我們藉由電位的訊號直接量測反離子(counterions)在溶液中的濃度，進而得知反離子的凝聚作用(counterion condensation)和釋放(release)的現象。首先，我們以界劑濃度的比值(即偵測到的離子濃度與實際添加離子型界劑的濃度為比值)去定義反離子凝聚作用的程度(the degree of counterion condensation)α，其值小於或等
於1﹔據我所知，離子型的界面活性劑濃度在低於其臨界微胞濃度(critical micelle concentration,CMC)時是完全解離的，然而，一旦超過其CMC 值，由於微胞的形成，微胞表面帶有高電荷數，導致反離子的凝聚作用開始產生，例如陰離子型界劑SDS(sodium dodecyl
sulfate)在形成微胞時，微胞表面帶幾十個負電，猶如一個強電場能吸引反離子（帶正電）的情形。所以在實驗上就發現α 隨著添加界劑的濃度增加而遞減。此外我們亦可由α vs. 添加的界劑濃度之圖形中，找出斜率變化的起始點來求得界劑之CMC 值，由此方法得到的值與大多數文獻是相符的。
在界劑和鹽類的混和溶液部分， 我們添加了一系列單價
(monovalent)的鹽類，來了解所謂的競爭凝聚的效應(competitive condensation effect) ， 由一些過去文獻凝聚效應增加隨著Li+<NA+<K+<RB+<CS+和F-<CL-
在界劑和高分子混和溶液部分，由於先前學長對於中性的高分子(neutral polymer)有較深入的研究，在此，我只利用離子濃度儀重現了少部分的結果，例如在PEG(poly ethylene glycol)和SDS 的系統中，發現SDS 的CMC 值有提前發生等等；另外還有一部分的實驗是帶電高分子(polyelectrolyte)和界劑的混和溶液，我們藉由離子濃度儀去探討帶電高分子與界劑之間的作用。

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with potentiometry. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, α<=1 . The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is
exceeded, the counterion ratio α declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Upon addition of multivalent salts, some of monovalent counterions are released to the bulk. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. In the vicinity of the micellar surface, multivalent ions replace the monovalent counterion easily because the electrostatic internal energy dominates. The above outcome
indicates that counterion condensation in micellar solutions is physical adsorption
origin instead of chemical binding. The experimental results are also supported by
Monte Carlo simulations based on the cell model.

[1] R.M. Fuoss, A. Katchalski, and S. Lifson, Proc. Natl. Acad. Sci. U.S.A. 37, 579
(1951); S. Lifson and A. Katchalski, J. Polym. Sci. 13, 43 (1954)
[2] T. Alfrey, Jr., R. W. Berg, and H. Morawetz, J. Polym. Sci. 7, 543 (1951)
[3] L. Onsager (private communication to G.S. Manning); G.S. Manning, J. Chem.
Phys. 51, 924 (1969); 51, 933 (1969); 3249 (1954)
[4] S. Alexander, P.M. Chaikin, P. Grant, G.J. Morales, P. Pincus, and D. Hone, J.
Chem. Phys. 80, 5776 (1984)
[5] G.V. Ramanathan, J. Chem. Phys. 88, 3887 (1988)
[6] L. Belloni, Colloids Surf. A 140, 227 (1998)
[7] J. Buffle, and G.G. Leppard, Environ. Sci. Technol. 29, 2169 (1995)
[8] J. Buffle, and G.G. Leppard, Environ. Sci. Technol. 29, 2176 (1995)
[9] T.Q. Li, and L. Odberg, Colloids Surf. A 115, 127 (1996)
[10] C. Botre, V.L. Crescenzi, and A. Mele, J. Phys. Chem. 63, 650 (1959)
[11] S.H. Chen, Annu. Rev. Phys. Chem. 53, 279 (1990)
[12] P. Paton-Morales, and F.I. Talens-Alesson, Langmuir, 18, 8295 (2002)
[13] V.E. Haverd, and G.G. Warr, Langmuir, 16, 157 (2000)
[14] Y. Moroi, Micelles. Theoretical and Applied Aspects, Plenum Press, New York,
1992.
[15] D.Myers, Surfaces, Interfaces, and Colloids, Principles and Applications, VCH
Publishers, Inc., New York, 1991.
[16] A. Hafiane, I. Issid, and D. Lemondart, J. Colloid Interface Sci. 142, 167 (1991)
[17] J.F. Rathman, and J.F. Scamehorn, J. Phys. Chem. 88, 5807 (1984)
[18] E.B. Abuin, E. A. Lissi, R. Nunez, and A. Olea, Langmuir 5,753 (1989)
[19] P. Mukerjee, and K.J. Kapauan, J. Phys. Chem. 71, 4166 (1967)
47
[20] J.M. Ruso, P. Taboada, V. Mosquera, and F. Sarmento, J. Colloid Interface Sci.
214, 292 (1999)
[21] H. Gustavsson, and B. Lindman, J. Am. Chem. Soc. 100, 4647 (1978)
[22] M.H. Ropers, G. Crichocki, and G. Brezesinski, J. Phys. Chem. B 107, 5281
(2003)
[23] J.E. Brady, D.F. Evans, G.G. Warr, F. Grieser, and B.W. Ninham, J. Phys. Chem.
90, 1853 (1986)
[24] P. Stilbs, K. Paulsen, and P.C. Griffiths, J. Phys. Chem. 100, 8180 (1996)
[25] P. Stilbs, and B. Lindman, J. Phys. Chem. 85, 2587 (1981)
[26] M. Sjoberg, U. Henriksson, and T. Warnheim, Langmuir, 6, 7 (1990)
[27] M. Sjoberg, U. Henriksson, and M. Jansson, Langmuir, 8, 409 (1992)
[28] V.K. Aswal and P.S. Goyal, Phys. Rev. E, 61, 2947 (2000)
[29] V.K. Aswal and P.S. Goyal, Phys. Rev. E, 67, 051401 (2003)
[30] V.K. Aswal, J. Phys. Chem. B, 107, 13323 (2003)
[31] Robb, I. D., In anionic surfactants, edited by Lucassen-Reynders, E. H.,
Plenum, New York, p.109 (1981).
[32] Goddard, E. D., Colloid Surf. 1986, 19, 255.
[33] Satio, S., In nonionic surfactants, edited by Schick, M. J., Dekker, New York,
p.881 (1987).
[34] Goddard, E. D., Colloid Surf. 1986, 19, 255
[35] Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294.
[36] Ruckenstein, E.; Huber, G.; Hoffmann, H. Langmuir 1987, 3, 382
[37] Xia, J.; Dubin, P. J. Phys. Chem. 1992, 96, 6805.
[38] Dubin, P. L.; Gruber, J. m.; Xia, J.; Zang, M. J. Colloid Interface Sci. 1992,
148, 35.
[39] Maltesh, C.; Somasundaran, P. J. Colloid Interface Sci. 1993, 157, 14
48
[40] Ruckenstein, E.; Huber, G.; Hoffmann, H. Langmuir 1987, 3, 382
[41] Cabane, B. J. Phys. Chem. 1977, 81, 1639
[42] Kamenka, N.; Burgaud, I.; Treiner, C.; and Zana, R. Langmuir, 1994, 10, 3455
[43] Wang, S.-C.; Wang, C.-K.; Chang, F.-M.; Tsao, H.-K. Macromolecules 2002,
35, 9551.
[44] Wang, S.-C. ; Tsao, H.-K. J. Chem. Phys. 2003 accepted