Zbigniew J. Grzywna

Z.J.G.'s photo email: Zbigniew.Grzywna@polsl.pl
phone: +48 32 2371752
fax: +48 32 2371722
Z.J.G.'s workplace


Full Professor of Physical Sciences

Silesian University of Technology (SUT)
Faculty of Chemistry
Department of Physical Chemistry and Technology of Polymers
Div. of Physical Chemistry
Section of Physics and Applied Mathematics
Strzody 9, 44-100 Gliwice, POLAND


Chemical Physics:
  • Diffusion Limited Aggregation (DLA)
  • Self-similar (fractal) Patterns Formation
  • Chemical Dynamics
Physics and Biophysics:
  • Nonlinear Diffusion Problems (semi and quasilinear problems)
  • Transport Through Membranes
  • Chaos and nonlinear phenomena in ionic transport through membranes
  • Fractals and Chaos in general
  • Structure and morphology problems
  • Analytical methods for solving nonlinear PDEs
  • Parabolic and hyperbolic heat-diffusion equations
  • Numerical and computational methods for solving DEs
  • Stochastic methods



Zbigniew Grzywna, Aleksandra Rybak, Przemysław Borys, Experimental physics. Laboratory for chemistry students, Gliwice : Wydaw. Politechniki ¦l±skiej, 2014, Skrypt nr 2531


  1. Z.Grzywna, J.Izydorczyk, J.Podkówka, J.Salwiński, Charakterystyka sorpcyjna poliestrowej folii Poltherm i Estrofol, Polimery, 20, 338, (1975)
  2. J.Podkówka, Z.Grzywna, J.Izydorczyk, J.Salwiński, Metoda sorpcyjna oznaczania współczynników dyfuzji par substancji lotnych w foliach polimerowych, Polimery, 20, 226, (1975)
  3. J.Podkówka, Z.Grzywna, Własno¶ci sorpcyjne poliestroimidowej folii PEI-D10, Polimery, 21, 164, (1976)
  4. Z.Grzywna, J.Podkówka, Zależno¶ć współczynnika dyfuzji od stężenia w układzie folia poliestroimidowa-para wodna, Polimery, 21, 164 (1976)
  5. Z.Grzywna, J.Podkówka, A method of solving the stationary state of diffusion through polymer films, Bull. Acad. Pol. Sci. Ser. Sci. Chem. 24, 811 (1976)
  6. J.IzydorczykJ.Podkówka, J.Salwiński, Z.Grzywna, A new method of determination of the permeability of vapors of volatile liquid substances through polymer membranes, J.Appl. Polym. Sci. 21, 1853 (1977)
  7. J.Podkówka, Z.Grzywna, D.Rudek, Oznaczanie przenikalno¶ci par substancji organicznych przez folie polimerowe metodą wagową, Polimery, 22, 14 (1977)
  8. Z.Grzywna, J.Podkówka, Effect of immobilizing adsorption of mass transport through polymer films, J.Membrane Sci. (Netherlands) 8, 23 (1981)
  9. Z.J.Grzywna, J.H.Petropoulos, Transient diffusion kinetics in media exhibiting axial variation of diffusion properties. Part I. Sorption Kinetics, J.Chem. Soc. Faraday Trans. II (GB) 79, 576 (1983)
  10. Z.J.Grzywna, J.H.Petropoulos, Transient diffusion kinetics in media exhibiting axial variation of diffusion properties. Part II. Permeation Kinetics, J.Chem. Soc. Faraday Trans. II (GB), 79, 585 (1983)
  11. J.Izydorczyk, J.Salwiński and Z.J.Grzywna, Application of reduction current measurements for investigating the diffusion of chloric derivatives of methane in polymeric membranes, Polish J. Chem. 57, 1287 (1983)
  12. Z.J.Grzywna, H.L.Frisch, An application of WKB approximation to transient diffusion in inhomogeneous membranes. Part I. General solutions, Polish J.Chem. 58, 211 (1984)
  13. Z.J.Grzywna, H.L.Frisch, An application of WKB approximation to transient diffusion in inhomogeneous membranes. Part II. Sorption, Polish J. Chem. 58, 221 (1984)
  14. Z.J.Grzywna, H.L.Frisch, An application of WKB approximation to transient diffusion in inhomogeneous membranes. Part III. Permeation, Polish J. Chem. 58, 227 (1984)
  15. H.L.Frisch, Z.J.Grzywna, Early time solution of the diffusion reaction equation, J. Phys. Chem. 90, 4111 (1986)
  16. Z.J.Grzywna, A.Gadomski, Agregacja limitowana dyfuzją (Diffusion limited aggregation), Prace IPPT, 41 60 (1987)
  17. Z.J.Grzywna, A.M.Simon, An Analytical Iterative Method For Solving Concentration Dependent Diffusion Problems, Polish J.Chem. 603, 4-12, (1989)
  18. A.Gadomski, Z.J.Grzywna, On Mullins-Sekerka Stability Analysis in DLA Models, Environmental Prot. Eng. 15, 3-4, 22 (1989)
  19. Z.J.Grzywna, A.Gadomski, Nonequilibrium thermodynamics in a form of dynamical system, Proceedings of the International Symposium on Gas Separation Technology, September 10-15, 1989, Antwerp, Belgium, Elsevier Sci.Publishers, Amsterdam, 49 (1990)
  20. Z.J.Grzywna, A.Gadomski, An influence of various fields on diffusion limited aggregation process, IFTR Reports, 52 109 (1990)
  21. Z.J.Grzywna, A.Gadomski, Structural Stability Analysis In Stationary Diffusion Limited Aggregation, Acta Physica Polonica 5, 112 (1990)
  22. Z.J.Grzywna, A.M.Simon, Transient Diffusion Experiments in Catalytically Active Membranes, Chem. Ing. Sci. 46, 1, 335 (1991)
  23. A.M.Simon, Z.J.Grzywna, On The Larche-Cahn Theory For Stress-Induced Diffusion, Institute For Mathematics And Its Appl. Univ.of Minnesota, MN, USA, Preprint Series # 868 August 1991
  24. A.Gadomski, Z.J.Grzywna, On the fractal properties of DLA-polymers, Proceedings of the Symposium on the Dynamics of Systems with Chemical Reaction, September 5-9, 1990, Świdno, Poland, World Scientific, Singapore, 416 (1991)
  25. J.Łuczka, A.Gadomski, Z.J.Grzywna, Growth Driven by Diffusion, Institute For Mathematics And Its Appl. Univ. of Minnesota, MN, USA, Preprint Series # 869, August 1991
  26. Z.J.Grzywna, J. Łuczka, Parabolic Versus Hyperbolic Diffusion in Membrane Transport, Acta Pharmaceutica Yugoslavica, 41, 327-344 (1991)
  27. J. Łuczka, A.Gadomski, Z.J.Grzywna, On the Diffusion Driven Growth : the Perturbed Sphere Problem Revisited, Czechoslovak Journal of Physics, 6, 42, 577-590 (1992)
  28. A.M.Simon, Z.J. Grzywna, On the Larch'e-Cahn Theory For Stress-Induced Diffusion, Acta Metalurgica et Materialia, 40, 12, 3465-3473, (1992)
  29. A.M.Simon, Z.J.Grzywna, Time Lags Analysis of Mass Transport Throught Catalytically Active Membranes, Chem. Eng. Sci., 48, 6, 1051-1060, (1993)
  30. A.Gadomski, Z.J.Grzywna, J.Łuczka, The Growing Processes in Diffusive and Convective Fields, Chem. Eng. Sci., 48, 21, 3713-3721, (1993)
  31. A.Gadomski, Z.J.Grzywna, J.Łuczka, An evolution equation applied to the perturbed sphere growth, Chem. Engng Sci. 48 3713 (1993)
  32. Z.J.Grzywna, O relacji między sorpcją, desorpcją a stanem stacjonarnym dyfuzji, Zeszyty Naukowe AGH, Chemia, 25, 19-32 (1993)
  33. Z.J.Grzywna, A.M.Simon, The Sorption-Desorption Problem As Related to Stationary Permeation For the Concentration Dependent Diffusion, Polish J.Chem. 68, 831-843 (1994)
  34. Z.J. Grzywna,Scaling in Diffusive Transport Through Membranes, Chem. Eng. Sci. 51, 17, 4115- 4125 (1996)
  35. Z.J. Grzywna, Z. Siwy, C.L. Bashford, Nonlinear Theory For Ionic Transport Through Track - Etched Nuclear Filters, J.Membr.Sci., 121, 2, 261-269 (1996)
  36. Z.J. Grzywna, Z. Siwy, C.L. Bashford, On the crowd model for the patch-clamp data, Cellular and Molecular Biology Letters 1, 3, 291-301 (1996)
  37. M.B.A. Djamgoz, Z.J. Grzywna, M.Krasowska, S. Vallerga, Fractal analysis of dendritic tree of transient amacrine cells of gold fish retina versus diffusion limited aggregate (DLA), Cellular and Molecular Biology Letters 1, 3, 259-271 (1996)
  38. Z.J. Grzywna, Z. Siwy, Chaos in Ionic Transport Through Membranes, Int. Journal of Bifurcation and Chaos, 7, 5, 1115-1123 (1997)
  39. Z.J. Grzywna, L.S. Liebovitch, Z. Siwy, On the self-similarity of logistic map, Cellular and Molecular Biology Letters, 2, 4, 449-466 (1997)
  40. Z.J. Grzywna, L.S. Liebovitch, Z. Siwy, Letter to Editor (discussion with Dr Palmeri on the article: A dual mode mechanism of conductance through fine porous membranes, J.Membr.Sci., 145¸253-263 (1998)) - J.Membr.Sci, 160, 277 (1999)
  41. A. Fuliński, Z.J. Grzywna, I. Mellor, Z. Siwy, P.N.R. Usherwood, On Non-Markovian Character of Ionic Current Fluctuations in Membrane Channels, Phys. Rev. E, 58 (1) 919-924 (1998)
  42. Z.J. Grzywna, On the "experimental way" of showing self·similarity, Acta Physica Polonica B, 29, 1565-1577 (1998)
  43. Z.J. Grzywna, M. Krasowska, Z. Siwy, Chaos i fraktale w opisie struktury i morfologii polimerów, Polimery, 43 (4) 221-231 (1998)
  44. Z. J. Grzywna, Z. Siwy, A. Fuliński, I. Mellor, P.N.R. Usherwood, Chaos in the potassium current through channels of locust muscle membrane, Cellular and Molecular Biology Letters, 4, 37-54 (1999)
  45. Z. Siwy, Z. J. Grzywna, On ionic transport through a high condunctance locust K+ channel in various voltages, Cellular and Molecular Biology Letters, 4 (4), 525-536 (1999)
  46. Siwy, Z., Mercik, Sz., Weron, K. Spohr R., Wolf, A. and Grzywna, Z. J. Comparison of single channel potassium current in biological and synthetic systems - dependence on voltage - Acta Physica Polonica B, 31, 149 (2000)
  47. Zbigniew J. Grzywna, Monika Krasowska, Łukasz Ostrowski, Jacek Stolarczyk, Can generalized dimension Dq and f(a) be used in structure-morphology analysis?, Acta Physica Polonica B, 32, 424 (2001)
  48. Zbigniew J. Grzywna, Jacek Stolarczyk, O dyfuzji w membranach z polimerów szklistych w indukowanym polu naprężeń , Polimery, 46, No 5, 351-358, (2001)
  49. M.B.A. Djamgoz, Z.J. Grzywna, M. Krasowska, O. Martinoli, S. Vallerga Structure- function correlation in transient amacrine cells of goldfish retina: Basic and multifractal analyses of dendritic trees in distinct synaptic layers, Journal of Neuroscience Research, 66 (2001)
  50. Zbigniew J. Grzywna, Jacek Stolarczyk, On some structure - morphology problems by Extended Partitioned Iterated Function System (PIFS-SF), Chaos, Solitons and Fractals 13, 4, 897 (2002)
  51. Zbigniew J. Grzywna, Jacek Stolarczyk Modelling of gold dispersion in glassy polymers by Smoluchowski equation International Journal of Modern Physics C, 13, 9,(2002)
  52. Z.J. Grzywna, M. Krasowska, J. Stolarczyk, On the Application of PIFS-SF and Dq (f(a)) to dendrites analysis. Acta Physica Pollonica B, 34, 7, 3681, (2003)
  53. J.K. Stolarczyk, Z.J. Grzywna, K.K. Koziol, Stress enhanced gold dispersion by solvent induced crystallization in BPA-PC membranes. Polymer, 45, 5, 113, (2004)
  54. M. Krasowska, P. Borys, Z.J. Grzywna, Lacunarity as a measure of texture. Acta Physica Pollonica B, 35, 4, 1519, (2004)
  55. Z.J. Grzywna, A. Michalec, From a Clannish Random Walk to Generalized Smoluchowski Equation. Acta Physica Polonica B, 35, 4, 1463 , (2004)
  56. M. Krasowska, Z.J. Grzywna, M.E. Mycielska, M.B.A. Djamgoz, Patterning of endocytic vesicles and its control by voltage - gated Na+ channel activity in rat prostate cancer cells: fractal analyses , Eur.Biophys. J., 33, 535, (2004)
  57. Z.J. Grzywna, J.K. Stolarczyk, Diffusion in Glassy Polymers - From Random Walks to Partial Differential Equations, Acta Physica Polonica B, 36, 1001, (2005)
  58. S.P.Fraser, J.K.J.Diss, A.M.Chioni, M.E.Mycielska, H.Pan, R.F. Yamaci, F.Pani, Z.Siwy, M.Krasowska, Z.J.Grzywna, W.J.Backenbury, D.Theodorou, M.Koyuturk, H.Kaya, E.Battaloglu, M.Tamburo de bella, M.J.Slade, R.Tolhurdt, C.Palmeri, J.Jiang, D.S.Latchman, R.C.Coombes, M.B.A. Djamgoz, Voltage-gated sodium channel expresion and potentiation of human breast cancer metastasis, Clin Cancer Res, 11(15), 5381, (2005)
  59. M.E.Mycielska, M.Krasowska, Z.J.Grzywna, M.B.A. Djamgoz, Endogenous and exogenous citrate transport and release in prostatic preparations: Semi-polarized two-dimensional cultures of human PNT2-C2 cells and isolated tubules and segments of rat prostate, Prostate, 12, (2005)
  60. P. Borys, Z. J. Grzywna, The Fokker Planck equation for chaotic maps, Acta Physica Polonica B, 2, 37, 519, (2006)
  61. P. Borys, Z. J. Grzywna, Design of a mapping for hyperbolic diffusion, Acta Physica Polonica B, 5, 37, 1445, (2006)
  62. Grzywna Z. J., Borys P., Dudek G., On the mathematical reconstruction of two dimensional plants, Bioscience Reports, 26 , 113 (2006)
  63. P. Borys, Z. J. Grzywna, Diffusion as a result of transition in behavior of deterministic maps, Chaos, Solitons and Fractals, 1, 30, 156, (2006)
  64. G. Dudek. P. Borys, Z. J. Grzywna, Loosy dictionary based image compression method, Image and Vision Computing, 25, 6, 883, (2007)
  65. K.Małysiak, P.Borys, Z.J.Grzywna, On the ball and chain model by simple and hyperbolic diffusion - an analytical approach, Acta Physica Polonica B, 5, (2007)
  66. A.Strzelewicz, Z.J.Grzywna, Studies on the air membrane separation in the presence of magnetic field, Journal of Membrane Sci. 294, 60 (2007)
  67. P. Borys, Z. J. Grzywna, Three dimensional ball and chain problem by the hyperbolic random walk, Acta Physica Polonica B, 5, 38, (2007)
  68. P. Borys, M. Lapkowski, J. K. Zak, Z. J. Grzywna, On the oxidation of polyaniline in the relaxation process by the voltammetric experiment, Chemical Physics Letters 446, 391, (2007)
  69. P. Borys, Z. J. Grzywna, A diffusive model of the ball and chain inactivation, Biosystems, 94, 267 - 269 (2008)
  70. P. Borys, M. Krasowska, Z. J. Grzywna, M. Djamgoz, M. Mycielska, Lacunarity as a novel measure of cancer cells behavior, Biosystems, 94, 276 - 281 (2008)
  71. G. Dudek, Z. J. Grzywna, M. L. Willcox, Classification of antituberculosis herbs for remedial purposes by using fuzzy sets, Biosystems, 94, 285 - 289 (2008)
  72. A.Strzelewicz, Z.J.Grzywna, On the permeation time lag for different transport equations by Frisch method,Journal of Membrane Sci. 322, 460 (2008)
  73. P. Borys, Z. J. Grzywna, On the recovery from inactivation by the chain in the ball and chain model, Cellular and Molecular Biology Letters, 13, 526-534 (2008)
  74. K.Małysiak, Z.J.Grzywna, On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation, Cellular and Molecular Biology Letters, 13, 535 - 552 (2008)
  75. K. Małysiak, Z. J. Grzywna, Electrostatic interactions durring Kv1.2 N-type inactivation: random walk simulation, European Biophysics Journal 38, 1003 (2009)
  76. M. Krasowska, Z. J. Grzywna, M. E. Mycielska, M. B. A. Djamgoz, Fractal analysis and ionic dependence of endocytic membrane activity of human breast cancer cells, European Biophysics Journal, 38, 1115 (2009)
  77. A. Rybak, M. Krasowska, A. Strzelewicz, Z. J. Grzywna, " Smoluchowski type" equations for modelling of air separation by membranes with various structure, Acta Physica Polonica B, 40, 1001 (2009)
  78. A. Rybak, Z.J. Grzywna, W. Kaszuwara, On the air enrichment by polymer magnetic membranes, J. Membr. Sci. 336, 79-85 (2009)
  79. Monika Krasowska, Anna Strzelewicz, Gabriela Dudek, Aleksandra Rybak, Zbigniew J. Grzywna, Analiza fraktalna i lacunarity w opisie materiałów polimerowych, Komputerowe wspomaganie badań naukowych Tom XVII (ISBN 978-83-7374-068-6) 63-70 (2010)
  80. Gabriela Dudek, Monika Krasowska, Anna Strzelewicz, Aleksandra Rybak, Biologiczne aspekty zastosowania zbiorów rozmytych Komputerowe wspomaganie badań naukowych Tom XVII (ISBN 978-83-7374-068-6) 27-34 (2010)
  81. Aleksandra Rybak, Zbigniew Grzywna, Wpływ matrycy polimerowej membran magnetycznych na proces rozdzielania powietrza w Materiały polimerowe. Praca zbiorowa. Pod red. T. Spychaja, S. Spychaj. [Zachodniopomorski Uniwersytet Technologiczny w Szczecinie]. Szczecin : Wydaw. Uczelnianie Zachodniopomorskiego Uniwersytetu Technologicznego, s. 541, (2010)
  82. Zbigniew Grzywna, Aleksandra Rybak, Anna Strzelewicz, Air enrichment by polymeric magnetic membrane w Membrane gas separation. Eds: Y. Yampolskii, B. Freeman. Chichester : John Wiley & Sons, s. 159-182, (2010)
  83. K. Pawełek, J. Kozak, Z. Grzywna, Asynchronous motion and transport of K+ in the KcsA selectivity filter, Phys. A., Stat. Mech. Appl. 389, 16, 3013-3022, 2010
  84. P. Borys, Z. J. Grzywna, and J. Łuczka, Hyperbolic diffusion in chaotic systems, Eur. Phys. J. B 82 (2011)
  85. P. Borys, K. Pawelek, Z. J. Grzywna, On the magnetic channels in polymer membranes, Phys. Chem. Chem. Phys., 13, 17122-17129, 2011
  86. Z.J. Grzywna, P. Borys, B.Kruczek, On the Well-Posed Problems for Diffusion with Time Dependent Boundary Condition, Separation Science and Technology, 46(15), 2427-2435, 2011
  87. I. Santamaria-Holek, Z. J. Grzywna, J. M. Rubi, A non-equilibrium thermodynamics model for combined adsorption and diffusion processes in micro- and nanopores, Journal of Non-Equilibrium Thermodynamics, 37(3), 273–290, 2012
  88. A. Wawrzkiewicz, K. Pawelek, P. Borys, B. Dworakowska, Z.J. Grzywna, On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory, Eur Biophys J, 41(6):505-26, (2012)
  89. M. Krasowska, A. Rybak,K. Pawełek, G. Dudek, A. Strzelewicz, Z.J. Grzywna, Structure morphology problems in the air separation by polymer membranes with magnetic particles, Journal of Membrane Science, vol. 415–416, 864–870, 2012
  90. G. Dudek, R. Turczyn, A. Strzelewicz, A. Rybak, M. Krasowska, Z.J. Grzywna, Preparation and characterization of iron oxides-polymer composite membranes, Separation Science and Technology 47(9),2012
  91. A. Rybak, A. Strzelewicz, M. Krasowska, G. Dudek, Z.J. Grzywna, Influence of Various Parameters on the Air Separation Process by Magnetic Membranes, Separation Science and Technology, 47(9), 2012
  92. P. Borys, A. Rybak, Z.J. Grzywna, On the Analysis of Concentration-Dependent Diffusion Using Transient Sorption and Permeation Measurements by the D1-D8 System, Industrial & Engineering Chemistry Research, 52, 8887-8896, 2013
  93. I. Santamaria-Holek, Z.J.Grzywna, J.M. Rubi, Entropic effects in diffusion-adsorption processes in micropores, The European Physical Journal- Special Topics, 222(1), 129-141, 2013
  94. P. Borys, Z.J. Grzywna, Effect of the magnetic membrane magnetization on the oxygen solubility, Journal of Membrane Science, 445, 107-111, 2013
  95. A.Rybak, G.Dudek, M.Krasowska, A.Strzelewicz, Z.Grzywna, P.Sysel, Magnetic mixed matrix membranes in air separation, Chem. Pap. - Chem. Zvesti, 68, 10, (2014)
  96. A.Rybak, G.Dudek, M.Krasowska, A.Strzelewicz, Z.Grzywna, Magnetic mixed matrix membranes consisting of PPO matrix and magnetic filler in gas separation, Sep. Sci. Technol., 49, 11, (2014)
  97. P.Borys, Z.Grzywna, An analytical solution to the idealized batch pervaporation experiment. A way to determine the diffusion and partition coefficients, J. Membrane Sci., 476, 525-529, (2015)
  98. A.Wawrzkiewicz-Jałowiecka, P.Borys, Z.Grzywna, On application of Langevin dynamics in logarithmic potential to model ion channel gate activity, CellMol Biol Lett, 20 (4) 663-84, (2015)
  99. P.Borys, Z.J.Grzywna, On the fractality of the Freundlich adsorption isotherm in equilibrium and non-equilibrium cases, Phys. Chem. Chem. Phys., 18, p. 20784-20789, (2016)
  100. K.Bernaczek, A.Mielańczyk, Z.J.Grzywna, D.Neugebauer, Interactions between fluorescein isothiocyanate and star-shaped polymer carriers studied by isothermal titration calorimetry (ITC), Thermochimica Acta, 641, p. 8-13, (2016)

Last updated on 5 September 2016