Layer-by-layer (LBL) polyelectrolyte capsules can be modified to incorporate stimuli such as superparamagnetic nanoparticles which respond to a magnetic field only when it is turned on. Thus, they can act as a switch to load or unload their drug cargo on demand. Specifically, magnetite is incorporated into bilayer capsules made of alternating poly(allylamine hydrochloride) (PAH) and poly(sodium-p-styrenesulfonate) (PSS) which surrounds calcium carbonate core. The core is then dissolved using ethylenediaminetetraacetic acid (EDTA). These capsules are loaded with at FITC-BSA conjugate and examined with fluorescence to show the unloading of the FITC-BSA from capsules as it brightens the entire field of view of the microscope. The results suggest that we can next load and unload an anticancer drug such as doxorubicin using the combination of microcapsule and alternating magnetic field (AMF) to treat the cancer cells. Preliminary data interprets that the low frequency AMF we use has little to no adverse effect cells viability. This coincides with the general thought that low frequency AMF signals are not harmful to humans. Therefore, as an alternative to hyperthermia methods which use heat, it may be possible to deliver the anticancer drugs specifically to the cells when and where it is needed.

High molecular weight star-shaped polystyrenes were prepared via the coupling of 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) terminated polystyrene oligomers with divinylbenzene (DVB) in m-xylene at 138 °C. Linear polystyrene oligomers (Mn = 19,300 g/mol, Mw/Mn = 1.10) were synthesized in bulk styrene using benzoyl peroxide in the presence of TEMPO at approximately 130 °C. In situ mid-infrared spectroscopy was successfully utilized to follow initiation, monomer conversion, and polymer formation. Real-time data allowed for the determination of apparent rate constants of 2.1E-5 s⁻¹ at 132 °C and 1.2E-5 s⁻¹ at 126 °C from the profile of the decaying styrene vinyl carbon-hydrogen (=CH₂) absorbance at 907 cm⁻¹. Coupling of the TEMPO terminated oligomers under optimum conditions resulted in a compact and dense product with a number average molecular weight exceeding 300,000 g/mol (Mw/Mn = 3.03) after 24 h, suggesting the formation of relatively well-defined star-shaped polymers. Synthetic factors that affected the molecular weight, yield, and composition of maleic anhydride (MAH), norbornene (Nb), and tert-butyl 5-norbornene-2-carboxylate (NbTBE) terpolymers were investigated. Pseudo first order kinetic analysis using in situ FTIR indicated that the observed rate of reaction was a strong function of the Nb/NbTBE ratio with a maximum of 6.7E-5 s⁻¹ for a 50/0/50 Nb/NbTBE/MAH monomer ratio and a minimum of 1.1E-5 s⁻¹ for a 0/50/50 Nb/NbTBE/MAH ratio. Polymer yields were also observed to be a function of the Nb/NbTBE ratio and also decreased with increasing NbTBE. Calculated work of adhesion values (Wadh) values were observed to increase as the content of NbTBE was increased. 193 nm photoresist formulations incorporating polymers with high NbTBE content showed increased imaging performance using 193 nm light and successfully produced sharp and defined features as small as 110 nm, which was demonstrated via scanning electron microscopy (SEM). Additional functionality was introduced via the copolymerization of MAH with several norbornene (Nb) derivatives that were synthesized from facile Diels-Alder cycloaddition reactions of cyclopentadiene with a-olefins containing electron withdrawing groups. Subsequent hydrolysis of the anhydride offered further versatility and provided an avenue to introduce aqueous base solubility into Nb/MAH copolymers. / Ph. D.

Novel, highly functional rod-like copolymers have been synthesized by alternating copolymerization of N, N, Nâ , Nâ -tetraalkyl-4, 4â -diaminostilbenes (TDAS) with maleic anhydride. Dynamic light scattering, 2H solid state NMR and persistence length measurement reveal high chain rigidity of the polymer backbone. Double quantum heteronuclear local field solid state NMR spectroscopy (2Q-HLF Solid State NMR) has been employed to investigate the chain structure of ¹³C labelled copolymer. The torsional angle of the H-13C-13C-H part of the anhydride ring was zero degrees, indicating an all cis configuration of the H-13C-13C-H moiety of the anhydride ring. Rod-coil block copolymers containing rigid polyampholyte blocks were designed and synthesized by addition-fragmentation chain transfer (RAFT) copolymerization. The rigid polyampholytes blocks were formed by hydrolysis of alternating copolymers and the flexible coil block consists of poly(oligo(ethylene glycol) methacrylate). The rod-coil block copolymers form polyion complex (PIC) aggregates even when the polyampholyte blocks are charge imbalanced. The aggregates did not dissociate upon the addition of high concentrations of NaCl unlike the dissociation of flexible polyampholytes in NaCl solution. These unique solution properties are induced by 'like-charge attractions' of the rigid polyampholytic alternating copolymer chains. An example, of what is birefringent to be a novel class of material, has been prepared which enables the control of the birefringence of a polymer film by controlling the rotation of aromatic groups pendant to the polymer backbone. A linear rigid bisphenol monomer, 4,4′-dihydroxyterphenyl (DHTP), has been incorporated into poly(aryl ether sulfone)s (PAES) in a study to impart crystallization to these amorphous polymers. Three bisphenols, 4, 4′-isopropylidenediphenol, 4, 4′-(hexafluoroisopropylidene)diphenol and 4,4′-dihydroxybiphenyl have been copolymerized with DHTP and dichlorodiphenylsulfone. Only the segmented polysulfone containing 50% BP and 50% DHTP was semi-crystalline. This PAES had a melting temperature (Tm) 320°C in the first heating cycle of a DSC measurement and the presence of crystallites was confirmed by wide angle X-ray diffraction (WAXS). / Ph. D.

Estrogen receptor (ER)-positive breast cancer is responsive to a number of targeted therapies used clinically. Unfortunately, the continuous application of any targeted therapy often results in resistance to the therapy. Our ultimate goal is to use mathematical modelling to optimize alternating therapies that not only decrease proliferation but also stave off resistance. Toward this end, we measured levels of key proteins and proliferation over a 7-day time course in ER-positive MCF7 breast cancer cells. Treatments included endocrine therapy, either estrogen deprivation, which mimics the effects of an aromatase inhibitor, or fulvestrant, an ER degrader. These data were used to calibrate a mathematical model based on key interactions between ER signaling and the cell cycle. We show that the calibrated model is capable of predicting the combination treatment of fulvestrant and estrogen deprivation. Further, we show that we can add a new drug, palbociclib, to the model by measuring only two key proteins, c-Myc and hyperphosphorylated RB1, and adjusting only parameters associated with the drug. The model is then able to predict the combination treatment of estrogen deprivation and palbociclib. Then we added the dynamics of estrogen concentration in the medium into the model and extended the short-term model to a long-term model. The long-term model can simulate various mono- or combination treatments at different doses over 28 days. In addition to palbociclib, we add another Cdk4/6 inhibitor to the model, abemaciclib, which can induce apoptosis at high concentrations. Then the model can match the effects of abemaciclib treatment at two different doses and also capture the apoptosis effects induced by abemaciclib. After calibrating the model to these different treatment conditions, we used the model to explore the synergism among these different treatments. The mathematical model predicts a significant synergism between palbociclib or abemaciclib in combination with fulvestrant. And the predicted synergisms are verified by experiments. This critical synergism between these Cdk4/6 inhibitors and endocrine therapy could reflect the reason that Cdk4/6 inhibitors achieve pronounced success in clinic trails. Lastly, we used protein biomarkers (cyclinD1, cyclinE1, Cdk4, Cdk6 and Cdk2) and palbociclib dose-response proliferation assays to assess the difference between mono- and alternating therapy after 10 weeks of treatments. But neither the protein levels nor palbociclib dose-response show significant differences after 10 weeks of treatment. Therefore, we cannot conclude that alternating therapy delays palbociclib resistance compared with palbociclib mono-treatment after 10 weeks. Longer term experiments or other methods will be needed to uncover any difference. However, in this research we showed that a mechanism-based mathematical model is able to simulate and predict various effects of clinically-used treatments on ER-positive breast cancer cells at different time scales. And this mathematical model has the potential to explore ideas for potential drug treatments, optimize protocols that limit proliferation, and determine the drugs, doses, and alternating schedule for long term experiments. / Doctor of Philosophy / Estrogen receptors are proteins found inside breast cancer cells that are activated by the hormone estrogen. Estrogen-receptor positive breast cancer is the most common type of breast cancer and accounts for about 70% of breast cancer tumors. Endocrine therapy, which inhibits estrogen receptor signaling, and Cyclin-dependent kinase 4 and 6 (Cdk4/6) inhibitors are the preferred first-line therapy for patients with estrogen receptor-positive cancers. We built a mathematical model of MCF7 cells (an estrogen receptor-positive breast cancer cell line) in response to these standard first-line therapies. This mathematical model can capture the experimentally observed protein and cell proliferation changes in response to various treatment conditions, including different drug combinations, different doses, and different treatment durations up to 28 days. The model can then be used to look for more effective treatment possibilities. In particular, our mathematical model predicted a strong synergism between Cdk4/6 inhibitors and endocrine therapy, which could allow significant reductions in drug dosage while producing the same effect. This synergism was verified by experiments. In addition to treatment methods where one drug or combination of several drugs is used continuously, we consider alternating among various therapies in a fixed cycle. The mathematical model can help us determine which drugs and which doses might be most appropriate. Since an alternating therapy doesn't inhibit one particular target non-stop, the hope is that alternating therapies can delay the onset of drug resistance, where the drug becomes less effective or stops working completely. Unfortunately, an initial 10- week experiment to test for differences in resistance to a mono-therapy versus an alternating therapy did not show a significant difference, pointing to the need for longer experiments to see if alternating therapies can actually make a difference in resistance. Mathematical models will be important for determining the drugs, doses, and time intervals to be used in these experiments, as figuring out the best options by trial and error in such long-term experiments is not practical.

With an increasing number of regulatory and economic factors making the operation of power systems more challenging, utilities must take full advantage of technological advances which allow more flexibility for operation. One of these advances is the combination of power electronic controllers and compensation devices known as F1exible AC Transmission Systems (FACTS) technology. This thesis will examine the ability of FACTS technology to improve dynamic stability when controlled with data obtained from another recent advancement, phasor measurement units (PMUs). Based on an overview of the relative capabilities of presently available FACTS devices, a specific device will be chosen to be modeled in a dynamic stability study. Eigenvalue sensitivity analysis will be used to determine the optimal placement for this FACTS device in regards to stability for a test power system. Then a state space model will be developed for the FACTS compensated test system, and eigenvalue sensitivity and time-domain methods will be used to determine the optimal controller characteristics for the modeled FACTS device. Stability results will be verified using eigenvalue analysis and time simulation techniques. / Master of Science

It was the purpose of this investigation to study the effect of varying the direct to reverse time ratio of periodically reversed direct current from 1.0 to 20.0 on the electrolytic production of lead chromate at an average anode current density of 0.0059 amperes per square centimeter, and to study the effect of 60 and 502.3 ± 7.7 cycles per second from 0.00113 to 0.01546 amperes per square centimeter of peak superimposed alternating current on direct current on the yield of lead chromate prepared by the electrolysis of a bath containing potassium chromate and sodium nitrate between lead electrodes. Electrolysis of a bath containing 3.60 grams of potassium chromate, 11.62 grams of sodium nitrate, end 1000 grams of water with simple direct current yielded 6.07 grams of lead chromate per ampere-hour, the purity being 92.7 percent lead chromate. The anode current density was 0.0049 amperes per square centimeter, and the current efficiency was 98.1 percent. During the electrolysis, by maintaining the ph of the electrolyte at 6.0, by adding a solution to 2.0 weight percent chromic acid, the purity of the product was increased. Electrolysis of the same bath using periodically reversed direct current yielded 4.53 grams of lead chromate per ampere-hour, the purity being 93.9 percent lead chromate. The time ratio was 20.0, the anode current density was 0.0049 amperes per square centimeter, and the current efficiency was 66.75 percent. Decreasing the direct to reverse time ratio gave lower yields and purities. Apparently, there is no advantage in using periodically reversed direct current over the use of direct current for this reaction under the above conditions. Electrolysis of the same bath with alternating current superimposed on direct current yielded 5.49 grams of lead chromate per direct current ampere-hour, at a purity of 99.4 percent lead chromate, when using 494.7 cycle alternating current. The alternating and direct current densities were 0.0078 and 0.0048 amperes per square centimeter, respectively. This was the purest product obtained in this investigation. Use of 60 cycle alternating current yielded 3.83 grams of lead chromate per direct current ampere-hour, at a purity of 93.9 percent lead chromate. The alternating and direct current densities were 0.00141 and 0.00484 amperes per square centimeter. Further experiments were made using direct current and periodically reversed direct current on a bath containing 6.80 grams of potassium chromate, 8.14 grams of sodium nitrate, and 1000 grams of water. Results from these electrolytes were much poorer than those obtained with the previous bath, so no experiments with superimposed alternating current on direct current were carried out with this latter bath. / Master of Science

It was the purpose of this investigation to study the effect of varying the direct to reverse time ratio of periodically-reversed, direct current from 1.0 to 20.0 at an anode current density of 4.5 amperes per square centimeter, and to study the effect of alternating current of 60, 240, and 500 cycles per second, 0.2 to 4.5 amperes per square centimeter, superimposed on direct current on the electrolytic production of peroxydisulfuric acid. Electrolyses of 200 milliliters of sulfuric acid of specific gravity 1.4, at a temperature of 5 to 10 °C were performed with direct current. The anode current density was varied. The surface area of platinum anode and lead cathode was 2.0 and 221.8 square centimeters, respectively. For one hour of electrolysis, the yields were 7.9, 14.0, 20.2, and 22.9 grams of peroxydisulfuric acid at the anode current density of 1.5, 3.0, 4.5, and 6.0 amperes per square centimeter, respectively. The current efficiencies corresponding to these anode current densities were 85.0, 77.0, 61.5, and 53.4 per cent. The results showed that the yield was increased and the current efficiency was decreased with increase in the anode current density. Electrolysis of the same concentration and volume of sulfuric acid using periodically-reversed, direct current yielded 14.2 grams at an anode current density of 4.5 amperes per square centimeter and at a temperature of 5 to 8 °C. The time of electrolysis was one hour and the time ratio of direct to reverse electrolysis was 20. The current efficiency obtained under these conditions was 42.6 per cent. Decreasing the direct to reverse time ratio gave lower yields and current efficiencies. Apparently, there is no advantage in using periodically-reversed, direct current over the use of direct current for this reaction under the above experimental conditions. Electrolyses of 200 milliliters of sulfuric acid of the same concentration were performed with 60 cycles per second, alternating current superimposed on direct current. The direct current density was 4.5 amperes per square centimeter for the ten tests, but the surface area of the platinum anode was changed from two to one square centimeter and the direct current was decreased from 9.0 to 4.5 amperes. The current efficiency decreased sharply from 61.5 to approximately 31.0 per cent as the ratio of peak alternating to direct current increased from zero to 0.2 and then it remained constant until the ratio reached one. The current efficiency decreased suddenly to almost zero when the ratio was greater than one. The same sulfuric acid was electrolyzed under the same experimental conditions with 240 and 500 cycles per second, alternating current superimposed on direct current. Both direct and alternating anode current densities were varied. The direct current density was 2.2 and 4.5 amperes per square centimeter. The current efficiencies obtained during these tests were almost the same as that obtained with 60 cycles per second, alternating current within a specific limit of the ratio of peak alternating to direct current. The ratio of peak alternating current to direct current at which the current efficiencies suddenly dropped to zero was 0.75 for 240 cycles per second, and 0.5 for 500 cycles per second, instead of one for 60 cycles per second, superimposed alternating current. The platinum anode was activated and dissolved into the sulfuric acid when the ratio of peak alternating to direct current was greater than 1.0, 0.75, and 0.5 for 60, 240, and 500 cycles per second, alternating current superimposed on direct current. Apparently, there is no advantage in using alternating current superimposed on direct current over the use of direct current for electrolytic production of peroxydisulfuric acid. / Master of Science

In this age, there are many applications of inverse problems to lots of areas ranging from astronomy, geoscience and so on. For example, image reconstruction and deblurring require the use of methods to solve inverse problems. Since the problems are subject to many factors and noise, we can't simply apply general inversion methods. Furthermore in the problems of interest, the number of unknown variables is huge, and some may depend nonlinearly on the data, such that we must solve nonlinear problems. It is quite different and significantly more challenging to solve nonlinear problems than linear inverse problems, and we need to use more sophisticated methods to solve these kinds of problems. / Master of Science / In various research areas, there are many required measurements which can't be observed due to physical and economical reasons. Instead, these unknown measurements can be recovered by known measurements. This phenomenon can be modeled and be solved by mathematics.

Decreasing gas prices and the pressing need for fast-responding electric power generators are currently transforming natural gas networks. The intermittent operation of gas-fired plants to balance wind generation introduces spatiotemporal fluctuations of increasing gas demand. At the heart of modeling, monitoring, and control of gas networks is a set of nonlinear equations relating nodal gas injections and pressures to flows over pipelines. Given gas demands at all points of the network, the gas flow task aims at finding the rest of the physical quantities. For a tree network, the problem enjoys a closed-form solution; yet solving the equations for practical meshed networks is non-trivial. This problem is posed here as a feasibility problem involving quadratic equalities and inequalities, and is further relaxed to a convex semidefinite program (SDP) minimization. Drawing parallels to the power flow problem, the relaxation is shown to be exact if the cost function is judiciously designed using a representative set of network states. Numerical tests on a Belgian gas network corroborate the superiority of the novel method in recovering the actual gas network state over a Newton-Raphson solver. This thesis also considers the coupled infrastructures of natural gas and electric power systems. The gas and electric networks are coupled through gas-fired generators, which serve as shoulder and peaking plants for the electric power system. The optimal dispatch of coupled natural gas and electric power systems is posed as a relaxed convex minimization problem, which is solved using the feasible point pursuit (FPP) algorithm. For a decentralized solution, the alternating direction method of multipliers (ADMM) is used in collaboration with the FPP. Numerical experiments conducted on a Belgian gas network connected to the IEEE 14 bus benchmark system corroborate significant enhancements on computational efficiency compared with the centralized FPP-based approach. / Master of Science / The increase in penetration of renewable energy in the electric power grid has led to increased fluctuations in the power. The conventional coal based generators are inept to handle these fluctuations and thus, natural gas generators, which have fast response times are used to handle the intermittency caused by renewable energy sources. This manuscript solves the problem of finding the optimal dispatch of coupled natural gas and electric power systems. First, the optimal dispatch problem is framed as a optimization problem and then mathematical solvers are developed. Using the mathematical tools of Feasible point pursuit and Alternating direction method of multipliers, a distributed solver is developed, which can solve the optimal dispatch for large power and natural gas networks. The proposed algorithm is tested on a part of a Belgian gas network and the IEEE 14 bus power system. The algorithm is shown to converge to a feasible point.

Alternating copolymers represent a special class of copolymers in which the two comonomers copolymerize in a regular alternating sequence along the polymer chain. Of particular interest in our group are the stilbene-maleic anhydride/maleimide alternating copolymers. These copolymers possess sterically congested backbones and precisely placed functional groups arising from the strictly alternating copolymerization. The research in this dissertation is focused on the synthesis, characterization, and potential application of functionalized copolymers that contain semi-rigid alternating copolymer sequences. The fluorescence properties of a series of non-conjugated, tert-butyl carboxylate functionalized alternating copolymers were investigated. Extraordinarily high fluorescent intensity with excellent linearity was observed for the di-tert-butyl group-containing stilbene and maleic anhydride alternating copolymer in THF. We attributed the origin of the strong fluorescence to the “through space” π – π interactions between the phenyl rings from the stilbene and C=O groups from the anhydride. The fluorescence was maintained when the copolymer was deprotected and hydrolyzed and the resulting carboxylic acid-functionalized copolymer was dissolved in water at neutral pH. The tert-butyl carboxylate functionalized alternating copolymer sequences were incorporated into highly crosslinked polymer networks using suspension polymerization. After removing the tert-butyl groups by acidic hydrolysis, the surface area of the networks increased significantly. Using this facile two-step strategy, we were able to achieve nanoporous polymers with BET surface area up to 817 m2/g and carboxylic acid-functionalized surfaces. The BET surface area of deprotected polymers increased with increasing crosslinking density, and the stilbene-containing polymers showed systematically higher BET surface area than the styrene-containing polymers due to the stiffness of the alternating sequences. The resulting nanoporous polymers have potential to be employed as solid sorbents for CO2. The same tert-butyl carboxylate functionalized alternating copolymer sequences were also incorporated into microgels via miniemulsion polymerization. The miniemulsion technique ensured the successful synthesis of microgels with ~100 nm diameter using solid stilbene and maleimide monomers. The resulting tert-butyl carboxylate-containing microgels were converted into carboxylic acid-containing aqueous microgels by acid hydrolysis. These aqueous microgels showed good and reversible lead and copper ion adsorption capacities. Amine-functionalized nanoporous polymers were synthesized by the post-modification of highly-crosslinked divinylbenzene-maleic anhydride polymers. High amine-contents were achieved by covalently attaching multiamines to the acid-chloride functionalized polymer surface. The resulting polymers showed medium to high BET surface areas (up to 500 m2/g) and high CO2 capture capacities. / PHD / Copolymers are polymers that consist of two or more different monomers in the polymer chain. Research on copolymers can be traced back to the 1930s. Since the early discoveries, the research on copolymers has received considerable attention because of the ease of synthesis and the versatile properties and applications of these materials. Alternating copolymers are one of the most studied types of copolymers. In an alternating copolymer, the two different monomers arrange in a regular alternating sequence along the polymer backbone. Of special interest in our group are the alternating copolymers that contain stilbene (1,2- diphenylethylene). The stilbene-containing alternating copolymers have relatively rigid (semi-rigid) structures, which lead to unusual and interesting properties. The research described in this dissertation is focused on incorporating these semi-rigid alternating copolymers into different types of systems and studying their structure/property relationships. Three different polymeric materials and their properties were explored. Fluorescent materials can glow when irradiated by a certain wavelength of light. This property is very useful in biomedical sensing, imaging and labeling. The semi-rigid stilbene-containing alternating copolymer exhibited fluorescence with extraordinarily high intensity, solely due to the conjugation from the exact juxtaposition of molecular orbitals. This high intensity fluorescence suggests potential application as novel light-emitting materials. The increasing atmospheric CO₂ concentrations due to human activities like transportation and manufacturing have caused public concerns. Currently, liquid amine scrubbing is one of the most well established methods for CO₂ capture in industry. However, due to the solvent evaporation, degradation, and the high energy demand during the solvent regeneration, solid polymeric materials are considered as attractive alternative CO₂ capture materials. We designed two kinds of polymers based on our semi-rigid alternating copolymer sequences, and they both exhibited pores smaller than 2 nm. With the help of different functional groups designed to interact with CO₂, these polymers showed enhancement in CO₂ capture properties, and show the viability as solid sorbents for atmospheric CO₂. Heavy metal contamination in water is a severe environmental and public health problem. The recent Flint water crisis raised the public awareness of this problem. We synthesized a series of hydrogel beads with diameters in the range of 100-200 nm. The incorporation of these functional alternating copolymer sequence into the microgels led to fast and reversible adsorption of the lead and copper ions in water.