2710
The Journal of Physical Chemistry, Val, 82, No. 25, 1978
S. Demirci, B. V. Enustun, and J. Turkevich
Stability of Colloidal Gold and Determination of the Hamaker Constant Sahlnde Demircl, B. V. Enustun, Department of Chemistry, Middle East Technical University, Ankara, Turkey
and John Turkevich" Department of Chemistry, Princeton University, Princeton, New Jersey 08540 (Received April 6, 1978; Revlsed Manuscript Received September 22, 1978) Publication costs assisted by the US. Department of Energy
Previous computation of stability factors of colloidal gold from coagulation data was found to be in systematic error due to an underestimation of the particle concentration by electron microscopy. A new experimental technique was developed for determination of this concentration. Stability factors were recalculated from the previous data using the correct concentration. While most of the previously reported conclusions remain unchanged, the absolute rate of fast coagulation is found to agree with that predicted by the theory. A value of the Hamaker constant was determined from the corrected data.
1. Introduction Previously, rate of coagulation of 200-A colloidal gold was investigated by electron microscopy as a function of concentration of NaC104 used as coagulation agent.l The results were analyzed in terms of the Derjaguin-Verwey-Overbeek theory of stability of lyophobic colloid^.^,^ The treatment necessitated an assessment of concentration of primary colloidal particles. However, we recently became aware of an error in our electron microscope measurements4 leading to underestimation of particle concentration by a factor of 10. In this paper we present the results of these studies and a description of an improved experimental method.
2. Experimental Section A droplet of ten-times-diluted standard sol containing 2.5 X lo4 % gelatine and some &Ca2+was transferred onto a grid and evaporated. By using a Geiger counter, the volume of the droplet was estimated as 7.4 X W4mL by the usual isotopic dilution method. Then, the radial distribution of particles on the circular residue was determined by electron microscopy. The results are given in Table I.
3. Discussion The results of the integral counting method are consistent with a value of 5.3 X 10-l' calculated from the amount of gold chloride used for the preparation, detailed analysis of particle size distribution, and establishment that the formation of colloidal gold from gold chloride was complete to the extent of 99.9%.4 In the previous treatment of the coagulation data an incorrect value of 5 X 1O1O particles/mL was used. Most of the conclusions reached in that treatment are independent of absolute particle concentration. However, some other conclusions based on stability factor have to be revised as follows: (a) Stability Factor. The stability factor W estimated from the Smoluchowski equation (eq 7 in ref 6) using the experimental coagulation data is proportional to the absolute concentration of primary particles. Then the previous value of W must be corrected by multiplying by a factor of 53/5.0. The correct W values for colloidal gold containing M sodium citrate are given in Table 11. The stability factors W are replotted in Figure 1 on a log-log scale against NaC104concentration C, together with M sodium citrate and those for a gold sol containing for that containing M sodium citrate + M NaC10, 0022-3654/78/2082-27 10$01.OO/O
TABLE I : Radial Distribution of Particles on the Circular Residuea distance from center, population density, cmx l o 2 part/cm2 X lo-' 0 (center) 1.3 0.88 1.5 1.8 1.38 2.00 2.2 2.50 3.5 3.25 (boundary) 5.2 a Using this data, the total number of particles n on the grid was calculated to be 4.0 X l o 7 and the particle concentration in the standard gold sol is 5.4 x 10".
TABLE 11: Stability Factor of 200-8 Gold Sol M Sodium Citrate at Various NaClO, Containing Concentrations NaClO, NaClO, concn, mM W concn, mM W 2 3 5 8 10.5 13
510 330 180 94 8.9
20 50 100 200 400
4.2 2.4 (1.8) (1.6) (1.6)
6.6
as described previously.' The curves in Figure 1 are, of course, obtainable by a vertical displacement of the previous curves. Therefore, the general explanations of the trends in these curves presented previously, including a sudden potential drop a t a certain electrolyte concentration, are still valid. A new important result is this that, a t high NaC104 concentrations, the limiting value of W for colloidal gold M sodium citrate is of the order of 1. It containing means that when repulsive interaction between particles disappears as a result of compression of the electrical double layer, coagulation proceeds in accordance with the theory of fast coagulation due to Smoluchowski.6~7Although the theory of stability of lyophobic colloids predicts that the limiting value of W should be somewhat less than 1 (cf. p 286 of ref 7 ) ,and that the value presently estimated is somewhat more than 1,the accuracy of the colorimetric experimental data in this fast coagulation region warrant only an order of magnitude comparison and does not allow to favor one theory more than the other. The previous statement that the coagulation in this region is faster than the theory predicts is, obviously, a false conclusion. 0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No.
Ion Condensation on Planar Surfaces
25, 1978 271 1
calculated, but still in agreement with the value estimated by Reerink and Overbeeks from Westgren's results for colloidal gold. With this value of A the previously proposed equation to represent the stability of 200-A gold sol in the presence of 1-1 type of an electrolyte for W 2. 1 now becomes log W = 2 1 . 5 log ~ ~ (1.068 X 105y4/C)
where C is the electrolyte concentration in millimolar and y is given by
I
)I ii
t
(2)
y = [exp(\k/51.2)
I
-
1]/[exp(\k/51.2)
+ 11
(3)
where \k is measured in millivolts. Using eq 2 and 3, \k values were calculated for various points of the curves in Figure 1 and are given in the same figure. These new values also reflect the stabilizing effects of citrate and perchlorate ions, as discussed previous1y.l
References and Notes I
I
I
I
4
I I 1 I
l
l
*
10
I
I
10
30
c. mu
,
, '0
,
l
,
I O 60 10 10 I,@
,
200
I
1
, I ,
,m
wo
NrnCIOI
Figure 1. log Wplotted vs. log C .
(b) Surface Potentials and Hamaker's Constant. In terms of the Derjaguin-Verwey-Overbeek theory, the initial straight line portion of the curve in Figure 1 for a gold sol containing lod M citrate corresponds to a constant surface potential value \k which is calculable as 25.0 mV from its slope as bef0re.l From the slope and intercept of this straight line, the Hamaker constant is found as A = 0.87 X erg which is smaller than that previously
(1) B. V. Enustun and J. Turkevich, J. Am. Chem. Soc., 85, 3317 (1963). (2) B. Derjaguin and M. Kussakow, Acta Physicochim. USSR, 10, 25, 153 (1939); B. Derjaguin, ibid., I O , 333 (1939); Trans. Faraday Soc., 36,203, 730 (1940); B. Derjaguin and Landau, Acta Physicochim. USSR, 14, (633) (1941); J. Expfl. Theor. Phys. USRR, 11, 802 (1941). (3) E. J. W. Verwey and J. T G. Overbeek, "Theory of the Stability of Lyophobic Colloids", Elsevier, Amsterdam, 1948. (4) S.Demirci, "Electrical Charge on Colloidal Gold Particles", Ph.D. Thesis, Middle East Technical University, Ankara, 1973. (5) J. Turkevich, P. S.Stevenson, and J. Hillier, Discuss. Faraday Soc., No. 11, 58 (1951). (6) M. Von Smoluchowski, Phys. Z., 17, 557, 585 (1916); Z. Phys. Chem., 92, 129 (1917). (7) H. R. Kruyt, "Colloid Science", Voi. 1, Eisevier, Amsterdam, 1952. (8) H. Reerink and J. T. G. Overbeek, Discuss. Faraday SOC.,No. 18, 74 (1954).
Ion Condensation on Planar Surfaces. A Solution of the Poisson-Boltzmann Equation for Two Parallel Charged Plates Sven Engstrom" and HAkan Wennerstrom Division of Physical Chemistry 2, Chemical Center P.O.B. 740, 5-220 07 Lund, Sweden (Received April 24, 1978)
The Poisson-Boltzmann equation is solved analytically for the case of two parallel plates with an intervening aqueous solution containing only counterions. This is the situation one has in lamellar liquid crystals. Different aspects of the counterion distribution are considered, and a number of invariance properties are found. A t large distances between the plates the counterion concentration remains constant far from the plates, as the surface charge density is varied. The counterion concentration close to the surface remains constant as the distance between the plates is varied at constant surface charge density. In the limit of an infinite distance between the plates and a reasonably high surface charge density, the counterion distribution is unaffected by salt addition at distances from the surface that are small compared to the Debye length. Finally, the counterion distribution is independent of temperature. Similar invariances are well known for solutions of rod-shaped polyions, where the behavior has been termed counterion condensation. It appears that the present treatment reveals fundamental and simple properties of the counterion distribution outside planar charge3 surfaces that should be of importance for the understanding of a number of chemical processes outside such surfaces, including biological systems.
1. Introduction Charged surfaces immersed in (aqueous) electrolyte solutions are of importance not only in electrochemical reactions, but also in certain systems of amphiphilic molecules, such as lamellar liquid crystals and biological membranes. The ion distribution in the solution outside 0022-3654/78/2082-2711$01 .OO/O
such a charged surface is of great importance for the chemical behavior of the system. This ion distribution is, in an electrostatic continuum model, described by the Pois~on-Bol~zmann equation (SI units)
0 1978 American
Chemical Society
