Skip to main content

Transport Cross Sections: Classical and Quantum Approaches

  • Chapter
  • First Online:
Fundamental Aspects of Plasma Chemical Physics

Abstract

The heart of the Chapmanā€“Enskog theory lies on some assumptions on the nature of elementary collisions, which are postulated to be binary, elastic, characterized by isotropic interparticle force field, and adequately described through classical mechanics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Traditionally the orders (1,1) and (2,2) are defined as diffusion-type and viscosity-type collision integrals, respectively, due to a direct dependence of binary diffusion and viscosity coefficients from the Ī© (1,ā€‰1) and Ī© (2,ā€‰2) values, when calculated in the first Chapmanā€“Enskog approximation.

  2. 2.

    Database is available on-line at the National Institute of Standards and Technology (NIST) website http://webbook.nist.gov/chemistry/

References

  • Amdur I (1961) An experimental approach to the determination of gaseous transport properties at very high temperatures. Planet Space Sci 3:228

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Amdur I, Mason EA (1958) Properties of gases at very high temperatures. Phys Fluids 1(5):370ā€“383

    ArticleĀ  MathSciNetĀ  ADSĀ  Google ScholarĀ 

  • Amdur I, Engler MJ, Jordan JE, Mason EA (1975) Short-range Heā€“Xe interaction from molecular-beam scattering. J Chem Phys 63(1):597ā€“597

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • AndrĆ© P, BussiĆØre W, Rochette D (2007) Transport coefficients of Ag-SiO2 plasmas. Plasma Chem Plasma Process 27(4):381ā€“403

    ArticleĀ  Google ScholarĀ 

  • Aquilanti V, Cappelletti D, Pirani F (1996) Range and strength of interatomic forces: dispersion and induction contributions to the bonds of dications and of ionic molecules. Chem Phys 209(2ā€“3):299ā€“311

    ArticleĀ  Google ScholarĀ 

  • Aziz RA, Slaman MJ (1990) The repulsive wall of the Arā€“Ar interatomic potential reexamined. J Chem Phys 92(2):1030

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Bell KL, Scott NS, Lennon MA (1984) The scattering of low-energy electrons by argon atoms. J Phys B At Mol Phys 17(23):4757

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Beneventi L, Casavecchia P, Pirani F, Vecchiocattivi F, Volpi GG, Brocks G, vanĀ der Avoird A, Heijmen B, Reuss J (1991) The Neā€“O2 potential energy surface from high-resolution diffraction and glory scattering experiments and from the Zeeman spectrum. J Chem Phys 95(1):195ā€“204

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Biolsi L, Biolsi KJ (1979) Transport properties of monatomic carbon II: Contributions from excited electronic states. J Geophys Res 84(A9):5311ā€“5318

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Biolsi L, Rainwater JC, Holland PM (1982) Transport properties of monatomic carbon. J Chem Phys 77(1):448

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Brunetti B, Pirani F, Vecchiocattivi F, Luzzatti E (1978) Absolute total cross sections for elastic scattering of Ne by Ar, Kr and Xe: characterization of long range interactions. Chem Phys Lett 55(3):565

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Brunetti B, Liuti G, Luzzatti E, Pirani F, Vecchiocattivi F (1981) Study of the interactions of atomic and molecular oxygen with O2 and N2 by scattering data. J Chem Phys 74:6734

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Brunetti B, Liuti G, Luzzatti E, Pirani F, Volpi GG (1983) The interaction of atomic and molecular nitrogen with argon by scattering measurements. J Chem Phys 79(1):273ā€“277

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Brunger MJ, Buckman SJ (2002) Electron-molecule scattering cross-sections. I. experimental techniques and data for diatomic molecules. Phys Rep 357(3ā€“5):215ā€“458

    Google ScholarĀ 

  • Bruno D, Catalfamo C, Laricchiuta A, Giordano D, Capitelli M (2006) Convergence of Chapman-Enskog calculation of transport coefficients of magnetized argon plasma. Phys Plasmas 13(7):072307

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Cambi R, Cappelletti D, Liuti G, Pirani F (1991) Generalized correlations in terms of polarizability for van der Waals interaction potential parameter calculations. J Chem Phys 95(3):1852ā€“1861

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Capitelli M, Ficocelli E (1972) Collision integrals of oxygen atoms in different electronic states. J Phys B At Mol Phys 5(11):2066ā€“2073

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Capitelli M, Ficocelli E (1973) Collision integrals of carbon-oxygen atoms in different electronic states. J Phys B At Mol Phys 6:1819ā€“1823

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Capitelli M, Lamanna UT, Guidotti C, Arrighini GP (1983) Comment on ā€˜spin-polarized atomic nitrogen and the 7 Ī£ u ā€‰+ā€‰ state of N2ā€™. J Chem Phys 79:5210

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Cappelletti D, Liuti G, Pirani F (1991) Generalization to ionā€”neutral systems of the polarizability correlations for interaction potential parameters. Chem Phys Lett 183(3ā€“4):297ā€“303

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Capitelli M, Gorse C, Longo S, Giordano D (2000) Collision integrals of high-temperature air species. J Thermophys Heat Transf 14(2):259ā€“268

    ArticleĀ  Google ScholarĀ 

  • Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F (2007) On the possibility of using model potentials for collision integral calculations of interest for planetary atmospheres. Chem Phys 338(1):62ā€“68

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Capitelli M, Colonna G, Dā€™Angola A (2011) Fundamental aspects of plasma chemical physics: thermodynamics. Springer series on atomic, optical, and plasma physics, volĀ 66. Springer, New York

    Google ScholarĀ 

  • Colonna G, Laricchiuta A (2008) General numerical algorithm for classical collision integral calculation. Comput Phys Commun 178(11):809ā€“816

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Dā€™Angola A, Colonna G, Gorse C, Capitelli M (2008) Thermodynamic and transport properties in equilibrium air plasmas in a wide pressure and temperature range. Eur Phys J D 46(1):129ā€“150

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Devoto RS (1967) Transport coefficients of partially ionized argon. Phys Fluids 10(2):354ā€“364

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Devoto RS (1968) Transport coefficients of partially ionized hydrogen. JĀ Plasma Phys 2(4):617ā€“631

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Geltman S (1969) Topics in atomic collision theory. Academic, New York

    Google ScholarĀ 

  • Gibson JC, Gulley RJ, Sullivan JP, Buckman SJ, Chan V, Burrow PD (1996) Elastic electron scattering from argon at low incident energies. J Phys B At Mol Opt Phys 29(14):3177

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Gryzinski M (1970) Ramsauer effect as a result of the dynamic structure of the atomic shell. Phys Rev Lett 24:45ā€“47

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Gupta RN, Yos JM, Thompson RA, Lee KP (1990) A review of reaction and thermodynamic properties for 11-species air model for chemical and thermal non-equilibrium calculations to 30Ā 000Ā K. NASA Report RP-1232

    Google ScholarĀ 

  • Hahn HS, Mason EA, Smith FJ (1971) Quantum transport cross sections in a completely ionized gas. Phys Fluids 14(2):278ā€“287

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Heck EL, Dickinson AS (1996) Transport and relaxation cross-sections for pure gases of linear molecules. Comput Phys Commun 95(2ā€“3):190ā€“220

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Hirschfelder JO, Eliason MA (1957) The estimation of the transport properties for electronically excited atoms and molecules. Ann New York Acad Sci 67(9):451ā€“461

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Hirschfelder JO, Curtiss CF, Bird RB (1966) Molecular theory of gases and liquids. Wiley, New York

    Google ScholarĀ 

  • Itikawa Y (2002) Cross sections for electron collisions with carbon dioxide. JĀ Phys Chem Ref Data 31(3):749ā€“767

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Itikawa Y (2006) Cross sections for electron collisions with nitrogen molecules. J Phys Chem Ref Data 35(1):31ā€“53

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Itikawa Y (2009) Cross sections for electron collisions with oxygen molecules. J Phys Chem Ref Data 38(1):1ā€“20

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Kalinin A, Dubrovitskii D (2000) The possibility of using repulsive interaction potentials for the calculation of high-temperature integrals of collisions between atoms and molecules. High Temp 38(6):848ā€“851. Translated from Teplofizika Vysokikh Temperatur 38(6) (2000) 88ā€“885

    Google ScholarĀ 

  • Kalinin A, Leonas V, Sermyagin A (1976) On the functionality of short-range potentials derived from the beam scattering data. Chem Phys Lett 39(1):191ā€“193

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Kihara T, Aono O (1963) Unified theory of relaxations in plasmas I. Basic theorem. J Phys Soc Japan 18(6):837ā€“851

    ArticleĀ  MathSciNetĀ  ADSĀ  Google ScholarĀ 

  • Kihara T, Taylor MH, Hirschfelder JO (1960) Transport properties for gases assuming inverse power intermolecular potentials. Phys Fluids 3(5):715ā€“720

    ArticleĀ  MathSciNetĀ  MATHĀ  ADSĀ  Google ScholarĀ 

  • Landau DL, Lifshitz EM (1981) Quantum mechanics: nonā€“relativistic theory. Butterworthā€“Heinemann, Oxford

    Google ScholarĀ 

  • Laricchiuta A, Colonna G, Bruno D, Celiberto R, Gorse C, Pirani F, CapitelliĀ M (2007) Classical transport collision integrals for a Lennard-Jones like phenomenological model potential. Chem Phys Lett 445(4ā€“6):133ā€“139

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Laricchiuta A, Bruno D, Capitelli M, Celiberto R, Gorse G, Pintus G (2008) Collision integrals of oxygen atoms and ions in electronically excited states. Chem Phys 344(1ā€“2):13ā€“20

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Laricchiuta A, Bruno D, Capitelli M, Catalfamo C, Celiberto R, Colonna G, Diomede P, Giordano D, Gorse C, Longo S, Pagano D, Pirani F (2009) High temperature Mars atmosphere. Part I: Transport cross sections. Eur Phys J D 54(3):607ā€“612

    Google ScholarĀ 

  • Leonas VB (1972) Studies of short-range intermolecular forces. Sov Phys Usp 15(3):266

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Leonas V, Sermyagin A, Kamyshov N (1971) The short-range interaction of molecules: the experimental investigation of potential energy surfaces. Chem Phys Lett 8(3):282ā€“284

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Levin E, Wright MJ (2004) Collision integrals for ion-neutral interactions of nitrogen and oxygen. J Thermophys Heat Tran 18(1):143ā€“147

    ArticleĀ  Google ScholarĀ 

  • Levin E, Partridge H, Stallcop J (1990) Collision integrals and high temperature transport properties for N-N, O-O and N-O. J Thermophys Heat Tran 4(4):469ā€“477

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Liboff RL (1959) Transport coefficients determined using the shielded Coulomb potential. Phys Fluids 2(1):40ā€“46

    ArticleĀ  MATHĀ  ADSĀ  Google ScholarĀ 

  • Liuti G, Pirani F (1985) Regularities in van der Waals forces: correlation between the potential parameters and polarizability. Chem Phys Lett 122(3):245ā€“250

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Longo S, Capitelli M (1994) A simple approach to treat anisotropic elastic collisions in Monte Carlo calculations of the electron energy distribution function in cold plasmas. Plasma Chem Plasma Process 14:1ā€“13

    ArticleĀ  Google ScholarĀ 

  • Maclagan RGAR, Viehland LA, Dickinson AS (1999) Ab initio calculation of the gas phase ion mobility of COā€‰+ā€‰ ions in He. J Phys B At Mol Phys 32(20):4947

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Mason EA (1954) Transport properties of gases obeying a modified Buckingham (expƤĆŖsix) potential. J Chem Phys 22(2):169

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Mason EA (1957) Scattering of low velocity molecular beams in gases. JĀ Chem Phys 26(3):667ā€“677

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Mason EA, Munn RJ, Smith FJ (1967) Transport coefficients of ionized gases. Phys Fluids 10(8):1827

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Meeks F, Cleland T, Hutchinson K (1967) On the quantum cross sections in dilute gases. J Chem Phys 10(10):2105ā€“2112

    Google ScholarĀ 

  • Monchick L (1959) Collision integrals for the exponential repulsive potential. Phys Fluids 2(6):695ā€“700

    ArticleĀ  MathSciNetĀ  MATHĀ  ADSĀ  Google ScholarĀ 

  • Morgan JE, Schiff HI (1964) Diffusion coefficients of O and N atoms in inert gases. Canad J Chem 42(10):2300

    ArticleĀ  Google ScholarĀ 

  • Mott N, Massey H (1965) The theory of atomic collisions. Clarendon, Oxford

    Google ScholarĀ 

  • Murphy AB (2000) Transport coefficients of hydrogen and argonā€“hydrogen plasmas. Plasma Chem Plasma Process 20(3):279ā€“297

    ArticleĀ  Google ScholarĀ 

  • Nahar SN, Wadehra JM (1987) Elastic scattering of positrons and electrons by argon. Phys Rev A 35:2051ā€“2064

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Neufeld PD, Janzen AR, Aziz RA (1972) Empirical equations to calculate 16 of the transport collision integrals Ī© (ā„“,ā€‰s)ā€‰ā‹†ā€‰ for the Lennard-Jones (12ā€“6) potential. J Chem Phys 57(3):1100

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Oā€™Hara H, Smith F (1971) Transport collision integrals for a dilute gas. Comput Phys Commun 2(1):47ā€“54

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Panajotovic R, Filipovic D, Marinkovic B, Pejcev V, Kurepa M, Vuskovic L (1997) Critical minima in elastic electron scattering by argon. J Phys B At Mol Opt Phys 30(24):5877

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Pirani F, Cappelletti D, Liuti G (2001) Range, strength and anisotropy of intermolecular forces in atomā€“molecule systems: an atomā€“bond pairwise additivity approach. Chem Phys Lett 350(3ā€“4):286ā€“296

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Pirani F, AlbertĆ­ M, Castro A, Teixidor MM, Cappelletti D (2004) Atomā€“bond pairwise additive representation for intermolecular potential energy surfaces. Chem Phys Lett 394(1ā€“3):37ā€“44

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Pirani F, Maciel GS, Cappelletti D, Aquilanti V (2006) Experimental benchmarks and phenomenology of interatomic forces: open-shell and electronic anisotropy effects. Int Rev Phys Chem 25(1ā€“2):165ā€“199

    ArticleĀ  Google ScholarĀ 

  • Rainwater J, Holland P, Biolsi L (1982) Binary collision dynamics and numerical evaluation of dilute gas transport properties for potentials with multiple extrema. J Chem Phys 77(1):434ā€“447

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Rat V, AndrĆ© P, Aubreton J, Elchinger MF, Fauchais P, Vacher D (2002) Transport coefficients including diffusion in a two-temperature argon plasma. J Phys D Appl Phys 35(10):981ā€“991

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Rat V, Murphy AB, Aubreton J, Elchinger MF, Fauchais P (2008) Treatment of non-equilibrium phenomena in thermal plasma flows. J Phys D Appl Phys 41(18):183001

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Singh NL, Jain DC (1962) The Rydberg-Klein-Rees method of constructing the true potential energy curves of diatomic molecules. Proc Phys Soc 79(2):274

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Smith FJ (1967) High order collision integrals. Final Report on contract NSR 52-112-001 National Aeronautics and Space Administration

    Google ScholarĀ 

  • Smith F, Munn R (1964) Automatic calculation of the transport collision integrals with tables for the Morse potential. J Chem Phys 41(11):3560ā€“3568

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Sourd B, Aubreton J, Elchinger MF, Labrot M, Michon U (2006) High temperature transport coefficients in e/C/H/N/O mixtures. J Phys D Appl Phys 39(6):1105ā€“1119

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Stallcop JR, Partridge H, Levin E (1991) Resonance charge transfer, transport cross sections, and collision integrals for Nā€‰+ā€‰(3P)-N(4S) and Oā€‰+ā€‰(4S)-O(3P) interactions. J Chem Phys 95(9):6429ā€“6439

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Stallcop JR, Partridge H, Levin E (1992) Collision integrals for the interaction of the ions of nitrogen and oxygen in a plasma at high temperatures and pressures. Phys Fluids B Plasma Phys 4(2):386ā€“391

    ArticleĀ  Google ScholarĀ 

  • Stallcop JR, Partridge H, Pradhan A, Levin E (2000) Potential energies and collision integrals for interactions of carbon and nitrogen atoms. J Thermophys Heat Tran 14(4):480ā€“488

    ArticleĀ  Google ScholarĀ 

  • Stallcop JR, Partridge H, Levin E (2001) Effective potential energies and transport cross sections for atom-molecule interactions of nitrogen and oxygen. Phys Rev A 64(4):042722 1ā€“12

    Google ScholarĀ 

  • Tang KT, Toennies JP (2003) The van der Waals potentials between all the rare gas atoms from He to Rn. J Chem Phys 118(11):4976ā€“4983

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Vanderslice JT (1962) Modification of the Rydberg-Klein-Rees method for obtaining potential curves for doublet states intermediate between Hundā€™s cases (a) and (b). J Chem Phys 37(2):384ā€“388

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Viehland LA, Dickinson AS, Maclagan RGAR (1996) Transport coefficients for NOā€‰+ā€‰ ions in helium gas: a test of the NOā€‰+ā€‰-He interaction potential. Chem Phys 211(1ā€“3):1ā€“15

    ArticleĀ  Google ScholarĀ 

  • Wright MJ, Bose D, Palmer GE, Levin E (2005) Recommended collision integrals for transport property computations part 1: air species. AIAA J 43(12):2558ā€“2564

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Wright MJ, Hwang HH, Schwenke DW (2007) Recommended collision integrals for transport property computations part 2: Mars and Venus entries. AIAA J 45(1):281ā€“288

    ArticleĀ  ADSĀ  Google ScholarĀ 

  • Yun K, Mason E (1962) Collision integrals for the transport properties of dissociating air at high temperatures. Phys Fluids 5(4):380ā€“386

    ArticleĀ  ADSĀ  Google ScholarĀ 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

Ā© 2013 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Capitelli, M., Bruno, D., Laricchiuta, A. (2013). Transport Cross Sections: Classical and Quantum Approaches. In: Fundamental Aspects of Plasma Chemical Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8172-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-8172-1_3

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-8171-4

  • Online ISBN: 978-1-4419-8172-1

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics