Does the ionic distribution in the electrical double layer modify second harmonic scattering?

Surface-specific nonlinear optical techniques are ideally suited to investigate the complex structure of aqueous interfaces. For colloidal particles dispersed in aqueous solutions, interfacial properties can be retrieved with angle-resolved second harmonic scattering (AR-SHS). The mathematical framework of AR-SHS does not require a priori knowledge on the electrostatic distribution in the first few nanometers close to the interface, therefore allowing us to formulate a molecular-level description of the electrical double layer (EDL) based on the experimental data. However, farther away from the interface, an analytical form of the electrostatic potential decay is necessary to account for the distance dependence of the surface electrostatic field propagating into the solution. This requirement is especially important at low ionic strengths, where the electrostatic field is not efficiently screened by counterions. Here, we examine to what extent the analytical form of the electrostatic potential decay impacts the AR-SHS data analysis. We analyze the effect of different functions on the scattering form factors, on the integrated AR-SHS signal intensity, and on the surface parameters extracted from fitting the AR-SHS data. We find that the trends of the surface parameters remain similar regardless of the chosen function, demonstrating the robustness of our approach to establish a molecular-level picture of the EDL. At ionic strengths <10-4M for 100-nm diameter particles, a functional form that physically represents counterions packed more densely in the vicinity of the surface than in the case of the Poisson-Boltzmann distribution has the largest impact, resulting in an overestimation of the obtained surface potential.