Total Absorptance of Water Vapor in the Near Infrared

Darrell E. Burch, Wilbur L. France, and Dudley Williams

The total absorptance f A(v)dv of water vapor in the vicinity of its vibration-rotation bands near 53323700, and 1595 cm-' has been determined as a function of absorber concentration w and equivalentpressure Pe for pure water vapor samples and samples of water vapor mixed with nitrogen. The presentresults, together with previously published results of Howard, Burch, and Williams, are presented ingraphical form; logarithmic plots give f A(v)dp for various values of Pe as a function of absorber con-centration w. These plots may be used in estimating total absorptance of water vapor in any samplefor which w and P, are known, and they may be applied in atmospheric studies.

The present paper is the fourth in a series of papers'-'dealing with the total infrared absorptance f A ()dvof atmospheric gases as a function of absorber concen-tration w and equivalent pressure P. The generalexperimental methods and the symbols and nomencla-ture employed were introduced in the first paper in theseries and in a still earlier paper on line broadening inthe infrared.4 The study of water vapor described inthe present paper was undertaken with a view to sup-plementing the previous work of Howard, Burch, andWilliams5 (HBW) and a still earlier investigation byChapman and Howard.6 The present work representsan advance over the previous studies of water vaporin view of (i) the use of improved optical and electronicequipment to give higher signal-to-noise ratios andhigher spectral resolution, (ii) a more reliable methodof determining absorber concentrations, and (iii) theuse of an improved method of taking account of theself-broadening effects of water vapor.4

Experimental Methods

The major vibration-rotation bands of water vaporin the near infrared are the combination band V2 + 3

at 5332 cm-', the 3 and v1 fundamentals near 3700cm-', and the v2 fundamental at 1595 cm-1. Al-

The authors were at the Laboratory of Molecular Spectroscopyand Infrared Studies, Department of Physics and Astronomy,The Ohio State University. Darrell E. Burch was a GeneralMotors Postdoctoral Research Fellow during the major portionof this investigation. Present address: Aeronutronic, Divisionof Ford Motor Company, Newport Beach, California.

Received 2 February 1962.This work was supported in part by Geophysics Research

Directorate, Air Force Cambridge Research Laboratories.

though the centers of the 3 and i bands occur, respec-tively, at 3756 cm-' and 3652 cm-', for the purposesof the present study these two overlapping bands arecalled the 3700 cm-' band; absorptance of the muchweaker band 2 2 at 3151 cm-' was measured but isnot included in the present analysis of total absorptance.

The major bands were studied by means of a Perkin-Elmer Model 99 spectrometer mounted in a vacuumtank to eliminate spurious effects due to atmosphericwater vapor and carbon dioxide; a LiF prism was usedfor the 5332 and 3700 cm-' bands and a NaCl prismfor the 1595 cm-' band. A Reeder thermocouple wasemployed as a detector for all bands. The use of amultiple-traversal cell designed to fill the spectrometeroptics provided absorption path lengths of 6 to 48meters; this range of path lengths is approximately thesame as that used by Chapman and Howard but isconsiderably less than the range 88 to 1408 meterscovered in the HBW work by means of a 22-metermultiple-traversal cell that was improperly matched tothe spectrometer optics. The temperature of the cellused in the present work was carefully monitored; pos-sible spurious effects due to slow temperature driftswere minimized.

Since water vapor is condensable, it is inappropriateto express absorber concentrations in atm cm at STPas in the case of the gases treated in the earlier papersin the present series. Water vapor concentrations wwill be expressed in precipitable centimeters (pr. cm),which gives the thickness of the layer of liquid waterthat would be formed if all water vapor in the absorp-tion path were condensed in a vessel having the samecross-sectional area as the cell. Values of w in pr. cmare numerically the same as if they were expressed ing/cm2. The relatively low saturated vapor pressures

June 1963 / Vol. 2, No. 6 / APPLIED OPTICS 585

of water at ambient temperatures together with uncer-tainties due to adsorption on the cell walls have pre-sented formidable difficulties to the accurate determina-tion of absorber concentrations in earlier studies; theinfluence of cell temperature variations and the influenceof the addition of nitrogen or other line broadening gaseshave introduced additional uncertainties.

When water vapor alone is in an absorption cell, itis possible to determine absorber concentration withsome certainty by measuring the pressure of the watervapor, since the absorber concentration is directlyproportional to the product of vapor pressure p andabsorption path length 1. In the absence of adsorption,it would also be possible to calculate absorber concentra-tion by allowing a known quantity of liquid water toevaporate into a previously well-evacuated absorptioncell of known volume, being careful to avoid condensa-tion; the vapor pressure p can be calculated onthe assumption that all the added water remains in thevapor phase with no adsorption. Experiments inthe present study showed that at ambient temperaturethe initial values of p as measured with a manometerwere 40 to 60% as great as the values calculated on thebasis of no adsorption; this result indicates that approx-imately one-half the water added was immediatelyadsorbed on the steel walls of the cell. If the samplewas left in the cell at constant temperature, the pressureas measured by the manometer was found to decreasegradually for several hours, a result showing that furtheradsorption occurred slowly before a final equilibriumvalue of p was attained. If the cell temperature wasthen increased, it was found that the measured valuesof p increased by an amount considerably greater thanthat to be expected on the basis of the gas laws; aconsiderable portion of the observed increase musttherefore be attributed to the desorption of water vaporaccompanying temperature increase.

Various coatings such as lacquer, glyptal varnish,and a thin layer of vacuum pump oil were applied to theinterior walls of the cell to reduce adsorption. Noneof these coatings seemed to change the effects of ad-sorption by a significant amount; however, more timewas required for the pressure to attain equilibrium andto "degas" the cell walls by evacuation when thesecoatings were used. Therefore, the cell was used withthe bare steel exposed; little differences in adsorptionwere observed for cell walls of freshly sand-blastedsteel and cell walls coated with a thin layer of "rust."It is possible that a porcelain or glass coating mighthave been desirable but would have involved consider-able expense not justified in view of the fact that a satis-factory method of monitoring water vapor pressure waseventually developed.

As indicated above, no serious problems in the de-termination of w ae encountered with pure samples ofwater vapor in the absorption cell since vapor pressure

can be monitored directly and continuously with amanometer. However, when nitrogen is added, thewater vapor pressure can no longer be measured directly.In the HBW work, it was assumed that, once an "equi-librium pressure" had been attained with water vaporalone in the cell, the addition of nitrogen would not dis-turb the equilibrium between adsorbed water and watervapor; in other words, that the nitrogen even at highpressures would neither displace adsorbed water norcause additional water to be adsorbed. The validity ofthis assumption has been questioned, and there hasbeen some speculation regarding the validity of certainof the HBW results for water vapor.

In the present study the partial pressure of watervapor, from which w can be calculated, was determinedby measuring the dew point of the sample in the absorp-tion cell. This was accomplished by means of a "well"consisting of a piece of Inconel tubing with its lowerend closed and with its upper end soldered to a holein the absorption cell wall. The Inconel well projectedapproximately 20 cm into the interior of the absorptioncell. Ether was placed in the well and nitrogen wasbubbled through until evaporative cooling reduced thewell temperature to the point at which the onset of con-densation on the external surface of the well occurred;condensation was observed through a small window inthe wall of the absorption cell. A thermometer im-mersed in the ether was used to determine the tempera-ture at which condensation began.

Turbulence in the ether produced by the nitrogenbubbles minimized temperature gradients in the ether;thermometer readings varied by not more than 4-0.1to 0.20C at various points in the ether. With slowcooling there was probably little difference in tempera-ture between the Inconel condensation surface and theether. However, the usual difficulties were encounteredin selecting proper criteria for the onset of true conden-sation; a light, fairly stable film appeared on the pol-ished surface at a temperature 0.20C above that atwhich continued condensation occurred. Experimentswith water vapor alone in the absorption cell indicatedthat the lower temperature corresponded more closelyto the true dew point; comparison of vapor pressuresgiven by dew point measurements with vapor pressuresmeasured by means of a manometer showed agreementto 2% for relatively high values of the dew point.It is believed that values of w based on dew point meas-urements in the present study are valid to 2% to43% for samples with dew points higher than 100C

and to 4t3% to 4% for samples having lower dewpoints.

In preparing samples consisting of water vapor andnitrogen, water vapor was first introduced into theevacuated cell by evaporation from liquid water,which had been admitted to a previously evacuatedsmall glass bulb. The water vapor passed through a

586 APPLIED OPTICS / Vol. 2, No. 6 / June 1963

ao

packless valve and a short piece of copper tubing; evap-oration was accelerated by gently heating the bulb andthe adjacent valve and tubing. The water vapor wasallowed to remain in the cell with the valve closed untiladsorption was "complete"; i.e., until for a constantcell temperature measured values of p no longer showedvariations. Various amounts of nitrogen were thenadded to produce total pressures P as high as one at-mosphere. Dew point measurements showed no ap-preciable variations in p as long as the cell temperatureremained constant. This result indicates that the addi-tion of nitrogen had no significant influence on watervapor adsorption. In order to detect possible slow vari-ations, samples were allowed to remain in the absorp-tion cell overnight without observable change in dewpoint or in total absorptance provided measurementswere made at the same temperatures.

Much of the present work was done during thesummer months when the ambient temperature of thelaboratory varied considerably during the day. Inview of the adsorption-desorption effects accompanyingtemperature variations, it was necessary to monitorthe partial pressure frequently during the course of arun by making dew point measurements.

In view of the present results, the HBW assumptionthat adsorption is not seriously influenced by the addi-tion of nitrogen would appear to be valid. Fortunately,most of the HBW measurements were made during aperiod of the year when the laboratory temperature didnot vary over wide ranges; their use of the massive22-meter absorption cell probably further minimizedtemperature variations, which the present study showedto give spurious effects. Comparison of the presenttotal absorptance results with those of HBW in similarranges of w and P, indicated that in general the two setsof data agreed within the limits of experimental error.

The data and results obtained in the present studyare presented in a manner similar to those used in theearlier papers in the present series except for the use of adifferent unit (pr. cm) for absorber concentrations.Some of the curves presented are based on both thepresent results and the HBW data. Values of equiva-lent pressure were calculated for each sample from therelation P, = P + 4p, where P is the total pressure andp is the partial pressure of water vapor. This relationis based on a value B = 5 for the self-broadening co-efficient of water vapor; the measured value4 B = 5i 1.5 is in fair agreement with values obtained in other

recent studies.7 -9 The "effective pressures" employedin the original HBW work correspond to an equivalentpressure based on B = 2, a value considerably lowerthan those obtained in more recent studies.

Experimental Results

Representative plots of spectral absorptance of watervapor in the vicinity of the 5332 cm-' band are shown

0

0F_

nrr0U)co

Li0LiJ0_

20

40

60

80

1005000 5400 5800

WAVENUMBER in cm-'Fig. 1. Spectral absorptance in the vicinity of the 5332 m-'band of water vapor. The effective slit width employed was

20 cm-'.

in Fig. 1; the values of w and P,, for each of the curvesare indicated in the figure. The effective slit widthemployed was 20 cm-'; forty-two runs for differentsamples were made during the present study. Theestimated uncertainties in values of f A (v)dv are i 6to ±8% for values of fA(v)dv greater than 50 cm-',and somewhat larger for smaller values of f A (v)dv.The accuracy of f A (v)dv for the other two bands isapproximately the same.

The curves in Fig. 2 give logarithmic plots of f A (Y)dvfor the 5332 cm-' band as a function of w for variousvalues of equivalent pressure. The curves in this figureare based on the 42 runs made in the present study,together with earlier HBW data; present results werein the range of small w and the HBW results were

1000l , , l l q ll'l'|0

H2

100

w in pr. cm

Fig. 2. Total absorptance f4A()dv of the 5332 cm-l band forvarious values of equivalent pressure Pc as a function of absorber

concentration .

June 1963 / Vol. 2, No. 6 / APPLIED OPTICS 587

0

chiefly in the range of large w. Over the small rangeof w in which the two sets of data overlapped, there wasagreement in corresponding values of f A (v)d to45 to 10% for most values of P,; this agreementis considered satisfactory in view of the estimated ex-perimental errors listed above; the agreement might beconsidered excellent in view of the fact that the rangeof overlap is the range in which the HBW values areleast accurate because the samples were smallest.Comparison of the present results with those obtainedin the early work of Chapman and Howard is muchless favorable; values of f A ()dv for similar samplesoften differed by as much as 20 or 30%.

0

20

40

60

80

20

40

60

80

1003000 3200 3600 4000

WAVENUMBER in cm-'Fig. 3. Spectral absorptance of water vapor in the vicinity ofthe strong bands near 3700 cm-'. The effective slit width was

approximately 10 cm-'.

In view of the improved experimental techniquesemployed in the present work, the present results weregiven "extra weight" in determining the positions andshapes of the curves shown in Fig. 2, which are believedto represent best all the data obtained in the present andin the HBW investigations. Values of f A (v)dv forgiven values of P, and w as given by the curves are be-lieved to be valid to ±46%. The same accuracy isestimated for the corresponding plots for the otherbands.

1000

400

E

co

100-

<5 40

l I I I I II I f I I I i I I -

P in mm Hc

760

_ 250

- 40

- 20

0.004 0.01 0.04 Cw inpr.c

k20 _

0.001

H

3700 cm-'

I1 0 I I,, 10 3. ).I 0.4 1,0 3,0~

m

Fig. 4. Total absorptance A(v)dv of the 3700cm-1 waterband for various values of equivalent pressure P as a function

of absorber concentration w.

Spectral absorptance records in the vicinity of the3700 cm-' band are shown in Fig. 3; values of w andP,, for each curve are indicated. The effective slitwidth employed was 10 cm-'. Forty-six "runs" weremade in the region of the 3700 cm-' band. The dashedvertical lines in the figure represent arbitrary bound-aries of "subregions"'; values of f A(V)dv for eachsubregion were tabulated for possible future use but arenot given in the present article. Total absorptance ofsamples having various values of P is plotted as afunction of w in the logarithmic plots of Fig. 4; theplotted values of f A (v)dV include all absorptance in the3340 to 4300 cm-' region but do not include the weak2

V2 band in the 2800 to 3340 cm-' region. The curvesin Fig. 4 give the best plot of present and HBW results.

Spectral absorptance curves in the vicinity of the1595 cm-' band of water vapor are shown in Fig. 5, inwhich values of w and P, are indicated; the spectralslit width employed was 6 cm-'. The dashed vertical

2: ~~~~~~~~~~~~~w in pr. cm

2 0 0.0_22

40 Pi mm HgZ - ~~~~~~~~~~~~~~~34.0

10

CIO0 1 20<0~

20 in in cm41~~~~~~~~~~~~~~~~~~004

I-~~~~~~~~~~~~~~~~~~~C

wa arit 6ii cm-'c

Fig 5.Seta bopa fwtrvp r in mme Hgint60 it 34.0naena t195c-.Te fetv si it

was approximately 6 cm - 1'C

588 APPLIED OPTICS / Vol. 2, No. 6 / June 1963

z0I-0

U)com

I-zLdJ00-

III

line at 1590 cm-' represents an arbitrary boundarybetween two subregions, for each of which fA(v)dvwas tabulated for possible future use. Plots of f A (v)dvfor the entire 1595 cm-' band for various values of Peas a function of w are shown in Fig. 6. As in the caseof the other bands, the curves in Fig. 6 represent thebest estimates that can be made on the basis of thepresent data-thirty-three runs-and the earlier HBWdata.

It is possible to develop empirical equations ex-pressing f A (v)dv in terms of Pe and w for each of thewater vapor bands studied. However, it is believed thatmore accurate estimates of the total absorptance to be

1000

400

lE

c 100

-.G

~5200.( 0.04 0.1

w in pr. cm

Fig. 6. Total absorptance fA(i')dv of the 1595 cm-' band forvarious values of equivalent pressure Pe as a function of absorber

concentration w.

expected for a sample of known w and P, can be obtainedby interpolation between the curves shown in Figs. 2,4, and 6 than by the use of empirical equations havinglimited ranges of validity. Extrapolations of the plotsin the figures to ranges of P,. and w not actually coveredin the experimental work should be avoided.

The authors wish to express their appreciation toJohn H. Shaw for his suggestions regarding theuse of dew point techniques for determining the partialpressures of water vapor, and to William Beard andJorgen W. Birkeland for their help during certainphases of the investigation. The use of library facilitiesof the Institut d'Astrophysique at the Universit deLiege during the preparation of the present paper isalso gratefully acknowledged.

References

1. D. E. Burch and D. Williams, Appl. Opt. 1, 473 (1962).2. D. E. Burch and D. Williams, Appl. Opt. 1, 587 (1962).3. D. E. Burch, D. A. Gryvnak, and D. Williams, A.ppl. Opt.

1, 759 (1962).4. D. E. Burch, E. B. Singleton, and D. Williams, A.ppl. Opt.

(in press).5. J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc.

Am. 46, 186, 237, 242, 334, 452 (1956).6. R. M. Chapman and J. N. Howard, J. Opt. Soc. Am. 42,

423, 856 (1952).7. C. H. Palmer, Jr., J. Opt. Soc. Am. 50, 1232 (1960).8. K. P. Vasilevskii and B. S. Neporant, Optics and Spectro-

scopy 7, 353 (1959).9. J. Izatt, Doctoral Dissertation, The Johns Hopkins Uni-

versity, 1960.

Books continued from page 584

Advances in Glass Technology. Compiled by the AMERICAN

CERAMIC SOCIETY. Plenum Press, New York, 1962. 639 pp.$21.00.

A bound book collecting all technical papers of the Sixth In-ternational Congress on Glass-the first to take place in theUnited States-was available to its participants at its startinghour. This great effort of volunteers did not only greatly facil-itate the preparation of a discussion in some depth of the selectedtopics of glass science and engineering presented, but has alsomade available to students, institutions, and industries an up-to-date cross section of information of reasonable coherence. Thiscoherence, it is true, is in part a consequence of necessary restric-tions due to the tremendous cost of simultaneous translationwhich, at least in this country, precludes parallel sessions in mostinstances. However, it certainly contributes greatly to thereading value of this book, which would not necessarily be ex-pected from the mere recording of a Glass Congress. (See alsopage 604 of this issue.)

The selected topics are balanced between fundamental, ap-plied, and engineering studies (48 in total). Major titles are:Structure, Diffusion Phenomena, Properties of New Glasses,Principles of Melting and Forming Processes, MechanicalProperties, and Glass Metal Interfaces. The present treatmentof glass structure has departed from classical techniques, such asx-ray diffraction, which has delivered by and large general andaverage structural features. The presentations at the Congressemphasize techniques that permit one to look at singularities

which affect structure and properties more than had been believedrecently: nuclear magnetic resonance, electron spin resonance,Rayleigh scattering, gamma-ray induced defect centers, dis-continuities in glass formation ranges. In all respects themethods of solid-state science that are applied to crystals havenow penetrated the investigation of noncrystalline solids. Inrelation to constitutional studies the investigation of diffusionphenomena has become significant enough to fill a separatesession. The understanding of the behavior of "water" or"dissolved protons" in glass has greatly increased. The newknowledge has benefited infrared applications as well as funda-mental problems. The behavior of helium, with a much smaller"chemical" relation to the glass structure, is described in con-trast. The diffusion of alkali (and, occasionally, Ag or Cu) inglass is the topic of numerous investigations because of its broadsignificance to phenomena as unrelated as electrical properties,dealkalization of surfaces, alkali vapor attack on special glasses,formation of color centers in filter glasses, etc.

A focus of attention at the meeting-and most likely on read-ing the book-is formed by the series of studies under the head-ing of properties of new glasses. In some papers-as in severalthat will, as "brief research announcements," follow in a secondvolume, together with the complete discussion of the papers inthis first volume-the practical value of the new uses has un-fortunately somewhat curtailed the depth of treatment. Never-theless, there will be enough to encourage the informed reader,to proceed in the development and conceptual analysis of the

June 1963 / Vol. 2, No. 6 / APPLIED OPTICS 589

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