콜로이드입자 주위의 정전위 분포에 관한 근사해석과 표면전하밀도의 측정

전명석; 박오옥

HWAHAK KONGHAK, Vol.30, No.2, 200-211, April, 1992

Approximate Analysis on the Electrostatic Potential Distributions around a Colloidal Particle and Measurement of the Surface Charge Density

전명석, 박오옥

초록

구형 Poisson-Boltzmann식의 비선형 항을 종속변수의 함수로 적분이 가능하도록 근사시켜 정확도를 상당히 높인 Ohshima 등[8]의 섭동방식을 기초로, 비대칭형 전해질에서의 단일입자 주위의 퍼텐셜 분포와 구형 및 실리더형 입자에 대한 표면전하밀도와 표면 퍼텐셜간의 관계식을 해석하였다. 구해진 근사해로부터, 평판에서의 페텐셜 분포와 입자에서 충분히 떨어진 경우의 leading order에 의한 점근상수 등 그의 점근특성을 고찰하였다. 구형 및 실린더형 모델 콜로이드입자들을 각각 선정한 후, 실험변수인 입자크기와 전해질 용액의 이온농도 변화에 따른 표면저하밀도를 실험적으로 측정하였고, 도출된 관계식에 의해 표면 퍼텐셜을 산출하였다. 0.1-10mM범위의 이온화세기 변화에 대해 산출된 표면 퍼텐셜값은, 폴리스타이렌 라텍스입자의 경우는 약 60-230mV, 잔탄검에서는 72-194mV 범위를 보였는데, 이온농도가 증가할수록 그 값은 감소하였다. 콜로이드입자들간의 정전 상호에너지 계산을 위해 요구되는 단일입자계에 대한 해석의 확장과, 이온농도에 따른 표면전하밀도와 표면 퍼텐셜의 변화현상에 관한 이해가 본 연구의 의의였다.

The extended approximate analysis on the electrostatic potential distribution around a spherical colloidal particle in asymmetric electrolytes has been performed. This analysis originated from the accurate perturbed scheme of Ohshima et al.[8] pertaining to the spherical poisson-Boltzmann equation for symmetric electrolytes. The advantage of this approach lies in the analytic expression for a flat plate very near the particle surface as well as its ability to yield the correct asymptotic behavior at distances far from th particle. The second order approximate solution for the surface charge density as functions of A(=ka) and surface potential has also been obtained from the similar method of perturbations to the Poisson-Boltzmann equation in spherical and cylindrical coordinates and compared with the exact numerical results. This study herein consisted of an analysis combined with experimental investigations to examine the changes in surface charge density and surface potential due to the variations of particle size and ionic concentration. Over an ionic strength range of 0.1 to 10mA, the evealuated surface potentials were found to lie in the ranges of about 60-230mV, and 72-149mV for three different sizes of polystyrene laties as a model spherical particle and the xamhen gum anionic polyelectrolyte as a cylindrical partcle, Indeed, the surface potential value increased as the particle size increassed, but decreased as the ionic concentration increased.

[References]

Russel WB, Saville DA, Schowalter WR, "Colloidal Dispersions," Cambridge Univ. Press, NY (1989)
Bell GM, Levine S, McCartney LN, J. Colloid Interface Sci., 33, 335 (1970)
Loeb AL, Overbeek JG, Wiersema PH, "The Electrical Double Layer around a Spherical Colloidal Particle," The MIT Press, MA (1961)
Stigter D, J. Colloid Interface Sci., 53, 296 (1975)
vanderDrift WPJT, deKeizer A, Overbeek JG, J. Colloid Interface Sci., 71, 67 (1979)
White LR, J. Chem. Soc.-Faraday Trans., 73, 577 (1977)
Parlange JY, J. Colloid Interface Sci., 57, 376 (1972)
Ohshima H, Healy TW, White LR, J. Colloid Interface Sci., 90, 17 (1982)
vander Hul HJ, Vanderhoff JW, "Polymer Colloids," edited by Fitch, R.M., Plenum Press, NY, p. 1 (1971)
Hunter RJ, "Zeta Potential in Colloid Science-Principles and Applications," Academic Press (1981)
Gradshteyn Is, Ryzhik IM, "Table of Integrals, Series, and Products," edited by Jeffrey, A., Academic Press (1965)
Nayfeh, Ali Hasan: "Problems in Perturbation," John Wiley & Sons, NY (1985)
Wu WC, El-Aasser MS, Micale FJ, vanderhoff JW, "Emusions, Latices, and Dispersions," edited by Becher, P. and Yudenfreund, M.N., Marcel Dekker, Inc., NY, p. 71 (1978)
Bagchi P, Gray BV, Birnbaum SM, "Polymer Colloids II," edited by Fitch, R.M., Plenum Press, NY, p. 225 (1980)
Chauveteau G, J. Rheol., 26, 111 (1982)
Chun MS, Park OO, Kim JK, Korean J. Chem. Eng., 7(2), 126 (1990)
이신영, 생물화공, 4(1), 24 (1990)
Bentz J, J. Colloid Interface Sci., 80, 179 (1981)
Silebi CA, McHugh AJ, AIChE J., 24, 204 (1978)
Buffham BA, J. Colloid Interface Sci., 67, 154 (1978)

[Referenced By]

[1] Russel WB, Saville DA, Schowalter WR, "Colloidal Dispersions," Cambridge Univ. Press, NY (1989)

[2] Bell GM, Levine S, McCartney LN, J. Colloid Interface Sci., 33, 335 (1970)

[3] Loeb AL, Overbeek JG, Wiersema PH, "The Electrical Double Layer around a Spherical Colloidal Particle," The MIT Press, MA (1961)

[4] Stigter D, J. Colloid Interface Sci., 53, 296 (1975)

[5] vanderDrift WPJT, deKeizer A, Overbeek JG, J. Colloid Interface Sci., 71, 67 (1979)

[6] White LR, J. Chem. Soc.-Faraday Trans., 73, 577 (1977)

[7] Parlange JY, J. Colloid Interface Sci., 57, 376 (1972)

[8] Ohshima H, Healy TW, White LR, J. Colloid Interface Sci., 90, 17 (1982)

[9] vander Hul HJ, Vanderhoff JW, "Polymer Colloids," edited by Fitch, R.M., Plenum Press, NY, p. 1 (1971)

[10] Hunter RJ, "Zeta Potential in Colloid Science-Principles and Applications," Academic Press (1981)

[11] Gradshteyn Is, Ryzhik IM, "Table of Integrals, Series, and Products," edited by Jeffrey, A., Academic Press (1965)

[12] Nayfeh, Ali Hasan: "Problems in Perturbation," John Wiley & Sons, NY (1985)

[13] Wu WC, El-Aasser MS, Micale FJ, vanderhoff JW, "Emusions, Latices, and Dispersions," edited by Becher, P. and Yudenfreund, M.N., Marcel Dekker, Inc., NY, p. 71 (1978)

[14] Bagchi P, Gray BV, Birnbaum SM, "Polymer Colloids II," edited by Fitch, R.M., Plenum Press, NY, p. 225 (1980)

[15] Chauveteau G, J. Rheol., 26, 111 (1982)

[16] Chun MS, Park OO, Kim JK, Korean J. Chem. Eng., 7(2), 126 (1990)

[17] 이신영, 생물화공, 4(1), 24 (1990)

[18] Bentz J, J. Colloid Interface Sci., 80, 179 (1981)

[19] Silebi CA, McHugh AJ, AIChE J., 24, 204 (1978)

[20] Buffham BA, J. Colloid Interface Sci., 67, 154 (1978)