ABSTRACT
We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological fluid dynamics and other modeling scenarios in which a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems involving viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constitutive equation. In the viscoelastic context, however, relatively little work has explored the accuracy or convergence properties of this numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using either the idealized Oldroyd-B constitutive model or the more physcially realistic, polymer-entanglementbased Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.
ABSTRACT
When irradiated with blue light in the presence of a Lewis base (L), [CpW(CO)3]2 undergoes metal-metal bond cleavage followed by a disproportionation reaction to form [CpW(CO)3L]+ and [CpW(CO)3]-. Here, we show that in the presence of pyridinium tetrafluoroborate, [CpW(CO)3]- reacts further to form a metal hydride complex CpW(CO)3H. The rection was monitored through in situ photo 1H NMR spectroscopy experiments and the mechanism of light-driven hydride formation was investigated by determining quantum yields of formation. Quantum yields of formation of CpW(CO)3H correlate with I-1/2 (I = photon flux on our sample tube), indicating that the net disproportionation of [CpW(CO)3]2 to form the hydride precursor [CpW(CO)3]- occurs primarily through a radical chain mechanism.
ABSTRACT
Rotating disc electrode (RDE) voltammetry has been widely adopted for the study of heterogenized molecular electrocatalysts for multi-step fuel-forming reactions but this tool has never been comprehensively applied to their homogeneous analogues. Here, the utility and limitations of RDE techniques for mechanistic and kinetic analysis of homogeneous molecular catalysts that mediate multi-electron, multi-substrate redox transformations are explored. Using the ECEC' reaction mechanism as a case study, two theoretical models are derived based on the Nernst diffusion layer model and the Hale transformation. Current-potential curves generated by these computational strategies are compared under a variety of limiting conditions to identify conditions under which the more minimalist Nernst Diffusion Layer approach can be applied. Based on this theoretical treatment, strategies for extracting kinetic information from the plateau current and the foot of the catalytic wave are derived. RDEV is applied to a cobaloxime hydrogen evolution reaction (HER) catalyst under non-aqueous conditions in order to experimentally validate this theoretical framework and explore the feasibility of RDE as a tool for studying homogeneous catalysts. Crucially, analysis of the foot-of-the-wave via this theoretical framework provides rate constants for elementary reaction steps that agree with those extracted from stationary voltammetric methods, supporting the application of RDE to study homogeneous fuel-forming catalysts. Finally, obstacles encountered during the kinetic analysis of cobaloxime, along with the voltammetric signatures used to diagnose this reactivity, are discussed with the goal of guiding groups working to improve RDE set-ups and help researchers avoid misinterpretation of RDE data.
ABSTRACT
The solubility of molecular transition metal complexes can vary widely across different redox states, leaving these compounds vulnerable to electron transfer-initiated heterogenization processes in which oxidation or reduction of the soluble form of the redox couple generates insoluble molecular deposits. These insoluble species can precipitate as suspended nanoparticles in solution or, under electrochemical conditions, as an electrode-adsorbed material. While this electrochemically-driven solubility cycling is technically reversible, the reverse electron transfer to regenerate the soluble redox couple state is a practical challenge if sluggish electron transfer kinetics result in a loss of electronic communication between the molecular deposits and the electrode. In this work, we present an example of this electrochemically-driven solubility cycling, report a novel strategy for catalytically enhancing the oxidation of the insoluble material using homogeneous redox mediators, and develop the theoretical framework for analysing and digitally simulating the action of a homogeneous catalyst on a heterogeneous substrate via cyclic voltammetry. First, a mix of electrochemical and spectroscopic methods are used to characterize an example of this electrochemically-driven solubility cycling which is based on the two-electron reduction of homogeneous [Ni(PPh 2NPh 2)2(CH3CN)]2+ (PPh 2NPh 2 = 1,3,5,7-tetraphenyl-1,5-diaza-3,7-diphosphacyclooctane). The limited solubility of the doubly-reduced product in acetonitrile leads to precipitation and deposition of molecular [Ni(PPh 2NPh 2)2]. While direct oxidation of this heterogeneous [Ni(PPh 2NPh 2)2] at the electrode surface is possible, this electron transfer is kinetically limited. We demonstrate how a freely diffusing redox mediator (ferrocene) - which shuttles electrons between the electrode and the molecular material - can be used to overcome these slow electron transfer kinetics, enabling catalytic regeneration of soluble [Ni(PPh 2NPh 2)2]2+. Finally, mathematical models are developed that describe the current-potential response for a generic EC' mechanism involving a homogeneous catalyst and surface-adsorbed substrate. This novel strategy has the potential to enable reversible redox chemistry for heterogeneous, molecular deposits that are adsorbed on the electrode or suspended as nanoparticles in solution.
