Analysis of Laminar Flow Electrochemical reactors: Self-supported Synthesis and the Effects of Ultrasound

The electrochemical synthesis of organic molecules provides a unique control over the reaction conditions: The electrical current flowing through the electrodes determines the conversion and the applied potential difference between the electrodes determines the selectivity. Electrolysis is therefore reported as an attractive method for the synthesis of organic molecules that have applications in the fine chemical, specialty chemical, and pharmaceutical industries. Although the majority of research is still done in beaker-like cells, some research groups make use of small-scale, continuous, parallel plate reactors. The electrodes are then placed as close as possible and kept apart only by a thin, non-conducting spacer. A channel is cut out from this spacer, allowing an electrolyte to flow between the narrow gap. Among the claimed advantages of these cells are the high and uniform current densities that can be achieved, as well as the low amounts of inert salts that have to be added. These salts are typically required to overcome the high electrolytic resistance of organic solvents, yet some syntheses in narrow gap electrolysis cells require no additional salt at all! The synthesis is then self-supported: ions generated at the electrodes during electrolysis provide the required conductivity to sustain a reasonably large current.

Although this sounds plausible at first, it remains paradoxical how such a synthesis can start. If there are no ionic species to begin with, then no electric current can pass through the cell. Consequently, if no electric current can pass, then no ions are generated. What ions could then ever sustain an electric current? Anyway, in case some cations and anions would be generated at the anode and cathode without any other (inert) ions in the neighborhood to compensate for these local charge excesses, then the generated ions must first diffuse towards each other before a state of electroneutrality is reached. The two charged diffusion layers will theoretically have an unrealistically high mutual electrostatic attraction, which is not observed in reality. Grotthuss’s hydrogen-hopping mechanism has been used to pooh-pooh this objection, but the resulting macroscopic increase in proton mobility is too modest for providing a satisfying explanation. Moreover, self-supported synthesis has been reported for aprotic solvents such as acetonitrile and dimethylformamide as well.

The main aim of this dissertation is to address this paradox and elucidate the peculiarities of self-supported synthesis. First, a pseudo-spectral method was developed that solves the Nernst-Planck-electroneutrality equations for a parallel plate or annular reactor, an arbitrary number of ionic species, and which is flexible towards user-defined electrode as well as homogeneous kinetics. It compares favorably to well-known limiting cases and calculations using a commercial software package (Comsol Multiphysics). The developed program is therefore a reliable tool for comparison with analytical approximations, which provide a deeper insight into the interrelationships between the applied voltage, flow rate, and current density. Notably, the paradox is resolved by assuming few ions are always present, either due to impurities or the self-dissociation of the solvent. The positive feedback between ion creation and cell resistance ultimately results in a critical ``blow-out'' flow rate. Below this critical flow rate, the synthesis is self-supported and sustains a current as if it is well-supported. Above this critical flow rate, the generated ions are flushed out of the reactor before the positive feedback mechanism becomes effective. The initial concentration of unintentionally added ions can be very low, as it only logarithmically affects the critical flow rate. Without taking great care in purifying the solvent or reagents, sufficient ions are always present for triggering exponential runaway. It was also found that self-supported synthesis has implications on very unstable intermediate ions that couple with each other in a paired synthesis. The homogeneous coupling reaction zone then shifts from the center of the channel, where the diffusion layers would ordinarily meet in a well-supported synthesis, to the electrodes. If the coupling product is prone to further oxidation or reduction, then the selectivity and yield of the overall process might be affected.

The critical flow rate, below which self-supported synthesis is possible, crucially depends on the diffusion coefficient of the intermediate ions. This suggests that mixing (or the absence thereof) at the channel inlet plays an important role in triggering the exponential growth. We therefore wondered whether mixing through ultrasound-induced acoustic streaming could affect the critical flow rate. Since acoustic streaming is a second-order phenomenon, a design methodology was developed that models an infinitely long channel actuated by periodically spaced piezoelectric actuators. The generation of ultrasound by the piezoelectric element, its propagation through the elastic reactor walls into the electrolyte, and the consequent Rayleigh streaming could then be modeled analytically. This allowed rapid mapping of the energetic efficiency for different actuator-spacing/operating frequency combinations.

Finally, preliminary experiments were conducted for ferrocene oxidation paired with benzylbromide reduction in acetonitrile. These experiments provide a strong indication that the proposed theory for self-supported synthesis is reasonable. In addition, acoustic irradiation at moderate piezoelectric element actuation voltages (40 V peak-to-peak) more than doubled the critical flow rate. To place the proposed theories on firmer footing, more experiments are nevertheless required for different chemical systems and operating conditions. Furthermore, the practical implementation of the sonicated reactor could still benefit from many improvements. In particular, a thin air layer between the actuator and the reactor walls is suspected of introducing a very large acoustic impedance mismatch, which must be addressed to avoid excessive energy losses.