Advertisement

Transport Processes in Tracks

  • D. Fink
  • V. Hnatowicz
  • P. Yu. Apel
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 65)

Abstract

The linearly extended overall radiation-induced change in free volume — either resulting in a net increase or a decrease — together with the extended distribution of newly formed radicals, is one of the most characteristic properties of ion tracks in polymers, and therefore deserves special attention. According to findings on tracks in, e.g., polyimide [1], the free ion-track volume by no means just forms a small empty cylinder of nanometric dimension in the ion-track center, unless the tracks are extremely short [2]. Rather, the polymeric ion tracks appear to have a sponge-like consistency of free volume intermixed with carbon-enriched radiochemical reaction products with a fractal structure, which therefore often enables an enhanced transport of matter along them.

Keywords

Surface Enhance Raman Scattering Free Volume Latent Track Polymer Foil Irradiate Polymer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Klett R, Charakterisierung von hochenergetischen Schwerionenspuren in Polyimid. PhD. Thesis, Humboldt-University, Berlin 1996 (in German)Google Scholar
  2. 2.
    Eyal Y, Gassan K, Observation of latent heavy-ion tracks in polyimide by means of transmission electron microscopy. Nucl Instrum Methods B156, 183–190 (1999)CrossRefGoogle Scholar
  3. 3.
    Wang L, Trautmann Ch, Vetter J, Quan Z, Cohen D, Fladry H, Adhesion enhancement by GeV heavy ion irradiation. Radiat Eff Defects Solids 126, 403–407 (1993)CrossRefGoogle Scholar
  4. 4.
    Wang L (1996) personal communication, and Wang L, Angert N, Trautmann C, Vetter J, Effect of ion irradiation and heat treatment on adhesion in the Cu/Teflon system. J Adhes Sci Technol 9, 1523–1529 (1995)CrossRefGoogle Scholar
  5. 5.
    Avasthi DK, Assmann W, Nolte H, Mieskes HD, Huber H, Subramaniyam ET, Tripathy A, Ghosh S, On-line study of ion-beam induced mixing at interface by swift heavy ions. Nucl Instrum Methods B156, 143–147 (1999)CrossRefGoogle Scholar
  6. 6.
    Bolse W, Atomic transport in hot ion tracks. Presented at the 5th Intl. Symposium on “Swift Heavy Ions in Matter”, May 22–25, 2002, Giardini Naxos, ItalyGoogle Scholar
  7. 7.
    Soares MRF, Kaschny JRA, dos Santos JHR, Amaral L, Behar M, Fink D, Diffusion and solubility of Au implanted into the AZ1350 photoresist, Nucl Instrum Methods B166–167, 615–620 (2000)Google Scholar
  8. 8.
    Soares MRF, Kaschny JRA, dos Santos JHR, Amaral L, Behar M, Fink D, Diffusion and solubility of Bi implanted into the AZ1350 photoresist. Nucl Instrum Methods B191, 690–694 (2002)CrossRefGoogle Scholar
  9. 9.
    Fink D, Müller M, Nakao Y, Hirata K, Kobayashi Y, Behar M, Kaschny JR, Vacík J, Hnatowicz V, Ion-induced redistribution of palladium in polymethyl methacrylate, Nucl Instrum Methods B166–167, 610–614 (2000)Google Scholar
  10. 10.
    Biswas A, Marton Z, Kanzow J, Kruse J, Zaporojtchenko V, Faupel F, Controlled generation of Ni nanoparticles in the capping layers of teflon AF by vapor phase tandem evaporation. In print (2003)Google Scholar
  11. 11.
    Biswas A, Avasthi DK, Kanzow J, Ding SJ, Fink D, Gupta R, Zaporojtchenko V, Faupel F, Nanostructural modifications in Au cluster arrays distributed in teflon AF layers upon MeV heavy ion impact. In print (2003)Google Scholar
  12. 12.
    Moiseev YuV, Zaikov GE Chemical Stability of Polymers in Aggressive Media. Khimia, Moscow (1979) (in Russian)Google Scholar
  13. 13.
    Born M, Volumen and Hydratationswärme der Ionen. Z Phys 1, 45–48 (1920)CrossRefGoogle Scholar
  14. 14.
    Markin VS, Chismadzhev YuA, Induced Ionic Transport. Nauka, Moscow (1974) (in Russian)Google Scholar
  15. 15.
    Samoilova LI, Apel PYu, Etching of small pores in PETP by different alkalis. Radiat Meas 25, 717–720 (1995)CrossRefGoogle Scholar
  16. 16.
    Parsegian A, Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature 221, 844–846 (1969)CrossRefGoogle Scholar
  17. 17.
    Her M, Lösungsmittel-induzierte Delegation molekularer Sonden in latente Kernspuren and ihre photophysikalische Analyse, PhD. Thesis, Technical University Clausthal, 1996 (in German)Google Scholar
  18. 18.
    Fink D, Muller M, Petrov A (2002) Etching kinetics of swift heavy ion irradiated polymers with insoluble additives or reaction products. Proc 5th Intl. Conf. on Swift Heavy Ions in Matter, May 22–25, 2002, Giardini Naxos, ItalyGoogle Scholar
  19. 19.
    Fink D, Muller M, Capillaric penetration of etchant solution into swift heavy ion irradiated silicone rubber. Nucl Instrum Methods B170, 134–144 (2000)CrossRefGoogle Scholar
  20. 20.
    Fink D, Petrov A, Müller M, Hnatowicz V, Vacík J, Cervenâ J, Marker penetration into high energy ion irradiated polymers. Surf Coat Technol 158–159, 228–233 (2002)CrossRefGoogle Scholar
  21. 21.
    Fink D, Dwivedi KK, Müller M, Ghosh S, Hnatowicz V, Vacík J, Cervenâ J, On the penetration of etchant into tracks in polycarbonate. Radiat Meas 32, 307–313 (2000)CrossRefGoogle Scholar
  22. 22.
    Luck HB, Kinetik and Mechanismus der Bildung and Atzung von Teilchen-spuren in Polyethylenterephthalat. PhD. Thesis, TU Dresden, published as report ZfK-473 of the “Zentralinstitut für Kernforschung Rossendorf bei Dresden”(1982), and references: Be51, Be60, LL56, RM72, RM75, GJ78, DB75, SB78, and RA60 therein (in German)Google Scholar
  23. 23.
    Ghosh S, Klett R, Fink D, Dwivedi KK, Vacík J, Hnatowicz V, Jervenâ J, On the penetration of aqueous solutions into some pristine and heavy-ion irradiated polymers, Radiat Phys Chem 55, 271–284 (1999)CrossRefGoogle Scholar
  24. 24.
    Apel PYu, Schulz A, Spohr R, Trautmann C, Vutsadakis V, Tracks of very heavy ions in polymers. Nucl Instrum Methods B131, 55–63 (1997)CrossRefGoogle Scholar
  25. 25.
    Ferry JD, Viscoelastic Properties of Polymers, 3rd. edn, Wiley, New YorkGoogle Scholar
  26. 26.
    Davenas J, Xu XL, Diffusion of iodine into polyimide films modified by ion bombardment. Nucl Instrum Methods B81, 33–38 (1992)Google Scholar
  27. 27.
    Fink D, Chaderton LT, Cruz SA, Fahrner WR, Hnatowicz V, TeKaat EH, Melnikov AA, Varichenko VS, Zaitsev AM, Ion track doping. Radiat Eff Defects Solids 132, 81–90 (1994)CrossRefGoogle Scholar
  28. 28.
    Fink D, Hnatowicz V, Vacík J, Chadderton LT, On the lithium uptake of MeV ion irradiated polymer foils from a LiC1 solution. Radiat Eff Defects Solids 132, 1–10 (1994)CrossRefGoogle Scholar
  29. 29.
    Thomas NL, Windle A, A theory of Case II diffusion. Polymer 23, 529–542 (1982)CrossRefGoogle Scholar
  30. 30.
    Fink D, Klett R, Mathis C, Vacík J, Hnatowicz V, Chadderton LT, Depth profiles of fullerene in ion irradiated polyimide. Nucl Instrum Methods B100, 69–79 (1995)CrossRefGoogle Scholar
  31. 31.
    Wood E, Sutton C, Beezer AE, Creighton JA, Davis AF, Mitchell JC, Surface enhanced Raman scattering (SERS) of membrane transport processes. Intl J Pharmaceut 154, 115–118 (1997)CrossRefGoogle Scholar
  32. 32.
    Fink D, Ghosh S, Klett R, Dwivedi KK, Kobayashi Y, Hirata K, Vacík J, Hnatowicz V, Cervenâ J, Chadderton LT, Transport processes during the incubation time of ion track etching in polymers. Nucl Instrum Methods B146, 486–490 (1998)CrossRefGoogle Scholar
  33. 33.
    Fink D, Ghosh S, Hirata K, Klett R, Dwivedi K, Vacík J, Hnatowicz V, On the Interaction of penetrant solutions with pristine and ion-irradiated polyimide. In: Yu.Ts. Oganessian, R. Kalpakchieva (eds.): Heavy Ion Physics. World Scientific, Singapore 1998, pp. 784–791Google Scholar
  34. 34.
    Fink D, Klett R, Hnatowicz V, Vacík J, Mathis C, Omichi H, Hosoi F, Chadderton LT, Wang L, Bonding of dopants to irradiated polymers, Nucl Instrum Methods B116, 434–439 (1996)CrossRefGoogle Scholar
  35. 35.
    Seki S, Kanzaki K, Yoshida Y, Tagawa S, Shibata H, Asai K, Ishigure K, Positive-negative inversion of silicon based resist materials: poly (di-nhexylsilane) for ion beam irradiation. Jpn J Appl Phys 36, 5361–5364 (1997)CrossRefGoogle Scholar
  36. 36.
    Fink D, Chung WH, Klett R, Döbeli M, Synal HA, Chadderton LT, Wang L, On the dyeing of ion tracks in polymers. Nucl Instrum Methods B108, 377–384 (1996)CrossRefGoogle Scholar
  37. 37.
    Fink D, Omichi H, Hosoi F, Tamada M, Hnatowicz V, Vacík J, Chadderton LT, Klett R, Solid and liquid phase doping of energetic ion tracks in polymers. Advanced Materials ‘83/Laser and Ion Beam Modification of Materials, I. Yamada et al. (eds.). Trans Mater Res Soc Jpn, Vol. 17, Elsevier B.V., 1994, pp. 581–583Google Scholar
  38. 38.
    Fink D, Klett R, Chung WH, Griinwald R, Döbeli M, Ames F, Chadderton LT, Vacík J, Hnatowicz V, Doping of C,n (n = 1, 3, 5, 8) cluster ion tracks in polyimide. Radiat Eff Defects Solids 140, 3–20 (1996)Google Scholar
  39. 39.
    Fink D, Vacik J, Klett R, Chadderton LT, Hnatowicz V, Doping of 20 MeV fullerene ion tracks in polyimide. Nucl Instrum Methods B119, 591–595 (1996)CrossRefGoogle Scholar
  40. 40.
    Vacík J, Cervenâ J, Hnatowicz V, Posta S, Fink D, Klett R, Strauss P, Simple technique for characterization of ion-modified polymeric foils. Surf Sci Technol 123, 97–100 (2000)Google Scholar
  41. 41.
    Vetter J, Mickler GH, Naumann I, TEM observation of latent tracks of heavy ions in semicrystalline polymers. Radiat Eff Defects Solids 143, 273–286 (1998)CrossRefGoogle Scholar
  42. 42.
    See, e.g., Munro HS, ESCA studies on the photooxidation and the gammaradiation-induced oxidation of low density polyethylene, Polym Degrad Stab 12, 249–259 (1985)CrossRefGoogle Scholar
  43. 43.
    Fink D, Klett R, Hu X, Müller M, Schiwietz G, Xiao G, Chadderton LT, Wang L, Mathis C, Hnatowicz V, Vacfk J, Characterisation of aged latent ion tracks in polyimide. Nucl Instrum Methods B116, 66–71 (1996)CrossRefGoogle Scholar
  44. 44.
    Steckenreiter TH, Charakterisierung von Spuren energiereicher Ionen in Polymeren. PhD. Thesis, TH Darmstadt (1997) (in German)Google Scholar
  45. 45.
    Ghosh S, Klett R, Fink D, Dwivedi KK, Vacík J, Hnatowicz V, Cervenâ J, On the penetration of aqueous solutions into pristine and radiation damaged polyimide. Radiat Phys Chem 55, 271–284 (1999)CrossRefGoogle Scholar
  46. 46.
    Eßer M, Apel PYu, Brüchle W, Fuhrmann J, Heinrich B, Remmert G, Spohr R, Trautmann C, Vetter J, Solvent induced sensitization, GSI-Nachrichten, 03–93 11–16 (1993)Google Scholar
  47. 47.
    Eßer M, Fuess H, Spohr R, Steckenreiter T, Trautmann C, Solvent induced track sensitization, role of amines. Nucl Instrum Methods B107, 393–396 (1996)CrossRefGoogle Scholar
  48. 48.
    Apel PYu, Angert N, Brüchle W, Hermann H, Kampschulte U, Klein P, Kravets LI, Oganessian YuTs, Remmert G, Spohr R, Steckenreiter T, Trautmann Ch, Vetter J, Solvent induced sensitization, extraction of oligomers. Nucl Instrum Methods B86, 325–332 (1994)CrossRefGoogle Scholar
  49. 49.
    Apel PYu, Track regression effects in polyethylene terephthalate after sensitization. Instrum Exp Techn, translated from Pribory I Tekhnika Experimenta No 5, 71–75 (1992)Google Scholar
  50. 50.
    Steckenreiter Th, Dimethylformamid-Sensibilisierung latenter Teilchenspuren in Poly(ethylenterephthalat)-Folien. Diplomarbeit, TH Darmstadt (1994) (in German)Google Scholar
  51. 51.
    Zachmann HG, Kinetik der Kristallisation von gequollenem Polyethylenterephthalat. Makromol Chem 118, 189 pp. (1968) (in German)Google Scholar
  52. 52.
    Tamada M, Yoshida M, Asano H, Omichi H, Kakakai R, Spohr R, Vetter J, Thermo-response of ion track pores in copolymer films of methacryloyl_Lalanine methyl ester and diethyleneglycol-bis-allylcarbonate. Polymer 33, 3169–3172 (1992)CrossRefGoogle Scholar
  53. 53.
    Torrisi L, Percolla R, Ion beam processing of polyvinylidene fluoride. Nucl Instrum Methods B117, 387–391 (1996)CrossRefGoogle Scholar
  54. 54.
    Renardy M, Planck H, Trauter J, Zschocke P, Siebers U, Zecorn T, Federlin K, In: Heime G, Soltész U, Lee AJC (eds.): Clinical implant material. Adv Biomater 9, 633 (1990)Google Scholar
  55. 55.
    Gebel G, Ottomani E, Allegrand JJ, Betz N, LeMoel A, Structural study of polystyrene grafted in irradiated polyvinylidene fluoride thin films Nucl In-strum Methods B105, 145–149 (1995)Google Scholar
  56. 56.
    Duraud JP, Le Moel A, Le Gressus C, Aging of fluoropolymers irradiated by X-rays, low energy electrons and enegetic heavy ions. Radiat Eff 98, 151–157 (1986)CrossRefGoogle Scholar
  57. 57.
    Friese K, Plack V, Mehnert R, Angert N, Spohr R, Trautmann Ch, Radiation-induced grafting of styrene onto polyimide ion track membranes. Nucl Instrum Methods B105, 139–144 (1995)CrossRefGoogle Scholar
  58. 58.
    Martin CR, Nanomaterials: A membrane-based synthetic approach. Science 266, 1961–1966 (1994)CrossRefGoogle Scholar
  59. 59.
    Petrov A, Production of micro-and nanoelectrotechnic devices by help of ion tracks in insulators. PhD Thesis, Fernuniversität Hagen (2004)Google Scholar
  60. 60.
    Neumann R, Ion induced modifications in solids: basic aspects and applications in nanoscience. 21’ Int. Conf. on Nuclear Tracks in Solids, New Delhi, 21–25 Oct. 2002Google Scholar
  61. 61.
    Singh S, Sinha D, Srivastava A, Ghosh S, Dwivedi KK, Some chemical applications of nuclear track microfilters, to be published, 2002Google Scholar
  62. 62.
    Chin VI, Ozkan M, Bhatia S, Rapid three-dimensional arraying of single cells, Proc MRS Boston, 27.11.-1.12. 2001, Contribution Y5. 8Google Scholar
  63. 63.
    Jaffrin MY, Innovative processes for membrane plasma separation. J Membr Sci 44, 115–129 (1989)CrossRefGoogle Scholar
  64. 64.
    Barber DJW, Thomas JK, Radiat Res 74, 51–65 (1978)CrossRefGoogle Scholar
  65. 65.
    Schön W, Gärtner H, Kraft G, Radiat Envir Biophysics 33, 233–242 (1994)CrossRefGoogle Scholar
  66. 66.
    Leyko W, Bartosz G, J Radiat Biol 49, 743–770 (1986)CrossRefGoogle Scholar
  67. 67.
    J Guillet, Polymer Photophysics and Photochemistry: An Introduction to the Study of Photoprocesses in Macromolecules. Cambridge University Press, Cambridge, 1985Google Scholar
  68. 68.
    Remmert G, Transporteigenschaften and Geometrie von Schwerionenspuren in Polymerfolien. PhD. Thesis, Johann Wolfgang Goethe Universität, Frankfurt am Main (1994) (in German)Google Scholar
  69. 69.
    Komaki Y, Growth of fine holes by the chemical etching of fission tracks in polyvinylidene fluoride. Nucl Tracks 3, 33–44 (1979)CrossRefGoogle Scholar
  70. 70.
    Packard RE, Pekola SP, Price PB, Spohr RNR, Westmacott KH, Zhu YQ, GSI Scientific Report 1985, Darmstadt 1986Google Scholar
  71. 71.
    Backmeister GU, Enge W, Observation of the latent track structure in polymers by diffusion measurements. Nucl Instrum Methods B131, 643–70 (1997)Google Scholar
  72. 72.
    Turowski T, Schockwellenmodell zur Beschreibung des ionendichteabhängigen Diffusionsverhaltens bestrahlter Polymerfolien. PhD. Thesis, ChristianAlbrechts-Universität Kiel (2001) (in German)Google Scholar
  73. 73.
    Fink D, Biersack JP, Compactation of polymers by energetic ions. HMI Berlin, internal report (1994 and 1999), forwarded in 1999 to Turowski T. as the basis of his PhD. Thesis, see Ref. [72]Google Scholar
  74. 74.
    Sudowe R, Penzhorn RD, Vater P, Abu-Jaber S, Brandt R, Filters with small holes (d 1 gm) as a tool to separate gases. Radiat Meas 28, 811–816 (1997)CrossRefGoogle Scholar
  75. 75.
    Ovchinnikov V.V., Seleznev V.D., Surguchev V.V., Tokmantsev V.I. Investigation of separation efficiency for gases on nuclear membrane with hyperfine pores. J Membr Sci 55, 311–323 (1991)CrossRefGoogle Scholar
  76. 76.
    Ghosh S, Klett R, Fink D, Dwivedi KK, Vacík J, Hnatowicz V, Cervenä J, On the penetration of aqueous solutions into some pristine and heavy-ion irradiated polymers. Radiat Phys Chem 55, 271–284 (1999)CrossRefGoogle Scholar
  77. 77.
    Fink D, Klett R, Latent tracks in polymers for future use in nanoelectronics, an overview about the present state-of-the-art. Braz J Phys 25, 54–75 (1995)Google Scholar
  78. 78.
    Deen WM, Hindered transport of large molecules in liquid-filled pores. AIChE Journal 33, 1409–1425 (1987)CrossRefGoogle Scholar
  79. 79.
    Wolf A, Reber N, Apel PYu, Fischer BE, Spohr R, Electrolyte transport in charged single ion track capillarities. Nucl Instrum Methods B105, 291–293 (1995)CrossRefGoogle Scholar
  80. 80.
    Grossmann PD, Colburn JC, Capillary Electrophoresis: Theory and Practice. Academic Press Incl., San Diego (1992)Google Scholar
  81. 81.
    Deamer D, Westphal A, Progress towards the development of a rapid DNA se-. quencer using etched relativistic ion tracks. Proc of the Workshop on European Network on Ion Track Technology, Caen, France, 24–26. Feb. 2002Google Scholar
  82. 82.
    Baur D, Apel PYu, Korchev YE, Müller C, Siwy Z, Spohr H, Spohr R, Surface gel in ion track etching — observations and consequences. Proc of the Workshop on European Network on Ion Track Technology, Caen, France, 24–26. Feb. 2002Google Scholar
  83. 83.
    Apel PYu, Korchev YuE, Siwy Z, Spohr R, Yoshida M, Diode-like single-ion track membrane prepared by electro-stopping. Nucl Instrum Methods B184, 337–346 (2001), and references therein, andGoogle Scholar
  84. Apel PYu, Tuchkin SV, Gotlib VA, Lebedeva NE, Lev AA, Rectification property of conical track etched pores and an explanation of the change of rectifying direction at some conditions. Proc of the Workshop on European Network on Ion Track Technology, Caen, France, 24–26. Feb. 2002Google Scholar
  85. 84.
    Berezkin VV, Kiseleva OA, Nechaev AN, Sobolev VD, Churaev NV. Kolloidn Zh 56, 319–325 (1994) (in Russian)Google Scholar
  86. 85.
    Marquet C, Buguin A, Talini L, Silberzan R, Rectified motion of colloids in asymmetrically structured channels. Phys Rev Lett 88, 168301/1–4 (2002)Google Scholar
  87. 86.
    Siwy Z. Fulinski, Fabrication of a synthetic nanopore ion pump. Phys Rev Lett 89, 198103–1–198103–4 (2002)Google Scholar
  88. 87.
    see, e.g., Liu DS, Astumian RD, Tsong TY, J Biolog Chem 265, 7260 (1990)Google Scholar
  89. 88.
    Pintauro PN, Verbrugge MW, The electric-potential profile in ion-exchange membrane pores. J Membr Sci 44, 197–212 (1989)CrossRefGoogle Scholar
  90. 89.
    Pasternak CA, Alder M, Apel PYu, Bashford CL, Korchev YE, Lev AA, Rostovtseva TK, Zhitariuk NI, Model pores for biological membranes: The properties of track-etched membranes. Nucl Instrum Methods B195, 332–334 (1995)Google Scholar
  91. Pasternak CA, Bashford CL, Korchev YE, Rostovtseva TK, Lev AA. In: Colloids Surf, A: Physicochem Eng Aspects 77, 119 (1993)Google Scholar
  92. 90.
    Lev AA, Korchev YE, Rostovtseva TK, Bashford CL, Edmonds DT, Pasternak CA, Proc Royal Soc B252, 187–192 (1993)CrossRefGoogle Scholar
  93. 91.
    Martin CR, Nishizawa M, Jirage K, Kang M, Lee SB, Controlling transport selectivity in gold nanotubule membranes, Adv Mater 13, 1351–1362 (2001)CrossRefGoogle Scholar
  94. 92.
    Jirage KB, Hulteen JC, Martin CR, Effect of thiol chemisorption on the transport properties of gold nanotubule menbranes. Anal Chem 71, 4913–4918 (1999)CrossRefGoogle Scholar
  95. 93.
    Fink D, Müller M, Szimkowiak P, Klett R, Vacík J, Hnatowicz V, Chadderton LT, Rutherford backscattering of laterally heterogeneous structures: the determination of radial density distributions in ion tracks in collodium. Nucl Instrum Methods B134, 87–97 (1998)CrossRefGoogle Scholar
  96. 94.
    Fink D, Müller M, Vacik J, Cervenâ. J, Hnatowicz V, Nanotomographic examinations of etched and latent ion tracks by ion energy loss spectrometry. Appl Phys A68, 87–91 (1999)Google Scholar
  97. 95.
    Stolterfoht N, Bremer JH, Hoffmann V, Fink D, Petrov A, Sulik B, Transmission of 3 keV Ne+ through nanocapillaries etched in polymer foils: evidence for capillary guiding. Phys Rev Lett 88, 133201/1–4 (2002)Google Scholar
  98. 96.
    Stolterfoht N, Hellhammer R, Pesic ZD, Hoffmann V, Bundesmann J, Petrov A, Fink D, Sulik B. Guiding of Ne’+ ions through nanocapillaries in a PET polymer: dependence on the capillary diameter. Presented at the Conf. IPMM03, Sendai, Japan, May 2003Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • D. Fink
  • V. Hnatowicz
  • P. Yu. Apel

There are no affiliations available

Personalised recommendations