Appendix 134
5 A: Spectroscopy of cis-cis HOONO and the HOONO/HONO2 Branching Ratio in the Reaction OH+NO2+M; Discharge Flow Studies
5.1 Previously Published Results
This paper is reproduced with permission from the Journal of Physical Chemistry A, volume 107, no. 36, p. 6974-6985. Copyright 2003, American Chemical Society.
135
136
137
138
139
140
141
142
143
144
145
146
147
5.2 Revisions to Branching-Ratio Results
As described in chapters 2 and 3, our understanding of the spectroscopy used to measure the branching ratio has improved since these results were published. This section briefly describes what revisions should be made to the published data. The smallest correction is to the calculated ratio of cross sections used. More recent calculations taking into account anharmonicities indicate that this should be changed from 2.87 to 2.71 [73, 74]. Since the publication of Bean et al. we have a much improved understanding of the cis-cis HOONO spectrum. In particular, we understand that there is considerable OH stretch intensity blueshifted outside the main peak we used to measure the HOONO absorbance. As described in Chapter 3, our observed HOONO absorbances should have been multiplied by 1.41 to correct for this. Our assumed correction for nonlinearities in the nitric acid absorbance was significantly too small. We had assumed we could correct our observed nitric acid absorbances by multiplying them by 1.2. As described in detail in Chapter 2, at the low pressures of these experiments we should instead have multiplied by 2.5. As a result, the Bean et al. results should be corrected using
BR new = BR published
2.71 1.2 1.41 = BR published 0.64 . 2.87 2.5
The branching ratio at 298K and 13 torr is thus revised from k2(c-c)/k1 = 0.0750.020 to
k2(c-c)/k1 = 0.0480.013. A revised version of Figure 6 from Bean et al. is shown below.
148
0.08
Branching Ratio
0.06 0.04 0.02 0 265
275
285
295
305
315
325
335
345
355
Temperature / K
Figure 5.1 Corrected ratio of cis-cis to HONO2 products in the reaction of OH + NO2 as a function of temperature, at 20 Torr.
149
6 Appendix B: Experimental Details
6.1 Room Temperature Photolysis Cells
Machine drawings are included of the Teflon blocks and photolysis cells used in photolysis-initiated CRDS studies described in Chapters 4 and 5. Teflon block drawings are courtesy of Brian Bean and were submitted to the machine shop for fabrication. The blocks were coupled to the purge tubes and vacuum line via stainless steel Ultratorr fittings threaded into the Teflon. Initial leaks at the stainless/Teflon interface were sealed by a generous helping of Teflon thread tape. The blocks were coupled the to the gas inlet and pressure gauges by Teflon Swagelock fittings, also threaded into the blocks. These generally seal well, although the Teflon Swagelock parts wear down over the course of repeated tightenings. The seal between the Teflon blocks and the photolysis cell was the most problematic. This was accomplished by fitting the photolysis cells into square grooves in the Teflon blocks and pressing the Teflon blocks together. Often it was found that inserting silicon gaskets between the cell and the Teflon block could improve the seal. With nothing holding the gaskets out they would often deform and be pulled in by the vacuum, breaking the seal. Over time, the Teflon surrounding the square groove was deformed and pressed down into the groove. This made the square groove quite uneven and prevented a seal from being made. Overall, the design of this cell was certainly functional. Once a good seal was made between the Teflon blocks and the photolysis cell, it would typically last until the cell need to be disassembled. Future cell designs may consider improving upon this seal
150 mechanism in one of two ways. A thin-walled stainless tube could be inserted inside the silicon gaskets to help them hold shape and resist deformation. This would have the disadvantage of reducing the inside diameter of the CRDS axis, which already can present difficulties for alignment. A compromise would have to be struck with the wall the tube weighing rigidity and inside diameter. The second solution would be to have a round plate welded to the end of the photolysis cells and then create an O-ring seal between this plate and the Teflon blocks. This would certainly seal quite well, but would have the disadvantage of creating significantly more volume containing precursors but not UV photons. This would increase the background for experiments such as the alkoxy experiments described in Chapter 4 and would require faster flow rates to accomplish the same flush duty cycle.
151
Name: Alkoxy Cell Assembly-2 Material: Teflon Design: Brian Bean Phone: x6014 Scale: 1:1 Units: Inches Pieces: 1 View B Tap for 1/8 NPT 2.0 View A 0.50 View B
Tap for 3/4 NPT
Mill 0.05" deep For gasket Drill Thru 4 x size F bi on 2.25 BCD Drill thru with size X bit View A
Tap for 1/8 NPT
Drill thru with #9 bit
3.0
Figure 6.1. Technical drawing for fabrication of Teflon block for coupling photolysis cell to CRDS mirrors and gas inlets.
152
Name: Alkoxy Cell Assembly-1 Material: Teflon Design: Brian Bean Phone: x6014 Scale: 1:1 Units: Inches Pieces: 1 View B Tap for 1/2 NPT 2.0 View A 0.50 View B
Tap for 3/4 NPT
Mill 0.05" deep For gasket Drill Thru 4 x size F bi on 2.25 BCD Drill thru with size X bit View A
Tap for 1/8 NPT
Drill thru with #9 bit
3.0
Figure 6.2. Technical drawing for fabrication of Teflon block for coupling photolysis cell to CRDS mirrors and gas pumpout.
153
Quartz Cell (Starna Cells: Quartz Fluorometer Cells 3-Q-10) 4.3 cm 1/8 cm 1.0 cm
Stainless Steel Cells, Fabricated from 1-cm ID stainless square tubing.
0.15 cm 1.0 cm
6.0 cm
7.5 cm 12 cm 13.5 cm
Figure 6.3. Diagrams of various photolysis cells used.
154
6.2 184.9 nm Intensity Measurements
The measurement of 184.9 nm intensities from a Hg lamp can be complicated by interference from other wavelengths. This section evaluates this possible interference for the experiments described in Chapter 2. These experiments used a mercury Pen-Ray lamp (UVP) to generate 184.9 nm light. As can be seen in Figure 6.4, these lamps produce many other wavelengths of light in addition to 184.9 nm.
184.9
385.0
relative intensity
3.0 2.0 1.0
312.5
100
200
300
400
404.7
500 wavelength (nm)
Figure 6.4. Stated relative line intensities for UVP Hg Pen-Ray lamp.
Intensity measurements were made with two slightly different detection apparatus. The original apparatus, used for measuring the nitric acid 185 nm cross section, consisted of two custom-made 185 nm interference filters and a PMT with a bialkali cathode. Our original concern when making these measurements was leakage from
435.8
100
253.8
155 the most intense emission line at 254 nm (I254 > 30*I185). This concern was addressed by filling the cell with a few hundred torr of N2O. The cross sections at 185 nm and 254 nm are 1.4310-19 cm2 and <10-23 cm2 respectively. The resulting optical depths of >30 at 185 nm and <0.01 at 254 nm allowed for direct measurement of the 254 nm leakage: <2% of the total intensity. This contribution was subtracted from future measurements of the 185 nm intensity.
0.06 0.05 Abs(185) / Ls 0.04 0.03 0.02 0.01 0 0 5E+16 1E+17 1.5E+17 2E+17 L*[N2O] 2.5E+17 3E+17 3.5E+17 4E+17 y = 1.32E-19x + 1.16E-03
Figure 6.5. Fit to N2O Beer's Law Absorbance w/ Hg lamp, double interference filter, and bialkali cathode. Ls = 30.2 cm.
The Beer's Law absorption as a function of N2O concentration, with the contribution from 254 nm leakage subtracted, is shown in Figure 6.5. The absorbance was linear over a wide range, and a linear fit to the data yielded an observed cross section of 1.3210-19 cm2. This was about 5% below the literature cross section of 1.4310-19 cm2. We were encouraged by the linearity of the plots and reproducibility of our
measured cross section and felt this relatively small discrepancy was within the experimental uncertainty. Our measurements of the nitric acid 185 nm cross section as well as the initial measurements of the IR nitric acid integrated cross section were made using this same apparatus, subtracting the contribution from 254 nm leakage. Our initial linear fit to the data yielded a cross section of 1.5310-17 cm2. Again, this was about 5%
lower than the accepted literature value [25].
156 This small discrepancy seemed
reasonable, especially considering the scatter in nitric acid measurements at such short wavelengths [25-27, 29, 32, 33]. After we finished these initial measurements, the interference filters were lost. Aaron Noell at JPL then used the same for UV measurements of methanol in his cell. The double interference filters were replaced by a commercial 185 nm interference filter (Acton Research Corporation, 24 nm FWHM). Using the bialkali PMT, it was found that leakage by 194 nm light, a mercury emission line not listed in the UVP table shown in Figure 6.4, was an important photon contaminant. The predicted relative intensities (194:185 ratio taken from the CRC) convolved with the filter transmission properties are shown in Table 6.1. The expected relative intensities as observed by the PMT (after the filter) with a bialkali cathode, with fairly constant quantum efficiency, are shown in the column labeled "postfilter intensity." We see that, despite the 194 nm intensity being much smaller than that at 254 nm, the 194 nm light is expected to be a much larger problem due to the properties of the filter. Aaron further reduced the contribution of 194 nm light by a factor of five by switching to a solar-blind CsI PMT. The resulting expected signal as seen by the CsI PMT is also shown in Table 6.1. We see that the contribution from non-185 nm light is expected to be about 5%. The values in Table 6.1 can only be trusted as a rough guide, though, as the specific output characteristics of PenRay lamps vary from lamp to lamp and over the lifetime of the lamp.
157
Table 6.1. Expected contribution of various Hg Pen-Ray lamp wavelengths. All values other than wavelengths are relative and unitless. wavelength /nm Intensity Filter transmission postfilter intensity CsI Response CsI Signal 184.95 194.23 253.65 1000 300 30000 0.18 0.15 0.0001 180 45 3 1 0.2 <0.2? 180 9 <0.6?
When we returned to IR integrated cross section measurements, we used the solar-blind CsI PMT that Aaron had used. Unfortunately, we did not re-measure the nitric acid UV cross section and so do not know if 194 nm contamination influenced this measurement. At the moment, the UV equipment necessary to re-measure this cross section is not available. Instead, I have tried to quantify the contribution of the 194 nm emission from the Pen-Ray lamp to our previous measurement of the nitric acid UV cross section. The apparatus used was a 160 cm stainless steel Raman cell with UV-transparent windows. The Hg Pen-Ray lamp output was sent through a 10 cm focal length CaF2 lens and a pinhole to collimate the light through the cell. A second pinhole was used at the output window to minimize the collection of photons that reflected within the cell. The same Acton Research 185 nm interference filter described above was used to drastically reduce the detection of 254 nm light. The PMT output was amplified and then sent to an oscilloscope for averaging. The pressure in the cell was measured by a 10K torr MKS Baratron. The experiments consisted of measuring the transmitted intensity as a function of CO2 pressure using both the bialkali and CsI cathode in the PMT and then comparing
158 the absorbance as a function of pressure for the two. CO2 was chosen because 185= 13194 and because the UV spectrum in this region lacks structure. Absorbance data as a function of CO2 concentration are shown in Figure 6.6. The data taken with the CsI cathode appeared linear for the range of absorbances measured (Abs 3). The fit to this data is almost identical to the literature value of 2.8510-22 cm2 [105]. The data taken with the bialkali cathode show obvious curvature, even at
absorbances below 0.5. The data can be simulated using only the cross sections at 185 nm and 194 nm. The simulation shown in Figure 6.6 assumes 90% 185 nm and 10% 194 nm and fits the data very well over the entire range of observed absorbances.
0.02 0.016
Absorbance/ cm
y = 2.86E-22x + 2.00E-06
0.012 0.008 0.004 0 0 2E+19 4E+19 6E+19 8E+19 1E+20
[CO2] / molecues cm^-3
CsI 1
alkali 1
alkali 2
CsI 2
sim alkali
Linear (CsI 2)
Figure 6.6. CO2 absorption data taken with two different PMT cathodes. The linear fit to the CsI data is shown in black. A simulation of the bialkali data using observed intensities of 90% 185 nm and 10% 194 nm is shown in orange.
As Figure 6.6 demonstrates, 184.9 nm intensities taken with the CsI cathode and new filter were likely free from 194 nm contamination. While we cannot re-test the interference filters used in conjunction with the bi-alkali cathode directly, it is likely they
159 had similar transmission properties to the current filter. Making this assumption, we can use the relative contributions of 185 and 194 nm light derived from Figure 6.6 to correct the intensities measured while measuring 185. The observed intensities were therefore corrected to be that of just 185 by
I185 = I obs - I 0,obs 0.095 exp(- 194 ls [HNO3 ]) . This led to very small changes (1%) in the intensities and only a 1% increase in our measured 185. Because we have had to assume the old filters had similar transmission properties to the new filter, this has been included as an uncertainty in the analysis of our 185 measurements described in Section 2.2.2.
160
6.3 Flow Cell Flush Times
In photolysis experiments, it is important to ensure that a fresh gas sample is being photolyzed with each excimer pulse. In this way secondary chemistry and other potential problems stemming from the photolysis of products are eliminated. The group lore when I joined was that, if you calculate the flush time of the photolysis region of the flow cell from the pressure and flowmeter readouts, you should multiply that number by two to get the actual time for a clean gas sample. This was assumed to be the result of diffusion of products into various parts of the cell, which would compete with efficient flushing of the cell. The nitric acid product from the OH + NO2 photolysis experiments provides a strong spectroscopic measure of "photolysis products." We therefore measured the flush rate directly by monitoring the nitric acid signal as a function of the YAG Excimer delay time. Figure 6.7 shows data taken at 600 torr and a calculated flush time of 80 ms.
800 700 1/tau - 1/tau0 600 500 400 300 200 100 0 0 20 40 60 80 100
Excimer - YAG delay time / mS
Figure 6.7 Nitric acid signal at 3540 cm-1 as a function of the Excimer YAG delay time, for a calculated flush time of 80 mS. The first point shown is taken at the typical delay time for OH + NO2 experiments of 500 S.
161 We see that the initial decrease in nitric acid signal exceeds that predicted by flushing alone, i.e., far less than half the initial nitric acid remains in the probe region 40 ms after the initial photolysis. Presumably this can be explained by diffusion of nitric acid out of the region of the cell being probed by the IR-CRDS. After this initial rapid decay, the signal decays much slower and asymptotes to 1.3% of the signal at 500 s. Given the notoriety of nitric acid as a very sticky molecule, this remaining signal may more reflect the desorption of nitric acid stuck to the walls of the flow cell than poor flushing of photolysis volume. Regardless, for our purposes the 1.5% signal at the calculated flush time of 80 ms reflects essentially complete flushing of the photolysis volume. This level of signal was used to determine a minimum flush time (the calculated flush time needed to reduce the signal to 1.5% its initial value at the next excimer shot) at a few different pressures. While this time at 400 torr was about the same as that at 600 torr (88 mS), at 200 torr a faster flush time of about 65 ms was needed. This implies that at lower pressures, diffusion may indeed begin to play an important role and the "factor of two" rule may once again apply. Fortunately, at lower pressures faster flush times are readily achieved.
162
6.4 Mass Flow Transducers
Mass flow transducers (flowmeters) are a critical component of the flow-cell experiments described in this thesis. They enable us to control and precisely know the concentrations of all gases in the cell. This information is critical for any kinetics simulations or cross-section measurements. As implied by their formal name, flowmeters determine mass flow of gas through their sensor. This is accomplished by detecting the heat transferred by a flowing gas, which is directly proportional to the mass flow of the gas. A diagram of the sensors used in Omega flowmeters is shown in Figure 6.8.
Figure 6.8. Schematic of mass flow sensor used in Omega Mass Flowmeters. Taken from Omega's Electronic Mass Flowmeters Flow Reference Section http://www.omega.com/toc_asp/frameset.html?book=Green&file=MASS_FLOW_REF
The temperature difference between the upstream and downstream temperature sensors is converted to a voltage that is linearly related to the mass flow. In order to interpret this voltage, the sensitivity of the flowmeter, given in sccm/volt, must be known
(sccm = standard cubic centimeter = 1cm of gas at 70 F and 1 atm). Because the sensor relies on the thermal conductivity of the gas, the sensitivity is gas specific, so the calibration changes when the gas is changed. The calibration for a new gas can be calculated using conversion tables provided in the manuals for each flowmeter. Sensitivities are provided with any new flowmeter, but should be calibrated upon arrival and re-calibrated periodically. This is accomplished by flowing through calibrated volumes, specifically those included in the calibration kit borrowed from the Sander group at JPL. This kit includes several volumetric cylinders (10, 100, and 1000 cm3) each with a ground glass joint on one end. This joint couples the cylinder to a specialty piece of glassware that introduces soap bubbles to the upstream end of the cylinder. The flow rate is then measured by measuring the time it takes for the soap bubbles to displace the volume of the cylinder. Following corrections for the temperature, pressure, and vapor pressure of water, the flow in standard cubic centimeters is determined and can be plotted as a function of the voltage readout of the flowmeter. The flowmeters in 17 Noyes were originally all manufactured by Edwards. These all had corrosion-resistant stainless steel bodies, bipolar electrical connections (although of a rather inconvenient design) and were generally robust. Unfortunately, as time has worn on, the sensors in the Edwards flowmeters have begun to go bad. Usually this is a gradually accelerating process of decreasing sensitivity to flow (an increase in the sccm/volt measured when calibrating). This is a serious problem because Edwards left the flowmeter business years ago and, when they left, apparently did not sell their extra sensors or the rights to make them to any other company. As a result, once a flowmeter sensor goes bad, the flowmeter is no longer useable and must be replaced.
3
163
164 So far, the flowmeters that have gone bad have tended to be those for higher flow used for dilution or purge flows of inert gas. As a result, they have been replaced with inexpensive brass-body flowmeters from Omega. These flowmeters must be used with inert gas only. Under ideal conditions, these flowmeters seem to work fine. Their sensitivities do not seem to vary between calibrations and the calibration curves are linear, yielding uncertainties in the flow on the order of 0.5%. However, problems with these Omega flowmeters do exist. First, the power supply is of a positive voltage only. As a result, the flowmeters cannot read any voltage below 0.0 V. This can be and has been a problem when the zero-flow offset is such that the voltage at no flow is not a positive value. When this occurs, there is a range of low flows that will all read zero. In a calibration curve, this is evidenced by a significant positive y-intercept. As a result, it is important to check that the zero-flow reading from the Omega flowmeters is above zero (it is wise to check the value before and after an experiment to account for drift), and then subtract this value from all readings that day. The more serious issue with the Omega flowmeters stems from the fragility of their electronics. The first time the Omega flowmeters broke, it was clearly my fault. I had been making changes to the power supply and readout box and accidentally reconnected the positive and negative leads backwards. This apparently fried all three Omega flowmeters. It is interesting to note that this did not seem to affect the Edwards flowmeters at all. This does not necessarily imply an inherent problem with the Omega flowmeters, but a better design would have included a fuse or other safety device that would have protected the sensor in case of lab idiot.
165 The second destruction of flowmeter confirms this. It is generally advised that before you connect or disconnect a flowmeter you turn its power supply off. I would again like to point out that the Edwards flowmeters were connected and disconnected with the power on for years before I joined the group without any drastic consequences. As a result of the shorted electronics mentioned above, I have been very careful to power down the flowmeters before performing any work on them. A recent addition to the lab (who will remain unnamed) changed the gas connections to the flowmeters with the power on. This was just a plumbing job, with no changes to the electronics. After the plumbing was done, one of the Omega flowmeters was broken. Presumably, something touched its nine-pin connector during the job and cased a short. While again this could have been prevented by powering down the flowmeters, relying on these Omega flowmeters that are so prone to breaking is not ideal (in this latter case, we were able to convince them to replace the unit for free, but not without nearly a month of downtime). As a result, I advise switching to a new company when next we need a new flowmeter. The flowmeter-readout-DIO system is a bit messy, which I believe is a large part of the slow response time of the flowmeter readouts (settling time after changing flow of about ten seconds). The setup could definitely be improved.
WARNINGS: With Omega flowmeters, flow ONLY INERT GAS. Turn power to flowmeters off (power strip mounted to laser table cover) before any work on flowmeters. Always check calibrations against the previous value to check for sensors that are beginning to fail.
166
7 Appendix C: CRDS Simulation Programs for Matlab
7.1 Introduction
I cannot give Gautham Nair enough credit for writing these. He did all the legwork on designing the program, wrote a version of the program for C++ and then wrote the original version of these fitting programs. I have made adjustments to the code to for convenience and flexibility, but Gautham should definitely be considered the author of the program. Many thanks also to Kana Takematsu for taking these programs through the motions and helping with the documentation included in this appendix. It should be noted that after Gautham left for some lesser school in Massachusetts, he wrote some of the programs on a different version of Matlab and there was a small compatibility issue. I worked with Matlab 7.0. To get these programs to work on other versions of Matlab it may be necessary to replace the comma separating output variables of a function with a space i.e. change function [ringspec,simplespec]= to function [ringspec simplespec]=
7.1.1 Motivation
As described in Chapter 2, pulsed CRDS measurements of spectra with narrow features can have significant errors in the form of incorrect lineshapes and observed integrated absorbances below the true value. These errors stem from fitting observed multi-exponential decays with a single exponential function to extract the decay lifetime
167 . The general goal of these programs is to simulate the expected CRDS signal for a given set of apparatus conditions if the underlying high-resolution spectrum is known. This high resolution spectrum is adjusted by pressure broadening and application of scale factors to take into account species concentration and convert the spectrum from absorbance units to 1/. This spectrum is then convolved with the laser profile to generate the simulated ringdown spectra. At each point in the simulated spectrum, a simulated ringdown decay is produced by summing the individual decays at each frequency weighted by the laser profile,
e
i
i i
, where is the normalized weighting function for the laser profile. The
simulated ringdown decay is then fit with a single exponential function to generate the "experimental" ringdown lifetime decay (1/'). This is then repeated for all frequencies in the simulated spectrum. The integrated absorption of the new spectrum and the convolved spectrum without re-fitting the decay, error in the CRDS spectrum. The magnitude of the CRDS errors and their sensitivity to various parameters can then be explored. Because there are many parameters which we might be interested in varying systematically, there are several versions of the program each designed to systematically vary an individual parameter. In theory these various programs could be combined into one generalized program, but so far I have found this to be unnecessary.
i
i
i
, can be compared to derive the
168
7.1.2 Using MATLAB:
Some general tips for running routines in Matlab. The program files must be contained in the Current Directory shown in Matlab. All saved files will also automatically go to the Current Directory. You can specify any output names you want. Inputs that are arrays or matrices must be pre-existing named items in the Matlab workspace. To run a routine, such as Lorentzbroaden.m broadening the high-resolution spectrum "inputspectrumname" to .05 cm-1, you would just type into the command line outputspectrumname = Lorentzbroaden(0.05, 2.0, inputspectrumname); and press enter. The semicolon at the end ensures that the output spectrum is not printed to the Command Window. When the program is finished, the new matrix "outputspectrumname" will appear in the Workspace. WARNING: If you run the program again and do not change the output name, it will be written over without any prompt to warn you! Comments can be added to any routine by beginning the line with "%". To save any output matrix to a text file for manipulation in another program, use "save savefilename.out matrixname ASCII" When trying to go through the program, it is helpful to generate a fake matrix to manipulate. Just define a matrix ("matrix=..." or [starting point: interval dist: finishing point].) The matrix will appear in the Workspace. If you want to manipulate it, just double click on it. To quickly generate an array (such as a column array of scalefactors for use in SFBatchFixCut.m) you can use newarrayname = (startnumber:stepsize:endnumber)';
169 The apostrophe at the end rotates the array from a row to a column. If you want column i of matrix, just write matrixname(:,i). If you want a row, write matrixname(i,:)). If you want to manipulate any matrix (change/add/delete elements), just double click on it. A flow diagram for the "SFBatchVarCut.m" top-level program to illustrate which programs are interconnected is shown here. The programs are highly modular so that changing and debugging programs is quite simple, even for a novice like me. An arrow indicates a flow of outputs. For example, RingSimVarCutBatch.m calls three different sub-routines, "Gaussiancomb.m", "LMDecdayFitVarCut.m" and "CombDecay3.m". It then uses the information gathered from those sub-routines and sends outputs to "SFBatchVarCut.m". It is important when running a program in Matlab that all needed sub-routines are contained in the Current Directory. findindex.m trapintegrate.m matrixtrapintegrate.m
SFBatchVarCut.m
(repeats below with different scalefactors) RingSimVarCutBatch.m (true work horse: prepare two spectra: before and after simulated ringdown fits) Gaussiancomb.m (generates laser profile) LMDecayFitVarCut.m (fits simulated ringdown) CombDecay3.m (convolves laser profile with spectrum)
170
7.2 Program Documentation
Programs are shown below in single-spaced text. If using higher-level programs, subroutines need to be saved with the titles shown in quotation marks.
7.2.1 Common Inputs
absspectrum = data spectrum used for simulation. Usually the output of
Lorentzbroaden.m
times = 1D column array specifying the time axis of the ringdowns. Should reflect the
number of points and sample rate of the experiment you are simulating.
background = background value for 1/tau. Should be in s-1. xi,xf = range of simulated spectrum. (xi-regionwidth) and (xi-regionwidth) should not
exceed the range of absspectrum.
scannedwavenumbers = 1D column array of frequencies you want in the output
spectrum. This is where you would define the stepsize of the spectrum. Could be used to eliminate xi and xf with a short re-program.
regionwidth = range in cm^-1 (or whatever units your spectra are in) over which the
laser profile will be used to calculate the simulated ringdown at each point. 2*laserfwhm was sufficient in HNO3.
laserfwhm=laserfwhm in cm^-1(or whatever units your spectra are in). Treats laser
profile as Gaussian (for most simulations assumed to be 1.0 cm-1). Actually treats profile as discrete spikes with spacing defined by ...
modespace = spacing of modes for Gaussian laser profile. Generally assumed to be
0.00666 cm-1 we expect from the YAG cavity.
171
7.2.2 "Lorentzbroaden.m"
DESCRIPTION: This program is designed to take a high resolution, Doppler-limited spectrum and convolve it with a Lorentzian lineshape to simulate pressure-broadening. 1 1 2
Reminder: Lorentzian
2 For nitric acid, we found that having regionwidth=2*fwhm was insufficient. If you can spare points at the edge of your spectrum, you should try for at least 4*fwhm. %Inputs %fwhm=fwhm of Lorentzian profile your are convolving %regionwidth=total width over which each spectral point will be "spread". %spectrum=2D matrix containing data spectrum to convolve. Can be imported %using Matlabs "Import Data" routine. First column must be x-axis %(frequency units must match fwhm and regionwidth) % second column can be any arbitrary frequency units. function broadspec=Lorentzbroaden(fwhm, regionwidth, spectrum); specspacing=spectrum(2,1)-spectrum(1,1); convpoints=round(regionwidth/(2*specspacing)); %this initiates the matrices used in the calculation Npoints=size(spectrum,1); broadspec=2*ones(Npoints-2*convpoints,2); %Here is the meat of it. If you wanted to change this to use a different %shape you would change the second line. %Motivation for loop: we are going to take each point of the spectrum. Each point is %going to be treated like a Lorentzian i.e. the intensity assigned to each point is going to %be redistributed as a Lorentzian. The transformed functions are then going to be %summed. for i=(convpoints+1):(Npoints-convpoints) lorweights=1./((spectrum((i-convpoints):(i+convpoints),1)-spectrum(i,1)).^2 ... +(fwhm/2)^2); lorweights=lorweights/sum(lorweights); broadspec(i-convpoints,1)=spectrum(i,1); broadspec(i-convpoints,2)=sum(spectrum((iconvpoints):(i+convpoints),2).*lorweights); end
( x - x ) 2 + ( 1 ) 2 0
172
7.2.3 "trapintegrate.m"
DESCRIPTION: Used to integrate spectra. Built into the Batch programs below, but can be used for any spectrum in the Workspace that is a 2D matrix with frequency in column 1 and absorbance in column 2. Fairly self explanatory. function trapintegral = trapintegrate(xi,xf,spectrum); ni = findindex (xi,spectrum); nf = findindex (xf,spectrum); trapintegral=0.0; trapintegral=sum(spectrum(ni:(nf-1),2).*(spectrum((ni+1):nf,1)-spectrum(ni:(nf-1),1)));
7.2.4 "matrixtrapintegrate.m"
DESCRIPTION: Can be used to get the integrals of multiple spectra contained in a 2D matrix where the columns are spectra (such as the outputs from the Batch programs below). xi and xf should be entered as numbers, wavelengths should be a column array such as "scannedwavenumbers" described above, and spectraonly should be a matrix with each column as the absorbance points corresponding to the frequencies in "wavelengths". function trapintegrals=matrixtrapintegrate(xi,xf,wavelengths,spectraonly) trapintegrals=[]; for i=1:size(spectraonly,2) trapintegrals=[trapintegrals trapintegrate(xi,xf,[wavelengths,spectraonly(:,i)])]; end
173
7.2.5 "Gaussiancomb.m"
DESCRIPTION: Generates a Gaussian shape for use in simulation programs using "laserfwhm", "regionwidth", and "modespace" to describe the laser profile. The "combpattern" output is 2D array describing a Gaussian with 0 as the center point. function combpattern = Gaussiancomb(laserfwhm,regionwidthcm,modespace); lasersigma=laserfwhm/sqrt(8*log(2)); temp1=0:modespace:regionwidthcm/2; temp2=-temp1; temp2(1)=[]; combpoints=[fliplr(temp2) temp1]'; combintensities=exp(-(combpoints.^2)/(2*lasersigma^2)); combpattern=[combpoints combintensities];
7.2.6 "findindex.m"
DESCRIPTION: Simple program called to give the index number. function n=findindex(x,spectrum) n=interp1(spectrum(:,1),(1:size(spectrum,1))',x,'nearest');
174
7.2.7 "SFBatchFixCut.m" and "SFBatchVarCut.m"
DESCRIPTION: To be used when you want to run several simulations at various "concentrations" (scalefactors). Shown is the program designed to do the ringdown fits cutting a fixed number of points at the start of the simulated ringdown, SFBatchFixCut.m. The program for cutting a fraction of a ringdown for each trace, SFBatchVarCut.m, is identical but calls "RingSimVarCutBatch.m" in the for-loop.
UNIQUE INPUTS: scalefactors = 1D column array containing all scalefactors you want used.
NOTE: later in the RingSimFixedCutBatch, the scales factor is multiplied by the arbitrary number 6.024*10^18. If working with known absorbances, it should be possible to change this number so that scaled absorbances represent the expected signal rather than its current arbitrary value. function [ringspecs,simplespecs,integrals,Summary] = SFBatchFixCut (scalefactors, xi, xf, absspectrum, background, scannedwavenumbers, times, laserfwhm, regionwidth, modespace); pringtemp=[]; rringtemp=[]; psimtemp=[]; rsimtemp=[]; ringspecs=[]; simplespecs=[]; Summary=[]; integrals=[]; Npoints=length(scannedwavenumbers); %length = # of rows in matrix %this iterates RingSimFixedCutBatch for each scalefactor for i=1:length(scalefactors) [ringspec,simplespec]=RingSimFixedCutBatch(laserfwhm, regionwidth, modespace, times, scannedwavenumbers, background, scalefactors(i), absspectrum);
175 %see later pages for RingSimFixedCutBatch.m. ringspecs=[ringspecs ringspec]; %[elements1 elements2] combines the elements into one large array simplespecs=[simplespecs simplespec]; integrals=[integrals [trapintegrate(xi,xf, [scannedwavenumbers ringspec]);... trapintegrate(xi,xf, [scannedwavenumbers simplespec])]]; %notice the ";" between the trapintegrates. This puts the results in two separate rows %this calculates the integrated absorption for ringsepc and simplespec. pringtemp=[pringtemp ringspec(1)]; rringtemp=[rringtemp ringspec(Npoints)]; psimtemp=[psimtemp simplespec(1)]; rsimtemp=[rsimtemp simplespec(Npoints)]; end %this creates a matrix with columns containing the simulated spectrum %integral, the integral of the spectrum with no CRDS error, and the first %and last point in the spectra for both the simulation and with no CRDS %error (critical for trying to evaluate the error outside the bounds of %your simulation). Summary=[integrals' pringtemp' psimtemp' rringtemp' rsimtemp'];
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7.2.8 "ScalefactorBatchCustom.m"
DESCRIPTION: This is the same as SFBatchVarCut.m but it is designed so that any arbitrary laser profile can be used (above routines used Gaussian profile). The normalized laser profile needs to be a pre-existing 2D matrix with the first column as (frequency) with the center of the profile as 0 and the second column the normalized intensity at each value of (frequency). function [ringspecs, simplespecs, integrals, Summary] = ScalefactorBatch (scalefactors, xi, xf, absspectrum, background, scannedwavenumbers, times, laserprofile); %in comparison with SFBatchFixCut, laserprofile has replaced inputs laserfwhm, %regionwidth and modespace. pringtemp=[]; rringtemp=[]; psimtemp=[]; rsimtemp=[]; ringspecs=[]; simplespecs=[]; Summary=[]; integrals=[]; Npoints=length(scannedwavenumbers); for i=1:length(scalefactors) [ringspec,simplespec]=RingdownSimCustom(laserprofile, times, scannedwavenumbers, background, scalefactors(i), absspectrum); %see later pages for RingdownSimCustom.m ringspecs=[ringspecs ringspec]; simplespecs=[simplespecs simplespec]; integrals=[integrals [trapintegrate(xi,xf, [scannedwavenumbers ringspec]);... trapintegrate(xi,xf, [scannedwavenumbers simplespec])]]; pringtemp=[pringtemp ringspec(1)]; rringtemp=[rringtemp ringspec(Npoints)]; psimtemp=[psimtemp simplespec(1)]; rsimtemp=[rsimtemp simplespec(Npoints)]; end Summary=[integrals' pringtemp' psimtemp' rringtemp' rsimtemp'];
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7.2.9 "fwhmBatch.m"
DESCRIPTION: Very similar to SFBatch programs above, but you can run a batch of various values of laser fwhm (laserfwhms) instead of scalefactors. widthfactor is a number which will be multiplied by each laser fwhm to define the "regionwidth" described above. function [ringspecs,simplespecs,integrals,Summary] = fwhmBatch (scalefactor, xi, xf, absspectrum, background, scannedwavenumbers, times, laserfwhms, widthfactor, modespace); pringtemp=[]; rringtemp=[]; psimtemp=[]; rsimtemp=[]; ringspecs=[]; simplespecs=[]; Summary=[]; integrals=[]; Npoints=length(scannedwavenumbers); for i=1:length(laserfwhms) [ringspec,simplespec]=RingdownSim3(laserfwhms(i), laserfwhms(i)*widthfactor, modespace, times, scannedwavenumbers, background, scalefactor, absspectrum); ringspecs=[ringspecs ringspec]; simplespecs=[simplespecs simplespec]; integrals=[integrals [trapintegrate(xi,xf, [scannedwavenumbers ringspec]);... trapintegrate(xi,xf, [scannedwavenumbers simplespec])]]; pringtemp=[pringtemp ringspec(1)]; rringtemp=[rringtemp ringspec(Npoints)]; psimtemp=[psimtemp simplespec(1)]; rsimtemp=[rsimtemp simplespec(Npoints)]; end Summary=[integrals' pringtemp' psimtemp' rringtemp' rsimtemp'];
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7.2.10
"RingSimFixedCutBatch.m" and
"RingSimVarCutBatch.m"
DESCRIPTION: Calculates the simulated CRDS spectrum and convolved spectrum for each scalefactor. Shown is RingSimFixedCutBatch.m which uses fits cutting a fixed time period at the start of each ringdown. RingSimVarCutBatch.m uses fits cutting a fraction of a lifetime at the start of each ringdown, and replaces LMdecayfitmodified.m with LMDecayFitVariableCut.m function [ringspec,simplespec]=RingSimFixedCutBatch(laserfwhm, regionwidth, modespace, times, scannedwavenumbers, background, scalefactor, absspectrum) combpattern=Gaussiancomb(laserfwhm,regionwidth,modespace); Nscans=size(scalefactor,1); Npoints=size(scannedwavenumbers,1); ringspec=zeros(Npoints,Nscans); %zeros(m,n) generates m x n matrix with all elements = 0 simplespec=zeros(Npoints,Nscans); tempdecay=zeros(size(times)); %if zeros(m), creates m x m matrix simpleinvlifetime=0.0; tempfitparam=[]; %This does the work of calling Combdecay3.m and LMDecayfitmodified.m for each %point in the simulated spectra and compiling those numbers for export to %SFBatchFixCut.m. for j=1:Nscans invlifetimes=[absspectrum(:,1) background + scalefactor(j)* 6.024*10^8* absspectrum(:,2...