Adsorbate-metal bond effect on empirical determination of surface plasmon penetration depth

The penetration depth of surface plasmons is commonly determined empirically from the observed response for adsorbate loading on gold surface plasmon resonance (SPR) substrates. However, changes in the SPR spectrum may originate from both changes in the effective refractive index near the metal surface and changes in the metal permittivity following covalent binding of the adsorbate layer. Herein, the significance of incorporating an additional adsorbate-metal bonding effect in the calculation is demonstrated in theory and in practice. The bonding effect is determined from the nonzero intercept of a SPR shift versus adsorbate thickness calibration and incorporated into the calculation of penetration depth at various excitation wavelengths. Determinations of plasmon penetration depth with and without the bonding response for alkanethiolate-gold are compared and are shown to be significantly different for a thiol monolayer adsorbate system. Additionally, plasmon penetration depth evaluated with bonding effect compensation shows greater consistency over different adsorbate thicknesses and better agreement with theory derived from Maxwell's equation, particularly for adsorbate thicknesses that are much smaller (<5%) than the plasmon penetration depth. The method is also extended to a more practically applicable polyelectrolyte multilayer adsorbate system.