A simulation-based analysis of optical read-out for electrochemical reactions using composite vortex beams

We propose an optical read-out method for extracting faradaic current in electrochemical (EC) reactions and analyze its performance using opto-EC simulations. Our approach utilizes structured electrodes to generate composite optical vortex (COV) beams upon optical illumination. Through opto-EC simulations, we demonstrate that the EC reaction of 10 mM potassium ferricyanide induces a refractive index (RI) change, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi></mml:math> RI, of approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>10</mml:mn> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>4</mml:mn></mml:mrow> </mml:msup> </mml:math> RI units, leading to the rotation of the COV beam's intensity profile with a peak rotation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>40</mml:mn> <mml:mo>∘</mml:mo></mml:msup> </mml:math> . This rotation's magnitude is proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi></mml:math> RI, while the rate correlates with the faradaic current ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>I</mml:mi> <mml:mi>f</mml:mi></mml:msub> </mml:math> ) density responsible for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi></mml:math> RI. As the opto-EC information is from bulk <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi></mml:math> RI, it remains unaffected by interfering non-faradaic components at the interface and is advantageous for studying intermediate species and bulk homogeneous reactions. Furthermore, as rotation depends on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>I</mml:mi> <mml:mi>f</mml:mi></mml:msub> </mml:math> density rather than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>I</mml:mi> <mml:mi>f</mml:mi></mml:msub> </mml:math> itself, this method proves beneficial in low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>I</mml:mi> <mml:mi>f</mml:mi></mml:msub> </mml:math> scenarios, such as when employing micro-electrodes to decrease solution resistance or obtain localized EC data. Even in low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>I</mml:mi> <mml:mi>f</mml:mi></mml:msub> </mml:math> density scenarios, like monitoring slow EC reactions, our method enables signal amplification by accumulating rotation over time. This interdisciplinary approach holds promise for advancing EC research and addressing critical challenges across various fields, including energy storage, corrosion protection, environmental remediation, and biomedical sciences.