Nanoparticle surfactants as a route to bicontinuous block copolymer morphologies

The surface chemistry of nanoparticles can be modified so that these particles behave like surfactants and localize at interfaces between two fluids. We demonstrate that small volume fractions phi(P) of such surfactant nanoparticles added to lamellar diblock copolymers lead initially to a decrease in lamellar thickness with phi(P), a consequence of decreasing interfacial tension, up to a critical value of phi(P), beyond which the block copolymer adopts a bicontinuous morphology. These bicontinuous morphologies have stable domain spacings below 100 nm that further decrease with increasing phi(P) and offer new routes to nanoscopically engineered polymer films with potential photovoltaic, fuel cell, and battery applications.     

Geometric frustration phases of diblock copolymers in nanoparticles

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.     

Crowding effect induced phase transition of amphiphilic diblock copolymer in solution

The crowding agent induced phase transition of amphiphilic block copolymers in solution was explicitly considered. The influence of the size and the volume fraction of the crowding agent on the phase separation of amphiphilic diblock copolymers is investigated by using self-consistent field theory (SCFT) method. The concentration of the disorder to order transition of the block copolymer decreases when the size of the crowding agent is larger than that of the solvent. The higher volume fraction of the crowding agent will induce the transition of the block copolymer from disorder to order state at a lower concentration. The relation between the size and the volume fraction of the crowding agent is elucidated. When the size of the crowding agent is larger, its volume fraction of the disorder to order transition of the block copolymer will be lower. The conformation of the crowding agent considered as a polymer chain is also studied and compared.     

多嵌段共聚物/纳米粒子杂化多级结构的光学性能

结合耗散粒子动力学模拟和时域有限差分方法,研究了A(BC)_n多嵌段共聚物和纳米粒子共混体系的自组装行为及其光学性能,分析了纳米粒子体积分数和嵌段间相互作用强度对自组装形貌及其光学性能的影响。结果表明,A(BC)_n多嵌段共聚物/纳米粒子共混体系可形成有机/无机杂化的多级结构,改变纳米粒子的体积分数和嵌段间相互作用强度可以调控纳米粒子的分布及其相应的多级结构。不同尺度的结构对不同频率光的反射作用有明显区别,而纳米粒子的加入显著增大了反射峰的强度和宽度。改变纳米粒子的分布可调控反射峰的强度和宽度。     

Non‐equilibrium phase behavior of diblock copolymer melts and binary blends in the intermediate segregation regime

The phase behavior of intermediately segregated (χN = 45) poly(ethylene)‐poly(ethylethylene) (PE–PEE) diblock copolymers and PE–PEE binary blends are characterized using transmission electron microscopy and small‐angle X‐ray scattering. Surprisingly, the preparation‐dependent, nonequilibrium phase behavior can be overwhelming even at this degree of segregation. A pure diblock with a poly(ethylene) volume fraction of f_PE = 0.46 exhibited coexisting lamellae and perforated layers when prepared using a precipitation technique, but contained only the lamellar morphology when solvent cast. This preparation dependence was more dramatic in binary diblock copolymer blends with average compositions of 〈f_PE〉 = 0.44, 0.46, and 0.48. Precipitated blends exhibited a microphase separated structure that was disordered and bicontinuous; however, solvent cast samples exhibited either a cylindrical, coexisting cylindrical and lamellar, or lamellar morphology. This nonequilibrium behavior is attributed to the high degree of segregation and the proximity to the cylinder/lamellae phase boundary. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2229–2238, 1999     

Many body effects on the phase separation and structure of dense polymer-particle melts

Liquid state theory is employed to study phase transitions and structure of dense mixtures of hard nanoparticles and flexible chains (polymer nanocomposites). Calculations are performed for the first time over the entire compositional range from the polymer melt to the hard sphere fluid. The focus is on polymers that adsorb on nanoparticles. Many body correlation effects are fully accounted for in the determination of the spinodal phase separation instabilities. The nanoparticle volume fraction at demixing is determined as a function of interfacial cohesion strength (or inverse temperature) for several interaction ranges and nanoparticle sizes. Both upper and lower critical temperature demixing transitions are predicted, separated by a miscibility window. The phase diagrams are highly asymmetric, with the entropic depletion-like lower critical temperature occurring at a nanoparticle volume fraction of approximately 10%, and a bridging-induced upper critical temperature at approximately 95% filler loading. The phase boundaries are sensitive to both the spatial range of interfacial cohesion and nanoparticle size. Nonmonotonic variations of the bridging (polymer-particle complex formation) demixing boundary on attraction range are predicted. Moreover, phase separation due to many body bridging effects occurs for systems that are fully stable at a second order virial level. Real and Fourier space pair correlations are examined over the entire volume fraction regime with an emphasis on identifying strong correlation effects. Special attention is paid to the structure near phase separation and the minimum in the potential of mean force as the demixing boundaries are approached. The possibility that nonequilibrium kinetic gelation or nanoparticle cluster formation preempts equilibrium phase separation is discussed.     

Morphology and domain size of a model graft copolymer

We prepared well-defined styrene (S)-2-vinyl-pyridine (P) graft copolymers of the ABB type or SPP graft copolymers, in which as block chain is grafted at the center of a block chain, as a model graft copolymer by anionic polymerization and coupling reaction. The composition dependence of morphology of SPP graft copolymers is qualitatively the same as that of SP diblock copolymers, but the composition range of each structure is shifted to the higher volume fraction of S block chain. The molecular weight dependence of lamellar domain size of SPP graft copolymers is almost the same as that of SP diblock copolymers, but the magnitudes are smaller. These experimental results are well explained by the difference in chain architectures.     

Coarse-grained molecular dynamics simulation on the placement of nanoparticles within symmetric diblock copolymers under shear flow

We present molecular dynamics simulations coupled with a dissipative particle dynamics thermostat to model and simulate the behavior of symmetric diblock copolymer/nanoparticle systems under simple shear flow. We consider two categories of nanoparticles, one with selective interactions toward one of the blocks of a model diblock copolymer and the other with nonselective interactions with both blocks. For the selective nanoparticles, we consider additional variants by changing the particle diameter and the particle-polymer interaction potential. The aim of our present study is to understand how the nanoparticles disperse in a block copolymer system under shear flow and how the presence of nanoparticles affects the rheology, structure, and flow behavior of block copolymer systems. We keep the volume fraction of nanoparticles low (0.1) to preserve lamellar morphology in the nanocomposite. Our results show that shear can have a pronounced effect on the location of nanoparticles in block copolymers and can therefore be used as another parameter to control nanocomposite self-assembly. In addition, we investigate the effect of nanoparticles on shear-induced lamellar transition from parallel to perpendicular orientation to further elucidate nanocomposite behavior under shear, which is an important tool to induce long-range order in self-assembling materials such as block copolymers.     

Effect of the supporting pattern on the orientation of hexagonal morphology in thin films of diblock copolymers

The model of a thin film sandwiched between two parallel planes the gap between which is filled with the melt of diblock copolymers is revisited. One of the planes (a supporting plane) has a pattern, whereas the other plane (an upper) is uniform. The proposed model is based on mean self-consistent field concepts. The parameters of diblock copolymers are selected so that the melt of diblock copolymers yields a hexagonal morphology in its volume. The upper boundary of the film and support avoid contact with the minor component of the diblock copolymer; as a result, in the film, a hexagonal morphology parallel to the support is formed. When hexagonal and rectangular patterns with preferential interaction with the minor component (the period of patterns coincides with the period of hexagonal symmetry in the volume), the hexagonal morphology changes its orientation from parallel to perpendicular relative to the support. The hexagonal morphology changes its orientation at sufficiently strong interaction between the pattern and minor component. Structural factor is calculated, and characteristic features in the location of peaks for perpendicular and parallel phases of hexagonal morphology are found. The development of additional peaks in the structural factor comes from deformations induced by the interaction between components of the melt of diblock copolymers with the upper boundary, support, and pattern.     

Structure rationalization and topology prediction of two-distinct-component organic crystals: the role of volume fraction and interface topology

We consider here small-length-scale crystal structures with two clearly different molecular components (e.g., hydrophobic and hydrophilic). Using a perspective developed by studies on large-length-scale block copolymers and liquid crystals, we focus on the crystalline interface between the two components. We examine four types of two-component crystals: aromatic ammonium carboxylates, aromatic oligo(ethylene oxides), cyclohexylammonium carboxylates, and ether-thioether compounds. Of the 111 crystal structures found in the Cambridge Structure Database (CSD), 108 adopt one of the five generic topologies found in diblock copolymers: spheres, columns, perforated layers, layers, and bicontinuous structures. As in diblock copolymers, a key factor controlling the interfacial topology is shown to be the volume ratio of the two components. When the volume fraction of one component is less than 30% of the whole, more than five-sixths of the examined crystal structures are of columnar or spherical type. For volume fractions between 40 and 50% more than three-quarters are of lamellar or bicontinuous type. We use this model to predict the topologies of small-length-scale two-component crystals. We predict the crystal topolgies of six new crystal structures: three are predicted to be columnar, and the other three, lamellar or bicontinuous. The crystal structures of these systems were then determined by single-crystal X-ray methods. Five of the structures form in topologies consistent with the predictions: three in columns and two in layers. The remaining one forms as a perforated layer instead of the predicted columnar structure. Such predictive accuracy is consistent with the statistics of the CSD investigation.     

Phase behavior and interfacial properties of diblock copolymer-homopolymer ternary mixtures: Influence of volume fraction of copolymers and interaction energy

We use a Monte Carlo method to study the phase and interfacial behaviors of A-b-B diblocks in a blend of homopolymers, A and B, which are confined between two asymmetric hard and impenetrable walls. Our results show that, when the interaction strength is weak, the block copolymersare uniformly distributed in the ternary mixtures under considered concentrations. Under strong interaction strength, distribution region of the block copolymers changes from a single smooth interface to a curved interface or multi-layer interface in the ternary mixtures. Furthermore, our findings show that with increasing volume fraction of A-b-B diblock copolymer(фC), copolymer profiles broaden while фC≥ 0.4, a lamellar phase is formed and by further increasing фC, more thinner layers are observed. Moreover, the results show that, with the increase of фC, the phase interface first gradually transforms from plane to a curved surface rather than micelle or lamellar phase while with the increase of the interaction between A and B segments(ε_(AB)), the copolymer chains not only get stretched in the direction perpendicular to the interface, but also are oriented. The simulations also revealthat the difference between symmetric and asymmetric copolymers is negligible in statistics if the lengths of two blocksare comparable.     

A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers

Pure diblock copolymer melts exhibit a narrow range of conditions at which bicontinuous and cocontinuous phases are stable; such conditions and the morphology of such phases can be tuned by the use of additives. In this work, we have studied a bidisperse system of diblock copolymers using theory and simulation. In particular, we elucidated how a short, lamellar-forming diblock copolymer modifies the phase behavior of a longer, cylinder-forming diblock copolymer. In a narrow range of intermediate compositions, self-consistent field theory predicts the formation of a gyroid phase although particle-based simulations show that three phases compete: the gyroid phase, a disordered cocontinuous phase, and the cylinder phase, all having free energies within error bars of each other. Former experimental studies of a similar system have yielded an unidentified, partially irregular bicontinuous phase, and our simulations suggest that at such conditions the formation of a partially transformed network phase is indeed plausible. Close examination of the spatial distribution of chains reveals that packing frustration (manifested by chain stretching and low density spots) occurs in the majority-block domains of the three competing phases simulated. In all cases, a double interface around the minority-block domains is also detected with the outer one formed by the short chains, and the inner one formed by the longer chains.     

Physical deposition behavior of charged amphiphilic diblock copolymers: Effect of charge distribution and electric field

Coarse-grained molecular dynamics simulations are used to investigate physical deposition behavior of charged amphiphlic diblock copolymers. The effects of solvent selectivity, charge distribution in amphiphlic diblock copolymers, and electric field strength on deposition conformations are studied qualitatively. Flat amphiphilic bilayers, which consist of hydrophilic monolayer and hydrophobic brush, are formed by physical deposition of charged amphiphlic diblock copolymers in nonselective solvents. For physically deposited amphiphlic diblock copolymers in selective solvents, amphiphilic bilayers consist of disc-shaped hydrophilic monolayers and hydrophobic nanospheres are found. This study sheds light on the formation of various amphiphlic diblock copolymer deposition conformations in different solvents and interaction mechanism of different components. Furthermore, the evolution of physical deposition process of charged amphiphlic diblock copolymers layer offers new insight to the controlling of amphiphilic bilayer thickness, hydrophobic nanosphere size, and interface property of depositional amphiphlic diblock copolymers.     

掺杂嵌段共聚物薄膜的相分离研究

采用Monte Carlo方法结合退火方法研究掺杂非对称两嵌段共聚物薄膜的相分离情况.发现随着掺杂极性粒子浓度的增加,嵌段共聚物薄膜体系由层状相逐渐转化成层状和柱状共混相,最后变成分布均匀的柱状相.当掺杂浓度增加到一定程度时,形成了如六边形(6-fold)、七边形(7-fold)和五边形柱状(5-fold)的相结构;六边形柱状相结构的比例随着浓度增加而增加,七边形(7-fold)和五边形柱状(5-fold)相结构的比例随着浓度增加而减小.同时还讨论了两嵌段共聚物大小与掺杂浓度的关系.     

Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers

Using the self-consistent field theory (SCFT), we investigate the phase behavior of a mixture of diblock copolymers and nanoparticles with monodisperse polymer chains tethered to their surfaces. We assume the size of the nanoparticles to be much smaller than that of the attached polymer chains and therefore model the particles with their grafted polymer "shell" as star polymers. The polymer chains attached to the particles are of the same species as one of the blocks of the symmetric diblock copolymer. Of primary interest is how to tune the shell of the particle by changing both the length and number of tethered polymers in order to achieve higher loading of nanoparticles within an ordered structure without macrophase separation occurring. We find that the phase behavior of the system is very sensitive to the size of the particle including its tethered shell. The region of microphase separation is increased upon decreasing the star polymer size, which may be achieved by shortening and/or removing tethered polymer chains. To explore the possible structures in these systems we employ SCFT simulations that provide insight into the arrangement of the different species in these complex composites.     

Macrophase‐separation in binary blends of symmetric polystyrene‐polybutadiene diblock copolymers

Binary blends of compositionally symmetric polystyrene‐polybutadiene diblock copolymers are investigated as a function of chain length ratio and blend composition using small‐angle neutron scattering. Three different low molar mass copolymers were blended with a high molar mass copolymer. The results are related to the theoretical phase diagram put forward by M. W. Matsen (J. Chem. Phys. 103 , 3268 (1995)). The conditions for macrophase‐separation are established, an observed asymmetry of the lamellae rich in long copolymers is discussed and the variation of the lamellar thickness with the volume fraction of short chains in the one‐phase state is compared with theoretical predictions.     

Surface-induced phase transitions in ultrathin films of block copolymers

We study theoretically the lamellar-disorder-lamellar phase transitions of AB diblock and tetrablock copolymers confined in symmetric slitlike pores where the planar surface discriminatingly adsorbs A segments but repels B segments, mimicking the hydrophobic/hydrophilic effects that have been recently utilized for the fabrication of environmentally responsive "smart" materials. The effects of film thickness, polymer volume fraction, and backbone structure on the surface morphology have been investigated using a polymer density-functional theory. The surface-induced phase transition is manifested itself in a discontinuous switch of microdomains or a jump in the surface density dictated by the competition of surface adsorption and self-aggregation of the block copolymers. The surface-induced first-order phase transition is starkly different from the thickness-induced symmetric-asymmetric or horizontal-vertical transitions in thin films of copolymer melts reported earlier.     

Effect of particle surface selectivity on composite nanostructures in nanoparticle/diblock copolymer mixture dilute solution

In this study the phase behavior of nanoparticle/diblock copolymer composites in dilute solution has been investigated by the hybrid particle-field (HPF) method. We focus on the influence of particle surface selectivity (i.e. hydrophobic and hydrophilic) on the distribution of nanoparticles in the micelles formed by the diblock copolymers. These two types of particle surface selectivity are simulated systematically. The different competition between the energy from enthalpy and the energy from entropy has been observed in the two kinds of composite systems. Our simulation results show that the particle surface selectivity is a crucial factor for determining the thermodynamic properties in the complex dilute solution, and the morphologies of micelles are controlled by the volume fraction of the nanoparticles. The change of particle distribution in various micelles enriches the composite microstructures that can be formed by nanoparticle and diblock copolymer.     

PE/PEO/PE-PEO 对称三元共混体系相行为的耗散粒子动力学模拟研究

建立了对应实验体系聚乙烯/聚氧化乙烯/聚乙烯-聚氧化乙烯嵌段共聚物(PE/PEO/PE-PEO)的对称三元共混模型,并采用耗散粒子动力学(DPD)模拟方法对其相行为进行了理论研究.研究结果表明,随着均聚物体积分数的增加,体系的平衡相态发生由层状相(LAM)到双连续微乳液(BME)再到相分离(PS)的转变,相态演化规律和...     

Mesophase Separation of Diblock Copolymer Confined in a Cylindrical Tube Studied by Dissipative Particle Dynamics

Summary: The morphologies of diblock copolymers confined in a cylindrical tube have been investigated by the dissipative particle dynamics (DPD) method. Results indicate that the morphology depends on the volume ratio of the immiscible blocks, the diameter of the cylindrical tube and the interactions between the blocks and between the confinement wall and blocks. For symmetric diblock copolymers, when the tube wall is uniform toward the two blocks, perpendicular lamellae or a stacked disk morphology are generally formed except when the diameter of the cylindrical tube is very small; in that case, a special bi‐helix morphology forms because of the entropy effect. When the tube wall is non‐uniform, as the diameter of the tube increases, perpendicular lamellae are first formed, then changing to parallel lamellae and, finally, back to perpendicular lamellae again. An intermediate morphology characterizing the transition between perpendicular and parallel lamellae is observed. If the non‐uniformity of the wall is further enhanced, only parallel lamellae can be found. In the case of asymmetric diblock copolymers, more complex morphologies can be obtained. Multi‐cylindrical micro‐domains and a multilayer helical phase as well as other complex pictures are observed. Generally, the morphologies obtained could find their counterparts from experiments or Monte Carlo simulations; however, differences do exist, especially in some cases of asymmetric diblock copolymers.

Bi‐helix and stacked disks morphologies of A₅B₅ diblock copolymer confined in two different neutral nanocylinders.