STUDIES ON SILICIC ACID GELS 11. The Time of Set as a Function of the Temperature* BY CHliRLES B. HURD AND P. SCHUYLER MILLER
Introduction In the preceding paper of this series of studies on the setting process of silicic acid gels' a series of determinations of the time of set as a function of the temperature was given. Aqueous solutions of one commercial brand of water glass were mixed with solutions of acetic acid a t various temperatures. The time of set was determined by the tilted rod method. It was pointed out in the article that if certain simple assumptions were possible, the time of set could be treated according to the ordinary laws for the velocity of a chemical reaction. By the use of Arrhenius' equation, a series of values for the heat of activation were obtained. The mean value, 16,940 calories, comes well within the limits for the heat of activation for ordinary reactions. The value was reasonably constant for various mixtures of solutions of the same water glass with acetic acid. I t was, of course, immediately apparent that a further study should be made of this phenomenon, in order to ascertain if the same value would be obtained with solutions of other samples of water glass and acetic acid. The next step would be to substitute other acids for the acetic acid. The third study should include the results where deliberate attempt had been made to modify the composition or structure of the original silicate. The work reported in the previous paper was carried out with a water glass which can no longer be obtained. The silicates used in the work reported in the present paper and in the work now under investigation can be secured at any time, and their soda-silica ratio can be obtained from the maker, the Philadelphia Quartz Company.* The present paper includes the results of a series of determinations on six brands of sodium silicate. Acetic acid only was used. The results appear interesting and will, we believe, assist somewhat in obtaining a useful picture of the process of setting of silicic acid gels. Historical As previously mentioned in this article, Hurd and Letteron have shown that it is possible, by means of certain simple assumptions, to treat the process of the setting of a silicic acid gel according t o the laws for the velocity * Contribution from the Chemical Laboratory of Union College, Schenectady, K.Y. I C . B. Hurd and H. A. Letteron: J. Phys. Chem., 36, 604 (1932). The writers wish to acknowledge their gratitude t o the Philadelphia Quartz Company for their courtesy in supplying not only all of the silicates used in these studies, but also for supplying analyses, methods of analysis, and other valuable information. 2
STUDIES ON SILICIC ACID GELS
2195
of ordinary chemical reactions. No other measurements of this kind have been found in the literature. It has also been found, by a search of the literature, that little is known concerning the heat of setting of silicic acid gels. Thomsenl has reported that he found no heat effect during the coagulation of silicic acid; but his coagulation was slow, the time being a t least 30 minutes, and he used dilute solutions. Graham2 however, had reported about twenty years before that a rise of I.I”C occurred during the setting of a 5% jelly. It does not appear possible to calculate the heat of formation from Graham’s data. On the ordinary interpretations of 5%, however, the value of heat of setting would appear to lie between 1100 cal. and 2000 cal. per gram. mol, of HzSiOg. Wiedemann and Ludekings attempted to determine the heat of setting of solutions of colloids by means of a calorimeter of about 18 cc. capacity. They accelerated the setting of a mixture of solutions of water glass and hydrochloric acid by means of ammonia. Their results appear consistent, but their values of C = 12.2 and 11.2 cal. are difficult to correlate to our present heats of reaction.
Experimental We have determined the time of set for various mixtures of solutions of six different brands of sodium silicate with solutions of acetic acid a t several different fixed temperatures. The silicate samples were supplied by the Philadelphia Quartz Company. The acetic acid from which the solutions were made was glacial acetic acid, C.P., J. T. Baker. All water used was freshly distilled water which was boiled in lots of 3 to 4 liters to expel all gases, especially carbon dioxide. After being boiled vigorously, it was cooled quickly in snow and was kept, as were all solutions, in tightly stoppered glass bottles. The strength of all solutions was determined by titration. Silicate solutions were titrated for their alkali content with standard sulfuric acid, using methyl orange. The acetic acid solutions were titrated with standard sodium hydroxide, using phenolphthalein. The silica content was determined for the silicate solutions from the alkali content and the known soda-silica ratio supplied by the maker. We have checked this gravimetrically in one case. The silicate solutions were not filtered. Very little suspended matter was visible. A very slight sediment was noticeable after several weeks, although at the time the samples were used practically no deposit was visible. Runs were made by mixing accurately measured volumes of the standardized dilute silicate solution, the standardized dilute acetic acid solution and distilled water. The solutions and the water had been standing for hours in tightly stoppered containers in an accurately controlled water thermostat. Two I O O cc. Pyrex Griffin beakers, carefully cleaned and dried, had stood for several minutes in the thermostat immersed to within I cm. of the top. J. Thomsen: “Thermochemische Untersuchungen,” 1, 21 I (1882).
*T.Graham: J. Chem. SOC.,17, 318 (1864). E. Wiedemann and C. Ludeking: Ann. Physik, (3) 25, 145 (1885).
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CHARLES B. HURD ASD P. SCHUYLER MILLER
They had been covered with watch glasses. The measured volume of dilute solution was placed in one, and the measured volume of dilute acetic acid in the other. The water was added to the acid. At a given time the silicate was quickly poured into the acetic acid with stirring. To avoid the loss of the silicate solution which adheres to the beaker, the same beaker had had the same amount of silicate poured from it a few minutes before. We found this method necessary and accurate. The possible error in the volume of the silicate solution was found to be negligible. This rapid mixing avoided errors in the timing, especially for short runs. The beaker containing the resulting mixture was covered with a watch glass and placed on a tray in the thermostat, immersed in the water so that the level of water on the outside was higher than that of the solution inside. The beakers with watch glass covers just failed to float. The volume in the beaker was always 80 cc., except in the case of the oo thermostat, where a different procedure proved necessary. The contents of a number of beakers in the thermostat were watched until the peculiar opalescent appearance preceding setting was observed. The stirring rod test for setting was then applied. This has been described in the preceding paper. I t is carried out as follows. A stirring rod IO em. in length and made of glass 3 mm. in diameter is drawn out to a short stubby point, the tapered portion being about 5 mm. long. The point is fire polished. The rod is thrust into the gel at an angle of about zoo to the vertical. The gel is considered set when the rod fails to fall over. An operator with a little experience can obtain check determination differing by less than z yo of the time easily and regularly. Two different operators can check each other. A deliberate attempt to mutilate the surface and body of the gel will not produce errors greater than 3%. The beakers are not removed from the bath during testing. Four thermostats were used. In the oo thermostat, the mixtures for which the time of set was to be determined were contained in zoo cc. Erlenmeyer flasks. These were corked and IOO cc. beakers were inverted over the cork to prevent water leaking inside. They were buried in damp fine snow. The snow was frequently replenished from above. The excess water produced was withdrawn from below. Tests showed that the contents of the flasks remained within .I' of oo C. A longer rod of the same diameter was used to determine the time of set. This method proved much simpler for the operator at oo C. than the method of keeping the mixed solutions, 80 cc. in volume, in IOO cc. beakers as was done at other temperatures. The method of burying the 160 cc. mixtures in flasks in the snow was not adopted, however, until careful tests showed that the same results were obtained with the easier method than with the method of beakers a t the same temperature. The method of burying the flasks guaranteed much closer thermal control. The three other thermostats were made out of metal tubs about 20 inches in diameter and 12 inches deep. The 26' bath had no external insulation but those at 40' and 56" were insulated by a layer of dry sawdust
H'FIJI~II'~S O N SILICIC ACID GELS
2197
between the tub and a much lurgcr tub. Each was stirred by a brass paddle stirrer. The temperatures of the 26O, 40' and 56' baths were controlled by toluene mercury regulators. The 26' bath had a 100 watt intermittent heater controlled through a relay by the regulator. The 40' bath had a Cenco 1 2 5 watt continuous heater of the knife type and a 1 2 5 watt intermittent heater controlled by the regulator and a relay. To reduce arcing a t the relay contacts a 15 watt carbon lamp was connected across the relay contacts. The 1 2 5 watt heater was, therefore, controlled by the regulator in that the relay simply shunted from time to time, as necessary, the 15 watt lamp in series. Using this scheme, no arcing even with 2 5 0 watt heaters has been observed and the telephone relays, Western Electric E 493, have worked satisfactorily. The 56" bath had one 2 5 0 watt continuous heater and a 2 5 0 watt heater controlled as in the case of the 40' bath. We have not found temperature variation as large as .I"C during any of our runs. Timing was accomplished by means of a stopwatch or a good ordinary watch for the longer runs. The temperature of the thermostat was checked frequently. The watch glasses fitted tightly and, apparently, during the setting, a negligible amount of water or acetic acid was lost through evaporation. Containers in which gel had set were washed carefully with dilute sodium hydroxide and thoroughly with water, although tests had shown no measurable effect on the time of set through the presence of particles of a previously set gel. I n all of the runs reported here, we have kept the silica concentration constant. Because of the different soda-silica ratios of the samples, this has meant a different sodium hydroxide concentration with different samples. For any one brand of silicate, however, the sodium hydroxide concentration was constant, as was, of course, the silica concentration. Six different concentrations of acetic acid were used. The results obtained are given in the following tables. Trouble was experienced in the case of the "B.W." brand of water glass. Here the high soda concentration necessitated the highest concentration of acetic acid. It was found that when the silicate was poured into the acetic acid-water mixture the result curdled somewhat except at oo. This caused an error which is readily observed in the tables. I n the results which follow the average of the time for at least two satisfactory runs is given for each mixture a t each temperature. Ordinarily three check runs were made. An immense amount of work was required. Each table gives the soda-silica ratio, the concentration in the resulting mixture, expressed in gram mols per liter and the time of set in minutes for four different temperatures expressed in degrees Centigrade. It should be noted that the soda-silica ratio as given is a weight ratio. The mol. ratio is 1.032 times the weight ratio; for example the weight ratio of the C brand is given by the maker as I:Z.OO, giving 1:z.o6 for the mol ratio.
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CHARLES B. HURD AND P. SCHUYLER MILLER
Tables showing Time of Set for Various Mixtures
TABLEI
“S” brand Water Glass Ratio NazO:SiOz = I :.?A6 Concentrations Mixture NaOH Si02 CHICOOH o ,323 ,644 ,500 ,, lf ,625 I 11 11 2 ,750 ,, ‘87.5 3 I’ 11
4
”
5
)’
11
1.000 1.125
o.oo
1308, 2001.
271j.
3242. 3807, 4502.
Time of Set--Minutes 26.2O 40.7’ 89. 24.0 134. 39,s 177. 53.3 224. 66.0 265. 74.0 308. 86.0
55.8”
7.0 11.0
14.0 18.0 21.8 25.0
T A B L E 11 ‘W’ brand R a t e r Glass Ratio NazO:SiOz = 1:3.22
Concentrations Mixture NaOH Si02 CHICOOH o ,388 ,646 ,625 I 2
3 4
5
11
1)
.750
>l
11
‘875
11
” 11 j 1
11 If
1.000
1,125 1.250
0.00
1440. 1990. 2787, 3550. 3891. 4700.
Time of Set-Minutes 28.0” 40.6’ 87. 26.5 121. 39.8 160. 53,o 196. 62.5 218. 74.0 260. 84.0
j5.8” 8.4 11.1
16.4 20.5
23.2 26.8
TABLEI11 “K” brand Water Glass Ratio Na2O:SiOz = 1:2.84 Concentrations Mixture NaOH Si02 CHGOOH o ,440 ,646 ,625 ,l 1) I ‘7.50
-
2
1,
,l 1,
3 4
”
5
’)
’)
11
I1
,875 1.000 I . 125 1.250
Time of Set-Minutes 27.4’ 40.4’ 1080. 66.0 19.7 97.0 29.2 1648. 41.3 2214. 133.0 53.0 2789. 166.0 3108. 201.0 63.0 3518, 233.0 68.7 0.0’
56.2” 5.9 9.1 11.8 15.0
18.0 19.4
TABLEIV
“U”brand Water Glass Ratio NazO:SiOz = 1 z . 4 4
1.250
Time of Set-Minutes 25.9’ 40.4’ 1568. 105.5 26.2 2118. 145.0 38.7 2720. 189.0 50.5 3264. 228.0 60.5 3585. 265.0 70.5
1.375
4092.
Concentrations Mixture NaOH SiOz CHsCOOH o ,508 ,640 ,750 I 2
3 4
5
,,
11
11
,f
”
,, ,,
j 1
’I
j’
,875 I ,000
I .125
0.0’
292.0
81.7
55.8’ 8.3 11.2
14.4 18.3 20.7
24.4
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2199
TABLEV ‘C” brand Water Glass Ratio NazO:SiOz = I : ~ . O O Concentrations Mixture NaOH SiOz CHzCOOH o .623 ,642 ,750 I 2
Jl
1.250
Time of Set-Minutes 25.9” 40.4O 560. 38.0 10.3 1063. 73.7 20.9 1568. 108.0 29.8 1972. 142.0 38.2 2375. 165.0 48.0
”
1,375
3113.
)l
1I
1)
,, >I
3 4
”
5
”
0.00
‘875 1.000
I .I 2 5
”
199.0
55.8‘
3.1 5.6
8.5 10.6 13.2
55.5
16.1
TABLEVI “B.W.” brand Water Glass Ratio NazO:SiOz = Concentrations Mixture NaOH Si02 CH3COOH o ,791 ,645 ,938 I 2
11
1)
i7
11
3
”
4
”
5
”
>I
” 9)
I
1:1.58
0.0’
,091
1.250
Time of Set-Minutes 26.3’ 40.3’
255. 730. 1076.
20.9 52.0
76.5
5.0 13.6 20.4
,408
1340.
100.0
28.5
I . 561
1570.
1.720
1900.
123.0 142.0
32.6 40.0
I
55.8’
1.8 3.9 . 6.4 8.1 9.8 11.4
For each brand of silicate the logarithm of the time of set given in Tables I to VI for each of the six mixtures was obtained. This was plotted as ordinate against the reciprocal of the absolute temperature as abscissa. A typical set of curves for the “C” brand is shown in Fig. I. From the curves for the six mixtures of each brand of silicate, the slope was obtained. The curves were found to be linear. These values are tabulated in the following table : TABLE VI1 Values for the Slope of the Curves for Log Time of Set against Reciprocal Absolute Temperature Mixture 0
I 2
3 4
5
Brand “S” 3668. 3632. 3673. 3667. 3628. 3601.
“N”
“K”
(Values in degrees) 3638. 3640. 3625. 3690. 3607. 3600. 3625. 3618. 3581. 3620. 3569. 3608.
“u”
“C”
3662. 3675. 3666. 3666. 3600. 3572.
3660. 3644. 3648. 3635. 3628. 3628.
“B.W.” 3512. 3616. 3582. 3593. 3584. 3600.
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CHAItLES B. H W l D A N D 1’. SCIICI’LEIl MILLE,II
PIO. I
Effect of Temperature on Time of Set.
The values are seen to show good agreement except for the “B.W.” brand. The mixtures for this silicate, except those a t oo, showed curdling, as has been mentioned. Their lack of agreement is, therefore, to be expected. The curdling was more pronounced, the higher the temperature. I t seems reasonable to assume that where curdling occurred, the concentration of reacting substances in the solution would be decreased. This would result in a slower reaction and a larger value of log time of set a t higher temperatures. This would flatten the log t’ against I / T curve6 and would give smaller values for the slope. This agrees with the results in Table VI1 for the “B.W.’.”brand. Interpretation of Results As one of us has suggested in a previous paper,’ we may make certain assumptions in our interpretation of these results. These assumptions are not unreasonable, and they lead to interesting results. They are: I . That we are dealing with a process which follows the laws of ordinary chemical reactions so far as its velocity is concerned. 2. That Arrhenius’ equation may be applied to our results. C. B. Hurd and H..4.Letteron: J. Phys. Chem., 36, 604 (1932).
STUDIES ON SILICIC ACID GELS
2201
3. That for a given run the time of set measures the time when a certain fixed proportion of the silica, in whatever form, has reacted. These assumptions are discussed in the paper to which reference has been made. If we develop our ordinary equations for the velocity of a chemical reaction where x = amount changed in time, t
a = original concentration n = order of reaction we shall obtain the following familiar equations:
dx = kdt (a-x)” gives I t is easily shown for any fractional change of the concentration a, that the time, t’ is given by the relation
where c’ = constant depending upon fraction x/a and on n. We may now write Arrhenius’ equation dlnk Q d T -RT2
dlnk
Or
dI/T -
Q
-E
From (4) we obtain In t’ = In c’
- In k -
(n-I) In a
(6)
If now we maintain a and x/a constant, we may obtain from ( 5 ) and (6) In t’ =
+Q - (n-I) RT
In a
+ c”
(7)
From our values of Table VII, obtained as the slope of the curves for log t’ against I/T illustrated by Fig. I , we may obtain values for the heat of activation, Q, for the setting process for gels from the six brands of water glass. They are obtained by multiplying the values given in Table VI1 by 2.303 R, since by equation (7) dlnt‘ d r/T
Q
- R’
Table VI11 gives the results.
CHARLES B. HURD AND P. SCHUYLER MILLER
2202
TABLE VI11 Values of the “Heat of Activation” for the Setting of Silicic Acid Gels “S” 0
I 2
3 4 5
mean
16795 16630 16815 r6790 16612 16505 16691
“*”
16667 16595 16483 16952 16395 16342 16572
“K”
“U”
16657
16767 16826 16786 16786 16483 16350 16666
16895 16515 16595 16575 16520 16626
“C” 16757 16684 16702 16643 16612 16612 16668
“B.W.” 16080 16555 16401 16451 16410 16482 16397
These figures show remarkable agreement. An estimate of the possible error from the accuracy of the timing and temperature measurements, considering that in all cases the logarithm of time plotted was the mean of a t least two separate determinations, gives as the maximum probable error in the value of the “heat of activation” less than 2%. It is noticeable, however, that the six values for each brand, going downward in each vertical column in Table VIII, show a drift toward lower values. That is, a general decrease in the heat of activation is shown for each brand as the acidity of the mixtures increases. This decrease is not large, but since it occurs in each of the five columns, it is apparently not the result of error. We should note a t this point, of course, that it is more difficult to thermostat a 250 cc. Erlenmeyer flask and its contents for three days at oo than it is to keep the contents of a beaker a t 26’ for three hours, but errors in the ice bath readings alone could not alter the slope of the curves. They are the result of points obtained from data at all four temperatures. Formulatzon of a Theory. I t is difficult to formulate a theory which shall give a clear picture of the process of setting of a silicic acid gel and which shall, of course, be subject to verification or rejection on the basis of experimental results. As has been pointed out in the preceding paper, the lack of sufficient quantitative data constitutes a real difficulty. From a study of existing data, however, and a consideration of certain of our own experimental results, a part of which are as yet unpublished, we are prepared to suggest the following theory for examination. When a solution of sodium silicate and a dilute acid are mixed, a practically instantaneous reaction occurs, forming silicic acid and the sodium salt of the acid used, the latter, of course, mainly in the ionized form. The silicic acid particles slowly coalesce to form a structural framework for the gel, Beyond a certain stage, this process proceeds rapidly. The mechanism of linkage appears to be that of the splitting out of water from two hydroxyl groups of neighboring molecules of silicic acid. This agglomeration continues until the whole mass is filled with a fibrillar framework. There is, in the literature, sufficient evidence to convince us that the exclusion of the solid-solution theory supported by K a t d and the emulsion 1
Katz: Kolloidchem. Beihefte, 9,
I
(1918).
STUDIES ON SILICIC ACID GELS
2203
theory, supported by Wo. Ostwald’ is justified. Certain work under investigation in this laboratory, on the electrical conductivity of mixtures of sodium silicate and acetic acid during the process of setting, cause us to favor the fibrillar or brush-heap theory rather than the cellular theory. I$ is impossible to give any definite reference for the genesis of the idea of the splitting out of water molecules from hydroxyl groups of neighboring molecules of silicic acid. It is a common idea to be found in both organic and inorganic chemistry. Compare the discussion on the polysilicic acids in Mellor.2 The formation of higher silicic acids,”in connection with silicic acid gels has been mentioned by Jordis3 while the idea of chains held together by chemical forces in the silicic acid gel was stated by Gaunt and Usher.4 They have even postulated a long, highly hydrated chain to give the ratio of metasilicic acid. The linkage is through oxygen atoms. A similar idea in the organic field has been suggested by Kienle5 in a theory for the formation of artificial resins. It should be noted that in this case the condensation takes place between hydroxyl groups on molecules of different substances, such as glycerine and phthalic acid. We had believed, when starting this research, that a difference might be found in the time of set and in the effect of temperature on the time of set if the composition of the original sodium silicate could be varied considerably. This we have done, varying the Na2O:SiOZ ratio from 1:3.86 in the “S” brand which gives a mol ratio of 1:3.99 or essentially 1:4., down to a mol ratio of 1:1.63 for the “B.W.” brand. If the process of gel formation requires the formation of chains of partially dehydrated silicic acid, formed by the splitting out of molecules of water from neighboring hydroxyl groups, it is evident that in a solution in which the process has already partially occurred, such as a solution containing trisilicic acid, the gel formation should occur more rapidly than in a solution containing ortho or metasilicic acid. It is conceivable though not necessarily probable, that the effect of temperature on the rate of reaction should be different. It is, of course, not a t all certain that we have in the solution of the “S” brand, let us say, any different form of silicic acid than we have in the solution of any of the others, although one might expect to find sodium salts of the higher silicic acids in those samples of silicate where the ratio of the number of mols of silica to one of soda is high, such as the “S” brand with the mol ratio Na2O:SiOe of 1:3.99. It has been shown in various studies of aqueous solutions of sodium silicates, such as the work of Kahlenberg and Lincolne on the lowering of the freezing point and the electrical conductivity of solutions of sodium metal Wo. Ostwald: “Theoretical and Applied Colloid Chemistry,” translated by Fischer, 1’33 (19x7). 2 J. W. Mellor: “A Comprehensive Treatise on Inorganic and Theoretical Chemistry,” 6, 308 (1925). 8E.Jordis: 2. anorg. Chem., 44, 200 (1905). 4 Gaunt and Usher: Trans. Faraday SOC.,24, 32 (1928). 6 R. Kienle: Ind. Eng. Chem., 22, 590 (1930). 6 L. Kahlenberg and A. T. Lincoln: J. Phya. Chem., 2, 77 (1898).
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CHARLES B. HURD AND P. SCHUYLER MILLER
silicate, NazSiOs.gHz0, that the experimental evidence shows the influence of 2 Na and z OH ions but shows no evidence of a Si03ion. This hydrolysis had been mentioned previously by Kohlrausch. On the other hand, Harman’ presents evidence to show the existence of the Si03 anion in solutions of silicates of low soda-silica ratio, such as I : I , but he states that in solutions of high ratio such as I :3 or I :4 the simple SiOs ion is not present, but there are present either aggregations of simple silicate ions with or without colloidal silica or definite complex silicate ions. We feel, therefore, unable to state with certainty that we are starting our reaction with silicic acid in different form, from the “S” brand down to the “C” brand. Our results show, however, that the effect of temperature on the time of set is the same, from the “S”to the “C” ratios in acid solutions, as is shown by the values given in Table VIII. I t would be very interesting to discover whether the actual time of set is affected by the original soda-silica ratio, in two solutions having the same final sodium hydroxide, silica and acetic acid concentrations, one of which was produced by adding acetic acid to a low soda-silica ratio silicate such as the “C” brand with its ratio NazO:SiOz = 1:2.06 mol ratio while the other was made by adding sodium acetate and acetic acid to a solution of a silicate such as the “S” brand with a soda-silica ratio 1:4, mol ratio. We cannot answer this question from the results given in this paper, but the results of a series of determinations of this type a t present under way in this laboratory should answer the question as to whether the original condition of the silica affects the time of set. A comparison of the values of the “heat of activation,” mentioned in this paper, the average being Q = 16,640 calories with the average value obtained in the previous paper by Hurd and Letteron, Q = 16,940 calories, confirms the results given in that paper with much greater accuracy.
Summary The time of set of various mixtures of solutions of six different commercial iodium silicates with acetic acid a t four different temperatures have been determined. The soda-silica ratios range from 1:4.0 to 1:1.63 mol ratio. The temperatures were approximately oO, 26’, 40’ and 56°C. The effect of temperature on time of set was found to be the same, regardless of the soda-silica ratio. A value was obtained for a quantity analogous to Arrhenius’ heat of activation for a homogeneous chemical reaction. The average value of 16,640 calories was obtained. The data given here confirm the former results, obtained by Hurd and Letteron, on various mixtures of one sample of sodium silicate with acetic acid. A theory for the mechanism of formation of a silicic acid gel has been suggested. The theory has been considered from the point of view of the effect of the temperature on the time of set. Schenectady, N . Y.
’ R. Harman: J. Phys. Chem., 29, 115j (1925); and more especially 30,359 (1926).
