Selectivity and temperature dependence of phase and phase transition in diblock copolymer solution

In order to study the effects of solvent selectivity and temperature on phase behavior and transition of diblock copolymer solution, self-consistent field theory is modified to incorporate the short-range interaction and non-local effects. Inhomogeneous free-energy density is shown to be dependent on solvent selectivity, temperature and copolymer concentration. Enthalpic quantity and entropic contributions are crucial to phase diagrams of diblock copolymer solution. Three selective strengths of solvent --weak, moderate and strong-- are chosen for comparison. For a weakly selective solvent, theoretical and experimental results illustrate the same variation tendency in the phase boundary of the order-disorder transition for a symmetric diblock of polystyrene and polyisoprene. Self-consistent field equations can be used to calculate the exact FCC-BCC structural phase transition temperatures in moderately and strongly selective solvents. Detailed comparison with the experimental phase diagrams including lamellar, cylindrical and spherical structures is presented.     

Orthorhombic Fddd network in triblock and diblock copolymer melts

The phase behavior of ABC triblock and AB diblock copolymer melts is investigated by self-consistent field theory, while allowing for (among other candidates) the orthorhombic Fddd (O70) network phase identified in recent experiments with poly(isoprene-b-styrene-b-ethylene oxide) (ISO) triblocks. Predicted phase diagrams for triblocks similar to ISO contain an O70 phase bordered by gyroid, lamellar, and alternating gyroid phases, in agreement with experiment. The O70 network is also found to be stable in diblock melts within a narrow region that overlaps the weak segregation end of the gyroid region found in previous calculations.     

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.     

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.     

A2B嵌段共聚物熔体的相分离

采用自洽场的方法对A2B共聚物熔体作了类似星形共聚物的处理，研究了该共聚物的相分离并给出了相图．与两嵌段共聚物的相图相比较而言，在A2B的相图中，只发现了三个经典的有序相：球状相、六角蜂窝形柱状相以及层状相．从两嵌段线形共聚物到Y形共聚物这一链结构上的变化使相图也发生了相应的改变：各相的相边界发生了很大的偏移并且层状相出现的区域被大大的拓宽了．因此，可以通过改变链的结构来控制高分子自组装的微相结构，从而代替传统的改变高分子链中各组分的比例．     

Free energy evaluation in field-theoretic polymer simulations

We present a thermodynamic integration method for free energy evaluation in field-theoretic simulations of classical fluids and polymers. The approach employs an Einstein crystal reference state, analogous to a method developed for particle simulations of crystals by Frenkel and Ladd, but applies equally well in the present context to ordered and disordered phases. Thermodynamic averages are computed using complex Langevin sampling, which is effective against the sign problem inherent to polymer field theories. Our method is illustrated in the context of a diblock copolymer melt, where we provide a demonstration of the experimentally observed transition between the cubic gyroid and disordered phases.     

Monte Carlo phase diagram for diblock copolymer melts

The phase diagram for diblock copolymer melts is evaluated from lattice-based Monte Carlo simulations using parallel tempering, improving upon earlier simulations that used sequential temperature scans. This new approach locates the order-disorder transition (ODT) far more accurately by the occurrence of a sharp spike in the heat capacity. The present study also performs a more thorough investigation of finite-size effects, which reveals that the gyroid (G) morphology spontaneously forms in place of the perforated-lamellar (PL) phase identified in the earlier study. Nevertheless, there still remains a small region where the PL phase appears to be stable. Interestingly, the lamellar (L) phase next to this region exhibits a small population of transient perforations, which may explain previous scattering experiments suggesting a modulated-lamellar (ML) phase.     

Large eddy simulation of compressible turbulent channel flow with spanwise wall oscillation

The influences of the modification of turbulent coherent structures on temperature field and heat transfer in turbulent channel flow are studied using large eddy simulation (LES) of compressible turbulent channel flows with spanwise wall oscillation (SWO). The reliability of the LES on such problems is proved by the comparisons of the drag reduction data with those of other researches. The high consistency of coherent velocity structures and temperature structures is found based on the analyses of the turbulent flow field. When the coherent velocity structures are suppressed, the transportations of momentum and heat are reduced simultaneously, demonstrating the same trend. This shows that the turbulent coherent structures have the same effects on the transportations of momentum and heat. The averaged wall heat flux can be reduced with appropriate oscillating parameters. Supported by the Key Subjects of National Natural Science Foundation of China (Grant No. 10732090), the National Natural Science Foundation of China (Grant No. 50476004), and the 111 Project (Grant No. B08009)     

Nanoscopic surface patterns of diblock copolymer thin films

The surface topography of thin diblock copolymer films is studied by atomic force microscopy (AFM). With AFM an island-to-ribbon transition is observed for symmetric polystyrene-b-poly (4-vinylpyridine) (PS-b-P4VP) on mica with increasing solution concentration. Our study also demonstrates how the formation of the pattern strongly depends on the copolymer composition based on the volume fraction. The substrate and solvent used both have great effects on the morphology of the thin films. Only by using highly polar substrate (mica), can we gain regular pattern. The reason why the regular islands cannot be obtained with symmetric PS-b-P4VP on graphite is also explained. On mica using nonselective and selective solvents, a rather regular pattern can be obtained. The difference is only in the solution concentration for forming regular patterns.     

Study on electromagnetic backscattering and Doppler spectrum of a moving spherical target above time-varying sea surface

The surface electric current of the sea surface and the first-order scattering field from the spherical target were obtained by employing Physical Optics method and Mie theory, respectively. The backscattering field of the time-evolving sea surface was calculated by using Kirchhoff Approximation. Meanwhile, by taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary coupling scattering fields from the spherical target above the sea surface was reduced. The dependence of the secondary coupling backscattering field on the size and the position of the spherical target was discussed, and the characteristic of the Doppler spectrum of the composite backscattering field with different incident angles was analyzed in detail. Supported by the National Natural Science Foundation of China (Grant No. 60571058) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070701010)     

两亲性类树枝状聚合物的合成与药物控释

结合阴离子开环聚合方法合成了内壳为聚(乙氧基乙基缩水甘油醚),外层为聚环氧乙烷的两亲性类树枝状嵌段共聚物PEEGE-G2-b-PEO(OH)₁₂. 使用核磁共振氢谱以及凝胶渗透色谱等表征了中间产物和目标产物. 选择阿霉素作为实验药物,研究了该聚合物的载药和控释行为. 聚合物的载药率和包覆效率分别为13.07%和45.75%,体外释放试验表现为持续性的释放,并受到释放介质pH影响.     

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.     

Bleustein-Gulyaev waves in a functionally graded piezoelectric material layered structure

This work presents a theoretical study of the propagation behavior of Bleustein-Gulyaev waves in a layered structure consisting of a functionally graded piezoelectric material (FGPM) layer and a transversely isotropic piezoelectric substrate. The influence of the graded variation of FGPM coefficients on the dispersion relations of Bleustein-Gulyaev waves in the layered structure is investigated. It is demonstrated that, for a certain frequency range of Bleustein-Gulyaev waves, the mechanical perturbations of the particles are restricted in the FPGM layer and the phase velocity is independent of the electrical boundary conditions at the free surface. Results presented in this study can not only provide further insight on the electromechanical coupling behavior of surface waves in FGPM layered structures, but also lend a theoretical basis for the design of high-performance surface acoustic wave (SAW) devices. Supported by the National Natural Science Foundation of China (Grant No. 10632060), the National Basic Research Program of China (Grant No. 2006CB601202), the National 111 Project of China (Grant No. B06024), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070698064)     

Mechanism for hierarchical self-assembly of nanoparticles on scaffolds derived from block copolymers

Lithographically patterned substrates can direct the self-assembly of block copolymer films into aligned structures that, in turn, template the self-organization of colloidal nanoparticles. Deposition on pristine diblock copolymer films does not lead to reproducible selective decoration, but films modified to have nanoscale corrugation act as scaffolds for highly selective nanoparticle adsorption. The mechanism for this selectivity relies on the lateral forces inherent to spin casting to remove all of the nanoparticle suspension not confined within the nanoscopic trenches. This technique does not rely on interactions between the surfactant capping molecules and the polymer and is therefore general to a wide class of nanoparticle materials. Prospects to obtain long-range ordering and associated potential applications are discussed.     

Tricontinuous cubic structures in ABC/A/C copolymer and homopolymer blends

Using the Monte Carlo lattice-simulation technique, we present numerical evidence of the formation of gyroid and nongyroid tricontinuous cubic phases in high polymeric systems of ABC/A/C triblock copolymer and homopolymer blends. By increasing the volume fraction of homopolymer, a remarkable phase sequence G (gyroid) --> D (diamond) --> P (primitive) is observed, which is common to certain surfactant systems. Our results indicate that the ABC triblock copolymer system with blending homopolymers may be a zoo of cubic phases, suitable for comparative studies of these phases.     

Comparing the efficiencies of different detect strategies in the ping-pong protocol

The way to compare the efficiencies of different detect strategies (DSs) in the “ping-pong” protocol is studied. The trade-off between information gain and disturbance is calculated and compared for different DSs. The comparison result primely tallies with our intuitional analysis. It is shown that the analysis of this trade-off is a feasible way to compare the performances of different DSs in theory. Supported by the National High Technology Research and Development Program of China (Grant No. 2006AA01Z419), the National Natural Science Foundation of China (Grant Nos. 90604023 and 6087319), the National Laboratory for Modern Communications Science Foundation of China (Grant No. 9140C1101010601), the Natural Science Foundation of Beijing (Grant No. 4072020), and the ISN Open Foundation.     

Structures and electronic properties of SimN8-m（0 〈 m 〈 8） clusters： a density functional theory study

The geometries, electronic structures and related properties of SimN8-m（0 〈 m 〈 8） clusters are studied using density functional theory （DFT） with hybrid functional B3LYP. The calculated results reveal several trends. For any stoichiometric clusters, the lowest energy isomers with an alteration of N and Si atoms are favourable in energy if the numbers of Si and N atoms are large enough to form ... Si N-Si-N... alternative chains. The bond lengths of single Si-N bonds are very close to the corresponding values of the bulk and other SiN clusters. The geometries for N-rich and Si4N4 clusters are planar structures, but three-dimensional structures are favourable in energy for Si-rich clusters. With the increase of m, the isotropic polarizability and average polarizability increase, the total binding energies generally decrease, the HOMO-LUMO gap and vertical ionization potential oscillate with increasing number of valence electrons, and their values with even valence electrons are larger than those with odd valence electrons. The atomic charges, IR and Raman properties are also reported.     

Study of valence intersubband absorption in tensile strained Si/SiGe quantum wells

The hole subband structures and effective masses of tensile strained Si/Sil-yGey quantum wells are calculated by using the 6 × 6 k·p method. The results show that when the tensile strain is induced in the quantum well, the light-hole state becomes the ground state, and the light hole effective masses in the growth direction are strongly reduced while the in-plane effective masses are considerable. Quantitative calculation of the valence intersubband transition between two light hole states in a 7nm tensile strained Si/Si0.55Ge0.45 quantum well grown on a relaxed Si0.5Ge0.5 （100） substrates shows a large absorption coefficient of 8400 cm^-1.     

Analytical solutions describing the phase separation driven by a free energy functional containing a long-range interaction term

We are primarily concerned with the variational problem with long-range interaction. This functional represents the Gibbs free energy of the microphase separation of diblock copolymer melts. The critical points of this variational problem can be regarded as the thermodynamic equilibrium state of the phase separation phenomenon. Experimentally it is well-known in the diblock copolymer problem that the final equilibrium state prefers periodic structures such as lamellar, column, spherical, double-diamond geometries and so on. We are interested in the characterization of the periodic structure of the global minimizer of the functional (corresponding to the strong segregation limit). In this paper we completely determine the principal part of the asymptotic expansion of the period with respect to epsilon (interfacial thickness), namely, we estimate the higher order error term of the period with respect to epsilon in a mathematically rigorous way in one space dimension. Moreover, we decide clearly the dependency of the constant of proportion upon the ratio of the length of two homopolymers and upon the quench depth. In the last section, we study the time evolution of the system. We first study the linear stability of spatially homogeneous steady state and derive the most unstable wavelength, if it is unstable. This is related to spinodal decomposition. Then, we numerically investigate the time evolution equation (the gradient flow of the free energy), and see that the free energy has many local minimizers and the system have some kind of sensitivity about initial data. (c) 1999 American Institute of Physics.     

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.