Surface energies and self-assembly of block copolymers on grafted surfaces

We present a theoretical analysis of the self-assembly of diblock copolymers on surfaces grafted with random copolymers. Our results demonstrate that the surface energies of homopolymeric components on grafted surfaces differ from the corresponding values for self-assembled morphologies. Moreover, grafted random copolymers are shown to adapt their conformations in response to the morphology of the overlaying block copolymer film to create chemical inhomogeneities which modulate the interfacial interactions. Consequently, the surface energy differences between the different components on the grafted substrate do not serve as a useful measure to predict the stability of self-assembly of the diblock copolymer film.     

Self-assembly of block copolymers grafted onto a flat substrate:Recent progress in theory and simulations

Block copolymers are a class of soft matter that self-assemble to form ordered morphologies on the scale of nanometers, making them ideal materials for various applications. These applications directly depend on the shape and size of the self-assembled morphologies, and hence, a high degree of control over the self-assembly is desired. Grafting block copolymer chains onto a substrate to form copolymer brushes is a versatile method to fabricate functional surfaces. Such surfaces demonstrate a response to their environment, i.e., they change their surface topography in response to different external conditions. Furthermore, such surfaces may possess nanoscale patterns, which are important for some applications; however, such patterns may not form with spun-cast films under the same condition. In this review, we summarize the recent progress of the self-assembly of block copolymers grafted onto a flat substrate. We mainly concentrate on the self-assembled morphologies of end-grafted AB diblock copolymers, junction point-grafted AB diblock copolymers(i.e.,Y-shaped brushes), and end-grafted ABA triblock copolymers. Special emphasis is placed on theoretical and simulation progress.     

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.     

Stress distributions in diblock copolymers

We demonstrate how a generalized self-consistent field theory for polymer melts that includes elastic stress and strain fields can be applied to the study of AB diblock copolymers melts. By obtaining the stress distributions for volume conserving strain loadings where lamellar and hexagonal morphologies are stable, we show that the local stress is reduced at the domain interface but slightly enhanced in the immediate vicinity of the interface. The overall stress profile is the result of the combined effects of chain connectivity across the interface, which yields a positive contribution, and the immiscible nature of the monomers, which leads to a stress reduction because of interfacial tension.     

Hydrodynamic-flow-driven phase evolution in a polymer blend film modified by diblock copolymers

We have studied surface-directed phase separation in thin films of deuterated polystyrene and poly(bromostyrene) (with 22.7% of monomers brominated) using ³He nuclear reaction analysis, dynamic secondary ion mass spectroscopy and atomic force microscopy combined with preferential dissolution. The crossover from competing to neutral surfaces of the critical blend film (cast onto Au) was commenced: polyisoprene-polystyrene diblock copolymers were added and segregated to both surfaces reducing in a tuneable manner the effective interactions. Two main stages of phase evolution are characterised by i) the growth of two surface layers and by ii) the transition from the four-layer to the final bilayer morphology. For increasing copolymer content the kinetics of the first stage is hardly affected but the amplitude of composition oscillations is reduced indicating more fragmented inner layers. As a result, a faster mass flow to the surfaces and an earlier completion of the second stage were observed. The hydrodynamic flow mechanism, driving both stages, is evidenced by nearly linear growth of the surface layer and by mass flow channels extending from the surface layer into the bulk. The final bilayer structure, formed even for the surfaces covered by strongly overlapped copolymers, is indicative of long-range (antisymmetric) surface forces. Received 15 March 2000 and Received in final form 9 February 2001     

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.     

Phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls are investigated by using a cell dynamics simulation of the time-dependent Ginzburg-Landau theory.The morphological dependence of the wall-block interaction and the distance between walls(confinement degree) has been systematically studied,and the effect of repulsive interactions between different monomers is also discussed.It is interesting that multiple novel morphological transitions are observed by changing these factors,and various multilayered sandwich structures are formed in the mixture.Furthermore,the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed.From the simulation,we find that much richer morphologies can form in a binary mixture of diblock copolymers than those in a pure diblock copolymer.Our results provide an insight into the phase behaviors under parallel wall confinement and may provide guidance for experimentalists.This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

Phase behaviors in binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in binary mixture of diblock copolymers confined between two parallel walls are investigated by using cell dynamics simulation of the time-dependent Ginzburg-Landau theory. The morphological dependence of the wall-block interaction and the distance between walls (confinement degree) has been systematically studied, and the effect of repulsive interactions between different monomers is also discussed. It is interesting that multiple novel morphological transitions are observed by changing these factors, and various multilayered sandwich structures are formed in the mixture. Furthermore, the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed. From the simulation, we find that much richer morphologies can form in binary mixture of diblock copolymers than those in pure diblock copolymer. Our results provide an insight into the phase behaviors under parallel walls confinement and may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

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.     

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.     

Ordering Mechanisms in Confined Diblock Copolymers

We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of confining flat surfaces. The surfaces are chemically patterned where different regions attract different parts of the copolymer chain. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. The propagation of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uniform and striped surface). It is further shown that complex morphology can be induced in a thin film even though the bulk is disordered. We next consider lamellar diblock copolymers (low temperature regime) in the presence of a striped surface. It is shown that lamellae acquire a tilt with respect to the surface, if the surface periodicity is larger than the bulk one. The lamellae close to the surface are strongly distorted from their perfect shape. When the surface and lamellar periodicities are equal, the lamellae are perpendicular to the surface. Lastly, the transition from parallel to perpendicular lamellae in a thin film is presented. The transition between the two states depends on the surface separation and strength of surface interactions. We further calculate the phase diagram in the presence of perpendicular electric field favoring perpendicular ordering. In the strong segregation limit we introduce a simple model to calculate the phase diagram of the fully parallel, fully perpendicular and mixed (parallel and perpendicular) states.     

Exploring Microstructures and Interphase Properties of Surface- Grafted Diblock Copolymers in a Homopolymer Melt by Self-Consistent Field Theory Simulations

Polymeric self-consistent field theory is used to investigate microstructures and interphase properties of diblock copolymers grafted onto solid surfaces in a homopolymer melt. The calculations show that the grafted diblock copolymers can self-assemble into hemispherical microstructures at low grafting densities of the diblock copolymers. The morphology transforms into hemicylinder-like and sandwich-like lamellar microstructures with an increase in the chain-grafting density. The effective thickness of the grafted block layer and the interphase width between the homopolymer melt and the grafted copolymers strongly depend on the physicochemical parameters of the system, such as the composition of the grafted copolymer, the chemical incompatibility between the different components, the length ratio of grafted copolymer to homopolymer, and the grafting density of the diblock copolymers. In addition, the above computational results of microphase-separated structures and interphase properties are qualitatively compared with our previous experimental observations. The comparison indicates that our theoretical results not only reproduce the general feature of the experimental observations, but also elucidate the internal structural information and complement the findings in the region of high grafting densities of diblock copolymers.     

Melt brushes of diblock copolymer

Using self-consistent field theory (SCFT), we investigate the morphologies formed by a melt brush of AB diblock copolymers grafted to a flat substrate by their B ends. In addition to a laterally uniform morphology, SCFT predicts three ordered morphologies exhibiting different periodic patterns at the air surface: a hexagonal array of A-rich dots, an alternating sequence of A- and B-rich stripes, and a hexagonal pattern of B-rich dots. When the phase diagram of the tethered film is plotted as a function of A/B incompatibility, N , and diblock composition, f , it resembles the bulk phase diagram with the periodic phases converging to a mean-field critical point at weak segregation. The periodic-phase region in the phase diagram shrinks with increasing grafting density and expands when the air surface acquires an affinity for the grafted B blocks.     

Polyelectrolytes tethered to a free surface

Several attempts have been already carried out in order to tether charged chains by an end at a free fluctuating surface. We review here most of these attempts and focus on how close the physics of charged brushes can be investigated by such an approach. We first describe results about films of charged-neutral diblock copolymers spread at the surface of water. Results can be mostly rationalized in terms of charged brushes although additional structurations and fluctuations of the interface can be observed. The latter deformations are also observed when adsorbed layers of charged-neutral diblock copolymers are considered. At last, we examine how free suspended films of charged-neutral diblock copolymers can be viewed as two opposing charged brushes, both in terms of thickness and pressure. Received 9 May 2000     

Confinement-induced novel morphologies of block copolymers

Self-assembly of block copolymers confined in cylindrical nanopores is studied systematically using a simulated annealing technique. For diblock copolymers which form two-dimensional hexagonally packed cylinders with period L0 in the bulk, novel structures such as helices and stacked toroids spontaneously form inside the cylindrical pores. These confinement-induced morphologies have no counterpart in the bulk system and they depend on the pore diameter (D) and the surface-polymer interactions, reflecting the importance of structural frustration and interfacial interactions. On tightening the degree of confinement, transitions from helices to toroids to spheres are observed. Mechanisms of the morphological transitions can be understood based on the degree of structural frustration parametrized by the ratio D/L0.     

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.     

两嵌段共聚物软受限自组装行为研究

采用模拟退火算法,系统研究了软受限条件下两嵌段共聚物自组装形貌极其转化机理。共聚物形貌可受到受限程度,组分体积分数,以及溶剂选择性3方面因素的调制。在弱受限条件下,共聚物形貌均为球状呈各向同性。核-壳-笼形貌可以极大的增加组分A和组分B之间的接触粒子数,达到增熵降能的效果,在我们的研究工作中是一种罕见的构型。形成多核结构的条件是： AB复合链末端距与其链长比值小于0.23。此次工作对于纳米颗粒的实验制作以及药品输运方面具有极大的理论指导意义。     

Cylindrical-confinement-induced phase behaviours of diblock copolymer melts

The phase behaviours of diblock copolymers under cylindrical confinement are studied in two-dimensional space by using the self-consistent field theory. Several phase parameters are adjusted to investigate the cylindrical-confinement-induced phase behaviours of diblock copolymers. A series of lamella-cylinder mixture phases, such as the mixture of broken-lamellae and cylinders and the mixture of square-lamellae and cylinders, are observed by varying the phase parameters, in which the behaviours of these mixture phases are discussed in the corresponding phase diagrams. Fur-thermore, the free energies of these mixture phases are investigated to illustrate their evolution processes. Our results are compared with the available observations from the experiments and simulations respectively, and they are in good agreement and provide an insight into the phase behaviours under cylindrical confinement.     

Solvent vapor induced morphology transition in thin film of cylinder forming diblock copolymer

The morphology formation and transition of thin film of a cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymer annealed under 1,1,2-trichloroethane (Tri-CE), toluene (Tol), and their binary mixed solvent vapors is investigated by using optical microscopy (OM) and transmission electronic microscopy (TEM). By modulating the annealing solvent vapor pressure and the preferential affinities, a detailed morphology evolution with increasing the vapor pressure and a series of morphologies depending on the preferential affinities have been observed. A phase diagram by plotting the morphologies as a function of the annealing solvent vapor pressure and its preferential affinity is subsequently constructed.     

End-tethered charged chains at surfaces

We present here a short review covering most of the experimental results on tethering charged chains by an end to a surface. A first class of experiments deals with solid surfaces where charged chains are either chemically grafted or adsorbed through a purposely chosen moiety. Structural studies have been carried out by scattering methods, spectroscopic techniques or microscopy. Forces between the polyelectrolyte layers covering the surfaces have also been obtained by using for instance, the surface force apparatus (SFA). A second class of experiments concerns polyelectrolytes, which are end-tethered to flexible surfaces like air–liquid or liquid–liquid interfaces. These experiments are fewer in number and mainly rely on the adsorption or spreading of charged diblock copolymers at the fluid interfaces.