Mobility and diffusion coefficients are generally extracted from experimental measurements of ion arrival time distributions using tensors of ranks one and two, i.e., in terms of the diffusion equation that is equivalent to Fick’s second law. The theory is extended here to tensors of rank three. It is shown that under customary circumstances, the generalized diffusion equation only contains a single third-order transport coefficient. This equation is used to generate synthetic data for ions moving through a pure gas. The mobility and diffusion coefficients and third-order transport coefficients inferred from these data are compared with values used to simulate the arrival time distribution. Finally, an existing computer program has been modified in order to compute one component of the third-order transport coefficient, and this program has been applied to Li+ in He.
REFERENCES
1.
https://fr.lxcat.net; accessed July 10, 2021.
2.
L. A.
Viehland
, Chem. Phys.
179
, 71
(1994
).3.
H. A.
Blevin
, J.
Fletcher
, S. R.
Hunter
, and L. M.
Marzec
, J. Phys. D: Appl. Phys.
9
, 471
(1976
).4.
I.
Simonović
, D.
Bošnjaković
, Z. L.
Petrović
, R. D.
White
, and S.
Dujko
, Eur. Phys. J. D
74
, 63
(2020
).5.
R. A.
Dressler
, H.
Meyer
, A. O.
Langford
, V. M.
Bierbaum
, and S. R.
Leone
, J. Chem. Phys.
87
, 5578
(1987
).6.
R. A.
Dressler
, H.
Meyer
, and S. R.
Leone
, J. Chem. Phys.
87
, 6029
(1987
).7.
R. A.
Dressler
, J. P. M.
Beijers
, H.
Meyer
, S. M.
Penn
, V. M.
Bierbaum
, and S. R.
Leone
, J. Chem. Phys.
89
, 4707
(1988
).8.
S. M.
Penn
, J. P. M.
Beijers
, R. A.
Dressler
, V. M.
Bierbaum
, and S. R.
Leone
, J. Chem. Phys.
93
, 5118
(1990
).9.
M. J.
Bastian
, C. P.
Lauenstein
, V. M.
Bierbaum
, and S. R.
Leone
, J. Chem. Phys.
98
, 9496
(1993
).10.
C. P.
Lauenstein
, M. J.
Bastian
, V. M.
Bierbaum
, S. M.
Penn
, and S. R.
Leone
, J. Chem. Phys.
94
, 7810
(1991
).11.
E. B.
Anthony
, M. J.
Bastian
, V. M.
Bierbaum
, and S. R.
Leone
, J. Chem. Phys.
112
, 10269
(2000
).12.
M. J.
Hogan
and P. P.
Ong
, J. Phys. B: At., Mol. Opt. Phys.
21
, 1417
(1988
).13.
A. D.
Koutselos
, J. Chem. Phys.
104
, 8422
(1996
).14.
A. D.
Koutselos
, J. Chem. Phys.
106
, 7117
(1997
).15.
A. D.
Koutselos
, J. Phys. B: At., Mol. Opt. Phys.
32
, 1225
(1999
).16.
T. H.
Lovaas
, H. R.
Skullerud
, O.-H.
Kristensen
, and D.
Linhjell
, J. Phys. D: Appl. Phys.
20
, 1465
(1987
).17.
S. B.
Vrhovac
, Z. L.
Petrović
, L. A.
Viehland
, and T. S.
Santhanam
, J. Chem. Phys.
110
, 2423
(1999
).18.
A. D.
Koutselos
, Chem. Phys.
270
, 165
(2001
).19.
I.
Simonovic
, D.
Bosnjakovic
, Z. L.
Petrovic
, P.
Stokes
, R. D.
White
, and S.
Dujko
, Phys. Rev. E
101
, 023203
(2020
).20.
L. A.
Viehland
, H. R.
Skullerud
, M.
Cordier
, J.
Dashdorj
, and A.
Trout
, J. Phys. B.
54
, 175202
(2021
).21.
L. A.
Viehland
, Gaseous Ion Mobility, Diffusion and Reaction
(Springer
, New York
, 2018
).22.
P. W.
Stokes
, I.
Simonović
, B.
Philippa
, D.
Cocks
, S.
Dujko
, and R. D.
White
, Sci. Rep.
8
, 2226
(2018
).23.
R. E.
Robson
, Aust. J. Phys.
28
, 523
(1975
).24.
25.
26.
C. F.
Curtiss
and J. S.
Dahler
, J. Chem. Phys.
38
, 2352
(1963
).27.
L. A.
Viehland
, Physica A
184
, 98
(1992
).28.
29.
H.
Senftleben
, Ann. Phys.
470
, 273
(1965
).30.
J. J. M.
Beenakker
, Festkörper Probl. VIII
1968
, 276
.31.
V. D.
Borman
, A. S.
Bruev
, B. I.
Nikolaev
, and V. I.
Troyan
, Sov. Phys. JETP
33
, 553
(1971
).32.
C. S.
Wang Chang
, G. E.
Uhlenbeck
, and J.
de Boer
, in Studies in Statistical Mechanics
, edited by J.
de Boer
and G. E.
Uhlenbeck
(North-Holland
, Amsterdam
, 1964
), pp. 243
–266
.33.
L.
Waldmann
, Z. Naturforsch. A
12
, 660
(1957
).34.
L.
Waldmann
, Z. Naturforsch. A
13
, 609
(1958
).35.
R. F.
Snider
, J. Chem. Phys.
32
, 1051
(1960
).36.
A.
Tip
, Physica
52
, 493
(1971
).37.
A.
Tip
, Physica
53
, 183
(1971
).38.
C. F.
Curtiss
, J. Chem. Phys.
74
, 6718
(1981
).39.
C. F.
Curtiss
, J. Chem. Phys.
97
, 1416
(1992
).40.
L. A.
Viehland
, Chem. Phys.
101
, 1
(1986
).41.
L.
Friedman
, Annu. Rev. Phys. Chem.
19
, 273
(1968
).42.
K. F.
Ness
and R. E.
Robson
, Phys. Rev. A
34
, 2185
(1986
).43.
R.
Robson
, R.
White
, and M.
Hildebrandt
, Fundamentals of Charged Particle Transport in Gases and Condensed Matter
(CRC Press
, Boca Raton, FL
, 2018
).44.
R. D.
White
, R. E.
Robson
, S.
Dujko
, P.
Nicoletopoulos
, and B.
Li
, J. Phys. D: Appl. Phys.
42
, 194001
(2009
).45.
S.
Dujko
, R. D.
White
, Z.
Petrovic
, and R. E.
Robson
, Phys. Rev. E
81
, 046403
(2010
).46.
S.
Dujko
, R. D.
White
, Z. L.
Petrović
, and R. E.
Robson
, Plasma Sources Sci. Technol.
20
, 024013
(2011
).47.
R. E.
Robson
, Introductory Transport Theory for Charged Particles in Gases
(World Scientific
, Singapore
, 2006
).48.
L. A.
Viehland
and E. A.
Mason
, J. Chem. Phys.
66
, 422
(1977
).49.
T.
Kihara
, Rev. Mod. Phys.
25
, 831
(1953
).50.
L. A.
Viehland
and W. F.
Siems
, J. Am. Soc. Mass Spectrom.
23
, 1841
(2012
).51.
B. A.
Finlayson
, The Method of Weighted Residuals and Variational Principles
(Academic Press
, New York
, 1972
).52.
L. A.
Viehland
and R.
Johnsen
, J. Chem. Phys.
149
, 074311
(2018
).53.
L. A.
Viehland
and R.
Johnsen
, J. Geophys. Res.: Atmos.
124
, 13593
, (2019
).54.
J. H.
Whealton
and E. A.
Mason
, Ann. Phys.
84
, 8
(1974
).55.
S. L.
Lin
, L. A.
Viehland
, and E. A.
Mason
, Chem. Phys.
37
, 411
(1979
).56.
L. A.
Viehland
and S. L.
Lin
, Chem. Phys.
43
, 135
(1979
).57.
I. S.
Gradshteyn
and I. M.
Ryzhik
, Tables of Integrals, Series and Products
(Academic Press
, New York
, 2014
).58.
J.
Lozeille
, E.
Winata
, P.
Soldán
, E. P. F.
Lee
, L. A.
Viehland
, and T. G.
Wright
, Phys. Chem. Chem. Phys.
4
, 3601
(2002
).59.
L. A.
Viehland
and Y.
Chang
, Comput. Phys. Commun.
181
, 1687
(2010
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.
