E. MATIJEVIC:,S. KRATOHVIL, AND J. STICKELS
564 arising from the C-H bend coordinate in monosubstituted and para-disubstituted benzenes should be less since the 1- and 4-hydrogen atoms which contribute to the normal mode are replaced. ?
No C-C stretch contribution is expected to this band for substituents of Cpv or higher symmetry and so a constant value of A1j2of less than 20.4 units is expected for monosubstituted benzenes and a constant but lower
still value is expected for para-disubstituted benzenes. These predictions seem substantiated by the results. Unfortunately, it was not possible to obtain corresponding values for asymmetric substituents because substituent vibration interfered in the available compounds. SpectroscopicAspects. The results above clearly provide valuable support for the normal coordinate analyses made for chloro and deuteriobenzenes being valid for other substituents. We intend to measure the intensities of a series of deuterated mono- and disubstituted benzenes to further this aspect of the work. Acknowledgment. R. D. Topsom is grateful for a grant from the Australian Research Grants Committee.
Counterion Complexing and Sol Stability. I. Coagulation Effects of Aluminum Salts in the Presence of Fluoride Ions1 by Egon MatijeviC, Stanka Kratohvil, and Jon Stickels Institute of Colloid and Surface Science and Department of Chemistry, Clarkson College of Technology, Potsdam, New York 13676 (Received July 2 2 , 1 Q 6 8 )
The coagulation and the reversal of charge of silver halide sols by aluminum ions in the presence of fluoride ions have been studied as a function of pH. Using known stability constants, the composition of the electrolyte environment was calculated. This included all aluminum fluoride complexes as well as the aluminuin hydrolyzed species. With the increasing addition of fluoride ions larger amounts of aluminum perchlorate are required to coagulate the sol. The calculations show that at pH 4 the hydrolyzed aluminum ion is the coagulant. The complexing of aluminum ions by fluoride produces lower charged species which have no effect upon the stability over the critical coagulation concentration range of the aluminum salt. The charge of the sols can be reversed by the hydrolyzed aluminum ions, but not by the fluoride complexes.
Introduction The effects of complexing of counterions upon the stability of lyophobic colloids have received considerable attention in recent years. The interactions of hydrolyzed metal ions with lyophobic sol particles have been particularly thoroughly investigated. Owing to hydrolysis, the charge of the counterion is most frequently changed causing great variations in the coagulation concentrations. In addition, the hydrolyzed species adsorb appreciably more strongly than the corresponding unhydrolyzed ions. Depending on the conditions, this adsorption may either enhance the coagulation or restabilize the sol, due to charge reversal.2J Much less attention was accorded to complexing with ligands other than hydroxyl. Recently, it was shown that chelation of metal counterions affects the sol stability4 in a most striking way. This study deals with the interactions of aluminum The Journal of Physical Chemistry
salts with silver halide sols in the presence of various amounts of fluoride ions. It was attempted to carefully evaluate the effect of an inorganic complexing ligand (other than hydroxyl) upon the coagulation and reversal of charge ability of a metal counterion. The aluminum fluoride system was chosen for theoretical and practical reasons. The counterion behavior of aluminum and of its hydrolyzed species has been extensively studied and it is rather well understood.Sv6 (1) Supported by the Federal Water Pollution Control Administration Grant WP-00815. (2) E. MatijeviE, 9. Kratohvil, and L. J. Stryker, Discussions Faraday Soc., 42, 187 (1966). (3) E. MatijeviB. "Charge Reversal of Lyophobic Colloids" in "Principles and Applications of Water Chemistry," John Wiley and Sons, Inc.,New York, N, Y., 1967. (4) E. Matijevi6 and N. Kolak, J. Colloid Interface Scl., 24, 441 (1967). ( 5 ) E. Matijevib, K. G. Mathai, R. H. Ottewill, and 14. Kerker, J. Phys. Chem., 6 5 , 826 (1961). (6) E. MatijeviB, G. E. Janauer, and M . Kerker, J. ColloZd SCi., 19, 333 (1964).
565
COUNTERION COMPLEXING AND SOLSTABILITY Also, good thermodynamic data are available for the aluminum fluoride complexes’-10 which make feasible a quantitative analysis of the interactions between the sol particles and the electrolyte environment. One of the practical aspects of this work is related to water chemistry, Many natural waters contain small amounts.of fluorides and a number of communities fluoridize their waters, Since aluminum salts are still the most frequently used coagulants, the interactions of fluoride with aluminum ions may significantly influence the purification procedures and the effectiveness of fluoridation. This is particularly true because of the great stability of aluminum fluoride complexes. Silver halide sols were employed because extensive studies of their stability are available and therefore rz comparison of the coagulation and reversal of charge data by aluminum in the absence of fluoride is possible. In addition fluoride ion alone will have little effect upon sol stability since silver fluoride is a rather soluble salt.
Experimental Section A . Materials. Aluminum perchlorate (K and K Laboratories) was used without further purification. The concentration of the stock solution was determined gravimetrically using the 8-hydroxy-quinoline reagent. To avoid aging effects,6 the necessary dilutions were made frequently, All other chemicals were of the highest commercial purity grade. Solutions were prepared with doubly distilled water from an allPyrex still. Silver bromide and silver iodide sols in statu nascendi served as colloidal systems. In all experiments the M with an concentration of the sols was 1 X M . Aged excess halide concentration of 1.9 X negative silver halide sols, used in some of the electrophoresis experiments, were prepared according to the procedure by Ottewill, et al.lltlz B. Methods. ( a ) Precipitation of Aluminum Fluoride. To determine the conditions which lead to the formation of precipitates when solutions of aluminum and fluoride salts are mixed, the entire solubility diagram was established. This was accomplished by observing the appearance of the first trace of precipitate in a series of systems in which the fluoride (or aluminum) concentration was kept constant while the concentration of aluminum (or fluoride) was gradually changed. The total volume of each system in a series was 10 ml. At first an attempt was made to detect the first appearance of the precipitate by turbidity or light scattering, but this failed to give reliable results. It was found that visual observation of the first trace of precipitate a t the bottom of the test tube, 24 hr after mixing the precipitating components, could be used to reproducibly establish the limiting concentrations a t which the precipitate still occurs. No further changes could be detected after 24 hr. The pH of the systems
was controlled and measured a t various periods of time. The results obtained by using fluoride as the variable component were in very good agreement with data obtained when the concentration of the aluminum salt was varied. ( b ) Coagulation and Reversal of Charge of Silver Halide Sols. Scattering intensities were measured on a series of systems prepared by mixing solutions containing the two precipitation components and other electrolytes as needed. As a rule in one series either the concentration of the aluminum salt was varied and the pH kept constant or vice versa. In the first case constant amounts of silver nitrate and potassium fluoride and varying amounts of aluminum perchlorate were in one series of test tubes while the other series contained potassium bromide and acid (HC101) or base (NaOH) as needed to keep the pH a t a desired value. In the second case the concentrations of aluminum perchlorate were kept constant while the addition of the acid or the base was varied gradually in order to change pH in rather small increments. Usually each test tube contained 5 ml of the solution to give 10 ml after mixing. All reported concentratians refer to this final volume of 10 ml. It was found t h a t identical results were obtained if the reaction components were contained in different volumes, such as 9 ml 1 ml.
+
Table I: Cumulative Formation Constants for Aluminum Fluoride Complexes
Pn
1% Pl log Pz log Pa log 04 log Ps log Pe
c
= [AIFn(8-n)*]/[Al*+][F--J’i
a
b
C
d
6.13 11.15 15.00 17.74 19.37 (19.84)
6.61 11.97 16.03 18.71 20.04
7.01 12.75 17.02 19.72 20.91 20.86
6.32 11.63 15.45 17.60 18.03
a Ionic strength 0.53,ref 7. *Ionic strength 0.07 (calcd), ref Ionic strength zero (calcd), ref 10. Ionic strength 0.1,ref 18.
9.
The rate of coagulation of silver halide sols in statu nascendi was followed by measuring the scattering intensities with an Aminco light scattering photometer. The procedure for the determination of the critical coagulation concentration (ccc) and the critical (7) 0 . Brosset and J. Orring, Svensk Kemisk Tddskr., 55, 101 (1943). (8)W. M. Latimer and W. L. Jolly, J . Amer. Chem. SOC.,75, 1548 (1953). (9) E. L. King and P. K. Gallagher, J . Phys. Chem., 6 3 , 1073 (1959). (10) J. D. Hem, Geological Survey Water-Supply Paper 1827-B, 1968, pp Bl-B33. (11) R . H. Ottewill and M. 5 . R,astogi, Trans. Farraday SOC.,56, 866 (1960). (12) R. W. Horne and R. H . Ottewill, J . Phot. Sei., 6 , 39 (1958). Volume 76,Number 9 March lQ60
E. MATIJEVI~, S. KRATOHVIL, AND J. STICKELS
566
stabilization concentration (csc) was described in detail earlier.13J4 Electrophoretic mobilities were measured in a niicroelectrophoresis cell of the Mattson typelS as described earlierS6 All determinations were made ten minutes after the mixing of the reaction components. A Beckman Model G pH meter with glass electrodes was used to adjust and control the pH. The instrument was calibrated regularly with appropriate buffer solutions.
Computations I n order to interpret the results it was necessary to compute the composition of the electrolyte environment for various experimental values of the ccc and csc of aluminum perchlorate in the presence of different amounts of potassium fluoride as a function of pH. I n the calculations, carried out by means of an IBM 360 digital computer, the existence of all aluminum fluoride complexes AlF,(3-n)+ for n = 1-6, the dissociation of HF, and the hydrolysis of aluminum ion were considered. It was assumed that only one hydrolyzed complex ion exists a t room temperature. Two different but very similar formulations have been suggested for the composition of the hydrolyzed aluminum species :5,6J6 Ala(OH)*04+ and A17(OH)174+, M'hile we believe that the octamer is the more likely species, in calculations in this work the heptamer has been assumed for which the formation constant is available,le log P17,7 = - 48.8. It should be noted that both suggested species are of the same charge (+4) which is essential in the discussion of sol stability. The composition of the various species was computed from the following two equations
+ pl[Al"][F-] + PZ[A~"][F-]~ + P3[Al3+][F-l3 + P,[A1"+I[F-I4 + Ps[A13+][F-15
[Alltot = [Al"]
+ 3&[F-]3[A13+] + 4,&[F-]4[A13+] + 5Ps[F-I6[Al3+]
+ GPs[F-]6[A13+] + [I-I+I[F-I 1/K
(2)
The value for the ionization constant of the hydrofluoric acid K = 6.7 X Table I contains several sets of values18 for the cumulative formation of aluminum fluoride complex constants
Pn = [A1F1L(B-n)+]/[A13+][F-]n where /In = k1.kz. . .Ln,and L, is the complex constant IC,
=
[A1F,(3-n)+]/[AIFn-i(4-n)+][F-]
The values for similar ionic strength as obtained by two different laboratories are in rather good agreement (Table Ia ,d) , Larger differences are observed only The Journal of Physical Chemistry
in the case of PS and P 6 . The value of the last constant is the least reliable. However, it turns out that the concentrations of AIFsz- and AlFe3- were negligible in the systems under investigation. Since it is impractical in the coagulation work to adjust and keep constant the ionic strength, calculations were carried out using formation constants for ionic strengths 0.53 and 0.07. N o significant differences resulted in the computed concentration of various complex species. Therefore only data as calculated using the values for Pn by Brosset and Orring7 will be reported. The Newton-Raphson iteration procedure was used to obtain the roots of the polynomial equations written for [Alltotal and [Fltota1. Equation 1 was used to solve for CAP] and eq 2 was used to solve for [F-1. Since a polynomial equation will have as many roots as the degree of the equation (real or imaginary and possibly degenerate) , a verification procedure was used to see that the most physically logical root was calculated. Initial estimates of the values of [AI3+] and [F-1, which are required for the Newton-Raphson method, were chosen so that the following ranges were M < [F-] < [Fltotal and M < checked: [Al+3] < [Alltotal. In all cases considered in this paper, only one root existed for [Al+3] and [F-] in these ranges of concentration. Finally, recently, considerable effort was made in presenting the composition of solutions containing complex fluorides by means of various graphical plots.lOJ9 While such graphical presentations may serve to give an approximate idea of the solution composition, they are inadequate for such an analysis as is being carried out in this work.
Results Figure 1 represents the solubility diagrams of aluminum fluoride mhen potassium fluoride was mixed with aluminum nitrate and aluminum perchlorate, respectively. The two solubility curves are similar except over the range of the highest aluminum salt concentrations. Solubility data obtained by using a concentration gradient of the aluminum salt keeping the fluoride concentration constant and vice versa gave the same results. The shape of the solubility curves is typical of systems which exhibit complex solubility, I n principle, it is possible to detect the composition of the predominant complex solute species from an analysis of the solubility dia(13) B. Teiak, E. Matijevib, and K. Schulz, J. P h y s . Chem., 55, 1557 (1951). (14) E . Matijevii: and M.Kerker, ibid.. 62, 1271 (1958). (15) 8 . Mattson, ibid., 32, 1532 (1938): 37, 223 (1933). (16) G. Biedermann, Soensk Kemisk Tidskr., 76, 362 (1964). (17) H . H. Broene and T. De Vries, J. Amer. Chem. Soc., 69, 1644 (1947). (18) K . E. Kleiner, Zh. Obshch. Khim., 20, 1747 (1950). (19) G . Goldstein, Anal. Chem., 36, 244 (1964).
COUNTERION COMPLEXING AND
AI(NO&-
KF
SOL STABILITY
567
:
I
AgBr/Br-- AI(CIO&-
I
pH-4,
0.4
25’,
IOmin
KF
I
‘ 1 1
l AgNO,~0.00010 d M-
-LOG. MOLAR CONC. OF AI(C104)a.
Figure 1. Solubility curves of aluminum fluoride a t 25’. The upper curve was obtained by mixing Al(NOa)3 with KF, and the lower curve by mixing A1 (Clod) a with KF. Precipitate is formed below these curves.
grams.20P21 I n order to do so the chemical composition of the solid phase has t o be known. In the case of aluminum fluoride this composition varies depending on the concentrations of the precipitating compon e n t ~ . ~No ~ attempt , ~ ~ was made to analyze the composition of the solid phase in order to detect the soluble complexes. The primary purpose of establishing the solubility diagrams was to ensure that no solid aluminum fluoride precipitates under the conditions of the coagulation experiments, Figure 2 gives a number of curves for a negatively charged silver bromide sol coagulated by aluminum perchlorate in the presence of various amounts of potassium fluoride. High scattering intensity indicates coagulated sols. The ccc is obtained by extrapolating the steep part of the curve to zero scattering intensity. All data are for 10 rnin after mixing the reacting components. This time was found to be critical for silver bromide sols in statu nuscendi.la It is quite apparent that with an increasing amount of fluoride ions the coagulation concentration of the aluminum salt also increases. The arrow indicates the ccc for the same sol using A1(C104)3in the absence of potassium fluoride. All experiments were carried out a t a pH close to 4.0. Similar series
Figure 2. Scattering intensities of a silver bromide sol in statu nascendi coagulated by aluminum perchlorate in the presence of various amounts of potassium fluoride, 10 min after mixing the reacting components. Concentrations: M ; p H -4, KF: AgNOs, 1.0 X 10-4 M ; KBr, 2 X as indicated next to each curve. Wavelength, 546 mfi; temperature, 25’.
Obviously both sols behave quite similarly. Above these lines the sols are coagulated and below the sols are stable. It is to be expected that pH would have a great effect upon the coagulation of silver halide sols by aluminum salts in the presence of fluoride ions. In addition t o fluoride complexes, hydrolysis products are formed at higher pH. Figure 4 gives as an example two curves where the scattering intensity is plotted against the pH. Both curves are for the same sol and identical fluoride concentration. The only difference is that each curve represents systems containing somewhat different but constant concentrations of AI(C10J3. The effect is quite striking. The “log [Al(C104)3]-pH” domain for a silver bromide sol in the presence of a constant concentration of KF (3 X lo4 M ) is given in Figure 5. Open circles are for experiments in which the aluminum perchlorate concentration was kept constant and the pH changed gradually while black circles were obtained when pH was kept constant and the concentra-
Volume Y% Number S March 1969
E. MATIJEVI~, S. KRATOHVIL, AND J. STICKELS
568
-2.01
I
I
I
I
1
I
AgBr/Br-- AI(CI04),-KF
PH 0 2.9-3.0
n 3.8-39 A 4.6-5.2
KF:
6
s
0.00030M
I
25OC, IOmin.
-50
I
4.0
30
6.0
5.0
70
PH.
,I 4.0
3.0
-LOG. M O L A R C O N C . O F Al(ClO&.
Figure 3. The dependence of the ccc of A1 (Clod) a for a silver bromide sol in statu nascendi as a function of the concentration of added K F (solid line) for three different p H ranges: 2.9-30 ( o ) ,3.8-3.9 ( D ) , and 4.6-5.2 ( A ) . The dashed line is for a silver iodide sol in statu nascendi at pH 2.9-3.0.
tion of AI(C104)a varied. The two blackened squares represent points of zero charge as measured electrophoretically. For the same concentration of AI( Clod) 3 the sols are negatively charged below the pH value indicated by the square and positively charged above this value. The latter is due to charge reversal. The sols are coagulated over the range indicated by hatch-
Figure 5. The “log [A1(ClO4)3]-pH” domain for a silver bromide sol in statu nasceltdi in the presence of a constant amount of KE’. Concentrations AgPJOa: 1.0 X M, KBr: 2.0 X 10-8 M , K F : 3.0 X 10-4 M . The coagulation region is indicated by hatching. Open circles give data obtained a t constant pH, and the blackened circles a t constant concentration of A1(CIOn)s. Blackened squares indicate points of zero charge.
ing. Below the shaded region the electrolyte concentration is too low t o affect the sol stability. Above this region the sols are stable due to charge reversal. Finally, Figure 6 gives a series of such domains for various concentrations of KF. The heavy lines indicate the ccc and csc in the absence of fluoride as determined before.6 The dashed line gives the pre-1.1
I
Ag Br/I Br-- AI (ClO41 13 I.
-KF
I
-2.1
0.5
n t
0 u
I
a
OA
>: t tn
AgN03a 0.00010 M
Eo,J-
259 IOmin.
z
KBr
:
KFs 3.0*10-4M AI(C104)sl 4. I O - ~ M
0.0020 M
I
LL 0
-3.1
v
z
8 a a
I
-I
0
I-4.1
w
3
- 5.1 I 3.0 3.0
4.0
PH
5.0
9
Figure 4. Scattering intensities of a silver bromide sol in statu nascendi in the presence of the same concentration and two different concentrations of Al(C104)a of K F (3.0 X (3.0 X lod4M , 0 ; 4.2 X M , 0) as a function of pH. The Journal of Physical Chemistrg
50
6.0
I
PH.
I
OL
4.0
Figure 6. The entire “log [Al(C104)8]-pH” domain for a silver bromide sol in statu nascendi in the presence of various amounts of KF. The heavy solid line gives the ccc and the csc in the absence of KF. Hatched areas represent coagulation regions for various concentrations of KF, as indicated in the diagrams. Dashed line gives the precipitation boundary of Al(0H) 8 in absence of AgBr.
569
COUNTERION COMPLEXING AND SOLSTABILITY cipitation boundary of aluminum hydroxide. Again, the shaded area in each case represents the conditions at which the silver bromide is coagulated.
., ..
Discussion A comparison of the coagulation concentrations (Figure 3) and of the “log [A1(C104)8]-pH’Jdomains (Figure 6) in the absence and the presence of fluoride ions best illustrates the large effects due to counterion complexing. Tlere an attempt will be made to interpret these results in terms of aluminum-fluoride interactions, At pH >4 the hydrolysis of aluminum ions will also be considered. No such analysis of metal ions complexing by anions other than hydroxyl has been applied to stability data heretofore. Table I1 contains the concentrations of all the species for a number of systems corresponding to the ccc of aluminum perchlorate in the presence of various fluoride concentrations for three diflerent pH values. These refer to the conditions along the straight line in Figure 3. An inspection of Table I1 reveals a very interesting fact, When hydrolysis is negligible (pH 3 and 4) all complex counterions are in concentrations much too low to exhibit any coagulation effect^.^^^^^ The calculations indicate that at pH 3 and 4 the concentration of the unhydrolyxed aluminum ion along the ccc line in Figure 3 is reasonably constant. The variations in values are small if one considers the complexity of the system. More importantly, the average value [Ala+] = 3 X 10-6 ilf is in excellent agreement with the ccc for trivalent counterions as determined for the same silver bromide Specifically, the coagulation concentration for A1 ( NOa)a in the absence of complexing anions is 2.: X It would seem then that the unhydrolyxed aluminum ion is the only effective coagulating species in the presence of fluoride ions a t pH
