Separating Detection Performance from Thermodynamic Interpretability in Quantum-Capacitance Affinity Assays

Abstract Quantum capacitance, Cq, is proportional to the electronic density of states of a redox monolayer and is used as a label-free transducer in affinity sensing. Here, we develop a theoretical framework and apply it to a reanalysis of previously published impedance data from a DNA-receptive interface; no new experimental data are reported. Under the isoscopic condition, the charging energy per accessible redox state is fixed at 2kBT, so that the analyte dependence of the ensemble Cq resides in the number of accessible states. Binding renders a fraction χ of these states electrochemically inaccessible, which gives a relative response of 1/Cq equal to χθ/(1 – χθ) and an apparent affinity Kaapp = (1 – χ)Ka. Because the titration does not reach saturation, only the product χθ is determined: χ is not identifiable, being bounded below at 0.169 (unamplified) and 0.625 (amplified with ferrocenecarboxylic acid, FcA), so that Ka cannot be recovered from Kaapp. The charge-relaxation resistance, 12.97 ± 0.72 kΩ, lies within 0.5% of h/2e2 and is invariant across the unamplified titration, an internal consistency criterion that the amplified configuration fails. The Cole–Cole exponent of the electronic relaxation, α = 0.888 ± 0.042, is invariant with concentration but does not establish that the receptor sites are energetically equivalent. The calibration is log-linear over five decades, a shape no Langmuir isotherm reproduces, and equilibrium was not independently established; the extracted constants are therefore reported as apparent, protocol-dependent interfacial parameters. The analysis separates analytical detection performance, including the previously reported attomolar detection limit of the FcA-amplified interface, from thermodynamic interpretability, which requires an identifiable χ, an invariant Rq and a demonstrated equilibrium.