^Konal Bureau of Standards

Library, M.W. Bldg

JET 1IB65

^ecltnic&l ^iot& 9fc. 322

SURFACE TENSIONS OF NORMAL

AND PARA HYDROGEN

R. J. CORRUCCINI

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

technical <Vlote 322

ISSUED August 11, 1965

SURFACE TENSIONS OF NORMAL AND PARA HYDROGEN

R. J. Corruccini

Institute for Materials Research

National Bureau of Standards

Boulder, Colorado

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.

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Price: 20*

CONTENTS

Page

ABSTRACT - - 1

1. INTRODUCTION 1

2. DISCUSSION OF THE EXPERIMENTAL RESEARCHES

AND THE CORRECTIONS OF THE DATA 2

2.1. Kamerlingh Onnes and Kuypers 2

2.2. Van Itterbeek 4

Table 1 - Original and Corrected Data from

Two Older Sources 5

2.3. Grigor'ev 6

Table 2 - Data by Grigor'ev [ 1964] Calculated

from Eqs. (5) and (6) 7

3. COMPARISON OF THE CORRECTED DATA 8

4. A FUNCTION TO FIT THE DATA 8

Table 3 - Smoothed Values of Surface Tension as Given by Eqs. (8) and (9) 10

5. APPENDIX I. Relation to Other Correlations 11

6. APPENDIX II. Contact Angle 12

7. ACKNOWLEDGMENT 13

8. REFERENCES 14

Figure 1. Schematic drawing of capillary rise method,

h' is the capillary rise (calculated) of the

annular meniscus in the reservoir above a hypothetical infinite reservoir. 16

Figure 2. Corrected experimental surface tension points

of Kamerlingh Onnes and Kuypers and of Van

Itterbeek and straight lines representing the

experimental points of Grigor'ev. 17

in

Surface Tensions of Normal and Para Hydrogen

R. J. Corruccini

The published data on the surface tensions of normal

hydrogen from three investigations are apparently in disagreement by about 10%. In this note it is shown that these data are

actually in agreement within about 1% if properly computed.

The resulting concordant data are represented by functions

and by a table suitable for linear interpolation.

Key Words: Hydrogen, Liquid, Surface tension

1. Introduction

Until recently, data on the surface tension of hydrogen were

available from only two experimental researches, namely, those of

Kamerlingh Onnes and Kuypers [ 1914] and Van Itterbeek [ 1940] . These

appeared to be in good agreement. However, in a paper on helium, Van

Urk, Keesom, and Kamerlingh Onnes [ 1925] stated in a footnote that a particular meniscus correction had not been properly applied by

Kamerlingh Onnes and Kuypers. They gave recalculated values for

hydrogen which were about 10% lower and which thus disagree by about

this much with Van Itterbeek' s later values. Some compilers [e. g. , Friedman 1954] have been unaware of the recalculation by Van Urk et

al. , and others have chosen to ignore it [e. g. , Stewart, Germann, and

McCarty, 1962]. Some have applied corrections like those of Van Urk

et al. to the data of Kamerlingh Onnes and Kuypers [e. g. , LandoltB'.rnstein Tabellen and the International Critical Tables], but the large

differences between the results so obtained and Van Itterbeek' s data

were not accounted for. Thus there has been no clear agreement in the

literature on a set of "best" values for this property.

Recently new measurements have appeared. Grigor'ev and

Rudenko [ 1964] have determined normal hydrogen, and Grigor'ev [ 19 64]

determined parahydrogen. (It must be assumed that the measurements

by Kamerlingh Onnes and Kuypers and Van Itterbeek were made on normal

hydrogen. ) This recent work agrees well with the corrected data of
Van Urk et al. but not with Van Itterbeek's data.

In this note the application of the meniscus corrections in the

older investigations is examined, and it is shown that Van Itterbeek's

data, if properly corrected, in fact agree well with both Grigor'ev's and

those of Kamerlingh Onnes and Kuypers as corrected by Van Urk et al.

All of the available experimental data are thus shown to be in close

accord. The resulting corrected data are represented by functions and

by a table suitable for linear interpolation.

2. Discussion of the Experimental Researches

and the Corrections of the Data

2.1. Kamerlingh Onnes and Kuypers

These authors measured the rise, h, in a capillary situated on

the axis of a tubular reservoir. The reservoir tube had an inside diameter of only about 1 cm, and hence the liquid in this reservoir itself had

an appreciable capillary rise, h', which had to be computed and added

to the observed rise in the capillary tube. Figure 1 shows the situation

and the notation used.

In an earlier work with similar apparatus but other fluids,

Verschaffelt [ 1895] had measured the height, d, of the annular meniscus

and had found it to be less than if the cross section of this meniscus in

an axial plane were semicircular. Hence he derived a formula for h'

on the assumption that the cross section was a semi-ellipse of semiminor axis, d, and major axis, R-r.:

r

, 2d/(R-r ) h + f A) ( 2

1/r -2d/(R-r ) 2

This formula was used by Kamerlingh Onnes and Kuypers, but

since they were unable to measure d, they made the simplest available,

but probably incorrect, assumption, namely, that the cross section was

semicircular, so that 2d = R-r . (There is a misprint in their statement of this equation, as well as in their value of r, which should have

read 0. 03316 cm rather than 0. 3316 cm; thus compare r/3 as given in

their Table II. Their calculations were apparently not affected by these
misprints. )

There is a further small and well-established correction for the

meniscus in the capillary tube. This, to a good approximation, has the

value r/3 [Adam 1941], Hence the corrected capillary rise is

H = h + h* + r/3 . (2)

This is the hypothetical rise above a reference surface of zero curvature; i. e. , above an infinite reservoir. It is related to the surface tension, Y, by the well established formula (see any text on surface

chemistry)

Y= grH(p^ - Pv)/2 (3)

in which g is the acceleration of gravity, p« is the density of the liquid,

and Ry is the density of the vapor above the meniscus.

Later, Verschaffelt [ 1921] re-examined the question of the shape

of the annular meniscus by a graphical construction and published tables

from which d and h' could be found, given the values of h and the three

radii, r, r j, and R. This procedure was an improvement, since it

avoided arbitrary assumption of too simple a meniscus shape.

The recalculation by Van Urk et al. used Verschaffelt 1 s 1921

tables, and their language gives the impression that this was the sole

change. However, inspection shows that this produced only a 3% reduction in H. Most of the roughly 10% reduction in Y resulted from correction of a different error which was not specifically mentioned. Thus, in

place of eq. (3), Kamerlingh Onnes and Kuypers had used the following

formula:

Y=gH(P

i

-P

v)/2(I-^-) (4)

The origin of this formula was not indicated. However, one can see that

it differs from eq. (3) by the term l/(R-r,), which is evidently a correction for the curvature of the annular meniscus. But such a correction is
already contained in h'. Hence eq. (4) applies it a second time. The

meaning of the various corrections is best seen by referring back to

Verschaffelt [ 1895] who was the only one to give an explanatory discussion. However, eq. (4) is not to be found in his paper.

In table 1 are listed the data of Kamerlingh Onnes and Kuypers

and the corrections by Van Urk et al. In table 1 two further adjustments

are shown which are small: (1) The temperature scale has been adjusted

from the n-H£ vapor-pressure scale of Kamerlingh Onnes and Keesom

[ 1913] to that of Woolley, Scott, and Brickwedde [ 1948], and thence to

the NBS 1955 scale, and (2) more modern density data recommended by

Stewart and Roder [ 19 64] have been used. The temperature of the lowest point given by Van Urk et al. was variously reported as 14. 78°

(Kamerlingh Onnes and Kuypers, table I), 14. 66° (Kamerlingh Onnes and

Kuypers, table II), and 14. 68° (Van Urk et al. ). Because of this ambiguity, this point has been omitted from consideration.

2. 2. Van Itterbeek

The experimental method was the same as that of Kamerlingh

Onnes and Kuypers, and the surface tension was calculated using the

same eqs. (1), (2), and (4). The only difference was that Van Itterbeek

measured the meniscus height, d. Kamerlingh Onnes and Kuypers had

been unable to do this. Van Itterbeek was aware of the use of Vers chaffelt's

tables of 1921 by Van Urk et al. He used these tables to obtain a value of

d but found it to be about twice as large as his experimental value (and,

incidentally, about the same as if the meniscus section were semicircular).

One must infer that he thought that this discrepancy cast doubt on

Verschaffelt' s 1921 tables since he proceeded to calculate h' from

Verschaffelt' s ellipse formula, eq. (1), inserting his measured value of

d.

However, analysis shows that it makes little difference which

method is used to obtain h' in this case, as the resulting H values differ

by only about 2%. It is not easy to make a choice. The correction given

by eq. (1) has the advantage of using the experimental and thus presumably

true value of d, but has the disadvantage that the assumed elliptical meniscus shape maybe incorrect. In contrast, Verschaffelt' s table undoubtedly

gives a more correct representation of the curvature of the meniscus at

its bottom, upon which h' depends directly. The unfortunate fact that it

yields too large a value of d could result from non-zero contact angle,

inasmuch as the derived d (but not h') would be evidently very sensitive

to contact angle at angles near zero. (However, see Appendix II. ) I have chosen to obtain h' from Verschaffelt's table.
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A much larger correction of about 12% results from using eq. (3)

rather than eq. (4). This is the principal adjustment made here to Van

Itterbeek's results. It brings his data into good agreement with the corrected Leiden values. The data are listed in table 1. Since Van Itterbeek

listed the vapor pressures at his experimental points, it was possible to

adjust his temperatures and densities to the same basis to which I have

adjusted the Leiden data. These adjustments are small, as can be seen

in table 1. *

2. 3. Grigor 'ev

The difference in rise in two adjacent capillaries of different

diameters was measured. This technique eliminates the correction h'.

As in most Russian papers the details are glossed over and the data

points appear only in a small graph. Nevertheless, the conventional

technique inspires confidence. The author's estimate of accuracy was

~0. 5%. For the first time both normal and parahydrogen were determined.

The data were determined from about 17° to 20. 4° K and were

represented by the following linear equations:

n - H : y= 5. 25 - 0. 162 T (5)

p - H : Y= 5. 27 - 0. 165 T. (6)

Several errors have been noted in Van Itterbeek's table I: (1) A

misprint of p v

at 17. 72° K which should read 0. 00061. (2) The two

values of h'. The second value is evidently a misprint. If rearranged

from 0. 0146 to 0. 1046, which is essentially the result obtained by

repeating his calculation, then it is possible to confirm his value of H,

otherwise not. (3) The value of H at 20. 32° cannot be accounted for by

using either his erroneous value of h' or the value 0. 0939 cm obtained

by following his method of calculation.
However, these extrapolate to zero at a temperature roughly one degree

below critical, whereas physical reality requires the surface tension to

vanish at the critical point. The temperature scale on which the results

are given is not defined; nor are the density data explicitly given, but

the usage in an earlier paper [Grigor'ev 19 63] suggests that the data of

Woolley, Scott, and Brickwedde were used for the liquid densities and

the ideal gas law for the vapor densities. If this were the case, adjustments might be made to real gas densities and to more modern density

data for liquid parahydrogen [Stewart and Roder] , but the net change

would not exceed 0. 1%. If Grigor'ev's temperatures were based on the

hydrogen vapor pressure data of Woolley, Scott, and Brickwedde, no

adjustment larger than 0. 005 degree would be called for. If, on the

other hand, he were on the Russian P. R.M.I, scale, recent comparisons have shown this to be as much as 0. 03 degree higher than the NBS

1955 scale in the range under consideration. This would correspond to a difference in surface tension of 0. 005 dyne/cm or about 0. 2%. Inasmuch as there is no clear basis for making any particular corrections

and the probable ones discussed above are smaller than Grigor'ev's

claimed accuracy of ~0. 5%, no adjustments were made in this note.

Also, rather than attempt to extract the data points from the graph in

Grigor'ev's paper, I have used values calculated from his equations at

the integral temperatures, 17, 18, 19, and 20°K, as if they were original data points. These are given in Table 2.

Table 2

Data by Grigor'ev [ 1964] Calculated from Eqs. (5) and (6)

n-H

2 p-H.

°K dynes/cm dynes/cm

17 2.496 2.465

18 2.334 2.300

19 2. 172 2. 135

20 2.010 1.970
3. Comparison of the Corrected Data

The corrected data from table 1 and the two linear equations of

Grigor'ev are plotted in figure 2. The spread in the data for n-H^ at

any given temperature is not more than 1. 3%. This is regarded as good

agreement for data taken over a span of fifty years. The n-H^ minus

p-H^ difference as given by Grigor'ev ranges from 1 to 2%.

The four Leiden points are accurately linear. However, both this

set and the data of Van Itterbeek extrapolate to zero at appreciably below

the critical temperature, thus demonstrating again the inadequacy of the

linear formula over a wide range.

4. A Function to Fit the Data

The simplest representation is a linear function of temperature,

as was used by Grigor'ev. If fitted to the data, it represents them

within the experimental precision, but is not reliable for extrapolation.

A straight line passed through the experimental points and constrained

to zero at the critical temperature provides a better wide-range representation, but deviates systematically from the line fitted to only the

experimental points by up to 1%. To put it another way, the slopes

would differ by at least 5%. Thus, use of a more elaborate function is

justified.

We will adopt the empirical equation of Van der Waals

[Guggenheim 1950]:

Y= Y (1 - T ) n

, (7) o r

in which Tr

is the reduced temperature and n is a constant, which for

many classical substances has been found to have the value 11/9. On

fitting this separately to the four sets of data in tables 1 and 2, the following parameters were found:

Investigation

n " H

2

1.

nH

6

5.

Y

o

Kamerlingh Onnes : 565

and Kuypers

Van Itterbeek : n " H

2

1. 08

3

5. 479

Grigor'ev : n " H

2

1. 05

6

5. 329

Grigor'ev : P

" H

2

1. 07

5

5. 372
In view of the near constancy of n for other substances, it is

reasonable to adopt a fixed value for both forms of hydrogen and let

only Y be a fitted parameter. Evidently n should be roughly 1. 1 rather

than ll/9. The decreased value of n is a quantum effect [Hirschfelder

et al. 1954] . A further decision must be made: namely, how to weight

the three investigations of n - H2. However this is to be done, it seems

desirable to preserve the normal vs para differences found by Grigor'ev,

inasmuch as these differences may well be more accurate than either set

of data alone due to partial cancellation of the systematic errors that we

may suppose to have been present. These differences could be preserved

in various ways, e. g. , by averaging the three sets of data on n - H2 and

subtracting from this the normal minus para differences by Grigor'ev.

It would also be reasonable to adopt only Grigor'ev' s data for both forms,

inasmuch as his experimental method is better established, and his curve

for n - H2 is seen to closely approximate the older data as corrected here.

The latter course has been adopted. We assume an average n of 1. 065

which leads to new values of Y of 5. 3 69 (n-P^) and 5. 328 (p-H^). Thus

the equations have the following equivalent forms:

Y = 5.369 (1 - T j

1 ' 065

n-H r

[

(8)

L log y= 0.729865 + 1. 065 log (1 - 0. 0301386T) J

Y= 5.328(1 - T )

1 ' 065

. P

" H J r

[ . (9)

2

log Y= 0.72653 + 1. 065 log (1 - 0. 0303251T)

The temperature reducing parameters used were as follows [Stewart and

Roder]:

n - H : T =33. 18°K

2 c

p - H •. T = 32.976°K

2 c

These formulas are within ±0. 2% of the equations of Grigor'ev in

the range of his experimental data. They deviate from the four points of

Kamerlingh Onnes and Kuypers by + 0. 6% (avg. ) and + 1. 3% (max. ) and

deviate from the two points of Van Itterbeek by - 0. 3% and - 0. 7%. In

table 3 are presented values at integral temperatures calculated from
Table 3

Smoothed Values of Surface Tension as Given

by Eqs. (8) and (9)

T Y T Y

n-H

2 p-H

2

n-H

2 p-H2

°K dynes/cm dynes/cm °K dynes /cm dynes /err

13.803 (t. p.) 2.990 23 1. 525 1.491

13.947 (t.p.) 3.004 - 24 1.366 1. 333

14 2.995 2.958 25 1. 208 1. 175

15 2.829 2.792 26 1.052 1.019

16 2.663 2. 627 27 .896 .864

17 2.498 2.462 28 .743 .711

18 2. 334 2.298 29 . 591 . 560

19 2. 171 2. 135 30 .442 .411

20 2. 008 1.973 31 .296 . 266

20.268 (n.b.p.) - 1.930 32 . 154 . 125

20.38 (n.b.p.) 1.946 - 32.976 (c .p. ) - 21 1.847 1.812 33. 18 (c .p. ) o -

22 1.686 1. 651 ,

10
eqs. (8) and (9). Up to 32° K linear interpolation in this table will introduce no errors larger than one in the last place.

5. Appendix I. Relation to Other Correlations

Friedman [ 1954] adopted the original data of Kamerlingh Onnes

and Kuypers and Van Itterbeek. He was apparently unaware of the corrections by Van Urk et al. He represented the combined data by a linear

equation not constrained at the critical point.

Chelton and Mann [ 1956] referenced Friedman and repeated his

equation. The original sources were not referenced.

The Arthur D. Little Hydrogen Handbook [Anon., I960] referenced Chelton and Mann and repeated the above equation. The earlier

sources in this sequence were not referenced. Thus, starting from this

Handbook, it is necessary to go through the two previous compilations in

order to ascertain the original sources of the data.

The CEL-WADD Compendium [Johnson, I960] states that "the

data of Kamerlingh Onnes and Kuypers appears to be the only available

to date. " It presents a table purporting to be from that source. However, the data and reference were actually taken from the obsolete

International Critical Tables (1928). The ICT compiler was the same

Verschaffelt already mentioned. Evidently he corrected the data of

Kamerlingh Onnes and Kuypers for presentation in the ICT, though without specifically saying that he had dons so. The ICT data are close to

the corrected values by Van Urk et al. , though not identical with them.

Landolt-Bornstein Tabellen . The 6th edition has sections on

surface tension and contact angle in Vol. II, Part 3 (1956). These contain no data on hydrogen. This is strange because the 5th edition [ 1931]

gives smoothed values based on Kamerlingh Onnes and Kuypers but corrected by Verschaffelt and de Block. These are very close to the corrected values by Van Urk et al.

Stewart, Germann, and McCarty [ 1962]. This work employed a quantum-mechanical corresponding states correlation of the available

data on the isotopic species of hydrogen and helium. The input data on

hydrogen were the original data of Kamerlingh Onnes and Kuypers, the

corrected data by Van Urk et al. , and the data of Van Itterbeek. The

data by Kamerlingh Onnes and Kuypers and by Van Urk et al. were

treated as independent investigations. The authors adopted the uncorrected data of Kamerlingh Onnes and Kuypers and of Van Itterbeek in

preference to the corrected data by Van Urk et al. because the former

were concordant.

11
Set 2.

In summary, the various experimental data, compilations, and

correlations may be seen to fall into two sets, the second set being of

the order of 10% higher than the first set from 14° to 20°K, but the

agreement within either set being of the order of ± 1%.

Set 1.

a) Data of Kamerlingh Onnes and Kuypers as corrected

by Van Urk et al. or by Verschaffelt (ICT, CEL-WADD

Compendium, and Landolt-Bornstein) or by this note.

b) Data of Van Itterbeek as corrected by this note.

c) Data of Grigor'ev.

d) This note.

a) Uncorrected data of Kamerlingh Onnes and Kuypers.

b) Uncorrected data of Van Itterbeek.

c) Correlation by Friedman of (a) and (b). Reproduction

in Cryogenic Data Book and Arthur D. Little Hydrogen

Handbook.

d) Correlation by Stewart, Germann, and McCarty.

6. Appendix II. Contact Angle

The meniscus correction methods applied to all of the experimental data that we have cited rely on the assumption that the contact angle

between the liquid hydrogen and the wall is zero. None of the experimenters on surface tension observed the contact angle.

Recently workers at Arthur D. Little, Inc. [ 1961] reported measurements of contact angles between liquid hydrogen and various solids,

including several metals and Teflon. These measurements were made

by observing a cross section of the meniscus on a round rod sample with

a protractor telemicroscope. The results varied from 0° to 90° and were

not consistent with each other or with reasonable expectations based on

the surface energies of the substances involved.

12
Later Good and Ferry [ 1963] experimented with the same substances. They observed the angle of normal reflections from the meniscus at the contact zone and found zero contact angle in all cases. They

pointed out that the method used at ADL readily gives apparent non-zero

angles if the telemicroscope is not focused exactly in the plane containing the rod axis.

In view of the precision, self-consistency, and reasonableness

of the results of Good and Ferry, the application of meniscus corrections based on the assumption of zero contact angle was evidently proper.

7. Acknowledgment

I am most appreciative of a painstaking review of this paper by

Dr. J. M. H. Levelt Sengers.

13
8 . References

Adam, N. K. (1941), The Physics and Chemistry of Surfaces, 3rd ed. , pp. 363-371. (Oxford University Press, Oxford).

Anon. (I960), Hydrogen Handbook, Arthur D. Little, Inc., AFFTC

TR-60-19.

Arthur D. Little, Inc. (Nov. 1961), Report No. 63270-00-03, pp. 93-96,

NASA Contract No. NAS5-664.

Chelton, D. B. , and D. B. Mann (1956), Cryogenic Data Book, UCRL3421.

Friedman, A. S. (1954), The Thermodynamic and Transport Properties

of Liquid Hydrogen and Its Isotopes. Part II. Unpublished.

Good, R. J. , and G. V. Ferry (1963), Advances in Cryogenic Engineering 8_, 306. (Plenum Press, Inc., New York, N. Y.).

Grigor'ev, V. N. (1963), Zh. Eksperim. i. Teor. Fiz. 45, 98: translation in Soviet Physics JETP 1_8, 72 (1964).

Grigor'ev, V. N. (1964), Zh. Eksperim. i. Teor. Fiz. 47, 484: translation in Soviet Physics JETP _20, 321 (1965).

Grigor'ev, V. N. , and N. S. Rudenko ( 1964), Zh. Eksperim. i. Teor.

Fiz. 47, 92: translation in Soviet Physics JETP _20, 63 (1965).

Guggenheim, E. A. (1950), Thermodynamics pp. 167-169. (North

Holland, Amsterdam/inter science, New York, N.Y.).

Hirschfelder, J. O. , C. F. Curtiss, and R. B. Bird (1954), Molecular

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Onnes Lab, Univ. Leiden, 137d.

14
Kamerlingh Onnes, H. , and H. A. Kuypers (1914), Commun. Kamerlingh

Onnes Lab, Univ. Leiden, 142d.

Landolt-Bornstein Phys. -Chem. Tabellen ( 193 1), 5th ed. , Suppl. 2,

Vol. 1, p. 166.

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Commun. Kamerlingh Onnes Lab, Univ. Leiden, 179a.

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Leiden, 18.

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15
r (cm) (cm)

R

(cm)

Onnes - Kuypers 0.03316 0.0801 0.554

Van Itterbeek .0393 .3264 .6635

Figure 1. Schematic drawing of capillary rise method, h

1 is the

capillary rise (calculated) of the annular meniscus in the

reservoir above a hypothetical infinite reservoir.

16
E

o

CO

27

2.6 -

25

co 24

C

~ 2.3

O

^ 2.2

L±J

LU 2.1

o

<

2.0

1.9 -

1.8

Onnes 8t Kuypers n-H

2

O Van Itterbeek n-H2 —Grigor'ev

16 17 18 19 20

TEMPERATURE, °K

21

Figure 2.

Corrected experimental surface tension points of Kamerlingh

Onnes and Kuypers and of Van Itterbeek and straight lines representing the experimental points of Grigor'ev.

17

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