NOTES
JuIy, 1958 NON-EQUILIBRIUM PROPERTIES OF RARE GASES BY M. P. MADAN Department of Phyaice, Univsreity o f Lucknow, India Received February $, 1968
and the Exponential :6 form
[:- ea(l-rh)
E(r) = 1 -'6/a
(rm/r)61]
(2)
where E is the minimum potential energy taken as negative, Tm is the separation distance for which energy is minimum and a is the steepness of the repulsion energy, the later potential being more realistic and flexible, Usually the information about the values of the parameters of eq. 1 and 2 is obtained from compressibility and crystal data. Nanequilibrium properties such as diffusion and thermal diffusion are comparatively more sensitive to the intermolecular force law than any other property and are preferable for the evaluation of potential parameters to be used for predicting the nonequilibrium properties.
893
the author.'+ For other gases, under the circumstances, the next best course is to utilize the temperature variation of self-diffusion for this purpose. This has been done in the present report using the data for neon by Winn4 and the most recent data for xenon bv Amdur and Schatzki6 for the potential
tensive experimental measurements, but nevertheless can be used to check the self-consistency of both the methods. The values of a can be found using a method given in ref. 6. For xenon a was taken t? a comparisonof various experlbe 13; for mental properties with the theoretical family of for (y suggested a value 13.5 < Ly < 14.5. We selected ff = 14 to provide a best fit with the experimental data. This is in good agreement with the value of a = 14.5 obtained by Mason and Rice6 and a = 13.6 by Corner? This gives for xenon, and Tm as e l k = 168.5"K. the average values of and rm = 4.883 A. and for neon as ~ / = k 36.22"K. and rm = 3.127 A. For the case of xenon these values can be compared with ~ / = k 184.6"K.and T, = 4.808 A. determined using the second
TABLH I COMPARISON OF VALUES OF POTENTIAL PARAMETERSCALCULATED USINQDIFFERENT METHODS Exp: Six Potential a
Xenon Self-diffusion
(OK.)
rm
(H.)
13
168.5
4.883
13
184.6
4.808
Thermal conduct. Viscosity virial and crystal properties Viscosity Crystal Neon Self-diffusion Viscosity virial and crystal properties Viscosity Crystal Crystal Virial
12:6 Potential
t/k
(OK.)
163 24 216.3
13
231.2
13.6
36.22 38.0
37.1
(1) M. P. Madan, J. Chem. Phye., 23, 763 (1955). (2) B. N. Srivartava and M. P. Madan, ibid., 21, 807 (1853). (3) M. P. Madan, ibid., 27, 113 (1957).
Present work first method Second method 5 10 6
4.552 4.460
3.127 3.147
11 6 Present work 6
35.7 36.3
3.132 3.160
11 6
35.7
3.076
6 11
3.160
For rare gases, the experimental data on thermal diffusion, the property most sensitive to the force between molecules, are available only for argon, krypton and neon. For neon there is a considerable doubt about the reliability of the data. For argon and krypton results have been reported by
Ref.
(A.1
4 . 8 1 f 0.24 4.511
4.450 229 228
14 14.5
rm
method. The two set of values obtained from selfdiffusion are consistent among themselves keeping in mind the comparative insensitiveness of the second method. The values used for calculating the (4) E. B. PJinn, Phys. Rev,, 80, 1024 (1950). (5) I. Amdur and T. F. Schataki, J . Chem. Phye., 27, 1049 (1957). (6) E. A. Maaon and W. E. Rice, ibid., 22, 843 (1954). (7) B. N. Srivaatava and M. P. Madan, PhiE. Mag., 43, 968 (1952). (8) J. Corner, Trans. Faraday Soc., 44,914 (1948).
COMMUNICATIONS TO THE EDITOR
894
-
non-equilibrium properties are, for xenon: e / i i 168.5"K., r , = 4.883 k., and for neon: E/,% = 36.22"K. and rm = 3.127 A. The values of the potential parameters are further compared with other determinations in Table I. The computed values of self-diffusion, viscosity and thermal conductivity for xenon and neon at several temperatures are reported in Tables I1 and 111. Mason and Rice,6 A m d ~ r ,SaxenalO ~ and others have also calculated these coefficients, using parameters obtained from different methods and with differently assumed potential forms, but the agreement has not been found to be satisfactory for these gases. Our values can be considered satisfactory, if the experimental errors in the measurement of self-diffusion are kept in mind, but cannot be taken t o be in excellent agreement. The values of the self-diff usion coefficient calculated on the basis of the Lennard-Jones 12:6 form also show somewhat similar agreement.5 This means that
the assumed law of molecular interaction does not truly represent non-equilibrium properties of these gases, even though the discrepancies are sufficiently reduced by a proper evaluation of potential parameters. The present investigations and the previous work by the author and others indicates that both the potential forms, one hardly better than the other in predicting the transport properties, doubtless fit the experiment to a fair extent but are inadequate over a wide temperature range and for all the properties taken together. However, if two sets of potential parameters are taken, one for the low temperature range and the other for the high temperature range, good agreement between theory and experiment can be found.5 It is a pleasure to thank Prof. P. N. Sharma for his interest in this work. TABLE I11 COMPARISON OF OBSERVEDTHERMAL CONDUCTIVITY AND VISCOSITY DATAWITH THOSE CALCULATED THEORETICALLY A 106, cal. em.-' sec.-l-deg.-I: - , TI. 106,. g. - cm.-1 sec.-l
TABLE IIA COMPARISON OF OBSERVEDSELF-DIFFUSION DATA FOR I: Temp. XENON WITH THOSE CALCULATED USI~G THE PARAMETERS (OK.) 01
=
13; e/lc = 168.5"K.; rm = 4.883A. D11incm.2seo.-l
Temp. (OK.)
Exptl.
Calcd.
Dev.
194.7 273.2
194.7 273.2 329.9 378,O
0.0257 i0.0003 .0480 f .0004 .0684 5Z .0013 .0900 f .0004
0.0250 .0483 .0695 .0896
f0.0007 .0003 .0011 -0004
373.2 491.2 579.1
-
+
TABLE IIB COMPARISON OF OBSERVEDSELF-DIFFUSION DATA FOR NEONWITH THOSE CALCULATED U ~ ~ I NPARAMETERS G 01 = 14; €/IC = 36.22"K.i rm = 3.127 A. Dll in cm.2sec.-1
'
Temp. (OK.)
Exptl.
Calcd.
Dev.
77.7 194.7, 273.2 298.2 353.2
0.0492 f 0 . 0 0 0 4 ,255 5Z .004 .452 f .005 .516 f .005 .703 f .005
0.0498 .255 .455 .528 ,704
-0.0006 .0000 - .003 - .012 - .001
(9) I. Amdur, J. Chem. Phys., 16, 190 (1948). (10)S. C. Saxena, Ind. J. Phys., 29, 587 (1955).
Vol. 62
A;
Xenon--cr = 13, a/k = 168.5OK., r m = 4.883 Thermal conductivity Temp. Viscosity Expt1.b Calcd. (OK.) Expt1.c Calcd.
0.91 1.21" 1.21 1.68 2.08 2.37
11: Neon-a
0.88 1.22
289.7 293
22.35 22.60
22.60 22.86
1.61 2.01 2.29
400 450 500 550
30.09 33.51 36.52 39.54
29.98 32.94 35.73 38.52
= 14, e / k = 36.2Z°K., r m = 3.127
A.
90.2 194.7 273.2 373.2 491.2
4.89 5.02 100 14.35d 14.71 8.76 8.96 140 18.41d 19.10 11.10 11.32 200 23.76d 24.63 13.57 13.95 240 27.08d 27.95 15.95 16.75 300 31.73d 32.53 a F. G. Keyes, Trans. A m r . Soc. Mech. Engrs., 1395 (Nov. 1955). W. G. Kannuluik and E. H. Carman, Proc. Phys. Soc. (London),B65, 701 (1952). M. Trauts and R. Heberling, Ann. Physik, [5] 20, 118 (1934). H. L. Johnston and E. R. Grilly, J. Chem. Phys., 46, 938 (1942). (11) Hirschfelder, Curtiss and Bird, "The Molecular Theory of Gases and Liquids," John Wiley and Sons, Inc., New York, N . Y., 1954.
COMMUNICATIONS TO THE EDITOR DETERMINATION OF THE INTRINSIC VISCOSITY OF RIGID PARTICLES AT ZERO RATE OF SHEAR Sir: The interpretation of intrinsic viscosity, [q], of highly asymmetric rigid particles often has been complicated by its rate of shear, D, dependence. Customarily, [q]D=o is determined through linear ext'rapolation ([?ID uersu8 D),using a multigradient viscometer. This extrapolation is arbitrary and
not consistent with theory,l and easily can lead to disastrous results,z especially when the [?ID us. D plot curves rapidly upward (Fig. 2). We have found that the determination of [q]D=O can be realized with the aid of flow birefringence without the necessity of an extremely low rate of shear viscometer, which a t present is unavailable to most workers. Sinae both the intrinsic viscosity and extinction (1) N. Saito. J . Phye. Soc. Japan, 6, 297 (1951). (2) E. Hisenberg, J . PoEymer Sci., 23, 579 (1957).
c
