젤형성에서의 조건부 확률법:분자내 반응으로의 확장

전상민; 이건흥

HWAHAK KONGHAK, Vol.32, No.2, 146-158, April, 1994

Export Citation

젤형성에서의 조건부 확률법:분자내 반응으로의 확장

Conditional Probability Method in Gelation : Extension to the Intramolecular Reaction

전상민, 이건흥

초록

조건부 확률법은 비이상 중합반응을 간단하게 예측하기 위하여 고안된 모델로서 이 방법의 핵심은 시스템에서 일어날 수 있는 모든 사건들을 분명하게 분류한 뒤 원하는 결과식을 유도할 때 조건부 확률을 사용하는 것이다. 본 연구에서는 젤화점 이전 영역의 이상 중합반응에 대해서만 적용되었던 기존의 방법을 확장하여 분자내 반응이 존재한 전체 반응영역을 예측할 수 있는 모델로 확장하였다. 또한 반응을 솔과 솔, 솔과 젤, 젤과 젤로 분류함으로써 솔과 젤에 대한 독립적인 결과식을 얻었으며 그 결과식으로서 고리형성 파라미터, 고리의 수, 수평균 분자량 및 질량평균 분자량이 유도되었다.

CPM(Conditional Probability Method) was devised as a simple method to handle the nonidealities of polymerizing systems. The key points of the method are to define clearly the probability of each event occurring in the system and to use conditional probability in formulating equations. Starting with this concept, we developed a systematic method which extended the existing theory. Furthermore, equations were derived separately for the sol and the gel by dividing all reactions into those between sol and sol, gel and sol, and gel and gel. Formulas for the ring forming parameter, number of rings, weight average molecular weight and number average molecular weight were obtained using this approach.

[References]

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Flory PJ, "Principles of Polymer Chemistry," Chap. 9, 10, Cornell Univ. Press, Ithaca (1953)
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Flory PJ, J. Am. Chem. Soc., 63, 3091 (1941)
Flory PJ, J. Am. Chem. Soc., 63, 3096 (1941)
Stockmayer WH, J. Chem. Phys., 11(2), 45 (1943)
Stockmayer WH, J. Chem. Phys., 12(4), 125 (1944)
Athreya KB, Ney PE, "Branching Processes," Chap. 1, Springer, Berlin (1972)
Dobson GR, Gordon M, J. Chem. Phys., 41(8), 2389 (1964)
Dobson GR, Gordon M, J. Chem. Phys., 43(2), 705 (1965)
Gordon M, Scantlebury GR, J. Polym. Sci. C: Polym. Lett., 16, 3933 (1968)
Dusek K, Gordon M, Ross-Murphy SB, Macromolecules, 11(1), 236 (1978)
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Macosko CW, Miller DR, Macromolecules, 9(2), 206 (1976)
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Miller DR, Macosko CW, Macromolecules, 13(5), 1063 (1980)
Mikes J, Dusek K, Macromolecules, 15(1), 393 (1982)
Leung YK, Eichinger BE, J. Chem. Phys., 80(8), 3877 (1984)
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Bansil R, Herrmann HJ, Stauffer D, Macromolecules, 17(5), 998 (1984)
Sarbian A, Macromolecules, 24(5), 1134 (1991)
Aharoni SM, Macromolecules, 24(1), 235 (1991)
Stauffer D, Coniglio A, Adam M, "Advances in Polymer Science 44," Springer, Berlin, 103 (1982)
Sander LM, Godreche C, "Solids far from Equilibrium," chap. 5, Cambridge University Press (1992)
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Hendriks EM, Ernst MH, J. Colloid Interface Sci., 97(1), 176 (1984)
Ziff RM, Stell G, J. Chem. Phys., 73(7), 3492 (1980)
Galina G, Szustalewicz A, Macromolecules, 22(7), 3124 (1989)
van Dongen P, Ernst MH, J. Phys. A: Math. Gen., 16, L327 (1983)
Gupta AM, Macromolecules, 24(11), 3459 (1991)
Kilb RW, J. Phys. Chem., 62, 969 (1958)
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전상민, 석사논문, 포항공과대학교, 포항, 한국 (1993)

[1] Family F, Landau DP, "Kinetics of Aggregationand Gelation," North-Horland, Amsterdam (1984)

[2] Flory PJ, "Principles of Polymer Chemistry," Chap. 9, 10, Cornell Univ. Press, Ithaca (1953)

[3] Flory PJ, J. Am. Chem. Soc., 63, 3083 (1941)

[4] Flory PJ, J. Am. Chem. Soc., 63, 3091 (1941)

[5] Flory PJ, J. Am. Chem. Soc., 63, 3096 (1941)

[6] Stockmayer WH, J. Chem. Phys., 11(2), 45 (1943)

[7] Stockmayer WH, J. Chem. Phys., 12(4), 125 (1944)

[8] Athreya KB, Ney PE, "Branching Processes," Chap. 1, Springer, Berlin (1972)

[9] Dobson GR, Gordon M, J. Chem. Phys., 41(8), 2389 (1964)

[10] Dobson GR, Gordon M, J. Chem. Phys., 43(2), 705 (1965)

[11] Gordon M, Scantlebury GR, J. Polym. Sci. C: Polym. Lett., 16, 3933 (1968)

[12] Dusek K, Gordon M, Ross-Murphy SB, Macromolecules, 11(1), 236 (1978)

[13] Dusek K, Goethals EJ, "Telechlic Polymers: Synthesis and Application," Chap. 12, CRC Press, Boca Raton (1989)

[14] Gordon M, Ross-Murphy SB, Pure Appl. Chem., 43, 1 (1975)

[15] Gordon M, Scantlebury GR, Trans. Faraday Soc., 60, 604 (1964)

[16] Luby P, J. Polym. Sci. Symp. Ser., 53, 23 (1975)

[17] Stanford JL, Stepto RFT, J. Chem. Soc.-Faraday Trans., 71, 1292 (1975)

[18] Stanford JL, Stepto RFT, J. Chem. Soc.-Faraday Trans., 71, 1308 (1975)

[19] Macosko CW, Miller DR, Macromolecules, 9(2), 199 (1976)

[20] Macosko CW, Miller DR, Macromolecules, 9(2), 206 (1976)

[21] Miller DR, Macosko CW, Macromolecules, 11(4), 656 (1978)

[22] Miller DR, Macosko CW, Macromolecules, 13(5), 1063 (1980)

[23] Mikes J, Dusek K, Macromolecules, 15(1), 393 (1982)

[24] Leung YK, Eichinger BE, J. Chem. Phys., 80(8), 3877 (1984)

[25] Leung YK, Eichinger BE, J. Chem. Phys., 80(8), 3885 (1984)

[26] Herrmann HJ, Stauffer D, Landau DP, J. Phys. A: Math. Gen., 16, 1221 (1983)

[27] Bansil R, Herrmann HJ, Stauffer D, Macromolecules, 17(5), 998 (1984)

[28] Sarbian A, Macromolecules, 24(5), 1134 (1991)

[29] Aharoni SM, Macromolecules, 24(1), 235 (1991)

[30] Stauffer D, Coniglio A, Adam M, "Advances in Polymer Science 44," Springer, Berlin, 103 (1982)

[31] Sander LM, Godreche C, "Solids far from Equilibrium," chap. 5, Cambridge University Press (1992)

[32] Hendriks EM, Ernst MH, Ziff RM, J. Stat. Phys., 31(3), 519 (1983)

[33] Hendriks EM, Ernst MH, J. Colloid Interface Sci., 97(1), 176 (1984)

[34] Ziff RM, Stell G, J. Chem. Phys., 73(7), 3492 (1980)

[35] Galina G, Szustalewicz A, Macromolecules, 22(7), 3124 (1989)

[36] van Dongen P, Ernst MH, J. Phys. A: Math. Gen., 16, L327 (1983)

[37] Gupta AM, Macromolecules, 24(11), 3459 (1991)

[38] Kilb RW, J. Phys. Chem., 62, 969 (1958)

[39] Jocobson H, Stockmayer WH, J. Chem. Phys., 18(12), 1600 (1950)

[40] Stepto RFT, Haward RN, "Developments in Polymerisation-3," Applied Science Publisher, 81 (1982)

[41] 전상민, 석사논문, 포항공과대학교, 포항, 한국 (1993)