Mean-Field Kinetic Modeling of Polymerization: The Smoluchowski Coagulation Equation

Advances in Polymer Science

Volumn 137, Issue , 1998, Pages 135-172

  Galina, Henryk ^a   Lechowicz, Jaromir B ^b  

^a RZESZOW UNIVERSITY OF TECHNOLOGY   (Poland)

^b NONE

Author keywords

Aggregation; Classical modeling; Cross linking polymerization; Gelation; Network formation; Size distribution

Indexed keywords

EID: 0001067872     PISSN: 00653195     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-69685-7_4     Document Type: Article

References (79)

1. For the process of graph-theoretical evolution of trees, which is analogous to the aggregation described by Eq. (1), the Smoluchowski equation was rederived rigorously, see Balinska K, Galina H, Quintas LV, Szymanski J (1996) Discr Appl Maths 67:13
2. Pauling L, Pauling P (1975) Chemistry. Freeman, San Francisco 1975
3. Smoluchowski M v (1916) Phys Z 17: 585
4. Smoluchowski M v (1917) Z Chem Phys 92: 129
5. Drake R (1972) In: Hidy GM, Brook JR (eds) Topics in current aerosol research. Pergamon, Oxford
6. Kuchanov SJ (1978) Methods of kinetic calculations in polymer chemistry (in Russian). Izd Chimia, Moscow
7. Ziff RM.(1984) In: Family F, Landau DP (eds) Kinetics of aggregation and gelation. Elsevier Sci Publ BV
8. j
9. Flory JP (1953) Principles of polymer chemistry. Cornell Univ Press, Ithaca
10. An equivalent generating function defined as formula presented can also be used
11. One can arrive at equivalent result by differentiating H(t,x) with respect to x followed by putting x=0, since formula presented
12. Gordon M, Scantlebury GR (1966) Proc R Soc London A 292: 380
13. Gordon M, Scantlebury GR (1964) Trans Faraday Soc 6: 604
14. Gordon M (1962) Proc Roy Soc (London) A268: 240
15. Dušek K, Prins W (1969) Adv Polym Sci 6: 1
16. Galina H (1995) Makromol Theory Simul 4: 801
17. Cheng K Ch, Chiu WY (1993) Macromolecules 26: 4658, 4665
18. Flory PJ (1946) Chem Rev 39: 137
19. Stockmayer WH (1943) J Chem Phys 11: 45
20. The appearance of a giant component in the evolution of random graphs, which corresponds to gelation in polymer science, was discovered to their surprise by Erdös P, Renyi A. ([34] below) more than a decade after Flory
21. Spouge JL (1983) Macromolecules 16: 121
22. McLeod JB (1962) Quart J Math (Oxford) 13: 119, 193
23. Drake RL (1972) In: Hidy GM, Brock GR (eds) Topics in current aerosol research, vol 3, pt 2
24. Ziff RM, Ernst MH, Hendriks EM (1984) J Colloid Interface Sci 100: 220
25. Drake RL, Wright TJ (1972) J Atmos Sci 29: 548
26. Treat RP (1990) J Phys A: Math Gen 23: 3003
27. Spouge JL (1983) J Stat Phys 31: 363
28. Ziff RM, Stell G (1980) J Chem Phys 73: 3492
29. Van Dongen PGJ, Ernst MH (1987) J Colloid Interface Sci 115: 27
30. Van Dongen PGJ, Ernst MH (1986) J Stat Phys 44: 785
31. Leyvraz F (1984) In: Family F, Landau DP (eds) Kinetics aggregation and gelation. Elsevier Sci Publ BV
32. Leyvraz F, Tschudi HR (1981) J Phys A: Math Gen 14: 3389; (1982) J Phys A: Math Gen 15: 1951
33. Leyvraz F, Tschudi HR (1981) J Phys A: Math Gen 14: 3389; (1982) J Phys A: Math Gen 15: 1951
34. Hendriks EM, Ernst MH, Ziff RM (1983) J Stat Phys 31: 519
35. Erdös P, Renýi A (1959) I Publ Math Debrecen 6: 290; (1960) MTA Mat Kut Int Kozl 5: 17
36. Erdös P, Renýi A (1959) I Publ Math Debrecen 6: 290; (1960) MTA Mat Kut Int Kozl 5: 17
37. Buffet E, Pulé JV (1991) J Stat Phys 64: 87
38. Stockmayer WH (1943) J Chem Phys 11: 45
39. Whittle P (1965): Proc Camb Phil Soc 61: 475
40. Whittle P (1965) Proc R Soc London A 285: 501
41. Spouge JL (1983) J Phys A: Math Gen 16: 767
42. Stockmayer W H (1943) J Chem Phys 11: 45
43. Macosko CW, Miller DR (1976) Macromolecules 9: 199
44. Miller DR, Macosko CW (1976) Macromolecules 9: 206
45. Kuchanov SI, Povolotskaya Ye S (1982) Vysokomol Soed A24(10): 2179, 2190
46. Galina H, Szustalewicz A (1989) Macromolecules 221 3124
47. Sarmoria C, Miller DR (1991) Macromolecules 24: 1833
48. Faliagas AC (1993) Macromolecules 26: 3838
49. Kuchanov SI (1979) Dokl Akad Nauk SSSR 249: 899
50. Galina H, Szustalewicz A (1990) Macromolecules 23: 3833
51. Galina H, Kaczmarski K, Para B, Sanecka B (1992) Makromol Chem Theory Simul 1: 37
52. Mikes J, Dušek K (1982) Macromolecules 15: 185
53. Šomvársky J, Dušek K (1994) Polym Bull (Berlin) 33: 369; 377
54. Galina H, Lechowicz J (1995) Comput Polym Sci
55. Dušek K (1979) Polym Bull (Berlin) 1: 523
56. Ziff RM (1980) J Stat Phys 23: 241
57. Good IJ (1963) Proc R Soc London A 272: 54
58. Van Dongen PGJ, Ernst MH, Ziff RM (1983) J Stat Phys 31: 519
59. Fukutomi T, Koshiro Y (1996) Polym J 28: 758
60. Irzhak TF, Peregudov NI, Irzhak VI, Rozenberg BA (1993) Vysokomol. Soed B 35: 905, 1545
61. Jackobson H, Stockmayer WH (1950) J Chem Phys 18: 1800
62. Flory P J (1969) Statistical mechanics of chain molecules. Interscience, New York
63. Friedman B, O'Shaughnessy B (1989) Phys Rev A 40: 5950
64. Lu B, Bak TA (1988) In: Kramer O (ed) Biological and synthetic polymer networks. Elsevier, Amsterdam
65. Galina H (1991) Makromol Chem Macromol Symp 40: 45
66. Galina H, Lechowicz J, Para B, Sanecka B (1994) Polimery (Warsaw) 39: 429
67. Müller H (1928) Kolloidchemische Beiheft 27: 223
68. Lushnikov AA (1974) J Colloid Interface Sci 48: 400; (1978) Izv Atm Ok Fiz 14: 738
69. Lushnikov AA (1974) J Colloid Interface Sci 48: 400; (1978) Izv Atm Ok Fiz 14: 738
70. Gabellini Y, Meunier J-L (1992) J Phys A: Math Gen 25: 3683
71. Kreer M, Penrose O (1994) J Stat Phys 75: 389
72. Van Dongen PGJ, Ernst MH (1987) J Stat Phys 49: 879
73. Stauffer D, Coniglio A, Adam M (1982) Adv Polym Sci 44: 103
74. Villarica M, Casey MJ, Goodisman J, Chaiken J (1992) J Chem Phys 98: 4610
75. Krivitsky DS (1996) J Phys A: Math Gen 28: 2025
76. Ziff RM, McGrady ED (1985) J Phys A: Math Gen 18: 3027
77. Ball JM, Carr J (1990) J Stat Phys 61: 203
78. Costas ME, Moreau M, Vicente L (1995) J Phys A: Math Gen 28: 2981
79. da Costa FP (1995) J Math Anal Appl 192:892