Steady vs. Dynamic Contributions of Different Doped Conducting Polymers in the Principal Components of an Electronic Nose’s Response

Abstract

Multivariate data analysis and machine learning classification have become popular tools to extract features without physical models for complex environments recognition. For electronic noses, time sampling over multiple sensing elements must be a fair compromise between a period sufficiently long to output a meaningful information pattern and sufficiently short to minimize training time for practical applications. Particularly when a reactivity’s kinetics differ from the thermodynamics in sensitive materials, finding the best compromise to get the most from the data is not obvious. Here, we investigate the influence of data acquisition to improve or alter data clustering for molecular recognition on a conducting polymer electronic nose. We found out that waiting for sensing elements to reach their steady state is not required for classification, and that reducing data acquisition down to the first dynamical information suffices to recognize molecular gases by principal component analysis with the same materials. Especially for online inference, this study shows that a good sensing array is not an array of good sensors, and that new figures of merit should be defined for sensing hardware using machine learning pattern recognition rather than metrology.

1. Introduction

Current advances in artificial intelligence and internet-of-things facilitate identifying new input layers as data generators to feed machine learning (ML) for information classification. Before this, electronic noses (eNoses) have nourished the fantasy for more than 60 years of emulating a biological sense to perform classification tasks that sensors can barely make with molecular patterns [1,2,3,4,5]. It is therefore very appropriate to wonder whether conventional approaches to selecting sensing hardware are adapted to information processing requirements, with pattern recognition having more standards nowadays.

Chemistry is no trivial physics: it is no 1D continuum nor spectrum, but volatile molecules compose a vast group of hundred billion countable objects [6,7]. Therefore, measuring all of them simultaneously with a restricted and well-chosen set of ultimately selective sensors is unrealistic. If such complexity suits better ML-supported recognition than quantification using metrological sensors, proposing clear sensing figures of merit (FoMs) that guide technologists to identify the right sets of materials is still needed in such context [8,9,10,11]. The main difficulty in identifying those lies in the fact that smart sensing arrays do not involve physical models at the opposite of metrological sensors: ML is purely mathematically driven, which does not help in identifying device physical features to generate qualitative data. Each output signal conditions individual components of input data, but the quality of the output data themselves relates to features that affect the performances of the classifier as a group of device properties. The relationship between the data transformation as a result and the physical properties of a chosen sensing hardware is not straightforward and largely depends on the association of a software classifier with a sensing hardware. For an eNose, conductometric sensing arrays are often used as a hardware [12,13,14,15], in conjunction with principal component analysis (PCA)/k-means clustering (k-means) as a classifier [5,16,17,18]. In such systems, time-dependent current signals are inputted by environmentally sensitive materials in an array. An information feature of a high-dimensional vector is composed of a single current signal for classification. PCA is a linear classifier as it involves only one matrix transformation from a dataset of input vectors to a set of scores. The PCA projects data on a subspace defined by a basis of the covariance matrix eigenvectors which have the highest eigenvalues. As a consequence, PCA aims to ignore the contributions of “silent” sensing elements, or the ones with activities that are uncorrelated to one another. Conventional sensors’ FoMs do not consider information correlation between sensing elements, as it relates strictly to physical properties of individual elements to be standalone: for instance, selectivity, sensitivity or time response [19]. The latter is an important FoM that usually determines if a technology is suitable for online application. If information speed is essential for telecommunication, it is not necessarily the case for the velocity of information carriers themselves. The implementation of recurrent networks for sensing elements can illustrate such fact, where the group dynamic of different slow sensing elements enables recognizing frequency-modulated signals [20]. Homogenizing the physical properties of the population of sensing elements can even degrade the classifier’s recognition performance, so when the dynamic of sensing devices carries information, a long-enough acquisition is crucial for classification [20]. However, time is also a resource to enrich a database to train a system: the slower the hardware, the longer the training, which ultimately conditions any classifier’s recognition performance. As a consequence, in case information lies in the dynamic of a hardware [21], a fair compromise must be found for data acquisition time to optimize training with enough meaningful data but reasonable training duration for environmental pattern recognition.

In the framework of recognizing volatile solvents with doped conducting polymers, we propose in this study to quantify how relevant it is to consider the acquisition time as a metrological FoM for effective molecular recognition with a conductometric nose using PCA/k-means. By using both static and dynamic descriptors, we show that a steady sensing element response is unnecessary for optimal classification, and that training duration can greatly be shortened for practical inference.

2. Experimental Section

Device Fabrication: The fabrication of sensing elements used in this study has been reported elsewhere [22]. Concentric spiral-shaped Au microelectrodes (channel length L = 400 nm, spiral electrodes length W such as W/L > 10³ in a round cavity of 28 μm in diameter) were micro-fabricated by electron beam lithography in a cleanroom environment. The devices’ active area features a large W/L over a restricted area to maximize conductance sensitivity while minimizing total area of an array of them for system integration. Contact lines are passivated by a conformal CVD-processed Parylene C passivation layer (2 μm thickness), structured by an O₂ dry etching to expose pads and the devices active area, so each device outputs an individual response for co-integration at small scale. The active materials were subsequently deposited on top of the sensing arrays by drop casting. Formulations of regio-regular P3HT and dopants solutions (composed of Fe(OTf)₃, Bi(OTf)₃, Cu(OTf)₂, In(OTf)₃, Al(OTf)₃, Dy(OTf)₃ and Ce(OTf)₃) were performed in two different steps to minimize the device electrical property distribution due to material heterogeneity if deposited with a single formulation.

Electrical Characterization: To obtain raw data, the study exploited current versus time measurements of eight populations of materials, composed of three different devices for each material. Each of the 24 current versus time trace sizes 6899 data points per current trace, sampled every second. The current measurements were performed with an Agilent 4155 parameter analyzer in an air blow, passing through a 5 mL vial that contains 1 mL of a volatile solvent [22]. The system was calibrated to blow at a rate of 1 mL/s over a sensing array. The control of the vapor exposure was manually operated with pneumatic valves (asynchronous delays up to five seconds can be considered between the actual operation of the valves and the attributions of the labels on the current traces). Elementary sequences of gas exposures were set to three minutes for sensing elements to reach their steady state. Each volatile solvent exposure was followed by a purging sequence when the air flow passes through an empty vial to enable the response of the sensing arrays recover their response.

Data Analysis: Raw data currents were compiled and treated without filtering. Raw data curves have already been published [22] and are available on a public repository. Principal component analysis (PCA) was used as a linear classifier by mean of the online open access tool Clustvis [23]. The PCA data were scaled by unit variance and computed by singular value decomposition. All PCA data are available as Supplementary Information of this article. Additionally, 95% confidence ellipsoids were determined by k-means clustering with k = 3, from random values for the initial centroids (in each case, k-means clustering was run at least three times to ensure repeatability of the resulting clusters).

3. Results

3.1. Data Collection and Feature Extraction

To interpret the physical significance of information features for the quality of a recognition, the machine learning (ML) approach is preferred to the deep learning (DL) one (see Figure 1 for the overall approach). DL algorithms are different from ML ones mostly by their complexity to allow the end-user not to have to identify information descriptors from raw data a priori. In our case, we chose specifically to compare two different features α₁ and α₂ that are extensively used in conductometric eNoses as information descriptors: the relative resistance modulation α₁ = R/R₀ − 1 and the drift resistance α₂ = Ṙ/R, with R being the Ohmic resistance of a conductometric sensing element measured at a given time during exposure to an environment of a specific class, Ṙ its first derivative of time and R₀ its value right before it starts to be exposed to an environment of a specific class at t₀. As α₁ compares two states before and after being exposed to a class, this information descriptor is qualified as a “thermodynamic feature” and relates to how much the signal’s transport is affected by the presence of a given environment compared to a reference, through a given material. Instead, α₂ uses a first-order derivative of time to quantify how fast or slow the signal decays or amplifies through a given material by the presence of a given environment: this information descriptor is qualified as a “kinetic feature”. Each feature is calculated for different scenarios of crossed-coupled environments/devices parameters, with a population of 24 different sensitive devices (composed of eight populations of sensitive materials measured on 3 different devices), exposed at 18 occurrences to different environments (six alternate permutations of 3 different solvent vapor exposures). The experimental details are fully described in a previous study [22], where the PCA was used exclusively with the feature α₁ calculated exclusively for the last ten seconds of each three-minute environment exposure. Although the steady-state response for these materials was relatively fast compared to that of other materials for comparable tests [24,25,26,27], the dataset totals over 44 h of acquisition time assisted by manual operations to expose the different materials on different devices with different environments repeatedly to train the system. Applying the same approach to exposing n! times the n different vapor classes for three minutes would result in over a week, over a month and over seven months of total data acquisition, without interruption, to respectively recognize four, five and six different classes only. As reducing the number of materials, devices or exposures would have consequences of degrading the recognition, it is straightforward to investigate decreasing the elementary period for one single environment exposure to minimize the total acquisition duration. To assess the classifier performance for a reduced acquisition time, the same dataset is considered, where data are pruned to ten seconds per acquisition sequences after the exposure starts in order to make sure that the recognition performances do not depend on the acquisition itself, keeping the same number of datapoints to analyze in each case. Also, PCA/k-means clustering was systematically used on all the different case scenarios with the same normalization and initialization settings to not bias the clustering by user-dependent factors. The recognition after clustering uses the same rules and thresholds in each case to assess a data sample as successfully, uncertainly or unsuccessfully recognized. All the individual PCA analyses are provided as Supplementary Information.

3.2. Steady Resistance Modulation as Thermodynamic Information Feature

The first analysis was performed using α₁ as an information descriptor (see Figure 2), as in the former studies using the same dataset [22,28]. The choice of this specific feature was informed by the hypothesis that the presence of volatile molecules modulates the polymer electrical conductance by interacting with its dopant and shifts its thermodynamic charge-transfer equilibrium [22]. As a thermodynamic property, the acquisition was set to three minutes per exposure to provide enough time for all devices to reach a quasi-steady state of conductance (steady output currents at a constant applied voltage). Here, from the whole dataset, 18 different sub-datasets were generated by segmenting the data to a concatenation of sequences of ten seconds after each exposure starts at t₀ (10 datapoints per exposures, 180 datapoints per sub-datasets—see Figure 2a). For each exposure, the feature α₁ takes into account two values: the resistance measured between the considered time interval and a reference resistance value R₀ measured while unexposed just before gas exposure. In each case, PCA was performed for the different sub-datasets, with the individual variance for each PC of each PCA for the different acquisition times shown in Figure 2b. From these values, one can observe that most of the variance (>66%) is explained within the first two PCs, except for data generated during the first ten seconds after t₀. It is also noticed that the variance for all 24 PCs does not change significantly for acquisitions occurring 30 s after exposure (Figure 2b, the color shade encodes the variance values in linear scale), suggesting that the feature α₁ is not enriched for the data separation in (PC1,PC2) if exposures last longer than 30 s. As shown by their scores in the (PC1,PC2) projection (Figure 2c), the PCA on α₁ during the first ten seconds of acquisition, denoted PCA^α1_0–9, embeds most variability from acetone exposures on PC1 compared to two other clusters of data for water and ethanol, which are almost entirely contained in the acetone confidence ellipsoid. Already for PCA^α1_10–19 (Figure 2d), acetone is completely separable from the other two gases, and a minor overlap remains between water and ethanol confidence ellipsoids. The final sequence PCA^α1_170–179 in Figure 2e shows an ideal clustering in the (PC1,PC2) projection, which was used in the previous study for gas recognition [22]. The loadings of PC1 and PC2 do not significantly depend on the acquisition sequences, except for the first ten seconds (Figure 2f,g). Excluding the first ten seconds, deviations overtime are however noticed: for instance, the contribution of Ce(OTf)₃-doped devices increases monotonically in PC1^α1, such as the contribution of pristine P3HT in PC2^α1. This suggests that materials that better facilitate the (PC1,PC2) data separation but are expressed slower than others do not necessarily enhance the clustering. The previous study concluded on the exclusive basis of the PCA^α1_170–179 analysis; two and three materials were preferred for recognizing ethanol from acetone from water using α₁ as and information descriptor [22]. Figure 2f,g show that such conclusion is highly acquisition-dependent (even for the same dataset considered) and that experiments performed with shorter time exposures might have concluded otherwise for the material selection. As such dependency on the sample acquisition time greatly conditions the preferred material choice for classification, it appears legitimate to investigate a dynamical feature such as α₂ as a better information descriptor for gas recognition with the same raw current data.

3.3. Resistance Drift as Kinetic Information Feature

Drift resistance α₂ in conductometric eNoses is less often used as an information descriptor, although it is worth noticing that most conventional techniques in analytical chemistry use dynamical information features as information descriptors, such as chromatography (retention time of molecules on a substrate) or surface-plasmon resonance (absorption/desorption kinetic constants of molecules on a substrate). In a material, drifts can often be associated to a memory effect that reversibly or irreversibly alters a structural property [29,30,31,32,33], rather than the transduction of environmental information in a device. In case such drift is irreversible, such behavior appears as a material instability due to ageing and is often associated as a drawback for the lifetime. However, since such reactivity on the material is environmentally induced per se, it is legitimate to wonder whether the information quality is preserved despite its effect on the information carrier itself. As an example, Kiselev et al. showed that such resistance drift (two-time median-resistance increase over four years) on a conductometric nose is totally decorrelated from the ability of the classifier to recognize a class, as the strong correlation between all sensing elements’ resistance drift does not bias linear discriminant analysis [34]. Suppose that part of the useful information to recognize gases lies in the diffusion kinetics of the volatile molecules through the doped polymers, or the adsorption/desorption kinetic constants of the molecular gases on the doped materials under flow, the drift resistance may be a relevant information descriptor as it takes into account the first derivative of time (Figure 3a). Replicating the same methodology as previously for relative resistance modulation, PCA on α₂ as an information descriptor was performed for the 18 different sub-datasets. As for α₁, the evolution of the variance for the individual PC depends on the acquisition time (Figure 3b), mainly at the beginning of the transient response (typically the first 20 s). A singular difference with α₁ is the degradation of the data variance on the first two PCs with the increase in acquisition time (from >66% for PCA^α1_170–179 down to <28% for PCA^α2_170–179). This was expected as the information becomes more sensitive to the signal’s noise on reaching the steady state; therefore, an increase in acquisition time decreases the contribution of the molecularly specific response compared in the overall information. We notice also in Figure 3b that significantly less variance is contained in PC2^α2 compared to that in PC2^α1, and more importantly that the variance in PC2^α2 is far less dependent on the acquisition time than that in PC2^α1. This suggests that despite the quality of the recognition, α₂ seems to separate data mostly because of one single parameter (if a linear model is considered), while α₁ seems to depend mostly on two parameters of a linear model. On the quality of the data separation (Figure 3c–e), similar trends in the (PC1,PC2) diagrams are observed depending on the acquisition time: in the first ten seconds of acquisition time after t₀, acetone data are better separated from the rest, followed by the ethanol data. Confidence ellipsoids seem to be always overlapping one another; however, we observe that even until three minutes after time t₀, the three volatile compounds are still recognizable, despite the residual dynamic of the sensing elements. It is also noticed that PCA^α2_170–179 (Figure 3e) clusters are more homogeneous than the ones of PCA^α1_170–179 (Figure 2e): smaller clusters within each ellipsoids can be distinguished in PCA^α1_170–179, which are attributed to experimental biases of the six repeated exposures for each class. The dependency of PCA^α2 loadings on acquisition time displays different trends than the one of PCA^α1 loadings (Figure 3f,g). For the first 20 s, all sensing elements except the ones coated with pristine P3HT and Ce(OTf)₃-doped P3HT seem to have comparable contributions in PC1^α2, and the Ce(OTf)₃-doped P3HT-coated devices mostly constitute PC2^α2–if t − t₀ < 20 s. From 20 s after t₀, Ce(OTf)₃-doped P3HT-coated devices become the most significant in PC1^α2, while PC2^α2 loadings seem highly random if t − t₀ < 20 s. This closer look on the PC1^α2 and PC2^α2 loadings highlights two different dynamics that successfully help in identifying the volatile compounds: before 20 s, “fast” and a “slow” dynamics yield the array response to recognize all three classes from PC1^α2 and PC2^α2. After 20 s, the fast dynamic of all sensing elements are faded away, leaving a minor contribution to the Ce(OTf)₃-doped P3HT devices exclusively.

3.4. Steady vs. Dynamical Resistances for Gas Recognition

To qualitatively compare the total variance distributions over the different PCs with either α₁ or α₂ as information descriptors, the scree plots are displayed on two different graphs and show the effect of acquisition time after t₀ for both descriptors (Figure 4a,b). Both of them confirm the trend of the variance with acquisition time for all principal components (not PC1 and PC2 exclusively). As Figure 4a shows, the increase in acquisition time after exposure at t₀ tends to diminish the variance contained in the lowest PC in the case of considering α₁ as an information descriptor, while it tends to increase the variance of the lower PC in the case of considering α₂ as an information descriptor in Figure 4b. We observe that this diminishing rate is different for both descriptors as displayed in Figure 4a,b, which might come from bias between the linear ad hoc model computed by the PCA and the actual physical model that governs the dependency of the information descriptors on the different sensing elements. The position of the elbows on both plots (indicated by arrows on the scree plots in Figure 4a,b) confirms that most of the useful variance for PCA^α1 is contained within the first three PCs, while only the first two for PCA^α2. Particularly, for the drift resistance α₂, this elbow is highly acquisition-dependent, and one may appreciate a richer model with more PCs to account for a shorter acquisition time. The variance analysis of PC1 and PC2 for both PCA^α1 and PCA^α2 shows an optimal acquisition time that contains most of the data variance in both PC1 and PC2 independently from the chosen information descriptor (Figure 4c). The histogram displayed in Figure 4c shows that if the acquisition time is set at the transient period between 10 and 19 s after t₀, both information features can gather at least 70% of the total variance in two different biparametric linear models. As both information features show opposed trends in the PC1 + PC2 variance evolution with acquisition time, it was expected to observe an acquisition time optimum for both PCAs independently from the quality of the data clustering. To quantify the recognition performances of the sensing array with PCA^α1 and PCA^α2, the confidence ellipsoids determined by k-means clustering were used as a threshold to declare whether the given data belonged to a given class or not, defining seven classes (as displayed in Figure 4d). The relative area of the overlap for the confidence ellipsoids was evaluated for the different acquisition times and displayed in two different histograms for each descriptor in Figure 4d–f. For α₁ (Figure 4e), one can observe that ellipsoids do not overlap from t − t₀ > 20 s, while in the case of α₂ (Figure 4f), confidence ellipsoids always overlap one another at any acquisition time. However, it should be noticed that the overlap in each case is only moderate: less than 20% of the total area of the ellipsoids. This suggests that recognition tests may be higher in the case where α₁ is used as an information descriptor than for α₂. To verify this, recognition tests were performed on the same sub-datasets using the 95% confidence ellipsoids as a threshold for classification (Figure 4g–i). Detection is considered as “positive” if the actual class of the PCA score is exclusively contained within the corresponding confidence ellipsoid, “uncertain” if the actual class of the PCA score is not exclusively contained within the corresponding confidence ellipsoid, and “negative” if the actual class of the PCA score is excluded from the corresponding confidence ellipsoid. On the one hand for α₁ (Figure 4h), one can observe that the positive detection rate 99.4 ± 0.6% for acquisition time is higher than 20 s after t₀. On the other hand for α₂ (Figure 4i), one can observe that the positive detection rate >80% for acquisition time is higher, falling between 20 s and 149 s after t₀. However, we noticed that using α₂ as an information descriptor enables substantially better recognition than α₁ for a short acquisition time below 10 s after t₀: typically, 36% positive and 38% uncertain using α₂, while 14% positive and 53% uncertain using α₁. Overall, this statistical study shows that the different materials used in the array allow recognizing volatile organic compounds because of the relative resistance modulation (α₁) rather than the resistance drift (α₂), and it points out the thermodynamics of the current modulations rather than the kinetics involved in the process.

4. Discussion

Although this study focuses specifically on doped conducting polymers, the approach is generic to any conductometric eNose and could be used for different classes of conducting materials used as transducers in an array. Despite the fact that α₁ and α₂ are frequently used as information descriptors for such application, our study proposes to investigate which feature gathers most of the useful information for an eNose. However, we want to highlight that for practical applications, such a choice may rather be conditioned by the application than by the quality of the data per se. Specifically for the resistance modulation α₁, the feature needs to routinely set a reference resistance R₀ when the environment is considered “neutral” between each data sampling. This therefore requires one to have influence over the sample exposure to periodically regenerate the device from stimuli: it is therefore practically more convenient to use α₁ as an information descriptor in cases where analytes can be exposed to a system in a supervised manner (to evaluate fragrance batch quality in an analytical laboratory, for instance). Such thermodynamic feature seems practically inadequate to extract for environment recognition in a case where the system is permanently exposed without periodic regeneration. For the drift resistance α₂, the feature does not depend on a buffered reference. However, a steady value of the sampling period must be set to measure the dynamic: it is therefore a more adequate feature for online inference for environment recognition, on the condition that the sampling period is set a posteriori given the dynamic of the pattern to recognize. It is therefore a more adequate feature to recognize stimuli that are governed by a rhythm (for instance, pollution cycles in urban environments). In this study, the selection of these features α₁ and α₂ is not based on the practical convenience to compute them in a conductometric eNose application, but on the quality of the data they output for conducting polymers used in recognition tests, which conveniently enables computing both of them at will.

In such framework, PCA confirmed that the useful information in the current response of conducting polymer materials doped with different metal triflates and exposed to different volatile organic compounds lies specifically in the thermodynamics of the device resistance modulation and not its kinetics. The analysis of the relative resistance modulation α₁ is more robust overtime when analyzed 20 s after each exposure at t₀: the first two PCs explain at least two thirds of the data variance, allow optimal clustering without overlap, and enable 99.4 ± 0.6% recognition. Considering that all devices have the same geometry, mechanisms responsible for the modulation of the electrical resistivity are pointed out. As different doping effects were assessed by varying the nature of the dopant [22], the modulation of the doping yield by the interaction of different volatile molecules as electron-donating ligands on an electrophilic Lewis acid [35,36,37] is not invalidated by this analysis. The statistical approach does not allow discriminating between the effect on the charge carrier density or the charge carrier mobility for the different materials exposed to different gases. Despite the fact that material conductivity is a function of two independent physical properties (the charge carrier density and the charge carrier mobility), one cannot conclude that any of these properties are purely marking PC1^α1 and PC2^α1 since conductivity is the product of both and PCA scores are linear combinations of PCs. Such investigation could be carried out using the logarithmic value of the resistance modulation α₃ = log(R/R₀) as an information descriptor for the PCA in order to assess the individual contributions of the carrier mobility “μ” and carrier density “n” as principal components, since α₃ = log(n₀/n) + log(μ₀/μ). Such validation would have to be confirmed by correlating the PC^α3 loadings with a systematic study of carrier density and mobility assessment in another study that couples this approach with further material characterizations.

5. Conclusions

By statistical analysis, we evidenced that the relative resistance modulation of a doped conducting polymer array is a better information descriptor than the drift resistance, to recognize volatile organic compounds with different metal-triflate-doped polythiophene sensing elements. This shows that the information carrier for the molecular recognition using these materials in an electronic nose is rather linked to the thermodynamic equilibrium that yields the doped conducting polymers’ conductivity with its environment, rather than kinetic limitations which would select molecular targets based on their drift diffusion through different doped polymers. Despite this result suggesting to wait for a complete steady state for each sensing element response, we evidenced that the thermodynamic properties for recognizing molecular gases lie already in the transience of the material response. Despite the materials reaching a fast quasi-steady response within three minutes of environment exposures, principal component analysis and k-means clustering show that the recognition is already higher than 99% after only 20 s of gas exposures. This suggests that the training time to recognize a molecular environment can be greatly optimized for practical applications, even in the case where conducting materials in an electronics nose show a slow response. Applied to practical recognition with an eNose, this approach of finding a preliminary optimum for data acquisition before a test would greatly increase information throughputs for using eNose for chemical quality assessments by reducing the training duration while preserving most of the data quality to train an eNose to recognize various volatile molecular patterns.