묽은 고분자 용액의 선형 점탄성과 완화 시간 스펙트럼

이일순; 안경현; 이승종

Korean Journal of Rheology, Vol.7, No.3, 211-224, December, 1995

Export Citation

묽은 고분자 용액의 선형 점탄성과 완화 시간 스펙트럼

Linear Viscoelastic Properties and Relaxation Time Spectrum of Dilute Polymer Solutions

이일순, 안경현, 이승종

초록

묽은 고분자 용액의 선형 점탄성과 완화시간 스펙트럼에 대하여 비드수, 유체역학적 상호작용, 배제 부피와 비선형 스프링들의 영향을 비드-스프링 모델(Bead-Spring Model, BSM)을 통하여 연구하였다. Fixman의 모델을 개량하였고, 비선형 스프링 개념을 도입한 후 선형 점탄성에 관한 식들을 유도하였다. 그 중에서 주로 복소 점도의 크기와 위상차에 대한 BSM파라미터들의 영향을 살펴보았다. 실험 데이터에서 진동수에 따른 위상차의 평평한 부분의 길이로부터 비드수를, Mark-Houwink식의 지수 값으로부터 유체역학적 상호작용 파라미터를, 그리고 fitting 파라미터로써 배제 부피 파라미터와 비선형 스프링 파라미터의 함수형태로 표현되는 동적 확장 파라미터를 결정할 수 있었다. 또한 광산란 실험 등으로부터 배제 부피 파라미터를 결정하게 된다면 이로부터 비선형 스프링 파라미터도 결정할 수 있음을 알 수 있었다. 한편 불연속적인 형태인 BSM의 완화시간 스펙트럼에 미치는 BSM 파라미터들의 영향을 분석함으로써 각 파라미터의 효과와 차이점을 분명히 알 수 있었다. 본 논문에서는 BSM에 비드수, 유체역학적 상호작용, 배제 부피 그리고 비선형 스프링 효과를 동시에 적용하는 방법을 제시하였으며, 이 방법을 통하여 묽은 고분자 용액의 선형 점탄성 실험 데이터를 정량적으로 설명할 수 있었다.

On the linear viscoelastic properties of dilute polymer solutions Bead number(N), hydrodynamic interaction(HI), excluded volume(EV), and non-linear spring(NS) effects were studied by using the bead-spring chain model(BSM). Linear viscoelastic properties were derived by modifying Fixman's model and introducing NS concept. Among them, the magnitude and the phase angle of complex viscosity were principally chosen to be investigated. Bead number was determined by the breadth of plateau region of the phase angle, and HI parameter was obtained from the exponent of Mark-Houwink equation. Whereas the dynamic expansion parameter which is the function of EV and NS parameters was acquired by data fitting. Once EV parameter is known through such an experiment as light scattering. NS parameter can be predicted. More over we studied the discrete relaxation time spectra of BSM, and knew that the effects of BSM parameters on the spectra are clearer than those on the linear viscoelastic properties. In this paper the method of accommodating bead number, HI, EV, and NS effects on BSM was suggested and resulted in the excellent agreement of linear viscoelastic properties with experimental data.

Keywords:Dilute polymer solutions;hydrodynamic interaction;excluded volume;non-linear spring;bead-spring chain model;relaxation time spectra

[References]

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Amstrong RC, J. Chem. Phys., 60, 729 (1974)
Wiest JM, Tanner RI, J. Rheol., 33, 281 (1989)
Zylka W, Ottinger HC, Macromolecules, 24, 484 (1991)
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Sammler RL, Landry CJT, Woltman GR, Schrag JL, Macromolecules, 23, 2388 (1990)
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Sahouani H, Lodge TP, Macromolecules, 25, 5632 (1992)
Lodge TP, J. Phys. Chem., 97, 1480 (1993)
Miyaki Y, Fujita H, Macromolecules, 14, 742 (1981)
Yoon SH, Ahn KH, Lee SJ, Korean J. Rheol., 4(2), 127 (1992)
Bird RB, Ottinger HC, Annu. Rev. Phys. Chem., 43, 371 (1992)
McAdams JE, Williams MC, Rheol. Acta, 25, 102 (1986)
Tschoegl NW, "The Phenomenological Theory of Linear Viscoelastic Behavior," Springer-Verlag, Heidelberg, New York (1989)
Ottinger HC, Zylka W, J. Rheol., 36, 885 (1992)

[1] Bird RB, Curtiss CF, Armstrong RC, Hassager O, "Dynamics of Polymeric Liquids," Vol. 2, 2nd edn., Wiley, New York (1987)

[2] Ferry JK, "Viscoelastic Properties of Polymers," 3rd edn., Wiley, New York (1980)

[3] Doi M, Edwards SF, "The Theory of Polymer Dynamics," Oxford University Press, New York (1986)

[4] Yamakawa H, "Modern Theory of Polymer Solutions," Harper and Row, New York (1971)

[5] Larson RG, "Constitutive Equations for Polymer Melts and Solutions," Butterworths, Boston (1988)

[6] Williams MC, AIChE J., 21, 1 (1975)

[7] Rouse PE, J. Chem. Phys., 21, 1272 (1953)

[8] Kirkwood JG, Riseman J, J. Chem. Phys., 16, 565 (1948)

[9] Zimm BH, J. Chem. Phys., 24, 269 (1956)

[10] Fixman M, J. Chem. Phys., 45, 3831 (1965)

[11] Fixman M, J. Chem. Phys., 45, 785 (1966)

[12] Warner HR, Ind. Eng. Chem. Fundam., 11, 379 (1972)

[13] Christiansen RL, Bird RB, J. Non-Newton. Fluid Mech., 3, 161 (1977)

[14] Bird RB, Dotson PJ, Johnson NL, J. Non-Newton. Fluid Mech., 7, 213 (1980)

[15] Wiest JM, Wedgewood LE, Bird RB, J. Chem. Phys., 90, 587 (1988)

[16] Amstrong RC, J. Chem. Phys., 60, 729 (1974)

[17] Wiest JM, Tanner RI, J. Rheol., 33, 281 (1989)

[18] Zylka W, Ottinger HC, Macromolecules, 24, 484 (1991)

[19] Ottinger HC, J. Chem. Phys., 86(6), 3731 (1987)

[20] Ottinger HC, J. Chem. Phys., 90(1), 463 (1989)

[21] Wedgewood LE, Ottinger HC, J. Non-Newton. Fluid Mech., 27, 245 (1988)

[22] Ottinger HC, J. Non-Newton. Fluid Mech., 26, 207 (1987)

[23] Ahn KH, Lee SJ, J. Non-Newton. Fluid Mech., 43, 143 (1992)

[24] Ahn KH, Schrag JL, Lee SJ, J. Non-Newton. Fluid Mech., 50, 349 (1993)

[25] Thurston GB, Peterlin A, J. Chem. Phys., 46, 4881 (1967)

[26] Sammler RL, Schrag JL, Macromolecules, 22, 3435 (1989)

[27] Sammler RL, Landry CJT, Woltman GR, Schrag JL, Macromolecules, 23, 2388 (1990)

[28] Amelar S, Eastman CE, Morris RL, Smeltzly MA, Lodge TP, Macromolecules, 24, 3505 (1991)

[29] Sahouani H, Lodge TP, Macromolecules, 25, 5632 (1992)

[30] Lodge TP, J. Phys. Chem., 97, 1480 (1993)

[31] Miyaki Y, Fujita H, Macromolecules, 14, 742 (1981)

[32] Yoon SH, Ahn KH, Lee SJ, Korean J. Rheol., 4(2), 127 (1992)

[33] Bird RB, Ottinger HC, Annu. Rev. Phys. Chem., 43, 371 (1992)

[34] McAdams JE, Williams MC, Rheol. Acta, 25, 102 (1986)

[35] Tschoegl NW, "The Phenomenological Theory of Linear Viscoelastic Behavior," Springer-Verlag, Heidelberg, New York (1989)

[36] Ottinger HC, Zylka W, J. Rheol., 36, 885 (1992)