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Akira Watanabe : The Coagulation of Colloidal Powders. The stability of hydrophobic colloids is mainly governed by the magnitude of the potential energy of repulsion due to the superposition of electrical double layers and van der Waals attraction between approaching particles. In the absence of potential barriers, every collision between particles leads to adhesion (rapid coagulation), and in the presence of potential barriers, the probability of collision is decreased, thus leading to slow coagulation. A quantitative theory was given by Reerink and Overbeek to describe the influence of the double layer thickness at constant Stern potential on colloid stability, a situation which occurs when indifferent inorganic electrolytes are added to sols. While, Ottewill, Rastogi and the present author gave a theory which treated the case where the change in the Stern potential occurs due to adsorption. An extended theory of coagulation was also given which treated the general case of changing ionic strength and potential. The experimental verification of the theory thus obtained was carried out by measuring the coagulation kinetics of positively charged silver iodide sols spectrophotometrically. Electrokinetic measurements were also made by using ultramicroelectrophoresis. The agreement between the theory and experiments was very good and a reasonable value of the van der Waals constant was obtained. Experiments were also shown which were carried out by employing the twin dropping mercury electrodes polarized at various potentials in electrolytic solutions. The condition of coalescence of the mercury droplets, i. e. the relation between the ionic strength and the critical potential of coalescence, was proved to be in excellent agreement with the theory of coagulation of colloid particles. Thus, the interaction between finely dispersed particles in hydrophobic colloids is essentially the same as that acting between macroscopic mercury droplets. (Received April, 10, 1964)

Fig.1 The Stern pictures for interfacial electrical double layer, in the presence of small (A), medium (B) and large (C) specific adsorption of oppositely charged ions. + cations ; - anions ; - deficit of cations ; + deficit of anions ; s, the slipping plane for electrokinetic phenomena.

Fig.9 Changes in the potential distribution in the electrical double layer. A, the double layer compression, and B, the Stern potential suppression.

Fig.14 Ċ vs. log concentration of dodecyl surface active agents for positive silver iodide cols. Table1 The adsorption of surface active agents on positive silver iodide sols.

Fig.15 Ċvs. log concentration of electrolytes for silver iodide sols covered with 10-4 M/l STS. La(NO3)3; Ba(N03)2; Ca(N03)2; CdSO4 ; ~ NaNO3. Table2 The counter ion binding of silver iodide sols covered with 10-4 M/l STS. a=100a, Ċ*=-89mv.

Fig.17 optical density vs. time for coagulation of positive silver iodide sols by sodium sulphate. AgI sol: 5 ~10-4M/l, pag 3, a=100a. Na2SO4: 6.67 ~ 10-4, œ 1.00 ~10-3, 1.33 ~10-3, 2.00 ~10-3, œ 3.00 ~10-2M/l.

Fig.19 Log stability vs. log molar concentration for alkyl sulphates. Fig.20 Log stablity vs. log molar concentration for surface active sulphonates. Fig.21 Log stability vs. Ċ curves for surface active sulphonates. --- theoretical curve for A=3 ~10-12erg.

Fig.22 Shift of the free energy minimum due to the Stern layer interaction. Fig. 23 Formation of tetradecyl sulphate salts. A, Electrophoretic mobility U, ƒê/sec/v/cm vs. log molar concentration of added electrolytes. B, Optical density, 90 sec after mixing, vs. log molar concentration of added electrolytes. Th(N03)4, La(N03)3, Ba(N03)2, Ca(N03)2. Fig.24 Formation of dodecyl benzenesulphonate salts. A, Electrophoretic mobility U, ƒê/sec/v/cm vs. log molar concentration of added electrolytes. B, Optical density, 90 sec after mixing, vs. log molar concentration of added electrolytes. Th(N03)4; La(N03)3; Ba(N03)2; Ca (NO3)2; ž MgSO4; CdSO4; ZnSO4; MnSO4.

Fig. 25 Log stability vs. K a curves for AgI sols covered with STS. Ÿ LiNO3 œ U02(NO3)2 Ba(NO3)2 Th(N03)4 ~ NaNO3 CdSO4 Ca(N03)2 La(NO3)3 KN03 ZnSO4 ž MgSO4 MnSO4 Fig.26 The coalescence experiment of mercury droplets. A, B, mercury droplets; C, reference (pool) electrode ; D, choke coil ; F, filter circuit ; P, potentiometer ; R1, R2, resistors ; T1, T2, transformers ;R1, standard variable resistor; Cx, standard variable capacitor; AMP, amplifier; AFO audiofrequency oscillator, 1,000 cps ; SYN, synchroscope ; TDME, twin dropping mercury electrodes.

Fig.28 Critical potential vs. log concentration curves for the coalescence of mercury droplets. A KC1; KF; œ Na2SO4; Zn(NO3)2; La(NO3)3; Th(NO3)4. A, B, the coagulation concentrations for the positive silver iodide sol, ƒä=+130mv ; A', B', the concentrations of mono-and divalent anions, corresponding to the critical potential E+=130mV.

u ² Ì æ Ñ ² è à v æ11šª æ2 Fig.29 Log critical potential vs. log ionic concentration curves for simple inorganic electrolyte solutions. K+ ; - - Na+; Zn++; La+++ ; Th++++ œ ; Cl-; NO3- V SO4--; 1, 2, 3, 4, the absolute values of ionic valencies. log ce=-6log z+ logb" (94) Fig.30 Critical potential vs. log ionic concentration curves for sodium citrate solutions.

Fig.31 The effect of various agents on the coalescence of twin dropping mercury electrodes. Supporting electrolyte, 10-1M/l KCl. Polyvinyl alchol (P=1,400), L Epan (copolymer of ethylene oxide and propylene oxide) ; œ SIDS; Cetylpyridinium chloride; Glycine. 10) D.L. Chapman : Phil. Mag. (6) 25, (1913) 475. 11) L. Gouy : J. Physique (4) 9, (1910) 457 ; Ann. Physique (9) 7, (1917) 129. 12) N. K. Adam : "Physics and Chemistry of Surfaces", 14) D.C. Grahame : Chem. Revs., 41, (1947) 441. 15) R. Parsons : "Modern Aspects of Electrochemistry 1", (ed. by O'M Bockris) Butterworths, London 1) K. J. Mysels : "Introduction to Colloid Chemistry", Interscience, New York (1959). 2) H. R. Kruyt : "Colloid Science 2", Elsevier, Amsterdam (1949). 3) H. R. Kruyt : "Colloid Science 1 ", Elsevier, Amsterdam (1952). 4) M. Smoluchowski : Physik. Z., 17, (1916) 557, Univ., 38 (1960) 158. 31) J. T. Davies, E. K..Rideal : "Interfacial Phenomena", Acad. Press, London (1961). 586. 5) J. Crank: "Mathematics of Diffusion", Oxford Univ. Press, London (1956). 6) A. Einstein: Ann. Physik, 17, (1905) 549 ; 19, (1906) 371. 7) E. A. Guggenheim: "Thermodynamics", North Holland, Amsterdam (1957) 373. 8) O. Stern: Z. Elektrochem., 30, (1924) 508. 9) J. Lyklema: Trans. Faraday Soc., 59, (1963) 418. Oxford Univ. Press, London (1941). 13) J. A. V. Butler : "Elect rocapillarity", Methuen, London (1939) ; "Electrical Phenomena at Interfaces", Methuen, London (1951). (1954). 16) 9218, ±B : Th, 20 (1952) 247, 308, 358, 419. 17) P. Debye, E. Hiickel : Physik. Z., 24, (1923) 184, 305. 18) E. J. Verwey, J. Th. G. Overbeek : "Theory of Stability of Lyophobic Colloids", Elsevier, Amsterdam (1948). 19) A. L. Loeb, J. Th. G. Overbeek, P. H. Wiersema: "The Electrical Double Layer around a Spherica Colloid Particle", M.I.T. Press, Cambridge, Mass. (1960). 20) A. Watanabe : Bull. Inst. Chem. Res., Kyoto Univ., 38, (1960). 235. 21) F. Booth: J. Chem. Phys., 19 (1951) 391, 1327, 651. 22) B. E. Conway, J. O'M Bockris, A. Ammar :, Trans. Faraday Soc., 47, (1951) 756. 23) D.C. Grahame : J. Chem. Phys., 18, (1950) 903. 24) M. Eigen, E. Wicke : Z. Elektrochem., 56, (1952) 551 ; J. Physic. Chem., 58, (1954) 703. 25) V. Freise: Z. Elektrochem., 56, (1952) 822. 26) H. Brodowsky, H. Strehlow : ibid., 63, (1959) 262. 27) n Ó ¹, Ò ŸŽõ, ã c à j: d», 29 (1961) 701, 777. 28) A. Watanabe, F. Tsuji, S. Ueda: Kolloid Z., 191, (1963) 147 ; 193 (1963) 39. 29) R. H. Ottewill, M. C. Rastogi, A. Watanabe : Trans. Faraday Soc., 56, (1960) 854. 30) A. Watanabe: Bull. Inst. Chem. Res., Kyoto

32) A. Watanabe, F. Tsuji, S. Ueda: Proc. 2nd Intern. Congr. Surface Activity, 3, (1957) 94. 33) I. Langmuir : J. Chem. Phys., 6, (1938) 893. 34) F. Booth : Disc. Faraday Soc., 18, (1954) 104. 35) B. V. Derjaguin : ibid., 18, (1954) 85 ; Trans. Faraday Soc., 36, (1940) 203. 36) S. Levine, G. P. Dube : Trans. Faraday Soc., 36, (1940) 215. 37) F. London : Z. Physik, 63, (1930) 245. 38) J. C. Slater, J. G. Kirkwood : Phys. Revs., 37, (1931) 682. 39) J. Th. G. Overbeek, M. J. Sparnaay : Disc. Faraday Soc., 18, (1954) 12. 40) B. V. Derjaguin, A. S. Titijevskaia, I. I. Abricossova, A. D. Malkina : ibid., 18, (1954) 24. 41) H. C. Hamaker : Physica, 4, (1937) 1058. 42) S. Chandrasekhar: Rev. Modern Phys., 15, (1943) 1. 43) J. Q. Umberger, V. K. La Mer : J. Amer. Chem. Soc., 67, (1945) 1099. 44) N. Fuchs : Z. Physik, 89, (1934) 736. 45) P. Debye : Trans. Electrochem. Soc., 82, (1942) 265. 46) H. Freundlich : Z. physik. Chem., 44, (1903) 129; 73, (1910) 385. 47) H. Freundlich, G. von Elissafoff : ibid., 79, (1912) 385. 48) W. B. Hardy: Proc. Roy. Soc., 66, (1899) 1100; J. Phys. Chem., 4, (1900) 235 ; Z. physik. Chem., 33, (1900) 385. 49) H. Schulze : J. prakt. Chem. (2) 25, (1882) 431 ; 27, (1883) 320. 50) H. Reerink, J. Th. G. Overbeek : Disc. Faraday Soc., 18, (1954) 74. 51) G. H. Jonker, H. R. Kruyt : ibid., 18, (1954) 170. 52) A. Watanabe: Bull. Inst. Chem. Res., Kyoto Univ., 38, (1960) 216. 53) R.H. Ottewill, A. Watanabe : Kolloid Z., 171, (1960) 33. 54) R. H.. Ottewill, A. Watanabe : ibid., 170, (1960) 38. 55) ã c à j, n Ó ¹:ŽÀŒ±»Šw u À7,ŠÛ P(1956) 386. 56) G. E. van Gils, H. R. Kruyt : Kolloid Beih., 45, (1937) 60. 57) S.A. Troelstra, H. R. Kruyt : Kolloid Z., 101, (1942) 182. 58) J. Th. G. Overbeek : Kolloid Beih., 54, (1943) 287. 59) D.C. Henry: Proc. Roy. Soc. (London) A, 133, (1931) 106. 60) A. Watanabe : Bull. Inst. Chem. Res., Kyoto Univ., 38, (1960) 179. 61) R. H. Ottewill, A. Watanabe : Kolloid Z., 170, (1960) 132. 62) P. Mukerjee, K. J. Mysels, C. J. Dulin : J. Phys. Chem., 62, (1958) 1390, 1937, 1400. 63) R. H. Ottewill, A. Watanabe : Kolloid Z., 173, (1960) 122. 64) G. Oster : J. Biol. Chem., 190, (1951) 55. 65) A. Watanabe : Bull. Inst. Chem. Res., Kyoto Univ., 38, (1960) 248. 66) I. M. Klotz : "The Proteins 1", (ed. by Neurath and Bailey), Acad. Press, New York (1953). 67) Œã õ ½, n Ó ¹: ú»,84, (1963) 480. 68) A. Watanbe, R. Gotoh : Kolloid Z., 191, (1963) 36. 69) n Ó ¹, ¼ { Y,Œã õ ½: \. 70) J. T. Edsall, J. Wyman : "Biophysical Chemistry 1", Acad. Press, New York (1957). 71) H. C. Hamaker : "Hydrophobic Colloids," Amsterdam (1938) 16; Rec. tray. chim., 55, (1936) 1015 ; 56, (1937) 3. 72) H. R. Kruyt, M.A.M. Klompe : Kolloid Beih., 54, (1942) 484. 73) A. Kuhn : "Kolloidchemisches Taschenbuch", Akad. Verlags., Leipzig (1960). 74) J. Lyklema, J. Th. G. Overbeek : J. Colloid Sci., 16, (1961) 501. 75) J. W. Mitchell : Lecture at the Univ. of Cambridge, England (1959). 76) R. H. Ottewill, J. A. Sirs: Bull. Photoelectr. Spectrometry Group, 10, (1957) 262. 77) R. W. Horne, R. H. Ottewill, A. Watanabe : Proc. 3rd Intern. Congr. Surface Activity, 1, Cologne (1960) 203. 78) R. H. Ottewill, A. Watanabe : Kolloid Z., 173, (1960) 7. 79) E. J. Verwey : Chem. Revs., 16, (1935) 363. 80) S. Hachisu, K. Furusawa : Science of Light, 12, (1963) 1. 81) M. B. M'Ewen, M. I. Pratt : Trans. Faraday Soc., 53, (1957) 535 ; M. B. M'Ewen, D. L. Mould, ibid, 53, (1957) 548. 82) R. N. Gurney: "Ionic Processes in Solution", Mc- Graw-Hill, New York (1953). 83) R. H. Ottewill, M. C. Rastogi : Trans. Faraday Soc., 56, (1960) 866, 880. 84) P. Becher : "Emulsions", Reinhold, New York (1957). 85) n Ó ¹,Šç, 7 (1963) 886, 915, 941. 86) n Ó ¹: ƒ [ƒ ƒ ƒoƒ ƒtƒb [, 10 (1962) 175.

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