hl Bureau or standards

Library, N.W. 31d«

PB 161645

jjoulder laboratories

^o. 144

DIELECTRIC CONSTANT OF

LIQUID PARAHYDROGEN

BY R. J. CORRUCCINI

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical Ntote

April 1962

DIELECTRIC CONSTANT OF LIQUID PARAHYDROGEN

by

R. J. Corruccini

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

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Price $ . 50

DIELECTRIC CONSTANT OF LIQUID PARAHYDROGEN

by

R. J. Corruccini

ABSTRACT

It is shown that the available data on the dielectric constant

of hydrogen conform to the Clausius-Mossotti equation within the

probable experimental errors. The published data cover temperatures from the triple point (M^K) to well above room temperature and a thousandfold range of densities. Using an average

value of the specific polarization, tables of the dielectric constant

of the liquid have been computed for temperatures from the triple

point (13. 803°K) to 32°K (58°R) and pressures from saturation to

340 atmospheres.

DIELECTRIC CONSTANT OF LIQUID PARAHYDROGEN

R. J. Corruccini

Introduction Capacitance measurements are used in liquid

hydrogen technology to determine liquid level and apparent density.

As will be shown, the dielectric constant is represented very well

as a function of density by the well known Clausius-Mossotti equation.

With the recent publication of extensive experimental data on the

density and specific volume of parahydrogen* it has now become

possible to compute the dielectric constant for a wide range of conditions. This note presents tables of dielectric constant as a function

of pressure up to 340 atm (5000 psia) and as a function of temperature

from the triple point to near the critical point. The basis of these

calculations will now be presented.

The Clausius-Mossotti equation can be written

e - 1

€ + 2 v = p

in which

e is the dielectric constant

v is the specific volume

p is the specific polarization, a property of the

substance having the same dimensions as v.

To the extent that p is a constant for a given substance, the substance

may be said to obey the Clausius-Mossotti equation. The equation is

derived from classical electrostatic theory on the assumptions that

the molecules are non-polar and spherical, there are no short-range

interactions between them, and their spatial distribution is isotropic .» * Hydrogen satisfies only the first assumption. However, errors due

to the other assumptions tend to vanish as the density increases 4and

are negligible for non -polar gases at ordinary pressures. More

complete theories have been developed ' ' that are valid up to

moderate densities, but none that are generally accurate at densities

characteristic of liquids.

Thus, in applying the equation to liquid hydrogen, deviations

certainly are to be expected due to violation of all of the assumptions

previously stated except the first. However, it is found that all of

the available data can be represented within the probable experimental
errors by a single value of the polarization, even though they cover

a thousandfold range of densities. Now the available experimental

data will be examined.

Liquid hydrogen. Of five known references, three are from

Leiden. A reading of the most recent of the three (Werner and

Keesom, 1925 } and examination of the scatter of the various e and p

values shows clearly that the earlier two (by Breit and Onnes, 1924

and Wolfke and Onnes, 1924) now should be given no weight. Measure

ments by Guillien appear to be comparable in precision and accuracy

to those of Werner and Keesom. Both of these papers cover the

range, 14-20. 4°K, and the authors conclude that their data show no

consistent variations in p that could be interpreted as deviations from

the Clausius-Mossotti equation. To these should be added a value at

the boiling point by van Itterbeek and Spaepen of apparently comparable reliability. Mean values of p obtained in these investigations

are given in table 1.

In addition it is possible to compute the dielectric constant

from refractive index data using the relation, e = n» , where rioo is

the refractive index extrapolated to very long wavelengths. Johns

and Wilhelm have measured the refractive index of liquid hydrogen

from 14° to 20. 4°K at wavelengths in the visible region. Guillien

has calculated the value, x^ - 1 . 2288 ± . 0003 at 20. 4°, from their

data. The corresponding value of p calculated using the specific

volume of normal hydrogen 'is shown in table 1.

5 Solid hydrogen. The data of Werner and Keesom disagree

markedly with those of Guillien. From Guillien' s work and similar

experiences at this laboratory in measuring the dielectric constant

of liquid and solid nitrogen, it is clear that discrepancies of this

kind readily occur due to the difficulty of ensuring that the solid,

which has to be cast in place in the measuring condenser, is free

from voids. In order to obtain a meaningful test of the ClausiusMossotti equation using a solid, either extreme care must be taken

with the preparation of the sample, or else its effective density must

be determined in place by an independent method.

Gaseous hydrogen. There have been many direct measurements of the dielectric constant of the gas, most of them near

ambient temperature and pressure. However, Maryott and

Buckley in providing a "best" value at 20 °C and 1 atmosphere have
based it entirely on optical and microwave measurements of the

refractive index using the relation, e = n^ . Maryott and Buckley

dismiss the direct measurements of e with this statement: "In a majority of cases, values of the dielectric constant measured at

radio frequencies do not appear to be of sufficient accuracy to provide useful information for reference purposes. " A value of p calculated from Maryott and Buckley's recommended dielectric constant

using the specific volume of the real gas •'is presented in table 1.

Of special interest to this inquiry are those few studies of

the dielectric constant that cover wide ranges of temperature,

pressure and density. The extremes of temperature are represented

1? 1 ^ by the work of van Itterbeek and Spaepen 1 '-(20 o - 291°K) and Forro iJ

(295°- 571 °K). Each of these authors obtained constant values of p

within their experimental limits of accuracy. A more rigorous test

is provided by the data of Michels, Sanders and Schipper at 25° and

100°C and at pressures from 1 to 1425 atm. The maximum density

achieved equals that of saturated liquid at 26°K. In spite of the great

range of densities covered by Michels et al, the polarization showed

no discernible trend with density or temperature. Their average

value is included in table 1. Summary of experimental results . The following table

summarizes the experimental results that are regarded as especially

significant. As indicated, some of the tolerances attached to the

mean values of polarization are based on estimates of accuracy by

the original authors. Others are guesses by the present author. In

most cases, the stated tolerance is approximately equal to the mean

deviation of several determinations. None of the investigators

referred to the matter of ortho-para composition, and so it is

assumed that the samples were normal hydrogen in all cases.

Inasmuch as none of the researches showed internal evidence

of dependence of p upon the experimental conditions, the variations

in p among the various investigations shown in table 1 cannot be

construed as evidence for deviations from the Clausius-Mossotti

equation. Parts of the discrepancies may be attributed to the use

of different data for the specific volumes and to accidental variations

in ortho-para composition. However, the discrepancies are too

large to be fully accounted for in these ways, and in large part must

be charged to undisclosed systematic errors in the experiments.
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The degree of constancy of polarization that has been

demonstrated for hydrogen is rather exceptional and raises the

question of how well the Clausius-Mossotti equation might fit other

cryogenic fluids. Bb'ttcher^(p. 209) attributes this result to hydrogen

having an exceptionally small value of the imperfection parameter,

a /a , where a is the average molecular radius, and the "polarizability", a, is given by P = Mp = 4/3 ttNcl , in which N is Avogadro's

number, and M is the molecular weight. Conversely, the imperfection parameter is larger for carbon dioxide, and, accordingly,

the polarization of this gas has been found to vary with pressure by

about 2% in 150 atm. Values of these quantities for some cryogenic

substances are shown in table 2. The trend of a /a suggests that

nitrogen and oxygen will show relative deviations from the ClausiusMossotti equation intermediate between those of hydrogen and carbon

dioxide, while helium should show even less deviation than hydrogen.

Table 2

Imperfe ction Parameters

Substance P 10 24

a #a a /a 3

cm /mol 3cm

oA

He 0. 51 0. 20 1. 28 0. 10

H

2

2.02 0. 79 1.47 0.25

N

2

4. 3 1. 71 1.85 0. 27

°2 4.0 1. 59 1.76 0.29

C°2 7. 3 2.89 2. 1 0. 31

Based on a collection 1Dof values determined from second virial

coefficients and viscosities. Those determined from second virial

coefficients were given greater weight.

Tables of dielectric constant . A value of p of 1. 00 cm^/g

(0.0160 ft^/lb) is seen to represent the experimental results listed

in table 1 within about ±1%. This value has been used to calculate

tables 3-7 using the Clausius-Mossotti formula,

v + 2p

e = —

v - p
and recently published provisional values of the specific volume of

parahydrogen. The latter are estimated to be accurate within 0. 2%

except near the critical point, where the equation of state used to

represent the data introduced systematic errors. The deviations due

to the equation of state were eliminated from the few values of

specific volume near the critical point before calculating the dielectric

constant. Consequently, the error in e is almost entirely due to the

one percent uncertainty in p. The error in (e - 1) from this source

is also about one percent, while the error in e is estimated to range

from 0. 15% at the lowest density to 0. 2 5% at the highest. It should

be noted that the densities at the higher pressures (below the stepped

lines in tables 3 and 6) exceed the maximum density at which the

dielectric constant has been experimentally measured by as much

as 15%. The validity of the adopted value of p at these higher

densities has not been established.
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Table 4. Dielectric Constant of Saturated Liquid

Parahydrogen vs. Temperature (°K)

T, °K

13.803* 1. 2503

14 1. 2497

15 1. 2467

16 1. 2436

17 1. 2403

18 1. 2369

19 1. 2333

20 1. 2295

20. 268** 1. 2285

21 1. 2255

22 1.2213

* Triple point

T, °K

23

24

25

26

27

28

29

30

31

32

2168

2119

2067

2011

1949

1880

1802

1710

1598

1444

** Normal boiling point

Table 5. Dielectric Constant of Saturated Liquid

Parahydrogen vs. Pressure (atm)

P, atm.

1 1. 2285

2 1. 2175

3 1. 2087

4 1.2010

5 1. 1937

P, atm.

6 1. 1865

7 1. 1794

8 1. 1720

9 1. 1641

1. 1553
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Table 7.

Dielectric Constant of

Saturated Liquid Parahydrogen

vs. Pressure (psia)

p T € psia °R

10 34. 260 1. 2329

15 36. 603 1. 2279

20 38.436 1. 2238

30 41. 291 1. 2168

40 43. 529 1. 2108

50 45.400 1. 2053

60 47. 022 1. 2001

70 48. 464 1. 1951

80 49. 768 1. 1902

90 50. 962 1. 1854

100 52. 067 1. 1806

120 54. 062 1. 1705

140 55. 832 1. 1594

160 57. 424 1. 1461

180 58. 860 1. 1257
11

References

1. H. M. Roder and R. D. Goodwin, Provisional Thermodynamic

Functions for Para-Hydrogen, NBS Tech. Note No. 130

(PB 161631), Dec. 1961.

2. C. J. F. Bottcher, Theory of Electric Polarization,

Elsevier (1952).

3. H. Frohlich, Theory of Dielectrics, Oxford (1949).

4. J. G. Kirkwood, J. Chem. Phys. , 4, 592 (1936).

5. W. Werner and W. H. Keesom, Leiden Comm. No. 178a (1925).

6. R. Guillien, Rev. Sci. , 77, 575 (1939); J. Phys. Radium, 1_, 29 (1940).

7. A. van Itterbeek and J. Spaepen, Physica, 9, 339 (1942).

8. H. E. Johns and J. O. Wilhelm, Can. J. Res. , 1 5A, 101 (1937).

9. H. W. Woolley, R. B. Scott and F. G. Brickwedde, J. Research

NBS, 41, 400 (1948); RP1932.

10. H. M. Roder, unpublished results.

11. A. A. Maryott and F. Buckley, Tables of Dielectric Constants

and Electric Dipole Moments of Substances in the Gaseous

State, NBS Circular 537 (1953).

12. A. van Itterbeek and J. Spaepen, Physica, 10, 173 (1943).

13. M. Forro, Z. Physik, 47, 430 (1928).

14. A. Michels, P. Sanders and A. Schipper, Physica, 2, 753

(1935).

15. J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular

Theory of Gases and Liquids, Wiley (1954), pp. 1110-1.

16. R. D. Goodwin, J. Research NBS, 65C, 239 (1961).

17. A. Isihara, Physica, 27_, 857 (1961).

18. W. F. Brown, Dielectrics, Sec. B. II. c. , Handbuch der

Physik, Vol. 17, Springer-Verlag, Berlin (1956).

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