EXTINCTION COEFFICIENTS OF T H E SILICIC ACID GEL-FORMING MIXTURES BY MATA PRASAD, S. M. MEHTA .4ND J . B. DESAI
Lord Rayleigh has derived mathematically an expression according to which I, the intensity of light scattered by a colloidal solution at right angles to the incident beam is proportional to n, the number of particles per unit volume and to the square of v, the volume of the particle i.e.
1 = -KnvZ
x
where K is a constant and X will be constant if the same source of light is used. Since c, the concentration of the colloid is given by nvp, where p is the density of the colloidal matter, I = -kcv P
That is, at constant concentration the intensity of the scattered light is proportional to the volume of the particles. This expression does not apply to concentrated sols and to the sols in which the particles are not optically isotropic. Mie1 has studied the absorption and scattering of light by colloidal solutions containing particles of various dimensions and has concluded that a t constant concentration the intensity of the diffused light increases with the size of the particles and is proportional to their volume. KrishnamurtP has emphasized the importance of the study of the optical properties of colloidal solutions as they reveal their structure without disturbing their internal equilibrium. He has studied the scattering of light by agar sols and gels and has found that the micelles in the gels are much bigger than those in the sols. In the present investigation the scattering of light from the silicic acid gel-forming mixtures has been studied during the process of gel-formation. The intensity of scattered light has been determined from the measurements of the extinction coefficients of these mixtures and the results obtained have been utilised in elucidating the changes in size and number of the colloidal particles which take place in these mixtures during the gel-formation.
Experimental The extinction coefficients were measured by means of h’utting’s photometer used in conjunction with the Hilger wave-length spectrometer. I
Ann. Physik, 25, 377 (1908).
* Proc. Roy. SOC., 122 A, 76 (1929).
EXTINCTION COEFFICIENTS OF GEL-FORMING MIXTURES
1325
Light from a 50 C.P. point-o-lite lamp was divided into two beams by a pair of prisms placed at a distance of 19 cms from the lamp. The two beams of light were incident on the two apertures of the Nutting’s photometer after emerging from which they fell on the slit of the spectrometer and were refranged into three consecutive spectral bands of light. The different parts of the apparatus were accurately aligned with each other to avoid diffraction bands from obliterating the field of vision. The nicol of the photometer was then adjusted so that the logarithmic scale on the disc of the photometer read zero when an empty rectangular glass cell, used to hold the gel-forming mixture, was interposed in the path of one of the beams. This was done with a view to eliminate any initial absorption due to the glass cell. The gel-forming mixture was placed in the cell and the equality of the intensity of the three spectra in the green region (A = 5430 pp) was restored by turning the disc of the photometer. The rotation read on the logarithmic scale, is equal to log I,/I where I, is the original intensity of the beam and I that of the beam transmitted through the mixture. Values of the extinction coefficient were obtained by dividing log I,/I by t , the thickness of the gelforming mixture. Solution of sodium silicate was prepared by keeping a large quantity of Merck’s extra pure dry sodium silicate (Na20.2.jSiO2) in contact with redistilled water for three days. It was then twice filtered and kept in a well stoppered Jena glass flask. It was found that this solution underwent no change in concentration for about six months. The strength of the solution was determined by analysis and has been expressed in grams of silica per I O O C.C. of the solution. Solution of acidic ammonium acetate which was first used for the preparation of gels11 was prepared by dissolving a large quantity of Kahlbaum’s extra pure ammonium acetate in redistilled water with the addition of a little acid to it. On analysis this solution was found to contain 39.99% free acetic acid. Solutions of acetic acid used later were prepared from Merck’s extra pure product. Equal volumes of solutions of sodium silicate and of acidic ammonium acetate or of acetic acid were thoroughly mixed in a test tube and transferred to the cell, which was thoroughly cleaned and dried beforehand. The stopwatch was started simultaneously with the mixing of the solutions and readings on the logarithmic scale of the photometer were taken a t definite intervals after mixing. The results obtained are given in the following tables and one set of the curves between the extinction coefficient and time is shown in Fig. I . The reaction of these mixtures towards litmus has been tested and the pH values of some of them have also been measured by the colorimetric method. Cf. Praaad and Hattiangadi: J. Indian Chem. SOC., 6,653 (1929).
1326
MATA PRASAD, 6 . M. MEHTA AND J. B. DEBAI
TABLEI Silica Content 3% Concentration of ammonium acetate Time I’ 0“
1’30” 3’ 0” 6’ 0” IO’ 0” 15’ 0” 2 0 ’ 0“
3%
0.009993 0.04396 0.1140 0.1599 0,1739 0.1819 0.1819
0 .I089
1) ow
13’ 0”
23’ O H 38’ 0” 56’
0’‘
0.1579 0.1859 0 .I859
0.1659 0.1899 0.I899
7%
3’ 0” 9’ 0”
5%
4%
Alkaline
6%.
Acidic
0.03996 0.08794 0.1599 0.1698 0.1819 0.1819
8%
10%
Acidic
0.003996 0.007995 0.009995 0.01399 0.01998 0.05597 0,09792 0.1219 0 .I359 0.1419 0.1419
0
0.003996 0.04396 0.084 0 .I379 0 .I539 0 .I539
70‘ 0” 90’ 0“ 104’0” 1201 0‘’
0 0
0.001998 0,005995 0.007995 0 . 0 1 199 0,01799 0.03396 0.06195 0,07995 0.092
TABLEI1 Silica Content 4% Time
Concentration of ammonium acetate 3% 4% 9% 10% Alkaline Acidic
0.01998 0.07394 2 ’45’’ 0.1279 7 ‘ 0’’ 0.1759 8’ 0’’ 0.1819 13‘ 0’’ 0.1819 14’ 0’‘ I’ or’
2’ 0’’
21‘ 0’’
22’
o”
26’ 0’’
0.1739 0.1819 0.1958 0.1958
0.01199 0.03396 0,07995 0.1579 0.1.599 0,1719 0.1739 0.1739
Concentration of ammonium acetate Time
0.01199 I’ 0)” 0.03396 2 ’ 0” 0,05995 8’ 0” 0.1079 2 5 ) 0” 0.1199 45’ 0’’ 0,1479 60’0’’ 0,1539 72‘ 0’’ 0.1819 96’0” 0.1859 114‘0’’ 0.1859 120’ 0”
15%
20
Acidic
0 0.01 199
%
0 0
0.01399 0.001998 0.01998 o.oojgg5 0.02798 o.ooggg3 0.05795 0.0=799 0.06995 0.02202 0.09994 0.04796 0.1159 0.07396 0 . 1 ~ 1 90.07794
EXTINCTION COEFFICIENTS OF GEL-FORMING MIXTURES
‘327
TABLE I11 Silica Content 3% Time
0.331 N
Alkaline
Concentration of acetic acid 0.34 N 0.36 N
4’ ou
0.007995
o ,01998 0.02598
14’ow
0,04197
0.06395
I’ 0”
0
0
Acidic
0.397 N 0
0.03198
0.001998
0.08392 0 .I339
0.007995 0.01079
0.1419
0.02598
0.I419
0.03198
24‘ ow
0.07396
35’ 0” 41’ox
0 .I 0 2 0
0,09393 0.1159
0.1059
0.1239
54’ ou
0.1239
0.1319
0.04796
73’0” 79’ ow 99‘ 0’’ 109’ ow
0.1299 0,1319
0,1319
0.07595 o ,08596 0.I099
0.1319
0.1140 0.1140
1 1 5 ’ 0”
TABLE IV Silica Content 4% Time I’ 0’’ 11’ ON
28‘ ow 42’0” 48’ 0” 62‘ 0’’
85’ 0” 98’ ow 106’0’’ I 18’0’’ 120’ 0’’
0.373 N ’PH(9)
0,009993 o ,02798 0.05196 0.06998 0.07596 0.09194 0.1119 0.1219 0,1239 0.1239
Concentration of acetic acid 0.397 N 0.55 N (8.1) (5-3)
0.60 N
(5.2)
0.04796
0,01399
0,01399
0,09993 0.1559 0.1719
0.01399 0.02598 0.04596
0.01599 0.01998
0 .I739
0.05597 0,07995 0.1159 0,1298
0.1739
0.02598 0.03198 0.04197
0,1359
0.06395 0.07595 0.08392
0 .I399
0,09194
0,1399
0 ,095 92
1328
MATA PRASAD, 6. M. MEHTA AND J. B. DESAI
TABLE V Silica Content 5% Concentration of acetic acid Time
0.45 N
PH (9.15) I ’ 0”
4’ 0’’ 6’ 0’’ 16’0’’ 29‘ 0’’ 43’ 0” 48’ 0’’ 68’ 0’’ 92, 0” I 03 ’ 0’’ I IO’ 0’’ 115‘ 0” 1 2 0 ’ 0’’
0.03198 0,03597 0.03597 0.04098 0.05196 0.06395 0,07194 0.09194 0 .I099 0,1159 0.1219 0.1239 0.1259
0.50 N (7.5)
0.1119 0,1819 0 .I998 0 .I998
0.67 N
(5.3)
0.01399 0.02997
0.03797 0.08794 0 .I459 0.1639 0.1679 0.1679
8.70 N’ (5.2)
0,01399 0.01799 0.02198 0,03597 0.07794 0.1199 0.1299 0.1539 0.1659 0,1679 0.1679 0.1679
Discussion of Results I t will be seen from the curves (Fig. I ) that in each case the extinction coefficient of the gel-forming mixture increases with time a t first slowly, then rather rapidly and finally more slowly until it reaches an almost constant value, when the curves run parallel to the time-axis. This indicates that the value of log. I or I continuously decreases, that is, the intensity of the scattered light increases with time. These curves, therefore, represent the manner in which the size of the particles of the gel increases during the process of gel formation. The extinction coefficients of the various gel-forming mixtures have been measured from the time of mixing the gel forming constituents until the mixtures set to a gel. Prasad and Hattiangadi’ have shown that when the gel forming constituents are mixed, a sol of silicic acid is first formed and the gel is formed from the coagulation of the sol. These observations, therefore, include those of the sols in the beginning and of the gels in the end. The higher values of the extinction coefficient in gels than in the corresponding sols definitely show that the particles in the gel are bigger in size than in the sol. Also the continuous nature of the curves indicates that in the gel forming mixtures the formation of the colloidal particles, their growth in size and increase in hydration and the final coalescence of these hydrated particles, resulting in the formation of definite structures, are continuous processes. From study of different properties of soap sols and gels hIcBain? concludes that the colloidal particles in the sol and the gel state are identical in
*
J. Indian Chem. SOC.,6, 893 ( 1 9 ~ 9 ) . J. Chem. SOC.,117, 1506 (1920).
EXTINCTION COEFFICIENTS O F GEL-FORMING MIXTURES
I329
nature and amount: gels differ from sols only in possessing elastic properties. This view is, however, not support,ed by the conclusions mentioned above, according t o which the formation of the bigger particles by the union of the smaller ones appears to be a necessary factor in the sol gel transformation.
FIG.I Silica Content: 370 (with ammonium acetate)
Krishnamurti' has also come to the same conclusion from the study of the agar sols and gels. Further it will be seen from Tables VI and VI1 that at the time of setting the extinction coefficients of alkaline gels are higher than those of the acidic ones, that is, the light scattered by the former gels is greater than that by the latter. Considering the gels containing the same concentration of silica it appears that the particles formed in the alkaline gels are bigger in size than those formed in the acidic ones and hence the alkaline gels appear more opalescent than the acidic ones.? 1 2
Loc cit. Cf. Prasad and Hattiangadi: loc. cit. p. 653.
MATA PRASAD, S. M. MEHTA AND J. B. DESAI
I330
TABLE VI Extinction coefficient a t the time of setting Concentration of ammonium acetate
Silica content 3%
4%
0.1899 (alk) 0.1859 ” 0.1819 ” 0.1539 (acidic) 0.I419 ” -
4%
5% 6%
7% 8%
9%
-
10%
0.1958 (alk)
-
0.1739 (acidic) 0.1859 ’,
TABLE VI1 Extinction coefficient a t the time of setting Concentration of acetic acid
0.331 N 0.34 N 0.36 N 0 , 3 7 3N 0.397 N
Silica content 3%
-
0 .I 140
(acidic)
-
0.50
N
0.55
N
-
0.67
N N
-
0.70
4%
0,1319(alk) 0.1319 ” 0.1419 ”
-
0.1739 (alk) 0,1399 (acidic) -
5%
-
0.1998 (alk)
0.1679 (acidic) 0.1679 ”
The conclusion regarding the size of the particles in alkaline and acidic gels is supported by the observation of Linder and Pictonl who found no Tyndall cone in the dialysed sol of silicic acid in the presence of large concentration of hydrochloric acid. I t is also known that when hydrochloric acid is added to isoelectric gelatin, it gets positively charged and has a greater tendency to disintegrate than the iso-electric gelatin. Prasad and HattiangadP have shown that the silicic acid particles in the acidic mixtures are positively charged. Losenbeck3 has shown that the density of the positive charge in the silicic acid is much greater than the negative charge. The fineness of the particles in the acid mixture may, therefore, be due to the greater disintegration of the positively charged silicic acid in these mixtures. I t will be seen from the curves shown in Fig. I that they ultimately run parallel to the time-axis. This indicates that the changes involved in the 1
J. Chem. SOC.,61, 154 (1892).
* LOC.cit. p. 893. 3
Kolloidchem. Beihefte, 16, 27 (1922).
EXTINCTION COEFFICIENTS OF GEL-FORMING MIXTURES
1331
setting of the gel have reached a final stage. These measurements can, therefore, be used to determine the time of setting of gels. The time of setting of silicic acid gels has been measured by Fleming’ by the criterion that the set gel does not flow out of the container. Fells and Firth2 have used the criterion of the pressure required to blow a bubble through the gel forming mixture. Prasad and Hattiangadis have calculated the time of setting from the intensity of light transmitted by the gel forming mixture a t different intervals during gel formation. The times of setting from the present investigation are given below.
TABLE VI11 (A) Silica Content 3% Concentration of ammonium
Alkaline
acetate 3% 4% Time of setting 15’ 0‘’ 3’ 0” Concentration of acetic acid 0.33N Time of setting 79‘ 0’’
Acidic 6%
5% I’
30”
10%
0.39N 109’ 0’’
4%
Alkaline
Acidic
acetate 3% Time of setting 8’ 0’’ Concentration of acetic acid 0.37 N
0.40 N
pH value 9 Time of setting 106’ 0’’
48‘
4% 2’45’’
9% 14‘ 0’’ 0 .j j
0’’
0.50
9.15
7.5 6’ 0’’
‘2.Physik, 41, 427 (1902). 2 Trans. Faraday SOC., 23, 625 (1927). LOC.cit. p. 653.
ol’
N
.N
More than two hours 0.60 N 5.2
More than two hours
11.8’0‘’
0.45 N
More than two hours
15%
10% 22’
5.3
8.1
(C) Silica Content Concentration of acetic acid pH value Time of setting
8%
o.36N 33’ 0’’
o.34N 55’ 0”
(B) Silica Content Concentration of ammonium
7%
38’ 0” 116’ 0’’More than two hours
I O ’ 0’’
j%
0.67 N 5.3 48’ 0”
0.70 N 5.2
I I O ’ 0’’
1332
MATA PRASAD, S. M. MEHTA AND J. B. DESAI
The relative effect of the silica content, on the time of setting, is shown in the following table:
TABLEIX Concentration of ammonium acetate Silica content Reaction Time of setting pH value Silica content Time of setting
(I)
(2)
3%
4%
3%
4%
3%
4%
Alkaline
Alkaline 8’ 0)’
15’ 0’’
3 ’ 0”
3’45”
5.3
5.2
4%
5%
4%
5%
118’ on
48’ o*
More than two hours
I IO’
ot’
The time of setting of the gel, therefore, depends upon (i) the concentration of silica and (ii) the H ion concentration of the mixture: it decreases as the concentration of silica is increased, while, with an increase in the H ion concentration the time of setting a t first decreases and then begins to increase.’ The mixtures having pH 6-8 set in minimum time. No extinction coefficient readings could be taken with mixtures within this range as they set in a very short time but the determination of the time of setting by Fleming’s method confirmed the results of previous workers, that the mixtures setting in minimum time are either slightly alkaline or neutral. Considering that the process of gel formation is one of coagulation of the sol2 it would be interesting to examine the applicability of Smoluchowski’s theory of kinetics of coagulation* to the case of silicic acid gel formation. The conditions of the theory require that the coagulation curves must be similar in shape and related to one another. This is indicated by the similarity of the curves shown in Fig. I . If then a particular value of the extinction coefficient is shown by various mixtures a t times t, t2, t3, 27 which represents the same stage of coalescence, has a fixed value and
or tl : t 2 : t 3
. .
.
. .
t,
=
TI : TP : T3
,
,
.
,
. T.
where TI, T2, Tt . . . . . T, are cbnstants. The ratio of TI, T2, T3 must, therefore, be a fixed ratio independent of the absolute values of the ext,inction coefficients. These values are taken from the curves drawn for Tables I to V and are given in the following tables. Cf. Praead and Hattiangadi: loc. cit. Cf. A r b : Kolloidchem. Beihefte, 7, I8 (1915);Prasad and Hattiangadi: 100. cit., P. 893; Dhar and Prakash: J. Indian Chem. SOC.,6, 391 (1929). a Physik. Z., 17, 557 (1916); Z. physik. Chem., 92, 129 (1917). 1
2
EXTINCTION COEFFICIENTS OF GEL-FORMING MIXTURES
gS
bvi
N N
.
N
.
N
0 0 0
N
N
N
N
.
I333
d
.
N
N
H
" 9 ? ? ? ? ? 0
N
d r r ) h N W
d d m w w w
rr)
V. i w. v.i w.
m 0 H
I
I m
v
i
.
m - 0 .
1
m
7
0.
h
3
lnv)
"9
h I
vi
. N. r r. ) v ) r O. h. h I
I
I
H
H
I
- 0 "-?a?? 0 0 0 0 0 0 0 Lor0
7°F
0
N
m
N
CI
N
vi N
.B
h m ? ? ? 0
w
v)
v)
""'9
0
0
r
0
vi
. m. h. o. ? ? N
N
rr)rr)d
I
0
H
v i N
0
~
~
I
10
v)
. N. v.i ? " 4 N
N
N
v
i
m
N
N
??PP?'o
0 0 0 0 0 0 0
MATA PRASAD, S. M. MEHTA AND J. B. DESAI
I334
d N
cN\
-
e
. .
N
*.
h m v,
".
-
-
3
.
H
2
2
6;
I 1
w
a
p:
&
10
3" 0
\o
h m
e
N
-
"
-
z 0
&e 0 ? 0 p0 - m0 ?a o1
48
0 0 0 0 0 0 0
G6
&8
w h w
0.0
-
N
0 ? ? 0 ? 1 ?
0 0 0 0 0 0 0
EXTIKCTION COEFFICIENTS QF GEL-FORMING MIXTURES
I335
TABLEXIV Silica Content 5 % Time in minutes with the following concentrations of acetic acid 0.45 N 0.50 N 0.67 N 0.70 N tl tz ta tk
Ext . coeff. 0.05
29.0
0.20
0.06
40.0
0.25
I2
0.07
48.0 56.0 66.0
0.08 0.09
9.5
20.0
.o
24.0
0.30 0.40
13 . o
27 0
15.0
0.55
16.0
29.5 32 .o
Ratios TI -
Tz I45 160 160 140 I20
T2 I I I I I
Ts -
Tz 47.5
48.0 43.34 37.5 29.09
T4 F 2
IO0
96 90 73.75 58.18
I t will be seen from these tables that in most of the cases the range of variation in the values of T is small. This shows that the ratios of the values of T are almost independent of the time or the stage of gelation. I t appears that within a certain range of extinction coefficients shown in the tables the gelation of silicic acid approximates to the case of an ideal coagulation assumed by Smoluchowski. It should however be noted that for very low or very high values of extinction coefficients the variations in the ratios are too great to be negligible. Prasad and Hattiangadil have pointed out that the colloidal particles of silicic acid are first formed after the gel-forming constituents are mixed. Krishnamurtil has followed the changes in the intensity of the Tyndall light with time during the hydrolysis of methyl silicate and has found that the primary particles first formed, grow into bigger aggregates. The continuity of the time-extinction coefficient curves, however, indicates that the formation of colloidal particles and their coagulation are taking place simultaneously. But it is reasonable to assume that in the beginning the rate of formation of the colloidal particles will be much greater than their coagulation. The discrepancy in the preliminary stage thus appears to be due to the simultaneous formation of colloidal particles. I n the later stage of gel-formation the discrepancy may be due to the high degree of hydration of the particles on account of which their collisions may not be perfectly inelastic and the assumptions of Smoluchowski’s theory are not satisfied. 1
LOC.cit. p. 893.
* Nature, 124,690-691 (1929).
‘336
MATA PRASAD, 8. M. MEHTA AND J . B. DESAI
summary
( I ) The extinction coefficients of various mixtures forming gels of silicic
acid have been measured by means of Hilger Nutting’s spectro-photometer. It has been shown that a t constant concentration the micelles in gels are bigger than those in sols. Also, at constant concentration the micelles in alkaline gels are bigger than in the acidic ones. (2) The time of setting of the gels has been calculated from the curves in which extinction Coefficients are plotted against time. (3) Application of Smoluchowski’s theory of kinetics of coagulation of a colloidal solution by electrolytes has been extended to the case of gelation. Physacal and Inorganic Chemistry Laboratories, Royal Institute of Science,
Bombay.
