Abneesh Srivastava and Joseph T. Hodges

Transcription

1 Supportng Informaton for Development of a Hgh-Resoluton Laser Absorpton Spectroscopy Method wth Applcaton to the Determnaton of Absolute Concentraton of Gaseous Elemental Mercury n Ar" Abneesh Srvastava and Joseph T. Hodges Chemcal Scences Dvson, Natonal Insttute of Standards and Technology, 100 Bureau Drve, Gathersburg, Maryland , Unted States Correspondng author: Abneesh Srvastava, emal: abneesh.srvastava@nst.gov S1: Smulaton of mercury absorpton spectrum Table of Contents Table S1.I: Summary of mercury 6 1 S P 1 transtons Fgure S1.1: Smulated spectrum for pure mercury vapor at T = 96 K S: Saturaton and photoreacton effects Fgure S.1: Dependence of ntegrated absorpton on laser ntensty for Hg, Hg-N and Hg- Ar samples S3: Effect of multple reflectons and cell orentaton S4: Uncertanty analyss Table S4.I: The number densty combned standard relatve uncertanty budget S1. Smulaton of mercury absorpton spectrum S-1

2 Table S1.I. Summary of mercury 6 1 S P 1 transtons, masses, sotopc abundances, absolute transton frequences, uncertantes, degeneracy ratos and unweghted and sotopcally weghted ntenstes. All frequences are based on the absolute poston of the 198 amu sotope (lne ) gven by Kramda (011) 1 and the postons and uncertantes relatve to ths lne from Schwetzer (1963) wth the excepton of the relatve poston of lne 1 (196 amu sotope) whch s taken from Btter (196) 3. Intenstes are based on A 1 = 8.41 ± 0.8 x 10 6 s -1 assumed for all transtons. Note that the sum of the sotopcally weghted ntenstes s S = m /s and s nearly ndependent of the relatve tot sotopc abundances. label m (THz) u( ) (MHz) g / g,, 1, S unweghted (10-8 m s) S, weghted (10-8 m s) A B a / b c / S-

3 Fgure S1.1. Smulated spectrum for pure mercury vapor at T = 96 K wth ndcated transtons. Natural sotopc abundance s assumed for the consttuent sotopes. Note the composte spectrum s offset by cm -1 along the vertcal axs for clarty. S. Saturaton and photoreacton effects We measured a seres of spectra for all three samples to dentfy the thresholds below whch ntensty saturaton and photoreacton effects (for the Hg-Ar samples) would be elmnated. Typcally, the laser beam power ncdent on the sample cells was less than approxmately (0.1 W) and was adjusted to avod obvous saturaton usng neutral densty flters. To quantfy the S-3

4 onset of saturaton, whch occurs when there s sgnfcant perturbaton to the equlbrum thermal populaton of the mercury atoms n the ground state caused by laser pumpng, we measured nhg A1l for the Hg-only, Hg-Ar, and Hg-N samples as a functon of maxmum ncdent laser ntensty, I. In ths smplfed analyss of saturaton, we consder only the peak ntensty of the beam, neglectng the transverse profle and strong beam attenuaton caused by absorpton for the Hg sample. We estmated the peak beam ntensty assumng a Gaussan beam profle and from the measured beam power, P t, and effectve 1/e radus, w wxwy as I P w, where w, w are the measured beam rad along two orthogonal drectons. t / ( ) x y We consdered peak ntenstes rangng from 10 - Wm - to 500 Wm -, whch wdely bracket the expected saturaton ntensty of the mercury transtons for the Hg-only sample gven by I sat h 107.1W/m 3 A1. The results for all three samples are summarzed n Fg. S.1, n whch the quantty sat ( I) nhg ( I) / nhg,0s plotted aganst I, where n Hg,0 s the mercury number densty n the lmt of 0 beam ntensty. As expected, for the pure Hg samples, sat exhbts a strong dependence on ntensty for I I sat. Assumng that saturaton s consstent wth nhomogeneously broadened (Doppler profles) then ( I ) 1/ 1 I / I. We ft ths sat sat expresson to the Hg sample data treatng nhg,0 and a factor scalng the measured effectve radus of the Gaussan-profle laser beam as ftted parameters. Based on the ftted saturaton curve and a typcal expermental ntensty of Wm - (ndcated by the vertcal dashed lne, and correspondng to saturaton parameter, I / I = ), we estmate that relatve amount of sat saturaton was less than We also estmated the saturaton broadenng 4 of the Dopplerbroadened lnes to be less than 30 khz at our typcal expermental ntensty. Also, at these S-4

5 fluences, the temperature rse n the cell caused by absorpton of the laser beam was calculated to be less than 1 mk and therefore was neglected. Fgure S.1 shows that the Hg-N samples do not saturate at the laser ntenstes consdered here. Ths s to be expected gven that relaxaton of the mercury atoms from the excted state s promoted by the collsons wth the N bath gas. In ths regme, the lne profles are mostly homogeneously broadened, and the relaxaton rate s domnated by the foregn pressure broadenng, gvng a relaxaton rate that exceeds A 1 by more than three orders of magntude. In contrast to the Hg-N results, the absorpton data n Fg. S.1 for Hg-Ar samples show a sgnfcant reducton n absorpton as the beam ntensty ncreases. We attrbute ths trend to well-studed photoreacton effects 5,6 occurrng va the quenchng of Hg excted state. Unlke ntensty saturaton n the Hg-only sample, the reducton n measured Hg number densty for the Hg-Ar sample was tme dependent and was a manfestaton of slow, photo-nduced reactons that lead to the formaton of HgO per 53.7nm Hg O HgO O 3 Ths effect was elmnated by operatng at ntenstes below about 10 - Wm -. The reported photoreacton threshold s also well below the 53.7 nm ultravolet photo-deposton results of Grante et al. 6,7 for Hg n oxygen-ntrogen mxture near room temperature n a quartz photoreactor under flowng condtons (1 mwcm - 10 Wm -, wth 81.5% mercury capture). Furthermore, we expect that n an open system, where Hg-Ar sample contnuously enter and leave the sample volume, sgnfcantly hgher beam ntenstes could be accommodated wthout encounterng ths complcaton. Addtonally, the nvarance of the number densty at low S-5

6 ntenstes (10 - Wm - ) across our sample-trad suggests no detectable anomalous surface effects, under of expermental uncertanty. Fgure S.1. Dependence of ntegrated absorpton on laser ntensty for Hg, Hg-N and Hg-Ar samples. The red lne represents the expected dependence for the Hg sample based on nhomogeneous broadenng and assumng Isat 107.1W/m. We note that the Hg-Ar case exhbts an ntensty dependence because of photothermal nduced oxdaton of the elemental mercury, not because of ntensty saturaton. All other data reported n the present study correspond to laser ntenstes near that ndcated by the blue lne, n whch saturaton effects are neglgble. S3. Effect of multple reflectons and cell orentaton We computed a modfcaton to the geometrcal pathlength, to account for potental multple reflectons between cell walls. Ths correcton, whch assumes ncoherent addton of the reflected felds and was estmated n terms of the effectve reflectvty of the fused slca wndows (equal to 0.08 for two surfaces) at 54 nm, leads to an effectve path length that s S-6

7 larger by (0. to 0.4) % compared to the geometrcal, sngle-pass value. Also, the senstvty of pathlength to cell orentaton relatve to the ncdent beam was evaluated and optmzed to result n the mnmum path length. The senstvty of path length to cell orentaton gves a 0.1 % overestmaton of path length for ±3 spread relatve to ts mnmum value. S4. Uncertanty analyss Here we provde equatons used to compute the ndvdual and combned relatve standard uncertanty for the Hg vapor mass concentraton reported n the man artcle. The resultng contrbutons wth a descrpton of the uncertanty terms are tabulated n Table S4.I. Least-squares analyss of the measured spectra (usng equatons 1,3 and 6 of man artcle) yelded the product, m nhg A1l as a ft parameter along wth ts assocated ft uncertanty. The values of sotopc abundance, and temperature T were kept fxed durng a gven data spectrum ft analyss. For the sotopc abundance, the ft nput value was set to the terrestral natural abundance and for temperature the nput was set to ts measured value durng the spectral scan. In ths fashon, the m value s computed for each spectral scan and ts varablty across the measurement dataset obtaned. The value of n Hg s subsequently calculated for each m value usng the known path length, l and spontaneous emsson Ensten coeffcent, A value. 1 Both path length and spontaneous coeffcent have uncertantes (Type B) whch wll contrbute to the uncertanty n n derved from m. The ft parameter m for each spectrum requres knowledge of and T as ndcated above. However, both and T have uncertantes that wll nfluence the value of the spectral ft S-7

8 parameter m and hence the derved value of n. In addton, the uncertanty n temperature wll contrbute to an uncertanty n n due to vapor pressure-temperature dependence. We therefore construct a combned uncertanty that ncludes the effect of A 1, m, T, l, usng propagaton of errors as, l 1 cal cal A1 m T T n n n m m n u( nhg ( T)) u ( ) u ( A ) u ( m) u ( ) u ( T) u ( T) l (S1) The senstvty of the ft parameter, m na1l to uncertanty n sotopc abundance, u( ), was estmated by computng ts values for varyng. The constrant of 1 was mposed. Here u( ) corresponds to the reported standard uncertantes n the terrestral natural sotopc abundance values of mercury. Ths analyss was found to produce m m A1, l u( )% = 0.. For fxed A 1, l values one gets the relatonshp m % n %. Hence the contrbuton of m A1, l n the sotopc abundance uncertanty to number densty values, n, derved from the ft parameter, m s n n A1, l = 0.. u( )% The senstvty of the ft parameter m to temperature was also evaluated. For ths the spectral fts were calculated to generate a seres of ft values of the quantty m as a functon of T. The m resultng contrbuton T u ( )% cal T m was found to be neglgble. Ths dependence reflects the S-8

9 senstvty to Doppler wdth to temperature. Here u cal refers to the Type B uncertanty n temperature assocated wth ts calbraton. The senstvty coeffcent n T s derved usng the Wagner-type equaton for the vapor pressure-temperature correlaton functon, ln p T pc T 6 c e a provded by Huber et al. and the 1 deal gas law relatonshp, p n kt B. Here a represents the vapor pressure correlaton functon ftted parameters, e represents the exponents wth values, T / Tc n whch Tc s the crtcal pont of mercury and k B s the Boltzmann constant. The resultng expresson for wrtten as n T can be n 1 p p T k T T T, (S) B where p p p ln T T pc 6 1 ae e (S3) 1 nt ( ) Ths analyss gves, T ( T )% = 8.14 % per unt Kelvn at T = K. The Type B nt ( ) n uncertanty n temperature that orgnates from calbraton source, T u cal ( T ) s used to calculate n the contrbuton of the uncertanty n n usng above senstvty relaton (Eq. S3). The contrbuton S-9

10 of the temperature data varablty to n s already ncluded n the spectral ft data varablty and s therefore not separately calculated. Table S4.I. The number densty combned standard relatve uncertanty budget. Row Contrbutng term Hg Hg-Ar Hg-N Type 1 Path length ( l ), ul () % l a Temperature, T (K), ut ( ) % T B dataset varablty A thermometer calbraton u ( T) cal % T B Combned u ( T) c % T 3 ua ( ) Ensten coeffcent, 1 % A1 4 Spectral ft m na l dataset varablty, 1 u( m) u( n) % % m n, A1, lconst 5 Spectral ft dependence on sotope abundance, ( m[ ]) u( ) % m[ ], estmated 6 Spectral ft dependence on T, 7 m T u ( )% c T m n Number densty dependence on T, T u cal ( T ) (%) n 8 combned standard relatve uncertanty, u ( n) c % n B A B A B a The contrbuton of temperature to the overall uncertanty s provded n rows 3 and 4 and s va the spectral ft dependence and number densty dependence, respectvely. The relatve combned uncertanty s obtaned by addng terms ndcated n rows 1,3-7 n quadrature. u ( n) c % n n row 8 S-10

11 Supportng Informaton References (1) Kramda, A. Journal of Research of the Natonal Insttute of Standards and Technology 011, 116, () Schwetzer, W. G. Journal of the Optcal Socety of Amerca 1963, 53, 1055-&. (3) Btter, F. Appled Optcs 196, 1, (4) Almog, G.; Scholz, M.; Weber, W.; Leschng, P.; Kaenders, W.; Udem, T. Rev. Sc. Instrum. 015, 86, 5. (5) Callear, A. B.; Patrck, C. R.; Robb, J. C. Transactons of the Faraday Socety 1959, 55, (6) Grante, E. J.; Pennlne, H. W. Ind. Eng. Chem. Res. 00, 41, (7) Grante, E. J.; Pennlne, H. W.; Hoffman, J. S. Ind. Eng. Chem. Res. 1999, 38, S-11