Comparison between Linear and Branched Polyethylenimine and Reduced Graphene Oxide Coatings as a Capture Layer for Micro Resonant CO2 Gas Concentration Sensors

The comparison between potential coatings for the measurement of CO2 concentration through the frequency shift in micro-resonators is presented. The polymers evaluated are linear polyethylenimine, branched polyethylenimine and reduced graphene oxide (rGO) by microwave reduction with polyethylenimine. The characterization of the coatings was made by using 6 MHz gold-plated quartz crystals, and a proof-of-concept sensor is shown with a diaphragm electrostatic microelectromechanical systems (MEMS) resonator. The methods of producing the solutions of the polymers deposited onto the quartz crystals are presented. A CO2 concentration range from 0.05% to 1% was dissolved in air and humidity level were controlled and evaluated. Linear polyethylenimine showed superior performance with a reaction time obtained for stabilization after the concentration increase of 345 s, while the time for recovery was of 126 s, with a maximum frequency deviation of 33.6 Hz for an in-air CO2 concentration of 0.1%.


Introduction
The measurement and capture of greenhouse gases such as CO 2 have been a subject of research in recent decades due to their significant impact on the environment and to quality of life concerns. In combustion vehicles, industrial processes, biochemical processes etc., the measurement of CO 2 concentration has become a critical factor in increasing process efficiency and reducing environmental impact [1,2]. Moreover, CO 2 concentrations in human-occupied environments is an important metric that can significantly impact air quality.
The constant need to monitor the concentration of gases such as CO 2 in open spaces or areas of common use among people, has encouraged the development of reduced cost, compact and low energy consumption measurement sensors. The market for gas sensors has grown significantly, having a market valued in more than USD 2 billion in 2018 with a predicted compound annual growth rate (CAGR) of 7.8% to reach in 2025. In this market, amongst the gas sensors with the greatest growth potential, are oxygen (O), carbon dioxide (CO 2 ), and nitrogen oxide (NOX) sensors. [3] It is currently possible to perform CO 2 measurement with great precision and in a matter of seconds by means of commercial sensors with various measurement principles, which can be optical, resistive or capacitive, amongst others [4][5][6][7][8][9]. These sensors have the disadvantage of being bulky and relatively expensive. Consequently, alternative CO 2 sensing solutions have been investigated in recent years [10][11][12].
The paper is structured as follows: the preparation of the coatings as well as the deposition techniques on the quartz crystals are detailed in Section 2. Subsequently, the methodology and instrumentation used to carry out the characterization processes are defined in Section 2.1. This is followed by Section 2.2 in which the manufacturing process of the micro-resonator device and its operating parameters are presented. Section 3 presents the results of the characterization of the quartz crystals and the micro-resonator device, including the adsorption and recovery time and frequency shift at different levels of CO 2 concentration, as well as the frequency shift in the presence of different levels of humidity. Section 4 discusses the results and compares them with other reported works. Finally, conclusions are presented.

Materials and Methods
The characterization of the CO 2 adsorbing coatings aims to compare their adsorption capabilities, but also evaluate their suitability of being used as the surface coating that will be deposited onto a micro-resonator in order to implement a resonant CO 2 sensor.
The CO 2 concentration range analyzed was 0.05% to 1% dissolved in air, at a steady temperature that remained between 23 and 25 • C. Additionally, the coatings were characterized under different humidity levels ranging from 15 to 75 %RH with a constant CO 2 concentration of 500 ppm.
For the initial characterization, quartz thickness monitor crystals of 6 MHz and 14 mm in diameter were used due to their high Q-factor of more than 15,000 at atmospheric pressure [32] and their stability to temperature variations. Branched and linear PEI coatings were analysed, and the one that yielded the best results was used to integrate with rGO to characterize its impact on adsorption performance.
Once the best performing coating was identified, a transducer proof-of-concept was implemented. This was done by using an electrostatic micro-resonator coated with the adsorbing material. The coated micro-resonator was exposed to varying CO 2 concentrations and the resulting resonant frequency shifts of the structure were monitored.

Coating Preparation
Branched PEI and linear PEI are shown in Figure 1. The branched PEI has an average Mw of 25,000 by LS, an average Mn of~10,000, and it was acquired through Sigma-Aldrich (San Luis, Misuri, Estados Unidos). The linear PEI has an average Mn of~10,000, PDI ≤ 1.3, and was also acquired through Sigma-Aldrich.
Sensors 2020, 20, 1824 3 of 20 Additionally, the performance of PEI is evaluated in combination with rGO, obtained by microwave reduction of graphene oxide [31]. The paper is structured as follows: the preparation of the coatings as well as the deposition techniques on the quartz crystals are detailed in Section 2. Subsequently, the methodology and instrumentation used to carry out the characterization processes are defined in Section 2.1. This is followed by Section 2.2 in which the manufacturing process of the micro-resonator device and its operating parameters are presented. Section 3 presents the results of the characterization of the quartz crystals and the micro-resonator device, including the adsorption and recovery time and frequency shift at different levels of CO2 concentration, as well as the frequency shift in the presence of different levels of humidity. Section 4 discusses the results and compares them with other reported works. Finally, conclusions are presented.

Materials and Methods
The characterization of the CO2 adsorbing coatings aims to compare their adsorption capabilities, but also evaluate their suitability of being used as the surface coating that will be deposited onto a micro-resonator in order to implement a resonant CO2 sensor.
The CO2 concentration range analyzed was 0.05 % to 1 % dissolved in air, at a steady temperature that remained between 23 and 25 °C. Additionally, the coatings were characterized under different humidity levels ranging from 15 to 75 %RH with a constant CO2 concentration of 500 ppm.
For the initial characterization, quartz thickness monitor crystals of 6 MHz and 14 mm in diameter were used due to their high Q-factor of more than 15,000 at atmospheric pressure [32] and their stability to temperature variations. Branched and linear PEI coatings were analysed, and the one that yielded the best results was used to integrate with rGO to characterize its impact on adsorption performance.
Once the best performing coating was identified, a transducer proof-of-concept was implemented. This was done by using an electrostatic micro-resonator coated with the adsorbing material. The coated micro-resonator was exposed to varying CO2 concentrations and the resulting resonant frequency shifts of the structure were monitored.

Coating Preparation
Branched PEI and linear PEI are shown in Figure 1. The branched PEI has an average Mw of ~25,000 by LS, an average Mn of ~10,000, and it was acquired through Sigma-Aldrich (San Luis, Misuri, Estados Unidos). The linear PEI has an average Mn of ~10,000, PDI ≤ 1.3, and was also acquired through Sigma-Aldrich.  [34].
Due to the high viscosity of the branched PEI and the granulated state of the linear PEI, a specific preparation process was necessary to obtain solutions suited to the deposition of a thin film on the quartz crystals. Similar processes used for the preparation of the solutions have been previously published in other works [29,35]. Figure 2 shows how the solutions were deposited onto the quartz crystals, characterized in Sections 3.1 to 3.3 or onto the micro-resonator, characterized in Section 3.4. A spin coating system was used for the former while a custom-designed piezoelectric micro positioning stage with a pipette was used for the latter. Due to the high viscosity of the branched PEI and the granulated state of the linear PEI, a specific preparation process was necessary to obtain solutions suited to the deposition of a thin film on the quartz crystals. Similar processes used for the preparation of the solutions have been previously published in other works [29,35]. Figure 2 shows how the solutions were deposited onto the quartz crystals, characterized in Sections 3.1-3.3 or onto the micro-resonator, characterized in Section 3.4. A spin coating system was used for the former while a custom-designed piezoelectric micro positioning stage with a pipette was used for the latter. using rGO, which was obtained by microwave reduction. This sought to increase the available area of adsorption and achieve a greater capture of CO 2 molecules, resulting in increased sensitivity [36,37]. As will be detailed in Section 3, characterization data indicates that the linear PEI performs better than the branched PEI for CO 2 sensing. Figure 3 shows the transformation of the graphene oxide (GO) treated by microwave radiation generating a considerable amount of heat followed by the reduction and then exfoliation of the GO generating the rGO.
Sensors 2020, 20, 1824 5 of 20 sensitivity [36,37]. As will be detailed in Section 3, characterization data indicates that the linear PEI performs better than the branched PEI for CO2 sensing. Figure 3 shows the transformation of the graphene oxide (GO) treated by microwave radiation generating a considerable amount of heat followed by the reduction and then exfoliation of the GO generating the rGO. The third coating that includes linear PEI and rGO was produced using methods that influenced this work [38,39]. The process is described below: 1. Sonification of 0.5 ml of linear PEI solution with 20 ml of distilled water for 10 minutes at 50 °C verifying the level of water periodically. 2. Sonification of 0.5 g of graphene oxide within the solution for 1 hour at 50 °C verifying the level of water periodically. 3. Filter the solution with graphene. 4. 3 microwave reduction cycles of 7 seconds each at a 600 W power with 20 seconds between each cycle. 5. Sonification of the reduced graphene oxide with the original linear PEI solution in a volumetric proportion of 1:1 for 3 hours at 55 °C verifying the level of water periodically. 6. Leave the solution at room temperature (25 °C ± 1 °C) for 24 h, at this temperature the solution will turn into a dark gray paste. For the deposition of this solution, the same process used for the deposition of the linear PEI coating was followed, however, it was important to verify that there were no agglutinated residues of rGO on the surface of the quartz. Figure 4 shows the SEM micrographs of the quartz crystal's surface for the three coatings investigated. This method is widely used to allow for the observation of the quality of the deposited material, and for the verification of the area of the quartz crystal that has been coated [40,41]. The uniformity is similar between the deposited PEI coatings, which is a critical factor to be able to make an equitable comparison and to maintain the high Q factor of the crystals. In the case of the coating of rGO + PEI, the deposition of the rGO is evident and the uniformity it is equivalent to the other coatings.  The third coating that includes linear PEI and rGO was produced using methods that influenced this work [38,39]. The process is described below: 1.
Sonification of 0.5 ml of linear PEI solution with 20 ml of distilled water for 10 minutes at 50 • C verifying the level of water periodically.

2.
Sonification of 0.5 g of graphene oxide within the solution for 1 hour at 50 • C verifying the level of water periodically.
3 microwave reduction cycles of 7 seconds each at a 600 W power with 20 seconds between each cycle.

5.
Sonification of the reduced graphene oxide with the original linear PEI solution in a volumetric proportion of 1:1 for 3 hours at 55 • C verifying the level of water periodically. 6.
Leave the solution at room temperature (25 • C ± 1 • C) for 24 h, at this temperature the solution will turn into a dark gray paste.
For the deposition of this solution, the same process used for the deposition of the linear PEI coating was followed, however, it was important to verify that there were no agglutinated residues of rGO on the surface of the quartz. Figure 4 shows the SEM micrographs of the quartz crystal's surface for the three coatings investigated. This method is widely used to allow for the observation of the quality of the deposited material, and for the verification of the area of the quartz crystal that has been coated [40,41]. The uniformity is similar between the deposited PEI coatings, which is a critical factor to be able to make an equitable comparison and to maintain the high Q factor of the crystals. In the case of the coating of rGO + PEI, the deposition of the rGO is evident and the uniformity it is equivalent to the other coatings.
of the quality of the deposited material, and for the verification of the area of the quartz crystal that has been coated [40,41]. The uniformity is similar between the deposited PEI coatings, which is a critical factor to be able to make an equitable comparison and to maintain the high Q factor of the crystals. In the case of the coating of rGO + PEI, the deposition of the rGO is evident and the uniformity it is equivalent to the other coatings.   In Figure 5, infrared (IR) absorption spectroscopy of the coating materials was carried-out in order to verify the integrity of the materials. For the coating formed by rGO + PEI, the presence of the linear PEI with the influence of the rGO is observed. The coatings of linear and branched PEI exhibited a typical response for these kind of polymers [42]. Notably, the characteristic peaks of the PEI that can be seen at 2799 cm −1 are caused by mode CH 2 -SS, at 3279 cm −1 caused by mode NH, and at 1644 cm −1 and 1599 cm −1 caused by C=N and N-H [42][43][44]. For the reduced graphene oxide, peaks are observed at 1730 cm −1 caused by C=O, at 1414 cm −1 caused by the carboxy C-O and at 1622 cm −1 caused by aromatic CC [38]. In Figure 5, infrared (IR) absorption spectroscopy of the coating materials was carried-out in order to verify the integrity of the materials. For the coating formed by rGO + PEI, the presence of the linear PEI with the influence of the rGO is observed. The coatings of linear and branched PEI exhibited a typical response for these kind of polymers [42]. Notably, the characteristic peaks of the PEI that can be seen at 2799 cm -1 are caused by mode CH2-SS, at 3279 cm -1 caused by mode NH, and at 1644 cm -1 and 1599 cm -1 caused by C=N and N-H [42][43][44]. For the reduced graphene oxide, peaks are observed at 1730 cm -1 caused by C=O, at 1414 cm −1 caused by the carboxy C-O and at 1622 cm -1 caused by aromatic CC [38].

Test Setup
For the control of the pressure, temperature, humidity and CO2 concentration conditions, an environmental test chamber was used, as shown in Figure 6. The S-parameter S21 measurements performed for the characterization of the crystals with the coatings were done using a Vector Network Analyzer (VNA) Keysight-E5061B (Santa Rosa, CA, USA). This was done to determine their resonant behavior in the presence of CO2 and humidity. In the case of the electrostatic microresonator, because the low Q-factor and the electrostatic actuation, a VNA could not be used. As such, the measurements were made using a Polytec OFV-534 (Waldbronn, Germany) vibrometer in closed loop with an OFV-2570 controller (Waldbronn, Germany).

Test Setup
For the control of the pressure, temperature, humidity and CO 2 concentration conditions, an environmental test chamber was used, as shown in Figure 6. The S-parameter S21 measurements performed for the characterization of the crystals with the coatings were done using a Vector Network Analyzer (VNA) Keysight-E5061B (Santa Rosa, CA, USA). This was done to determine their resonant behavior in the presence of CO 2 and humidity. In the case of the electrostatic micro-resonator, because the low Q-factor and the electrostatic actuation, a VNA could not be used. As such, the measurements were made using a Polytec OFV-534 (Waldbronn, Germany) vibrometer in closed loop with an OFV-2570 controller (Waldbronn, Germany).
performed for the characterization of the crystals with the coatings were done using a Vector Network Analyzer (VNA) Keysight-E5061B (Santa Rosa, CA, USA). This was done to determine their resonant behavior in the presence of CO2 and humidity. In the case of the electrostatic microresonator, because the low Q-factor and the electrostatic actuation, a VNA could not be used. As such, the measurements were made using a Polytec OFV-534 (Waldbronn, Germany) vibrometer in closed loop with an OFV-2570 controller (Waldbronn, Germany). The CO2 introduction and concentration level control were made with a constant low flow of air to maintain the atmospheric pressure and obtain a smooth increasing and decreasing CO2 concentration in the chamber through the pumping station. The air introduced to the chamber comes from the laboratory where the temperature and humidity are automatically controlled, in a range of ±2.5 %RH and ±0.5 °C. Even so, during the tests the humidity, temperature and CO2 levels in the The CO 2 introduction and concentration level control were made with a constant low flow of air to maintain the atmospheric pressure and obtain a smooth increasing and decreasing CO 2 concentration in the chamber through the pumping station. The air introduced to the chamber comes from the laboratory where the temperature and humidity are automatically controlled, in a range of ±2.5 %RH and ±0.5 • C. Even so, during the tests the humidity, temperature and CO 2 levels in the laboratory were constantly supervised to avoid unexpected changes that could affect the tests. Due to the susceptibility of the coatings to these parameters, any variation would be detected immediately so the test could be eliminated and repeated.
The full setup was designed to be able to develop a complete characterization in almost a fully automated process. The VNA and vibrometer were integrated with a MATLAB (Natick, Massachusetts, USA) platform that registered and controlled the process, while the micro-positioner was used for the alignment of the MEMS resonator with the vibrometer laser.
The characterization equipment is shown in Figure 7. The fully integrated setup allows the characterization of various types of sensors. In Figure 7b, a close-up of the vibrometer with the micro-resonator seed through the viewport of the chamber is shown. This allows to characterize the low Q-factor micro-resonators at different pressures, temperatures and humidity, while electrostatically actuating them.
Sensors 2020, 20, 1824 7 of 20 laboratory were constantly supervised to avoid unexpected changes that could affect the tests. Due to the susceptibility of the coatings to these parameters, any variation would be detected immediately so the test could be eliminated and repeated. The full setup was designed to be able to develop a complete characterization in almost a fully automated process. The VNA and vibrometer were integrated with a MATLAB (Natick, Massachusetts, USA) platform that registered and controlled the process, while the micro-positioner was used for the alignment of the MEMS resonator with the vibrometer laser.
The characterization equipment is shown in Figure 7. The fully integrated setup allows the characterization of various types of sensors. In Figure 7b, a close-up of the vibrometer with the microresonator seed through the viewport of the chamber is shown. This allows to characterize the low Qfactor micro-resonators at different pressures, temperatures and humidity, while electrostatically actuating them.

Micro-resonator Characteristics
The micro-resonator that was used was a diaphragm structure to increase its mechanical stability and provide enough deposition area for the coating, although the Q-factor was reduced as a result of this geometry. The resonator device, with cross-section shown in Figure 8, was manufactured using the MEMSCAP PolyMUMPS (Crolles Cedex, France) commercial fabrication process. A polysilicon

Micro-resonator Characteristics
The micro-resonator that was used was a diaphragm structure to increase its mechanical stability and provide enough deposition area for the coating, although the Q-factor was reduced as a result of this geometry. The resonator device, with cross-section shown in Figure 8, was manufactured using the MEMSCAP PolyMUMPS (Crolles Cedex, France) commercial fabrication process. A polysilicon layer (Poly2) was used as the structural layer of the diaphragm and it was anchored at its sides. An underlying polysilicon layer (Poly1) allowed for the electrostatic driving of the resonator. An oxide layer (Oxide2) between both polysilicon layers was used as a sacrificial layer which was chemically removed to release the structure. The achieved gap between the diaphragm and the underlying driving electrode was of 0.75 µm. Such a small gap allowed for a reduced driving voltage requirement. The CO 2 absorbing coating was deposited above the diaphragm post-fabrication by processing the dies received from the foundry. This was done using a micro-needle that was carrying at its tip a small drop of the coating as shown in Figure 2b. With micro-positioners the needle was placed at the center of the micro-resonator, slowly descending until the polymer touched the surface of the resonator. After removing the needle, the deposited size of the coating drop is estimated to be of around 40 µm in diameter.  Figure 9 shows the 3D view of the imaged micro-resonator and its mode-shape simulation carried out using COMSOL (Stockholm, Sweden). The resonator is a diaphragm with external opening to reduce the damping caused by the air flow between the plates and the increase of the amplitude of resonance. The diameter of the resonator is 200 µm and it is 1.5 µm thick.
The Eigenfrequency finite element method (FEM) mode shape simulation of the resonator estimated a resonance frequency of the first mode at 1.16 MHz. The measured resonant frequency of the fabricated resonator obtained by using the vibrometer was of 1.15 MHz, matching well with the simulations. The measured Q-factor was of 8 at atmospheric pressure and of 300 at a 1 mTorr ambient pressure. Once the micro-resonator was characterized, the Linear PEI coating was deposited following the process previously mentioned. The measured resonant frequency of the microresonator with the coating was of 1.139 MHz. The decrease of resonant frequency is due to the mass loading of the coating on the resonant structure.

Results
The characterization of the coatings deposited in the quartz crystals focused on three main  Figure 9 shows the 3D view of the imaged micro-resonator and its mode-shape simulation carried out using COMSOL (Stockholm, Sweden). The resonator is a diaphragm with external opening to reduce the damping caused by the air flow between the plates and the increase of the amplitude of resonance. The diameter of the resonator is 200 µm and it is 1.5 µm thick.  Figure 9 shows the 3D view of the imaged micro-resonator and its mode-shape simulation carried out using COMSOL (Stockholm, Sweden). The resonator is a diaphragm with external opening to reduce the damping caused by the air flow between the plates and the increase of the amplitude of resonance. The diameter of the resonator is 200 µm and it is 1.5 µm thick.
The Eigenfrequency finite element method (FEM) mode shape simulation of the resonator estimated a resonance frequency of the first mode at 1.16 MHz. The measured resonant frequency of the fabricated resonator obtained by using the vibrometer was of 1.15 MHz, matching well with the simulations. The measured Q-factor was of 8 at atmospheric pressure and of 300 at a 1 mTorr ambient pressure. Once the micro-resonator was characterized, the Linear PEI coating was deposited following the process previously mentioned. The measured resonant frequency of the microresonator with the coating was of 1.139 MHz. The decrease of resonant frequency is due to the mass loading of the coating on the resonant structure.

Results
The characterization of the coatings deposited in the quartz crystals focused on three main factors, the maximum frequency shift before stabilizing in the presence of a higher concentration of CO2 in a range of 0.05 to 1 %, the stabilization time and the recovery time needed to return to the starting point. If during the recovery the resonant frequency did not reach the initial value, the maximum time was considered to be that required to stabilize the recovery response. In that case, the final frequency value achieved was considered as hysteresis. The impact of air humidity in a range of 15 % to 75 % RH at a CO2 concentration of 500 ppm was also analyzed.
The measurements were made at three different CO2 concentrations of 0.1 %, 0.5 % and 1% to The Eigenfrequency finite element method (FEM) mode shape simulation of the resonator estimated a resonance frequency of the first mode at 1.16 MHz. The measured resonant frequency of the fabricated resonator obtained by using the vibrometer was of 1.15 MHz, matching well with the simulations. The measured Q-factor was of 8 at atmospheric pressure and of 300 at a 1 mTorr ambient pressure. Once the micro-resonator was characterized, the Linear PEI coating was deposited following Sensors 2020, 20, 1824 9 of 21 the process previously mentioned. The measured resonant frequency of the micro-resonator with the coating was of 1.139 MHz. The decrease of resonant frequency is due to the mass loading of the coating on the resonant structure.

Results
The characterization of the coatings deposited in the quartz crystals focused on three main factors, the maximum frequency shift before stabilizing in the presence of a higher concentration of CO 2 in a range of 0.05 to 1%, the stabilization time and the recovery time needed to return to the starting point. If during the recovery the resonant frequency did not reach the initial value, the maximum time was considered to be that required to stabilize the recovery response. In that case, the final frequency value achieved was considered as hysteresis. The impact of air humidity in a range of 15% to 75% RH at a CO 2 concentration of 500 ppm was also analyzed.
The measurements were made at three different CO 2 concentrations of 0.1%, 0.5% and 1% to analyze the linearity of the frequency deviation. Comparisons were made between the different coatings at the same concentrations in order to compare the maximum deviation frequency, adsorption time and recovery time.
During this test the CO 2 was introduced until the desired concentration was reached in the chamber, during this process the coatings began to adsorb the CO 2 molecules, and this was reflected in the deviation of the oscillation frequency of the quartz crystal. Throughout the test, the pumping equipment maintained a constant flow of air output, so that the CO 2 had to be continuously introduced to maintain the concentration. This allowed the CO 2 concentration to be decreased naturally by closing the CO 2 valve without any alteration in the pressure or abrupt changes in the atmosphere inside the chamber.

Linear and Branched Polyethylenimine Coatings Characterization
The first characterization was made with the coatings formed by linear and branched PEI, to define which one exhibited better performance, and to later use it to make the solution with the rGO.
Once the frequency deviation stabilized, the introduction of gas was stopped in order to decrease the concentration of CO 2 inside the chamber to the external value of 500 ppm. Once the quartz crystal returned to its initial frequency, the CO 2 was introduced again to the next concentration value.
The test results are shown below. Within each graph, the CO 2 concentration level inside the test chamber is indicated in colored lines, the 0.1% in red, 0.5% in blue and 1.0% in green. The frequency deviation of the crystal is shown with the black line. As can be seen, the CO 2 concentration level in the chamber is increased rapidly until reaching the level determined for the test. Once the adsorption phase by the coating is finished, the CO 2 level is rapidly decreased to analyze the recovery time of the coating that is in characterization. Each coating is analyzed individually to facilitate the interpretation of the information provided by each test, then a comparison of the three coatings is made in detail.
In Figure 10, the reaction of both coatings complies with the adsorption theory and a deviation of the frequency is seen in response to the introduction of CO 2 . However, the frequency shift amount and recovery time is different for each material. In all cases, the frequency shift obtained using the linear PEI coated crystal generated between 15% and 30% greater deviation than the branched PEI coating. An identical time scale has been used in both plots to compare the adsorption time between the coatings. The recovery time was between 2 to 3 times faster for the crystal coated by linear PEI.
of the frequency is seen in response to the introduction of CO2. However, the frequency shift amount and recovery time is different for each material. In all cases, the frequency shift obtained using the linear PEI coated crystal generated between 15 % and 30 % greater deviation than the branched PEI coating. An identical time scale has been used in both plots to compare the adsorption time between the coatings. The recovery time was between 2 to 3 times faster for the crystal coated by linear PEI. In Figure 11, the frequency shift in response to humidity changes is plotted for both the branched and linear PEI coated crystals. The CO2 concentration in these cases is constant at 500 ppm. In both cases, the frequency deviation can be considered as linear in the range shown, however, the deviation is much greater in the case of the branched PEI coated crystal, showing more than a 60 % increased shift compared to the linear PEI coated crystal. The measurement was carried out for both increasing (adsorption) and decreasing (recovery) humidity levels and both coatings exhibited similar hysteresis. In Figure 11, the frequency shift in response to humidity changes is plotted for both the branched and linear PEI coated crystals. The CO 2 concentration in these cases is constant at 500 ppm. In both cases, the frequency deviation can be considered as linear in the range shown, however, the deviation is much greater in the case of the branched PEI coated crystal, showing more than a 60% increased shift compared to the linear PEI coated crystal. The measurement was carried out for both increasing (adsorption) and decreasing (recovery) humidity levels and both coatings exhibited similar hysteresis. The results above indicate that the linear PEI coating has better performance in comparison to the branched PEI. This is the case in terms of the frequency shift amount (sensitivity), reaction time and susceptibility to ambient humidity. Therefore, the linear PEI solution was chosen to be integrated with the reduced graphene oxide as the third coating for investigation.

Linear Polyethylenimine with reduced Graphene Oxide Coating Characterization
Through the methodology discussed in Section 2, the linear PEI with rGO was deposited onto a quartz crystal to characterize its performance. Figure 12 shows the characterization results of the coated crystal. As expected, the coating formed by linear PEI and rGO showed the same adsorption tendency, however, during the recovery process, the coating does not allow the adsorbed molecules to be released readily. Indeed, the desorption was limited to about 15 % when dropping the CO2 concentration, and very little recovery was observed at the higher 1% CO2 concentration. This phenomenon occurs due to the combination of the rGO with the polymer-based amines, which has shown excellent properties of capturing CO2. Accordingly, external processes are required for recovery, either by increasing temperature and/or decreasing the atmospheric pressure in order to force degassing [45,46]. Accordingly, forced degassing was carried-out here in order to reset the coating between CO2 concentration cycles. It was necessary to place the coated quartz crystal at a 10 mTorr vacuum for 30 minutes and subsequently for 2 hours in ambient conditions at no more than 500 ppm CO2 concentration in order to reset the coating. The linear PEI with rOG coated crystal exhibits a frequency deviation in response to humidity variations that is similar to that of the quartz crystal coated with branched PEI. The results above indicate that the linear PEI coating has better performance in comparison to the branched PEI. This is the case in terms of the frequency shift amount (sensitivity), reaction time and susceptibility to ambient humidity. Therefore, the linear PEI solution was chosen to be integrated with the reduced graphene oxide as the third coating for investigation.

Linear Polyethylenimine with Reduced Graphene Oxide Coating Characterization
Through the methodology discussed in Section 2, the linear PEI with rGO was deposited onto a quartz crystal to characterize its performance. Figure 12 shows the characterization results of the coated crystal. As expected, the coating formed by linear PEI and rGO showed the same adsorption tendency, however, during the recovery process, the coating does not allow the adsorbed molecules to be released readily. Indeed, the desorption was limited to about 15% when dropping the CO 2 concentration, and very little recovery was observed at the higher 1% CO 2 concentration. This phenomenon occurs due to the combination of the rGO with the polymer-based amines, which has shown excellent properties of capturing CO 2 . Accordingly, external processes are required for recovery, either by increasing temperature and/or decreasing the atmospheric pressure in order to force degassing [45,46]. Accordingly, forced degassing was carried-out here in order to reset the coating between CO 2 concentration cycles. It was necessary to place the coated quartz crystal at a 10 mTorr vacuum for 30 minutes and subsequently for 2 hours in ambient conditions at no more than 500 ppm CO 2 concentration in order to reset the coating. The linear PEI with rOG coated crystal exhibits a frequency deviation in response to humidity variations that is similar to that of the quartz crystal coated with branched PEI. tendency, however, during the recovery process, the coating does not allow the adsorbed molecules to be released readily. Indeed, the desorption was limited to about 15 % when dropping the CO2 concentration, and very little recovery was observed at the higher 1% CO2 concentration. This phenomenon occurs due to the combination of the rGO with the polymer-based amines, which has shown excellent properties of capturing CO2. Accordingly, external processes are required for recovery, either by increasing temperature and/or decreasing the atmospheric pressure in order to force degassing [45,46]. Accordingly, forced degassing was carried-out here in order to reset the coating between CO2 concentration cycles. It was necessary to place the coated quartz crystal at a 10 mTorr vacuum for 30 minutes and subsequently for 2 hours in ambient conditions at no more than 500 ppm CO2 concentration in order to reset the coating. The linear PEI with rOG coated crystal exhibits a frequency deviation in response to humidity variations that is similar to that of the quartz crystal coated with branched PEI.  Note that the CO 2 capture behavior of the PEI with rOG may be suitable for sensors that aim to detect whether a CO 2 concentration occurs in an environment over time and retain this information. Such a sensor may be read periodically in order to determine if a high enough CO 2 concentration was reached or not at some point in time. Because this type of application is not part of objective of this work, no quantitative study retention time or loss level tests were carried out for prolonged periods and these should be further investigated to confirm the applicability of PEI with rOG in such applications. However, by considering others published works on coatings based on amines with graphene or carbon nanotubes, and where it is concluded that it is necessary to expose the coating to a vacuum and/or a high temperature process for recovery, it is possible that the coating in this work would yield long-term CO 2 retention and be suitable to the aforementioned application [47,48].

Performance Comparison between the Coatings
The performance comparison of all coated quartz crystals under the same CO 2 concentration was carried out in order to analyze the total frequency deviation and reaction times of each. The results at different concentrations are shown in Figure 13.
The performance of the coatings when compared by levels of CO 2 concentration show the same tendency to adsorb the gas molecules, however, the frequency shift rate showed a disproportional increase between branched PEI, linear PEI and linear PEI + rGO due to CO 2 concentration. This is outlined in Table 1.

Performance Comparison between the Coatings
The performance comparison of all coated quartz crystals under the same CO2 concentration was carried out in order to analyze the total frequency deviation and reaction times of each. The results at different concentrations are shown in Figure 13. The performance of the coatings when compared by levels of CO2 concentration show the same tendency to adsorb the gas molecules, however, the frequency shift rate showed a disproportional increase between branched PEI, linear PEI and linear PEI + rGO due to CO2 concentration. This is outlined in Table 1.   The difference in the frequency deviation of each coating can be observed, which shows that Linear PEI with + rGO has the greatest adsorption capacity, an advantage of the inclusion of rGO. This frequency shift is followed by that of the linear PEI. Table 2 shows the linearized value of the frequency deviation per unit of ppm of CO 2 , outlining the sensitivity of each coating. The PEI+rGO exhibits a 25% greater adsorption capacity than the linear PEI coating, which is 45% more adsorbent than the branched PEI coating. The frequency shift in response to the CO 2 concentration is shown in Figure 14. The ideal response for this type of sensor would be linear for any level of CO 2 concentration, however, the PEI has a saturation limit of up to 2 to 3 mmol/g for the branched and linear PEI. Accordingly, concentrations ranging from 0 to 0.2% yield a linear response. However, at higher concentration values, the proportion of adsorption capacity is progressively reduced until it reaches its saturation point [49,50]. In the case of the rGO with linear PEI, a higher adsorption capacity of 8.10 mmol/g of CO 2 at 273 K and low pressure has been reported [30,40]. Due to this, the results obtained show a higher adsorption ratio from 0.05% to 0.15%, followed by a progressive reduction in the frequency deviation.
The frequency shift in response to the CO2 concentration is shown in Figure 14. The ideal response for this type of sensor would be linear for any level of CO2 concentration, however, the PEI has a saturation limit of up to 2 to 3 mmol/g for the branched and linear PEI. Accordingly, concentrations ranging from 0 to 0.2 % yield a linear response. However, at higher concentration values, the proportion of adsorption capacity is progressively reduced until it reaches its saturation point [49,50]. In the case of the rGO with linear PEI, a higher adsorption capacity of 8.10 mmol/g of CO2 at 273 K and low pressure has been reported [30,40]. Due to this, the results obtained show a higher adsorption ratio from 0.05 % to 0.15 %, followed by a progressive reduction in the frequency deviation. The adsorption time for each coating was also characterized and is plotted in Figure 15a. The adsorption was defined as the time for the frequency shift to go from 0 % to 90 % of its steady state value. The absorption time of the coatings maintains a linear increase up to 0.5 % of CO2 concentration, subsequently the adsorption time it is reduced but still maintaining the same proportion among all the coatings evaluated. The adsorption times for each coating are summarized in Table 3.  The adsorption time for each coating was also characterized and is plotted in Figure 15a. The adsorption was defined as the time for the frequency shift to go from 0% to 90% of its steady state value. The absorption time of the coatings maintains a linear increase up to 0.5% of CO 2 concentration, subsequently the adsorption time it is reduced but still maintaining the same proportion among all the coatings evaluated. The adsorption times for each coating are summarized in Table 3.
has a saturation limit of up to 2 to 3 mmol/g for the branched and linear PEI. Accordingly, concentrations ranging from 0 to 0.2 % yield a linear response. However, at higher concentration values, the proportion of adsorption capacity is progressively reduced until it reaches its saturation point [49,50]. In the case of the rGO with linear PEI, a higher adsorption capacity of 8.10 mmol/g of CO2 at 273 K and low pressure has been reported [30,40]. Due to this, the results obtained show a higher adsorption ratio from 0.05 % to 0.15 %, followed by a progressive reduction in the frequency deviation. The adsorption time for each coating was also characterized and is plotted in Figure 15a. The adsorption was defined as the time for the frequency shift to go from 0 % to 90 % of its steady state value. The absorption time of the coatings maintains a linear increase up to 0.5 % of CO2 concentration, subsequently the adsorption time it is reduced but still maintaining the same proportion among all the coatings evaluated. The adsorption times for each coating are summarized in Table 3.   The branched and linear PEI exhibit similar adsorption times over the range of concentrations measured. In the case of the rGO + PEI, the adsorption time for low concentrations is shorter than that observed with the other coatings because of the high absorbance capacity of the rGO [30]. For all coatings, after the CO 2 concentration is sufficiently increased, the slope of the adsorption time begins to decrease, this is attributed to the reduction of the adsorption capacity of the coating at higher concentrations [51,52].
The recovery times of each coating was also characterized and is plotted in Figure 15b and summarized in Table 4. The recovery time for the PEI with rGO coating was not characterized in the same fashion because of the coating's capture of CO 2 precluding from a return of the resonant frequency to its initial condition without forced degassing. The recovery time of the coating formed by branched PEI is more than 3 to 5 times longer than that of linear PEI, which is an important characteristic to consider for sensing applications.  Figure 16 shows the frequency shift of the quartz crystals in response to different levels of humidity. The behavior of the branched PEI and lineal PEI is linear, while the PEI with rGO shows a reduced adsorption as the humidity level increases. Overall linear PEI shows lower sensitivity to humidity variations. measured. In the case of the rGO + PEI, the adsorption time for low concentrations is shorter than that observed with the other coatings because of the high absorbance capacity of the rGO [30]. For all coatings, after the CO2 concentration is sufficiently increased, the slope of the adsorption time begins to decrease, this is attributed to the reduction of the adsorption capacity of the coating at higher concentrations [51,52].
The recovery times of each coating was also characterized and is plotted in Figure 15b and summarized in Table 4. The recovery time for the PEI with rGO coating was not characterized in the same fashion because of the coating's capture of CO2 precluding from a return of the resonant frequency to its initial condition without forced degassing. The recovery time of the coating formed by branched PEI is more than 3 to 5 times longer than that of linear PEI, which is an important characteristic to consider for sensing applications.  Figure 16 shows the frequency shift of the quartz crystals in response to different levels of humidity. The behavior of the branched PEI and lineal PEI is linear, while the PEI with rGO shows a reduced adsorption as the humidity level increases. Overall linear PEI shows lower sensitivity to humidity variations. Once the results obtained from the tests of characterization of the coatings are analyzed, it can be concluded that the formed by linear PEI presents qualities and superior performance for the type of application for which it has been proposed. Therefore this will be the coating to be used in the MEMS resonator to perform the proof of concept.

Micro-resonator CO2 sensor Proof-of-concept
Following the above methodology, the electrostatic diaphragm micro-resonator described in section 2.3 was coated with the linear PEI solution, which exhibited the overall better behavior for a proof-of-concept. The micro-resonator was first characterized to determine its behavior before and Once the results obtained from the tests of characterization of the coatings are analyzed, it can be concluded that the formed by linear PEI presents qualities and superior performance for the type of application for which it has been proposed. Therefore this will be the coating to be used in the MEMS resonator to perform the proof of concept.

Micro-resonator CO 2 Sensor Proof-of-concept
Following the above methodology, the electrostatic diaphragm micro-resonator described in Section 2.3 was coated with the linear PEI solution, which exhibited the overall better behavior for a proof-of-concept. The micro-resonator was first characterized to determine its behavior before and after a CO 2 concentration variation. The adsorption and recovery frequency shift response of the micro-resonator to a 0.8% CO 2 concentration increase is shown in Figure 17. The nominal resonant frequency of the micro-resonator is of 1.139 MHz.
The coated micro-resonator shows a behavior that is similar to that obtained by the quartz crystal. However, the low Q-factor decreases the accuracy with which measurements can be made. Even so, a deviation shift of 0.0675 Hz/ppm was attained which compares favourably to the quartz crystal-based sensors. Another important factor to mention is the overshoot that appears in the last phase of the recovery, where the value of the frequency exceeds the original value by approximately 35 Hz before stabilising a few minutes later.
Sensors 2020, 20,1824 14 of 20 after a CO2 concentration variation. The adsorption and recovery frequency shift response of the micro-resonator to a 0.8 % CO2 concentration increase is shown in Figure 17. The nominal resonant frequency of the micro-resonator is of 1.139 MHz. The coated micro-resonator shows a behavior that is similar to that obtained by the quartz crystal. However, the low Q-factor decreases the accuracy with which measurements can be made. Even so, a deviation shift of 0.0675 Hz/ppm was attained which compares favourably to the quartz crystal-based sensors. Another important factor to mention is the overshoot that appears in the last phase of the recovery, where the value of the frequency exceeds the original value by approximately 35 Hz before stabilising a few minutes later.
The observed overshoot is attributed to the kinetics of the gas molecules adsorption in linear PEI because generally the CO2 is adsorbed on the surface of the material and then diffuses into the bulk of the absorbent. This causes the stabilization process to not always be progressive resulting in overshoots [51,53]. Moreover, in high concentrations (>20%) and for long periods, the capacity of the adsorbent to release the molecules is reduced and hysteresis is generated.
The micro-resonator was also characterized by performing a cycling of different CO2 concentrations in order to determine its stability throughout each concentration period. For this, CO2 was introduced to obtain a 1 % concentration for a period of 15 minutes, followed by 2.5 % for an equal period of 15 minutes, and 5% for a period of 20 minutes. Subsequently the concentration was reduced to 1.5 % for a period of 50 minutes and finally 0.05 % for 30 minutes. Note that the initial CO2 concentration before the test was of 0.05 %. The resulting response is shown in the Figure 18. During this test the resonator was able to maintain the upward and downward trend adequately, both in reaction time and in frequency deviation. Again, the overshoot can be seen at each The observed overshoot is attributed to the kinetics of the gas molecules adsorption in linear PEI because generally the CO 2 is adsorbed on the surface of the material and then diffuses into the bulk of the absorbent. This causes the stabilization process to not always be progressive resulting in overshoots [51,53]. Moreover, in high concentrations (>20%) and for long periods, the capacity of the adsorbent to release the molecules is reduced and hysteresis is generated.
The micro-resonator was also characterized by performing a cycling of different CO 2 concentrations in order to determine its stability throughout each concentration period. For this, CO 2 was introduced to obtain a 1% concentration for a period of 15 minutes, followed by 2.5% for an equal period of 15 minutes, and 5% for a period of 20 minutes. Subsequently the concentration was reduced to 1.5% for a period of 50 minutes and finally 0.05% for 30 minutes. Note that the initial CO 2 concentration before the test was of 0.05%. The resulting response is shown in the Figure 18. The coated micro-resonator shows a behavior that is similar to that obtained by the quartz crystal. However, the low Q-factor decreases the accuracy with which measurements can be made. Even so, a deviation shift of 0.0675 Hz/ppm was attained which compares favourably to the quartz crystal-based sensors. Another important factor to mention is the overshoot that appears in the last phase of the recovery, where the value of the frequency exceeds the original value by approximately 35 Hz before stabilising a few minutes later.
The observed overshoot is attributed to the kinetics of the gas molecules adsorption in linear PEI because generally the CO2 is adsorbed on the surface of the material and then diffuses into the bulk of the absorbent. This causes the stabilization process to not always be progressive resulting in overshoots [51,53]. Moreover, in high concentrations (>20%) and for long periods, the capacity of the adsorbent to release the molecules is reduced and hysteresis is generated.
The micro-resonator was also characterized by performing a cycling of different CO2 concentrations in order to determine its stability throughout each concentration period. For this, CO2 was introduced to obtain a 1 % concentration for a period of 15 minutes, followed by 2.5 % for an equal period of 15 minutes, and 5% for a period of 20 minutes. Subsequently the concentration was reduced to 1.5 % for a period of 50 minutes and finally 0.05 % for 30 minutes. Note that the initial CO2 concentration before the test was of 0.05 %. The resulting response is shown in the Figure 18. During this test the resonator was able to maintain the upward and downward trend adequately, both in reaction time and in frequency deviation. Again, the overshoot can be seen at each During this test the resonator was able to maintain the upward and downward trend adequately, both in reaction time and in frequency deviation. Again, the overshoot can be seen at each stabilization point. On this occasion, the final hysteresis was approximately 55 Hz. Table 5 lists the frequency shift and ppm/Hz variation achieved over each phase. An absolute value ppm/Hz average of all the cycles was also calculated to be of 0.0646 Hz/ppm. This is consistent with the 0.0675 Hz/ppm value observed in the prior single concentration test reported above.

Discussion
The results obtained have shown the possibility of using PEI as a coating layer for CO 2 sensors. Linear PEI shows superior performance mainly during the recovery phase over [49]. Table 6 compares the performance of the coatings evaluated in this work to other previously published works that consider adsorbing coatings for CO 2 concentration sensors as well. The performance obtained by the lineal PEI is similar than that reported using acrylonitrile-styrene copolymer (AS3), where the recovery time for the lineal PEI coating is slower by 1.85 minutes. The results obtained from the coating formed by linear PEI with rGO showed results not initially anticipated, however, it opens the opportunity to develop in depth the study of the capabilities of such a coating as a CO 2 gas sensor for industrial and/or environmental applications. It can also be studied as an adsorbent coating for sensors where it is desired to retain the highest concentration value recorded during a given time period. The linear PEI with rGO recovery process must be further studied, as it would be possible to add an integrated heater to the micro-resonator structure in order to reset the sensor. This could allow to benefit from the higher adsorption capabilities of that coating while mitigating its CO 2 capture limitation. Interestingly, the increased sensor response of the diaphragm micro-resonator sensor proof-of-concept presented in comparison to the linear PEI coated quartz (i.e., −474 ppm vs. −16.8 ppm) illustrates the advantage of miniaturizing the resonant structure of the sensor.
During the development of this work, the ambient temperature was maintained in a controlled manner at 25 ± 1 • C and the ambient humidity was maintained between 20 and 35 %RH. It can be relevant to perform a similar study with more tightly controlled conditions as ambient conditions may influence the coatings performance.
Ultimately, the sensitivity to humidity of all of the coatings will require the use of calibration alongside a humidity sensing device that is not sensitive to CO 2 in order to implement a reliable sensing device.
The micro-resonator used in this study could demonstrate the sensing operation and the miniaturization capabilities of such a device, however, as the Q-factor was relatively too low, the device makes it difficult to obtain high-precision measurements without significant averaging. Accordingly, a higher-Q micro-resonator structure should be considered.
As previously commented, the measurement of CO 2 concentration has multiple applications with different requirements in sensing range and reaction time. Among some applications such as the monitoring of exhaust gases from a combustion engine, the reaction time must be as short as possible. In this case, IR sensors are used with reaction time can be as low as between 5 to 30 ms, while a resistive sensor for the same application can take up to 30 seconds, in both cases with sensors capable of measure until 90% of CO 2 [60,61]. There also exists applications that do not require such short reaction times such as CO 2 monitoring in the environment, which can range from a few seconds to minutes, with measuring ranges of less than 10% [62]. Accordingly, the results obtained in this work determine that the use of PEI-based coatings for the measurement of the CO 2 concentration is limited to applications such as atmospheric sensing, whether for indoor or open areas. This is due to the reaction time, mainly in the recovery stage. The detection of the sharp increase in CO 2 in an accelerated form such as a fire or laboratory safety sensor can be another application where this coating is used.

Conclusions
The purpose of this work was to study different CO 2 adsorbing coatings and to assess whether a micro-resonator CO 2 gas sensor could be implemented. Linear or branched PEI were considered as the adsorbent coating. Additionally, a linear PEI with rOG coating was also studied.
Results showed congruence with previously published studies and has opened the possibility of deepening its application in micro-resonators. Linear polyethylenimine coating has stood out for its capture and recovery properties, as well as its reduced hysteresis and reduced sensitivity to humidity. Linear PEI with rOG has shown interesting adsorption capabilities but captures the CO 2 molecule which requires an active reset mechanism, making this coating ill-suited for some application. However, the coating can be further investigated to integrate a reset mechanism within the sensor.
This work also presented a proof-of-concept micro-resonator based CO 2 gas sensor operating with a linear PEI coating. The sensor represents a highly integrated solution which could be batch fabricated, as the underlying resonant structure is fabricated using a commercial MEMS fabrication process. This work thus represents an initial effort towards achieving a highly integrated low-cost CO 2 sensor structure and future work could focus on integrating electronics to the structure in order to obtain a full-featured sensor device.
Author Contributions: A.P. did all the experimental work, data acquisition, and analysis; F.N. contributed expertise, direction, materials, and experimental tools. All authors have read and agreed to the published version of the manuscript.

Funding:
The authors wish to thank the Natural Science and Engineering Research Council (NSERC) of Canada for its financial support of this work.