Experimental confirmation of solvated electron concentration and penetration scaling at a plasma–liquid interface
Daniel C. Martin, David M. Bartels, Paul Rumbach, David B. Go
Abstract
Abstract In this work, the transport of the plasma injected solvated electron is experimentally studied using total internal reflection absorption spectroscopy (TIRAS). A recently derived a theoretical model predicts power-law scalings between the interfacial concentration n 0 and penetration depth l with plasma current density j , namely <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>j</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>l</mml:mi> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>j</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> . Here, we extend this model to show that the optical absorption intensity should follow a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> power law behavior with current density, and we perform TIRAS measurements to confirm this behavior. By altering the ionic strength (salt concentration) of our electrolyte solution to control the current density, we find that at higher concentrations a scaling of approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> power is observed. However, the scaling is linear at lower concentrations, which we show is due to the transient response of the TIRAS experiment operating in a modulated mode. Ultimately, the experimentally-confirmed scaling law predicts approximate upper limits of penetration depth and interfacial concentration for solvated electrons, findings essential for tailoring plasma-liquid systems for specific applications.