Chemical Hardness of Mesoscopic Electrochemical Systems Directly Analyzed from Experimental Data

Abstract

The absolute chemical hardness η for a chemical system under a steady external potential υ containing N electrons and an energy E(N) was defined by Robert Parr and Ralph Pearson as η = (δ2 E/δN 2)υ. Chemical hardness is a widely accepted concept in chemistry that serves as a reactivity index for describing the stability of compounds and reaction mechanisms in the framework of hard and soft acid and base theory. In a previous study, we demonstrated that it is possible to formulate a total energy functional of electronic density that is directly correlated to the experimental data obtained from mesoscopic electrochemical systems. The present study extends the use of this experimentally designed functional to determine and analyze the chemical hardness of mesoscopic electrochemical systems directly from the experimental data. We demonstrate that it is possible to rapidly scan the physical properties and chemical reactivity indexes of mesoscopic electrochemical systems at different external potentials and a finite temperature using the grand canonical ensemble.

Nanostructured Titanium Dioxide Surfaces for Electrochemical Biosensing

“…Electrochemical impedance spectroscopy (EIS) is an interfacial analytical tool, and it is widely used due to its high sensitivity with minimal hardware demand, easy production and low-cost [57]. EIS data processing produces different electrical function responses as impedance [2], admittance, complex capacitance [58], experimental chemical hardness [59] and others; in this way, EIS allows to characterize the resistive and capacitive (dielectric) properties of electrochemical systems by measuring the change in impedance when subjected to an alternating current flow [4,57]. Two setups, potentiometric and galvanometric, can measure the impedance spectrum.…”

“…where ω = 2πf is the angular frequency [47]. Furthermore, the measurement of the experimental chemical hardness has been proposed as the inverse of the capacitance [59,60]. The choice of the electrical function to be plotted depends on the detector response; if the behavior is mainly capacitive, the complex capacitance or the chemical hardness is the right choice, whereas the impedance should be selected in case of a main resistive response.…”

Improving the Analytical Reproducibility of Electrochemical Capacitive Sensors Using the Chemical Hardness of the Interface

“…where q = (e℧ρ). ρ is the electron density at a given electrochemical potential µ and ℧ is the volume of the system, with E 0 being the energy reference [16], [18]. According to conceptual DFT, the chemical reactivity index η, known as chemical hardness, is defined as the second derivative of the energy functional E q [ρ] with respect to the electron density ρ [16]- [18], [24], [26], [27]:…”

“…1, demonstrating that the inverse of C q is directly associated with the chemical energy. Furthermore, following conceptual density functional theory (DFT), the variation in 1/C q as a function of occupancy can be demonstrated to be related to the chemical hardness of the interface [9], [16]- [18] (see details below). The chemical hardness η ∝ 1/C q is an important chemical reactivity index able to quantify the reactivity between interacting or reacting substances [18].…”

“…Furthermore, following conceptual density functional theory (DFT), the variation in 1/C q as a function of occupancy can be demonstrated to be related to the chemical hardness of the interface [9], [16]- [18] (see details below). The chemical hardness η ∝ 1/C q is an important chemical reactivity index able to quantify the reactivity between interacting or reacting substances [18]. By monitoring the η of the interface, this reactivity index can be used to quantify and detect biomolecules of interest that interact or react with biological receptors coupled to suitably designed interfaces.…”