Experimental verification that spectrometer signal is linear function of absorber partial pressure for pure gase

Rinehart, E. A.

English

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UNIVERSITY OF WYOMING 
DEPARTMENT OF PHYSICS 
Status Report 
on 
NASA Grant NGR 51-001-020 
f o r  the per iod 1 January 1967 t o  1 January 1969 
submi t t e d  by 
Edgar A. Rinehart 
In t roduct ion 
I t  was o r i g i n a l  l y  proposed t h a t  an experimental i nves t iga t ion  be made 
o f  Har r i  ngton ' s theory s f  Intensity measurements, and a c r i  t i c a l  study be 
undertaken t o  determine the sources o f  possib le instrumental e r ro rs .  The 
u l t ima te  aim o f  such studies being t ha t  o f  determining the necessary pro- 
cedures required t o  perform quan t i ta t i ve  analyses o f  po lar  gases i n  gaseous 
mixtures . 
Experimental Methods and Results 
I n  Figure 1 i s  shown a block diagram o f  the Hewlett-Packard R-8400 B 
Microwave Spectrometer purchased under t h i s  grant. The spectrometer i s  an 
i n - l i n e  type ra the r  than a br idge type. A c a l i b r a t i o n  arm i s  included f o r  
accurate measurements o f  A P the power absorbed by the gas due t o  a t ran- g ' 
s i  t i on .  This al lows the accurate determination o f  e i t h e r  the r defined by 
1 Harr i  ngton as : 
o r  the Beers Law i n t e n s i t y  coe f f i c i en t ,  y defined ( f o r  small yL) as: 
I n  the theory o f  saturated i n tens i t y  coe f f i c i en t s  developed by Harringtonl '2, 
the c o e f f i c i e n t  r i s  expressed as the product o f  two functions, r = r14, i n  
which on ly  the function 0 contains molecular- itlforntation, and the value o f  
' ~ a r r i n ~ t o n ,  H. W., J .  Chem. Phys. 46, 3698 (1967) 
' ~ a r r i n ~ t o n ,  H. W .  , J . Chem. Phys . 49, 3023 (1 968) 

+ may be varied by the variation of incident power, Po. The conclusion 
reached by ~ a r r i n ~ t o n '  is tha t  a curve of "Intensity" (here defined as spec- 
trometer signal) vs incident power will have the same shape independent of 
molecular species o r  specific transit ion. That t h i s  is indeed the case i s  
shown in Figure 2. Such curves are shown f o r  three transit ions i n  methanol, 
One may see that  a1 though the curves are  shifted i n  both maximum signals 
available, and i n  the power a t  which maximum signal i s  obtained, t he i r  shapes 
are the same. 
A comparison was then made of the saturation method and "constant 
crystal  current" method of the variation of signal with pressure of the 
absorbing gas, The resul ts  are  shown i n  Figure 3 fo r  the strong t ransi t ion 
i n  methanol a t  37703.72 LlHg. The constant crystal current curve was made 
under conditions of partial  saturation. A t  higher pressures, i n  accordance 
w i t h  the Van Vleck-Weiskopf l ine  shape theory, the signal will become constant 
with pressure. The data represented by the curve was obtained by saturating 
the t ransi t ion to  maximum signal fo r  each pressure. The pressures f o r  this 
and a l l  subsequent experiments were measured w i t h  an MKS Barytron manometer. 
The l inear i ty  of signal vs pressure is evident from the figure,  although 
the graph does not pass through the origin as predicted by Harrington's theory. 
A detailed examination of the spectrometer signal a t  very low pressures 
was then made. These resu l t s  fo r  two transi t ions in methanol a re  shown i n  
Figure 4. Both curves approach l inear i ty  below 1 mill i  t o r r  and above 
3.5 mtorr. The curvature i n  the region between 1.0 and 3.5 mtorr i s  believed 
to  be due to  the t ransi t ion between molecule-wall collision relaxation, and 
mol ecul e-molecule re1 axation processes. Further study of th i s  phenomenon i s  
in progress, 
' ~ a r r i n ~ t o n ,  H. W . ,  J .  Chem. Phys. 49 3023 (1968) 



U t i l i z a t i o n  o f  the l i n e a r i t y  of signal vs pressure o f  the absorber t o  
determine quan t i t y  o f  absorbing species present was attempted using these 
c a l i b r a t i o n  graphs. A small quan t i t y  of methanol was admitted t o  the absorp- 
t i o n  ce l l s ,  and was then d i l u t e d  wi th  a i r .  A measurement o f  the s ignal  f o r  
two t r ans i t i ons  should then produce a measure o f  the p a r t i a l  pressure o f  
methanol. This i s  depicted i n  Figure 5, where a remarkably close agreement 
i s  shown. For p a r t i a l  pressures lower than 5 mtorr,  however, the agreement 
was poor. It was noted emperical ly, t ha t  the apparent i n te rcep t  of the 
2 graph w i t h  the x-axis f o r  a d i l u t e  gas var ied as B = # Bo v~here Bo was the  
in te rcep t  o f  the extended graph fo r  a pure absorber, and N i s  the mole f r ac -  
t ion .  This emperical r u l e  was used i n  f u r t h e r  d i l u t i o n  experiments. The 
resu l t s ,  i n  Table I, demonstrate t h a t  t h i s  r u l e  does g ive se l f -cons is tent  
r esu l t s .  
TABLE I 
f4ETHANOL DILUTION EXPERIMENT 
PARTIAL PRESSURES (mTorr) 
From Cal i b .  Graph 2 Calculated (B=N Bo) Total  
RUN 
-- 
1 
r ,  
2 
3 
4 
5 
6 
6 1 
I. ITERATED .a0 
361 69 
4.22 
4.10 
3.31 
3.90 
4.46 
4.47 
37703 
4.09 
3.93 
3.02 
3.71 
4.29 
4.21 
I 
A 
- . I3  
-.I7 
-.29 
-. 19 
-. I7 
- .26 
361 69 
3.71 
3.55 
2.25 
3.23 
3.83 
3.75 
37703 
3.73 
3.54 
2.27 
3.24 
3.83 
A 
+. 02 
-.01 
t .02 
+.01 
-00 
12.60 
-. 
Press 
(mtorr ) 
3.70 
7.45 
7.60 
14.00 
8.60 
9.60 
-.05 
C 

However, since no sol  i d  theoret ica l  reasons have been developed as y e t  f o r  
t h i s  behavior, such a procedure cannot be considered r e l i a b l e .  I n  sp i t e  o f  
t h i s  lack of s o l i d  theoret ica l  resu l ts ,  an attempt was made t o  determine 
mole f rac t ions  of methanol i n  ethanol. Considerable time was spent i n  pro-  
v i d i  ng exceptional clean1 iness o f  the vacuum system, and i t  was found tha t  
the concentrat ion o f  methanol var ied w i t h  time w i th in  the absorption c e l l .  
This i s  apparently a problem o f  d i f f e r e n t i a l  adsorption o f  the molecules on 
the wal ls  o f  the c e l l s  and vacuum system, and d i f f e r e n t i a l  absorption i n t o  
mater ia ls w i t h i n  the vacuum system. The concentration o f  methanol was, 
therefore, measured as a funct ion of t ime f o r  several runs. For most of 
these runs, the c e l l  was "seasoned" a t  a pressure s l i g h t l y  higher than the 
operating pressure. Pumping time between runs, except f o r  one run, was j u s t  
su f f i c ien t  t o  reduce current  i n  the Ion pump t o  below 100 PA, corresponding 
t o  a pressure o f  the order o f  t o r r .  I n  the exception, the pumping time 
was longer, bu t  the c e l l  was seasoned i n  a manner s im i l a r  t o  the other runs. 
The resu l t s  o f  t h i s  experiment are shown i n  Figure 6. The exception i s  Run 1, 
sample A. The measured mole f rac t ion  as a funct ion o f  t ime i s  seen t o  ap- 
proach the prepared mole f rac t ion .  For sample A, the average of the l a s t  
measurements f o r  a11 four  runs was .I287 and f o r  sample B the average was 
.1065. The agreement i s  bel ieved t o  be f o r t u i t ous .  
These r e s u l t s  were presented a t  the 155th National ACS I~leeting i n  San 
Franci sco i n  Apri  1 1968. 
I n  the course o f  the experiments discussed up t o  t h i s  po in t ,  i t  was 
noted t ha t  the slope o f  a ca l i b ra t i on  curve could vary from day t o  day. 
A more s tab le  c a l i b r a t i o n  was required, p re fe r rab ly  one which could be made 
constant from instrument t o  instrument, as wel l  as f o r  one instrument from 
day t o  day. Furthermore, ca re fu l  considerat i  on o f  detector  c rys ta l  response- 
as a funct ion o f  c r ys ta l  current  d ic ta ted  a more re f ined  ca l ib ra t ion  technique. 
FIGURE V
I 
.
 
-)Q- 
i 
-
 
-
 
-
 
-
 
-
_
-
_
 
,
 
, 
-
 
.
 
An examination of the detector crystal sens i t iv i ty  as a function of current 
(in Figure 7 )  reveals tha t  a t  higher powers, therefore higher pressures, the 
sens i t iv i ty  remains almost constant with crystal current. T h i s  imp1 ies  tha t ,  
although the higher pressure measurements (above 3.5 mtorr) vary l i t t l e  due 
to th i s  fac tor ,  the lower pressure measurements could be i n  serious e r ror  
due t o  reduced sens i t iv i ty .  To circumvent t h i s  d i f f icu l ty  with an in-line 
spectrometer, the calibration arm was used to  provide a constant reference 
signal with which the molecular absorption signal could be compared. 
The experiment then proceeded as follows: 
The attenuators in the calibration arm were s e t  so that  the signal ap- 
pearing a t  the synchronous detector output due to  the calibration signal was 
near the mid range of the molecular signal.  The molecular signal i s  then 
designated as Vstark and the signal from the cal i bration arm as Veal. For 
a given absorption by the gas AP the r a t io  of these signals should remain 
g 3  
constant despite variations in detection system sens i t iv i ty .  The "signal" 
v 
was then redefined as -- stark.  The improvement i n  consistency of resul ts  was 
'cal 
remarkable. Previously, a calibration curve was prepared and used the same 
day. Afterwards, data from several days' operation could be combined to  
provide a single calibration curve. Such curves, for  the same methanol 
t ransi t ions discussed previously, are shown i n  Figure 8. The improvement 
a t  low pressure (therefore low power and low crystal current) may be seen 
immediately. I t  may be seen tha t  the apparent intercept with the x-axis i s  
identical , within experimental e r ror  fo r  the two transi t ions . Insufficent 
data is available a t  present to  generalize on th i s  particular point. I t  would 
seem, however, that  since the absorbtion a t  pressures below 1 mtorr depends 
almost who1 ly  upon wa9 4 col l is ions fo r  the relaxation process, that  t h i s  in- 
deed should be the case. Transferring cal ibration figures from instr-ument 
- 4 1 -  
DETECTOR CRYSTAL 
SENSITIVITY 
(Constant micro- 
wave signal) 
FIGURE VIII 
-13- 
.
 ,
 
t~ instrument now depends upon accurate absolute calibration factors for 
each individual instrument, and upon the adoption of suitable standards, by 
analytical microwave spectroscopists, for a definition of "signal ". 
The region below 3.5 mtorr i s  shown, in greater detai 1,  in Figure 9. 
The data  points below 1 mtorr give a fair  least squares f i t  to a straight 
line passing tlwough the origin. A t  these pressures, the mean free path i s  
considerably 1 arger t h a n  the cell dimensions, reinforcing the conclusion t h a t  
the relaxation process in largely due to  wall collisions. A series of 
saixpl es of methanol in benzene were then prepared, and measurements were 
made t o  determine i f  the slopes of signal vs partial pressure graphs were 
constant for dilution. The results are shown in Figure 10. Partial 
pressures were determined from the measured total pressure and the known, 
prepared, mole fraction. A least squares f i t  to the data  showed the slopes 
t o  be identical , wi thin experimental error. Furthermore, as di luti on was 
increased, the graphs tended t o  pass closer t o  the origin. This is  reason- 
able, since, even a t  low partial pressures, solvent molecules are available 
for collisions between molecules t o  produce relaxation. This indicates t h a t  
the slope of the signal vs partial pressure of absorber i s  the critical quan- 
t i t y  to be determined for analytical purposes, and i s  the quantity containing 
molecular density information. A simple technique for determining concentra- 
t i o n  of absorbing species could be that of measuring the actual signal. If 
this technique were used, and the assumption made that the curve i s  linear 
through the origin, serious errors can result. The data discussed above, 
for several dilutions, was examined to  determine how large these errors might 
be. A "Relative Signalt1 was defined as the actual partial pressure divided 
by the partial pressure using the linear approximation (as if  the curve 
passed linearly through the origin). This was plotted vs the partial pres- 
sure, and i s  shown in Figure 11. The errors from this approximation may be 
-1 4- 
Ff GURE' IX 
,
 -i
L
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seen t o  become qu i t e  la rge  a t  very low p a r t i a l  pressures. This indicates 
t h a t  a more carefu l  procedure must be followed. I f  the behavior o f  the ap- 
parent in te rcep t  can be confirmed by carefu l  theore t i ca l  work, then the pre- 
v i  ous procedure can be u t i  1 i zed. An a1 t e r n a t i  ve procedure i s suggested , how- 
ever, by Figure 12. I n  t h i s  f igure,  the s ignal  i s  p l o t t ed  vs t o t a l  pressure. 
Although data points are not  shown, the curves are a l e a s t  squares f i t  t o  
the data presented i n  Figure 10. The slopes from t h i s  l e a s t  squares fit were 
compared, and i t  was found t h a t  the r a t i o  *'N "N=1 = N where i s  the 
zFbT-- - AP 
slope of the .curve f o r  mole f r a c t i o n  N. An examination o f  Harr ington's 
theory shows t ha t  t h i s  should be the case, These slope r a t i o s  are compared 
v i i tn the prepared mole f rac t ions ,  and w i t h  the r a t i o  o f  s ignals method i n  
Table 11. 
TABLE I1 
METHANOL DILUTION 
Prepared N 
S l  ope N 
Ratios 
's1 -Nprep 
Signal FJ ,805 ,612 .418 
Ratios N~ i g-Nprep .017 .012 ,021 
The mole f rac t ions  determined by signal r a t i o s  are seen t o  be cons is tent ly  
high, i nd i ca t i ng  a systematic e r ro r .  The slope r a t i o  method appears t o  
produce much be t t e r  resu l t s ,  and fur ther  study of t h i s  method, p a r t i c u l a r l y  
for  concentrations i n  the par ts  per m i l  l i o n  range, i s  being undertaken a t  the 
present time. 
FIGURE XII 
An examination of the energies o f  the tors iona l  v ibra t ions i n  benzalde- 
hyde and re la ted  substances has been undertaken a lso i n  t h i s  laboratory.  
Since these to rs iona l  v ib ra t iona l  energy l eve l s  have been studied i n  the f a r  
I -R , t h e i r  determination f o r  microwave in tens i  ty  measurements provi  des a  
convenient cross-check o f  the v a l i d i t y  o f  these measurements. I n  the process 
of studying both benzaldehyde and deutero-benzaldehyde, the problems o f  
i n t e n s i t y  measurements i n  a  very r i ch ,  weak spectrum proved t o  d i f f i c u l t ,  
but  not  impossible. A  t yp i ca l  graph o f  s ignal  vs pressure f o r  a  s ing le  r o -  
t a t i ona l  t r a n s i t i o n  i n  two to rs iona l  v ib ra t iona l  states i s  shown i n  Figure 13. 
Such measurements f o r  several r o ta t i ona l  t r ans i t i ons  have resu l ted i n  a  
f i gu re  o f  110.8 k2 cm-' f o r  the energy separation o f  the tors iona l  states.  
3 The energy reported from f a r  I R  studies3 i s  111 +I cm-l. I n t ens i t y  measure- 
ments have a1 so revealed another v ib ra t iona l  mode which i s  acc identa l ly  near 
degenerate w i t h  the second exci ted to rs iona l  state.  The benzaldehyde work 
has a1 so resu l  ted i n  the assignment o f  a  very 1  arge number o f  r o ta t i ona l  
t rans i t i ons .  This work i s  nearing completion, and w i l l  be reported i n  the 
l i t e r a t u r e ,  as wel l  as being a  pa r t  o f  a  fu tu re  repor t .  
Discussion 
The work reported herein may be considered as experimental v e r i f i -  
ca t ion o f  the value o f  Harrington's satura t ion approach t o  I n t e n s i t y  
measur&-r~ents, and o f  the value o f  t h i s  type o f  measurement i n  quan t i ta t i ve  
ana ly t i ca l  microwave spectroscopy. It has been demonstrated t h a t  spectro- 
meter s ignal  i s  a  l i n e a r  funct ion o f  p a r t i a l  pressure o f  the absorber over 
a  pressure range above 3.5 mtorr  f o r  pure gases. For gases o f  much higher 
d i l u t i on ,  the l i n e a r  range extends t o  much lower pressures. A s t r a i g h t  
3~pect roch imica Acta, 23A, 981, (1967) 
-20- 
FIGURE XLll 
forklard technique has been developed for the determination of concentrations, 
based upon the s l ~ p e  ratios. A less straightforward method, based on 
signal measurements only, has a1 so been demonstrated. Accurate partial 
pressure measurements of individual components i n  a gaseous mixture have 
been shown to be feasible. The tremendous amount of data which could be 
made avai lable from measurements on many compounds i s ,  however, far to large 
to coll lect  wi t h  any efficiency under manual operati on anc~ recording. 
Operator errors would also tend t o  make such data unreliable. Operation 
under control of a small computer was, therefore, indicated, Such a com- 
puter was purchased w i  t h  funds from this grant and was del i vered i n  March 1969. 
Specific interfacing and programming methods wi 11 be reported in the future. 
A program of study of the sulfur dioxide content of selected a i r  
samples was commenced near the end of the reporting period. This will pro- 
vide a test  of the methods reported here for very small quantities of polar 
consitutents of a mixture of gases. Concentrations i n  the parts per mill ion 
range are easily determined, and the ultimate sensitivity appears t o  be 
several parts per billion. This work will be reported i n  a future reporting 
period. 
A few inadequacies exist in the present instrumentation, These are: 
(1) Low microwave power. Operation a t  higher pressures would be possible i f  
powers above 50 milliwatts were available to saturate a t  shorter relaxation 
times. Backward wave oscillator tubes are now available to produce these 
powers, and instrument modification should include conversion to these higher 
power tubes. 
(2)  Restriction to in-1 i ne operati on. Conversion of the instrument to 
bridge operation would allow operation of the detector diode a t  optimum 
current and s t i l l  a? low variation of input power t o  the ce l l s .  
(3)  Inadequate sampling system. A t  the present time the vacuum system 
contains elastomers which absorb many of the gases of in te res t .  Furthermore, 
i t  i s  somewhat d i f f i cu l t  to  add a small, precisely known amount of gas to  
the system. A sampling valve which w i  11 a1 leviate  the l a t t e r  d i f f icu l ty  i s  
being constructed f o r  th i s  instrument and will be instal led soon. Some 
modification of the present vacuum system will be required to correct the 
f irst  d i f f icu l ty .  
A problem related to  number 3 above is tha t  of separating compounds out 
of a many-component mixture. A large number of components may produce an 
extremely dense spectrum with overlapping stark lobes, making analysis 
d i f f i cu l t .  Some method of pre-separati on would, therefore, be very useful. 
Separation o f  polar consti tuents out of sample highly diluted with non-pol a r  
gases would greatly enhance the sens i t iv i ty  of the system. Two methods are 
now available i n  t h i s  laboratory. The f i r s t  amounts t o  simply freezing out 
the condensi ble components and pumping away the N2 and O2 i n  a i r  samples. 
The second i s  a small, simplified gas chromatagraph arranged to  co l lec t  i n -  
dividual peaks and pass the samples into the spectrometer individually. 
The l a t t e r  system i s  nearing the t e s t  phase. 


An experimental investigation of Harrington's theory of intensity measurements Status report, 1 Jan. 1967 - 1 Jan. 1969

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