Emeraldine salt molecules were modeled for one chain and for several overlapping chains, both with or without gas molecules. Every second nitrogen in the chain was doped. For the gas molecule interacting with the chain, several positions were considered, namely close to the doped and undoped nitrogen (Figure 2), in the vicinity of the benzene center, and, if several chains were modeled, between two chains (Figure 3 and Figure 4). Also, the orientation of the gas molecule was varied. Apart from these variations, one position and one orientation of the gas molecule was determined utilizing energy minimizing optimization. For all these situations, computation of the transmission spectrum was carried out. Transmission spectra were used to obtain relevant I–V characteristics.

Figure 2: One PANI chain and four NO2 molecules. Two in position “d” (doped) and two in position “u” (undoped), also denominated 2D+2U.

Figure 3: Two PANI chains overlapping in the middle with a gap of 3 Å. The position (c) is for ammonia or nitrogen dioxide molecules. Further positions are doped (d) and undoped (u), shown here with an ammonia molecule.

Figure 4: Two PANI chains overlapping in the middle with a gap of 3 Å top view. Between the chains one ammonia molecule is located.

There were only one or two molecule chains in the calculations and only several ammonia or nitrogen dioxide molecules are affecting the PANI molecules. Therefore, the quantity of free charge carriers is limited and very small in comparison with macroscopic PANI media. This leads to current saturation. The electric resistance was estimated from the initial linear behavior of the I–V characteristics before saturation.

At first, we have computed only models with one PANI chain. We have chosen fixed positions of ammonia and nitrogen dioxide molecules. We have computed the local energy minima through molecular dynamics, which results in the optimized position and orientation of the gas molecule. The spatial orientation of the gas molecules was estimated by these optimizations. Next, one up to four molecules were placed near the chain according to the optimization, either next to the doped nitrogen atom (D) or next to the undoped one (U). For ammonia, the nitrogen of NH3 was 2.09 Å away from the doped/undoped nitrogen of the PANI chain, while the bond length between N and H was 0.9994 Å. For nitrogen dioxide in the position “D”, the distance of N–N was 3.04 Å and the gas molecule angle was 103.904°, while in the position “U”, the N–N distance was 2.65 Å and the gas molecule angle was 103.671°. Resistance values for (i) one gas molecule near the doped nitrogen atom (1D+0U), (ii) one gas molecule near the undoped nitrogen atom (0D+1U), (iii) one gas molecule near the doped nitrogen atom and one gas molecule near the undoped nitrogen atom (1D+1U), and one gas molecule near the doped nitrogen atom and two gas molecules near each undoped nitrogen atom (1D+2U), were estimated from the I–V characteristics.

The relative resistance change Res,

(6)

was estimated, where R0 is the electrical resistance of PANI without any gas molecules and R is the electrical resistance of PANI in the presence of ammonia or nitrogen dioxide. The relative resistance change for ammonia gas molecules and one chain of emeraldine salt is shown in Figure 5. One can see, that the main part of the resistance change is due to the ammonia molecule near the doped nitrogen in the polyaniline chain and that the resistance change for more ammonia molecules on different positions (near the doped/undoped polyaniline nitrogen) is like the sum of the resistance changes of both positions. Further, the resistance seems to grow up linearly for the ammonia gas molecule positions.

Figure 5: The relative resistance change of emeraldine salt, one molecule chain was taken into account, by the presence of several ammonia gas molecules near the chain, in the positions as described above.

By the same means, the relative resistance of the polyaniline chain with and without one or more nitrogen dioxide molecules was computed as well. The I–V characteristics were computed for several molecule positions near the doped and near the undoped nitrogen atoms, see above. The molecule orientation was estimated through molecular dynamics optimization. The resistance from the linear part of the I–V characteristics was used to estimate the relative resistance, see Equation 6, and was computed for all sets, see Figure 6.

Figure 6: The relative resistance change of emeraldine salt, one molecule chain was taken into account, by the presence of several nitrogen dioxide gas molecules near the chain, as described above.

Similar to the case of ammonia, the resistance change depends strongly on the nitrogen dioxide molecule position. A gas molecule near the doped nitrogen makes the polyaniline chain more sensitive than one near the undoped nitrogen. Also, the resistance change of more nitrogen dioxide molecules on different positions (near the doped/undoped polyaniline nitrogen) is rather the sum of the resistance changes of both positions. The increasing linear resistance change for the gas molecule positions is seen as well. These one-polyaniline-chain data were recalculated for different concentrations of 3, 6, 9, and 12 ppm. We have compared them with experimental data, as shown below. The ppm concentration was calculated from the modeled volume with the polyaniline chains and the corresponding amount of gas molecules acting on the chains.

As a next step, sets with two chains of polyaniline were calculated, where (i) no NH3 gas molecules, (ii) one NH3 gas molecule near a doped nitrogen (1D+0U+0C), (iii) one NH3 gas molecule near an undoped nitrogen(0D+1U+0C), (iv) one NH3 molecule between the chains in the central benzene region (0D+0U+1C), see Figure 4, and (v) their combinations were modeled. The relative resistance was estimated in the same way as for one chain with ammonia and nitrogen dioxide described above.

As a first step, the effect of a discontinued polyaniline chain was studied. The gap between two chains of about 3 Å was estimated by determining energy minima using molecular dynamics. For this geometry, the I–V characteristics were computed and compared with results for one PANI chain. From the linear part of this characteristic, the resistance and, thus, the resistance change compared to the one-chain case was computed. Next, the same geometry with one gas molecule was computed. The resistance change results are displayed in Figure 7.

Figure 7: Relative resistance of emeraldine salt in the presence of NH3 computed for two overlapping chains of polyaniline, see Figure 4. On the left is the reference value for one chain of polyaniline without any gas molecule.

The hopping resistance change is rather large in comparison to the resistance change due to the presence of ammonia gas molecules. But one can see the effect of the ammonia gas molecule as well. The resistance increase is higher for the ammonia position near the doped polyaniline nitrogen and lower at the undoped position. Due to higher resistance of the hopping process, the current is flowing mainly through the direct connection of the sensor electrodes through unperturbed PANI chains. Therefore, the hopping influence can be ignored in the comparison with the experimental data.

Limitations and validity of the model

The extended Hückel method is a semi-empirical method and cannot display reality completely. To compare this model with experimental results, consideration of the computational limits is crucial. The molecule models consists only of one or two PANI molecule chains with a transmission area of 166 Å. These chains are interacting with only several gas molecules. These conditions affect the I–V characteristics. They affect its slope and the resistance effect of ammonia/nitrogen dioxide gas on polyaniline. The abovementioned current saturation in the I–V characteristics arises from the one or two relatively short chains that were used for computation. That is, only a small, limited quantity of free charge carriers is available. Also, as seen in the I–V characteristic obtained through the extended Hückel method, in the saturated part, ballistic charge carrier transport of one particle takes place. Thus, for the relative resistance change data, only the initial part of the I–V diagram was taken into account. Also, the numerical experiment models only a small region and, therefore, the results are influenced by the limitations of the modeled environment.

The gas concentration in ppm for the numerical experiment was calculated approximately as the next step. In this case, one gas molecule in the active area of the device was computed using dimensions of the polyaniline polymer to correspond to about 3 ppm concentration.

Finally, in this numerical model many effects are not taken into account, among others, the fact that the bulk material contains a large number of polymer chains and that there are, for example, kinetic effects and inter-carrier influences. Therefore, polyaniline bulk material would have a slightly different resistance values than the computed model.

Comparison with experimental data

Numerical models for a one-chain polyaniline sensor were compared with experimental data. Chemiresistive gas sensors for ammonia and nitrogen dioxide containing a flexible PANI thin film sensing area deposited on interleaved electrodes were produced by Posta et al. [13] and by Kroutil and co-workers [7]. In the experiments of Posta and Kroutil, the gas sensors for ammonia and nitrogen dioxide were exposed for 20 min to synthetic air with defined concentrations of NH3 and NO2. Subsequently, they were exposed to clear synthetic air without added gases for the next 20 min.

The experimental results were fitted for saturation values and the results were compared with the computed resistance values (Figure 8 and Figure 9). The modeled resistance values of polyaniline fit the experimental results rather well.

Figure 8: Relative resistance change in the presence of ammonia for different concentrations; red squares: computation, black crosses: experimental data form [7], black squares: experimental data from [13].

Figure 9: Relative resistance change in the presence of nitrogen dioxide for different concentrations; red squares: computation, black crosses: experimental data from [7].

Comparing both experiments of Kroutil et al. and Posta et al. (Figure 8), unlike linear dependencies are found. The mismatch of the absolute values comes from the difference of the experimental setups. Different samples with different polyaniline resistance values led to unequal resistance differences.

The numerical values for NO2 in Figure 9 have slightly stronger slopes than the linear trend of the experimental data. This effect arises from the limitation of the numerical model as explained above. In the experiment, the PANI sensor was 100 μm wide and overlaying molecules contributed to the conductivity, sharing their charge carriers and allowing for carrier hopping, while the numerical experiment consisted of only one, 166 Å long molecule with non-interacting charge carriers. Considering these limitations, the agreement between the experiment and the numerical model is good.