Chemometric Approach to the Calibration of Light Emitting Diode Based Optical Gas Sensors Using High-Resolution Transmission Molecular Absorption Data

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1 Electronic Supplementary Information Chemometric Approach to the Calibration of Light Emitting Diode Based Optical Gas Sensors Using High-Resolution Transmission Molecular Absorption Data Parvez Mahbub 1,2, *, John Leis 3, Mirek Macka 1,4 1 Australian Centre for Research on Separation Science (ACROSS) and School of Natural Sciences, University of Tasmania, Private Bag 75, Hobart 7001, Australia 2 Institute for Sustainability and Innovation, Victoria University, Footscray Park Campus, Melbourne, Victoria 3011, Australia 3 School of Mechanical and Electrical Engineering, University of Southern Queensland, Australia 4 Department of Chemistry and Biochemistry, Mendel University in Brno, Zemedelska 1, CZ Brno, Czech Republic *corresponding author: Parvez.mahbub@utas.edu.au This electronic supplementary information includes the details of emission spectra in blank and that in 1% to 5% CH 4, the optical pathlength calculation, the LED absorption spectra calculation for different CH 4 concentrations, HITRAN simulation details, discussions on near-field, mid-field and far-field electromagnetic radiation zones in the context of propagation of light from LED as well as the gas cuvette configuration. S-1

2 Relative Intensity, a.u. 1 A 0.8 NIR LED emission spectra in blank Wavelength, nm S-2

3 Relative Intensity, a.u B NIR LED attenuated emission spectra in 1% CH4 HITRAN Absorption cross-section of CH4 7.0E E E E E E E-22 Absorption cross section, cm 2.molecule E Wavelength, nm S-3

4 Relative Intensity, a.u C NIR LED attenuated emission spectra in 2% CH4 HITRAN Absorption cross-section of CH4 7.0E E E E E E E-22 Absorption cross section, cm 2.molecule E Wavelength, nm S-4

5 Relative Intensity, a.u D NIR LED attenuated emission spectra in 3% CH4 HITRAN Absorption cross-section of CH4 7.0E E E E E E E-22 Absorption cross section, cm 2.molecule E Wavelength, nm S-5

6 Relative Intensity, a.u E NIR LED attenuated emission spectra in 4% CH4 HITRAN Absorption cross-section of CH4 7.0E E E E E E E-22 Absorption cross section, cm 2.molecule E Wavelength, nm S-6

7 Relative Intensity, a.u F NIR LED attenuated emission spectra in 5% CH4 HITRAN Absorption cross-section of CH4 7.0E E E E E E E-22 Absorption cross section, cm 2.molecule E Wavelength, nm Figure S1 (A) NIR LED emission spectra ( nm) in blank and (B-F) NIR LED attenuated emission spectra ( nm) in 1% to 5% 12 CH 4 (natural abundance 98.82%) calculated from the HITRAN generated absorption cross sections of CH 4 within the nm wavelength range, gas concentrations and optical pathlength. S-7

Optical Pathlength The beam divergence of NIR LED in TO-18 package with cap (Fig. S2) is provided by LED micrsensor NT (http://lmsnt.com/leds1600-5000/beam-divergence/): Figure S2.

8 Optical Pathlength The beam divergence of NIR LED in TO-18 package with cap (Fig. S2) is provided by LED micrsensor NT ( Figure S2. Spatial directivity of LMS16LED-R with TO-18 package where the black bold lines demonstrating a V shaped envelope consisting of all the rays emitted from 0 to 70 and covering ~99% of the emission from the LED. The following Fig. S3 illustrates the schematic drawing of IR rays spread at an angle from 0 to 35 (we considered the spread of IR radiation up to 35 which was the vendor reported viewing angle of our used LED; detailed discussions presented in the main manuscript in the spatial directivity section) from the IR LED inside the tube employed by Noori. 1 S-8

9 Figure S3. The scheme of optical paths resulting from the infrared rays spread at 0 to 35 in an 80 cm long tube with 0.75 cm diameter. An example calculation of the optical pathlength resulting from the rays emitted at 35 is shown below: a 1 = = cm; a tan 35 1 = = cm sin 35 a 2 = 0.75 = cm; a tan 35 2 = 0.75 = cm sin a n = 80 a 2 74 a 1 = = cm; a n = cos 35 = cm Effective Pathlength, Leff = a 1 + a a n = ( ) cm = cm We used a manual iterative process to calculate number of times the beam a 2 will reflect from the inner surface of the 80 cm long tube. As a n cannot be negative, we calculated the number of reflection with the excel expression: IF(80 a 2 number of reflection a 1 )>0. As soon as we found a negative value we stopped the iteration and used the previous value as the number of times the light beam a 2 will reflect from the tubular inner surface of S-9

10 the 80 cm long gas sensing tube. The screenshot of the excel ray tracing calculations is given below: The above example is showing the calculation of the optical pathlength resulting from IR rays emitted at 35. In the similar manner, we calculated other optical pathlengths at 1 intervals starting from 0 and ending at 70. The calculations for LED attenuated emission spectra are described in the next section. LED Attenuated Emission Spectra Calculation from HITRAN Absorption Cross Section The blank emission spectra of the NIR LED will be attenuated in the gas sensor depending on the absorption cross section, concentration of the gas and the optical pathlength. The attenuated spectra of the LED in 1% to 6% CH 4 is calculated as a product of LED emission spectra in blank and transmittance (i.e., 10 -absorbance ), as shown in eqn. 1 in main paper, where the absorbance is a product of HITRAN generated absorption cross section, gas concentration and the optical pathlength according to Bouguer-Beer-Lambert law. The total absorbances were calculated as the negative logarithm of the ratio of area under the attenuated emission S-10

11 spectra to the blank emission spectra of LED (i.e., -LOG(I/I 0 ) according to eqn. 2 in the main paper. Units of concentrations of gases in ppm were converted to molecule.cm -3 For example, 1% CH 4 = ppm = molecule of gas / molecule of air Using PV= nrt for 1 atm pressure, 25 C temperature, Avogadro number 6.023E+23, Boltzman Constant R= L atm Molecule -1 K -1, 1 V = ; V = 4.062E 14 cm E+23 Hence, ppm = 10000/4.062E-14 molecule.cm -3 At a particular wavelength, say at 1400 nm, HITRAN generated absorption cross section of CH 4 = 1.23 E-22 cm 2 /molecule. Therefore, calculated absorbance of 1% CH 4 at 1400 nm for 80 cm optical pathlength (i.e., IR beam is emitting at 0 angle) = 1.23 E-22 * 10000/4.062 E- 14 * 80 = The optical pathlength will vary for rays emitted at other angles, such as, in this study the IR rays are emitted from 0 to 70 according to Fig. S1. Therefore, the total absorbance of 1% CH 4 at 1400 nm can be calculated by integrating the absorbance as a function of optical pathlength from 0 to 70. Once, the total absorbance of 1 % CH 4 at 1400 nm is calculated, the transmittance can be calculated as 10 -absorbance. At 1400 nm, the attenuated emission of LED in 1% CH4 can then be calculated as a product of blank emission and transmittance at this wavelength. This process was repeated for all wavelengths from 1400 to 1800 nm to acquire the calculated LED attenuated emission spectra for 1 % CH 4. Then the whole process was repeated for 2% to 6% CH 4. All calculations were performed in excel spreadsheet and excel functions were employed to filter the required spectral data from HITRAN within the 1.4 to 1.8 μm wavelength range. The screenshot of HITRAN simulation parameters to acquire the CH 4 absorption cross sections is given below: S-11

Effects of Electromagnetic Radiation Zones on Light Emission from LED Although we demonstrated excellent agreement between the HITRAN calculated absorbance and the experimentally measured absorbance

12 Effects of Electromagnetic Radiation Zones on Light Emission from LED Although we demonstrated excellent agreement between the HITRAN calculated absorbance and the experimentally measured absorbance values by including ~99% of the emitted light from the LED in Fig. 2C in the main manuscript, we do not rule out the effect of near-field and mid-field electromagnetic regions on the propagation of the remaining ~1% light emitted from the LED. The propagation of light from an LED is affected by three basic electromagnetic working conditions: near-field, mid-field and far-field. 1 The near-field is a very short region near the chip containing the LED junction, where strong electromagnetic waves affect the radiation pattern. In the mid-field region, the light pattern significantly varies with distance due to the finite size of chip and LED package structure. In the far-field region, which is further away from the mid-field, the angular intensity distribution remains practically constant with distance. Hence, the emission from an LED can be modelled as directional point source emission only when far-field condition is met. 2 Moreno and Sun 2 derived general conditions for the distance beyond which the far-zone approximation can be S-12

13 used in measuring or modelling propagation of light from an LED array. Although the classical rule-of-thumb dictates any detector distance should be 5 times the size of the source so that the source can be considered as a directional point source, Moreno and Sun 2 demonstrated that the near-zone of a square LED array with highly directional emission with a commensurate small viewing angle can extend to more than 70 times the cluster size. In our study, the angular spread of emitted beams rays from 0 to 70 with a 35 viewing angle according to the spatial directivity plot (Fig. S2 in ESI) suggests that our NIR LED was not a highly directional emitter and consequently, the near-field and mid-field electromagnetic zones existed much closer to the chip and LED package structure. Therefore, the effects of near-field and mid-field zones on a quite insignificant (<1%) amount of light in our study did not impact the overall HITRAN calculation adversely. However, these facts strengthen our viewpoint of requirement of investigations of the spatial directivity plot of an LED in terms of angular spread of the beams rays and the viewing angle during HITRAN based calculation of absorbance. Configuration of the Gas Cuvette The NIR LED and corresponding photodiode (PD) were paired using an 80 cm long Al-tube consisting of in-house made mounts as shown in Fig. S4. The vacuum pump used in this system maintained a gas flow rate of 2 l/min and was on for 3 secs after CH 4 sampling which provided adequate time for gas to be flushed from the 80 cm gas cuvette (internal diameter ca mm and internal volume ca. 35 cm 3 ). S-13

14 Figure S4 Schematic diagram of the arrangement of gas cuvette with the NIR LED and PD optopair (partially adapted from Noori 3 ) References (1) Sun, C.-C., Chien, W.-T., Moreno, I., Hsieh, C.-C., Lo, Y.-C. Opt. Express, 2009, 17, (2) Moreno, I., Sun, C.-C. (2008). LED array: where does far-field begin? In Proc. SPIE 7058, Eighth International Conference on Solid State Lighting, 70580R, Ferguson, I. T., Taguchi, T., Ashdown, I, E., Park, S.-J. (Editors), 2 September 2008, doi: / (3) Noori, A. (2018). Radiometric analysis of LEDs and the use of rapidly pulsed infra-red LEDs for portable sensing of gases, PhD Thesis, Hobart, University of Tasmania. S-14

R O Y G B V. Spin States. Outer Shell Electrons. Molecular Rotations. Inner Shell Electrons. Molecular Vibrations. Nuclear Transitions

R O Y G B V. Spin States. Outer Shell Electrons. Molecular Rotations. Inner Shell Electrons. Molecular Vibrations. Nuclear Transitions Spin States Molecular Rotations Molecular Vibrations Outer Shell Electrons Inner Shell Electrons Nuclear Transitions NMR EPR Microwave Absorption Spectroscopy Infrared Absorption Spectroscopy UV-vis Absorption,