Model-derived conversion formula for real-time gas monitoring based on chemiresistive sensors

Chemiresistive gas sensors transduce gas adsorption into changes in the electrical resistance across a pair of electrodes connected by a sensitive layer of material. This type of sensor is used due to its simple operation, high sensitivity, low cost, and convenience for scaled-up manufacturing of microsized devices. The conversion of the electrical resistance to a corresponding gas concentration is often performed through calibration procedures using empirical formulas, overlooking part of the physical phenomena involved in the process, both on the sorption kinetics and on the transduction. Consequently, a direct evaluation of gas concentration is plagued by the response delays and slow recovery intrinsic to these processes. In contrast to this approach, here we first propose a physical model, based on gas-modulated potential barriers, and considering the out-of-equilibrium dynamic response. Based on this model, we derive an original conversion formula able to dynamically convert the resistance changes into a corresponding gas concentration thus eliminating the main drawback related to slow response and recovery. This new strategy is demonstrated for real-time NO2 gas sensing, using chemiresistors based on oxidized PbS nanocrystals. In addition, the broader application of the proposed model and strategy is demonstrated for NH3 sensing, based on polypyrrole/gold junctions.

💡 Research Summary

The paper addresses a fundamental limitation of chemiresistive gas sensors: the slow response and recovery times that hinder real‑time concentration measurements. Traditional calibration relies on empirical relationships between resistance and gas concentration, which ignore the underlying sorption kinetics and the physics of charge transport. To overcome this, the authors develop a physically based model that explicitly couples gas adsorption dynamics with the modulation of inter‑grain potential barriers in a nanocrystal (NC) sensing layer.

The model treats each NC as a conductive core separated by insulating interfaces that form double‑Schottky barriers. The barrier height ϕB depends on the surface occupancy of two types of adsorption sites (neutral Pb⁰/Pb²⁺ and passivated Pb⁴⁺). The time‑dependent occupancy θ₀(t) and θ₂⁺(t) obey kinetic equations derived from Langmuir‑type adsorption–desorption dynamics, incorporating adsorption (kₐ) and desorption (k_d) rate constants, temperature, and gas concentration C(t). The total sensor resistance R is assumed proportional to the individual junction resistance rᵢⱼ, which follows a Richardson‑type thermionic emission expression involving ϕB, junction area S, temperature T, and the Richardson constant A*.

By solving the kinetic equations for θ(t) and substituting into the resistance expression, the authors obtain a closed‑form conversion formula that directly maps measured resistance changes to instantaneous gas concentration, without waiting for the sensor to reach equilibrium. This dynamic conversion also yields analytical expressions for the characteristic response and recovery times (T₉₀ and T₁₀), providing a quantitative handle on sensor speed.

Experimental validation is performed with two lead‑sulfide (PbS) nanocrystal sensors fabricated by a simple drop‑dry method followed by either vacuum or air annealing. Surface analysis (XPS, XRD) confirms distinct oxidation states and sulfur content, which translate into different site populations and thus different kinetic parameters. Under stepwise NO₂ exposures from 0.1 to 0.5 ppm, the measured resistance transients of both sensors are accurately reproduced by the model, and the dynamic conversion yields correct NO₂ concentrations throughout the transient phase.

The same modeling framework is applied to a polypyrrole/gold junction sensor for NH₃ detection, demonstrating that the approach is not limited to PbS NCs but is applicable to any chemiresistive system where charge transport is governed by gas‑modulated potential barriers.

Key contributions of the work include: (1) a physically grounded description of barrier‑controlled conduction in nanocrystal networks; (2) incorporation of out‑of‑equilibrium adsorption kinetics into sensor response modeling; (3) derivation of an analytical, real‑time resistance‑to‑concentration conversion formula; (4) experimental verification on both oxidized PbS NCs and PPy/Au junctions; and (5) a pathway toward low‑temperature, low‑power, scalable gas sensors suitable for IoT and portable applications.

Overall, the study provides a robust theoretical and practical toolkit for transforming chemiresistive sensors from slow, calibration‑dependent devices into fast, quantitative, real‑time gas monitors, potentially reshaping environmental monitoring, indoor air quality control, and wearable sensing technologies.