Chemiluminescent reactions of group IIIb atoms with O2: Spectral simulations andextended energy dependenceD. M. Manos and J. M. Parson Citation: The Journal of Chemical Physics 69, 231 (1978); doi: 10.1063/1.436390 View online: http://dx.doi.org/10.1063/1.436390 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/69/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Chemiluminescent reactions of electronically excited alkaline earth atoms. II. Energy dependence inBa*+O2→BaO*+O J. Chem. Phys. 94, 4913 (1991); 10.1063/1.460576 Product vibrational distributions and collision energy dependence of chemiluminescent reactions of group IVAelements with O2, N2O, and NO2 J. Chem. Phys. 92, 4839 (1990); 10.1063/1.457701 Collision energy dependence of the chemiluminescent reaction: Ba+N2O→BaO+N2 J. Chem. Phys. 89, 1945 (1988); 10.1063/1.455092 Mechanisms of central Oatom abstraction reactions: A molecular beam, laserinduced fluorescence study ofGroup IIIB + ROH systems J. Chem. Phys. 68, 1794 (1978); 10.1063/1.435895 Crossed molecular beam study of chemiluminescent reactions of Group IIIb atoms with O2 J. Chem. Phys. 63, 3575 (1975); 10.1063/1.431798

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Chemiluminescent reactions of group Ilib atoms with O2:

Spectral simulations and extended energy dependence D. M. Manosa) and J. M. Parsonb)

Department of Chemistry, The Ohio State University, Columbus, Ohio 43210 (Received 14 March 1978)

Spectral simulations have been performed of visible chemiluminescence from crossed-molecular-beam reactions of La, Y, and Sc with O2, Experiments analyzed include previous thermal energy results, as well as new hyperthermal energy measurements using an 02/He seeded beam. The simulations allow more precise determinations of product monoxide vibrational energy distributions and also provide information on product rotational energy distributions. Previous indications of statistical behavior in the product energy distributions are confirmed. Deviations from the information-theoretic prior translational energy dependence of rate coefficients occur for the endoergic formation of YO(B 2~) and ScO(A 2II.

INTRODUCTION

In an earlier paper! (hereafter called Paper I), we de­scribed the energy disposal of chemiluminescent reac­tions of La, Y, and Sc and 02' In that paper we also re­ported on the effect of variation of reactant translation over a limited range. This paper reports on refine­ments and continuations of the original study. The anal­ysis of energy disposal has been improved by extensive computer simulation of the earlier chemiluminescent spectra and also of new spectra produced by using reac­tants at much higher collision energy. The dependence of the rate of formation of the various electroniC states on reactant collision energy has been studied at higher energies using heated, seeded supersonic nozzle meth­ods. Theoretical predictions based on statistical models have been compared to the experimental findings and show considerable agreement.

COMPUTER FITS OF SPECTRA

A detailed description of the computer calculations has been given, 2 and a recent paper3 describes the method as applied in the simulation of laser-induced-fluorescence spectra.

The spectra were forward simulated from assumed vibrational and rotational population distributions to yield line positions and intensities which were convoluted with measured instrument response functions. Succes­sive iterations, with improved population distributions, were performed to yield acceptable agreement between observed and calculated spectra. Line positions and in­tensities were calculated from formulae4 derived for the angular momentum coupling case intermediate to Hund's case (a) and case (b) for the II states of the molecules including A doubling. For these systems, the substant;al population of high rotational levels, where angular mo­mentum decoupling effects are large, renders these re­finements beyond the limiting case (a) formulae highly deSirable.

Initial estimates for the vibrational populations of the systems were obtained from the crude deconvolution

a1present address: Chemistry Department, The University of Toronto, Toronto, Ontario, Canada.

blAlfred P. Sloan Foundation Fellow.

methods of Paper I. The rotational population distribu­tions were assumed to be of the form pv(J ') =J '(1- J 'N)M, where J' =J /J"max, and J':n"" (for a given vibrational lev­el, v) is the maximum J value permitted by energy con­servation. This form was chosen for its high degree of flexibility and computational convenience. Because such simulations require substantial computer time it was not possible to average over the reactant energy distribu­tions. Instead, J':n"a~ was allowed to vary along with N and M to obtain fits to the data. The variation of J~ was required to be within reasonable limits of the J:;'~ specified by the nominal reaction exoergicity in Paper I; hence, J~ is a highly constrained parameter. This parameter, once optimized, then determined J':nox for all other vibrational levels via energy conservation. Hence the entire family of rotational distributions which is contained in the bivariate distribution density pv(J ') is represented by the three parameters N, M, J':n~. It was found that near the nominal exoergicity the simula­tions were only very weakly dependent on J~ within its constrained domain, and for our purposes the model can be safely considered as a two parameter fit (N, M). Iter­ations were continued for each of the chemiluminescent reaction systems until the best fit (in the mean) was achieved.

Figure 1 shows the results for the Y + 02 reaction at two different values of nominal reactant translational energy, 2.6 and 15.3 kcal/mol. The higher translation­al energy was obtained by heating and seeding the 02 in He, and was determined experimentally by methods de­scribed below. While the band shapes are well repro­duced, indicating a good choice of pv(J '), the locations of the band origins do not agree well. The more recent calculations of Liu and Parson3 use improved vibrational

_ constants which facilitate the comparison of the calcula­tion and the data. The results presented here are not adversely affected by this mismatch. Simulations of spectra from the other systems may be found in Ref. 2.

The vibrational population distributions obtained by this method are given in Table 1. When comparison is made with the distributions found by the deconvolution methods of Paper I, the differences observed are not large « 15%), indicating that the cruder methods can provide good estimates which are easily obtained.

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232 D. M. Manos and J. M. Parson: Chemiluminescent reactions of Group Illb atoms

( 0)

~~~~~~~ 5960 6000

(b)

6000

WAVELENGTH

FIG. 1. Chemiluminescence spectra for Y + O2 - YO(A 2m + O. Black dots are experimental pOints and lines are best-fit simu­lations. The nominal translational energy was 2.6 kcal/mol for spectrum (a) and 15.3 kcal/mol for spectrum (b).

The best-fit rotational parameters are given in Table n. In order to determine the range of values which

TABLE I. Vibrational population vectors from simulations.

System ~ conditions Pv

ScO A 2rrl/2 Pure, 280 K (0.753, 0.247)

5%, 1100 K (0.510, 0.204, 0.153, 0.133)

ScO A 2rr3/2 Pure, 280 K (0.677, 0.323)

5%, 1100 K (0.407, 0.291, 0.233, 0.070)

YO A 2rrl/2 Pure, 280 K (0.405, 0.360, 0.173, 0.054, 0.008)

5%, 1100 K (0.228, 0.192, 0.150, 0.124, 0.102, 0.070, 0.060, 0.036, 0.029, 0.008)

YO A 2rr3/2 Pure, 280 K (0.396, 0.334, 0.194, 0.074)

5%, 1100 K (0.225, 0.196, 0.187, 0.157, 0.114, 0.070, 0.036, 0.014)

LaO A 2rrl/2 Pure, 280 K (0.092, 0.091, 0.083, 0.075, 0.071, 0.071, 0.070, 0.068, 0.067,0.065)

LaO A 2n3/2 Pure, 280 K (0.099,0.098, 0.087, 0.079, 0.069, 0.069, 0.065, 0.063, 0.060)

LaO B 2~ Pure, 280 K (0.129, 0.138, 0.112, 0.109, 0.108, 0.107, 0.083, 0.074, 0.051, 0.031)

LaO C 2nl/2 Pure, 280 K (0.248, 0.223, 0.206, 0.122, 0.080, 0.048, 0.037, 0.021, 0.016)

TABLE II. Parameters of rotational and vibrational distribu-tions.

System 0, conditions JV"j) max N M T rot (v ~ 0) TVib

ScOA 'nil, Pure, 280 K 92 2 1430 1120 5%. 1100 K 116 0.5 8680 2050

ScOA 2n3/2 Pure, 280 K 90 1 2 .1340 1680 5%, 1100 K 115 1 0.5 8680 4440

YOA2nl/2 Pure, 280 K 135 1 2 2300 1700 5%, 1100 K 174 0.5 2 2200 4340

YOA 2n 3/2 Pure, 280 K 131 1 2 2200 3230 5%, 1100 K 171 0.5 2 2100 3040

LaOk2n1!2 Pure, 280 K 189 2 0.5 18020 21040

LaO A 'n3/2 Pure, 280 K 182 2 0.5 16710 17480

LaOB 2~ Pure, 280 K 150 2 0.33 13390 11350

LaO C 2n1!2 Pure, 280 K 201 2 4600 2980

would reproduce the observed spectra acceptably, the rotational parameters were varied one at a time about the values shown. These variations allowed the con­struction of a family of acceptable distributions whose spread indicates the uncertainty in the best-fit distribu­tion. Figure 2 shows typical distribution spreads deter­mined in this manner. The narrowness of the cross­hatched regions indicates that the rotational distributions represented by the best-fit parameters have a high con­fidence level.

DISCUSSION OF PRODUCT ENERGY DISTRIBUTIONS

The Vibrational distributions have been compared to two statistical models in Paper I, the information theo­retic "prior" model of Levine, Bernstein, and co-work­ers5 and the phase space theory of Light and co-work­ers.6 Since the refined vibrational distributions do not

SeO A-X LoO C-X

P(J)

LoO A-X YO A-X

J

FIG. 2. Uncertainties associated with the best-fit rotational distributions determined for four systems, which are typical of all of the systems simulated. Distributions chosen from within the cross-hatched bands will reproduce the observed spectra adequately.

J. Chern. Phys., Vol. 69, No.1, 1 July 1978

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D. M. Manos and J. M. Parson: Chemiluminescent reactions of Group III b atoms 233

0.6

0.2 , 2 SCO(A2TI y2 ) YO(A TI

(2)

, OA

, , 0.1 , ,

0.2

> 00 00 2 2 4 0.. 0.6 ,

YO(A~3 ) SCO(A2rr3 ) 0.2 , Vz 0.4

Y2 , \

\ \

0.1 0.2

~"n'~ 00 0

2 4 6 8 0 4 v

FIG. 3. Vibrational populations in YO A 2Ill/2 and A 2Ils/2 formed at a nominal translational energy of 15.3 kcal/mol, and ScO A 2Ill/2 and A 2IlS/2 formed at a nominal translational energy of 12.9 kcal/mol. Dashed lines give the convoluted predictions of the prior statistical model.

differ significantly from those presented in Paper I, the conclusion that the vibrational energy disposal agrees with statistical predictions stands unaltered. This con­clusion is also now found to hold for the reactions of Y + Oz and Sc + Oz at elevated nominal translational energies of 15.3 kcal/mol and 12.9 kcal/mol, respectively. Fig­ure 3 compares the experimental vibrational distributions for those conditions with the prior model, and shows generally good agreement. Averaging of the prior model predictions over the initial distributions of energy (trans­lational, vibrational, and electronic) has been incorpo­.rated as in Paper I.

The experimental rotational distributions were also compared with the averaged prior model predictions. Re ... sults are shown in Fig. 4 for the rotational distributions of ground vibrational states produced in the low ene rgy experiments. In accord with the vibrational results, the rotational distributions agree quite well with the statis­tical predictions. One notes that these reactions were studied unde r s ingle- collis ion conditions, and that the systems shown in Fig. 4 span a large range of exoer­gicity (- 5 to 36 kcal/mol). These results for the rota­tional distributions of electronically excited states con­trast with the restuls of Liu and Parson3 for the elec­tronic ground states of YO and ScO as determined by laser- induced fluorescence. Those authors found that the rotational distributions peaked Significantly lower than predicted by the prior model.

Although the systems studied were clearly not in equi­librium, we tested the utility of a Boltzmann distribu­tion for characterizing the distributions. The rotational temperature was chosen so as to match the peak posi­tion of the experimental distribution. In all cases, ex­cept for the LaO A zIT and B z~ states, the Boltzmann distributions agreed well with the observed distributions. In addition, a vibrational temperature was derived for each system by forcing a Boltzmann distribution for the observed populations. Table IT shows the derived rota-

tional and vibrational temperatures, and indicates that the vibrational temperatures are not in close agreement with the rotational temperatures. Note that these rota­tional temperatures apply only to the ground vibrational levels, and smaller values would be obtained if higher vibrational levels were considered because of the v de­pendence of J::'"" in the experimental distributions.

For the above systems it was possible to calculate the fraction of the total energy partitioned into the internal modes of the products for varying amounts of reactant translational energy. These fractions are given in Ta­ble ill along with the total energy available to the prod­ucts and the nominal reactant translational energy. It can be seen that large increases of reactant translation do not substantially change the fraction of energy chan­neled into product vibration. Polyanyi7 and his co-work­ers have shown that for direct reactions on single sur­faces increased reagent translation is preferentially channeled into product translation and rotation. The contrast here supports the earlier suggestion of indirect reaction on multiple surfaces.

EXTENDED TRANSLATIONAL ENERGY DEPENDENCE

Experimental

In order to characterize the seeded nozzle beams em­ployed in this study the apparatus described in Paper I was modified. The nozzle beam chamber was displaced 38 cm by the addition of a separately pumped cylindrical chamber to give an adequately long (62 cm) time-of­flight path. The nozzle beam was interrupted by a wheel, 13.5 cm in diameter, having six equally spread slots, 0.635 mm wide by 2. 54 mm long, on its outer edge. rhe whee I was driven by a variable speed motor at speeds

LaO <fn

250

FIG. 4. Comparison of best­fit rotational distributions (solid lines) to convoluted pre­dictions of the prior statistical model for five systems (dashed lines).

J. Chern. Phys., Vol. 69, No.1, 1 July 1978

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234 D. M. Manos and J. M. Parson: Chemiluminescent reactions of Group IIlb atoms

TABLE III. Fractions of energy channeled to various product modes.

Nom. ET (E avail) System ~ conditions (kcal/mol) <tv) <tR> <tT>

ScOA 2IIl/2 Pure, 280 K 2.8 -0.7 (1. 9)a (2.3) 5%, 1100 K 12.9 9.7 0.23 0.42 0.35

ScOA 2n3/2 Pure, 280 K 2.8 -1.0 (2.0) (2.2) 5%, 1100 K 12.9 9.4 0.26 0.43 0.31

YOA 2nl12 Pure, 280 K 2.6 9.8 0.20 0.36 0.44 5%, 1100 K 15.3 23.0 0.25 0.20 0.55

YO A 2II3/2 Pure, 280 K 2.6 8.6 0.24 0.38 0.38 5%, 1100 K 15.3 21.8 0.23 0.21 0.56

LaO A 2IIl/2 Pure, 280 K 2.5 43.6 0.29 0.21 0.50

LaO A 2II3/2 Pure, 280 K 2.5 41.1 0.30 0.20 0.50

LaOB2~ Pure, 280 K 2.5 28.7 0.25 0.22 0.53

LaO C 2IIl/2 Pure, 280 K 2.5 15.0 0.30 0.48 0.22

"Values shown in parentheses are actual product energies given for cases where the average energy available to products is negative.

up to 400 Hz. The resulting intensity against time pro­file was trapezoidal with a width of 3.5 fls for the high­est wheel speed employed. An Extranuclear quadrupole mass spectrometer was mounted 23 cm downstream of the collision zone on a translatable stage having :I: 25 mm of movement perpendicular to the beam axis. Additional collimating apertures were positioned to yield optimal beam profiles.

The signal from the mass spectrometer was routed through a PAR model 115 amplifier to a PAR model 164/ 162 boxcar averager, which was triggered synchronously by the wheel apertures. The net system time constant was less than 10 fls, which was fast enough to provide good time resolution for aU of the systems studied. An­alysis of the resulting intensity against time profiles was done by assuming the form for the nozzle velocity dis­tributions :

where a2 ", 2kT /{m[l + (y- 1)M 2/2]), y is the specific heat ratio, and M is the Mach number. For a pure gas u F

'" row(y /2) 1/2, and y and M were adjusted to fit the ob­served pure O2 distribution. Values found for 02 ex­panded from 350 torr at 280 K through a O. 15 mm noz­zle were y = 1. 4 and M = 10. For a seeded gas uF cannot be related to 'Y and M in general because of the occur­rence of slippage of the heavier molecule from the flow velocity of the lighter one, which ranged from 5% to 16% under our conditions. Hence uF was adjusted at each of four temperatures to fit the observed distributions, and values at intermediate temperatures were obtained by interpolation. With y", 1. 4, values of M obtained by fit­ting distributions for mixtures of 2%, 5%, 10%, 20%, and 40% O2 in helium were 18.5, 18.2, 16.0, 16.3, and 14.0, respectively. Calibrations of the method were made by repeated measurements using pure monatomic gases (He and Ar) in order to determine effective values for the flight path and detection delay.

In order to locate experimental pOints on a relative colliSion energy axis the nominal translational energy was defined as the center-of-mass system energy cor­responding to the velocities of maximum beam number density for both beams.

In addition to characterizing the parameters of the velocity distributions, the mass spectrometer was also used to monitor the O2 beam densities for all seeding conditions.

The method of study of translational energy dependence was similar to that previously employed. Time normal­ized emission intensities were recorded for approxi­mately 12 different temperatures in each of five mix­tures of 02 in helium (2%, 5%, 10%, 20%, and 40%). The relative rates were calculated in the manner described in Paper I, using number densities directly measured mass spectrometrically. The confidence level of the nominal energy axis is much higher than before, how­ever, since this was determined by actual measure­ment. The rates for each run were normalized so that each run represents an extension of the others over its energy range. The resulting curves are shown in Figs. 5, 6, and 7 for formation of LaO, YO, and ScO, re­spectively.

Discussion

The results are again compared to the predictions of the information theoretic "prior" model, convoluted over the initial energy distributions, as described in Paper I. In this model the rate coefficient is taken to be proportional to the density of product translational states, summed over all rotational states in the mea­sured vibrational level. The rate coeffiCient then has the nonphysical property that it increases without bound as the total energy increases. Despite this shortcoming the model works well for all of the exoergic reactions studied, as seen in Fig. 5 for formation of LaOA2

II1/ 2,

B 2~, and C 2II1/2' and in Fig. 6 for formation of YO

J. Chern. Phys., Vol. 69, No.1, 1 July 1978

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D. M. Manos and J. M. Parson: Chemiluminescent reactions of Group" I b atoms 235

10

5

... ~ e(

a:

... > ~ 4 e(

..J ... a:: 2

4

2

o

LaO c2.rr, ~2 ,

. ~.

.~.~ .

ET • keal/mol

FIG. 5. Translational energy dependence of the La+Oz chemi­luminescent reactions. The ground vibrational level was ob­served in each case. Solid lines give the predictions of the prior model.

A 2JI 1/2• In the endoergic reactions forming YO B 2~ and ScO A 2JI 1/2 , though, the prior model is seen to increase

... I-

30

~ 20

'" > l­e(

..J

'" cr 10

4

" .-/ .1 /

, ,

/ /

/ . "" '1

I'

2

°O~--~5~--~IO~--~15~---2~O ET• keal/mol

FIG. 6. Translational energy dependence of the Y=Oz chemi­luminescent reactions. The ground vibrational level was ob­served in each case. Solid lines give the predictions of the prior model. The dashed line gives the line-of-centers hard sphere model prediction.

'" l-e(

cr

40

:30

. .

'" 20 > /

/ /

/

~ <I

/ /

..J /

'" cr / I

'/

10

o~ __ ~ ____ ~ ____ ~ __ ~~ o 10 15 20

ET • keal/mol

FIG. 7. Translational ene rgy dependence of the reaction SC +Oz- ScO(A 2111/Z , v = 0) +0. The solid line gives the prior model prediction. The dashed line gives the line-of-centers hard sphere model prediction.

too rapidly at the highest energies attained (see Figs. 6 and 7). This discrepancy cannot be removed in either case by minor adjustments in the reaction endoergici­ties, as was found to give agreement for lower energy measurements of endoergic processes described in Pa­per I.

2

'" I- 0 <I a: 0

'" 0 > ~ . e( 0 ..J

'" a:

O~ __ -L __ ~ ____ ~ __ ~ __ ~

o ET • keal/ mol

FIG. 8. Translational energy dependence of the reaction Y +02-YOIA 2A3/2 , v=3 (open circles) and v=4 (closed circles») +0. The solid lines are predictions of the prior model, the lower prediction corresponding to v = 4.

J. Chern. Phys., Vol. 69, No.1, 1 July 1978

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236 D. M. Manos and J. M. Parson: Chemiluminescent reactions of Group IIlb atoms

Because of the deviations from the prior model, sev­eral other models for the translational energy depen­dence were also compared with the experimental results for the reactions forming YO B 2~ and Sc A 211 1/ 2, A line-of-centers hard sphere model was employed in which the cross section is proportional to 1 - I::.E l/ET ,

where I::.Ei is the endoergicity for reaction from initial internal state i and E T is the initial translational energy. Figures 6 and 7 give the predictions of this model which have been convoluted over the initial energy distributions Agreement with experiment is fair for YO B 2~ but poor for ScO A 211 1/ 2, which would require for agreement a larger threshold than indicated by thermochemical data. A step function form for the cross section at threshold gave worse agreement than the line-of-centers model for both reactions.

Phase space calculations, as employed in Paper I, were also carried out for the translational energy depen­dence in these reactions in order to test the importance of angular momentum conservation. The main change from the prior results was a tendency of the phase space curves to round off at the highest translational energies, in agreement with experiment. Because of extensive computation time for each energy, it was impractical to convolute the phase space results over the initial energy distributions for quantitative comparisons with experi­ment.

Chalek and Gole9 have precisely characterized the pre­viously unknown 21::. states of YO and ScO. The 21::._2~+ transitions are quite weak and poor signal statistics made the study of the energy dependence of the ScO 21::.

state impracticaL A limited range of energies were available in the case of Y02I::.S/2' however, and Fig. 8 shows the results for this system. Once again the con­voluted prior model yields good agreement with the data. This suggests that the dynamics governing the formation of this relatively long-lived state are quite similar to

those governing the higher lying, short-lived states. In Paper I we showed that if the 21::. state lay below the A 2fI, as is now known, the higher states would necessarily require nonadiabatic processes for their formation. In spite of the numerous constraints and complications such a multipliCity of crOSSings can engender, the dynamics of both the entrance and exit channels for all of the nu­merous electronic manifolds are well represented by a simple statistical model at low energies.

ACKNOWLEDGMENTS

We would like to acknowledge the Research Corpora­tion for partial support of this work. Computer time was provided by The Ohio State University Computation Center.

lD. M. Manos and J. M. Parson, J. Chern. Phys. 63, 3575 (1975).

2D• M. Manos, Ph.D. dissertation, The Ohio State University, 1976.

sK. Liu and J. M. Parson, J. Chern. Phys. 67, 1814 (1977). 4(a) I. Kovacs, Rotational Structure in the Spectra of Diatomic

Molecules (American Elsevier, New York, 1969); (b) R. S. Mulliken, Rev. Mod. Phys. 2, 60 (1931); ibid. 3, 89 (1331); (c) G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules (Van Nostrand, New York, 1950).

5See , for example, R. D. Levine and R. B. Bernstein, Acc. Chem. Res. 7, 383 (1974).

6J. C. Light, Faraday Discuss. Chern. Soc. 44, 14 (1967); P. Pechukas andJ. C. Light, J. Chem. Phys. 42, 3281 (1965); P. Pechukas, J. C. Light, and C. Rankin, J. Chem. Phys. 44, 794 (1966).

1J. C. Polanyi, Acc. Chern. Res. 5, 161 (1972). 8(a) J. A. Alcalay and E. L. Knuth, Rev. Sci. Instrum. 40,

438 (1969); (b) O. F. Hagena and A. K. Varrna, Rev. Sci. Instrurn. 39, 47 (1968); (d) w. s. Young, W. E. Rodgers, and E. L. Knuth, Rev. Sci. Instrum. 41, 380 (1970).

9C• L. Chalek and J. L. Gole, J. Chern. Phys. 611, 2845 (1976).

J. Chem. Phys., Vol. 69, No.1, 1 July 1978

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