Weak segregation theory and non-conventional morphologies in the ternary ABC triblock copolymers

The statistical theory of microphase separation in the ternary ABC triblock copolymers is presented and the corresponding phase diagrams are built both for the linear and miktoarm copolymers. For this purpose the Leibler weak segregation theory in molten diblock copolymers is generalized to multi-component monodisperse block copolymers with due regard for the 2nd shell harmonics contributions defined in the paper. The Hildebrand approximation for the χ-parameters is used. The physical meaning of this and alternative choices for the χ-parameters is discussed. The symmetric A_fB_1-2fC_f copolymers with the middle block non-selective with respect to the side ones are shown to undergo the continuous ODT not only into the lamellar phase but also, instead, into various non-conventional cubic phases (depending on the middle block composition it could be the simple cubic, face-centered cubic or non-centrosymmetric phase, which reveals the symmetry of I4₁ 32 space group No. 214 first predicted to appear in molten block copolymers). For asymmetric linear ABC copolymers a region of compositions is found where the weakly segregated gyroid (double gyroid) phase exists between the planar hexagonal and lamellar or one of the non-conventional cubic phases up to the very critical point. In contrast, the miktoarm (star) ABC block copolymers with one of its arm non-selective with respect to the two others are shown to reveal a pronounced tendency towards strong segregation, which is preceded by increase of stability of the conventional BCC phase and a peculiar weakly segregated BCC phase (BCC₃), where the dominant harmonics belong to the 3rd coordination sphere of the reciprocal lattice. The validity region of the developed theory is discussed and outlined in the composition triangles both for linear and miktoarm copolymers. We present also the list of the 2nd shell harmonics (SAXS reflections) allowed and prohibited in some of the non-conventional morphologies due to the weak segregation considerations and comparison of our results with the preceding SCFT treatment of the ABC copolymers by Matsen.     

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.     

Extension of integral equation theory to microphase separation of block copolymers

The confined polymer reference interaction site model (Wall-PRISM) integral equation theory was applied to investigate the microphase separation behaviour of copolymers at a solid surface or in bulk. In particular, the effects of the solid surface on polymer conformation were taken into account for constructing a set of novel bridge functionals for different segments to improve the theory. After the integration of the bridge functionals, the theory can well reproduce the simulated density profiles at different microphase domains of flexible–flexible, flexible–rigid, and linear–branched copolymers. As a consequence, the application scope of the inhomogeneous theoretical approach has been extensively extended. This work provides a prospective way to quantitatively predict the density profiles in microphase separation for block copolymers with sophisticated conformation.     

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.     

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.     

Investigation of phase separation in multiblock copolymers consisting of polysulfone and a liquid crystalline polymer

Multiblock copolymers (MBCPs) consisting of polysulfone (PSU) segments and segments of the liquid crystalline poly(ethyleneterephthalate-co-oxybenzoate) (PET/HBA) form rather complex morphologies. Scanning electron microscopy (SEM), small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM) investigations of two block copolymers with significantly different block molecular weights proved the existence of both macro-and microphase separation. These morphologies, existing on different length scales, were found to be superimposed in the samples. A suitable fractionation procedure was used to suppress macrophase separation. Then, it was found that microphase separation is controlled by the segment molecular weights.     

Wetting-driven structure ordering of a copolymer/homopolymer/nanoparticle mixture in the presence of a modulated potential

We investigate pattern formation on a solid substrate of a diblock copolymer-homopolymer mixture containing doping wettable nanoparticles with a preferential attraction for one component of the copolymers, using a three-order-parameter model. The presence of doping nanoparticles under the surface-interaction modulation breaks the isotropy in the process of microphase-separation and macrophase-separation. This leads to the formation of orientational microphase and macrophase structures due to the interplay between the phase separation and wetting particle ordering under a modulated potential at the late stage. Simulations suggest that the microphase morphology and macrophase morphology can be changed through adjustment of the wetting strength, the amplitude as well as the period of the modulated potential. It provides some important insights for changing microphase and macrophase structures in polymer blends by wetting-driven spinodal decomposition.     

Diblock and triblock copolymer thin films on a substrate with controlled selectivity

Using self-consistent field theory (SCFT), morphology development in symmetric linear ABC triblock copolymer films on neutral and selective substrates has been studied, and it is compared with the triblock copolymer morphologies in bulk. In particular, the effects of the substrate preferable to B (interior) block on nanopattern formation of the copolymer films are of our central interest. Here, we report various nanopatterns with tunable square morphologies. The domain patterns are much more diverse than those parallel to the substrate with substrate selectivity for end-block or those vertical to the substrate without substrate selectivity. Furthermore, in order to figure out an economical and efficient way to fabricate useful passive pattern transfer layers, which have potential applications in microelectronic processes and ultrahigh density storage media, we propose a two-step strategy and scrutinize the conditions for generating square symmetries using cylinder-forming or lamella-forming AB diblock copolymers deposited on substrates created from ABC triblock copolymer films. It is found that a thinner film with weak incompatibility can produce square patterns.     

Self-assembly of rod-coil block copolymers from weakly to moderately segregated regimes

We report on the self-assembly behaviour of two homologue series of rod-coil block copolymers in which, the rod, a π -conjugated polymer, is maintained fixed in size and chemical structure, while the coil is allowed to vary both in molecular weight and chemical nature. This allows maintaining constant the liquid crystalline interactions, expressed by Maier-Saupe interactions, ω , while varying the tendency towards microphase separation, expressed by the product between the Flory-Huggins parameter and the total polymerization degree, χN . Therefore, the systems presented here allow testing directly some of the theoretical predictions for the self-assembly of rod-coil block copolymers in a weakly segregated regime. The two rod-coil block copolymer systems investigated were poly(DEH-p-phenylenevinylene-b-styrene), whose self-assembly takes place in the very weakly segregated regime, and poly(DEH-p-phenylenevinylene-b-4vinylpyridine), for which the self-assembly behaviour occurs under increased tendency towards microphase separation, hereby referred to as moderately segregated regime. Experimental results for both systems are compared with predictions based on Landau expansion theories.     

Discovering new ordered phases of block copolymers

We propose a new and general method for discovering novel ordered phases of block copolymer melts. The method involves minimizing a free energy functional in an arbitrary unit cell with respect to the composition profile and the dimensions of the unit cell, without any prior assumption of the microphase symmetry. Varying the initial conditions allows to search for different stable and metastable structures. Application of this method to ABC star and linear triblock copolymers using an approximate free energy reveals new morphologies not yet observed in experiment.     

基于自洽场理论两亲高分子自组装的研究

运用扩展的自洽场和密度泛函理论(SCF/DFT),研究ABC蝌蚪形两亲高分子在稀溶剂中的自组装形态,其中蝌蚪形两亲高分子由线形嵌段共聚物链AB嫁接到球形纳米颗粒C上构成.与以往研究的线形ABC两亲高分子相比,蝌蚪形两亲高分子的自组装形态有着很大的不同.在粒子亲溶剂,嵌段共聚物疏溶剂时,各组分间弱分凝条件下,蝌蚪形两亲高分子自组装成胶球状形貌;在强分凝条件下,随着嵌段共聚物疏溶剂性的增强,两亲高分子的自组织态由胶球状转变成四角、三角状形貌,其中嵌段B主要分布在各角上.通过改变各组分间的相互作用,在嵌段A亲溶剂,嵌段B和粒子疏溶剂时,粒子呈平行棒状或小方块状分布在胶球中.     

Dynamics and order-disorder transitions in bidisperse diblock copolymer blends

We employ the dynamic extension of self-consistent field theory (DSCFT) to study dynamics and order-disorder transitions (ODT) in AB diblock copolymer binary mixtures of two different monodisperse chain lengths by imitating the dynamic storage modulus G′ corresponding to any given morphology in the oscillatory shear measurements. The different polydispersity index (PDI) is introduced by binary blending AB diblock copolymers with variations in chain lengths and chain number fractions. The simulation results show that the increase of polydispersity in the minority or symmetric block introduces a decrease in the segregation strength at the ODT, (χN)_ODT, whereas the increase of polydispersity in the majority block results in a decrease, then increase and final decrease again in (χN)_ODT. To the best of our knowledge, our DSCFT simulations, for the first time, predict an increase in (χN)_ODT with the PDI in the majority block, which produces the experimental results. The simulations by previous SCFT, which generally speaking, is capable of describing equilibrium morphologies, however, contradict the experimental data. The polydispersity acquired by properly tuning the chain lengths and number fractions of binary diblock copolymer blends should be a convenient and efficient way to control the microphase separation strength at the ODT.     

Self-organization of triblock copolymer patterns obtained by drying and dewetting

Self-organized block copolymer structures derived from dewetting of thin films are becoming important in nanotechnology because of the various spontaneous and regular sub-micrometric surface patterns that may be obtained. Here, we report on the self-organization of a poly(styrene)-b-poly(ethene-co-butene-1)-b-poly(styrene) triblock copolymer during drying of its solution over a mica substrate. Regular submicrometric arrangements with long-range order were formed at critical polymer concentrations, consisting of parallel ribbons and hexagonal arrays of dots (droplets). This variety of highly ordered structures is explained by the interplay between forming mechanisms, mainly due to “fingering instabilities” at the three-phase line of the copolymer solution during drying. The thickness of the structures was “quantized” due to the microphase separation of the block copolymer. The formation of hexagonal patterns may be attributed to Marangoni instability at the liquid film surface prior to dewetting.     

Effect of Polymer-Substrate Interactions on the Surface Morphology of Polymer Blend Thin Films: Comparison between Simulation and Experiment

Microphase and macrophase separation phenomena can simultaneously appear in ABA/C copolymer blend systems due to the immiscibility among monomers A, B, and C. In this work, the surface morphologies and compositions of ABA/C blend thin films confined between two walls, which were used to mimic SEBS/PMMA films, have been simulated by a lattice Monte Carlo (MC) method. The effect of the polymer-wall interaction on the surface morphologies and compositions of thin films was investigated as a function of blend composition and film thickness. It is shown that the simulated surface morphologies of thin films resulting from the macrophase separation between copolymer ABA and homopolymer C and the microphase separation between block A and block B in ABA copolymer are similar to the experimental surface morphology of SEBS/PMMA polymer blend films observed by atomic force microscope (AFM). The effect of substrate on the surface morphologies by MC simulation is qualitatively consistent with the experimental results. The composition profiles of thin films are given to characterize the micro- and macrophase separation in thin films. It is indicated that the surface energy of the substrate (substrate/air) plays a crucial role on the surface composition. For a fixed surface, the adsorptions of polymer on the substrate and film thickness are also important.     

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.     

Analysis of acoustic directivity of spherical cap transducers

In order to study the acoustic radiation from the spherical cap transducer,a theoretical model is used by solving the wave equation in spherical coordinates using the method of separation of variables,based on the spherical harmonic Fourier transform and boundary condition.The calculation formulas for the far field radiated pressure and directivity of spherical cap are derived.Some theoretical results are presented in the form of far-field directivity patterns of the spherical cap transducer for various polar angles of the spherical cap,radii of sphere baffle and operating frequencies.Both the diameter of the sphere baffle and the wavelength determine the directivity of acoustic radiation from a spherical cap.When the frequency is lower or the wavelength is longer than the diameter of the sphere baffle,the acoustic radiation from a spherical cap is omnidirectional.With the increase of the frequency or the diameter of the sphere baffle,the acoustic radiation from a spherical cap is more directional and the beamwidth more tends to spherical cap angle.Furthermore,the ripple in the beam is more obvious.The high frequency spherical cap transducer was fabricated and the directivity pattern was tested and the measurement data is shown to coincide with the theoretical results.This research can provide a guideline for designing the spherical cap transducers and arrays.     

球冠型换能器声辐射指向性分析

为了研究球冠型换能器的声辐射特性,在分离变量法求解球面坐标系下波动方程的基础上,采用基于球谐基傅里叶变换及边界条件的求解模型,给出了球冠型换能器声辐射的远场声压计算表达式和远场指向性表达式;仿真计算了球冠换能器的远场指向性随球冠极角、球半径及振动频率变化的特性,球冠所在球障板的直径和介质中声波的波长比决定着球冠声辐射指向性,在低频或波长大于球障板直径时,球冠声辐射呈无指向性,随着频率的增高即波长的减小或者球障板直径的增大,球冠声辐射的指向性越明显,波束开角越趋向于球冠的开角,而且波束开角内出现波浪状起伏越明显;试制了高频球冠型换能器基阵,测试了换能器基阵300 kHz的指向性,测试结果与理论计算相符合,验证了理论计算表达式的正确性,可为设计球冠型换能器及基阵提供理论指导。      

Morphology and strength of elastic films of structured latices

Thermoplastic elastomers (TPEs) are conventionally made of block copolymers or partly cross-linked polymer blends. Alternatively, TPEs can be prepared from structured latices, too. Hard-soft latex particles with a thermoplastic core and an elastomeric shell yield highly extendable elastic films, the strength of which depends sensitively on the relative core size and the particle architecture. Core-shell particles were prepared, by two-step emulsion polymerization, with the thermoplastic polystyrene (PS) in the core and the elastomer polyethylacrylate (PEA) in the shell. PEA particles were synthesized first. The PS cores were then incorporated in them in the second step. This method permits the design of monocore. as well as multicore, particles. These PS-PEA particles were not cross-linked in the core or in the shell. They can be classified as microblends. Compression-molded films of them exhibited, therefore, a coarsened microphase morphology that was, however, still much finer than that of simple melt-mixed blends PS/PEA. The film morphologies of monocore and multicore particles were different as far as the former yielded spherical PS domains, while the latter yielded extended PS clusters. This was strongly reflected by the stress-strain behavior: Films from multicore particles responded in a viscoelastic, rubbery manner, while films from monocore particles behaved like viscous liquids.     

受限壁的选择性对软受限下星形三嵌段共聚物形貌的影响

基于嵌段共聚物在软受限条件下能够自组装形成很多有序结构,在催化、电子器件、光学传感等领域有广泛的应用价值,目前只对线性三嵌段共聚物在软受限下的自组装形貌做了分析,对星形三嵌段共聚物在软受限下的自组装行为还未有一个统一的定论.在这项研究中,应用模拟退火来研究ABC星形三嵌段共聚物在软受限下的自组装行为,嵌段与溶剂没有选择性下(中性壁),通过调整三个嵌段(f_A、f_B和f_C)的体积分数来构建相图,我们的模拟预测了各种独特的自组装纳米结构,包括薄片+球形、圆柱状,穿孔层,薄片+圆柱体,核壳补丁.然后通过改变嵌段与溶剂的选择性预测了链长度比为1:x:1的共聚物粒子形貌.通过计算接触数、均方根末端距与平均链长的比值以及平均键长随x的变化,验证了形貌转变机制.     

Universality of striped morphologies

We present a method for predicting the low-temperature behavior of spherical and Ising spin models with isotropic potentials. For the spherical model the characteristic length scales of the ground states are exactly determined but the morphology is shown to be degenerate with checkerboard patterns, stripes and more complex morphologies having identical energy. For the Ising models we show that the discretization breaks the degeneracy causing striped morphologies to be energetically favored and therefore they arise universally as ground states to potentials whose Hankel transforms have nontrivial minima.