KINETICS FOR SOLUTION OF SILICA IN AQUEOUS SOLUTIONS
Oct., 1958
1195
THE KINETICS FOR THE SOLUTION OF SILICA I N AQUEOUS SOLUTIONS B Y T. L.
O ' C O N N O R " AND
s. A. G R E E N B E R G t
Ionics, Incorporated, * Cambridge, Massachusetts, and Seton Hall University, t South OTange, New Jersey Received March 5 , I968
A study of the rates a t which silica dissolves in stirred aqueous and alkaline solutions showed that the rate of solution is proportional to the surface area. In water, because of the reverse reaction of polymerization, the rate is also proportional to the concentration of silicic acid in solution. The following rate equations are found to apply for (1) alkaline media and (2) for water: dC/dt = klS (1); dC/dt = kzS(C, - C) (2), where k is the rate constant, C is the concentration of monosilicic acid (C, at equilibrium) and S is the surface area of the silica. Equation 2 must be modified if flocculation occurs. It is shown that the surface of pulverized quartz is covered with a layer of amorphous silica and that colloidal silicas exhibit inhomogeneous structures.
Introduction solubility of colloidal silica is greater than that of The rate at which silicas go into solution as vitreous silica, and quartz is the least soluble of the monosilicic acid has been shown t o be a function three varieties.lOvl' a suspension of silica in of the t e m p e r a t ~ r e , l -the ~ degree of ~ r y s t a l l i n i t y , ~ . ~ Rate Equations.-If the surface area,5 the amount of mechanical and water is stirred sufficiently to maintain a uniform heat treatment6s7 and t,he degree to which the distribution of the dissolved species and to keep all silicas were washed with water, alkaline or acid the surface of the solid in contact with water, it is solutions.5 However, only a few attempts have reasonable to assume the rate of solution is been made t o explain the kinetics,8,9and equilibria E (3) for the solution of silica on the basis of the usual dt = klS rate and thermodynamic equations. Intimately connected with the problem is the the rate of deposition, or polymerization, is nature of silica surfaces. Much research has been --dC - - kzCS (4) reported t o demonstrate the presence of an amordt phous layer on ground quartz5 and the nature of and the net change in solution concentration is the the surface of amorphous silicas. ',lo difference It is the purpose of the present study to show that the experimental data and reported results (5) dt = klS - kzCS can be explained by the usual rate equations and by the equilibrium solubilities for the several varieties where kl and k2 are rate constants, C is the concenof silica. tration of monosilicic acid in moles/l. and S is the surface area. At equilibrium therefore dC/dt is Theoretical zero and Equilibrium Equations.-The equilibrium between each form of solid silica and aqueous solutions saturated with monosilicic acid may be represented On substitution of k2Cefor k l , equation 7 is obtained SiOz(s)
+ nHzO = Si(OH)r.aq.
(1)
For this equilibrium the constant K is equal t o the activity of the monosilicic acid in solution. Since the solubility of silica is low, the activities and concentrations of silicic acid are essentially the same.ll From the relationship between the standard free energy change and the solubility, K , of silica AFn = -RT In K
(2)
it is easy t o see that the more crystalline a silica species the more iiisoluble it is. For example, the (1) For an excellent discussion see R. K. Iler, "The Colloid Chemistry of Silica and the Silicates," Cornel1 University Press, Ithaca. N. Y.. 1955. (2) G. B. Alexander, W. M. Heston and R. K. Iler, THISJOURNAL, 58, 453 (1954). (3) 9. A. Greenberg, J . P h y s , Chem., 61, 196 (1957). (4) G. C. Kennedy, Econ. G'eol., 45, 629 (1950). (5) For discussion see P. F. Holt and D. T. King, J . Chem. Soc., 773 (1955). (6) C. C. Lucas and M. E. Dolan, Canad. Med. Assoe. J . , 40, 127 (1939). (7) Y. V. Morochesvky and M. M. Piryutko, Bull. Acad. Sci. USSR, Diu. of Chem. Sci., 8 , 894 (1956). (8) K. Goto, THIS JOURNAL, 60, 1007 (1956). (9) P. H. Kitto and H. S. Patterson, J . Ind. H y g . 8: Toxic., 2 4 , 59 (1942). 60, 325 (1956). (10) 8. A. Greenberg, THISJOURNAL, (11) S. A. Greenberg and E. W. Price, ibid., 61, 1539 (1957).
dC _ dt
-- kzS(C, - C)
(7)
In this derivation of the equilibrium constant K , it is assumed that the moiiosjlicic acid is deposited by condensation reactions on the surface of the is thus apparent that the solu~ i l i c a . ' ~ ~ ' ~It- ' ~ bility of silica is independent of the surface area 8, provided there is enough silica present to saturate the solution. Where no stirring is applied, the rate becomes also a function of the rate of diffusion of the monosilicic acid product from the surface of the s0lid'6-~~ and of the completeness of contact between the solid surface and water. I n the application of eq. 5 to solution of silica in alkaline media, it is possible to neglect the term k2CS because the rate of polymerization is negligible above pH 11.12 The total concentration of silica polymer Cp in moles/l.is distributed among n spherical particles all of radius r and of density p. (12) (13) (14) (15)
S. A. Greenberg and D. Sinclair, ibid., 69, 435 (1955). S. A. Greenberg, J . P o l s . Sei., 2 7 , 523 (1958). S. A. Greenberg. THIS JOURNAL, 61, 900 (1957). W. Nernst, Z . physik. Chem., 47, 53 (1904). (16) A. A. Noyes, and W. R. Whitney, ibid., 23, 689 (1897). (17) N. Brunner and A. St. Tolloczo, ibid., 35, 283 (1900).
T. L.
119G
O'CONNOR A N D
0
15 A .a
50
e'
0,
.-
1
-2 rl
10
rj
h
$
8
90
4
I
4
'5
E
I
- 5
8
g 0
\
100. 20 30 40 50 Time, minutes. Fig. 1.-(Lt - L m ) ' / S vs. t showing rate dependence on surface area for the-solution of Sp. B. silica in 0.025 N NaOH a t 40". Numbers on the curves are the Na2O:SiOz ratios. 10
S.A. GREENBERQ
Vol. 62
started immediately. After the solution reached the desired temperature (approximately five minutes), samples were withdrawn periodically. The measured volumes of solutions were added to acidified molybdate reagent and centrifuged for five minutes before a reading of transniittance was made. The molybdate method for determining monosilicic acid has already been described.PJ1 In the case of samples containing a relatively large amount of silica, it was necessary to use a special blank. To make this blank a volume of suspension equal to that used in determinations, but which had been just brought to temperature, was immediately added to molybdate reagent at room temperature and centrifuged for the Atandard five minutes.
Results and Discussion Solution in Alkaline Media.-In a previous studyI4of the rates silicas dissolve in alkaline solutions, it was found that the rate is independent of hydroxyl ion concentration above pH 11, is directly proportional to the amount of silica, is influenced by the speed of stirring and is proportional to the surface areas of the silicas. T o test the proposed mechanism (eq. lo), the rates of solution at 40' were examined as a function Of the amount Of Equation lo was converted to (L
- L,)%
= (Lo
- L,)l/: - kqt
(12)
The surface area S in a liter of solution is then 4w2n where IC4 is a constant and the specific conductivity and the concentration of polymer C, is L subscripts refer. to time 1, time infinity and time zero. I n Fig. 1, (Lt - L m ) ' / a is plotted as a function of time. A good linear relationship was found where 60 is the molecular weight of silica. It is over 90% of the reaction with all the lines contherefore possible to write verging a t a common point. Both of these observations agree with the mechanism described by (9) equation 10. The kinetics which hold when depolymerization is almost complete have been diswhich when integrated becomes cussed. l 4 C,'/s = Cw'/a - kat (10) In equation 12, k4 is a constant including the where Cp0is the concentration of polymer at t = number of particles, thus -IC4 CY kl*n'/a. Since the number of particles is directly proportional to 0 and ICl* and k3 are constants. For the application of eq. 7 to neutral solutions, the silica content a plot of k43 vs. the Si02/Na20 it is first necessary to integrate the equation. ratio should be a straight line. The experimental Where sufficient silica is present, it is apparent that data gave a straight line with a slope of 1.72 X the surface area S will remain essentially constant 10-8. The influence of the surface areas of silica on the during the reaction. If it is assumed that C = rate of solution at 40" was examined. It was found 0 at t 2 0, then the integral of eq. 7 is that the time to reach complete solution was not inversely proportional to the surface areas. The times for complete solution of S.L., Sp.B., and where k2* = -kz and C , is the concentration of aerogel silicas with surface areas of 750, 380 and monosilicic acid at equilibrium. Equation 11 is in 250 sq.m./g.l0 were 10, 50 and 140 minutes, respecthe same form as those obtained by assuming that a tively. Quartz with a surface area of less than one diffusion step is rate determining's sq.m./g. does not go into solution with a comparable rate. This lack of correlation has been Experimental Materials.'O-In this study the rates of solution of stand- attributed to the differences in structures of the ard luminescent (S.L.) and special bulky (Sp.B.) silicas were silicasI4 and to the difficulty of measuring available surface by nitrogen adsorption measurements. lo examined. Equipment.1l-A Bausch and Lomb Model 20 SpectromeFrom a comparison of the rate constants as a ter was used to make transmittance measurements for the function of t e m p e r a t ~ r e ' according ~ to the Ardetermination of monosilicic acid in solution.* The solutions were equilibrated in a constant temperature (f0.01') bath. rhenius equation, the energy of activation was estiReactions were conducted in a three-necked flask. The mated t o be 18 f 0.2 kcal./mole for the solution of st,irrer was inserted in the center neck and a thermometer special bulky silica in alkaline solutions. was placed in another neck. From the third neck samples Solution in Water.-Holt and King5 have sumcould be removed periodically. 1 Procedures.-The silicas were brought to 500 ml. total marized the experimental results relating t o the volume and poured into the reaction flask. Stirring was rates of solution of silicas in water. The approach described in the theoretical section of the present (18) For discussion sea H. S. Taylor, "A Treatise on Physical Chempaper will be used t o interpret some of the reistry." edited by H. S. Taylor, Vol. 11, D. Van Nostrand Co., New ported results and those obtained in this study. York. N . Y.,1930, p. 1032.
KINETICS FOR SOLUTION OF SILICA IN AQUEOUS SOLUTIONS
Oct., 1958
1197
First, a discussion of the solution of quartz in the surface area available t.o the solution is dependwater will be given. It must be pointed out that ent upon flocculation as well as the amount of when quartz is ground a layer of amorphous silica silica present. It is also interesting to note that the is formed on the surface. Also as the quartz is equilibrium solubility varies as a function of the ground to smaller particles this layer becomes more amount of solid silica present. This indicates that amorphous.20 Therefore in order to study the rate the S. L. silica is not homogeneous and possesses a of solution or solubility of quartz it is necessary to surface layer of higher energy than the matrix as remove the amorphous layer. Otherwise the data was found in the case of quartz. obtained in such a study pertain to amorphous silica. Actually the solubility of quartz is ex1.0 tremely small at 2503and the rate of solution is very slow because of the relatively small surface areas of quartz. Therefore it would be somewhat d i 6 0.8 cult to measure the rate of solution of quartz below approximately 150". The data reported by Lucas and DolanBon the 0.6 dissolution in water of ground quartz can be treated as the rate a t which amorphous silica goes 0, into solution. This is illustrated by the 0.0105% G I SiOz (g. SiO2/1O0 ml. water) solubility at 37" of the 0.5-3 p fraction which is approximately the solu- 2 0.4 bility of colloidal silicas (0.015% at 25"; 0.0230% 3 at 50°).'-3 It has been observed by King and Mc- 4 George2I and Lucas and Dolan that a certain minimum amount of ground quartz is required to saturate the solution. When less than this minimum is used the solution does not become saturated because the amorphous layer is exhausted. 0.2 I I I I I I I The data for the solution of a 0.5-3 p fraction of 30 60 90 120 150 180 quartz as a function of time reported by Lucas and Time, minutes. Dolan has been tested by equation 11. The reFig. 2.-Rate of solution of S. 1,. silica in water at 50" as a sults are summarized in Table I. function of the per cent. silica suspended.
I
\
'
TABLE I RATEDATAFOR THE SOLUTION OF 0.3-5 p ON QUARTZFROM THE EXPERIMENTAL DATAOF LUCABA N D DOLAN
-
YoSi02
Ce, mg./100 ml.
0.5 1.0 2.0 5.0
1.5 4.5 7.5 10.5
A l o g [(Ce C)/ Ce] / A1 X 104
0.088
.I98 .400 .680
Rate constant ratio
0.5 1.0 2.0 3 4
The rate of solution of S. L. silica as a function of temperature was measured for 0.4% solutions at 40, 50, 60 and 70". The equilibrium concentration (C,) for this per cent. silica at the various temperatures is always less than the saturation concentration (C,) for colloidal silica. This is in agreement with the values reported in Table I for Ce as a function of concentration where all concentrations below 47& show less than the saturation concentration. Log(Ce - C)/Ce os. t plots give straight line relationships for the four curves. An Arrhenius plot of the rate constants us. 1/T yields an activation energy of 17.8 kcal./mole.
In all cases a straight line relationship was found for log(Ce - C)/Ce VS. t as predicted by equation 11. The slope of the lines, column 3 Table I, includes a reaction rate constant and a surface area term. The surface area should be directly proportional to the SiOz present and column 4 indiConclusions cates that this is approximately the case. Appli1. The rate equation for solution in alkaline cation of the equation to the 5-7 p fraction did not media holds very well. fit. the data. The experimental results for the solution of S. L. 2. The rate equation for solution in water holds silica in water at 50" are given in Fig. 2. The plots only if the silica is completely dispersed as with of log (C, - C)/C, vs. time gave straight lines. quartz. Solutions with 0.2, 0.4, 1.0 and 4.0y0 silica showed 3. In alkaline solution a negative surface equilibrium solubilities Ce of 18, 18, 20 and 23 charge prevents flocculation. mg. Si02/100 ml. and the ratio of rate constants ob4. Quartz has an amorphous layer in a free tained from the slopes of the curves were 0.55, energy state between quartz and colloidal silica as 0.80, 1.0 and 1.5, respectively. In this case the rate constant ratios are not pro- shown by solubility data. The solubility of portional to the per cent. silica. Apparently the colloidal silica is 0.01870 at 37" and the amorphous silica is not dispersed on addition to the water and layer of a 0.5-3 p fraction of ground quartz is 0.011% at 37". (20) P. B. Dempster and P. D. Ritchie, J. A p p l . Chsm., 8 , 153 5. It is necessary to have a minimum amount (1953). of colloidal or quartz silica present to saturate a (21) E. L. King and M. McGeorge, Biochem. J.. 32, 417 (1838).
1198
P. V. POPAT AND N. HACKERMAN
solution with respect to the most amorphous layer. 6. The activation energy for the solution of Sp. B. silica in dilute caustic is 18 kcal./mole and 17.8 kcal./mole for S. L. silica in water. 7. This study shows that it is possible to
Vol. 62
characterize silicas by solubility and kinetic data for solution. Acknowledgment.-Thanks are due the Research Department of the Diamond Alkali Company for their financial support of this work.
CAPACITY OF THE ELECTRICAL DOUBLE LAYER AND ADSORPTION AT POLARIZED PLATINUM ELECTRODES. I. ADSORPTlON OF ANIONS BY PRANJIVAN VELJIPOPAT AND NORMAN HACKERMAN Department of Chemistry, University of Texas, Austin, Texas Received March S, 1968
The differential capacity of the electrical double layer a t polarized platinum electrodes has been investigated as a function of the type and concentration of anions. The method of charging curves, utilizing a square-wave signal was employed. The “hump” in the potential-capacity curve is characteristic of the anion involved and is explained in terms of adsorption or desorption of the anion. The tenacity of adsorption is found to increase with the covalent character of the adsorbed anion as NOa- and F- < SOI-- < C1- < Br- < I-. Evidence is presented to indicate that the adsorbed iodide, bromide and chloride ions are dehydrated before their anodic discharge. Fluoride and nitrate ions do not appear to be dehydrated even on the anodic side of the zero point of charge. A similarity is established between polarized platinum and mercury electrodes and the location of the zero point of charge for platinum is indicated. It is observed that hydrogen over-voltage on platinum is a function of the type of anions present.
Introduction There have been several investigations of the differential capacity of the electrical double layer (e.d.1.) a t polarized platinum electrodes. Ershlerl and Dolin and Ershler2 studied the capacity of smooth platinum electrodes in acidic and alkaline media as a function of the frequency of alternating current in order to determine the slow step in the discharge of hydrogen ions on platinum. Schuldiner3 used capacity data to estimate true surface area of platinum electrodes. Robertson4 investigated the effect of a.c. frequency and HC1 concentration on the capacity of platinum electrodes. Kheifets and Krasikov6 used capacity measurements to study the effect of surface active substances on the hydrogen overvoltage on platinum. A review6 of these studies showed little similarity between the several results. One reason for this may be found in the fact that no two investigators used the same experimental conditions. A recent paper reported7 on the capacity of polarized platinum electrodes in KBr and KI solutions. All of these measurements were made with impedance bridges. This method is the most accurate but it is limited to microelectrodes which, with solid metals, are difficult to prepare in a reproducible manner. Moreover, it is tedious and time-consuming.8 Recently, Brodd and Hackermang reported a variation of the charging curve method. This is (1) B. Ershler, Acta Physicochim. U.R.S.S., 7 , 327 (1937). (2) P. Dolin and B. Ershler, ibid., 13, 747 (1940). (3) 5. Schuldiner, J . Electrochem. Soc., 99, 4 8 8 (1952). (4) W. D. Robertson. ibid., 100, 194 (1953). (5) V. L. Kheifets and B. S. Krasikov, Doklady Akad. Nauk S.S.S.R., 94, 101 (1954). ( 6 ) D. C . Grahame, Ann. Reu. Phys. Chem., 6 , 337 (1955). (7) J. N. Sariuoosakis and M . J. Prager, J . EZectrochem. Soc., 104,454 (1957). (8) B. Breyer, Revs. Puw and A p p . Chem., 6 , 249 (1956). (9) R . J. Brodd and N. Hackerman, J . EZeclrochsm. Soc., 104, 704 (1957).
suitable for projected surface areas of about 2 and is relatively fast. The method utilizes a square-wave signal of known frequency to obtain time potential traces on a cathode ray oscilloscope. McMullen and Hackermanlo modified the method and obtained reproducible results with mercury and with several solid metal electrodes. The results with mercury were in good agreement with those obtained by the impedance bridge method. These authors showed that for sufficiently small charging times (ie., when the change in the potential of the test electrode is a linear function of time), the capacity of a polarized electrode can be obtained from the relationship
where E , is the potential of the test electrode, t is the time, Ei is the magnitude of the input squarewave signal, R, is a standard resistance through which the square-wave signal passes before entering the test electrode and C is the differential capacity of the electrode. This method is currently being used here for studies of the electrical double layer a t platinum and other solid metal electrodes. The problem of immediate interest was to determine whether there is a similarity between polarized platiiium and polarized mercury electrodes. Robertson4 and Sarmousakis and Prager’ found no similarity between the two electrodes. Another important aspect of the work was to try t o locate the zero point of charge (z.P.c.) for platinum by this method. Other problems of interest concerning the electrical double layer in general have been discussed by BreyerS8 One of these is whether ions in the layer are. solvated. Anions in the layer are believed to be much less solvated than cations and it is assumed that, with the possible exception of (10) J . J. MoMulIen and N. Hackerman (to be published).
