STUDY OF COARSENING OF MICRODOMAINS IN BLOCK COPOLYMERS BY LATTICE BOLTZMANN METHODS

In order to understand the coarsening of microdomains in symmetric diblock copolymers at the late stage, a model for block copolymers is proposed. By incorporating the self consistent field theory with the free energy approach Lattice Boltzmann model, hydrodynamic interactions can be considered. Compared with models based on Ginzburg-Landau free energy, this model does not employ phenomenological free energies to describe systems. The model is verified by comparing the simulation results obtained using this method with those of a dynamical version of the self consistent mean field theory. After that,the growth exponents of the characteristic domain size for symmetric block copolymers at late stage are studied. It is found that the viscosity of the system affects the growth exponents greatly, although the growth exponents are all less than 1/3 Furthermore, the relations between the growth exponent, the interaction parameter and the chain length are studied.

Nucleation in A/B/AB blends: Interplay between microphase assembly and macrophase separation

We study the interplay between microphase assembly and macrophase separation in A/B/AB ternary polymer blends by examining the free energy of localized fluctuation structures (micelles or droplets), with emphasis on the thermodynamic relationship between swollen micelles (microemulsion) and the macrophase-separated state, using self-consistent field theory and an extended capillary model. Upon introducing homopolymer B into a micelle-forming binary polymer blend A/AB, micelles can be swollen by B. A small amount of component B (below the A-rich binodal of macrophase coexistence) will not affect the stability of the swollen micelles. A large excess of homopolymer, B, will induce a microemulsion failure and lead to a macrophase separation.

Bump-Surface Multicompartment Micelles from a Linear ABC Triblock Copolymer: A Combination Study by Experiment and Computer Simulation

Novel bump-surface multicompartment micelles formed by a linear amphiphilic ABC triblock copolymer via self-assembly in selective solvent were successfully observed both in simulation and experiment. The results revealed that the block A forms the most inner core, and the blocks B and C form the inner and outer layers, respectively, and the bumps were formed by block A and more likely to be born on curving surfaces. Moreover, the micelle shape could be controlled by changing the solvent selectivity of the blocks A and B. Spherical, cylindrical, and discoidal micelles with bumpy surfaces were obtained both in experiment and simulation.

Effect of Solvent Molecular Size on the Self-Assembly of Amphiphilic Diblock Copolymer in Selective Solvent

Real-space self-consistent field theory (SCFT) is employed to study the effect of solvent molecular size on the self-assembly of amphiphilic diblock copolymer in selective solvent. The phase diagrams in wide ranges of interaction parameters and solvent molecular size were obtained in present study. The results indicate that the solvent molecular size is a key factor that determines the self-assembly of amphiphilic diblock copolymer. The self-assembled morphology changes from circle-like micelle to line-like micelle, then to loop-like micelle by decreasing the solvent molecular size in a wide range of solvent selectivity. We analyze and discuss this change in terms of the solvent solubility and the entropy contribution.

Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Colloidal photonic crystals with a graded lattice-constant distribution

In this work, a gradient polystyrene colloidal photonic crystal was fabricated by annealing in a graded temperature field. The lattice constant of the gradient crystal gradually varied along the temperature-gradient direction. The positional bandgap wavelength as well as the attenuation of the bandgap wavelength could be tuned dependent on the position of the gradient colloidal crystal along the gradient direction because of the lattice-constant variation.

Comparing the morphology and phase diagram of H-shaped ABC block copolymers and linear ABC block copolymers

By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymers, we have investigated the morphology of H-shaped ABC block copolymers (A(2)BC(2)) and compared them with those of the linear ABC block copolymers. By changing the ratios of the volume fractions of two A arms and two C arms, one can obtain block copolymers with different architectures ranging from linear block copolymer to H-shaped block copolymer. By systematically varying the volume fractions of block A, B, and C, the triangle phase diagrams of the H-shaped ABC block copolymer with equal interactions among the three species are constructed. In this study, we find four different morphologies ( lamellar phase ( LAM), hexagonal lattice phase ( HEX), core-shell hexagonal lattice phase (CSH), and two interpenetrating tetragonal lattice (TET2)). Furthermore, the order-order transitions driven by architectural change are discussed.

Inverted to normal phase transition in solution-cast polystyrene-poly(methyl methacrylate) block copolymer thin films

We have investigated the inverted phase formation and the transition from inverted to normal phase for a cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymer in solution-cast films with thickness about 300 nm during the process of the solution concentrating by slow solvent evaporation. The cast solvent is 1, 1,2,2-tetrachloroethane (Tetra-CE), a good solvent for both blocks but having preferential affinity for the minority PMMA block. During such solution concentrating process, the phase behavior was examined by freeze-drying the samples at different evaporation time, corresponding to at different block copolymer concentrations, phi. As phi increases from similar to 0.1 % (nu/nu), the phase structure evolved from the disordered sphere phase (DS), consisting of random arranged spheres with the majority PS block as I core and the minority PMMA block as a corona, to ordered inverted phases including inverted spheres (IS), inverted cylinders (IC), and inverted hexagonally perforated lamellae (IHPL) with the minority PMMA block comprising the continuum phase, and then to the lamellar (LAM) phase with alternate layers of the two blocks, and finally to the normal cylinder (NC) phase with the majority PS block comprising the continuum phase. The solvent nature and the copolymer solution concentration are shown to be mainly responsible for the inverted phase formation and the phase transition process.

Effective thermal conductivity of graded nonlinear composites with heat contact resistance

The perturbation expansion method is used to find the effective thermal conductivity of graded nonlinear composites having thermal contact resistance on the inclusion surface. As an example, we have studied the graded composites with cylindrical inclusions immersed in a homogeneous matrix. The thermal conductivity of the cylindrical inclusion is assumed to have a power-law profile of the radial distance r measured from its origin. For weakly nonlinear constitutive relations between the heat flow density q and the temperature field T, namely, q = -mu del T - chi vertical bar del T vertical bar(2) del T, in both the inclusion and the matrix regions, we have derived the temperature distributions using the perturbation expansion method. A nonlinear effective medium approximation of graded composites is proposed to estimate the effective linear and nonlinear thermal conductivities. by considering the temperature singularity on the inclusion surface due to the heat contact resistance. (c) 2006 Elsevier B.V. All rights reserved.

Dielectric responses of anisotropic graded granular composites having arbitrary inclusion shapes

The transformation field method (TFM) originated from Eshelby's transformation field theory is developed to estimate the effective permittivity of an anisotropic graded granular composite having inclusions of arbitrary shape and arbitrary anisotropic grading profile. The complicated boundary-value problem of the anisotropic graded composite is solved by introducing an appropriate transformation field within the whole composite region. As an example, the effective dielectric response for an anisotropic graded composite with inclusions having arbitrary geometrical shape and arbitrary grading profile is formulated. The validity of TFM is tested by comparing our results with the exact solution of an isotropic graded composite having inclusions with a power-law dielectric grading profile and good agreement is achieved in the dilute limit. Furthermore, it is found that the inclusion shape and the parameters of the grading profile can have profound effect on the effective permittivity at high concentrations of the inclusions. It is pointed out that TFM used in this paper can be further extended to investigate the effective elastic, thermal, and electroelastic properties of anisotropic graded granular composite materials.

中国近海和西北太平洋温跃层时空变化分析、模拟及预报

温度跃层是反映海洋温度场的重要物理特性指标，对水下通讯、潜艇活动及渔业养殖、捕捞等有重要影响。本文利用中国科学院海洋研究所“中国海洋科学数据库”在中国近海及西北太平洋（110ºE-140ºE,10ºN-40ºN）的多年历史资料（1930-2002年，510143站次），基于一种改进的温跃层判定方法，分析了该海域温跃层特征量的时空分布状况。同时利用Princeton Ocean Model(POM)，对中国近海，特别是东南沿海的水文结构进行了模拟，研究了海洋水文环境对逆温跃层的影响。最后根据历史海温观测资料，利用EOF分解统计技术，提出了一种适于我国近海及毗邻海域，基于现场有限层实测海温数据，快速重构海洋水温垂直结构的统计预报方法，以达到对现场温跃层的快速估计。 历史资料分析结果表明，受太阳辐射和风应力的影响，20°N以北研究海域，温跃层季节变化明显，夏季温跃层最浅、最强，冬季相反，温跃层厚度的相位明显滞后于其他变量，其在春季最薄、秋季最厚。12月份到翌年3月份，渤、黄及东海西岸，呈无跃层结构，西北太平洋部分海域从1月到3月份，也基本无跃层结构。在黄海西和东岸以及台湾海峡附近的浅滩海域，由于风力搅拌和潮混合作用，温跃层出现概率常年较低。夏季，海水层化现象在近海陆架海域得到了加强，陆架海域温跃层强度季节性变化幅度(0.31°C/m)明显大于深水区(约0.05°C/m)，而前者温跃层深度和厚度的季节性变化幅度小于后者。20°N以南研究海域，温跃层季节变化不明显。逆温跃层主要出现在冬、春季节（10月-翌年5月）。受长江冲淡水和台湾暖流的影响，东南沿海区域逆温跃层持续时间最长，出现概率最大，而在山东半岛北及东沿岸、朝鲜半岛西及北岸，逆温跃层消长过程似乎和黄海暖流有关。多温跃层结构常年出现于北赤道流及对马暖流区。在黑潮入侵黄、东、南海的区域，多温跃层呈现明显不同的季节变化。在黄海中部，春季多温跃层发生概率高于夏季和秋季，在东海西部，多跃层主要出现在夏季，在南海北部，冬季和春季多温跃层发生概率大于夏季和秋季。这些变化可能主要受海表面温度变化和风力驱动的表层流的影响。 利用Princeton Ocean Model(POM)，对中国东南沿海逆温跃层结构进行了模拟，模拟结果显示，长江冲淡水的季节性变化以及夏季转向与实际结果符合较好，基本再现了渤、黄、东海海域主要的环流、温盐场以及逆温跃层的分布特征和季节变化。通过数值实验发现，若无长江、黄河淡水输入，则在整个研究海域基本无逆温跃层出现，因此陆源淡水可能是河口附近逆温跃层出现的基本因素之一。长江以及暖流（黑潮和台湾暖流）流量的增加，均可在不同程度上使逆温跃层出现概率及强度、深度和厚度增加，且暖流的影响更加明显。长江对东南沿海逆温跃层的出现，特别是秋季到冬季初期，有明显的影响，使长江口海域逆温跃层位置偏向东南。暖流对于中国东南沿海的逆温跃层结构，特别是初春时期，有较大影响，使长江口海域的逆温跃层位置向东北偏移。 通过对温跃层长期变化分析得出，黄海冷水团区域，夏季温跃层强度存在3.8年左右的年际变化及18.9年左右的年代际变化，此变化可能主要表现为对当年夏季和前冬东亚地区大气气温的热力响应。东海冷涡区域，夏季温跃层强度存在3.7年的年际变化，在El Nino年为正的强度异常，其可能主要受局地气旋式大气环流变异所影响。谱分析同时表明，该海域夏季温跃层强度还存在33.2年的年代际变化，上世纪70年代中期，温跃层强度由弱转强，而此变化可能与黑潮流量的年代际变化有关。 海洋水温垂直结构的统计预报结果显示，EOF分解的前四个主分量即能够解释原空间点温度距平总方差的95%以上，以海洋表层附近观测资料求解的特征系数推断温度垂直结构分布的结果最稳定。利用东海陆架区、南海深水区和台湾周边海域三个不同区域的实测CTD样本廓线资料，对重构模型的检验结果表明，重构与实测廓线的相关程度超过95%的置信水平。三个区重构与实测温度廓线值的平均误差分别为0.69℃，0.52℃，1.18℃，平均重构廓线误差小于平均气候偏差，统计模式可以很好的估算温度廓线垂直结构。东海陆架海区温度垂直重构廓线与CTD观测廓线获得的温跃层结果对比表明，重构温跃层上界、下界深度和强度的平均绝对误差分别为1.51m、1.36m和0.17℃/m，它们的平均相对误差分别为24.7%、8.9%和22.6%，虽然温跃层深度和强度的平均相对误差较大，但其绝对误差量值较小。而在南海海区，模型重构温跃层上界、下界和强度的平均绝对预报误差分别为4.1m、27.7m和0.007℃/m，它们的平均相对误差分别为16.1%、16.8%和9.5%，重构温跃层各特征值的平均相对误差都在20%以内。虽然南海区温跃层下界深度平均绝对预报误差较大，但相对于温跃层下界深度的空间尺度变化而言（平均温跃层下界深度为168m），平均相对误差仅为16.8%。因此说模型重构的温度廓线可以达到对我国陆架海域、深水区温跃层的较好估算。 基于对历史水文温度廓线观测资料的分析及自主温跃层统计预报模型，研制了实时可利用微机简单、快捷地进行温跃层估算及查询的可视化系统，这是迄今进行大范围海域温跃层统计与实时预报研究的较系统成果。

Colliding and Moving Bose-Einstein Condensates: Studies of superfluidity and optical tweezers for condensate transport

In this thesis, two different sets of experiments are described. The first is an exploration of the microscopic superfluidity of dilute gaseous Bose- Einstein condensates. The second set of experiments were performed using transported condensates in a new BEC apparatus. Superfluidity was probed by moving impurities through a trapped condensate. The impurities were created using an optical Raman transition, which transferred a small fraction of the atoms into an untrapped hyperfine state. A dramatic reduction in the collisions between the moving impurities and the condensate was observed when the velocity of the impurities was close to the speed of sound of the condensate. This reduction was attributed to the superfluid properties of a BEC. In addition, we observed an increase in the collisional density as the number of impurity atoms increased. This enhancement is an indication of bosonic stimulation by the occupied final states. This stimulation was observed both at small and large velocities relative to the speed of sound. A theoretical calculation of the effect of finite temperature indicated that collision rate should be enhanced at small velocities due to thermal excitations. However, in the current experiments we were insensitive to this effect. Finally, the factor of two between the collisional rate between indistinguishable and distinguishable atoms was confirmed. A new BEC apparatus that can transport condensates using optical tweezers was constructed. Condensates containing 10-15 million sodium atoms were produced in 20 s using conventional BEC production techniques. These condensates were then transferred into an optical trap that was translated from the ‘production chamber’ into a separate vacuum chamber: the ‘science chamber’. Typically, we transferred 2-3 million condensed atoms in less than 2 s. This transport technique avoids optical and mechanical constrainsts of conventional condensate experiments and allows for the possibility of novel experiments. In the first experiments using transported BEC, we loaded condensed atoms from the optical tweezers into both macroscopic and miniaturized magnetic traps. Using microfabricated wires on a silicon chip, we observed excitation-less propagation of a BEC in a magnetic waveguide. The condensates fragmented when brought very close to the wire surface indicating that imperfections in the fabrication process might limit future experiments. Finally, we generated a continuous BEC source by periodically replenishing a condensate held in an optical reservoir trap using fresh condensates delivered using optical tweezers. More than a million condensed atoms were always present in the continuous source, raising the possibility of realizing a truly continuous atom lase.

AC and DC magnetic levitation: melting, fluid flow and oscillations

The presented numerical modelling for the magnetic levitation involves coupling of the electromagnetic field, liquid shape change, fluid velocities and the temperature field at every time step during the simulation in time evolution. Combination of the AC and DC magnetic fields can be used to achieve high temperature, stable levitation conditions. The oscillation frequency spectra are analysed for droplets levitated in AC and DC magnetic fields at various combinations. An electrically poorly conducting, diamagnetic droplet (e.g. water) can be stably levitated using the dia- and para-magnetic properties of the sample material in a high intensity, gradient DC field.