Synthesis, Modification, and Application of Siloxane Materials for Environmental Sensing

As human populations and resource consumption increase, it is increasingly important to monitor the quality of our environment. While laboratory instruments offer useful information, portable, easy to use sensors would allow environmental analysis to occur on-site, at lower cost, and with minimal operator training. We explore the synthesis, modification, and applications of modified polysiloxane in environmental sensing. Multiple methods of producing modified siloxanes were investigated. Oligomers were formed by using functionalized monomers, producing siloxane materials containing silicon hydride, methyl, and phenyl side chains. Silicon hydride-functionalized oligomers were further modified by hydrosilylation to incorporate methyl ester and naphthyl side chains. Modifications to the siloxane materials were also carried out using post-curing treatments. Methyl ester-functionalized siloxane was incorporated into the surface of a cured poly(dimethylsiloxane) film by siloxane equilibration. The materials containing methyl esters were hydrolyzed to reveal carboxylic acids, which could later be used for covalent protein immobilization. Finally, the siloxane surfaces were modified to incorporate antibodies by covalent, affinity, and adsorption-based attachment. These modifications were characterized by a variety of methods, including contact angle, attenuated total reflectance Fourier transform infrared spectroscopy, dye labels, and 1H nuclear magnetic resonance spectroscopy. The modified siloxane materials were employed in a variety of sensing schemes. Volatile organic compounds were detected using methyl, phenyl, and naphthyl-functionalized materials on a Fabry-Perot interferometer and a refractometer. The Fabry-Perot interferometer was found to detect the analytes upon siloxane extraction by deformation of the Bragg reflectors. The refractometer was used to determine that naphthyl-functionalized siloxanes had elevated refractive indices, rendering these materials more sensitive to some analytes. Antibody-modified siloxanes were used to detect biological analytes through a solid phase microextraction-mediated enzyme linked immunosorbent assay (SPME ELISA). The SPME ELISA was found to have higher analyte sensitivity compared to a conventional ELISA system. The detection scheme was used to detect Escherichia coli at 8500 CFU/mL. These results demonstrate the variety of methods that can be used to modify siloxanes and the wide range of applications of modified siloxanes has been demonstrated through chemical and biological sensing schemes.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.