Counterion distribution in a spherical charged sparse brush

The counterion distribution within a spherical polyelectrolyte sparse brush was measured by small-angle X-ray scattering using contrast variation with different counterions by means of ion dialysis. The brush was made by self-association of charged diblock copolymers. Thanks to the contrast variation method, we were able to separate the signal due to the monomers and the signal due to the counterions. At a small length scale, it is demonstrated that the system behaves as independent charged rods whose counterion distribution follows the Poisson-Boltzmann model. Received 14 February 2001 and Received in final form 2 May 2001     

Dynamical pattern formation for diblock copolymer films under stretch by moving walls

We propose a computational method that takes into account the dynamical influence of moving rigid walls over the pattern formation for thin films of diblock copolymers. The competition between the surface field energy and elastic stretching energy, and the effects of the molecular relaxation on pattern formation are studied. Finally, it is also observed that stretching the film enhances the ordering of patterns in it.     

Self—assembly behaviour of amphiphilic diblock copolymer in selective solvents studied by synchrotron small—angle x—ray scattering

The aggregation behaviour of styrene-vinyl benzoic acid (PS_m-b-PVBA_n) amphiphilic diblock copolymers in selective solvents with different m and n was investigated by synchrotron small-angle x-ray scattering (SAXS). We have carried out a detailed analysis of scattering intensity, dimension, shape and microstructure of the diblock copolymers of narrow distribution in water, methanol, ethanol and isopropanol selective solvents, respectively. We have found that the aggregation behaviour of the copolymer depends on the nature of the solvent and the micelle forms flat disc objects with the ratio of radius ω=0.4. The average radius gyration R_g of the copolymer decreases as solvents change from isopropanol to ethanol and to methanol, and increases with increasing pH in aqueous solution, but decreases with the addition of CoCl_2 in ethanol solvent. The scattering intensity of diblock copolymer micelle follows I(h)∝h^{-α} in different selective solutions, suggesting that the PS_m-b-PVBA_n coils have self-similar structure behaviour or a fractal structure in the selective solvents. All of these revealed that the aggregation behaviour of the diblock copolymer changes dramatically with experimental condition in the selective solvent. The increase of mass fractal dimension (D_m) from 2.12 to 2.47 indicates that the copolymer chain changes from a swollen coil to a rather compact disc in the course of changing solvents, decreasing surface fractal dimension (D_s) from 2.98 to 2.58 indicates that the copolymer micelle change from a rather rough surface to a smooth form in the course of increasing pH in aqueous solutions, and increasing D_m and D_s from 2.29 to 2.35 and 2.70 to 2.90, respectively, indicates the shrinkage of copolymer micelle to a rather compact and rough disc form by adding CoCl_2 in ethanol solvents.     

Binary-component micelle and vesicle: Free energy and asymmetric distributions of amphiphiles between monolayers of vesicle

The real-space two-dimensional self-consistent field theory (SCFT) is employed to study the free energies of micelles and vesicles constituted by binary amphiphilic diblock copolymer AB in homopolymer A. With increasing volume fraction of copolymer AB, there are morphological transitions from the circle micelles to oblate circle-like micelles, to compound structure with inverted micelles in the inner center and micelles outer layer, and to vesicles. Special attentions are paid to the role of the copolymer AB in controlling free energies of the micelles and vesicles, by examining the effect of length ratio of A/B with the fixed whole chain length of AB copolymer, the length effect of A or B block with the corresponding fixed length of B or A block, for one component of copolymer, and the effect of different amphiphile compositions for binary-component copolymer system. The quantity η is provided to describe the asymmetric density distribution of amphiphiles between the inner and outer monolayers of vesicles, and to quantify the relative asymmetric extent of the density distribution between two species of copolymers in binary component vesicles.     

Collective dynamics and self-diffusion in a diblock copolymer melt in the body-centered cubic phase

The structure and dynamics of a strongly asymmetric poly(ethylene propylene)-poly(dimethylsiloxane) (PEP-PDMS) diblock copolymer in the melt have been studied over a wide temperature range. Small-angle neutron scattering reveals that the sample exhibits two stable phases in this temperature range: Above the order-to-disorder transition temperature, it is disordered, whereas the domain structure is body-centered cubic (bcc) below, being stable down to the lowest temperatures measured. In the disordered state, dynamic light scattering (DLS) in the polarized geometry reveals the heterogeneity mode and the cluster mode. In the bcc phase, the PEP and the PDMS blocks form the micellar cores and the matrix, respectively. Here, two modes are observed in DLS, and the diffusion coefficients measured using pulsed field gradient (PFG) NMR are broadly distributed with the most probable diffusion coefficient coinciding with the slow DLS mode. We attribute the fast process in the bcc state to concentration fluctuations of the micellar cores (PEP), relaxing by mutual diffusion of the micelles with copolymers dissolved in the PDMS matrix. The slower process in the bcc state is ascribed to activated long-range self-diffusion of single copolymers from micelle to micelle through the PDMS matrix. This assignment is corroborated by the good coincidence of the reduced diffusivities with the ones from the literature. However, this mode may also be assigned to the rearrangement of entire micelles.This paper is dedicated to the memory of G. Fleischer     

Scaling theory of mixed amphiphilic monolayers

We predict the elastic properties of mixed amphiphilic monolayers in the swollen state within the blob model using scaling arguments. First the elastic moduli and the spontaneous curvature of a bimodal brush are determined as a function of the composition and the relative chain length. We obtain simple and useful scaling functions which interpolate between the elastic moduli of a pure short-chain brush and a pure long-chain brush. By using the analogy between block copolymer interfaces and polymeric brushes, the effect of mixing on self-assembled diblock copolymer monolayers is investigated in the swollen state. We calculate various interfacial properties, such as the equilibrium surface coverage, interface curvature, and the mixing free energy as a function of the composition. In general, we find a nonlinear dependence on the composition, which deviates from the simple linear averaging of the properties of pure components. Our results are used to discuss a recent experiment on the effect of amphiphilic block copolymers on the efficiency of microemulsions. Received 29 December 2000 and Received in final form 19 March 2001     

Thickness and density profiles of polyelectrolyte brushes: dependence on grafting density and salt concentration

We have performed neutron reflectivity measurements on a monolayer of charged diblock copolymers in a Langmuir trough, and determined precise density profiles of the polyelectrolyte brush at different densities. We obtain profiles in good agreement with existing self-consistent field computations, both for the osmotic and the salted brush regime. We show that the osmotic brush's thickness increases with density.     

Multiscale coarse graining of diblock copolymer self-assembly: from monomers to ordered micelles

Starting from a microscopic lattice model, we investigate clustering, micellization, and micelle ordering in semidilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse-graining strategy, whereby the AB copolymers are mapped onto ultrasoft dumbells with monomer-averaged effective interactions between the centers of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n approximately 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.     

Elastic property of bilayer membrane in copolymer-homopolymer mixtures

We study the domain morphology in a phase separated state of diblock copolymer-homopolymer mixtures. In the situation that one of the blocks of copolymers is incompatible with homopolymers, formation of a bilayer membrane of block copolymers is shown to be possible in the matrix of homopolymers. Starting with the free energy functional in terms of the local volume fractions of each monomer, we derive the bending and curvature rigidities in the Helfrich free energy for a membrane. It is found that the curvature modulus is negative only in a limited region of the parameters, where a closed shape of a membrane like a vesicle is possibly formed. We establish a method to calculate the rigidities without a molecular picture in a consistent way with the field theoretic model free energy. Stability of a bilayer membrane compared with micelles is also investigated. Received: 22 July 1997 / Received in final form: 1 December 1997 / Accepted: 22 January 1998     

Block copolymer morphologies confined by square-shaped particle:Hard and soft confinement

The self-assembly of diblock copolymers confined around one square-shaped particle is studied systematically within two-dimensional self-consistent field theory(SCFT).In this model,we assume that the thin block copolymer film is confined in the vicinity of a square-shaped particle by a homopolymer melt,which is equivalent to the poor solvents.Multiple sequences of square-shaped particle-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of the particle size,the structural portion of the copolymer,and the volume fraction of the copolymer.A rich variety of aggregates are found with complex internal self-assembled morphologies including complex structures of the vesicle,with one or several inverted micelle surrounded by the outer monolayer with the particle confined in the core.These results demonstrate that the assemblies of diblock copolymers formed around the square-shaped particle in poor solvents are of immediate interest to the assembly of copolymer and the morphology of biomembrane in the confined environment,as well as to the transitions of vesicles to micelles.     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.     

Tuning surface interactions to control shape and array behavior of diblock copolymer micelles on a silicon substrate

The micellar shape of liquid crystalline diblock copolymers, PEO_m-b-PMA(Az)_n, consisting of high surface energy components was controlled by tuning surface interactions. On a fluorinated surface, the diblock copolymers formed ordered arrays of spherical micelles consisting of PEO cores surrounded by PMA(Az) coronas. Gold ions could be doped into the PEO cores by immersion in a solution of the gold ion. The Au³⁺-doped micelles were subsequently etched and reduced by VUV radiation to form hexagonally ordered gold nanodots.     

Influence of Grafting Density of Diblock Copolymers on Interfacial Assembly Behavior and Interfacial Shear Strength of Glass Fiber/Polystyrene Composites

To investigate the influence of the grafting density and the molecular structure of block copolymers on the interfacial assembly behavior and interfacial shear strength, macromolecular coupling agents, hydroxyl-terminated poly(n-butyl acrylate-b-styrene) (HO-P(BA-b-S)) were synthesized by atom transfer radical polymerization, and then chemically anchored on the glass fiber surfaces to form a well-defined monolayer. The phase separation and 'hemispherical' domain morphologies of diblock copolymer brushes at the polystyrene/glass fiber interface were observed. The interfacial assembly morphology differs with changes in the grafting density of diblock copolymers. When the grafting density is greatest, the highest height difference of the hemispherical domain and the largest surface roughness are achieved, as well as the best interface shear strength. It was also found that the copolymer brush with a PBA block of the polymerization degree (Xn) about 77 is the optimal option for the interfacial adhesion of PS/GF composites. Thus, the grafting density and molecular structure of diblock copolymers determines the interfacial assembly behavior of copolymer brushes, and therefore the interfacial shear strength.     

Triblock terpolymer micelles: A personal outlook<Superscript>a</Superscript>

This outlook paper focuses on micelles formed by ABC triblock copolymers (triblock terpolymers) and related systems resulting from mixtures of diblock copolymers. Micelles with different internal structure such as micelles with a heterogeneous core and a homogeneous corona or micelles with a homogeneous core and a mixed corona are presented. More complex nanoobjects such as vesicles and Janus particles are also reviewed. Finally, potential applications of these objects are discussed.     

The segregation of poly(styrene-b-isoprene) diblock copolymers to the surface of a polystyrene melt: the effect of the ratio of block lengths

The effect of the ratio of block lengths on the interfacial partitioning of poly(styrene-block-1,4 isoprene) diblock copolymers from their mixtures with polystyrene homopolymer melt is investigated utilizing a series of copolymers with almost constant molecular weight but different compositions. The concentration profile of the copolymer is measured directly using the nuclear reaction analysis technique; a segregation of the diblock is found at both the air/polymer surface, due to the lower surface energy of polyisoprene, and at the substrate/polymer interface. No significant effect of the block length ratio on the free-surface excess was observed. The block molecular weights have apparently led to dangling chain conformations in the non-overlapping mushroom and in the overlapping mushroom regimes whereas the brush regime was not accessible; no indications of a real border between the two former regimes was found. Received: 20 July 1998 / Received in final form and Accepted: 11 September 1998     

Oppositely charged polyelectrolytes grafted onto planar surface: Mean-field lattice theory

Equilibrium structures of planar polyelectrolyte brushes formed by grafted chains carrying charges of opposite sign are examined by employing mean-field lattice theory. Two brushes of different architecture are considered: one formed by grafted diblock copolymers with oppositely charged blocks and the other being a mixed brush composed of oppositely charged homopolymers. The systems display nontrivial intrinsically inhomogeneous brush structures originating from the chain connectivity and the electrostatic interaction among the segments. In addition, a coexistence of stretched and coiled chains inside the brush is observed. The influence of the charges of the blocks, the relative length of the oppositely charged blocks, and the ionic strength of the solution on the brush inhomogeneity and structural differences between the two types of brushes are discussed. Received 14 March 2001 and Received in final form 18 June 2001     

The influence of chain stretching on the phase behavior of multiblock copolymer and comb copolymer melts

The subject of this paper is inspired by microphase-separated copolymer melts in which a small-scale structure is present inside one of the phases of a large-scale structure. Such a situation can arise in a diblock copolymer melt, if one of the blocks of the diblock is in itself a multiblock copolymer or a comb copolymer. Due to the presence of the large-scale structure, the chains are stretched. The aim of this paper is to investigate the influence of this chain stretching on the formation of the small-scale structure. To gain insight we study infinite melts of infinitely long copolymer chains that are subjected to a stretching force. For melts of monodisperse multiblock copolymers we find that the stretching destabilizes the homogeneous phase. If the stretching is strong, the lamellar structure is the only stable structure. The periodicity increases with the degree of stretching. For melts of monodisperse comb copolymers the chain stretching has no influence on the stability of the homogeneous phase. If the stretching is strong, the lamellar structure and the hexagonal structure are the only stable structures. The periodicity is independent of the degree of stretching. For the multiblock copolymer we investigated the influence of block length polydispersity. For small polydispersity the period of the structure increases monotonically with the degree of stretching. For intermediate polydispersity, the period initially decreases before it starts to increase. For large polydispersity, the mean-field period at the spinodal is infinite, becoming finite once the stretching force exceeds some critical value. For very large polydispersity the mean-field period at the spinodal remains infinite for any value of the stretching force. Received: 14 February 2002 / Accepted: 24 March 2003 / Published online: 29 April 2003 RID="a" ID="a"e-mail: hindrik.angerman@abp.nl     

Driven self-assembly of hard nanoplates on soft elastic shells

The driven self-assembly behaviors of hard nanoplates on soft elastic shells are investigated by using molecular dynamics(MD) simulation method, and the driven self-assembly structures of adsorbed hard nanoplates depend on the shape of hard nanoplates and the bending energy of soft elastic shells. Three main structures for adsorbed hard nanoplates,including the ordered aggregation structures of hard nanoplates for elastic shells with a moderate bending energy, the collapsed structures for elastic shells with a low bending energy, and the disordered aggregation structures for hard shells,are observed. The self-assembly process of adsorbed hard nanoplates is driven by the surface tension of the elastic shell,and the shape of driven self-assembly structures is determined on the basis of the minimization of the second moment of mass distribution. Meanwhile, the deformations of elastic shells can be controlled by the number of adsorbed rods as well as the length of adsorbed rods. This investigation can help us understand the complexity of the driven self-assembly of hard nanoplates on elastic shells.     

Structure of polymer micelles close to the solid interface

Block copolymers are widely used in industry. For scientific interests their aqueous solutions offer a model system for the investigation of crystallisation as the macromolecules agglomerate for elevated concentrations into micelles, which crystallise when a critical volume fraction is reached. We report on grazing incidence small angle neutron scattering (GISANS) or near surface small angle neutron scattering (NS-SANS) as an experimental tool to investigate the micelle crystallisation close to interfaces with different chemical termination. We find that in general crystallization is suppressed at a repulsive surface and favoured at an attractive one. Furthermore we show that the crystallization close the interface can be controlled by the micelle stability, resulting from the different composition and length of the monomers. The effect of the interface is found more important for a high micelle stability, whereas for a low stability it is shadowed by adsorbed monomers.     

Self-assembly of lamella-forming diblock copolymers confined in nanochannels: Effect of confinement geometry

The self-assembly of symmetric diblock copolymers confined in the channels of variously shaped cross sections(regular triangles, squares, and ellipses) is investigated using a simulated annealing technique. In the bulk, the studied symmetric diblock copolymers form a lamellar structure with period LL. The geometry and surface property of the confining channels have a large effect on the self-assembled structures and the orientation of the lamellar structures. Stacked perpendicular lamellae with period LLare observed for neutral surfaces regardless of the channel shape and size, but each lamella is in the shape of the corresponding channel’s cross section. In the case of triangle-shaped cross sections, stacked parallel lamellae are the majority morphologies for weakly selective surfaces, while morphologies including a triangular-prism-shaped B-cylinder and multiple tridentate lamellae are obtained for strongly selective surfaces. In the cases of square-shaped and ellipse-shaped cross sections, concentric lamellae are the signature morphology for strongly selective surfaces, whereas for weakly selective surfaces, stacked parallel lamellae, and several types of folding lamellae are obtained in the case of square-shaped cross sections, and stacked parallel lamellae are the majority morphologies in the case of ellipse-shaped cross sections when the length of the minor axis is commensurate with the bulk lamellar period. The mean-square endto-end distance, the average contact number between different species and the surface concentration of the A-monomers are computed to elucidate the mechanisms of the formation of the different morphologies. It is found that the resulting morphology is a consequence of competition among the chain stretching, interfacial energy, and surface energy. Our results suggest that the self-assembled morphology and the orientation of lamellae can be manipulated by the shape, the size, and the surface property of the confining channels.