Selectivity, activity, and stability of ruthenium-carbene based olefin metathesis initiators

The olefin metathesis reaction has found many applications in polymer synthesis and more recently in organic synthesis. The use of single component late metal olefin metathesis catalysts has expanded the scope of the reaction to many new applications and has allowed for detailed study of the catalytic species.

The metathesis of terminal olefins of different steric bulk, different geometry as well as electronically different para-substituted styrenes was studied with the ruthenium based metathesis initiators, trans-(PCy₃)₂Cl₂Ru=CHR, of different carbene substituents. Increasing olefin bulk was found to slow the rate of reaction and trans internal olefins were found to be slower to react than cis internal olefins. The kinetic product of a11 reactions was found to be the alkylidene, rather than the methylidene, suggesting the intermediacy of a 2,4-metallacycle. The observed effects were used to explain the mechanism of ring opening cross metathesis and acyclic diene metathesis polymerization. No linear electronic effects were observed.

In studying the different carbene ligands, a series of ester-carbene complexes was synthesized. These complexes were found to be highly active for the metathesis of olefinic substrates, including acrylates and trisubstituted olefins. In addition, the estercarbene moiety is thermodynamically high in energy. As a result, these complexes react to ring-open cyclohexene by metathesis to alleviate the thermodynamic strain of the ester-carbene ligand. However, ester-carbene complexes were found to be thermolytically unstable in solution.

Thermolytic decomposition pathways were studied for several ruthenium-carbene based olefin metathesis catalysts. Substituted carbenes were found to decompose through bimolecular pathways while the unsubstituted carbene (the methylidene) was found to decompose unimolecularly. The stability of several derivatives of the bis-phosphine ruthenium based catalysts was studied for its implications to ring-closing metathesis. The reasons for the activity and stability of the different ruthenium-based catalysts is discussed.

The difference in catalyst activity and initiation is discussed for the bis-phosphine based and mixed N-heterocyclic carbene/phosphine based ruthenium olefin metathesis catalysts. The mixed ligand catalysts initiate far slower than the bis-phosphine catalysts but are far more metathesis active. A scheme is proposed to explain the difference in reactivity between the two types of catalysts.

Stability of Electrode-Electrolyte Interfaces during Charging in Lithium Batteries

In this thesis we study the growth of a Li electrode-electrolyte interface in the presence of an elastic prestress. In particular, we focus our interest on Li-air batteries with a solid electrolyte, LIPON, which is a new type of secondary or rechargeable battery. Theoretical studies and experimental evidence show that during the process of charging the battery the replated lithium adds unevenly to the electrode surface. This phenomenon eventually leads to dendrite formation as the battery is charged and discharged numerous times. In order to suppress or alleviate this deleterious effect of dendrite growth, we put forth a study based on a linear stability analysis. Taking into account all the mechanisms of mass transport and interfacial kinetics, we model the evolution of the interface. We find that, in the absence of stress, the stability of a planar interface depends on interfacial diffusion properties and interfacial energy. Specifically, if Herring-Mullins capillarity-driven interfacial diffusion is accounted for, interfaces are unstable against all perturbations of wavenumber larger than a critical value. We find that the effect of an elastic prestress is always to stabilize planar interfacial growth by increasing the critical wavenumber for instability. A parametric study results in quantifying the extent of the prestress stabilization in a manner that can potentially be used in the design of Li-air batteries. Moreover, employing the theory of finite differences we numerically solve the equation that describes the evolution of the surface profile and present visualization results of the surface evolution by time. Lastly, numerical simulations performed in a commercial finite element software validate the theoretical formulation of the interfacial elastic energy change with respect to the planar interface.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

Computation of high-stability DC balancing scheme for ferroelectric liquid crystal on silicon holograms using graphics processing units.

Spatial light modulators based around liquid crystal on silicon have found use in a variety of telecommunications applications, including the optimization of multimode fibers, free-space communications, and wavelength selective switching. Ferroelectric liquid crystals are attractive in these areas due to their fast switching times and high phase stability, but the necessity for the liquid crystal to spend equal time in each of its two possible states is an issue of practical concern. Using the highly parallel nature of a graphics processing unit architecture, it is possible to calculate DC balancing schemes of exceptional quality and stability.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

Measuring spin diffusion of electrons in bulk n-GaAs using circularly dichromatic absorption difference spectroscopy of spin gratings

Circular dichromatic absorption difference spectroscopy is developed to measure the spin diffusion dynamics of electrons in bulk n-GaAs. This spectroscopy has higher detection sensitivity over homodyne detection of spin-grating-diffracted signal. A model to describe circular dichromatic absorption difference signal is derived and used to fit experimental signal to retrieve decaying rate of spin gratings. A spin diffusion constant of D-s=201 +/- 25 cm(2)/s for bulk n-GaAs has been measured at room temperature using this technique and is close to electron diffusion constant (D-c), which is much different from the case in GaAs quantum wells where D-s is markedly less than D-c.

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nanoelectronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master equation with the well-known time-dependent density functional theory. The key ingredients of this paper include (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e., the device); and (iii) the construction of Kohn-Sham master equations for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOMs) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along with the propagation of the Kohn-Sham master equation and the EOMs of the auxiliary functions.