UNITED STATES EPARTMENT OF CMMERCE

UBLICATION

National Bureau of Standards

Library, E-01 Admin. Bldg.

MAY 1 9 1970

NBS TECHNICAL NOTE 390

Far Infrared Absorption

in Liquefied Gases
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NBS TECHNICAL NOTE 390

ISSUED APRIL 1970

Nat. Bur. Stand. (U.S.), Tech. Note 390, 39 pages (April 1970)

CODEN: NBTNA

Far Infrared Absorption in Liquefied Gases

M. C. Jones

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

^*T °

F c

.

^rAU of *

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LIST OF FIGURES

page

Figure 1. Schematic Arrangement 3

Figure 2. Optical Dewar . 4

Figure 3. Absorption Cell-Quartz Windows. Path Length 5

Variable from 4. 1 mm to 25.4 mm

Figure 4. Absorption Cell-Polyethylene Windows. Path Length

32.5 mm. The Cell is Shown Inserted in the

Reflux Channel Yoke 6

Figure 5. Absorption Cell-Polyethylene Windows. Path Length

5 . 9 mm 8

Figure 6. Temperature Measurement and Control System. . 10

Figure 7. Schematic of Possible Paths Through a Typical

Absorption Cell 15

Figure 8. Far Infrared Absorption in Liquid HydrogenTranslational Band 22

Figure 9. Far Infrared Absorption in Liquid HydrogenRotational Band 24

Figure 10. Far Infrared Absorption in Liquid Nitrogen ... 25

Figure 11. Far Infrared Absorption in Liquid Oxygen .... 26

Figure 12. Far Infrared Absorption in Liquid Carbon Monoxide 30

Figure 13. Far Infrared Absorption in Liquid Methane .... 32
FAR INFRARED ABSORPTION IN LIQUEFIED GASES "

M. C. Jones

Cryogenics Division

Institute for Basic Standards, National Bureau of Standards

Boulder, Colorado

ABSTRACT

Experimental results are given for the absorption

coefficient of the liquids hydrogen (three para concentrations), nitrogen, oxygen, carbon monoxide, methane and

argon in the wavenumber range 20-Z50 cm" (40-500 |~lm).

In addition, data for liquid hydrogen are given at wave

numbers up to 600 cm" (16. 7 |~l m). The results are

discussed in terms of the induced dipole, and, in the

case of carbon monoxide, the permanent dipole. An

indication of the way in which the data may be employed

in calculations of thermal radiative transfer is made by

calculation of the modified Planck mean absorption

coefficient.

Key Words: Far infrared; absorption coefficient; liquefied

gases; hydrogen; nitrogen; oxygen; carbon monoxide; methane;

argon.

* This work was performed at the National Bureau of Standards

under the sponsorship of the National Aeronautics and Space

Administration. Space Nuclear Propulsion Office, Fund Transfer

R-45.

VI
1. INTRODUCTION

Absorption spectra of simple molecules in the far infrared are

generally related to rotational transitions. For transitions involving

permanent dipole moments the effect of increase of density is to broaden

the rotational lines. However, at sufficiently high densities absorption

also occurs in non-polar species where none had been apparent at low

densities. Such absorption is well known (e.g. Bosomworth and Gush,

1965) and is attributed to electric dipole moments induced on collision

by the quadrupole and higher multipole fields of neighboring molecules.

It is conveniently studied at liquid densities where path lengths of a few centimeters are sufficient for observation. Unfortunately, as with

other phenomena dependent on collisions none of the theory of induced

absorption is applicable at these densities so that the resulting spectra

do not yield molecular constants (e.g. quadrupole moments). Nevertheless, because the spectra result exclusively from the molecular

interactions of the liquid state it was felt that an exploratory investigation of several simple molecular species would be useful apart from the

value of such reference data as might result.

In this report we present the far infrared spectra of liquids

hydrogen (three different para-hydrogen concentrations), nitrogen,

oxygen, methane, and carbon monoxide. In addition, we have examined

liquid argon in our absorption cell and verified that within the uncertainty limits of our experiments it does not absorb. Since the work

involved the solution of several problems peculiar to this type of

measurement we give a fairly full account of experimental details

(sections 2 and 3). In section 4 the experimental results are presented

and discussed and in section 5 we indicate briefly the application of

the data in calculations of thermal radiative transfer.
2. EXPERIMENTAL

2. 1 The Spectrophotometer

The spectrophotometer could be used with conventional globar or

high pressure mercury lamp sources, crystal choppers, reststrahlen

and wire mesh reflection filters. The monochromator had an aperture

ratio of //3.8 and used Littrow mounted gratings in first order in a

single pass arrangement. The detector was a Golay cell. In all

measurements reported here the instrument was used in single beam

operation using a lock-in amplifier to drive a chart recorder with

reference signal taken from a breaker on the chopper drive (see figure

1.) For all measurements the instrument was kept purged with dry

nitrogen gas from a boiling liquid nitrogen reservoir.

2.2 Optical Dewar and Liquid Absorption Cells.

A special dewar, figure 2, was constructed to enable liquid

cells to be held at predetermined temperatures. In all experiments

liquid hydrogen was used as refrigerant in the inner container and a

liquid cell was attached at the lower end of the reflux tube — a thinwalled stainless steel tube passing through the refrigerant container.

Variable thermal conductance between the refrigerant and the liquid

cell could be obtained by variation of hydrogen gas pressure inside

the reflux tube. The liquid cell was surrounded by a nitrogen-temperature radiation shield except for holes to allow the passage of the

spectrophotometer beam. When liquid hydrogen was used as sample,

a second hydrogen-temperature shield attached to the refrigerant

bath was used. The outer vacuum jacket of the dewar was fitted with

1/8" thick polyethylene windows.

Two choices of window are available in the far infrared, namely:

crystal quartz and polyethylene. Polyethylene is desirable on account
1-a: or < LlJ X q o or

Q. oo

CC UJ

\- or co 1 Q< . o OH in z< or 02 UJ

l-

_i ^ o

or

U. o M

(J CO

0)u

bo
Liquid Hydrogen

Fill Tube

Liquid Nitrogen

Fill Tube

Ion Pump

Connection

Refrigerant Vents

'O" Ring Seal

Hydrogen Reflux

Tube

Radiation Shields

(Gold Plated)

Sample Fill Line

Polyethylene Window

Liquid Nitrogen

Liquid Hydrogen

"0" Ring Seal

Spectrophotometer Seal

Absorption Cell

Polyethylene Window

Figure 2. Optical Dewar.

4
REFLUX TUBE (3/4"0.D.)-y

FILL LINE

COMPRESSION

SPRING ASSEMBLY

CRYSTAL QUARTZ

WINDOWS (1/4"

THICK)

HEATER

GERMANIUM

RESISTANCE

THERMOMETER

REFLUX TUBE (3/4" CD.)

THERMOMETER LEAD

TEMPERING GROOVE

INDIUM GASKETINDIUM SEAL

Figure 3. Absorption Cell-Quartz Windows. Path Length

Variable from 4. 1 mm to 25. 4 mm.

/
UJo

I'A'A'A'A 1

B^BBssg

<D

>-l <u 2n £+-> i? C

Oh •-

XI . OJ

tfi +-> O co ^a £ •iH ^ ^ ^ £

<D

fl Xi

0)

W i—4>s U) X -h

O

m -" <u

<D

H

X ^ <D o O ^ >H Oh <D 1—1 i x: 0) 3 H u .

rt X

a ki

U

.2

a

X

-i-> E) d, lO i—

Jh .

<-H

O (M <u CO rO «

XI<•

0)^3

CUD h
of its wide spectral range as a window (0 to 600 cm ) and again on

account of the low reflectance loss at a polyethylene /vacuum interface

(about 5%). However, it is less satisfactory than quartz where window

rigidity is important. Our earlier attempts at making vacuum tight

low temperature liquid cells with polyethylene windows were, however,

unsuccessful due to its excessive shrinkage on cooling, and so experiments were begun using the cell of figure 3. This cell was fitted with

crystal quartz windows cut perpendicular to the x or y axes. Crystal

quartz is readily sealed using indium wire as a gasket material. However, we found that a spring load on the seal was required to maintain

the seal through temperature cycles. This was achieved by use of the

' U' cross section steel spring ring shown in the figure. With it a force

of 200 pounds was continually maintained against the window seal. The

path length of this cell could be changed from 12. 7 to 25. 4 mm by the

inclusion of the spacer shown. For an even shorter path length,

4. 1 mm, one window could be raised by including a spacer between

window and seat.

The cell of figure 3 was used for all experiments on liquids

nitrogen, oxygen, methane, carbon monoxide, and argon and some

preliminary runs with hydrogen. It had a usable wave number range

from to 250 cm and an almost constant reflectance of 15 percent

was measured at a vacuum/quartz interface in this range.

For measurements on liquid hydrogen, where much of the interest

is at wave numbers beyond 250 cm , we eventually designed a successful polyethylene window seal and this is embodied in the cell shown in

figure 4. This cell had a path length of 32. 5 mm and could be used

where the absorption coefficient was less than about 1 cm . The

polyethylene windows are forced over the drum forming the cell body

with vacuum grease as sealant. On cooling down, the outer flange
VACUUM GREASE

FILL LINE

POLYETHYLENE

WINDOWS

INDIUM

GASKET

RESISTANCE

THERMOMETER

Figure 5. Absorption Cell-Polyethylene Windows. Path Length

5.9 mm.
shrinks on to the drum forming an ever tighter seal. Whereas the

cell of figure 3 could be simply screwed to the end of the reflux tube, in

order to obtain low enough temperatures for hydrogen liquid samples in

this cell we found it necessary to extend the reflux tube in the form of

a channel around the cell. The cell body then simply slides into the

yoke formed by this channel. Thermal contact with the channel was

maintained by use of a zinc-oxide-filled silicone grease.

For short path lengths and higher pressures the design of figure

5 was used in which the same window sealing principle is embodied,

but now pressure in the cell acts to seal it further. This cell can also

be slid into the reflux channel yoke of figure 4. The path length was

5. 9 mm.

All cells were fitted with a single 1/8" diameter copper fill

line, a 40 Q heater and a well to receive a germanium resistance thermometer bulb. When liquid hydrogen was to be condensed into a cell,

the fill time was shortened considerably by routing the fill line down

through the reflux tube, thereby precooling the incoming gas before it entered the cell. For all other samples, the fill line remained on the

outside of the radiation shields.

2. 3 Thermometry and Temperature Control

Temperatures of the sample cells were measured with the

germanium resistance thermometer. This had received a manufacturer's calibration, but due to the irreproducibility of the resistance we checked it against temperatures obtained by measuring vapor

pressures of sample liquids in half filled cells. This was done with

liquids nitrogen methane and hydrogen. From our vapor pressure

determinations we feel that temperatures quoted are within 0. 1 K,

which is sufficient for these experiments.
i\—www\

STANDARD

RESISTOR

ABSORPTION

*/ CELL

V

v

7 x IOOO

DIGITAL

VOLTMETER

ANALOG

OUTPUT

V

SET POINT

ADJUSTMENT

NULL DETECTOR

Figure 6. Temperature Measurement and Control System.

10
Much more important than the absolute value of the temperature

itself when using quartz windows in the cell is the stability of the cell

temperature. The transmission of the quartz is quite temperature

sensitive above about 25 K so it is necessary to make transmission

measurements with cell empty and cell full at temperatures within

about 0.1 K of each other. With the control system shown schematically in figure 6, control within a few hundredths of a degree was

easily achieved. The same thermometer as is used to indicate temperature via the amplifier and digital voltmeter is also used to drive the

controller by making use of an isolated analog output of the digital

voltmeter.

2. 4 Liquid Samples

All samples, regardless of their origin were passed through a

synthetic zeolite bed at room temperature before entering the cell to

guard against possible moisture inclusion.

Normal hydrogen was obtained from a gas cylinder which was

known to have been filled several years previously with para-hydrogen

from storage boil-off gas. Such cylinders are known to be as pure as

the best commercial high purity hydrogen.

Para-hydrogen was obtained from the boil-off of our refrigerant.

Its composition was found with a thermal conductivity analyzer to be

identical to samples which had been prepared by passing normal

hydrogen over an iron oxide catalyst at 20 K and is therefore considered

to be essentially equilibrium hydrogen at 20 K, i.e., 99.8 percent

parahydrogen.

An intermediate concentration of parahydrogen was obtained by

passing normal hydrogen through an iron oxide catalyst held in a

liquid nitrogen bath. This method produced a composition which varied

11
somewhat with flow rate as determined on the thermal conductivityanalyzer. At the flow rates used in filling our liquid cell a composition of from 44 to 48 percent parahydrogen was indicated.

Nitrogen was obtained as boil-off gas from commercial liquid

for which the manufacturers analysis showed a typical purity of

99, 997 percent.

Oxygen, methane, carbon monoxide, and argon were all obtained

from cylinders with manufacturers purity specifications of 99. 5,

99.95, 99.5, and 99.996 percent respectively.

2. 5 Experimental Procedure

Prior to taking data, the dewar was placed in the spectrophotometer and with all power on the assembly was allowed to reach steady

operating conditions.

With the absorption cell evacuated and cooled down to the

required temperature, the transmitted signal was recorded for each

of about 8 frequencies. At each frequency the signal was recorded

when steady for up to five minutes with suitable filtering (up to a time

constant of 100 sees). After this the sample gas was admitted to the

cell and condensed in. This process was monitored by both gas flow

rate and by continuously recording the signal at a particular frequency;

the signal reduced until the beam became completely submerged.

When gas flow had stopped the cell was returned to its original

temperature and the signal recorded again at each of the chosen

frequencies. On conclusion, the cell was evacuated and again returned

to its original temperature to check the original cell empty readings.

Readings were repeated unless the cell empty readings agreed to

within 2 percent.

12
Finally, at each of the amplifier gain settings used, the signal

was recorded with the spectrophotometer slit closed. This was necessary due to the tendency of the Golay cell to pick up mechanical vibration from the chopper and breakers, which being in constant phase

relation to the light signal, appear as a false signal. The resulting

offset from the recorder zero is thus a function of the amplifier gain

setting.

3. RESULTS

3. 1 Data Reduction

In deriving the absorption coefficient, a , from the recorded

signals one must take into account the phenomenon of dielectric mismatch at the window /liquid and window/vacuum interfaces and the resulting multiple reflections between pairs of parallel interfaces. In

our case the multiple reflections would not give rise to observable interference effects as may easily be shown.

The resonant condition for parallel interfaces separated by a

distance d is

mX

d

2

where m is an integer and X the wavelength. For adjacent resonant

wavelengths

1 V \ ) 1 Am 2d

In our experiments the smallest value of d was about 3 mm, therefore

resonance separation A i—r- ) is about 1.6 cm at the most. Most of

the data reported here were taken with a spectral slit width approaching

10 cm so that each recorded signal represents an average of several

resonances and none would be observed.

13
The total intensity at the detector may be calculated by summing the intensities from every possible path through the cell. Referring

to figure & 7, let E.., and I. ., be the amplitude and intensity of an emergljk ijk b

ing ray from a path in which there were i double reflections inside the

first window, j double reflections between the windows and k double

reflections inside the second window. Let E and l„be the incident

amplitude and intensity respectively and let the amplitude transmission

coefficients be t for a vacuum/window interface, t _ for a window/

liquid interface and t and t the corresponding coefficients for the

reverse order of the media. With the same subscript notation r represents the appropriate amplitude reflection coefficient. Then for

a general ray the transmitted amplitude is

The contribution to the intensity from this ray is

2 2 / \2i2 4j .(2j+l)ff l 2 / \2k 2 ,,*

I =E t r r ) t r

J e t (r r t_ (2

ijk 01 V 10 12/ 12 21 21 ^ 12 10/ 10

The total intensity transmitted through the cell is obtained by summing

over i j and k from zero to infinity:

iT

= SE'£v«. (3)

i

j k iJ k

or

I t 2

t2

t 2

t 2 e^^ (4) T 01 12 21 10

I. /. 2 2W 4 -2ofJ&W. 2 2 °

V

1 - r iO

r i2)^ 1 - r 2i

e JC^'lo'l-Z

The transmittances T and reflectances R at the interfaces can now

be introduced and related to the transmission coefficients via the refractive

indeces, n, as follows:

14
Et.It

EOOO

VACUUM WINDOW

(0) (!)

LIQUID WINDOW VACUUM

(2) (I) (0)

Figure 7. Schematic of Possible Paths Through a Typical

Absorption Cell.

15
^t2

01 n 01

n

12

2

t 2

n 12

(5)

n

i 2

2 1 = —— t

i n

2

21

Whereas for the reflectances

2

10

-°-t2

n 10

R

10 10

R n = r „ etc.

12 12

(6)

We note also that T

01

1-R etc. The refractive index ratios all

cancel upon substitution of (5) and (6) into (4) giving

•oiJl T

1-R.

10

2

\

2

1 - R

i 2 )

e

1 - R

io

R

12)

2 1-R^e'

(7)

The corresponding transmitted intensity I' for the evacuated cell is

immediately obtained from (7) on replacing the subscript 2 by giving

\4

I'T

1-R

10

2 \2 / 2

1 " R

io) ^^lO

(8)

On dividing (7) by (8) and taking logarithms

oi = In

>-*

12)

2 Ko)2

(^o

1-R

10

UR

10

R

12 W»^J

)

+ In

T

An approximation to (9) differing in cases of interest by about l%is

the following

I / \2 / 7. \ C

I

1 1

01 = T i 1-R i9 )

2

(l-R

2

12/ V 10

1-R

TO

1 - R

io

R

i 2 ;

+ In

T

L

9)

(io;

16
This formula was used in the reduction of data. Its suitability was

checked by comparing the resulting absorption coefficient of liquid

nitrogen with that obtained from data at two different path lengths. In

this case, for path length I we have from equations (7) and (8)

2 2 2

i^ , U-R o ) U-R U-R n e T, 1 V 12/ \ 10/ V 10

"'-I KJK^'IW

Similarly, for path length 2

(11)

I'm -, 2 N 2

I.

T, 2

R

2

„e2Q^yi-R

10 10

On dividing (11) by (12)

I_ I-_. .... U-H?.." 20

^

T, 1 T, 2 —cv (Ai-j&2 ) _V 12 / (13)

I'm , I , /\ o

2 -2tfAA T,l T,2 ^1-R

i2

e

Again, the quotient on the right hand side of equation (13) is very close

to unity regardless of the value of <y so that, in this case, the data reduction formula would be

\ h

l T,l T,2

The absorption coefficient of liquid nitrogen was calculated

from equation (10) for data from a path length of 25.4 mm and from

equation (14) for data from path lengths of 25.4 mm and 4. 1 mm. With

17
the absorption coefficient reaching a maximum value of 1. 1cm ~* a

-1 maximum discrepancy of 0.03 cm resulted between the two methods.

This was considered to be within experimental error and so the less

tedious approach of measurement at a single path length was adopted

for all other liquids. It may be appreciated that any error involved

is of less consequence with polyethylene windows with their lower

refractive index than with quartz.

In order to use equation (10) data were required for the various

reflectances involved. The reflectance of the quartz windows in a vacuum was measured in a separate apparatus at liquid nitrogen temperature; the reflectance of high density polyethylene was calculated from

published figures (MIT, 1957) for the dielectric constant using the

Fresnel equation for normal incidence. Since polyethylene, like quartz,

has a low absorption coefficient throughout the far infrared it is sufficient to use microwave measurements of the dielectric constant, e , and

to assume a frequency independent refractive index. However a correction must be made for low temperatures on account of the large temperature dependence of density (Corruccini and Gniewek, 1961). This

was done assuming invariance of the Clausius-Mossotti function,

e - 1 1 • — , with changes in density.

e + 2 p

To calculate the reflectance at a window/liquid interface, it is

necessary to know the relative refractive index of the window material

to the liquid. Again the absolute refractive index of all liquids measured could be obtained from published values of the microwave or d.c.

dielectric constant (Stewart, 1 964; Guillien, 1938; Werner and Keesom,

1926; van Itterbeek and Spaepen, 1943; and McLennan, et al. , 1930)

since these are all weakly absorbing materials. The absolute refractive index of the quartz was calculated from its reflectance while

that for polyethylene we already had from its dielectric constant.
3. 2 Errors

Systematic errors in calculating the absorption coefficient

arise from non-linearity of the detector -amplifier- recorder system,

from scattered light, and from errors in path length measurement.

Non-linearity has been checked and found to be within 0. 3 percent.

Scattered light is a function of frequency and can best be checked by

measuring the transmitted signal of a sample at a frequency where

complete extinction is known to occur. However, a randomly selected

test frequency does not exhaust the possibilities for scattered light.

Some indication of scattered light was available from two of

our experimental runs in which complete extinction occurred. In the

first, parahydrogen gave complete extinction at 390 cm in a path

length of 32. 5 mm. At this frequency, the signal could not be distinguished from that with slits closed and the scattered light is therefore

estimated to be less than 0. 3 percent. However, because of the width

of the parahydrogen absorption peak, this figure conservatively only

applies to that component of the scattered light arising from incomplete

filtering of higher order radiation, i.e., radiation of higher frequencies

reflected by the grating in second and higher orders.

A second run in which complete extinction occurred was with

liquid methane in the frequency range 70 to 250 cm in a path length

of 25. 4 mm. In this range scattered light was generally less than 1 percent although an occassional point as bad as 6 percent appeared.

Again this was a very broad (~ 200 cm ) band and conclusions must

be conservatively limited to higher order radiation.

Our findings are in general agreement with the manufacturer' s

specifications which state that scattered light is less than 1 percent

between 32 and 665 cm except in the region 165 to 200 cm where

it approaches but does not exceed 4 percent. Between 20 and 32 cm

19
the manufacturer gives an upper limit of 10 percent.

Path length measurements were made at room temperature with

the aid of a micrometer. The major uncertainties in path length arise

from shrinkage on cooling down to sample temperature and from the

fact that, being in a converging-diverging beam, the infrared rays do

not in general follow an axial path through the cell. The total uncertainty in path length from these causes is considered to be less than 1 percent.

Random errors in the recorded signal are by far the more

serious. The situation was aggravated by the long period between

recording signals with cell empty and cell full, usually as long as

- 1 1-1/2 hours. In the frequency region above 32 cm , fluctuations in

the signal of about ± 2 percent occurred in a period of five to ten

minutes. Below 32 cm fluctuations were often as great as 20 percent.

It is normally not possible to average such long term fluctuations.

For all points where absorption did not exceed 50 percent the

combined errors amount to 7 percent in the absorption coefficient calculated from equation (4) for frequencies above 32 cm . Below

32 cm the data must be regarded as of qualitative interest only.

Unfortunately peak absorptions for nitrogen and hydrogen were recorded

as high as 90 percent in the path lengths available. In this case the

error is dominated by the scattered light problem, but an upper limit

of 15 percent can be set.

The experimental absorption coefficients are plotted against

wave number (reciprocal wavelength) in units of cm . Wave number

repeatability is estimated to be better than 1 cm . A recent check

of the manufacturers calibration of the gratings was made by recording

drum readings at which higher order images of the mercury green

line were incident on the exit slit of the monochromator. A worst

20
systematic error of 3 cm was recorded, while for most of the

spectrum it was less than 1 cm . The error is hardly significant

for the broad bands recorded here, particularly since the spectral slit

width was sometimes as high as 10 cm

4. DISCUSSION

The molecular species investigated in this work have one thing

in common: they are of zero or low polarity (carbon monoxide has

a small permanent electric dipoie moment; oxygen has an even smaller

magnetic dipoie moment. With these two exceptions they show no

infrared absorption spectra in the gaseous state at low pressures. At

higher pressures, say, of the order of 100 atmospheres, some of the

far infrared spectra observed are qualitatively similar to those observed

here (Bosomworth and Gush., 19&5) and it is fairly well established

that they have their origin in collision-induced dipoles. This has one

undesirable consequence: as with other properties dependent on collisions there is no theory applicable at densities encountered in the liquid

state. At this stage, therefore, a discussion must remain fairly

qualitative.

Our data for liquid hydrogen at wave numbers between 20 and

250 cm are new as are those for liquids oxygen, carbon monoxide

and methane. The far infrared spectrum of liquid nitrogen and that

part of the spectrum of liquid hydrogen above 300 cm have been

published previously (Stone and Williams, 1965 and Kiss, 1959).

4. 1 Liquid Hydrogen

The spectrum of liquid hydrogen is the most interesting since it consists of two distinct parts each of which is strongly dependent on

the ortho-para composition. The weak band below 250 cm (figure 8)

is discussed elsewhere (Jones, 19&9). It i s considered to be a

21
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translational band and its intensity is roughly linear with the concentration of ortho molecules in accordance with theory. Above 300 cm

(figure 9) is a strong band having a peak at 390 cm . This has been

identified previously as arising from the pure rotational transition

from the state J=0 to J=2 of the para molecules (Kiss 1959). We were

unfortunately not able to record the second maximum observed by Kiss

_ 1 at about 600 cm attributable to the ortho transition J=l-*3 since this

was the high frequency limit of our polyethylene windows.

The results of Kiss differ slightly from the present results.

While the J=0->2 band is of typically Lorentzian shape in our case — although somewhat asymmetric — Kiss's spectrum shows a pronounced shoulder close to the low density Raman frequency of 354 cm

(Stoicheff, 1957). Furthermore, Kiss also gives spectra for the solid

and then the shoulder becomes a very narrow line (< 4 cm width)

shifted only 1.2 cm from the Raman frequency. Apparently our

resolution was poorer and we were not able to show the two components

of this band, namely: a pure rotational line and a translational summation band according to Kiss.

A discrepancy also exists in the value of the maximum

absorption coefficient at 390 cm . For para-hydrogen our peak

absorption is some 40% higher while for normal hydrogen it is 30%

lower than Kiss's results. These discrepancies are well outside our

estimate of experimental uncertainty and remain unexplained.

4. 2 Liquid Nitrogen

Our spectrum for liquid nitrogen (figure 10) is quite similar to

that obtained by Stone and Williams differing only in the magnitude of

the peak absorption coefficient. The values of 1.08 and 1.66 cm

respectively differ by far more than the total uncertainty estimated

23
200 300 400 500

WAVE NUMBER , cm" 1 600

Figure 9« Far Infrared Absorption in Liquid HydrogenRotational Band.

24
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for our data. A possible explanation may lie in the difficulties mentioned by Stone and Williams in connection with the presence of ice

crystals in their liquid samples. We too encountered such difficulties

in earlier experiments which showed large absorption peaks at intervals

over the entire spectrum. We feel that in the present data this problem

has been entirely eliminated by the method of sample preparation

described above.

The band is quite similar to that observed for compressed nitrogen

gas (Bosomworth and Gush, 1965) for which a quadrupole-induced pure

rotational origin is fairly well accepted. The broad rotational lines

are more closely spaced than in the case of hydrogen (For the selection

rule AJ=2 these are 8.0 cm and 230 cm respectively) and a large

number of them are superimposed to form a continuous band.

Bearing in mind the low density limitations of existing theory

one can make a crude calculation of band shape based on the binary

absorption coefficient. To do this one superimposes individual

broadened lines of similar shape with relative intensities given, for

example, by the formula of Colpa and Ketelaar (1958). We have done

this using the asymmetric line shape suggested by Kiss and Welsh

(1959) with a half width at half intensity of 20 cm (Ketelaar and

Rettschnick, 1964). The calculated band does not give a good fit at

all frequencies but predicts the band maximum fairly well; we calculate

60 cm compared to about 65 cm from experiment.

4. 3 Liquid Oxygen

The spectrum of liquid oxygen, Figure 11, is quite similar to

that of liquid nitrogen. However, the peak absorption coefficient is

only 1/3 of that for nitrogen and the width of the band is greater. This

difference was also noted by Bosomworth and Gush (1965) for the compres

sed gases. They point out that the difference is related to the weaker

27
quadrupole moment of the oxygen molecule and the resultant weaker — 4

induced dipole moment. In Table I the quantity Qot/a is listed for

different molecules. Here Q is the quadrupole moment, (X the mean

polarizability and a the molecular diameter parameter of the LennardJones potential function. This quantity is a useful measure of the

induced dipole moment and the relative magnitudes of the absorption

coefficient in figures 10 and 11 are in accord.

An explanation is demanded by the presence of a permanent

magnetic dipole moment for oxygen, also listed in Table I. Rotational

spectra in this wavelength region have been observed in the low pressure

gas (Gebbie et al 1969) and attributed to magnetic dipole transitions.

From the value given in Table I one might expect the resulting absorption coefficient in the liquid to be even greater than that shown for

nitrogen in figure 10. But in fact these magnetic dipole rotational

transitions are "approximately forbidden" and the value of the magnetic

dipole itself does not tell the complete story; in order to observe them

Gebbie et al used a path length of 180 m and the pure oxygen gas pressure

was 3 atm. Assuming linearity of intensity with density the equivalent

liquid path would be about 600 mm compared to 25. 4 mm used here.

Thus the magnetic dipole transitions appear to give only a minor contribution in figure 11. Similarly, in Gebbie' s measurements the collision-induced transitions would have contributed only a minor part of

the intensity because this part varies as the square of the density.

An envelope was again calculated as for nitrogen, but here a half

width of 50 cm was required in order to obtain a maximum at the

observed frequency of 80 cm

28
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4. 4 Liquid Carbon Monoxide

The far infrared spectrum of liquid carbon monoxide, Figure 12,

is composed of a sharp peak superimposed on a diffuse background.

The carbon monoxide molecule is similar to the nitrogen molecule in

that it has the same mass and the same number of electrons. In fact

the molecular constants important in collision induced absorption are

also similar as seen from Table I. It is thus to be expected that the

spectra would also be similar, as indeed they are toward the higher

frequencies. The existence of a small permanent dipole moment for

CO, however, is considered to be the source of the only major difference: i.e., the sharp low frequency peak. However, even this

small permanent dipole moment is an order of magnitude larger than

the quadrupole -induced dipole and its effect should dominate that of

the induced dipole moment, This can be seen from Table I. On

account of this permanent dipole moment pure rotational absorption

must take place according to the selection rule A J= 1 in addition to

A J= 2 from the induced dipole. For this process, one can calculate

the relative intensities of the rotational lines (Herzberg, 1950) to find

the position of peak absorption. For liquid CO at 80. 9 K we find the

transition from J- 6 to J= 7 the most intense. The corresponding irequency is

figure 12.

27 cm in fair agreement with the value of 35 era from

4. 5 Liquid Methane

The spectrum for liquid methane is presented in figure 13.

Some comment on this spectrum is called for because the methane

molecule has neither permanent dipole nor quadrupole moment by

virtue of its tetrahedral symmetry. The lowest order multipole allowed by symmetry is the octopole and this has been calculated from theory

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32
and from experimental second virial coefficients (Spurling, et. al. , 1968). An order of magnitude estimate of the octopole-induced dipole

moment at the point of closest approach of two molecules can be made

— 5 from the quantity Oct, /a (see Table I). The results would lead one to

expect pure rotational absorption intensities comparable to those observed for nitrogen and thus we conclude that it is entirely feasible

that the spectrum arises primarily from collision octopole-induced

pure rotational transitions.

Since our measurements were completed the far infrared spectrum of compressed methane gas at room temperature has been published by Birnbaum and Rosenberg (1968) who have calculated the

octopole moment from their data. Their spectrum is similar in form

to ours but as would be expected for pure rotation at a higher temperature it is more intense and the maximum is at a higher frequency.

4.6 Liquid Argon

At wave numbers below 250 cm no significant difference could

be observed in the transmission through path lengths of 4. 1 mm and

25. 4 mm. We conclude that compared with the other five liquids

studied the absorption coefficient is negligible. This is in accord with

the findings of Kiss and Welsh (1959) for compressed noble gases at

room temperature and up to 180 atm. pressure and wave numbers

greater than 300 cm . It is also in accord with the theory of induced

absorption (Poll and van Kranendonk, 1961); no induced dipole can

result from the collision of identical noble gas atoms,

5. APPLICATIONS-ABSORPTION OF THERMAL RADIATION

From a practical point of view it is of interest to be able to

describe the absorption of thermal radiation in a liquid or dense vapor.

Unfortunately this becomes involved with system parameters related

33
to the sources of radiation. However to illustrate how this might be

done in a typical case we calculate here the modified Planck mean

absorption coefficient (Sparrow and Cess, 1966) defined as

J

a(n, T

p

) I b

(n, T) dn

K

p

(T F

, T) -

00 I

Ib

(n, T) dn

o

Here n is the wave number and I (n, T) is the black body spectral

intensity for temperature T. This quantity is the correct mean absorption coefficient in optically thin conditions for incident black body radiation of temperature T when the fluid is at temperature T . The quantity

r calculated when T = T_ is the Planck mean absorption coefficient and F

is seen to be a property of the fluid alone; i. e. , contains no system

parameters, However, this quantity is only of interest in emission,

and, in the present, case at low temperatures is of little use. The modified coefficient as defined here contains only one system parameter, T.

For a typical problem we take T = 300 K and calculate

K (20 K, 300 K) for liquids para and normal hydrogen. To do this

with the data of figures 7 and 8 it is necessary to make an extrapolation on the high frequency side. We have determined that the high

frequency side of the para-hydrogen J=0 line is representable by the

Lorentz line profile within experimental error as has been observed

frequently in connection with rotational lines. Thus we have extrapolated using the relation

b a

, , max

a (n) =

2 2

(n - n ) + b

o

34
where a is the maximum value of the absorption coefficient at the

max

line center, n , and b is the half width (86 cm ). For normal

o hydrogen we have had to estimate a for the J= 1 line, the peak max

of which was not observable in our experiments. We have taken the

same ratio for the J= 1 line to the J= line as observed by Kiss, i. e„ , 1.88:1. The integrals were evaluated numerically and were carried

to a high enough wave number that the residual contribution became

negligible.

For para-hydrogen we calculate K = 0. 53 cm and for normal

-1

hydrogen K - 0. 40 cm „ Thus for para-hydrogen 63% of the radiation

is absorbed in a path length of 1.9 cm, while for normal hydrogen the

same absorption occurs in a path length of 2. 5 cm. It will be appreciated that for oxygen, nitrogen and carbon monoxide absorption of

thermal radiation will be considerably less since only a narrow wave

number region is covered by the observed spectra. Liquid methane

on the other hand would appear to be an intermediate case. It is interesting to note that the fundamental band of liquid hydrogen in the

range 4000 - 5000 cm only accounts for at most 3 parts per million

of the 300 K black body radiation and is thus of negligible importance

in radiative transfer from such a source compared to the far infrared

band described here.

6. CONCLUSIONS

We have measured the far infrared absorption coefficient of six

cryogenic liquids at temperatures close to their normal boiling temperatures. A variety of behavior was found which could be mostly related

to the molecular constants which determine the induced electric dipole

moment. No theoretical relationship is available to calculate the

absorption coefficient at liquid densities, but the data as such should

be useful in applications such as the calculation of absorption of thermal

35
radiation. As an example of this the modified Planck mean absorption

coefficient was calculated for normal and para-hydrogen and a 300 K

source.

7. ACKNOWLEDGMENTS

The work on hydrogen was sponsored by the National Aeronautics and Space Administration, Space Nuclear Propulsion Office,

under contract R-45.

The assistance of Patricia J. Giarratano is gratefully acknowledged for her help with the experiments and with data reduction. The

loyal assistance of F. W. Windmoeller was also greatly appreciated.

36
8. REFERENCES

Birnbaum, G. and A . Rosenberg (1968), Collision induced absorption

in gaseous CH and CD in the far infrared region, Physics

Letters 27A , no. 5, 272-273.

Bosomworth, D. R. and H. P. Gush (1965), Collision-induced absorption of compressed gases in the far infrared, Part II, Canadian

Journal of Physics 43, 751-769.

Colpa, J. P. and J. A. A. Ketelaar (1958), The pressure-induced

rotational absorption spectrum of hydrogen: II, Molecular Physics

1_, 343-357.

Corruccini, R. J. and J. J c Gniewek (1961), Thermal expansion of

technical solids at low temperatures, National Bureau of Standards

Monograph 29, p. 14.

Guillien, R. (1938), Sur la variation de la constante dielectrique a la

solidification des liquides homopolaires, Comptes Rondues 207,

393-395.

Gebbie, H. A., W. J. Burroughs and G„ R. Bird (1969), Magnetic

dipole rotation spectrum of oxygen, Proc. Roy. Soc. A. 310,

579-590.

Gush, H. P., W. F. J. Hare, E. J. Allin, and H. L. Welsh (I960),

The infrared fundamental band of liquid and solid hydrogen,

Canadian Journal of Physics 38, 176-193.

Herzberg, G. (1950), Molecular spectra and molecular structure, I. Spectra of diatomic molecules. (D. Van Nostrand Co. , Inc. , Princeton, New Jersey).

Hirschfelder, J. A., C. F. Curtiss, and R . B. Bird (1954), Molecular theory of gases and liquids (John Wiley and Sons, Inc. , New York, N. Y.), pp. 1028, 1110, and 1111.

37
Jones, M. C, Far infrared absorption in liquid hydrogen, Journal

of Chemical Physics 51, no. 9, 3833-3834.

Ketelaar, J. A. A. and R . P. H. Rettschnick ( 1964), The quadrupole

moment of nitrogen deduced from the pressure-induced rotational

spectrum of nitrogen, Molecular Physics 7, 191-193.

Kiss, Z. J., and H. L. Welsh (1959), The pressure-induced rotational

absorption spectrum of hydrogen, II. Analysis of the absorption

profile, Canadian Journal of Physics 37, 1249-1259.

Kiss, Z. J., and H. L. Welsh (1959), Pressure-induced infrared

absorption of mixtures of rare gases, Physical Review Letters

2, no. 4, 166-168.

Kiss, Z. J. (1959), The rotational absorption spectrum of hydrogen,

thesis submitted for the degree of Doctor of Philosophy, University of Toronto, Toronto, Canada.

Tables of dielectric materials Vol. 5, Technical Report 119, (April

1957) Laboratory for Insulation Research, Massachusetts

Institute of Technology.

Mc Lennan, J. D. , R. C. Jacobsen, and J. O. Wilhelm (1930),

Dielectric constants of liquefied gases, Transactions of the Royal

Society (Canada) 24, 37-46.

Nelson, R. D. , D. R. Lide, and A. A. Marryott ( 1967), Selected

values of electric dipole moments for molecules in the gas phase,

National Standard Reference Data Series — National Bureau of

Standards 10. p. 15.

Poll, J. D. , and J. van Kranendonk ( 1961), Theory of translational

absorption in gases, Canadian Journal of Physics 39, 189-204.

38
Sparrow, E, M„ , and R. D. Cess (1966), Radiation heat transfer,

(Brooks/ Cole Publishing Co. Belmont, California).

Spurling, T. H. , A. G. DeRocco, and T. S. Storvida ( 1968), Intermolecular Forces in Globular Molecules, VI. Octopole Moments

of Tetrahedral Molecules, Journal of Chemical Physics 48,

1006-1008.

Stewart, J. W. (1964), The dielectric polarizability of fluid parahydrogen, Journal of Chemical Physics 40, 3297.

Stoicheff, B. P. (1957), High resolution Raman spectroscopy of gases

IX. Spectra of H , HD and D . Canadian Journal of Physics 35,

730-741.

Stone, N. B. W. and D. Williams (1965), Far infrared absorption in

liquid nitrogen, Molecular Physics 10, 85-86.

van Itterbeek, A. and J. Spaepen (1943), Mesures sur la constante

dielectrique de quelques gas non polaires (H_, D», He, O , et

l'air) et CO entre la temperature ordinaire at 20°Abs., Physica

1_0, 173-184.

van Kranendonk, J. and Z. J. Kiss (1959), Theory of the pressureinduced rotational spectrum of hydrogen, Canadian Journal of

Physics _37, 1187-1198.

Werner, W. , and W. H. Keesom (1926), The variation of the dielectric

constant of liquid oxygen with temperature, Verslag. Afdeel.

Naturk. Kon. Akad. Wetenschap. Amsterdam 35, 18-25.

39 GPO 857 - 506
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