THE RATE O F COAAGUL-ATIOSO F SILVER HE-DROSOL R T E. W. 1%. BTEACIC
Introduction Smoluchowski’s theory of the kinetics of coagulation’ assumes that the function of the coagulator is to remove the charge on the colloid particles. Once the charge is removed coagulation ill occur whenever a particle enters the sphere of attraction of another particle. This leads to the expression l’i)
nzI
+ t,,T
,
where n is the total number of particles remaining at timet, no is the number of particles present at the start, and T is a constant usually called the “coagulation time.” The foregoing expression depends on the assumption that the particles are completely discharged by the addition of the coagulating agent. Coagulation under these conditions is called r a p i d coagulation. If the coagulator concentration is so low that the adsorption of ions is not sufficient to discharge the particle completely, we have what is called slolc coagulation. Smoluchowski assumes that under these conditions only a certain fraction of the collisions will be effective, and nrrivcs at the expression for the rate of slow coagulation,
n
= -___ no I
+ et,/T
where e is the “probability of adhesion.” To test this hypothesis there are two methods of investigation: (aj. Indirect methods in which some physical property of the sol is measured from time to time as coagulation proceeds. This property is then assumed to vary with the amount of coagulation in a linear manner. (b). The number of particles present at any time is determined directly by counting under the ultramicroscope. The first method is the easier and has been applied in a number of cases.? The results, however, are open to considerable doubt since the exact relationship between the physical property under investigation and the amount of coagulation is unknown. The second method gives much more reliable results, but has been applied to only two sols; gold,3 and se1enium.l It seems 1
Physik. Z., 17, 557, 583 ( 1 9 1 6 ; Z. physik. Chem., 92, 129 iIgl71; Kolloid-Z., 21, 98
(1917;.
* See for example Gann Iiolloidchcm. Beihefte, 8, 64 (1916 ; Hatsrhek: Trans Faraday S o c , ?7, a99 t. . . _ 11921 , IT-estgren: Z. anorg. Chem.. 93, 2,31 (19151; Arkiv Krmi. Mineral. Geol., 7 , no. 6 r191Xj; Kestgren andReitstotter: Z. pliysik. Chem.. 92. ; j i ir917,; Zsigmondy:ihid.,92,600 (1917). Kruyt and van Arkrl: Rec. Trav. rhim., 39, 656 1(1920!;40, 169 (1921).
RATE O F COAGULATION O F SILVER HYDROSOL
I849
advisable to extend these direct observations to other sols, and the present investlgatlon deals with the rate of coagulation of silver hydrosol by sodium chloride. Preparation of the Sol The sol was prepared by reducing silver oxide with hydrogen by the method of Kohlschutter.' As ordinarily prepared, the particles obtained are much too small for ultramicroscopic counting. In order to obtain a sol with coarser particles, the reduction was carried out a t 95"C, and the sol was kept at this temperature for 8 hours. The particle size in the resultant sol was large enough for counting purposes, and was satisfactorily uniform. Experimental Procedure The usual method was adopted of allowing coagulation to proceed for a definite length of time and then arresting it by the addition of gelatin solution. I t was found that the protective action of gelatin was notentirelysatisfactory. While no measurable change in the number of particles in the sol occurred in the first 2 0 or 3 0 minutes after adding the gelatin, a considerable change took place overnight. For this reason each point on the coagulation velocity curve was determined by a separate experiment. Thus, for example, a solution was made up with a definite concentration of sol and sodium chloride. I t was allowed to stand for z minutes and was then run into gelatin solution and the particles were immediately counted. Another sample with the same concentrations was then takenJhallowedto stand for five minutes, gelatin added, and the particles counted, and so on. Ultramicroscope X Zeiss slit-ultramicroscope with a Biltz cell was used. The illuminated volume was calibrated using fluorescin solution and a micrometer eyepiece. The dimensions were 7 3 . 4 X 73.4 X I j . 4 mu. Hence the illuminated volume was 83.0 X IO-^ C.C. The number of particles in this volume was counted every 5 seconds for 2 5 counts. h few drops of liquid were then run through the cell and another series of z 5 counts was made. This process was repeated until zoo counts had been made. The average number of particles in the illuminated volume was then computed. Results In each of the following experiments 5 C.C. of sol was made up to IOO c c. with sodium chloride solution, and coagulation allowed to proceed for the desired length of time. The silver content of the diluted sol was 0.195 milligrams per litre, and the sol contained 0 . 5 2 5 X 108 particles per C.C. The number of particles in the sol was constant over a period of one month. -111 the experiments were carried out a t zo°C. In Tables I to V the rates of coagulation are given for various concentrations of sodium chloride. I n the last column of each table is given the coagulation time, T, in the Smoluchowski equation. 1
Z. Elektrochemie, 14, 49 (1908).
I850
E. W. R. STEACIE
TABLE I S a C l concentration Time
!"
mins.
per
0
0.525
20
0.474
40 I08
0.438 0.405 0.386 0,332
187 360
=
5 millimols per litre
No. of particles
Per cent. of original number.
C.C.
x
I08
100.0
90.2 83.5 77.1 73.6 63.2
Coagulation time in mins.
'83 203 364 521
619
TABLE I1 KaC1 concentration =
25
millimols per litre
0
0.525
100.0
4
0,475 0.432 0.368
90.5
IO
30
7s 205
358
82 . 3 70 . o 56.5 44.9 37.1
0,997 0.236 0.195
38.1 47.6 69.8 97.4 166 212
TABLE I11 NaCl concentration =
IOO
millimols per litre
0
0,525
100.0
2
79.4 67.6
40 85
0,417 0,355 0.276 0.231 0,173
200
0.111
21.2
330
0.111
21.2
5 20
7.7 10.4
52.5
22.2
44 .o 33 .o
31.5 41.8 53 ' I 89.2
TABLE IV NaCl concentration = 2 j o millimols per litre 0
0.525
100.0
2
0.258
5
0.159
49.1 30.3
20
0.104
19.9
80
o ,079 0.074 0.056
15 .o
I 80
325
14.0 10.6
2.17
4.98 14.1 '9.3 38.5
1851
RATE O F COAGULATIOS O F SILVER HYDROSOL
TABLE 5’ S a C l concentration = 400 millimols per litre ‘?
mins.
x
Coagulation time in mins.
Per cent. of original number.
No. of particles per c.c.
Time
IO*
100.0
0
0,525
I
0.263
50.0
I
5
0.081
15.5
0.93
.oo
IO
0.049
9.3
I .02
20
0.026
60
0.009
5.0 I .8
1.10
0
50
100
I .os
150
Mins.
TIME FIG.I No.
I-
The Rate of Coagulation j millimols S a c 1 per litre
The results given in Tables 1-1- are also plotted in the accompanying diagram, Fig. I .
Discussion In the above tables the values of the coagulation time are given. It will be seen that the Smoluchowski equation holds well for conditions of rapid coagulation, where the concentration of the coagulating agent is high (Table V). At smaller concentration of sodium chloride, where we have slow coagulation, the results diverge very greatly from the Smoluchowski equation.
1852
E. W. R. STEACIE
This is in agreement with the results of Kruyt and van Arkel for selenium. The same behavior has also been found by indirect methods for gold,' and ferric hydroxide.* On account of the magnitude of the discrepancies there seems to be no doubt that the Smoluchowski equation as applied to slow coagulation is fundamentally in error. At the lower concentrations of sodium chloride the results seem to point t o the fact that complete coagulation is never reached. The same behaviour has been noticed by -1nderson with gold sol. He explains this by assuming that the initial particles are unequally charged. Hence at low concentrations of the coagulating agent some of the particles are not discharged sufficiently and remain stable for an indefinite period.
Summary The rate of coagulation of silver hydrosol by sodium chloride has been investigated by the ultramicroscopic method. The results confirm the Smoluchowski equation for rapid coagulation but show very large divergences for slow coagulation. There are indications that the initial particles are unequally charged. Physacal Chemaslry Laboratory, McGall Unz L C T S L ~ Y , Montreal Anderson: Trans. Faraday Soc., 19, 623 (19231; Mukherjee and Papaconstantinou: Phil. Mag., (6), 44, 305 (1922). * Jablczynski and Knaster: Bull., 43. 156 (1928); Jablczynski a n d Soroczynski: 43, 1.59 (1928).
