高分子溶液中物理凝胶化的Monte Carlo模拟和小角中子散射研究

高分子凝胶广泛地存在于自然界以及日常生活中，按其形成作用力不同分为化学凝胶和物理凝胶两大类。由于高分子物理凝胶具有凝胶化的可逆性及其对环境条件强烈的响应性，因此，在近半个世纪的研究与应用中受到极大的关注。高分子溶液中的物理凝胶因其结构及形成机制复杂，在实验方面，除了散射技术及流变技术能够有效地揭示它的部分信息外，其它的实验手段很难用于这个领域的研究；在理论方面，化学凝胶的理论已经比较成熟，而物理凝胶的粘弹性质以及凝胶化是一个远离平衡态的松弛过程，除了一些特征的标度指数外，人们还没有得到适用于高分子物理凝胶的普适规律。当前，由于计算机模拟理论及模拟方法的发展，使得计算机模拟成为除了实验和理论研究方法之外的第三个重要的研究方法。但是，由于物理凝胶化行为的复杂性，用实验和理论获得的信息很难较好地描述凝胶化过程，而计算机模拟的高度透明性及反映信息的完整性，有助于理解这一复杂过程中所涉及的物理本质。因此，利用计算机模拟结合实验及理论方法深入研究高分子物理凝胶的形成机制、结构与性能关系已成为目前最有效的手段之一。 本论文主要运用Monte Carlo模拟方法，并结合小角中子散射（Small-Angle Neutron Scattering, SANS）和流变（Rheology）等实验手段从多个角度探讨了以下几类典型的高分子溶液物理凝胶化行为。 1. 温度对遥爪型三嵌段共聚物在选择性溶剂中的自组装及凝胶化行为影响的研究：采用二维简单方格子Monte Carlo模拟方法，结合逾渗（Percolation）理论，建立了溶胶－凝胶转变相图在统计热力学中的确定方法；甄别了具有特征构象的链，讨论了链及胶束的聚集，明晰了相互作用（体现为约化温度）、构象转变、聚集与凝胶化的一致的关联关系；提出了构象转变模型，进而明确了此体系的凝胶化过程，在微观尺度上表现为桥型链和环型链之间的竞争。 2. 模拟模型改进及其应用到持续长度对稀溶液中高分子链构象影响的研究：考虑到原始八位置键涨落模型效率低，实现复杂且不能应用到复杂的高分子体系，对该模型进行了改进，使其实现简单、效率高，并拓宽了该模型的应用范围。然后，以刚性对均聚物构象的影响为例，发现随着刚性增加，均聚物构象从球形椭球到棒状椭球的转变，并对比了自由连接链（Free Joint Chain, FJC）模型和蠕虫链（Wormlike Chain, WLC）模型在不同刚性范围内对高分子链末端距预测的偏差，首次给出了这两个经典模型的半定量的适用边界。 3. 溶剂尺寸对遥爪型三嵌段共聚物在选择性溶剂中的自组装及凝胶化行为影响的研究：用改进后的八位置键涨落Monte Carlo模型，研究了遥爪型三嵌段共聚物在选择性溶剂条件下的聚集和凝胶化对溶剂尺寸的依赖性，发现溶剂尺寸效应对凝胶化的作用是非单调的。由一个均聚物体系的对比模拟证明这种作用主要是由熵驱动的，并给出了中分子溶剂的半定量定义。在均聚物和嵌段共聚物溶液中，不同尺寸的溶剂分子可以使溶液由于高分子聚集不同而具有不同的微结构，并影响高分子链构象和溶液的性质。从多个角度研究了三嵌段共聚物在不同尺寸溶剂的溶液中所遵循的三种不同的凝胶化机理。 4. 聚氧化乙烯－氧化丙稀－氧化乙烯三嵌段共聚物（poly(ethylene oxide)-poly (propylene oxide)-poly-(ethylene oxide), PEO-PPO-PEO）重水溶液凝胶化的小角中子散射（SANS）和Monte Carlo研究：结合Pluronic F127（EO65PO99EO65）/D2O三嵌段共聚物溶液的特征，对照SANS数据，用改进后的八位置键涨落模型成功地从模拟中获得了F127/D2O的溶胶－凝胶转变相图。详细地考察了体系的微观结构，提出此类高分子溶液中形成的物理凝胶包含高分子逾渗网络的生成，以及被束缚溶剂（Bound Solvent）必须超过离散组分体系逾渗的临界体积分数的机理。着重研究了一定浓度的F127水溶液随温度升高引起的溶胶－凝胶转变以及凝胶－溶胶转变的Reentrant相行为，发现体系在低温区域的溶胶－凝胶转变遵循相同的机理，而在中等温度和较高温度以及不同浓度区域中的凝胶－溶胶转变遵循不同的机理。 5. 极性基团饱和度和溶剂条件对两亲性聚合物在溶液中的聚集行为和凝胶化影响的研究：用改进后的八位置键涨落模型，针对两亲性聚合物在不同溶剂条件的溶液建立了粗粒化模型，以两亲性聚合物中极性基团的饱和度，溶剂条件和高分子浓度为变量，考察了其对链构象、聚集及其凝胶化的影响。 6. 多糖水溶液凝胶化的流变和小角中子散射研究：用流变和SANS考察了两个多糖水溶液中物理凝胶化过程，针对由氢键主导的水基凝胶体系的典型特征进行了讨论，从分子链构象，聚集体结构及其关联以及流变特征等方面对聚强电解质角叉胶（Carrageenan）水溶液和聚弱电解质明胶（Pectin）水溶液进行了详细的讨论。考察了不同多糖的种类（聚合物链的电荷密度），盐的种类和浓度，溶液温度等对凝胶化和凝胶结构的影响，分析了不同多糖溶液的凝胶化机理。

DETERMINATION OF SURFACE-ROUGHNESS OF INP (001) WAFERS BY X-RAY-SCATTERING

The surface roughness of polished InP (001) wafers were examined by x-ray reflectivity and crystal truncation rod (CTR) measurements. The root-mean-square roughness and the lateral correlation scale were obtained by both methods. The scattering intensities in the scans transverse to the specular reflection rod were found to contain two components. A simple surface model of surface faceting is proposed to explain the experimental data. The sensitivities of the two methods to the surface structure and the role of the resolution functions in the CTR measurements are discussed.

X-RAY-SCATTERING FROM A ROUGH-SURFACE AND DAMAGED LAYER OF POLISHED WAFERS

Theoretical and experimental investigations were performed to show the application of x-ray crystal truncation rod scattering combined with x-ray reflectivity in the measurements of surface roughness and near-surface damage of mechanochemically polished wafers. By fitting the measured crystal truncation rod curves it has been shown that polished wafers are divided into three parts -irregular steps on the surface, a damaged thin layer beneath the surface and a perfect bulk. The results show that the root mean square of the surface roughness of mechanochemically polished Fe-doped and/or S-doped InP wafers is one to two atom layers, and that the lateral correlation length of the surface roughness is about 3000-7500 Angstrom. The thickness of the damaged region is found to be about 1000 atom layers.

SCATTERING AND RESONANT-TUNNELING THEORY FOR A CYLINDRICAL WELL IN PLANAR STRUCTURES

A two-dimensional atomic scattering theory is developed for scattering of electrons by a circularly symmetric quantum structure in the two-dimensional electron gas. It is found that the scattering cross section oscillates as a function of ka where k is the electron wave vector and a is the radius of the cylindrical potential barrier. If there is a quantum well inside the potential barrier, there appears a series of sharp resonant-tunneling peaks superposed on the original scattering-cross-section curves. The width of the resonant-tunneling peak depends sensitively on the thickness, the height of the potential barrier, and the electron energy.

NEAR-RESONANT RAMAN-SCATTERING FROM GAAS/ALAS SUPERLATTICES

This article presents the results of near-resonant Raman scattering measurements on GaAs/AlAs superlattices at room temperature. A strong enhancement of GaAs LO phonon-even modes resulted owing to a dipole-allowed Frohlich interaction in superlattices. Similar to the previous results, the LO phonon-even modes in a polarized configuration are observed. In contrast to previous work, however, what we observed in depolarized configurations is the LO phonon-odd modes instead of even modes. It is confirmed that the selection rules for near-resonant Raman scattering from LO phonons in this kind of superlattices are the same as those for off-resonant scattering. From the second-order Raman scattering, it is confirmed that polarized second-order Raman scattering spectra consist of overtones and combinations of two even modes, and depolarized second-order Raman scattering spectra consist of combinations of an even mode and an odd mode. Our experimental results coincide with the predictions using the recently developed Huang-Zhu model. A brief discussion on interface modes and their combination with confined modes is also presented.

MANY-BEAM SIMULATIONS AND OBSERVATIONS OF LARGE-ANGLE CONVERGENT-BEAM ELECTRON-DIFFRACTION IMAGING OF CRYSTAL DEFECTS

Many-beam dynamical simulations and observations have been made for large-angle convergent-beam electron diffraction (LACBED) imaging of crystal defects, such as stacking faults and dislocations. The simulations are based on a general matrix formulation of dynamical electron diffraction theory by Peng and Whelan, and the results are compared with experimental LACBED images of stacking faults and dislocations of Si angle crystals. Excellent agreement is achieved.

NEAR-RESONANCE RAMAN-SCATTERING OF LONGITUDINAL OPTICAL PHONON MODES AND INTERFACE MODES IN GAAS/ALAS SUPERLATTICES

The near-resonance Raman scattering of GaAs/AlAs superlattices is investigated at room temperature. Owing to the resonance enhancement of Frohlich interaction, the scattering intensity of even LO confined modes with A1 symmetry becomes much stronger than that of odd modes with B2 symmetry. The even modes were observed in the polarized spectra, while the odd modes appear in the depolarized spectra as in the off-resonance case. The second-order Raman spectra show that the polarized spectra are composed of the overtone and combinations of even modes, while the depolarized spectra are composed of the combinations of one odd mode and one even mode. The results agree well with the selection rules predicted by the microscopic theory of Raman scattering in superlattices, developed recently by Huang and co-workers. In addition, the interface modes and the combinations of interface modes and confined modes are also observed in the two configurations.