3149
J . Phys. Chem. 1991, 95, 3149-3152
Kinetics of Dissoiutlon of Calcium Fluoride Crystals In Sodium Chloride Solutions: I nfluence of Additives Salem M. Hamza* and Samia K. Hamdonat Chemistry Department, Faculty of Science, El- Menofa University, Shebin El- Kom, Egypt (Received: March 5, 1990)
The kinetics of dissolution of calcium fluoride crystals in sodium chloride solutions has been investigated at 25 "C by using a constant composition method in which the undersaturation and ionic strength were maintained constant. Over a range of relative undersaturation, 0.075-0.40, the dissolution reaction appears to be controlled by a surface mechanism. The crystal dissolution rates are markedly inhibited by the addition of inorganic orthophosphate and organic polyphosphonates. The action of additives can be interpreted in terms of a Langmuir-type adsorption isotherm. Direct adsorption experiments have also been made by using ethylenediaminetetramethylenephosphonic acid.
Introduction The alkaline-earth-metal fluorides are of importance in view of their application in many industrial fields as well as their involvement in a number of biological and environmental precipitation processes.'-3 The addition of fluoride ion to drinking water is now almost universal, yet there is still considerable uncertainty about the manner in which it reduces the incidence of dental caries. These residual fluoride wastes may result in solutions supersaturated with respect to alkaline-earth-metal fluorides which may Later precipitate and dissolve in the fluctuating concentration conditions. The factors that govern the mechanism of precipitation and dissolution of these fluoride salts are therefore of considerable interest, especially the influence of foreign cations and anions which may exert a marked effect on the rates of crystallization and dissolution. In the present work, the kinetics of dissolution of calcium fluoride crystals has been investigated by the constant composition method? in which the rate of reaction was measured for extended periods under conditions of constant ionic strength and solution composition. The influence of a number of polyphosphonates upon the rate of dissolution has also been investigated.
filter. The filtrate was analyzed for calcium ion by atomic absorption spectroscopy in order to verify the constancy of the concentrations (fl.O%). The solid phases collected during the experiment were investigated by X-ray diffraction and by scanning electron microscopy. Experiments made in the presence of phosphonates were also analyzed for this anion by using a UVcatalyzed phosphate to orthophosphate oxidation method (persulfate/UV oxidation method, Hach Co.). Direct measurements of the adsorption of phosphonate ions on calcium fluoride crystals were made by adding 100 mg of the seed crystals to 50 mL of saturated calcium fluoride solution containing various E N T M P concentrations. The crystals were exposed to the solutions for at least 1 h. The phosphonate concentrations were then determined as described above.
Results and Discussion The concentrations of free-ion species in the solutions were calculated from mass-balance and electroneutrality expressions as described previou~ly,~ using the thermodynamic equilibrium constants, K, for the various associated species: H+ + F * H F
Experimental Section Materials. Undersaturated solutions of calcium fluoride were prepared in triply distilled deionized water, using reagent grade (J.T. Baker) chemicals. Solutions were filtered (0.22 pm, Millipore filters) before use; calcium ion concentrations were determined by passing aliquots through a cation-exchange resin (Dowex 50) in the hydrogen form and titrating the eluted acid with standardized potassium hydroxide. Seed crystals of the calcium fluoride were prepared by precipitation from a mixed solution of sodium fluoride and calcium nitrate at 25 "C.The seeds were washed with saturated solutions of the calcium fluoride and allowed to age for at least 1 month at 25 "C.At this point the specific surface area (SSA) reached a constant value (1.72 f 0.1 m2 g-l). Methods. Dissolution experiments were made at 25 f 0.1 "C in a double-walled reaction cell of 300 mL capacity fitted with a Teflon lid. Nitrogen gas was first bubbled into a solution of the electrolyte at the temperature of the reaction for saturation with water vapor, and then into the reaction vessel throughout the duration of the experiment. At the beginning of each experiment the fluoride electrode was standardized by adding aliquots of sodium fluoride solution in the cell. Subsequently, undersaturated solutions of desired concentrations were prepared by slow addition of calcium nitrate to sodium fluoride solutions. The ionic strength was maintained constant (0.5 f 0.01 mol dm") during the dissolution experiments by the addition of sodium chloride solution. Aliquots of reaction mixture were withdrawn at regular time intervals and filtered through a 0.22-pm Millipore 'National Institute of Oceanography and Fisheries, Alexandria, Egypt.
(1.51 X IO3,ref 6)
HF + F * HF2Ca2+ Ca2+
(3.39, ref 6)
+ F * CaF+
(10.46, ref 7)
+ OH- + CaOH+
H+ + OH-
F=
H20
(23.44, ref 8)
( 1 .OO X 1OI4, ref 9)
The numbers in parentheses are values of A ? a t 25 "C. Activity coefficients were calculated from the extended form of the Debye-Huckel equation proposed by Davies.Io The degree of relative undersaturation, u, for calcium fluoride solutions may be defined by eq 1 where [Ca2+], [ F ] and [Caz+lch u
= ( [Ca2+Io[FIo2) 1/3 - ( [Ca2+][F]2,
[Ca2+lO[F l o 2 )' I 3 (1) ~
~~
(1) Hamza, S. M.; Nancollas, G. H. J . Chem. SOC.,Faraday Trans. I 1985,81. 1833. (2) Shyu, L. S.; Nancollas, G. H. Croat. Chem. Acra 1980, 53, 281. (3) Barone, J. P.; Sverjcek, D.; Nancollas. G.H. J . Cryst. Growth 1983,
62, 27.
(4) Koutsoukos, P.; Amjad, Z.; Tomson, M. B.;Nancollas, G.H. J . Am. Chem. Soc. 1980, 102, 1553. (5) Nancollas, G. H. Interacrions in Electrolyte Solurions; Elsevier: Amsterdam, 1966. (6) Ellis, A. J. J . Chem. SOC.1963, 4300. (7) Connick, R. E.; Tsae, M. S.J . Am. Chem. SOC.1956, 76, 5311. (8) Gimblett, F. G. R.; Monk, C. B. Tram. Faraday Soc. 1954,50,965. (9) Ackermann, T. Z . Elekrrochem. 1958.62, 411. (IO) Davies, C. W. Ion Association; Butterworth: London, 1962.
0022-3654191 12095-3149%02.50/0 0 199 1 American Chemical Society
3150 The Journal of Physical Chemistry, Vol. 95, No. 8,1991 TABLE I: Dissolution of Calcium Fluoride Crvstab at 25 T ~ I J0-3 rate/lOd mol
expt no. IO I1
12 13 14 15 16 17
18 19b 20 21 22 23 24 25 26 27 28b 29 34b 356
mol dm-3 0.129 0.129 0.129 0.129 0.129 0.129 0.129 0.1 16 0.147 0.1 16 0.154 0.164 0.173 0.173 0.173 0.173 0.173 0.173 0.164 0.178 0.173 0.154
IOU 3.3 3.3 3.3 3.3 3.3 3.3 3.3 4.0 2.4 4.0 2.0 1.5 1.0 1.0 1.0 1.0 1.0
1.0
1.5 0.75 1.0
2.0
seed/mg 12.5 14 16 18 20 22 24 16 16 16 16 16 8.2 IO 12 14 16 18.5 16 16 16 16
Hamza and Hamdona
'I
mi& m-2
3.61 3.72 3.88 3.82 3.59 3.67 3.68 4.39 2.71 2.41 1.47 0.80 0.32 0.39 0.37 0.42 0.41 0.43 0.81 0.22 0.42 1.48
" T c l : T ~= 1:2, ionic strength = 0.5 mol/dm3 (NaCI) bStirring speed 200 rpm, with 300 rpm for experiments 19, 28, 34, and 35.
-tog
e X1Q
Figure 2. Plots of - log R against - log u for the dissolution of calcium
fluoride.
TABLE 11: Effect of Phosphate and Polyphospbonateson the Rate of Dissolution of Calcium Fluoride Crystals" expt Tc,/ I 0-' additives/lO-' rate/lOd mol % no. mol dm-' IOU mol dm-' min-l m-2 inhibition
20 90 91 92 93 94 95 96 97 98 99 100 101
102 108 109 110 Ill
112
0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154 0.154
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
KHZP04 IO KH2PO420 KH2P04 40 KH2PO4 50 KH2PO4 70 KHZPO, 100 HEDP IO HEDP 20 HEDP 30 HEDP 50 HEDP60 HEDP80 HEDP 100 ENTMP IO ENTMP 20 ENTMP40 ENTMP 70 ENTMP 100
1.47 1.097 0.887 0.641 0.562 0.470 0.361 0.861 0.626 0.493 0.399 0.322 0.261 0.203 0.667 0.405 0.255 0.192 0.121
25.37 39.66 56.39 61.18 68.03 75.44 41.43 57.41 66.46 72.86 79.00 82.24 82.19 54.63 72.45 82.65 86.94 91.77
Tca:TF= 1:2, [NaCI] = 0.5 mol dm-', 16 mg seed, and at 25 O C .
2o
40
min.
60
80
Figure 1. Plots of amount of calcium fluoride dissolved against time: experiment 17 (0),12 (O), 18 ( O ) , 20 (A),21 (A),26 (bsd), and 29 (X).
[TIoare the concentrations of free calcium and fluoride ions at and at equilibrium, respectively, at the ionic strength of the experiments (0.5 mol dm" in the present work). The rate of dissolution, R, can be expressed in terms of the relative undersaturation by eq 2 in which m is the number of moles rate = R = dm/dt = ksdl (2)
t
dissolved at time t , k a rate constant, s a function of the initial seed surface area, and n the apparent order of the reaction. The results of the dissolution experiments are summarized in Table I, in which T,, and TF are the molar concentrations of calcium and fluoride, respectively. Typical plots of the amount of calcium fluoride dissolved, calculated from the titrant addition, as a function of time are shown in Figure 1. Assuming, as a first
approximation, simple spherical or cubic particles, corrections were made for changes in surface area during the dissolution reactions by introducing a factor ( W ~ / W , ) ~where / ~ ) , wi and w, are masses of solid phase present initially at time t , respectively. Since the extent of the dissolution reaction was very small (less than 5% of the total surface area of the seed crystals), changes in crystal surface area accompanying dissolution could be ignored. During the reactions, the crystals maintained their cubic morphology, as observed in the scanning electron microscope. It can be seen in Table I that the rates of dissolution were proportional to the mass of seed crystals used to initiate the reactions, and a plot of the rate of dissolution according to eq 2, shown in Figure 2, confirms that the reaction rates follow a parabolic rate law with (n N 2). The suggestion of a predominantly surface-controlled process over a range of relative undersaturation may also be supported by the observed independence of the experimental rate of dissolution of changes in fluid dynamics, as shown in Table I (compare experiments 26 and 34, 20 and 35). However, this evidence may be inconclusive for such small particles for which changes in stirring rate may have little influence on the fluid shear forces at the crystal surfaces. The particles will tend to move with the fluid flow. The precipitation rates of divalent metal ion salts in are greatly inhibited by added substances. Dissolution experiments ( 1 1) Nielson, A. E.; Christoffersen, J. In Biological Mineralization and Demineralization; Nancollas, G. H.,Ed.; Springer-Verlag: Berlin, 1982. (12) White, D. J.; Nancollas, G. H.J . Crysr. Growth 1982, 57, 267. (13) Hamza, S. M. Presented at The Eighth National Conference on Crystal Growth and Materials (CCCG-I), Guilin, China, November 1-6,
1988. (14) Nancollas, G. H. Adu. Colloid Interface Sei. 1979, 10, 215. (15) Collins, F. C.; Leineweber, J. P. J . Phys. Chem. 1956.60, 389. (16) Christoffersen, J.; Christoffersen, M.R.; Christensen, S. B.; Nancollas, G. H.J . Cryst. Growth 1983, 62, 254.
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3151
Dissolution of CaF2 in NaCl Solutions
1.5
I
4
I\\ \
i
A
Iy
E
2
20
60
100
12bird-' L mol-' Figure 4. Plots of Ro (Ro - RJ-' against [additive]-I; KH,PO,(O), HEDP (A),and ENTMP (0).
I 20
40
60
80
100
120 c
lo'
[Additive]
mol
e- 2
'P
1-l
Figure 3. Plots of rate of dissolution against [additive] at ( u = 0.2): KH2P04(0),HEDP (A),and ENTMP (A).
in the presence of orthophosphate as KH2P04, hydroxyethylidene- l ,I-diphosphonic acid, HEDP, and ethylenediaminetetramethylenephosphonic acid, ENTMP, summarized in Table I1 show that concentrations as low as IOd mol dm-3 for each additive reduced the dissolution rates by at least 25.4,41.4, and 56.6% compared to that in pure solution at the same relative undersaturation for the presence of KH2P04, HEDP, and ENTMP, respectively. The rate constants are plotted as a function of additives concentration in Figure 3. It can be seen that the order of the degree of inhibition is KH2P04< HEDP < ENTMP at the relative undersaturation (a = 0.2). As the concentration of additive molecules increases, the active dissolution sites on the crystal surfaces are blocked through adsorption and the rate of crystal dissolution decreases. Phosphonate concentrations of IO7 mol dm-3 have been shown to reduce the rate of dissolution of strontium fluoride by a much as 70%.' In contrast, magnesium fluoride dissolution is inhibited to a much lesser degree and concentrations of phosphate of lod mol dm-3 have been shown to reduce the rate by as much as 50%.17 In spite of the worldwide application of additives as growth and dissolution inhibitors, their mechanisms of inhibition are still largely unknown. Dissolution inhibitors are able to retard or to block the dissolution process even if added in trace amounts. Their effectiveness can therefore only be explained either by complexation of the inhibitor, usually a chelating of or sequestering agent, with the lattice cation, or by adsorption of the molecules at active sites on the crystal surfaces. The latter effect may be interpreted in terms of a Langmuir adsorption isotherm.'* This requires a linear relationship between the inverse of the relative reduction in rate, Ro/(Ro- R i )and the reciprocal of the inhibitor concentration. The adsorption affinity constants, given by the inverse slopes of the lines in Figure 4, are 2.5 X lo5 dm3 mol-' for added ENTMP. It can be seen that the inhibition of dissolution is considerably greater in the presence of phosphonate, although E N T M P markedly reduces the rate of dissolution of calcium fluoride. Experiments have also been done in the presence of E N T M P at different relative undersaturations in order to investigate the (17) Hamza, S.M.; Nancollas, G. H. Lungmuir 1985, I , 573. ( 18) Koutsoukos, P.; Amjad. Z.; Nancollas, G. H. J. Colloid Interface Sci. 1981, 83, 599.
I
d Y
! a 1
4b
20
104
60
Bo
.:B"TY'L mol-'
1w
Figure 5. Plots of Ro (Ro- p)-'against [ENTMPI-I at different relative undersaturations: u = 0.4 (O), 0.2 (0),and 0.1 (A). TABLE 111: Effect of the Presence of ENTMP on the Dissolution of Calcium Fluoride Crystals at Different Relative Undersaturations expt Tca/ 1O-' additives/ lo-' rate/ 10" I no. mol dm-' 10u mol dm-' min-l m-* inhibition
26 103 104 105 106 107 20 108 109 110
117
0.173 0.173 0.173 0.173 0.173 0.173 0.154 0.154 0.154 0.154 0.154 0.154 0.116 0.116 0.116 0.116 0.116 0.116
1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.0 2.0 4.0 4.0 4.0 4.0 4.0 4.0
118
0.116
4.0
111 112 17
113 114
115
116
1.0 1.0 1.0
IO 20 40 60 80 10 20 40 70 100 IO 20 40
50 80 100
0.4 10 0.135 0.085 0.064 0.052 0.030 1.470 0.667 0.405 0.255 0.192 0.121 4.390 2.420 1.729 1.018 0.920 0.640 0.580
67.07 79.27 84.39 87.32 92.68 54.63 72.45 82.65 86.94 91.77 44.87 60.62 76.81 79.04 85.42 86.79
influence of the dissolution driving force upon the degree of inhibition. Table 111 shows that the rate of dissolution of calcium fluoride decreases with the progressive addition of E N T M P to the medium at all the levels of relative undersaturation studied. It can be seen from Figure 5 that the degree of inhibition by ENTMP increased with decreased driving force for the dissolution reaction. The values of the adsorption affinity constants are 4.2 X IO', 5.5 X lo', and 6.6 X IO' dm3 mol-' at relative undersat-
J . Phys. Chem. 1991, 95. 3152-3158
8 ''
6
24
io ,~NTMPJ
32 mol
c1
Figure 6. Adsorption of ENTMP on calcium fluoride crystals at equilibrium. Plots of r against [ENTMP]. uration g = 0.4, 0.2, and 0.1 respectively. These values reflect the high adsorption affinity at low relative undersaturation in the presence of ENTMP. A similar dependence of the degree of inhibition with change in driving force has been observed for the influence of phosphonate on the dissolution rate of magnesium fluoride" and barium fluoride19 in aqueous solution. As noted
for the crystallization of gypsum by Van Rosmalen and coworkers,m the effectiveness of the HEDP as an inhibitor depends on the degree of supersaturation. In order to investigate the adsorption of phosphonate on the calcium fluoride crystals surface, adsorption equilibrium experiments were made for E N T M P on calcium fluoride crystals at u = 0. A typical adsorption isotherm is plotted in Figure 6. Assuming that the area occupied by an ENTMP molecule is 50 X m2, the fraction of the solid surface covered by adsorption molecules is only 6% at the plateau in Figure 6. At this ENTMP concentration, the dissolution rate is reduced by more than 92%. Adsorption affinity constant at equilibrium 5.2 X lo5dm3 mol-' is in satisfactory agreement with the kinetic adsorption affinity constants los dm3 mol-'. The dissolution rate of magnesium fluoride was reduced by more than 80% when only 9% of the crystal surface was covered by HEDP molecule^.^' Moreover, the rate of crystallization may be reduced virtually to zero when only 5-7% of the crystal surface was covered by adsorbed inhibitor moIecules.2',22 Registry No. HEDP,2809-21-4; ENTMP, 1429-50-1; CaF,, 778915-5; NaCI, 7647-14-5; KH2P04, 7718-77-0. (19) Hamza, S . M.; El-Hamolly,S . J. Chem. Soc.,Furuduy Trum. I 1989, 85, 3725.
(20) Weijinen, M. P. C.; Marchee, W. G. J.; Van Rosmalen, G. M. Desulinution 1983, 43, 8 l . (21) Leung, W. H.; Nancollas, G. H. J . Cryst. Growth 1978, 44, 163. (22) Gill, J. S.; Nancollas, G. H. Corrosion 1981, 37, 120.
Ion Recombination Rates in Rare-Gas Cation-Halide Anion Systems. 2. KrF" and XeCl" Stephen P. Mezyk,*" Ronald Cooper, and John Shenvellt Department of Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia (Received: May I, 1989; In Final Form: September 12, 1990) The emission spectroscopy/pulse radiolysis method of determining three-body ionic recombination rate constants in raregas-halogen source gas mixtures has been extended to systems where the emission is produced by both ionic and nonionic pathways. This has enabled recombination coefficient measurements to be done over a large pressure range for irradiated Kr/SF, and Xe/CFC13 gas mixtures. The rate constants measured for both these systems show the typical pressure dependence of an increase to a maximum value of -2.5 X I O l 5 M-l s-l (-4 X IOd cm3 d),before the onset of the diffusion-controlled reaction. These values have been compared to the predictions of the Langevin-Harper diffusion-controlledand the Bates termolecular recombination models. The large discrepancies between theory and experiment have shown that other recombination processes dominate the ionic recombination.
Introduction
R+
The electron pulse radiolysis work'-' done on the rare-gashalogen source gas (R/AX) mixtures has shown that under suitable experimental conditions, the general mechanism for exciplex formation is
e-(s) + M e-(,,,)
R* + AX RX*
-
R
---
e-(th)
+ AX
-
+A
-
R*, R+,e-(s)
initiation
hot electron thermalization (M = R or AX) AX-/X-
thermal electron capture
direct reaction of rare-gas excited states
Rz+
0022-3654/91/2095-3 152$02.50/0
- -+
Rz+ R
cation dimerization
+ AX-/X- (+M) RX* + products three-body ionic recombination RX* R + X + hv excimer fluorescence
-
(5) (6)
(7)
In a previous investigation* the techniques of pulse radiolysis and emission spectroscopy were used to determine the reaction 6 rate constants for irradiated Xe/SF, gas mixtures. This system was chosen for initial study as the XeF* exciplex was formed only (1) Cooper, R.; Grieser, F.: Sauer Jr., M. C. J . Phys. Chem. 1977, 81, 1889. (2) Maeda, M.;Nishirarumizu, T.; Miyazoe, Y . Jpn. J. Appl. Phys. 1979, 18, 439. (3) Grieser, F.; Shimamori, H. J. Phys. Chem. 1980, 84, 247. (4) Grieser, F. Ph.D. Thesis, University of Melbourne, 1976. ( 5 ) Cooper, R.; Grieser, F.; Sauer Jr., M. C. J. Phys. Chem. 1976, 80, 2138. - ~ .
'Present address: Department of Chemistry and Biochemistry,University of Notre Dame, Notre Dame, IN 46556. Author to whom correspondence should be addressed. !Present address: Radian Corp., P.O.Box 201088, Austin, TX 78721.
+ 2R
.
(6) Cooper, R.; Denison, L. S.; Zeglinski, P.; Roy, C. R.: Gillis, H. J . Appl. Phys. 1983,54, 3053. (7) Cooper, R.; Mezyk, S. P.;Armstrong, D. A. Radial. Phys. Chem. 1984, 24, 545. (8) Mezyk, S. P.; Cooper, R.; Sherwell, J. J . Phys. Chem. 1989, 93,8187.
0 199 1 American Chemical Society
