Integral equation theory of random copolymer melts: self-consistent treatment of intramolecular and intermolecular correlations

A self-consistent integral equation theory is presented for the conformational properties and spinodal lines of random copolymer melts. The theory combines field-theoretic methods with the polymer reference interaction site model (PRISM) theory. The many-chain problem is replaced by a single chain where the sites interact via a bare plus a self-consistently determined medium-induced potential, and the conformational properties are obtained using a variational method. The theoretical prediction for the spinodal line is qualitatively similar to that of non-self-consistent PRISM theory. The theory predicts macroscopic phase separation for all values of the monomer correlation strength, lambda. The inverse spinodal temperature is a nonmonotonic function of lambda with a maximum at lambda(max). For large values of lambda( approximately 1), the values of spinodal temperatures are almost identical to those of non-self-consistent PRISM theory. For low values of lambda, however, the theory predicts higher values for spinodal temperatures than non-self-consistent PRISM theory. The theory predicts significant changes in the mean-square end-to-end distance as the temperature is decreased.     

Self-assembly of star ABC triblock copolymer thin films: self-consistent field theory

Microphase separation and morphology of star ABC triblock copolymers confined between two identical parallel walls (symmetric wetting or dewetting) are investigated with self-consistent field theory (SCFT) combined with the "masking" technique to describe the geometric confinement of the films. In particular, we examine the morphology of confined near-symmetric star triblock copolymers under symmetric and asymmetric interactions as a function of the film thickness and the surface field. Under the interplay between the degree of spatial confinement, characterized by the ratio of the film thickness to bulk period, and surface field, the confined star ABC triblock copolymers are found to exhibit a rich phase behavior. In the parameter space we have explored, the thin film morphologies are described by four primary classes including cylinders, perforated lamellae, lamellae, and other complex hybrid structures. Some of them involve novel structures, such as spheres in a continuous matrix and cylinders with alternating helices structure, which are observed to be stable with suitable film thickness and surface field. In particular, complex hybrid network structures in thin films of bulk cylinder-forming star triblock copolymers are found when the natural domain period is not commensurate with the film thickness. Furthermore, a strong surface field is found to be more significant than the spatial confinement on changing the morphology of star triblock copolymers in bulk. These findings provide a guide to designing novel microstructures involving star triblock copolymers via geometric confinement and surface fields.     

Self-assembly of ABC star triblock copolymer thin films confined with a preferential surface: a self-consistent mean field theory

The microphase separation and morphology of a nearly symmetric A(0.3)B(0.3)C(0.4) star triblock copolymer thin film confined between two parallel, homogeneous hard walls have been investigated by self-consistent mean field theory (SCMFT) with a pseudospectral method. Our simulation experiments reveal that under surface confinement, in addition to the typically parallel, perpendicular, and tilted cylinders, other phases such as lamellae, perforated lamellae, and complex hybrid phases have been found to be stable, which is attributed to block-substrate interactions, especially for those hybrid phases in which A and B blocks disperse as spheres and alternately arrange as cubic CsCl structures, with a network preferred structure of C block. The results show that these hybrid phases are also stable within a broad hybrid region (H region) under a suitable film thickness and a broad field strength of substrates because their free energies are too similar to being distinguished. Phase diagrams have been evaluated by purposefully and systematically varying the film thickness and field strength for three different cases of Flory-Huggins interaction parameters between species in the star polymer. We also compare the phase diagrams for weak and strong preferential substrates, each with a couple of opposite quality, and discuss the influence of confinement, substrate preference, and the nature of the star polymer on the stability of relatively thinner and thick film phases in this work.     

Improved convergence in block copolymer self-consistent field theory by Anderson mixing

A modification to real space polymeric self-consistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing [D. G. Anderson, J. Assoc. Comput. Mach. 12, 547 (1965)], and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.     

Aggregate morphologies of amphiphilic ABC triblock copolymer in dilute solution using self-consistent field theory

The complex microstructures of amphiphilic ABC linear triblock copolymers in which one of the end blocks is relatively short and hydrophilic, and the other two blocks B and C are hydrophobic in a dilute solution, have been investigated by the real-space implementation of self-consistent field theory (SCFT) in two dimensions (2D). In contrast to diblock copolymers in solution, the aggregation of triblock copolymers are more complicated due to the presence of the second hydrophobic blocks and, hence, big ranges of parameter space controlling the morphology. By tailoring the hydrophobic degree and its difference between the blocks B and C, the various shapes of vesicles, circlelike and linelike micelles possibly corresponding to spherelike, and rodlike micelles in 3D, and especially, peanutlike micelles not found in diblock copolymers are observed. The transition from vesicles to circlelike micelles occurs with increasing the hydrophobicity of the blocks B and C, while the transition from circlelike micelles to linelike micelles or from the mixture of micelles and vesicles to the long linelike micelles takes place when the repulsive interaction of the end hydrophobic block C is stronger than that of the middle hydrophobic block B. Furthermore, it is favorable for dispersion of the block copolymer in the solvent into aggregates when the repulsion of the solvent to the end hydrophobic block is larger than that of the solvent to the middle hydrophobic block. Especially when the bulk block copolymers are in a weak segregation regime, the competition between the microphase separation and macrophase separation exists and the large compound micelle-like aggregates are found due to the macrophase separation with increasing the hydrophobic degree of blocks B and C, which is absent in diblock copolymer solution. The simulation results successfully reproduce the existing experimental ones.     

Topomers: a validated protocol for their self-consistent generation

The hypothesis underlying topomer development is that describing molecular structures consistently may be at least as productive as describing them more realistically but incompletely. A general protocol is detailed for deterministically generating self-consistent shapes of molecular fragments from their topologies. These and other extensions to the topomer methodology are validated by repetition of earlier benchmark studies.     

Synthesis of Globular Precursors

o‐Carborane (C₂B₁₀H₁₂) was adapted to perform as the core of globular macromolecules, dendrons or dendrimers. To meet this objective, precisely defined substitution patterns of terminal olefin groups on the carborane framework were subjected to Heck cross‐coupling reactions or hydroboration leading to hydroxyl terminated arms. These led to new terminal groups (chloro, bromo, and tosyl leaving groups, organic acid, and azide) that permitted ester production, click chemistry, and oxonium ring opening to be performed as examples of reactions that demonstrate the wide possibilities of the globular icosahedral carboranes to produce new dendritic or dendrimer‐like structures. Polyanionic species were obtained in high yield through the ring‐opening reaction of cyclic oxonium compound [3,3′‐Co(8‐C₄H₈O₂‐1,2‐C₂B₉H₁₀)(1′,2′‐C₂B₉H₁₁)] by using terminal hydroxyl groups as nucleophiles. These new polyanionic compounds that contain multiple metallacarborane clusters at their periphery may prove useful as new classes of compounds for boron neutron capture therapy with enhanced water solubility and as cores to make a new class of high‐boron globular macromolecules.     

Lateral structures of buried interfaces in ABA-type triblock copolymer films

The lateral structure of an ABA-type triblock copolymer polyparamethylstyrene- block-polystyrene- block-polyparamethylstyrene at the buried silicon substrate interface is studied as a function of different substrate surface treatments. With grazing incidence small-angle neutron scattering (GISANS), high interface sensitivity is reached. With GISANS, the orientation and degree of order of the morphology are probed. The powderlike oriented lamellar structure in the bulk orients along the surface normal in the vicinity of the substrate. A modification of the short-ranged interface potential of the substrate introduces a lateral stretching of this lamellar structure of up to 8% as compared to the bulk. The decay in stretching toward the volume structure is probed with depth profiling. It extends at least up to a distance of 51 nm from the solid surface.     

Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: exact formula and its approximate treatment

An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method.     

Non-equilibrium self-assembled structures in thick PS-b-PMMA copolymer films

Phenomena associated with the order-disorder transition (ODT) of block copolymers have been studied by optical light microscopy, SAXS, SEM, TEM and DSC. Observations have been made on almost symmetric polystyrene-block-poly(methyl methacrylate) samples of three molecular weights and their mixture. We observed non-equilibrium supermolecular structures several microns in diameter in the bulk of thick PS-b-PMMA films (ca. 100 μm thickness) prepared by vacuum drying of films cast from a non-selective solvent (after a short-term annealing above the T_g). Apparent LDOT (lower disorder-to-order transition) behaviour is observed for samples with non-equilibrium morphology surviving from solution as deduced from SAXS 1/I_m vs 1/T and the full width at half-maximum vs 1/T plots.The measurements point to complex behaviour near the ODT, but homogenization of samples upon long-term annealing well above the T_g temperature call into existence common stacks of lamellae observable in SEM images of microphase-separated samples. This verifies the opinion that the observed apparent LDOT behaviour of samples II, III and II + III is associated with the frozen non-equilibrium morphology surviving from solution. This is confirmed by SAXS measurement on a homogenized sample displaying the expected UDOT behaviour. It has been demonstrated that self-assembled structures prepared by vacuum drying of films cast from a non-selective solvent are non-equilibrium structures and their successive ordering is difficult due to a relative narrow temperature interval between T_g and degradation temperature. The conditions under which BCP films are prepared thus have a pronounced effect on the microstructure and microphase ordering process.     

Thermodynamics of the DNA helix-coil transition

The thermodynamics of the DNA helix-coil transition is studied, starting from the thermodynamical potential difference between the states helix and coil; this potential difference is understood as the difference in free energies. With only three parameters obtained from experimental data different quantities of the T₂ phage DNA molecule are calculated. It is observed that the phase transition is of second order.     

Crowding effect on helix-coil transition: beyond entropic stabilization

We report circular dichroism measurements on the helix-coil transition of poly(L-glutamic acid) in solution with polyethylene glycol (PEG) as a crowding agent. The PEG solutions have been characterized by small angle neutron scattering and are well described by the picture of a network of mesh size ξ, usual for semi-dilute chains in good solvent. We show that the increase of PEG concentration stabilizes the helices and increases the transition temperature. But more unexpectedly, we also notice that the increase of concentration of crowding agent reduces the mean helix extent at the transition, or in other words reduces its cooperativity. This result cannot be taken into account for by an entropic stabilization mechanism. Comparing the mean length of helices at the transition and the mesh size of the PEG network, our results strongly suggest two regimes: helices shorter or longer than the mesh size.     

Controlled copolymer structures via anionic/insertion polymerization of cyclic carbonates

Cyclic carbonates are polymerized in a ring-opening fashion by means of anionic and insertion type initiatiors. Different hexacyclic carbonates are copolymerized in a random way when both monomers are added to the initiator simultaneously. Block copolymers are obtained when the monomers are added in sequential way. With anionic initiators cyclic carbonates are polymerized preferentially as compared with lactones while insertion initiators are less selective. A special case is the preparation of copolymers of carbonates with lactams. When the polycarbonate is formed first the lactam unit is inserted into carbonate bond to form urethane and ester bonds. Thus, eventually an alternating polyesterurethane is formed with negligible amount of carbonate, amide, and urea units. Moreover, the anionic ring-opening polymerization of cyclic carbonates may be combined with vinyl polymerization. In the case of group transfer polymerization a transformation of the active site to the non-metallic anionic initiation of the cyclic carbonate occurs.     

Effects of radiation crosslinking on structures and properties of SBS triblock copolymer

There is considerable interest in the effect of high energy radiation on triblock copolymer, SBS. Basheer and Dole have done some works about that(Basheer and Dole, 1982). In this paper, we study the effects of radiation crosslinking on the structure and mechanical properties of SBS, about which there have been no reports up to now. The following scientific problems are discussed: The variation of glass transition temperatures with dose; The effects of the ratio of B/S on the gel content; Mechanical properties of the irradiated samples.     

Emulsion polymerization of supermicron,monodisperse acrylic copolymer particles with core-shell structures

The emulsion polymerization of large MMA/BA copolymer particles with narrow particle size distributions and core-shell structure is described. A series of sequential seeded growth emulsion polymerizations were used to obtain monodisperse particles with diameters of at least 3 μm, at 30% solids contents. Because the core and shell polymers used here were chemically similar, core-shell structures could not be verified by differential staining tech-niques. Core-shell structure was demonstrated by minimum film-forming temperature studies and by scanning electron microscopy in conjunction with energy dispersive x-ray analysis, using chlorine-labeled core polymers. © 1995 John Wiley & Sons, Inc.     

Gate-controlled current and inelastic electron tunneling spectrum of benzene: a self-consistent study

We use density functional theory based nonequilibrium Green's function to self-consistently study the current through the 1,4-benzenedithiol (BDT). The elastic and inelastic tunneling properties through this Au-BDT-Au molecular junction are simulated, respectively. For the elastic tunneling case, it is found that the current through the tilted molecule can be modulated effectively by the external gate field, which is perpendicular to the phenyl ring. The gate voltage amplification comes from the modulation of the interaction between the electrodes and the molecules in the junctions. For the inelastic case, the electron tunneling scattered by the molecular vibrational modes is considered within the self-consistent Born approximation scheme, and the inelastic electron tunneling spectrum is calculated.     

Sterically stabilized lock and key colloids: a self-consistent field theory study

A self-consistent field theory study of lock and key type interactions between sterically stabilized colloids in polymer solution is performed. Both the key particle and the lock cavity are assumed to have cylindrical shape and their surfaces are uniformly grafted with polymer chains. The lock-key potential of mean force is computed for various model parameters, such as length of free and grafted chains, lock and key size matching, free chain volume fraction, grafting density, and various enthalpic interactions present in the system. The lock-key interaction is found to be highly tunable, which is important in the rapidly developing field of particle self-assembly.