Effect of Electrode Roughness On the Capacitive Behavior of Self-Assembled Monolayers

Abstract

Analytical gold electrodes were polished mechanically and electrochemically and the true area of the electrode surface was measured by quantitative oxidative/reductive cycling of the electrode. A roughness factor for each electrode was determined from the ratio of the true area to the geometric area. The roughness is fully described by a combination of microscopic roughness (up to tens of nanometers) and macroscopic roughness (on the order of hundreds of nanometers) terms. The electrodes were then derivatized with a self-assembled monolayer (SAM) of dodecanethiol or a thioalkane azacrown and characterized by impedance spectroscopy. The behavior of the electrodes was modeled with either a Helmholtz or Randles equivalent circuit (depending on the SAM used) in which the capacitance was replaced with a constant phase element. From the model, an effective capacitance and an alpha factor that quantifies the nonideality of the SAM capacitance was obtained. The effective capacitance divided by the roughness factor yields the capacitance per unit true area, which is only a function of microscopic roughness. The relationship between this capacitance and the alpha factor indicates that microscopic roughness predominantly affects the nonideality of the film while macroscopic roughness predominantly affects the magnitude of the film's capacitance. Understanding the contribution of the electrode topography to the magnitude and ideality of the SAM capacitance is important in the construction of SAM-based capacitive sensors because it predicts the importance of electrode-electrode variations.

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“…The roughness, which is defined by the ratio of the true to the geometric surface area, is around 2.7. This value is similar to the one for a macroelectrode [26].…”

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“…The elements of this equivalent electric circuit are the C dl , which models the interfacial capacitance that arises from the double layer capacitance at the film/ electrode interface, and R b and C b , associated in parallel, which represent the bulk resistance and the geometrical capacitance of the film/electrode interface, respectively. As the real system is much more complicated and the capacitance at solid electrodes does not behave ideally, two constant phase elements substitute the capacitors C dl and C b considering the inhomogeneity of the system and the roughness and irregularities of the electrode surface [48,49]. After fitting the experimental data to an equivalent electrical circuit it was found that PLA and PLA-P3TMA blends of wt% ratio 5:1 and 2:1 adjust to the circuit depicted in Figure 6c, while the fitting of a circuit to the 1:1 blend was much more difficult to achieve.…”

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“…1 using the nonlinear least squares fitting routine provided by the ZView software program. A constant phase element (CPE) was used to model the interfacial capacitance, to account for deviations from ideal capacitive behavior [24,25] and to achieve a more accurate fit to the experimental data. The impedance of a CPE is given by (Q(ix) n ) À1 , and is equivalent to an ideal capacitor when the CPE exponent, n, is equal to 1.…”

“…However, in situations where the CPE exponent is slightly less than one but constant over a potential window or solution conditions, it is a fair approximation to use the magnitude of the CPE parameter as the film's capacitance. In our experiments, we observed a change in the CPE exponent over the potential window of interest and, to account for this change, converted the magnitude of the CPE (Q) into an effective capacitance (C) using the following correction [24,38,39]:…”