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.     

Surface-field-induced effects on morphologies of lamella-forming diblock copolymers in nanorod arrays

The surface-induced effect on the morphologies of lamella-forming diblock copolymers in nanorod arrays is studied by using the self-consistent field theory.In the simulation study,a rich variety of novel morphologies are observed by variations in the strength of the surface field for the diblock copolymers.Different surface-field-induced effects are examined for the diblock copolymers in the arrays with distinct preferential surfaces.It is observed that the majority-block preferential surfaces have more obvious induced effects than those of minority-block preferential surfaces.The strong surface fields exhibit different behaviours from those observed in the weak surface fields,by which the morphologies possess cylindrical symmetries.Results from this research deepen the knowledge of surface-induced effects in a confinement system,which may aid the fabrication of polymer-based nanomaterials.     

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.     

Disordered network state in hydrated block-copolymer surfactants

Hydration of poly(butadiene-b-ethylene oxide) diblock copolymers leads to various ordered and disordered phases, analogous to the aqueous phase behavior of surfactants and lipids. Small-angle x-ray scattering measurements corroborated by cryogenic scanning electron microscopy imaging reveal a random network (N) morphology at polymer compositions and water content intermediate to those associated with ordered cylinders (H1) and lamellae (L). This sequence of self-assembled structures is strikingly similar to the phase behavior of certain water-oil-surfactant microemulsions.     

Structural changes in block copolymers: coupling of electric field and mobile ions

We argue that the presence of dissociated ions in block copolymers under electric fields can induce strong morphological changes and even lead to phase transitions. We investigate, in particular, diblock copolymers in the body centered cubic (bcc) phase. In pure dielectric materials (no free charges), a dielectric breakdown is expected to occur for large enough electric fields, preempting any structural phase transition. On the other hand, dissociated ions are predicted to induce a phase transition to a hexagonal array of cylinders, at fields of about 10 V/microm or even lower. The strength of this mechanism can be tuned by controlling the amount of free ions present.     

非对称半结晶两嵌段共聚物的微相分离与结晶行为的模拟退火研究

利用模拟退火方法研究非对称半结晶两嵌段共聚物熔体分别在弱分离和强分离条件下的结晶过程.考察微相分离作用和结晶作用的相对强度对柱状组成的两嵌段共聚物平衡形态的影响.研究结果表明,当嵌段间的相互排斥作用较弱时,结晶便破坏了柱状畴;当此相互作用足够强时,结晶过程可以有效地被限制在熔体微相分离所形成的柱状畴内.另外,介于上述两种情形之间还存在一个模板区域,此时熔体形成的柱状畴大部分被保留下来,但在局部会变形或连通.这些结果和文献报道的实验结果一致.当嵌段间的相互排斥作用非常强时,结晶被抑制,微相分离主导最终形态,观察到了非晶态结构.     

非对称线棒线ABA三嵌段共聚物自组装的自洽场研究

利用自洽场方法在三维空间模拟计算非对称型线/棒/线ABA三嵌段共聚物的自组装.在线棒嵌段体积比例相等的条件下,改变两端的线嵌段体积比例,观察到层状、螺旋状、条状和柱状结构.相分离相互作用参数随着一侧线嵌段体积比例增加而逐渐增大,并且当一侧线体积分数为0.05时,相行为最为丰富.随着相互作用参数增大,层状、螺旋和层状结构依次出现,这与相应的线/棒二嵌段共聚物是不同的;层状、螺旋、条状和柱状结构的出现与相应的对称线/棒/线三嵌段共聚物的自组装行为也不同.     

Ring pattern solutions of a free boundary problem in diblock copolymer morphology

The cross section of a diblock copolymer in the cylindrical phase is made up of a large number of microdomains of small discs with high concentration of the minority monomers. Often several ring like microdomains appear among the discs. We show that a ring like structure may exist as a stable solution of a free boundary problem derived from the Ohta-Kawasaki theory of diblock copolymers. The existence of such a stable, single ring structure explains why rings exist for a long period of time before they eventually disappear or become discs in a diblock copolymer. A variant of Lyapunov-Schmidt reduction process is carried out that rigorously reduces the free boundary problem to a finite-dimensional problem. The finite-dimensional problem is solved numerically. A stability criterion on the parameters determines whether the ring solution is stable.     

Multiple patterns of diblock copolymer confined in irregular geometries with soft surface

The different confinement shapes can induce the formation of various interesting and novel morphologies, which might inspire potential applications of materials. In this paper, we study the directed self-assembly of diblock copolymer confined in irregular geometries with a soft surface by using self-consistent field theory. Two types of confinement geometries are considered, namely, one is the concave pore with one groove and the other is the concave pore with two grooves. We obtain more novel and different structures which could not be produced in other two-dimensional(2D) confinements. Comparing these new structures with those obtained in regular square confinement, we find that the range of ordered lamellae is enlarged and the range of disordered structure is narrowed down under the concave pore confinement.We also compare the different structures obtained under the two types of confinement geometries, the results show that the effect of confinement would increase, which might induce the diblock copolymer to form novel structures. We construct the phase diagram as a function of the fraction of B block and the ratio of h/L of the groove. The simulation reveals that the wetting effect of brushes and the shape of confinement geometries play important roles in determining the morphologies of the system. Our results improve the applications in the directed self-assembly of diblock copolymer for fabricating the irregular structures.     

Undulated cylinders of charged diblock copolymers

We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable. By modeling the shape of the cylinder ends, we find that the free-energy barrier for the transition from cylinders to spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity. This suggests that observed undulated cylinder phases are kinetically trapped structures.     

Discovering ordered phases of block copolymers: new results from a generic Fourier-space approach

A generic Fourier-space approach to solve the self-consistent field theory of block copolymers is developed. This approach is based on the fact that, for any computational box with periodic boundary conditions, all spatially varying functions are spanned by the Fourier series determined by the size and shape of the box. The method reproduces all known diblock copolymer phases. The application of this method to a model "frustrated" triblock copolymer leads to a phase diagram with a number of new phases. Furthermore, the capability of the method to reproduce experimentally observed structures is demonstrated using the knitting pattern of triblock copolymers.     

嵌段共聚物受限于软孔内的自组装

利用自洽场方法研究两嵌段共聚物受限于接枝均聚物链(聚合物刷)圆孔中的自组装相形貌.研究表明,当圆孔内径一定时,嵌段比f和聚合物刷C的体积分数φ_C是调控嵌段共聚物相形貌的主要因素,聚合物刷的弹性熵也起着重要作用.当f＝0.7时,在聚合物刷的浸润下,贴近刷表面处AB嵌段共聚物构成环层状结构,随着φ_C的减小这种结构会周而复始地出现.当f处于0. 关键词： 嵌段共聚物 圆孔受限 聚合物刷 自洽场     

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。     

Modelling of the viscoelastic behavior of homogeneous and heterogeneous blends of polyisoprene and polybutadiene

The mechanical model of Takayanagi has been used to describe the viscoelastic behavior of various blends of a ternary elastomer system (cis-1, 4 polyisoprene, 1, 4-polybutadiene, and the corresponding polyisoprene/polybutadiene diblock) for which extensive mechanical properties data have already been reported. Through the use of appropriate composition-temperature shifts which rely on the assumption of free volume additivity, it was possible to model the behavior of the homogeneous diblock copolymers of polyisoprene and polybutadiene as well as various homogeneous binary and ternary blends of a diblock with either or both of the diene homopolymers. Heterogeneous ternary blends were also modelled successfully by assuming that the diblock was solubilized preferentially by one of the phases in the blend. The model predictions were very sensitive to the location of the diblock, and thus comparison with experimental results provided a useful tool for verifying earlier assumptions regarding the role of the homogeneous diblock copolymers in these elastomer blends.     

Effect of shear on the symmetric diblock copolymer/nanorod mixture: A dissipative particle dynamics study

The phase behaviours of a lamellar diblock copolymer/nanorod composite under steady shear are investigated using dissipative particle dynamics.We consider a wide range of nanorod concentrations,where the nanorods each have a preferential affinity to one of the blocks.Our results suggest that shear not only aligns the orientations of the diblock copolymer templates and nanorods towards flow direction,but also regulates the distribution of the nanorods within the polymer matrix.Meanwhile,the shear-induced reorientation and morphology transitions of the systems also significantly depend on the nanorod concentration.At certain nanorod concentrations,the competitions between shearinduced polymer thinning and nanorods dispersion behaviours determine the phase behaviours of the composites.For high nanorod concentrations,no morphology transition is observed,but reorientation is present,in which the sheared nanorods are arranged into hexagonal packing arrays.Additionally,the orientation behaviour of nanorods is determined directly by the applied shear,also interfered with by the shear-stretched copolymer molecules.     

Theoretical investigation of the phase behaviour of model ternary mixtures containing n-alkanes,perfluoro-n-alkanes,and perfluoroalkylalkane diblock surfactants

We have used the hetero-SAFT-VR approach developed by McCabe and collaborators [Mol. Phys. 104, 571 (2006)] to investigate the phase equilibria of a number of binary and ternary mixtures of n-alkanes, perfluoro-n-alkanes, and perfluoroalkylalkane diblock surfactants. We focused our work on the understanding of the microscopic conditions that control the phase behaviour of these mixtures, with a particular emphasis of the effect on the liquid–liquid separation and the stabilisation of n-alkane + perfluoro-n-alkane mixtures when a diblock surfactant is added. We used very simple molecular models for n-alkanes, and perfluoro-n-alkanes that describe the molecules as chains with tangentially bonded segments with molecular parameters taken from the literature. In the particular case of semifluorinated alkanes or SFA surfactants, we used an hetero-segmented diblock chain model where the parameters for the alkyl and perfluoroalkyl segments taken from the corresponding linear alkanes and perfluoroalkanes, as shown in our previous work [J. Phys. Chem. B 111, 2856 (2007)]. Our goal was to identify the main effects on the phase behaviour when different perfluoroalkylalkane surfactants are added to mixtures of n-alkanes and perfluoro-n-alkanes. We selected the n-heptane + perfluoromethane binary mixture, and studied the changes on the phase behaviour when a symmetric (same number of alkyl and perfluoroalkyl chemical groups) or an asymmetric (different number of alkyl and perfluoroalkyl chemical groups) diblock surfactants is added to the binary mixture. We have obtained the phase diagrams of a wide range of binary and ternary mixtures at different thermodynamic conditions. We have found a variety of interesting behaviours as we modify the alkyl or/and the perfluoroalkyl chain-length of the diblock surfactants: the usual changes in the vapour–liquid phase separation, changes in the type of phase diagrams (typically from type I to type V phase behaviour according to the Scott and Konynenburg classification), azeotropy, and Bancroft points. We noted that the main effect of adding a symmetric or an asymmetric surfactant to the n-heptane + perfluoromethane mixture is to stabilise the system, i.e. to decrease the two-phase (liquid–liquid) immiscibility region of the ternary diagram as the surfactant concentration is increased. This effect becomes larger as the chain length of the surfactant is increased, which is consistent with a higher number of alkyl–alkyl and perfluoroalkyl–perfluoroalkyl favourable interactions in the mixture.     

Geometric theory of diblock copolymer phases

We analyze the energetics of spherelike micellar phases in diblock copolymers in terms of well-studied, geometric quantities for their lattices. We argue that the A15 lattice with Pm3;n symmetry should be favored as the blocks become more symmetric and corroborate this through a self-consistent field theory. Because phases with columnar or bicontinuous topologies intervene, the A15 phase, though metastable, is not an equilibrium phase of symmetric diblocks. We investigate the phase diagram of branched diblocks and find that the A15 phase is stable.     

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.     

Theory of microphase separation on side-chain liquid-crystalline polymers with flexible spacers

We model a melt of monodisperse side-chain liquid-crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded-volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free-energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases or phases with modulated wave vector but without nematic ordering. Such microphases are the result of the competition between the incompatibility among the blocks and the connectivity constraints imposed by the spacer and the backbone. Also the effects of the polymerization degree and structural conformation of the monomeric units on the phase behavior of the side-chain liquid-crystalline polymers are studied.