준희박과 농축용액에서 약간의 유연성을 갖는 막대형 고분자의 다분산성이 회전확산과 점도에 미치는 영향

정성은; 이영철; 정인재

Korean Journal of Rheology, Vol.1, No.1, 54-62, November, 1989

The Effect of Polydispersity on Diffusivity and Viscosity of a Slightly Flexible Rod-Like Polymer in Semidilute and Concentrated Solutions

정성은, 이영철, 정인재

초록

준희박과 농축용액에서 약간의 유연성을 갖는 강성막대형 고분자의 회전확산계수와 zero shear rate점도를 예측하기 위해 한정된 강성 사슬모델이 제시되었다. 본 연구에서는 이 제시된 모델을분자량 분포를 갖는 다분산계로 확장시켰다. 분자들의 분자량분포(M_w/M_n)와 분포함수를 알 수 없기 때문에 해당분자에 가장 적당한 분자량 분포와 함수를 취하였다. 만약 이것들을 알고 있다면 제시된 모델로 회전확산계수와 zero shear rate점도 등과 같은 인자들을 예측할 수 있었다. 단분산계의 경우와 같이 다분산계에서도 회전확산계수의 평균분자 윤곽길이 의존도는 L^-7에 비례하는 것으로 나타났다. Doi와 Edwards의 튜브모델에 의한 L^-9과 다른 이유는 분자들의 거동을 관찰하기 위해 임의로 선정된 하나의 막대형 고분자운동을 제약하는 정도가 심하지 않았으며 따라서 제약 완화시간도 훨씬 짧았기 때문이다. 더구나 점도와 회전확산계수가 단분산계에서는 정성적으로 일치한데 반하여 분자량 분포를 고려한 다분산계에서는 더욱 정량적인 일치를 나타내었다. 이 모델을 기준으로 하여 분자들의 길이와 종류에 관계없이 하나의 master curve를 그릴 수 있었다.

A confined stiff chain model was developed to predict the rotational diffusion coefficient of a slightly flexible rigid rod-like polymer in semidilute and concentrated solutions. In this work this model was extended to a polydisperse system to observe the effect of polydispersity. Because polydispersity index and molecular weight distribution function were unknown, their plausible values were selected and used . If they were known, this model could be used for the prediction of parameters. Rotational diffusion coefficient turned out to be proportional to L^-7 for a polydisperse as well as a mondisperse system where L was average contour length of molecules. It was different from proportionality to L^-9 predicted by the tube model of Doi and Edwards because the constraint on a test rod was not severe and disengagement time was much shorter than that given by the tube model. While the theoretical values of viscosity and diffusivity were qualitatively consistent with experimental data for monodisperse system, they could be fitted quantitatively by considering polydispersity effect for polydisperse system. Our model obtained a master curve consistent with all data irrespective of molecular length and species.

Keywords:semiflexible rod-like polymer/rotational diffusivity/viscosity/polydispersity effect

[References]

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[1] Onsager L, Ann. N.Y. Acad. Sci., 51, 627 (1949)

[2] Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 74, 560 (1978)

[3] Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 74, 918 (1978)

[4] Doi M, J. Polym. Sci. B: Polym. Phys., 19, 229 (1981)

[5] Kirkwood JG, Auer PL, J. Chem. Phys., 19, 281 (1981)

[6] Kirkwood JG, Plock RJ, J. Chem. Phys., 24, 665 (1958)

[7] Zero K, Pecora R, Macromolecules, 15, 87 (1982)

[8] Odell JA, Keller A, Atkins EDT, Macromolecules, 18, 1443 (1985)

[9] Mori Y, Okubo N, Hayakawa R, Wada Y, J. Polym. Sci. B: Polym. Phys., 20, 2111 (1982)

[10] Maguire JF, McTague JP, Rondelez F, Phys. Rev. Lett., 45, 1891 (1980)

[11] Maguire JF, McTague JP, Rondelez F, Phys. Rev. Lett., 47, 148 (1981)

[12] Chung SE, Chung IJ, Polym. Bull., 21, 105 (1989)

[13] Doi M, Edwards SF, "The Theory of Polymer Dynamics," Clarendon Press, Oxford p. 324 (1986)

[14] Odijk T, Macromolecules, 16, 1340 (1983)

[15] Allen SR, Filippov AG, Farris RJ, Thomas EL, J. Appl. Polym. Sci., 26, 291 (1981)

[16] Graessly WW, Adv. Polym. Sci., 16, 1 (1982)

[17] Ferry JD, "Viscoelastic Properties of Polymers," 3rd Ed., John Wiley, N.Y., p. 515 (1980)

[18] Daoud M, de Gennes PG, J. Polym. Sci. B: Polym. Phys., 17, 1971 (1979)

[19] Kim HY, Chung IJ, J. Polym. Sci. B: Polym. Phys., 25, 2039 (1987)

[20] Marrucci G, Grizzuti N, J. Polym. Sci. C: Polym. Lett., 21, 83 (1983)

[21] Marrucci G, Grizzuti N, J. Non-Newton. Fluid Mech., 14, 103 (1984)

[22] Lekkerkerker HNW, Coulon P, Haegen RVD, Deblieck R, J. Chem. Phys., 80(7), 3427 (1980)

[23] Arpin M, Strazielle C, Polymer, 18, 591 (1977)

[24] Kiss G, Porter RS, J. Polym. Sci. Polym. Symp., 65, 193 (1978)

[25] Hermans J, J. Colloid Sci., 17, 638 (1962)