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.     

Shear-induced ordering of lamellar and gyroid structures observed in a nonionic surfactant/water system

The shear-induced ordering of lamellar and gyroid structures of a nonionic surfactant C₁₆E₇/D₂O system in a Couette shear cell ( 0.001 < < 10 s^-1, : shear rate) has been investigated by using a small angle neutron scattering technique. In the lamellar phase, the steady shear flow having > 0.01 s^-1 suppresses undulation fluctuations of lamellae (Maxwell effect). This suppression of fluctuations brings two effects; 1) shear-induced lamellae ordering toward a parallel orientation and 2) obstruction of a lamellar↦gyroid transition. It is quite interesting to note that there is a characteristic shear rate range ( 0.01 < < 0.3 s^-1), where both effects take place. We have also investigated the shear effects on the gyroid phase. Below the characteristic shear rate range, the gyroid structure keeps three-dimensional network lattice, while above the characteristic shear rate range, the gyroid structure transforms to the parallel orientation lamellae (shear-induced gyroid-lamellar transition). Thus the shear flow having the characteristic shear rate plays very important roles in shear ordering phenomena. Received 26 June 2000 and Received in final form 12 January 2001     

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite c \chi N . With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical ( S _cp phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd ( O⁷⁰ morphology, showing that conformational asymmetry has a significant effect on its stability.     

Elasticity effects on domain coarsening of the lamellar-gyroid transition observed in a nonionic surfactant system

The coarsening process of the gyroid phase of a nonionic surfactant system is investigated by time resolved small angle neutron scattering (SANS) and small angle neutron Laue diffraction techniques. The time evolution of SANS patterns shows anomalous coarsening of the gyroid domains. The observed Laue spot from a gyroid domain becomes elongated along the radial direction with the elapse of time and at a certain time the elongated spot is split into two spots. The results can be interpreted as follows. During the coarsening process, mismatch of the lattice orientation at the domain boundary brings strong stress to the gyroid domain, resulting in the distortion of the domain. The stored stress in the domain finally brings splitting of the gyroid domain. The elastic and fragile nature of the gyroid domains composed of the "soft matter" is responsible for the anomalous coarsening.     

Gyroid symmetry and phase diagram of weak crystallization

The phase diagram in the (τ-δ) plane, where τ is the reduced temperature and δ is a parameter characterizing the anisotropy of the fourth vertex of the effective Hamiltonian, is constructed on the basis of the standard mean-field approximation of the theory of weak crystallization. It is shown that the region of the gyroid phase dominates the phase diagram for intermediate values of the parameters τ and δ. An expression is obtained for the free energy of the gyroid phase. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 436–440 (25 March 1996)     

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.     

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.     

Bonding in the superionic phase of water

The predicted superionic phase of water is investigated via ab initio molecular dynamics at densities of 2.0--3.0 g/cc (34-115 GPa) along the 2000 K isotherm. We find that extremely rapid (superionic) diffusion of protons occurs in a fluid phase at pressures between 34 and 58 GPa. A transition to a stable body-centered cubic O lattice with superionic proton conductivity is observed between 70 and 75 GPa, a much higher pressure than suggested in prior work. We find that all molecular species at pressures greater than 75 GPa are too short lived to be classified as bound states. Up to 95 GPa, we find a solid superionic phase characterized by covalent O-H bonding. Above 95 GPa, a transient network phase is found characterized by symmetric O-H hydrogen bonding with nearly 50% covalent character. In addition, we describe a metastable superionic phase with quenched O disorder.     

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.     

Spherical/gyroid phase diagram of the diblock copolymer in the median selective solvent

The effect of the median selective solution on the lamellar, spherical and gyroid structures is studied. The self-consistent field equations of the diblock copolymer solution are solved by using the reciprocal space method. It is shown that the spherical and gyroid phases have the lowest free energy in the certain range of the solution concentration. Furthermore, the phase diagram of the ordered structures in the diblock copolymer solution with the median selective solvent is calculated, which is consistent with the experimental results. Supported by the National Natural Science Foundation of China (Grant Nos. 10834014, 10674173, and 30770517) and the National Basic Research Program of China (Grant No. 2009CB930704)     

From 2D hyperbolic forests to 3D Euclidean entangled thickets

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra- and octa-continuous forms. Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts. Received 10 December 1999     

Entropy-driven formation of the gyroid cubic phase

We show, by computer simulation, that tapered or pear-shaped particles, interacting through purely repulsive interactions, can freely self-assemble to form the three-dimensionally periodic, gyroid cubic phase. The Ia3d gyroid cubic phase is formed by these particles on both compression of an isotropic configuration and expansion of a smectic A bilayer arrangement. For the latter case, it is possible to identify the steps by which the topological transformation from nonintersecting planes to fully interpenetrating, periodic networks takes place.     

Effects of compositional asymmetry in phase behavior of ABA triblock copolymer melts from Monte Carlo simulation

We simulate ABA triblock copolymer melts using a lattice Monte Carlo method, known as cooperative motion algorithm, probing various degrees of compositional asymmetry. Selected order-disorder transition lines are determined in terms of the segment incompatibility, quantified by product χN , and the triblock asymmetry parameters, α and β. We correlate the results of the simulation with the self-consistent field theory and an experimental study of polyisoprene-polystyrene-polyisoprene triblock melt by Hamersky and coworkers. In particular, we confirm the mean-field prediction that for highly asymmetric triblocks the short A -block is localized in the middle of the B -domain due to an entropic advantage. This results in the middle block relaxation and is consistent with the experimental data indicating that as the relatively short A -blocks are grown into AB diblock, from the B -block side, the order-disorder transition temperature is considerably depressed.     

Pressure-induced structural transformations and the anomalous behavior of the viscosity in network chalcogenide and oxide melts

It is known that a number of compressed melts undergo structural phase transitions. Data on the structural changes at high pressures in chalcogenides (AsS, As₂S₃) and oxide (B₂O₃) melts with a network structure have been reviewed. Viscosity is one of the fundamental physical properties of a liquid. For various melts, it varies in a very wide range. Structural transformations in melts induce the corresponding changes in all physical properties, in particular viscosity. The measurements of the viscosity of a number of melts at high pressures and temperatures by the radiographic method have been reported. Changes in the viscosity by several orders of magnitude have been detected when the pressure is varied by several gigapascals. The diffusion mechanism in network-structure melts at various pressures has been analyzed. The prediction of the behavior of the viscosity of various melts at superhigh pressures is of high importance for the physics of glass transition, geophysics, and materials science.     

硅酸盐熔体团粒结构类声子振动的高温拉曼光谱研究

硅酸盐熔体是典型的近程有序,远程无序的准稳定态分数维体系,文章采用X射线小角散射(SAXS)、低波数拉曼光谱(LWRS)及高温拉曼光谱(HTRS)实时、原位分析等技术,对高温熔融法和溶胶凝胶法合成的CaO-Al₂O₃-SiO₂和Na₂O-Al₂O₃-SiO₂系列低维非晶硅酸盐试样进行了团粒结构粒度及其类声子振动频率的定量测定,获得了低温硅酸盐凝胶、高温硅酸盐熔体及其淬火玻璃相均具有纳米级(几个纳米至几十纳米)自相似团粒结构和类声子振动模的重要结论,进而建立了测定高温熔体介观团粒结构粒度的HTRS测定法,结果表明硅酸盐熔体的团粒结构粒度在高温下均会比其室温玻璃相的团粒尺度小,且高温熔体的网络结构基元也向桥氧数减少之基元转变。这些结论为探索自然界岩浆的地球化学特征、岩浆的结晶和演化以及低维硅酸盐材料结构性能的改进提供重要理论依据及信息。     

Molecular order and dynamic mechanical behavior of polyurethanes based on liquid crystalline diol

Synthesis of the liquid crystalline (LC) diol 6,6′-[ethylenebis(l,4-phenylene-oxy)]-dihexanol (I) is described. The structure of polyurethanes prepared from diol I and 4,4′-methylenedi(phenyl isocyanate) (MDI), 4,4′-methylenedi(cyclohexyl isocyanate) (HMDI), or 2(4)-methyl-l,3-phenylene diisocyanate (TDI) at 1:1 molar ratios of isocyanate and hydroxy groups is studied by dynamic mechanical spectroscopy, differential scanning calorimetry (DSC), polarizing microscopy, and x-ray scattering. The polymer prepared from HMDI and the diol (I/HMDI) shows, on cooling, thermal behavior typical of amorphous polymers. A frequency-temperature superposition could be applied to the mechanical data, and the horizontal shift factor satisfied the Williams-Landel-Ferry (WLF) equation. A more-complex thermal behavior was found for I/HMDI polymer during subsequent heating; above 70°C, the formation of an ordered structure takes place, and this structure melts at about 120°C. Complex thermal behavior is exhibited by I/TDI polymer. On cooling its melt, the polymer forms a nematic phase at about 80°C, which freezes into the LC glassy state. On heating, the mesophase melts, and. subsequently, a better-ordered smectic phase is formed at 95°C, which melts at 120°C. This structure buildup is accompanied by a rapid increase in storage modulus G′, and the sample shows thermorheologically complex mechanical behavior. The polymer formed from the diol and MDI (I/MDI) exhibits a most-complex thermal behavior. On cooling and heating, four transitions can be detected in its thermal mechanical behavior, and the structure of the polymer is strongly dependent on its thermal history.     

Bend-induced melting of the smectic-A phase: analogy to a type-I superconductor

Using an atomic force microscope to nanopattern a substrate for liquid crystal alignment, a bend distortion is imposed on a liquid crystal. In regions of large bend the smectic-A phase melts into the nematic phase, and the width of the melted region is measured as a function of temperature. The results are consistent with type-I superconducting (nematic-smectic-A) behavior, wherein a large magnetic field (bend or twist distortion) induces an order to disorder transition. A model that accounts for non-mean-field behavior is presented.     

Direct measurement of interfacial curvature distributions in a bicontinuous block copolymer morphology

Self-consistent field theory predicts that the complex phase behavior of block copolymers does not originate solely from the interface seeking constant mean curvature as once thought, but instead reflects competing minimization of interfacial tension and packing frustration. To test this prediction, we directly measure interfacial curvature distributions from a 3D image reconstruction of the bicontinuous gyroid morphology. Results obtained here reveal that the gyroid interface is not constant mean curvature and confirm the importance of packing frustration in the stabilization of such complex nanostructures.     

Melting transition of a network model in two dimensions

The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths. Received 4 June 1999 and Revised in final form 1 September 1999