as expected from theory. All of the ordered phases had a lamellar morphology, even in the case of ϕNte = 0.11. Our results are in qualitative disagreement with all known theories of microphase separation in block copolymers. This raises new questions about the intertwined roles of monomer architecture and polydispersity in the phase behavior of diblock copolymers.

Orientational interactions in block copolymer melts: Self-consistent field theory

We study the phase behavior of diblock copolymer melts with one block possessing orientation-dependent segmental interactions using self-consistent field theory. A generalized coarse-grained description is introduced based on the local (polar) orientational order parameter and K, an effective Frank elastic constant for orientational gradients. To explore the role played by orientational interactions in assembly thermodynamics, we apply the theory to two-dimensional melt morphologies for a range of K. As microphase segregation necessarily introduces splay deformations of the segment orientation, we find that increasing the stiffness K raises the critical χN at the onset of microphase separation. Furthermore, we find that strong orientational interactions in one block give rise to highly asymmetric phase diagrams due to the large penalty for high-splay morphologies, such as the cylindrical phase. Finally, we analyze the costs of inter-segmental splay as well as the size dependence of domain spacing on K based on a strong-segregation picture of morphologies.

Effects of Polydispersity on Phase Behavior of Diblock Copolymers

The influence of polydispersity on the phase behavior of diblock copolymer melts is studied using a self-consistent field theoretic model. A perturbation theory is developed for the polydisperse sy...

Structural Changes of Diblock Copolymer Melts Due to an External Electric Field: A Self-Consistent-Field Theory Study

We study the phase behavior of diblock copolymers in presence of an external electric field. We employ self-consistent field theory and treat the relevant Maxwell equation as an additional self-consistent equation. Because we do not treat the electric field perturbatively, we can examine its effects even when its magnitude is large. The electric field couples to the system's morphology only through the difference between the dielectric constants of the two blocks. We find that an external field aligns a body-centered cubic phase along the (111) direction, reducing its symmetry group to $R{\bar 3}m$. Transitions between this phase and the disordered or hexagonal phases can occur for external electric fields ranging from a minimum to a maximum value beyond which the $R{\bar 3m}$ phase disappears completely. This electric-field range depends on diblock architecture and temperature. We present several cuts through the phase diagram in the space of temperature, architecture and applied field, including one applicable to a system recently studied.

Computer simulation of copolymer phase behavior

Discontinuous molecular dynamics simulation is used to study the phase behavior of diblock copolymers modeled as chains of tangent hard spheres with square shoulder repulsions between unlike species as a function of chain length, volume fraction and interaction strength (χ). The location of the order–disorder transition for a symmetric copolymer is close to the predictions of Fredrickson and Helfand. Our simulation results for packing fractions of 0.35, 0.40, and 0.45 and chain lengths 10 and 20 are summarized in phase diagrams which display disordered, lamellae, perforated lamellae (PL), cylindrical, and BCC spherical (S) phases in the χN versus f plane. These phase diagrams are consistent with phase diagrams from other simulation studies. Contrary to theoretical predictions we observe the PL phase near regions of predicted gyroid stability, and the S phase only in the systems with high packing fraction and long chain length. These discrepancies may be due to the short chain lengths considered, as they are less evident in the 20-bead chains than the 10-bead chains. We examine the structural spacing of the microphases and the variation of that spacing with χN. We also examine the internal energy and entropy and their variation with χN. Our results are consistent with self-consistent field theory results for the strong segregation limit.

Phase Behavior of Diblock Copolymers Dilated with Light Alkanes: Influence of Solvent Compressibility on Upper and Lower Ordering Transitions

The phase behaviors of polystyrene-block-poly(n-butyl methacrylate) (P(S-b-nBMA)) and polystyrene-block-polyisoprene (P(S-b-I)) copolymers were studied in the presence of methane, ethane, propane, butane, and tetradecane. Sorption of the light alkanes induces phase segregation in P(S-b-nBMA), depressing the lower disorder-to-order transition (LDOT). The chain length of the solvent dictates the severity of the depression. At equivalent volume fractions, methane induces the most substantial shift of the LDOT, and as the length of the alkane chain is increased, the degree of the depression is diminished. In contrast to the influence of expanded solvents, dilution of the P(S-b-nBMA) melt with tetradecane slightly increases the miscibility of the segments. In all P(S-b-I)/alkane systems studied, solvent sorption increases the region of miscibility and depresses the upper order-to-disorder transition (UODT). This effect is independent of alkane chain length and depends only on the volume fraction of alkane sorb...

Thermodynamic Behavior of Particle/Diblock Copolymer Mixtures: Simulation and Theory

We investigate the influence of hard nanoparticles on the phase behavior of diblock copolymers. Using Monte Carlo simulations, we obtain phase diagrams as a function of the nanoparticle size and concentration. When the size of the nanoparticles becomes comparable to the radius of gyration of the minority (A) block, we observe the formation of new superstructures, where the particles self-assemble inside the copolymer micelles. We develop a theoretical model, based on the strong segregation limit approximation, and show that these self-assembled structures can be either stable or metastable, depending on the particle size and volume fraction. The formation of such phases is due to the interplay between the particle−particle excluded-volume interactions, preferential particle/block-A interactions, and the enthalpic and stretching interactions within the diblock.

Phase Behavior of Diblock Copolymers between Styrene and n-Alkyl Methacrylates

In contrast to most diblock copolymers which exhibit the classical upper critical ordering transition (UCOT), polystyrene-b-poly n-butyl methacrylatePS-b-PBMAhas been shown to undergo ordering upon heating through a lower critical ordering transition (LCOT). Here we report the phase behavior of a family of diblock copolymers formed from styrene and a homologous series of n-alkyl methacrylates, as determined by combined dynamic rheological testing and small-angle neutron scattering (SANS). It is shown that the shortest side chain methacrylates, with the exception of methyl methacrylate, exhibit the LCOT, while for side chains longer than n-butyl, the copolymers exhibit the classical UCOT behavior. Combined group contribution/lattice fluid model calculations of the solubility parameter and specific volume of the corresponding homopolymers qualitatively support these observations. The same calculations were further employed to molecularly design LCOT behavior into a new diblock material consisting of styrene and a random copolymer of methyl and lauryl methacrylate, denoted PS-b-P(MMA-r-LMA). The success of this approach suggests a simple semiquantitative method for predicting and designing the phase behavior of weakly interacting polymer pairs.

Phase behavior of diblock copolymers; pressure and temperature dependence studied by small‐angle neutron scattering

AbstractThe structure factor of a poly(ethylene‐propylene)poly(dimethylsiloxane) diblock copolymer has been measured by SANS as a function of temperature and pressure. In contradiction to the random phase approximation the conformational compressibility exhibits a pronounced maximum at the order‐disorder phase transition. The phase boundary shows an unusual shape: with increasing pressure it first decreases and then increases. Its origin is an increase in, respectively, the entropic and the enthalpic part of the Flory‐Huggins interaction parameter. The Ginzburg parameter describing the limit of the mean‐field approximation is not influenced by pressure.

Complex layered phases in asymmetric diblock copolymers

The phase behavior of diblock copolymers near the order-disorder transition is studied using transmission electron microscopy, small-angle neutron scattering (SANS) and dynamical mechanical spectroscopy. For a series of polyolefin diblocks with volume fraction, f1, of the block with the larger segment length in the range f1 = 0.63 - 0.75, we find that the transition from lamellae to hexagonally packed cylinder phases occurs via intermediate layered phases that are always characterized by in-plane hexagonal order. One class of diblock forms a hexagonally modulated lamellar (HML) phase, then a hexagonally perforated layer (HPL) phase upon heating from lamellae, while another class forms a modulated hexagonally packed cylinder phase from the HML phase. We attempt to rationalize this based on the differences in inter-layer ordering in the HML phase evidenced by SANS patterns. Detailed phase diagrams for the diblocks depend on molecular weight, and a conformational asymmetry parameter, which is discussed. These results are similar to those found in certain smectic liquid crystal polymorphs, suggesting an analogy between thermotropic liquid crystalline behavior and the intermediate layered phases of diblock copolymer melts.

Self-consistent mean field theory of the microphases of diblock copolymers

Using self-consistent mean field theory, the phase behavior of diblock copolymers was examinedfrom the weak to the strong segregation regimes, considering spherical, cylindrical, and lamellar microphases. It was shown that the phase diagram depends on three quantities: χrc where rc is an effective degree of polymerization, the relative volume fractions of each block, and e= (ρ 0B b B 2 )/(ρ 0A b A 2 ) where ρ 0P and b p are the pure component density and Kuhn length for each block. The phase diagram, domain sizes and density profiles were calculated for e= 1.