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The development of nanotechnology relies crucially on the ability to fabricate materials with desired nanostructures. Because of their precise side-chain structure and versatile ordered morphologies, side-chain liquid crystalline polymers can provide a novel material platform to obtain sub-10 nm structures via their self-assembly. Here we show that for a newly designed side-chain liquid crystalline (LC) polynorbornene (P1) with a slim hemiphasmid mesogen microphase separation between the main and side chains drives the spontaneous formation of hexagonal columnar phase (Φh) composed of cylinders with a uniform diameter of 8.3 nm. At every cross section of the cylinder there are more than a dozen P1 chains laterally bundled together. The cylinders can grow axially when more chains join in becoming extraordinarily long to over several micrometers. Simple shearing can produce P1 thin films with very good orientation of the Φh phase at the macroscopic scale. More interestingly, we show that directed self-assem...

Block copolymers (BCPs) under nanoscale confinement can self-assemble to form novel nanostructures that are not available in the bulk state. Particularly, the ordering process of block copolymers a...

Quasicrystalline (QC) phases have been observed in various condensed matter systems including self-assembling block copolymer (BCP) melts. Theoretical study of the thermodynamic stability of QC phases presents a long-standing unsolved problem because of the aperiodic nature of the structures. Here, we report a combination method to study the thermodynamic stability of two-dimensional dodecagonal quasicrystalline (DDQC) phase with both ideal tiling and random tiling patterns formed by ABCB tetrablock terpolymers. This method applies the self-consistent field theory coupled with the Stampfli self-similarity construction to accurately calculate the free energy of the periodic DDQC approximants and then uses a cluster model to predict the stability of aperiodic DDQC phase. Surprisingly, we find a stable DDQC approximant but metastable ideal tiling DDQC structures. Moreover, the random tiling DDQC structures as a mesoscopic coexistence of two neighboring periodic substructures of DDQC might become stable.

Well-ordered perpendicular cylinders of star-block copolymers (BCPs) composed of polystyrene and poly(dimethylsiloxane) blocks with high aspect ratio can be achieved by using a combination of architecture effect (entropy effect) and surface air plasma treatment (enthalpy effect). An interesting morphological evolution from disordered texture to hexagonally packed cylinders with perpendicular orientation has been observed, in which perpendicular cylinders are initiated at the top surface and bottom substrate of the thin film, followed by a self-alignment process, resulting in span-thru cylinders through the thin film. The self-alignment process is systematically examined by a combination of real space imaging using transmission electron microscopy, reciprocal space imaging using grazing incidence small-angle X-ray scattering, and three-dimensional tomography. The experimental results reveal a unique mechanism for the formation of highly ordered BCP thin films via surface-induced nucleation of perpendicular...

Controlling the orientation of nanostructured block copolymer (BCP) thin films is essential for next-generation lithography. However, obtaining BCP with perpendicular orientation remains a challenge because of the surface selectivity to the different blocks. This challenge is especially severe for silicon-containing BCPs which is notorious for its high surface energy difference between constituted blocks. Here, we demonstrate a new approach to achieve perpendicular orientation with high aspect ratio using a combination of architecture effect (entropy effect) and surface air plasma treatment (enthalpy effect). Specifically, perpendicular cylinders of star-block copolymers composed of polystyrene and poly(dimethylsiloxane) blocks can be formed from the bottom substrate to the top surface of the thin film.

We report a remarkable sensitivity of self-assembled structures of giant surfactants on their chemical compositions and molecular topology, which facilitate the engineering of various nanophase-separated structures with sub-10 nm feature sizes. Two classes of giant surfactants composed of various functionalized polyhedral oligomeric silsesquioxane (POSS) heads tethered with one or two polystyrene (PS) tails were efficiently prepared from common precursors of vinyl-substituted POSS–PS conjugates via one-step “thiol–ene” postpolymerization functionalization. With identical molecular weights of the PS tails, the resulting giant surfactants exhibited distinct highly ordered phases, as evidenced by small-angle X-ray scattering and transmission electron microscopy observations. Moreover, comparison between the topological isomers revealed that the self-assembled structures are also highly sensitive to molecular topology. Introduction of two PS tails with half-length not only shifted the boundaries between diffe...

Controlling the orientation of nanostructured thin films of block copolymers (BCPs) is essential for next-generation lithography using BCPs. According to conventional wisdom, the orientation of BCP thin films is mainly determined by molecular interactions (enthalpy-driven orientation). Here, we show that the entropic effect can be used to control the orientation of BCP thin films. Specifically, we used the architecture of star-block copolymers consisting of polystyrene (PS) and poly(dimethylsiloxane) (PDMS) blocks to regulate the entropic contribution to the self-assembled nanostructures. The study unequivocally demonstrate that for star-block copolymers with the same volume fractions of PS and PDMS, perpendicularly oriented BCP nanostructures could be induced via an entropic effect regulated by the number of arms. Also, the feasibility of using the star-block copolymer thin films for practical applications is demonstrated by using the thin film as a mask for nanolithography or as a template for the fabri...

The phase behavior of double-hydrophilic AB diblock copolymers in concentrated aqueous solutions is investigated using a simulated annealing technique. Phase diagrams of the system are constructed as a function of the volume fraction and concentration of the copolymer (Φ) as well as the hydrophilicity difference between the two blocks. Rich phase transition sequences, especially reentrant phase transitions, such as lamellae → gyroid → hexagonally packed cylinders → gyroid → lamellae → disorder, are observed for a given copolymer with decreasing Φ. By analyzing the variations of the average contact numbers between the A or B monomers and solvents, and of the effective volume fractions, the mechanisms of the reentrant, the order–order, and the order–disorder transitions are elucidated. The difference in hydrophilicity or in volume fraction can be used to tune the degree of swelling of the two blocks, resulting in a nonmonotonic variation of the effective volume fraction of the A (or B)-rich domain with the ...

The kinetic pathways connecting the lamellar and gyroid phases in weakly segregated block copolymers are examined by combining the string method and the self-consistent mean-field theory for polymers. In particular, phase transition from arbitrarily oriented lamellae to gyroid is studied. The results reveal that initially the lamella will evolve into a metastable structure via a nucleation and growth mechanism, and then a secondary nucleation of the gyroid occurs in the metastable phase. The observed metastable structures include the perforated lamellae (PL), the O70 phase, and the tetragonally perforated layers (TPLabc). Nucleation and growth is the dominant mechanism, and prior phase transition passed by HPLabc, which is a long-lived metastable structure, has the minimal energy barrier.

The self-assembly behaviors of fluorinated polyhedral oligomeric silsesquioxane (FPOSS)-based giant surfactants, consisting of an FPOSS cage and a polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer tail, are studied in the bulk. The tethering point of the FPOSS cage on the PS-b-PEO diblock copolymer chain can be controlled precisely either at the end of the PS block or the junction point between the PS and PEO blocks, resulting in topological isomer pairs with almost identical chemical compositions but different architectures. Phase separation between the FPOSS head and the block copolymer tail creates a spatially confined environment for the PS-b-PEO component, which are uniformly end- or junction-point-immobilized on the FPOSS layer, providing a unique model system to study phase behaviors and chain conformation of tethered diblock copolymer in the condensed state. The polymer tails are highly stretched because the cross-sectional area of FPOSS head is smaller than that of the unperturb...

The phase behavior of linear ABCBA pentablock terpolymers is examined and compared with corresponding linear ABC triblock terpolymers by using the 3-D self-consistent field theory. In particular, phase diagrams of the melts are constructed and used to discuss how the self-assembled morphologies are influenced by the compositions of the three components and the block number per chain. Since the two free ends of A blocks in the ABCBA copolymers enable the macromolecules to relieve the packing frustration within the structures as well as more types of chain conformation, the ABCBA pentablocks exhibit diverse complex network structures and binary crystalline phases of cylinders and spheres. Compared with most linear diblock and triblock copolymers, for which the gyroid phase occupies a narrow region in the phase space, the ABCBA pentablocks tend to form a variety of continuous networks including diamond, hexagonally perforated lamellae, Fddd network, and gyroid. Moreover, the ABCBA pentablocks exhibit differe...

The ordering dynamics of cylinder-forming diblock copolymer/homopolymer blends confined in hexagonal potential wells is systematically investigated using time-dependent Ginzburg–Landau (TDGL) theory. It is demonstrated that a high-efficient method to obtain large-scale ordered hexagonal patterns is to utilize corner-induced heterogeneous nucleation processes, in which nucleation events with controlled positions and orientations are triggered exclusively at the six corners of the confining hexagonal wells. Subsequent growth of the six domains originated from the corners leads to the formation of perfectly ordered patterns occupying the entire hexagonal well. The heterogeneous nucleation rate is regulated by the homopolymer concentration as well as the surface potential of the confining walls. Defect-free hexagonal patterns are obtained in hexagons with a diagonal size containing up to 61 cylinders (about 2 μm). The robustness of the method is examined by studying the tolerance window of the size-commensura...

The phase behavior of binary blends composed of BABCB-type pentablock terpolymers and ABC-type triblock copolymers is investigated using the self-consistent field theory in the grand canonical ensemble. Specifically, the study is focused on how the simpler copolymers regulate the phase behavior of two sphere-forming multiblock copolymers of the type B1AB2CB1 and AB2CB3. For certain compositions, these two multiblock copolymers self-assemble to form mesocrystalline phases composed of binary A and C spheres with the ZnSC and ReO3 structures, respectively. It is discovered that the addition of symmetric ABC triblocks or AB diblocks to the two multiblock copolymers leads to the formation of different binary crystalline phases including symmetric binary crystalline phase of NaCl type for the A/C-component symmetric blends and asymmetric Cu2O, SnI4, TiO2, and CaF2 phases for the A/C-component asymmetric blends. In particular, the binary mesocrystals of the Cu2O and SnI4 structures observed in the blends of the ...

A series of unique heterofunctionalized asymmetric giant “bolaform-like” surfactants composed of a polystyrene (PS) chain end-capped with two distinctly functionalized polyhedral oligomeric silsesquioxane (POSS) cages [one with seven isobutyl groups (BPOSS) and the other with 14 hydroxyl groups (DPOSS)] were designed and synthesized, and their self-assembly behaviors were investigated. Combining the atomic transfer radical polymerization using a BPOSS-containing initiator and the sequential “click” approach, BPOSS-PSn-DPOSS samples with different PS molecular weights were obtained. Investigation on their self-assembly behaviors revealed that they could form a variety of different ordered structures, such as lamellae, double gyroids, hexagonally packed cylinders, and body-center-cubic spheres, with feature sizes around or below 10 nm. Functional groups on the POSS cages govern the interaction parameters of different POSS cages with the PS interconnect and thus their compatibility. Hydrophilic DPOSS cages a...

Blends of AB-diblock copolymers and C-homopolymers (AB/C), in which A and C are capable of forming hydrogen bonds, are used as a model system to examine and validate two approaches for modeling the effects of hydrogen bonding on the phase behavior of polymeric systems. The first model assumes a negative Flory–Huggins parameter between the A/C monomers. This attractive-interaction model reproduces qualitatively correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C-homopolymers. The second model assumes that hydrogen bonding leads to A/C complexation. The interpolymer-complexation model predicts correctly the order–order phase transition sequences and the decrease of lamellar spacing at strong hydrogen bonding. The results demonstrate that hydrogen bonding of polymers should be modeled by the interpolymer-complexation model.

The self-assembling behavior of ABC linear triblock copolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the knitting-pattern (KP) phase. The KP is one of the most intriguing unconventional phases formed from ”frustrated” linear triblock copolymers, where the interaction between the two end blocks is much weaker than those between neighboring blocks. Specifically phase diagrams for linear ABC triblock copolymer melts are constructed by comparing the free energy of about 10 candidate structures, including the knitting patterns, three-color lamellae (L3), core–shell cylinders (CSC), perforated lamellae (PL), cylinders-within-lamellae (LC), triple/quadruple cylinders-on-cylinders (C3/C4), double/triple helices-on-cylinders (H2C/H3C), and perforated circular lamella-on-cylinders (PC). The results of the phase behavior are presented for three cases with increasing complexity of the block copolymers. First of all, we investigate the stable ...

The emergence and stability of superstructured cylindrical phases in frustrated ABC linear triblock copolymers are investigated by the self-consistent field theory. Our results reveal that the complex single/double/triple helices-on-cylinder phases are formed when the straight cylinders-on-cylinder and rings-on- cylinder phases are frustrated due to packing constraints. A free energy comparison indicates that the double and triple helical phases are stable, whereas the other cylinders-on-cylinder phases are metastable. In addition, the chirality and rotation for the helical supercylinders are considered in our calculations. Our theoretical prediction is consistent with a number of experimental observations.

Phase behavior of blends of two AB diblock copolymers, with the long one at relatively strong segregation, is studied using the self-consistent field theory, focusing on the effect of compositions ...

Ordered phases of ABC star terpolymer melts are investigated using a generic reciprocal-space implementation of the self-consistent field theory (SCFT) of polymers. The most important feature of ABC star triblock terpolymers is that their three blocks are joined at one junction point. This distinct topology of ABC star terpolymers constraints the junction points in one-dimensional lines in an ordered phase, resulting novel microphase-separated morphologies such as tiling patterns. Two types of star triblock terpolymers, with symmetric and asymmetric interaction parameters, are studied in detail. A variety of tiling patterns in ABC star terpolymers have been predicted from the SCFT calculation and relevant phase diagrams have been constructed. The predicted phase transition sequences from the SCFT calculations are in qualitative agreement with experimental and Monte Carlo simulation results.

The self-assembly of gyroid-forming diblock copolymers confined in cylindrical geometry is studied using a combination of computer simulations and experiments. The simulations, based on a system qualitatively representative of poly(styrene-b-isoprene), are performed with cylindrical nanopores of different diameter (D) and surface selectivity. The effects of the pore size and surface selectivity on morphology are systematically investigated. Different morphological sequences are predicted for two gyroid-forming diblock copolymers. The experiments are carried out on two gyroid-forming poly(styrene-b-dimethylsiloxane) block copolymer samples confined in the core of continuous core−shell nanofibers of different diameters, which are obtained by a coaxial two-fluid electrospinning technique. The internal microphase-separated morphologies of these fibers are investigated by transmission electron microscopy (TEM). Both simulations and experiments demonstrate that a rich variety of structures spontaneously form for the gyroid-forming diblock copolymers, depending on the conditions of cylindrical confinement. Many of these confinement-induced structures are quite different from those of cylinder-forming or lamella-forming block copolymers. Simulations further show that these structures depend sensitively on the block copolymer composition, surface selectivity, and the ratio D/L0 where L0 is the period of the equilibrium gyroid phase. While the simulation and experimental systems are representative of different chemistries, the morphological predictions of simulations are qualitatively consistent with the experimental observations., Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract DAAD-19-02-D-0002), United States. Army Research Office

The ordering dynamics of directed self-assembly of cylinder-forming diblock copolymers is studied by cell dynamics simulations. The directing field, mimicking chemically or topologically patterned substrates, is in the form of hexagonally arranged potential wells attractive to minority blocks. Time evolution of the defect concentration is used to characterize the ordering dynamics of the self-assembled cylindrical structures of the block copolymers. When the period of the external potential, Ls, is a small integer multiple of the cylinder-to-cylinder distance, L0, of the block copolymer microphase, the defect concentration decays exponentially. The defect annihilation becomes slower as Ls is increased, and eventually, the exponential decay law is broken. When the ratio Ls/L0 is a square root of an integer, large polycrystalline grains with different orientations are observed. The results are consistent with available experimental and theoretical results.

A self-consistent mean-field theory (SCMFT) study on the phase behaviors of AB-diblock copolymer solutions is presented. All of the possible thermodynamically stable ordered structures verified by ...

A new real-space numerical implementation of the self-consistent field theory for semiflexible polymers is developed. Specifically, a finite volume algorithm on a unit sphere with an icosahedron tr...

The phase behavior of ternary homopolymer/gradient copolymer blends is studied theoretically using a multiblock model of gradient copolymers. Critical lines and Lifshitz points of the blends are determined by a random phase approximation analysis. Phase diagrams and microphase structures of the blends are studied using self-consistent mean-field theory. It is discovered that the chain gradient distribution has a significant effect on the phase behavior of the blends. When the chain gradient distribution is gradual, a larger amount of copolymers and a higher incompatibility are needed for the formation of a microphase. In addition, the ability of copolymer domains to absorb homopolymers decreases, whereas the solubility of copolymers in homopolymer matrix increases, as the gradient distribution becomes gradual. Another important effect is that gradient copolymers lead to a broad interface between two incompatible polymers. These results indicate that interfacial structure and morphology of these blends can be fine-tuned by specifically designed gradient distributions.

The phase behavior of A(BC)nBA multiblock copolymer melts is investigated using self-consistent mean-field theory (SCMFT). Solutions of the SCMFT equations corresponding to hierarchical lamellar structures are obtained. The free energy of these structures are used to construct phase diagrams. It is predicted that hierarchical lamellar structures with different number of “internal” BC layers can be formed. The number of BC layers of the stable lamellar structure is determined by the competition between chain entropy and interfacial energy. It is found that more BC layers are preferred when the interactions between A and BC blocks are much stronger than that between B and C blocks.

Self-assembly of cylinder-forming diblock copolymers under spherical confinement is studied using real-space self-consistent field theory calculations (SCFT). Various microstructures are found at different confinement dimensions and surface fields. Most of these microstructures are center-symmetric and they could not be formed in bulk or under planar and cylindrical confinements. It is also observed that the interactions between the confinement surface and the polymers have a large effect on the self-assembly. When the spherical confinement’s surface attracts the short blocks, the self-assembled structures become similar to those under a neutral surface field. On the other hand, when the spherical confinement’s surface attracts the long blocks, the equilibrium structures become different from those under a neutral surface field.

A multiblock model is developed for the study of the phase behavior of gradient copolymers. The model is able to describe gradient copolymer chains with arbitrary composition profiles. The validity of the multiblock model of gradient copolymers is established by good agreement between RPA (random phase approximation) results for a continuous composition distribution and a multiblock model. The phase behavior of gradient copolymers is examined using self-consistent mean-field theory (SCMFT) for multiblock copolymers. Phase diagrams of gradient copolymer melts with different gradient profiles are constructed by solving the SCMFT equations. It is discovered that the phase behavior depends sensitively on the gradient profiles. In particular, new triple points are observed, and the stability region of phases with curved interfaces shrinks as the gradient profile becomes smooth. For linear gradient copolymers, the lamellar phase is predicted to be the only stable ordered phase.

Self-consistent field theory (SCFT) is presented to study the adsorption of flexible polyelectrolytes (PE) onto uniformly oppositely charged cylinders. We focus on the curvature effect of adsorbing surface on the adsorption−depletion phase-transition-like behavior. Numerical solutions for SCFT functions are derived. In terms of the scaling expression (Csalt∗ ∼ pασβ) of the critical quantities, i.e., the salt concentration Csalt∗, the charge fraction p of PE chain and the area density of surface charge σ, at the adsorption−depletion transition point, we divide the whole curvature dimension into two regimes, i.e., the planar regime and the cylindrical regime. In particular, we have numerically determined the crossover point of the two regimes at which the cylinder radius r0 approximately equates to 2 times the gyration radius Rg of PE chain, or, r0 ∼ 2Rg. In the planar regime (r0 > 2Rg), the scaling expression is invariable with surface curvature and is reduced to the planar case, or Csalt∗ ∼ (pσ)2/3. In th...

Self-assembly of cylinder-forming diblock copolymers confined in cylindrical nanopores is studied systematically using a simulated annealing method. The diblock copolymers form hexagonally packed cylinders in the bulk with a period L0, whereas novel structures spontaneously form when the copolymers are confined inside cylindrical pores. It is discovered that the sequence of structures is controlled by the ratio between the pore diameter (D) and L0, as well as the selectivity of the pores. For selective small pores (D/L0 2.7), the outer ring of the minority block-domain forms helices or stacked toroids, while the inner structure repeat the sequence of structures observed in smaller pores. ...

Self-assembly of symmetric diblock copolymers confined in spherical nanopores is studied using simulated annealing Monte Carlo simulations. The dependence of the self-assembled morphologies and chain conformations on the degree of confinement and the strength of the surface interactions is examined systematically. A rich variety of novel structures under the three-dimensional confinement has been revealed. As the strength of the surface preference is increased gradually from neutral to weakly preferential and finally strongly preferential to one of the blocks, the observed sequence of stable structures is from perpendicular lamellae to helices and/or embedded structures and finally to concentric-spherical lamellae. As the degree of confinement decreases, the stable region of the concentric-spherical lamellae becomes larger, while that of the embedded structures becomes smaller. For the structures obtained in spherical nanopores, corresponding counterparts in two-dimensional (2D) confined systems can be id...

The self-assembly of asymmetric diblock copolymers confined within cylindrical pores is studied using the self-consistent-field theory. The cylinder-forming asymmetric diblock copolymer is chosen t...

Various types of hydrogen bonds, their temperature dependence and water−polymer interaction in hydrated poly(acrylic acid) (PAA) were systematically investigated using 1H CRAMPS solid-state NMR techniques in the temperature range from 25 to 110 °C. The 1H CRAMPS NMR methods are based on a recently developed continuous phase modulation technique for 1H−1H homonuclear dipolar decoupling. The 1H CRAMPS experiments revealed four types of protons in hydrated PAA which are assigned to protons from the mutually hydrogen-bonded COOH groups (1), from the free COOH groups (2), from the COOH groups bounded with water or from water bounded with COOH groups which are undergoing fast chemical exchange mutually (3), and from main chain groups (4), respectively. Furthermore, we proposed double-quantum filtered and dipolar filtered 1H CRAMPS experiments to further assign the protons according to their dipolar coupling strength. In addition, high-resolution spin echo 1H CRAMPS experiments were further employed to accuratel...

We report a simulated annealing study of the morphology of block copolymer brushes in selective solvents. The investigation is carried out with a lattice model, in which the ends of A-blocks of mon...

Changes in the crystal growth mechanism were observed in pseudo-dewetted, thin layers of low molecular weight (MW) poly(ethylene oxide) (PEO) on a hydrophilic mica surface. The studies were conducted using two PEO fractions (HPEO and MHPEO) with similar MW's (number-average MW of around 4500 g/mol) but different end-group chemistries. For the HPEO, both ends of the chain are capped by −OH groups. For the MHPEO, one end is capped by an −OH group, while the other end is capped by an −OCH3 group. Utilizing in-situ atomic force microscopy, the growth of single crystals as a function of time (t) was monitored at different crystallization temperatures (Tx). Depending on the end-group chemistry and Tx applied, two growth laws were observed, which state that the crystal lateral size r or the crystal volume V can be linearly proportional to t (r ∝ t or V ∝ t). Combined with morphological observations of the single crystals, it could be deduced that when r ∝ t, the crystal growth was nucleation-limited (NL), while ...

Studies on heteroepitaxy of polymers mostly dealt with the resulting mutual orientation relationship of the involving polymer pairs. The molecular dynamics during the expitaxial crystallization process of a polymer was, however, not concerned so far. To disclose the expitaxial crystallization process of polymers on a molecular scale, the structure evolution of polycarprolactone (PCL) in the molten state on highly oriented polyethylene (PE) substrate was followed by time-resolved Fourier transform infrared spectroscopy and wide-angle X-ray diffraction (WAXD). The results clearly indicate the existence of surface-induced anisotropic chain ordering of PCL in its molten state on highly oriented PE substrate, i.e., the occurrence of soft epitaxy. These ordered PCL chain segments in turn initiate the epitaxial crystallization of PCL on highly oriented PE substrate during the subsequent cooling process.

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...

The rheological properties of liquid polybutadiene rubber/organo-clay nanocomposite gels were investigated by rheological experiments, focusing on the effects of clay exfoliation and orientation−disorientation as well as polymer−clay interaction and temperature. Both irreversible and reversible viscosity transitions were observed in the temperature range from 26 to 136 °C in steady shear experiments on as-prepared and exfoliated samples. These transitions depend strongly on the end groups, molecular weight of the liquid rubber, and the shear field. The irreversible transition is attributed to the exfoliation of the clay, and the reversible transition can be understood as a shear-induced orientation−disorientation transition of the clay sheets. Polymer−clay interaction is confirmed to be a key controlling factor of the orientation−disorientation transition, whereas the shear field plays a critical role to induce such a transition. To our knowledge, this is the first rheological observation of the in-situ e...

The phase behavior of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) triblock copolymers in aqueous solutions is studied by using a self-consistent-field theory. The spectral method is extended to polymer models with internal degrees of freedom. Phase diagrams of PEO−PPO−PEO and PPO−PEO−PPO triblock copolymers in water are constructed in the concentration−temperature space. A variety of lyotropic liquid crystalline phases is found. The effects of temperature, copolymer concentration, the block (EO/PO) ratio and the chain architecture are investigated. Good agreements were found between experimental results and theory.

The adsorption of homopolymers on spherical particles with a strong attractive potential has been studied using the self-consistent field theory. The particles are immersed in concentrated polymer solutions and the structure of the adsorbed polymer layer has been examined as a function of the particle size, focusing on the average loop and tail length at different bulk concentrations and solvent qualities. The scaling relationship between the average tail/loop length and the degree of polymerization has been investigated. It is found that the average loop length is insensitive to the particle size or surface curvature. However, the average tail length depends strongly on the particle size. In particular, tails become longer for smaller particles or larger surface curvatures. It is argued that this size effect may provide a mechanism for the excess entanglements induced by adding nanoparticles to polymer solutions.

Lamellar single crystals grown in dilute solutions can be used as templates for tethered chain analysis. Two series of diblock copolymers, poly(ethylene oxide)-block-polystyrene (PEO-b-PS) and poly...

Using a continuous chain length distribution, the effect of polydispersity on the structures of vesicles self-assembled by amphiphilic polydisperse diblock copolymers in dilute solutions is investigated by two-dimensional (2D) real-space self-consistent-field theory. It is discovered that larger polydispersity favors the formation of smaller vesicles or quasi-vesicles. This polydispersity effect can be attributed to the segregation of copolymers according to their chain lengths. Two types of chain segregations are observed. First of all, the shorter chains tend to localize at the A/B interfaces while the longer chains tend to stretch to the outer surfaces. Second, there is a separation of copolymers to the inner and outer monolayers of the bilayers, leading to a longer average chain length in outer monolayer.

Solid-state NMR methods were used to characterize the heterogeneous dynamics, miscibility, and microdomain structure in nanostructured thermoset blends of epoxy resin (ER) and amphiphilic poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) triblock copolymers (PEO−PPO−PEO). NMR experiments show that there is a distinct dynamic difference between the block copolymer (both PEO and PPO) and cured-ER matrix indicating the presence of phase separation, which also confirms the existence of the interphase region including a considerable amount of immobilized PEO and mobilized partially cured ER. An improved method based on spin-diffusion experiments enabled a quantitative determination of the interphase thickness. It is shown that a large percentage of PEO were intimately mixed with ER in the interphase region of the blends, while the rest mobile PEO and all PPO segregated from the ER network. It is observed that the domain size and long period depend strongly on the PEO fraction in the c...

In the weak segregation limit, we investigate the surface-induced structures in the body-centered-cubic phase of diblock copolymers. Employing the Landau−Brazovskii mean field theory, we obtain the extent of surface-induced region as a function of temperature and surface field strength. At strong surface field strengthes, the lamellar and cylindrical characters are much more profound, and the surface-induced structure persists to a larger extent. A “phase diagram” of surface reconstructions is constructed, which describes the surface-induced structure. These results demonstrate that the coupling between the local average excess polymer concentration and the surface leads to lamella-like and cylinder-like structures close to the surface. Some of our theoretical results are in agreement with relevant experimental results. Our predictions about these interesting surface-induced structures should be observable in experiments under suitable conditions.

The phase behavior of ABCD tetrablock copolymer melts is studied using self-consistent mean-field theory. In particular, the noncentrosymmetric (NCS) lamellar phase (with sequence ...ABCDABCD...) and the centrosymmetric (CS) lamellar phase (...ABCDDCBA...) are examined in two cases. First, an enthalpically stabilized NCS lamellar phase is investigated by varying the interaction between the A and D blocks from repulsive to attractive while keeping all block lengths equal. In the second case, an entropically stabilized NCS lamellar phase is investigated by changing the lengths of the two end blocks, which are taken to be chemically identical (ABCA tetrablock melt). In both cases, the NCS phase is found in regions of the phase diagram, and direct disorder to NCS transitions are possible. In addition, two partially mixed centrosymmetric (MCS) lamellar phases are observed between the disordered and fully ordered (NCS and CS) phases. This study extends our previous work on triblock−diblock blends which revealed...