Experimental Study and Mathematical Modeling of a Glyphosate Impedimetric Microsensor Based on Molecularly Imprinted Chitosan Film

: A novel impedimetric microsensor based on a double-layered imprinted polymer ﬁlm has been constructed for the sensitive detection of the herbicide, glyphosate (GLY), in water. It is based on electropolymerized polypyrrole ﬁlms, doped with cobaltabis(dicarbollide) ions ([3,3 (cid:48) -Co(1,2-C 2 B 9 H 11 ) 2 ]), as a solid contact layer between the gold microelectrode surface and the molecularly imprinted chitosan ﬁlm (CS-MIPs / PPy / Au). Electrochemical Impedance Spectroscopy (EIS) was used for the characterization of the CS-molecular imprinted polymers (MIPs) / PPy / Au in the presence of GLY concentrations between 0.31 pg / mL and 50 ng / mL. Experimental responses of CS-MIPs / PPy / Au are modeled for the ﬁrst time using an exact mathematical model based on physical theories. From the developed model, it was possible to deﬁne the optimal range of the parameters that will impact the quality of impedance spectra and then the analytical performance of the obtained microsensor. The obtained microsensor shows a low detection limit of 1 fg / mL (S / N = 3), a good selectivity, a good reproducibility, and it is regenerable. functioning, to analyze it, to explain it, and to predict certain aspects of it. Modeling is a tool, which helps understand the intrinsic mechanisms of these analytical instruments. It makes it possible to find relationships between the variables and the parameters that are considered to influence the metrological characteristics of these sensors such as the resistance of the solution, the resistance to charge transfer, or geometry. It is essential for optimization before a


Introduction
Glyphosate (GLY) is an effective systemic weed herbicide that was introduced for weed control in agricultural production fields around the world. Glyphosate is very resistant to degradation due to the inert C-P bond in the molecule [1]. GLY was frequently detected in rain and air and it is a major pollutant of rivers and surface waters. GLY can contaminate organisms, including humans, food, and ecosystems [2,3], which suggests its potential risks. Increasing studies have shown that glyphosate-based herbicides show neurotoxicity, cytotoxicity, and endocrine toxicity [4]. Therefore, development of methods for GLY detection is attracting more interest. Numerous analytical methods have been reported in the current literature, such as gas chromatography, high performance liquid chromatography, capillary electrophoresis [5], Mass spectrometry [6], resonance spectrometry, fluorescent spectrometry, an enzyme-linked immunoassay, and electrochemical sensors [7].
Molecular imprinted polymers (MIPs) are techniques based on an artificial recognition of target molecules. MIPs are prepared with a reaction mixture composed of a template (target molecule) and a functional monomer. During the polymerization, a complex is formed between the matrix and Polypyrrole (PPy) is one of the most promising materials for many applications because of its good chemical and thermal stability, facile synthesis, high conductivity, and its environmentally friendly properties [14,15]. PPy has attracted much attention in many electrochemical applications such as sensors and biosensors. It was used as a solid internal contact between the metal and the ionselective membrane to facilitate the charge transfer at the substrate/film interface [16]. PPy admits a porous structure with a large specific surface area. This property is an asset for several applications because of the high charge/discharge rate [17]. Many doping anions can be incorporated into PPy films. The cobaltbis(dicarbollide) anion [3,3′-Co-(1,2-C2B9H11)2] -was established as an ideal hydrophobic anion for ion extraction through an ion-pair mechanism [18]. The resulting PPy polymer doped with cobalt bis(dicarbollide) anion showed enhanced thermal stability and a dramatic enhancement of its overoxidation threshold, which demonstrated a great improvement of the electrical characteristics of film [19].
The response of 'miniaturized developed' sensors is closely related to the presence of specific molecular imprints on the biopolymer film's surface of the working micro-electrode, and also related to factors inherent to the structure of the sensor itself and its mode of operation. Explaining the operation in the depths of this sensor requires an in-depth knowledge of all the parameters involved in such a design. Modeling is a simplified representation of a real physical system or phenomenon, making it possible to reproduce its functioning, to analyze it, to explain it, and to predict certain aspects of it. Modeling is a tool, which helps understand the intrinsic mechanisms of these analytical instruments. It makes it possible to find relationships between the variables and the parameters that are considered to influence the metrological characteristics of these sensors such as the resistance of the solution, the resistance to charge transfer, or geometry. It is essential for optimization before a Polypyrrole (PPy) is one of the most promising materials for many applications because of its good chemical and thermal stability, facile synthesis, high conductivity, and its environmentally friendly properties [14,15]. PPy has attracted much attention in many electrochemical applications such as sensors and biosensors. It was used as a solid internal contact between the metal and the ion-selective membrane to facilitate the charge transfer at the substrate/film interface [16]. PPy admits a porous structure with a large specific surface area. This property is an asset for several applications because of the high charge/discharge rate [17]. Many doping anions can be incorporated into PPy films. The cobaltbis(dicarbollide) anion [3,3 -Co-(1,2-C 2 B 9 H 11 ) 2 ] − was established as an ideal hydrophobic anion for ion extraction through an ion-pair mechanism [18]. The resulting PPy polymer doped with cobalt bis(dicarbollide) anion showed enhanced thermal stability and a dramatic enhancement of its overoxidation threshold, which demonstrated a great improvement of the electrical characteristics of film [19].
The response of 'miniaturized developed' sensors is closely related to the presence of specific molecular imprints on the biopolymer film's surface of the working micro-electrode, and also related to factors inherent to the structure of the sensor itself and its mode of operation. Explaining the operation in the depths of this sensor requires an in-depth knowledge of all the parameters involved in such a design. Modeling is a simplified representation of a real physical system or phenomenon, making it possible to reproduce its functioning, to analyze it, to explain it, and to predict certain aspects of it. Modeling is a tool, which helps understand the intrinsic mechanisms of these analytical instruments. It makes it possible to find relationships between the variables and the parameters that are considered to influence the metrological characteristics of these sensors such as the resistance of the solution, the resistance to charge transfer, or geometry. It is essential for optimization before a device or process goes to market. A reliable model is one that simulates a sensor in real conditions. In addition, there arises the problem of determining the parameters, which intervene in the equations of the model.
In this study, a novel MIP electrochemical impedance spectroscopy (EIS) sensor has been constructed for the sensitive detection of GLY. The gold microelectrode surface was coated with a functional conducting polymer doped with cobaltbis(dicarbollide) anion ([3,3 -Co(1,2-C 2 B 9 H 11 ) 2 ]) via electrochemical polymerization by cyclic voltammetry (CV). Then, the chitosan sensitive membrane was electrodeposited on the conductive polymer layer. Electrochemical Impedance Spectroscopy (EIS) was used for the characterization of the CS-MIPs/PPy/Au in the presence of GLY concentrations. A mathematical model based on physical theories is developed to analyze the data obtained experimentally. The analysis of the observed impedance metric response leads to the estimation of the microscopic parameters of the sensors. The validation of the model is obtained by comparing the experimental data to the theoretical impedance model.

Apparatus
All electrochemical techniques were carried out using a multi-channel potentiostat (Biologic-EC-Lab VMP3) analyser. All measurements were carried out using a transducer fabricated at the National Center for Microelectronics (CNM), CSIC, Spain. It holds an array of four bare-gold working microelectrodes (WE) (surface area: 0.64 mm 2 ), one counter microelectrode (CE) (surface area: 0.13 mm 2 ), and two Ag/AgCl reference microelectrodes (RE) (surface area: 1.37 mm 2 ), connected at the same time and controlled by a personal computer (see transducer in Figure 2A). The pH of solutions was measured using a pH-meter: Mettler Toledo FE20/EL20. Scanning electron microscopy (SEM) micrographs were obtained using a FEI Quanta FEG 250 (University of Lyon 1, France). device or process goes to market. A reliable model is one that simulates a sensor in real conditions. In addition, there arises the problem of determining the parameters, which intervene in the equations of the model. In this study, a novel MIP electrochemical impedance spectroscopy (EIS) sensor has been constructed for the sensitive detection of GLY. The gold microelectrode surface was coated with a functional conducting polymer doped with cobaltbis(dicarbollide) anion ([3,3′-Co(1,2-C2B9H11)2]) via electrochemical polymerization by cyclic voltammetry (CV). Then, the chitosan sensitive membrane was electrodeposited on the conductive polymer layer. Electrochemical Impedance Spectroscopy (EIS) was used for the characterization of the CS-MIPs/PPy/Au in the presence of GLY concentrations. A mathematical model based on physical theories is developed to analyze the data obtained experimentally. The analysis of the observed impedance metric response leads to the estimation of the microscopic parameters of the sensors. The validation of the model is obtained by comparing the experimental data to the theoretical impedance model.

Apparatus
All electrochemical techniques were carried out using a multi-channel potentiostat (Biologic-EC-Lab VMP3) analyser. All measurements were carried out using a transducer fabricated at the National Center for Microelectronics (CNM), CSIC, Spain. It holds an array of four bare-gold working microelectrodes (WE) (surface area: 0.64 mm 2 ), one counter microelectrode (CE) (surface area: 0.13 mm 2 ), and two Ag/AgCl reference microelectrodes (RE) (surface area: 1.37 mm 2 ), connected at the same time and controlled by a personal computer (see transducer in Figure 2A). The pH of solutions was measured using a pH-meter: Mettler Toledo FE20/EL20. Scanning electron microscopy (SEM) micrographs were obtained using a FEI Quanta FEG 250 (university of Lyon 1, France).

CS-MIPs electrodeposition step:
The experimental conditions were optimized in our previous work [21]. In total, 1 g of CS powder was dissolved in 100-mL 0.1 M acetic acid and ultra-sonicated for 6 h at room temperature. The GLY-CS suspension system was prepared by dispersing 10 mg GLY into a 10-mL chitosan solution with a template/monomer ratio equal to 1/10, and mixed for 2 h to promote interactions between glyphosate and chitosan. Then, the pH value of solution was adjusted to be 5, using 0.1M NaOH. GLY-CS suspension was deposited using cyclic voltammetry (CV) for five scans in the range of −1.5 to 0.5 V at a scan rate of 80 mV/s ( Figure 3B). After electrodeposition, the microelectrodes were rinsed with deionized water and dried using nitrogen.
Cross-linking and template removal steps. They consisted of incubating the (GLY + CS)/Au sensor in 0.5 M H2SO4 solution for 1 h, which was then followed by an incubation in acetic acid/methanol solution (1:1, v/v) for 30 min to remove the GLY template.
Thus, an electrochemical sensor based on electropolymerized polypyrrole films, doped with cobaltabis (dicarbollide) ions ([3,3′-Co(1,2-C2B9H11)2]), as a solid contact layer between the gold microelectrode surface and the molecularly imprinted chitosan membrane was developed. The process is shown in Figure 2B. The non-imprinting polymer sensor (CS-NIPs/PPy/Au) followed similar steps as the CS-MIPs/PPy/Au electrodes with only one major difference. The CS mixture for the NIPs did not contain GLY. Lastly, sensors were stored at room temperature for further use.

Electrochemical Measurements
CS-MIPs/PPy/Au was immersed in water containing GLY with different concentrations (0.31 pg/mL to 50 ng/mL) for 30 min. Then, EIS (Initial potential E = 0.2 V. Higher Freq = 100 kHz,

CS-MIPs electrodeposition step:
The experimental conditions were optimized in our previous work [21]. In total, 1 g of CS powder was dissolved in 100-mL 0.1 M acetic acid and ultra-sonicated for 6 h at room temperature. The GLY-CS suspension system was prepared by dispersing 10 mg GLY into a 10-mL chitosan solution with a template/monomer ratio equal to 1/10, and mixed for 2 h to promote interactions between glyphosate and chitosan. Then, the pH value of solution was adjusted to be 5, using 0.1 M NaOH. GLY-CS suspension was deposited using cyclic voltammetry (CV) for five scans in the range of −1.5 to 0.5 V at a scan rate of 80 mV/s ( Figure 3B). After electrodeposition, the microelectrodes were rinsed with deionized water and dried using nitrogen.
Cross-linking and template removal steps. They consisted of incubating the (GLY + CS)/Au sensor in 0.5 M H 2 SO 4 solution for 1 h, which was then followed by an incubation in acetic acid/methanol solution (1:1, v/v) for 30 min to remove the GLY template.
Thus, an electrochemical sensor based on electropolymerized polypyrrole films, doped with cobaltabis (dicarbollide) ions ([3,3 -Co(1,2-C 2 B 9 H 11 ) 2 ]), as a solid contact layer between the gold microelectrode surface and the molecularly imprinted chitosan membrane was developed. The process is shown in Figure 2B. The non-imprinting polymer sensor (CS-NIPs/PPy/Au) followed similar steps as the CS-MIPs/PPy/Au electrodes with only one major difference. The CS mixture for the NIPs did not contain GLY. Lastly, sensors were stored at room temperature for further use.

Electrochemical Measurements
CS-MIPs/PPy/Au was immersed in water containing GLY with different concentrations (0.31 pg/mL to 50 ng/mL) for 30 min. Then, EIS (Initial potential E = 0.2 V. Higher Freq = 100 kHz, Lower Freq = 1 Hz) was used to characterize microelectrode surfaces and to investigate the charge transfer resistance of the film. EIS measurements were performed in ferro-ferricyanide with phosphate buffer saline solution (PBS). Cyclic voltammetry from 0 to 0.45 V at a scan rate of 80 mV/s was also used to characterize microelectrode surfaces.

Electrochemical Characterization of CS-MIPs/PPy/Au
Polypyrrole doped with [3,3 -Co(1,2-C 2 B 9 H 11 ) 2 ] anion was grown onto gold substrate in order to improve charge transfer and adhesion properties at the interface. The use of conducting polymers as solid contact materials was proposed as a conductive interface between the chitosan-MIPs film and the metal substrate. Figure 4A,B show the electrochemical impedance spectroscopy diagrams and the cyclic voltammograms of gold microelectrodes after electropolymerization of PPy[3,3 -Co(1,2-C 2 B 9 H 11 ) 2 ] on the microelectrode, after electrodeposition of CS-MIPs onto a solid contact layer crosslinked with sulfuric acid, and after template removal of CS-NIPs/PPy/Au. It can be seen from the EIS ( Figure 4A,B) that the impedance presented a clear decrease after electropolymerization of the PPy (R ct = 68.7 Ω), compared to the bare electrode (R ct = 342.4 Ω) ( Figure 4A, a) due to the presence of the conductive polymer that enhances the electric-charge-transfer properties of the electrode. Then, the electrodeposition of CS on the Au/PPy surface resulted in a clear increase of the charge transfer resistance due to blockage of the surface by the chitosan film (R ct = 17,691 Ω) ( Figure 4A, c). If we compare with the NIP film (R ct = 3555 Ω) ( Figure 4A, e), a larger Re (Z) is observed for the MIP film, which would show that MIPs film is thicker than NIPs film. After extraction of the GLY template, a significant decrease in impedance has been observed (R ct = 991.2 Ω) ( Figure 4A, d). Moreover, a lower charge transfer resistance is observed comparing to that of NIPs. This difference is due to the imprinted cavities, which promote the electron transfer. Lower Freq = 1 Hz) was used to characterize microelectrode surfaces and to investigate the charge transfer resistance of the film. EIS measurements were performed in ferro-ferricyanide with phosphate buffer saline solution (PBS). Cyclic voltammetry from 0 to 0.45 V at a scan rate of 80 mV/s was also used to characterize microelectrode surfaces.

Electrochemical Characterization of CS-MIPs/PPy/Au
Polypyrrole doped with [3,3′-Co(1,2-C2B9H11)2] anion was grown onto gold substrate in order to improve charge transfer and adhesion properties at the interface. The use of conducting polymers as solid contact materials was proposed as a conductive interface between the chitosan-MIPs film and the metal substrate. Figure 4A,B show the electrochemical impedance spectroscopy diagrams and the cyclic voltammograms of gold microelectrodes after electropolymerization of PPy[3,3′-Co(1,2-C2B9H11)2] on the microelectrode, after electrodeposition of CS-MIPs onto a solid contact layer crosslinked with sulfuric acid, and after template removal of CS-NIPs/PPy/Au. It can be seen from the EIS ( Figure 4A Figure 4A, e), a larger Re (Z) is observed for the MIP film, which would show that MIPs film is thicker than NIPs film. After extraction of the GLY template, a significant decrease in impedance has been observed (Rct = 991.2 Ω) ( Figure 4A, d). Moreover, a lower charge transfer resistance is observed comparing to that of NIPs. This difference is due to the imprinted cavities, which promote the electron transfer. This is further confirmed by cyclic voltammetry (CV), which was used to assess the electron transfer rate for the modified working electrode (WE). This was done by submerging the modified WE in ferro-ferricyanide and running the CV from 0 to 0.45 V at a scan rate of 80 mV/s. It can be seen from the cyclic voltammogram ( Figure 4B) how redox peaks increased in terms of intensity current This is further confirmed by cyclic voltammetry (CV), which was used to assess the electron transfer rate for the modified working electrode (WE). This was done by submerging the modified WE in ferro-ferricyanide and running the CV from 0 to 0.45 V at a scan rate of 80 mV/s. It can be seen from the cyclic voltammogram ( Figure 4B) how redox peaks increased in terms of intensity current after the electrodeposition of PPy[3,3 -Co(1,2-C 2 B 9 H 11 ) 2 ] layer (the anodic current I a increases from 24 µA to 30 µA) ( Figure 4B, b). Then it was decreased after electro-polymerization of the chitosan-MIP film (I a = 5.6 µA) ( Figure 4B, c) diminished the electric charge transfer properties of the microelectrode. Comparing to the NIP film (I a = 10 µA), ( Figure 4B, e), the lower value of redox peaks is observed for the MIP film, which shows that the latter is thicker than the NIP film. After extraction of the GLY template, a significant increase in redox peaks has been observed (I a = 7.5 µA) ( Figure 4B, d) due to the opening of the imprinted cavities.

Surface Morphology
Scanning electron microscopy (SEM) was employed to investigate the surface morphologies of bare electrode, PPy/Au, CS-MIPs/PPy/Au, and CS-NIPs/PPy/Au ( Figure S1). The morphology of the microelectrode modified with PPy ( Figure S1B) is completely different when compared with the surface of the bare gold ( Figure S1A), which indicates the success of the electro-polymerization of the conductive layer. After electro-polymerization of the chitosan onto a solid contact layer, another layer has appeared on the surface of the microelectrode, which further changes the morphology and confirms the deposition of the CS ( Figure S1C). Morphologies of the MIP ( Figure S1C) and of the NIP films ( Figure S1D) present a globular aspect. It is difficult to differentiate between them.

Electrochemical Responses of the CS-MIPs/PPy/Au
EIS was employed for the quantitative detection of GLY. As shown in Figure 5, a gradual increase of EIS was observed with the increase in GLY concentration, indicating a correlation between GLY concentration and the impedance of the CS-MIP/PPY/Au microelectrode. after the electrodeposition of PPy[3,3′-Co(1,2-C2B9H11)2] layer (the anodic current Ia increases from 24 µA to 30 µA) ( Figure 4B, b). Then it was decreased after electro-polymerization of the chitosan-MIP film (Ia = 5.6 µA) ( Figure 4B, c) diminished the electric charge transfer properties of the microelectrode. Comparing to the NIP film (Ia = 10 µA), ( Figure 4B, e), the lower value of redox peaks is observed for the MIP film, which shows that the latter is thicker than the NIP film. After extraction of the GLY template, a significant increase in redox peaks has been observed (Ia = 7.5 µA) ( Figure 4B, d) due to the opening of the imprinted cavities.

Surface Morphology
Scanning electron microscopy (SEM) was employed to investigate the surface morphologies of bare electrode, PPy/Au, CS-MIPs/PPy/Au, and CS-NIPs/PPy/Au ( Figure S1). The morphology of the microelectrode modified with PPy ( Figure S1B) is completely different when compared with the surface of the bare gold ( Figure S1A), which indicates the success of the electro-polymerization of the conductive layer. After electro-polymerization of the chitosan onto a solid contact layer, another layer has appeared on the surface of the microelectrode, which further changes the morphology and confirms the deposition of the CS ( Figure S1C). Morphologies of the MIP ( Figure S1C) and of the NIP films ( Figure S1D) present a globular aspect. It is difficult to differentiate between them.

Electrochemical Responses of the CS-MIPs/PPy/Au
EIS was employed for the quantitative detection of GLY. As shown in Figure 5, a gradual increase of EIS was observed with the increase in GLY concentration, indicating a correlation between GLY concentration and the impedance of the CS-MIP/PPY/Au microelectrode.

Mathematical Model
The general diagram of the impedance spectrum obtained by spectroscopic measurement for the experimental cell is illustrated in Figure 6. The overall impedance spectrum is made up of two wellseparated regions: From 100 kHz to 150 Hz corresponding to a semi-circle, which associates the charge transfer resistance in parallel with the double layer capacitance usually described by the Constant Phase Element (CPE). At high frequency (100 KHz), the intersection of the impedance curve with the abscissa axis makes it possible to determine the resistance s, which models the electrical conductivity of the solution due to mobile ions. From 150 Hz to 1 Hz, the linear part of the diagram corresponds to the Warburg impedance (diffusion of electroactive species) [22,23].

Mathematical Model
The general diagram of the impedance spectrum obtained by spectroscopic measurement for the experimental cell is illustrated in Figure 6. The overall impedance spectrum is made up of two well-separated regions: From 100 kHz to 150 Hz corresponding to a semi-circle, which associates the charge transfer resistance in parallel with the double layer capacitance usually described by the Constant Phase Element (CPE). At high frequency (100 KHz), the intersection of the impedance curve with the abscissa axis makes it possible to determine the resistance R s , which models the electrical conductivity of the solution due to mobile ions. From 150 Hz to 1 Hz, the linear part of the diagram corresponds to the Warburg impedance (diffusion of electroactive species) [22,23].
The response of the designed micro-sensors is marked by the variation of the semi-circles toward the concentrations of GLY incubated. This variation, according to the impedance spectra, is more significant in comparison with the variation in the Warburg diffusion.  The response of the designed micro-sensors is marked by the variation of the semi-circles toward the concentrations of GLY incubated. This variation, according to the impedance spectra, is more significant in comparison with the variation in the Warburg diffusion.
To simplify the equations of the physical model, the response of the sensor is modeled with a series combination of the resistance of the solution Rs and the electron resistance transfer Rct placed in parallel with CPE. The equivalent circuit is shown in Figure 7. As defined in the literature, the CPE represents many elements such as the inhomogeneity of the surface, the inhomogeneity of the charge distribution, and of the coupling between the faradic and capacitive currents. It can, therefore, be expected that a better fit for real systems will be obtained by using the CPE as a replacement for the Cdl capacitance [24]. To model this behavior, a fractional element CPE is proposed and expressed as follows [25].
With Q (F s (n−1) ) representing the CPE coefficient, −1 ≤ n ≤ 1 is the correction factor, ω = 2πf, where f represents the frequency (Hz). Equation (1) can also be written as shown below.
The global impedance equivalent to the circuit in Figure 7 is given by: To simplify the equations of the physical model, the response of the sensor is modeled with a series combination of the resistance of the solution R s and the electron resistance transfer R ct placed in parallel with CPE. The equivalent circuit is shown in Figure 7. The response of the designed micro-sensors is marked by the variation of the semi-circles toward the concentrations of GLY incubated. This variation, according to the impedance spectra, is more significant in comparison with the variation in the Warburg diffusion.
To simplify the equations of the physical model, the response of the sensor is modeled with a series combination of the resistance of the solution Rs and the electron resistance transfer Rct placed in parallel with CPE. The equivalent circuit is shown in Figure 7. As defined in the literature, the CPE represents many elements such as the inhomogeneity of the surface, the inhomogeneity of the charge distribution, and of the coupling between the faradic and capacitive currents. It can, therefore, be expected that a better fit for real systems will be obtained by using the CPE as a replacement for the Cdl capacitance [24]. To model this behavior, a fractional element CPE is proposed and expressed as follows [25].
With Q (F s (n−1) ) representing the CPE coefficient, −1 ≤ n ≤ 1 is the correction factor, ω = 2πf, where f represents the frequency (Hz). Equation (1) can also be written as shown below.
The global impedance equivalent to the circuit in Figure 7 is given by: As defined in the literature, the CPE represents many elements such as the inhomogeneity of the surface, the inhomogeneity of the charge distribution, and of the coupling between the faradic and capacitive currents. It can, therefore, be expected that a better fit for real systems will be obtained by using the CPE as a replacement for the Cdl capacitance [24]. To model this behavior, a fractional element CPE is proposed and expressed as follows [25].
With Q (F s (n−1) ) representing the CPE coefficient, −1 ≤ n ≤ 1 is the correction factor, ω = 2πf, where f represents the frequency (Hz). Equation (1) can also be written as shown below.
The global impedance equivalent to the circuit in Figure 7 is given by: That can be broken down into: Re(Z) = R s + R ct 1 + R ct Qω n cos nπ 2 1 + (R ct Qω n ) 2 + 2R ct Qω n cos nπ 2 (5) − Im(Z) = R ct 2 Qω n sin nπ 2 1 + (R ct Qω n ) 2 + 2R ct Qω n cos nπ 2 (6) where Re (Z) is the real part of the impedance and −Im (Z) is the imaginary part of the impedance. The reactions at the electrodes involve the redox couple Ferri/ferrocyanide in which ferricyanide is the oxidant and the ferrocyanide is the reducing agent. The electrochemical equation corresponding to this couple is as follows. Fe In the case where the reactions at the electrodes are governed by the kinetics of electron transfer, the resistance to charge transfer (R ct ) is known as the opposition to the movement of the electrons. For C Ox = C Red = C, and, for a simple one-electron process (n = 1), R ct is given by Equation (8).
where R: Ideal gas constant (J·mol −1 ·K −1 ), T: Temperature (K • ), F: Faraday constant (C·mol −1 ), A: surface of the working electrode (cm 2 ), and k 0 : standard rate constant (cm/s). The global impedance Z tends toward the resistance of the solution Rs when the frequency tends towards zero. R s is defined by Equation (9) [26,27].
where ρ is the resistivity of the solution (Ω cm), A is the surface area of the electrode (cm 2 ), and l is the coating thickness (cm). The resistivity of the Ferri/ferrocyanide solution is calculated by the following relationships.
where σ is the conductivity of the solution (s/m) that can be calculated from redox ion conductances [28,29], q i is the number of charges of the ion, λ i is the equivalent molar ionic conductivity (λ(Fe III (CN) 6 −3 ) = 10.09 ms·m 2 /mol, λ(Fe II (CN) 6 −4 ) = 11.04 ms·m 2 /mol), and C i is the concentration of the ion (mol/m 3 ). The resistivity value determined is 2.687 Ω m.

Numerical Simulation
To be able to determine the parameters of this model from experimental data, the Matlab software was used to simulate the physical model. The temperature (T), the ideal gas constant (R), the resistivity of the solution (ρ), the Faraday constant (F), the surface of the electrode (A), the concentration (C), the angular velocity vector (ω), the permissible error (e 0 ), the experimental Re (Z), and the −Im (Z) are used as input parameters.
Theoretical Re (Z) and −Im (Z) have been calculated in several iterations for each step of the membrane thickness (l), the speed constant (k • ), the CPE coefficient (Q), and the correction factor (n). The variation interval of each parameter and the values of the input parameters are shown in Table 1.
The values of various parameters are determined by minimizing the error between the experimental data and the simulated responses. This error is calculated according to the following relationship.
Error(e 2 ) = (−Im(Z)) theoritical − (−Im(Z)) experimental The iterations are stopped when e 1 ,e 2 ≤ e 0 in this study and the tolerated error is e 0 = 10 −3 . The general algorithm of the numerical program is given in Figure 8.
/ Ω The values of various parameters are determined by minimizing the error between the experimental data and the simulated responses. This error is calculated according to the following relationship.
Error(e ) = ∑ The iterations are stopped when e1,e2 ≤ e0 in this study and the tolerated error is e0 = 10 −3 . The general algorithm of the numerical program is given in Figure 8.

Model Validation
To validate the proposed model, we compared the results of the simulations given by the model to the experimental data. For this purpose, we have shown in Figure 9 the theoretical and experimental evolution of Re (Z) as a function of −Im (Z). A good fit is achieved between the experimental and the theoretical data calculated with a low error (<10 −3 ). To validate the proposed model, we compared the results of the simulations given by the model to the experimental data. For this purpose, we have shown in Figure 9 the theoretical and experimental evolution of Re (Z) as a function of −Im (Z). A good fit is achieved between the experimental and the theoretical data calculated with a low error (<10 −3 ).

Analysis of Theoretical Results
The various parameters determined by the model are gathered in Table 2. The thickness of the chitosan membrane is estimated at 88 µm. From the second incubation, a slight decrease in the latter was recorded (83 µm), which can be caused by the interpenetration of the chitosan in the polypyrrole surface. The resistance of the solution decreased from a value of 369.5 Ω to 348.5 Ω after the second incubation. This variation is related to the change in thickness. The value of the coefficient n predicted by the physical model is 0.71, indicating that the membrane of the MIPs is of porous morphology. This coefficient increased slightly (0.73) from the second measurement. The simulated value of the standard rate of the electron transfer reaction k° on the characterized electrode before incubation in the GLY solution is equal to 55 µm/s. k° decreases with an increasing concentration of incubated GLY. This decrease is due to the occupation of the complementary cavities by GLY molecules, increasing the opposition to the transfer of electrons.

Analysis of Theoretical Results
The various parameters determined by the model are gathered in Table 2. The thickness of the chitosan membrane is estimated at 88 µm. From the second incubation, a slight decrease in the latter was recorded (83 µm), which can be caused by the interpenetration of the chitosan in the polypyrrole surface. The resistance of the solution decreased from a value of 369.5 Ω to 348.5 Ω after the second incubation. This variation is related to the change in thickness. The value of the coefficient n predicted by the physical model is 0.71, indicating that the membrane of the MIPs is of porous morphology. This coefficient increased slightly (0.73) from the second measurement. The simulated value of the standard rate of the electron transfer reaction k • on the characterized electrode before incubation in the GLY solution is equal to 55 µm/s. k • decreases with an increasing concentration of incubated GLY. This decrease is due to the occupation of the complementary cavities by GLY molecules, increasing the opposition to the transfer of electrons.
In Figure 10A, we have represented the evolution of the constant k • as a function of the resistance R ct obtained from the model. k • varies linearly as a function of R ct with a correlation coefficient R 2 = 0.981. The regression equation, thus, found is: k • = −0.014 R ct + 70.72. In Figure 10A, we have represented the evolution of the constant k ° as a function of the resistance Rct obtained from the model. k° varies linearly as a function of Rct with a correlation coefficient R 2 = 0.981. The regression equation, thus, found is: k° = −0.014 Rct + 70.72.  Figure 10D). Q slightly varies with the GLY concentration, whereas Rct largely varies with the GLY concentration. It comes that the Faradic current is highly disturbed when GLY increases, which gives a high contribution to the global impedance whereas the capacitive current is slightly modified.

Effect of Coefficient n
Using Equations (5) and (6), we can show the variation of the overall impedance for different values of the coefficient n ( Figure 11). The variation of n from 0.6 to 1 shows an effect on the    Figure 10D). Q slightly varies with the GLY concentration, whereas R ct largely varies with the GLY concentration. It comes that the Faradic current is highly disturbed when GLY increases, which gives a high contribution to the global impedance whereas the capacitive current is slightly modified.

Effect of Coefficient n
Using Equations (5) and (6), we can show the variation of the overall impedance for different values of the coefficient n ( Figure 11). The variation of n from 0.6 to 1 shows an effect on the impedance spectrum, which increases proportionally. Over the same frequency range with increasing n, the impedance spectrum moves away from the x-axis in the high-frequency domain and approaches the same axis in the low frequencies. Therefore, there is an optimal value of n that leads to a well-defined semicircle (0.8). Experimentally, n can be modified by varying the thickness of the MIPs' film by changing the number of cycles during the electrodeposition. It can be decreased by using a poro-gene solvent in the synthesis [30], which can increase the porosity and tortuosity on the film. impedance spectrum, which increases proportionally. Over the same frequency range with increasing n, the impedance spectrum moves away from the x-axis in the high-frequency domain and approaches the same axis in the low frequencies. Therefore, there is an optimal value of n that leads to a well-defined semicircle (0.8). Experimentally, n can be modified by varying the thickness of the MIPs' film by changing the number of cycles during the electrodeposition. It can be decreased by using a poro-gene solvent in the synthesis [30], which can increase the porosity and tortuosity on the film.

Effect of Electron Transfer Rate Constant k°
The effects of varying the standard rate constant k° on the microsensor response can be seen in Figure 12. k° has no effect on the value of the impedance at the high frequency range. At the same time, the initial imaginary impedance increases with decreasing k°. Furthermore, the maxima of Re (Z) and -Im (Z) are inversely proportional to the increase in k° and they shift toward the low frequencies. For obtaining a higher value of k°, the thickness of the film should be decreased. The concentration of the redox couple should be increased. The integration of conductive nanomaterials in the CS film could also increase the value of k°.

Effect of Electron Transfer Rate Constant k •
The effects of varying the standard rate constant k • on the microsensor response can be seen in Figure 12. k • has no effect on the value of the impedance at the high frequency range. At the same time, the initial imaginary impedance increases with decreasing k • . Furthermore, the maxima of Re (Z) and −Im (Z) are inversely proportional to the increase in k • and they shift toward the low frequencies.
For obtaining a higher value of k • , the thickness of the film should be decreased. The concentration of the redox couple should be increased. The integration of conductive nanomaterials in the CS film could also increase the value of k • . impedance spectrum, which increases proportionally. Over the same frequency range with increasing n, the impedance spectrum moves away from the x-axis in the high-frequency domain and approaches the same axis in the low frequencies. Therefore, there is an optimal value of n that leads to a well-defined semicircle (0.8). Experimentally, n can be modified by varying the thickness of the MIPs' film by changing the number of cycles during the electrodeposition. It can be decreased by using a poro-gene solvent in the synthesis [30], which can increase the porosity and tortuosity on the film.

Effect of Electron Transfer Rate Constant k°
The effects of varying the standard rate constant k° on the microsensor response can be seen in Figure 12. k° has no effect on the value of the impedance at the high frequency range. At the same time, the initial imaginary impedance increases with decreasing k°. Furthermore, the maxima of Re (Z) and -Im (Z) are inversely proportional to the increase in k° and they shift toward the low frequencies. For obtaining a higher value of k°, the thickness of the film should be decreased. The concentration of the redox couple should be increased. The integration of conductive nanomaterials in the CS film could also increase the value of k°.

Effect of the CPE Coefficient (Q)
In Figure 13, we have shown the impedance spectrum for different values of the CPE coefficient (Q). A well-defined semi-circle impedance spectrum is obtained for a given value Q, which is called optimal Q (Q opt ), 10 −6 s n Ω −1 . For Q > Q opt , −Im (Z) approaches zero, Re (Z) tends toward the value of the resistance of the solution R s . For Q < Q opt , −Im (Z) tends towards zero, and Re (Z) tends to the value of the charge transfer resistance R ct . Q can be varied by the variation of the concentration of the redox couple, the variation of the movement of the ions by agitation of the electrolyte, the variation of the temperature, the variation of the applied potential, or the changes in the morphology of the membrane [31][32][33]. In Figure 13, we have shown the impedance spectrum for different values of the CPE coefficient (Q). A well-defined semi-circle impedance spectrum is obtained for a given value Q, which is called optimal Q (Qopt), 10 −6 s n Ω −1 . For Q> Qopt, -Im (Z) approaches zero, Re (Z) tends toward the value of the resistance of the solution Rs. For Q <Qopt, -Im (Z) tends towards zero, and Re (Z) tends to the value of the charge transfer resistance Rct. Q can be varied by the variation of the concentration of the redox couple, the variation of the movement of the ions by agitation of the electrolyte, the variation of the temperature, the variation of the applied potential, or the changes in the morphology of the membrane [31][32][33].

Effects of Membrane Thickness and Surface of CS-MIPs
From Equations (5) and (6), the thickness of the membrane ( ) influences the resistance of the solution Rs only involved in the actual impedance equation. In Figure 14A, we have shown the variation of the impedance spectrum for different values of . The maximum of Re (Z) increases for greater thickness, which is explained by the change in the resistance of the solution. On the other hand, the maximum value of -Im (Z) remains constant.

Effects of Membrane Thickness and Surface of CS-MIPs
From Equations (5) and (6), the thickness of the membrane (l) influences the resistance of the solution Rs only involved in the actual impedance equation. In Figure 14A, we have shown the variation of the impedance spectrum for different values of l. The maximum of Re (Z) increases for greater thickness, which is explained by the change in the resistance of the solution. On the other hand, the maximum value of −Im (Z) remains constant.

Effect of the CPE Coefficient (Q)
In Figure 13, we have shown the impedance spectrum for different values of the CPE coefficient (Q). A well-defined semi-circle impedance spectrum is obtained for a given value Q, which is called optimal Q (Qopt), 10 −6 s n Ω −1 . For Q> Qopt, -Im (Z) approaches zero, Re (Z) tends toward the value of the resistance of the solution Rs. For Q <Qopt, -Im (Z) tends towards zero, and Re (Z) tends to the value of the charge transfer resistance Rct. Q can be varied by the variation of the concentration of the redox couple, the variation of the movement of the ions by agitation of the electrolyte, the variation of the temperature, the variation of the applied potential, or the changes in the morphology of the membrane [31][32][33].

Effects of Membrane Thickness and Surface of CS-MIPs
From Equations (5) and (6), the thickness of the membrane ( ) influences the resistance of the solution Rs only involved in the actual impedance equation. In Figure 14A, we have shown the variation of the impedance spectrum for different values of . The maximum of Re (Z) increases for greater thickness, which is explained by the change in the resistance of the solution. On the other hand, the maximum value of -Im (Z) remains constant.  The variation of the membrane surface (A) strongly influences the overall impedance ( Figure 14B). Re (Z) and −Im (Z) record larger values for a minimum area A. In addition, A affects the resistance of the solution, which tends toward 0 for a larger area A.
These variations caused by l and A are the minimum that can be recorded on the overall impedance. In reality, l and A can also influence the Faradic impedance by varying the rate of electron transfer expressed in units of distance per unit of time. They can also modify the capacitive impedance caused by the change in membrane characteristics such as the coefficient n. The variation of l and A modify the number of imprinted sites available in the film, which modifies the sensitivity of the sensor. In fact, larger A and l are higher when the number of imprinted sites leads to a higher sensitivity of detection.

Effects of Temperature and Concentration of the Ferri/Ferrocyanide Solution
The higher temperatures of the ferri/ferrocyanide solution, used for the characterization of the electrode, cause an increase in the real and imaginary impedance, as shown in Figure 15A. The change in temperature shows an effect on the charge transfer resistance R ct . However, it can also cause a change in the resistance of the solution R s by modifying its resistivity. According to this interpretation, it is recommended to work at a low temperature, which allows having a low charge transfer resistance. 14B). Re (Z) and -Im (Z) record larger values for a minimum area A. In addition, A affects the resistance of the solution, which tends toward 0 for a larger area A.
These variations caused by and A are the minimum that can be recorded on the overall impedance. In reality, and A can also influence the Faradic impedance by varying the rate of electron transfer expressed in units of distance per unit of time. They can also modify the capacitive impedance caused by the change in membrane characteristics such as the coefficient n. The variation of and A modify the number of imprinted sites available in the film, which modifies the sensitivity of the sensor. In fact, larger A and are higher when the number of imprinted sites leads to a higher sensitivity of detection.

Effects of Temperature and Concentration of the ferri/ferrocyanide Solution
The higher temperatures of the ferri/ferrocyanide solution, used for the characterization of the electrode, cause an increase in the real and imaginary impedance, as shown in Figure 15A. The change in temperature shows an effect on the charge transfer resistance Rct. However, it can also cause a change in the resistance of the solution Rs by modifying its resistivity. According to this interpretation, it is recommended to work at a low temperature, which allows having a low charge transfer resistance. The concentration of the ferri/ferrocyanide solution greatly influences the overall impedance Z. We have shown in Figure 15B, the variation of Z as a function of three concentrations of the redox couple (C = 1, 5, 10 mM). Increasing the concentration in the assay medium causes a decrease in Re (Z) and -Im (Z), including a decrease in Rct. The concentration of the redox couple also influences the resistance of the solution by modifying its resistivity. A higher concentration leads to lower Rs. According to this interpretation, it is recommended to work at a high concentration (≥ 5mM), which means having a low charge transfer resistance.
The temperature and the concentration of the redox couple can also influence the rate of charge transfer characterized by its constant k°. These changes are due to the movement and density of electrons.

Analytical Performances of the CS-MIPs/PPy Functionalized Gold Electrode
The experimental conditions defined for the fabrication of the CS-MIPs/PPy functionalized gold electrode led to optimal values for n (0.7), Q (<2.5 10 −6 s n Ω −1 ), concentration of the redox (5 mM), measurements at room temperature, and too low of a value for k° (<5.5 10 −3 cm/s), too low value of A (0.0064 cm 2 ) for obtaining optimal impedance spectra. After the determination of the analytical performance, some ways for the improvement could be defined. The concentration of the ferri/ferrocyanide solution greatly influences the overall impedance Z. We have shown in Figure 15B, the variation of Z as a function of three concentrations of the redox couple (C = 1, 5, 10 mM). Increasing the concentration in the assay medium causes a decrease in Re (Z) and −Im (Z), including a decrease in R ct . The concentration of the redox couple also influences the resistance of the solution by modifying its resistivity. A higher concentration leads to lower R s . According to this interpretation, it is recommended to work at a high concentration (≥5 mM), which means having a low charge transfer resistance.
The temperature and the concentration of the redox couple can also influence the rate of charge transfer characterized by its constant k • . These changes are due to the movement and density of electrons.

Analytical Performances of the CS-MIPs/PPy Functionalized Gold Electrode
The experimental conditions defined for the fabrication of the CS-MIPs/PPy functionalized gold electrode led to optimal values for n (0.7), Q (<2.5 × 10 −6 s n Ω −1 ), concentration of the redox (5 mM), measurements at room temperature, and too low of a value for k • (<5.5 × 10 −3 cm/s), too low value of A (0.0064 cm 2 ) for obtaining optimal impedance spectra. After the determination of the analytical performance, some ways for the improvement could be defined.
The relative variation of the charge transfer resistance of each electrode was then normalized using the following equation |R ct -R ct Blank |/R ct Blank (∆R/R). In Figure S2, the ∆R/R versus the logarithmic value of the GLY concentrations plot produced a linear relationship ranging from 0.31 pg/mL to 50 ng/mL with a correlation coefficient of 0.996. The limit of detection (LOD) of the considered sensor was estimated at 1 fg/mL. The analytical performance of the CS-MIPs/PPy/Au microsensor was compared to that of other MIP-based electrochemical sensors for the detection of GLY reported in the literature (Table 3). To our knowledge, this microsensor had better performance compared to most of the previously reported sensors.  In order to assess the effectiveness of the imprinting, the detection of glyphosate is performed using CS-NIPs/Au. As reported in Figure 16, ∆R/R of the CS-MIPs/PPy/Au sensor is stronger than that of the CS-NIPs/PPy/Au sensor. The ratio of the sensitivities of MIP versus NIP is determined, leading to an imprinting factor of 11.5. This point indicates that the adsorption of GLY by the non-imprinted Chitosan is negligible and the effectiveness of the template imprinting is demonstrated. literature (Table 3). To our knowledge, this microsensor had better performance compared to most of the previously reported sensors. In order to assess the effectiveness of the imprinting, the detection of glyphosate is performed using CS-NIPs/Au. As reported in Figure 16, ΔR/R of the CS-MIPs/PPy/Au sensor is stronger than that of the CS-NIPs/PPy/Au sensor. The ratio of the sensitivities of MIP versus NIP is determined, leading to an imprinting factor of 11.5. This point indicates that the adsorption of GLY by the nonimprinted Chitosan is negligible and the effectiveness of the template imprinting is demonstrated.  The specificity of MIPs was tested with the detection of different pesticides that might be present in the same medium as GLY. Gluphosinate-ammonium (GLU), chlorpyrifos (CHL), and phosmet (PHO) were chosen to investigate the selectivity of this imprinted sensor ( Figure 16). On the CS-MIPs/PPy/Au, ∆R/R of GLY was higher than that of the other three substances at the same concentration. The ratio of sensitivities were 32.6, 100, and 50 for GLU, CHLO, and PHO, respectively. Thus, we can conclude that the tested compounds will not interfere with the detection of GLY in the same concentration range, proving the selectivity of the MIP sensor.
To investigate the reproducibility of the CS-MIPs/PPy/Au microsensor, the experiment was performed using three individual electrodes, which were prepared in similar conditions. The results showed an acceptable reproducibility with a 1.29% relative standard deviation.
The CS-MIPs/PPy/Au microsensor was regenerated by incubating it in acetic acid/methanol solution (1:1, v/v) for 5 min to remove adsorbed GLY. The cycle was repeated five times ( Figure S3). The second and the third cycles showed weak relative variation of the charge transfer resistance compared with the first cycle.
To evaluate the feasibility of the proposed sensor for its potential applications, the CS-MIPs/PPy/Au was used to determine GLY levels in a river water sample collected from the Rhone River in Lyon, France. EIS measurements were performed before and after incubation of the sensor in the Rhone river water for 30 min, and their respective Nyquist plots are almost superimposed, indicating that this sample does not contain GLY (Figure 17).
concentration. The ratio of sensitivities were 32.6, 100, and 50 for GLU, CHLO, and PHO, respectively. Thus, we can conclude that the tested compounds will not interfere with the detection of GLY in the same concentration range, proving the selectivity of the MIP sensor.
To investigate the reproducibility of the CS-MIPs/PPy/Au microsensor, the experiment was performed using three individual electrodes, which were prepared in similar conditions. The results showed an acceptable reproducibility with a 1.29% relative standard deviation.
The CS-MIPs/PPy/Au microsensor was regenerated by incubating it in acetic acid/methanol solution (1:1, v/v) for 5 min to remove adsorbed GLY. The cycle was repeated five times ( Figure S3). The second and the third cycles showed weak relative variation of the charge transfer resistance compared with the first cycle.
To evaluate the feasibility of the proposed sensor for its potential applications, the CS-MIPs/PPy/Au was used to determine GLY levels in a river water sample collected from the Rhone River in Lyon, France. EIS measurements were performed before and after incubation of the sensor in the Rhone river water for 30 min, and their respective Nyquist plots are almost superimposed, indicating that this sample does not contain GLY (Figure 17). To confirm the above observation, the standard addition method was used to detect GLY. This was done by gradually increasing GLY concentration in the sample. A remarkable variation of EIS was observed with the increase in GLY concentrations ( Figure 18A). The variation of the charge transfer resistance is linearly proportional to the logarithmic value of the GLY concentrations in the range of 0.31 pg/mL to 50 ng/mL with R 2 equal to 0.986 ( Figure 18B), indicating a good correlation between GLY concentration and the change of the impedance. The linear regression goes through zero (ΔR/R = 0.316 log [GLY]), which likely confirms the absence of GLY in the basic sample. Additionally, the sensitivity of this proposed sensor in the river water is the same as in the buffer, which revealed that the CS-MIPs/CMA/Au exhibited high recognition selectivity toward GLY in river water samples and almost without interference. To confirm the above observation, the standard addition method was used to detect GLY. This was done by gradually increasing GLY concentration in the sample. A remarkable variation of EIS was observed with the increase in GLY concentrations ( Figure 18A). The variation of the charge transfer resistance is linearly proportional to the logarithmic value of the GLY concentrations in the range of 0.31 pg/mL to 50 ng/mL with R 2 equal to 0.986 ( Figure 18B), indicating a good correlation between GLY concentration and the change of the impedance. The linear regression goes through zero (∆R/R = 0.316 log [GLY]), which likely confirms the absence of GLY in the basic sample. Additionally, the sensitivity of this proposed sensor in the river water is the same as in the buffer, which revealed that the CS-MIPs/CMA/Au exhibited high recognition selectivity toward GLY in river water samples and almost without interference.

Conclusions
In this work, a novel sensor has been constructed for the sensitive detection of glyphosate in water. It was based on electropolymerized polypyrrole films, doped with cobaltabis(dicarbollide) ions ([3,3′-Co(1,2-C2B9H11)2]), as a solid contact layer between the gold microelectrode surface and the molecularly imprinted chitosan membrane for the sensitive detection of GLY (CS-MIPs/PPy/Au). Electrochemical Impedance Spectroscopy (EIS) was used for the selective detection of GLY between a wide range of concentration from 0.31 pg/mL to 50 ng/mL. EIS responses of the different microsensors were modeled by using mathematical modelization that described the phenomena at the electrode/electrolyte interface, while showing the effect of each parameter on the response signal, highlighting how GLY concentration and the experimental conditions can affect EIS parameters. The experimental conditions defined for the fabrication of the CS-MIPs/PPy functionalized gold electrode led to optimal values for n (0.7), Q (<2.5 10 −6 s n Ω −1 ), concentration of the redox (5 mM), measurements at room temperature. Some parameter values were found to be too low (k°<5.5 10 −3 cm/s, A = 0.0064 cm 2 ). After the determination of the analytical performance (LOD = 1fg/mL), some ways for improvement could be defined in terms of sensitivity of detection.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1. Figure Figure S4: Regeneration of the CS-MIPs/PPy/Au microsensor. Figure S5: EIS of CS-MIPs/PPy/Au before and after incubation in the Rhone river water. Figure S6

Conclusions
In this work, a novel sensor has been constructed for the sensitive detection of glyphosate in water. It was based on electropolymerized polypyrrole films, doped with cobaltabis(dicarbollide) ions ([3,3 -Co(1,2-C 2 B 9 H 11 ) 2 ]), as a solid contact layer between the gold microelectrode surface and the molecularly imprinted chitosan membrane for the sensitive detection of GLY (CS-MIPs/PPy/Au). Electrochemical Impedance Spectroscopy (EIS) was used for the selective detection of GLY between a wide range of concentration from 0.31 pg/mL to 50 ng/mL. EIS responses of the different micro-sensors were modeled by using mathematical modelization that described the phenomena at the electrode/electrolyte interface, while showing the effect of each parameter on the response signal, highlighting how GLY concentration and the experimental conditions can affect EIS parameters. The experimental conditions defined for the fabrication of the CS-MIPs/PPy functionalized gold electrode led to optimal values for n (0.7), Q (<2.5 × 10 −6 s n Ω −1 ), concentration of the redox (5 mM), measurements at room temperature. Some parameter values were found to be too low (k • < 5.5 × 10 −3 cm/s, A = 0.0064 cm 2 ). After the determination of the analytical performance (LOD = 1 fg/mL), some ways for improvement could be defined in terms of sensitivity of detection.