In this thesis we synthesize two organic materials, one is discotic liquid crystal Acid-6, and the other is novel discotic liquid crystal polymer DLC-PAM. After demonstrating the molecular structures of Acid-6 and DLC-PAM by FT-MS, 1H-NMR and FT-IR, we use the two materials as photo-sensitized dyes for dye-sensitized solar cells(DSSCs) and manufacture two kinds of cells. We use polyacrylamide(PAM) as main chain of the novel discotic liquid crystal polymer DLC-PAM and graft the discotic liquid crystal monomer Acid-6 onto PAM by chemical synthesis. DLC-PAM belongs to side-chain liquid crystal polymer, and it can show the properties of it¡¦s discotic liquid crystal function. One of the properties is absorption of visible light. By observing the UV-Vis spectrum, we can realize the absorption band is located between 200 ~ 450 nm and confirm that it is able to be a photo-sensitized dye. Another property of discotic liquid crystal is the self-assembly ability, the moleculars can assemble into hexagonal columnar structure by themselves, and the property enable discotic liquid crystal to have better mobility. In this part, we can demonstrate DLC-PAM and Acid-6 really have hexagonal columnar structure by X-ray diffractmeter. After qualitative demonstrating and optical analysis, we use DLC-PAM and Acid-6 as photo-sensitized dyes for DSSCs and manufacture two kinds of cells successfully. The more photocurrent occur when the two DSSCs are woking. Besides, the two DSSCs have good performance on power conversion efficiency which can achieve 0.047 % for DLC-PAM and 0.364 % for Acid-6. Therefore, in this research we prove that DLC-PAM and Acid-6 are able to be photo-sensitized dyes for DSSCs and successfully demonstrate that using the two materials to manufacture DSSCs is feasible.

Thermal behavior and molecular packing of alkylated poly(ethylene- alt- maleic anhydride) and poly(styrene-alt-maleic anhydride) were studied by means of differential scanning calorimetry, thermogravimetry, polarizing optical microscopy, and X-ray diffraction. Effects of the length and graft density of alkyl side chains and backbone rigidity on the thermal behavior and on the structure of the mesophases are discussed.

Thermal behavior and molecular packing of a series of £\-helical poly(L-glutamates), with n-alkyl side chain of various lengths (m(number of carbons in the alkyl group) = 1, 2, 6, 12,18), were studied by means of differential scanning calorimetry, polarizing light microscopy and X-ray diffraction. For polymers of m = 1 and 2, There is a pseudohexagonal structure below ca. 130 oC and above this temperature the stable phase is the hexagonal columnar phase. There exists a layered structure in the polymer of m = 6, as well as a solvent induced hexagonal columnar structure which formed during solution casting process. In the polymer of m = 12, a layered structure was formed in the temperature range between 20 to 255 oC. However, for longer side chain, m = 18, tendency of crystallization of alkyl long side chain forced the backbone to pack into layer structure. There are two distinct melting temperature at ca. 60 oC, and the enthalpy are ca. 53 and 19 J/g, which corresponding to the melting of hexagonal and monoclinic side chain crystallines. The polymers with longer side chain (m = 6, 12 and 18) tend to be lyotropic liquid crystalline phase within lamellar inter-rod distance of 1.25 nm in solution state, and the structure will remain after drying. However, the inter-rod distance will collapse at the temperature above ca. 200 ¢J and will not recover after cooling.

Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program can be obtained efficiently in both theory and practice, provided that the semidefinite program and its dual satisfy the Slater condition. This thesis focuses on the situation where the Slater condition (i.e., the existence of positive definite feasible solutions) does not hold for a given semidefinite program; the failure of the Slater condition often occurs in structured semidefinite programs derived from various applications. In this thesis, we study the use of the facial reduction technique, originally proposed as a theoretical procedure by Borwein and Wolkowicz, as a preprocessing technique for semidefinite programs. Facial reduction can be used either in an algorithmic or a theoretical sense, depending on whether the structure of the semidefinite program is known a priori. The main contribution of this thesis is threefold. First, we study the numerical issues in the implementation of the facial reduction as an algorithm on semidefinite programs, and argue that each step of the facial reduction algorithm is backward stable. Second, we illustrate the theoretical importance of the facial reduction procedure in the topic of sensitivity analysis for semidefinite programs. Finally, we illustrate the use of facial reduction technique on several classes of structured semidefinite programs, in particular the side chain positioning problem in protein folding.

This dissertation proposes new optimization algorithms targeting protein-protein docking which is an important class of problems in computational structural biology. The ultimate goal of docking methods is to predict the 3-dimensional structure of a stable protein-protein complex. We study two specific problems encountered in predictive docking of proteins. The first problem is Side-Chain Positioning (SCP), a central component of homology modeling and computational protein docking methods. We formulate SCP as a Maximum Weighted Independent Set (MWIS) problem on an appropriately constructed graph. Our formulation also considers the significant special structure of proteins that SCP exhibits for docking. We develop an approximate algorithm that solves a relaxation of MWIS and employ randomized estimation heuristics to obtain high-quality feasible solutions to the problem. The algorithm is fully distributed and can be implemented on multi-processor architectures. Our computational results on a benchmark set of protein complexes show that the accuracy of our approximate MWIS-based algorithm predictions is comparable with the results achieved by a state-of-the-art method that finds an exact solution to SCP. The second problem we target in this work is protein docking refinement. We propose two different methods to solve the refinement problem. The first approach is based on a Monte Carlo-Minimization (MCM) search to optimize rigid-body and side-chain conformations for binding. In particular, we study the impact of optimally positioning the side-chains in the interface region between two proteins in the process of binding. We report computational results showing that incorporating side-chain flexibility in docking provides substantial improvement in the quality of docked predictions compared to the rigid-body approaches. Further, we demonstrate that the inclusion of unbound side-chain conformers in the side-chain search introduces significant improvement in the performance of the docking refinement protocols. In the second approach, we propose a novel stochastic optimization algorithm based on Subspace Semi-Definite programming-based Underestimation (SSDU), which aims to solve protein docking and protein structure prediction. SSDU is based on underestimating the binding energy function in a permissive subspace of the space of rigid-body motions. We apply Principal Component Analysis (PCA) to determine the permissive subspace and reduce the dimensionality of the conformational search space. We consider the general class of convex polynomial underestimators, and formulate the problem of finding such underestimators as a Semi-Definite Programming (SDP) problem. Using these underestimators, we perform a biased sampling in the vicinity of the conformational regions where the energy function is at its global minimum. Moreover, we develop an exploration procedure based on density-based clustering to detect the near-native regions even when there are many local minima residing far from each other. We also incorporate a Model Selection procedure into SSDU to pick a predictive conformation. Testing our algorithm over a benchmark of protein complexes indicates that SSDU substantially improves the quality of docking refinement compared with existing methods.

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Fluorinated compounds are produced on a large scale and their releases are contaminating the environment. Among these are side-chain fluorinated polymers found in technical mixtures of Scotchgard™, which are used as surfactants in fabric coating. Today, the knowledge about these Scotchgard products (Pre-2002 and Post-2002, formulations used in Scotchgard products before and after 2002) and side-chain fluorinated polymers, in general, are limited, and more studies need to be performed to increase the understanding of the behaviour of the compounds and their fate in the environment. This study performed sorption tests in liquid to sediment ratio of 100:1, with sediment from Lake Hjälmaren, Sweden, and water spiked with Pre-2002 and Post-2002. The waters were Milli-Q water, containing CaCl2, adjusted to different pHs (range between 4.4 and 11.2) with NaOH, and on water from Lake Hjälmaren. The solutions were shaken for 0.5, 1, 2, 4, 8, 12, 24 and 168 h. Liquid-liquid extraction with tert-butyl methyl ether (MTBE) was used to extract the remaining target compounds in the aqueous phase and analysed using ultra-performance liquid chromatography (UPLC). For the different pH solutions, the result showed both Pre-2002 and Post-2002 readily sorbed to the sediment with close to 0 % remaining in the aqueous phase after 4 hours. For the first time point, 0.5 h, more than 7 % remained in the aqueous phase with a pH of 11.2, while under 1 % remained with a pH of 4.4 for both Pre-2002 and Post-2002, showing that the sorption capacity was dependent on pH. In water from Lake Hjälmaren, neither of the target analytes were under the limit of detection (LOD) until the time point of 168 h. In contrast to the result of the pH solutions, Post-2002 were shown to be more prone to sorb to the sediment in the water from Lake Hjälmaren than Pre-2002. This might be due to particles, ions and competing per- and polyfluoroalkyl substances (PFAS) present in the water. However, the pH of Lake Hjälmaren was around 5; when comparing the data, the amount sorbed, somewhat aligned with what would be expected based on the sorption test with different pHs, indicating that the sorption capacity might be more dependent on pH than water chemistry.