Langmuir 1985, 1, 573-576 the photochemical properties of RuII that is adsorbed at the clay water interface or between the layers of the clay. Furthermore, the quenching of excited RuII with coadsorbed materials tends to indicate that adsorption is not a homogeneous event and that adsorption sites occur in
573
patches or in zones on the clay surface. Registry No. Cu, 7440-50-8;laponite, 53320-86-8;hectorite, 12173-47-6;montmorillonite, 1318-93-0;tris(2,2'-bipyridine)ruthenium(II),63338-38-5;dimethylaniline, 121-69-7;nitrobenzene, 98-95-3.
Kinetics of Dissolution of Magnesium Fluoride in Aqueous Solution S. M. Hamzat and G. H. Nancollas* Chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214 Received March 11, 1985. I n Final Form: June 4, 1985 The kinetics of dissolution of magnesium fluoride seed crystals has been investigated in aqueous solution at 25 O C by a constant composition method in which the undersaturation and ionic strength were maintained constant. Over a range of relative undersaturation, 0.25-0.8, the dissolution reaction appears to be controlled by a surface polynucleation process which, in contrast to a bulk diffusion reaction, is markedly inhibited by the presence of additives. The influence of a number of polyphosphonates on the rate of reaction has been investigated. The reduction in dissolution rate can be interpreted in terms of a Langmuir-type adsorption isotherm. Direct adsorption experiments have also been made by using hydroxyethylidene1,l-diphosphonic acid.
Introduction The alkaline-earth fluorides are of importance in view of their application in many industrial fields.lJ The crystallization and dissolution reactions are of concern since fluoride is introduced into the environment as a natural impurity in ores used to produce phosphoric acid. These residual fluoride wastes may result in solutions supersaturated with respect to alkaline-earth fluorides which may later precipitate and dissolve in the fluctuating concentration conditions. The study of the kinetics of crystal growth of magnesium fluoride under conditions in which the supersaturation was maintained constant has suggested a surface-controlled spiral growth process at low supersaturation and a predominating polynuclear mechanism as the concentration is i n ~ r e a s e d . In ~ contrast, the dissolution of a number of sparingly soluble hydrated salts has been shown to be controlled by the diffusion of lattice ions from the crystal surface into the bulk solution.* For anhydrous salts, however, the reaction may be controlled by processes taking place a t the surface of the crystals rather than by a transport m e ~ h a n i s m . In ~ ~these ~ cases, the rate of reaction is considerably smaller than that calculated on the basis of diffusion, following Fick's Law, of lattice ions away from the surface and for which the linear rate of dissolution will be inversely proportional to the crystal radius.' For surface-controlled dissolution, the rate will be independent of the size of the crystals and of the fluid dynamics. Moreover, the concentration of electrolyte near the crystal surface will be the same as that in the bulk solution. In the present work, the kinetics of dissolution of magnesium fluoride has been investigated by the constant composition method>g in which the rate of reaction was measured for extended periods under conditions of constant ionic strength and solution composition. The influence of hydroxyethylidene-1,l-diphosphonic acid (HEDP) a n d ethylenediaminetetrakis(methy1enet On leave from Menoufia University, Egypt.
0743-7463/85/2401-0573$01.50/0
phosphonic acid) (ENTMP) upon the rate of dissolution has also been investigated.
Experimental Section Undersaturated solutions of magnesium fluoride were prepared using both Ultrapure (Alfa Chemicals) and Reagent Grade (J.T. Baker) chemicals with triply distilled deionized water. Solutions were filtered (0.22 pm, Millipore filters) before use. Magnesium 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 sodium hydroxide. Magnesium fluoride seed crystals were prepared by adding 100 mL of potassium fluoride (0.48mol L-l) to 100 mL of magnetically stirred magnesium nitrate (0.24 mol L-l), at 25 "C. The crystals were washed by decantation until free from nitrate ion and stored as a suspension in polyethylene bottles. Specific surface areas were measured by nitrogen BET adsorption (30/70% nitrogenlhelium mixture, Quantasorb 11, Quantachrome Corporation). The crystals were characterized as magnesium fluoride by X-ray powder diffraction (copper K a radiation, Phillips XRG 3000 Diffractometer). Particle sizes, measured with an Electrozone Celoscope particle counter (Particle Data Inc.), showed a mean size of 2.3 f 1.8pm for 83% of the particles. Fluoride solutions were prepared in polyethylene bottles and the concentrations were determined using a fluoride ion selective electrode (Orion Model 94-09) with silver/silver chloride reference electrode. The latter consisted of a thermal electrolytic silver/silver chloride probe immersed in 4 mol L-' potassium chloride solution saturated with silver chloride in a thermostated limb of the reference electrode (1) Shyu, L. S.; Nancollas, G. H. Croat. Chem. Acta 1981, 52, 281. (2) Barone, J. P.; Sverjcek, D.; Nancollas, G. H. J . Cryst. Growth 1983, 62, 27. (3) Yoshikawa, Y.; Nancollas, G. H. J. Cryst. Growth 1983,64, 222. (4) Liu, S. T.; Nancollas, G. H. J.Znorg. Nucl. Chem. 1971,33, 2311. (5) Little, D. M. S.; Nancollas, G. H. Trans. Faraday SOC.1970, 66, 3103.
(6) Christoffersen, J.; Christoffersen, M. R.; Kjaergaard, N. J. Cryst. Growth 1978, 43, 501. (7) Levich, V. G. "Physicochemical Hydrodynamics"; Prentice-Hall: Englewood Cliffs, NJ, 1962. (8) Koutsoukos, P.; Amjad, Z.; Tomson, M. B.; Nancollas, G. H. J. Am. Chem. SOC.1980,102, 1553. (9) White, D. J.; Nancollas, G. H. J. Cryst. Growth 1982, 57, 267.
0 1985 American Chemical Society
574 Langmuir, Vol. 1, No. 5, 1985
Hamza and Nancollas 1
I
Table I. Dissolution of Magnesium Fluoride at 25 "C, Tw./Ta = 0.5, Ionic Strength = 0.15 mol L-' (KNOR) ratejlo-' mol min-'
~ ~ ~ 1 0 - 3
expt no.
mol L-'
u
seed, mg
m-2
144 145" 146 148 147 149 151 154O 190b 191'
1.040 0.832 0.832 0.728 0.634 0.520 1.560 0.634 1.040 1.040
0.50 0.60 0.60 0.65 0.70 0.75 0.25 0.70 0.50 0.50
25 25 25 25 25 25 500 25 25 25
0.63 1.17 1.11 1.59 2.04 3.30 0.04 2.12 1.81 2.86
"Stirring rate 300 rpm. In all other experiments the stirring rate was 200 rpm. *At 35 "C. 'At 40 "C. assembly. This was separated from the cell solution by an intermediate liquid junction constructed of Teflon and containing a solution of ionic strength identical with that of the cell solution. In this way, errors due to variation in liquid junction potential and leakage of reference electrode salt-bridge solution into the cell were eliminated. Dissolution experiments were made in water thermostated double-walled Pyrex glass vessels having Teflon lids and polyethylene liners to prevent fluoride attack on glass surfaces. The cells were maintained at the required temperature by circulating thermostated water through the outer jackets. The cell contents were stirred with a magnetic stirrer and presaturated nitrogen gas was bubbled through the solutions during the experiments to exclude carbon dioxide. In addition, samples were periodically withdrawn and filtered at the reaction temperature through Millipore filters (0.22 pm), prior to solution and solid-phase analyses. Experiments made in the presence of phosphonates were also analyzed for this anion by using a UV-catalyzed phosphonate to orthophosphate oxidation method (Persulfate/W oxidation method, Hach Co.). In the dissolution experiments, magnesium fluoride seed crystals were added to undersaturated solutions of magnesium fluoride prepared by mixing magnesium nitrate and potassium fluoride in the cells and the fluoride ion selective electrode was used to control the addition of titrant solution consisting of 0.15 mol L-' potassium nitrate. This maintained the undersaturation constant duriqg the experiments and the rate of dissolution was calculated from the rate of titrant addition. Direct measurements of the adsorption pf phosphonate ions on magnesium fluoride crystals were made by adding 100 mg of the seed crystals to 50 mL of saturated magnesium fluoride solution containing various HEDP concentrations at known pH values. The crystals were exposed to the solutions for at least 24 h and it was shown, in parallel experiments, that adsorption equilibrium was attained in less than 2 h. The phosphonate concentrations were then determined as described above.
Results and Discussion The concentration of ionic species in the solutions was calculated as described previouslylO by using expressions for mass balance and ion-pair association constants by successive approximation for the ionic strength, I , and by using activity coefficients calculated from the extended form of the PebyeHuckel equation proposed by Davies.l' The relative undersaturation, u, is defined by 0 = (no1/3 - @/3)/no113 (1) in which II is the molar concentration product of magnesium fluoride, [Mg2'][F-l2, in the solutions, and x , the solubility value a t the same ionic strength (0.15 mol L-' in the present work). (IO) Nancollas, G. H. "Interactionsin Electrolyte Solutions"; Elsevier: Amsterdam, 1966. (11) Davies, C. W. 'Ion Association"; Butterworths: London, 1962.
MIN
Figure 1. Plots of moles of magnesium fluoride dissolved against 175 (A); 176 (V);177 (0);180 time. Experiment 149 (0);147 (0); (0).
I 80
'2 3
0 J
1
,20
-40
-60
-LOG U
Figure 2. Plots of -log R against -log u for the dissolution of magnesium fluoride.
Dissolution experimental conditions are summarized in Table I in which TMgand TFare the total molar concentrations of magnesium and fluoride, respectively. Typical time plots of the amount of magnesium fluoride dissolved, calculated from the titrant addition, are shown in Figure 1. The slope of these lines, reflecting the rates of dissolution, are summarized in Table I. 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 (ISI, Model 11). For many sparingly soluble salts, M,Ab, the rate of dissolution, normalized for seed surface area, can be expressed by eq 2,12 in which k is the dissolution rate con-
R = d[M,Ab]/dt = ksu"
(2)
stant, s is proportional to the number of dissolution sites available on the seed crystals, and n is the effective order of reaction, determined from the slopes of typical plots of -log R against -log u such as that shown in Figure 2. Under all experimental conditions of the present work, the value of n was 3.5 f 0.1. From the rate constants at temperatures of 25,35, and 40 O C (Table I), the effective activation energy for the reaction was 86.2 f 2 kJ mol-l. As can be seen in Table I, changes in stirring speed had a negligible effect on the rates of dissolution (experiments 145 and 146; 147 and 154). This evidence, together with the relatively (12) Nancollas, G. H. Adu. Colloid Interface Sci. 1979, 10, 215.
Kinetics of Dissolution of Magnesium Fluoride
Langmuir, Vol. 1, No. 5, 1985 575
Table 11. Dissolution of Magnesium Fluoride, T M ~ I=T ~ 0.5, in the Presence of Phosphonate, Ionic Strength = 0.16 mol L-'(KNO,)
Tw/ expt no. 146 155 156 157 158 159 160 147 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 151 182
mol L-l 0.832 0.832 0.832 0.832 0.832 0.832 0.832 0.634 0.634 0.634 0.634 0.634 0.634 0.634 0.832 0.832 0.832 0.832 0.832 0.832 0.832 0.832 0.634 0.634 0.634 0.634 0.634 0.634 1.560 1.560
inhibitor
HEDP HEDP HEDP HEDP HEDP HEDP HEDP HEDP HEDP HEDP HEDP HEDP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP ENTMP
rate/W inhibitor/ mol min-' lo4 mol L-' m-2 11.1 3.50 4.52 5.00 3.06 10.0 2.56 15.0 2.05 30.0 1.81 40.0 1.50 20.4 5.00 9.40 10.0 6.40 5.00 15.0 20.0 3.90 30.0 2.98 40.0 2.30 1.00 5.98 2.50 4.35 5.00 3.26 10.0 3.01 15.0 2.82 20.0 2.72 30.0 2.61 40.0 2.27 2.50 9.79 5.00 8.50 10.0 5.89 15.0 4.83 20.0 3.93 30.0 3.62 0.40 5.00 0.24
high activation energy, again points to a surface rather than a bulk diffusion controlled dissolution reaction. The slope of the linear plot in Figure 2 suggests a polynuclear dissolution mechanism in the range of undersaturation 0.25 < u < 0.75. In a study of the kinetics of dissolution of hydroxyapatite, Christoffersen et al.6 expressed the rate of reaction by eq 3, in which k is the rate constant and moand m are
R = km,g(a)F(m/mo)
(3)
the masses of crystals at time zero and time t , respectively. The functions g and F were determined by experiment. It w a shown ~ that the rate of dissolution depended not only upon the degree of undersaturation, u, but also upon the extent of reaction, with F(m/m,J E (m/%)0.6. In contrast, the rate of dissolution of magnesium fluoride was constant a t each undersaturation for as much as 40% dissolution of the added seed crystals. As for HAP dissolution, however, the value of n in eq 2 pointed to a polynucleation controlled mechanism in which the reaction is controlled by the production of unit pits on the surface of the crystals. In general, the rates of crystallization and dissolution of alkaline earth salts are markedly inhibited by the addition of certain organic molecule^.'^^^ Experiments in the presence of HEDP and ENTMP, summarized in Table (13)H a " , S.M.; Nancollas, G. H.J. Chem. SOC.Faraday D a m . 1, in press. (14)Nancollas, G. H.;Bochner, R. A.; Liolios, E.; Shyu, L. J.; Yoshikawa,Y.;Barone, J. P.; Svrjcek, D. AZChE S y m p . Ser. 1982,215, 26. (15)Bochner, R. D.;Abdul-Rahman A.; Nancollas, G. H.J. Chem. SOC.,Faraday Trans. 1 1984,80,217. (16)Hamza, S. M.;Abdul-Rahman, A.; Nancollas, G. H.J. Cryst. Growth in press. (17)Weijnen, M. P. C.; Marchee, W. Q.J.: van Rosmalen, G. M. Desalination 1983,47, 81. (la) Leung, W. H.;Nancollas, G. H.J. Cryst. Growth 1978,44,163. (19)Gill, J. S.;Nancollas, G. H.Corrosion (Houston) 1981, 37, 120.
IO
20
30
IO6 [ENTMP]
Figure 3. Dissolution in the presence of ENTMP. Plots of rate against [ENTMP] for experiments 175-180 (0) and 167-173 (0).
-L 3 d
60
I20 I 0-3 [HE DP]-'
I80
Figure 4. Dissolution of ma esium fluoride in the presence of HEDP. Plots of Ro(Ro- Ri)-F against [HEDPI-'. Experiments: 161-166 (0); 156-159 (A).
I1 show that concentrations as low as 1.0 X lo* mol L-' reduced the dissolution rates by a t least 50% compared to that in pure solution. In contrast, strontium fluoride dissolution is inhibited to a much greater extent and concentrations of phosphonate of lo-' mol L-' have been shown to reduce the rate by as much as 70%.13 Typical plots of the rate of dissolution in the presence of ENTMP are shown in Figure 3. It can be seen that the degree of inhibition is markedly increased a t lower values of undersaturations (a = 0.6). In general, inhibitor molecules exert their influence through adsorption at active dissolution sites on the crystal surfaces. Chelating anions may be adsorbed a t cationic sites and inhibit the disssolution when present at very low levels. The adsorption can be interpreted in terms of a Langmuir-type isothermz0leading to an equation of the form
Ro/(Ro - Ri) = (KLC)-' (4) in which Ri and Ro are the rates of dissolution in the presence and absence of inhibitor respectively, KLis the adsorption affinity, and C is the concentration of additive. Typical adsorption plots according to eq 4 in Figure 4 confirm the applicability of this simple adsorption isotherm a t all undersaturations studied. The values of the adsorption affinity constants KL are 3.5 X lo5and 2.3 X lo5L mor1 for HEDP and 6.6 X lo5and 3.8 X lo5L mol-' for ENTMP a t relative undersaturations, cr = 0.6 and 0.7, respectively. These values reflect the high adsorption affinity a t low undersaturation in the presence of both phosphonate inhibitors. A similar dependence of the degree of inhibition with change in driving force has been observed for the influence of phosphonate and magnesium (20) Koutaoukos, P.; Amjad, 2.;Nancollas, G. H.J. Colloid Interface Sci. 1981,83, 599.
Langmuir 1985, 1, 576-587
576
II y 90 H _I
60
L
e
52
8
16
24
IO6 [HEDP]
Figure 5. Adsorption of HEDP on magnesium fluoride crystals at equilibrium and constant pH. Plots of r against [HEDP]. ion on the rate of dissolution in strontium fluoride in aqueous ~ o l u t i o n . ' ~ JAs ~ noted for the crystallization of gypsum by van Rosmalen and co-workers,l' the effectiveness of the HEDP as an inhibitor is dependent on the degree of supersaturation. The observed increased inhibition of surface-controlled dissolution with decreasing undersaturation is especially interesting. If inhibitor molecules are adsorbed on the crystal surfaces between the advancing dissolution steps, the reaction can proceed provided that adjacent adsorbed molecules are separated by a distance greater than that of the critical etch pit.21 The effect of the inhibitor may be described as the prevention or strong retardation of the nucleation of etch pits in areas around the adsorbed in-
hibitor molecules. Due to interaction with the inhibitor, lattice ions in these areas will be strongly attached to the crystal surface. If sufficient inhibitor molecules are adsorbed onto the surface, the whole crystal may be inactivated and no dissolution will occur. Prevention of retardation of dissolution may occur by preferential adsorption of the inhibitor molecules at the edges of the subcritical etch pits forming on the surface thus preventing their development beyond the critical size.22 In order to investigate the adsorption of phosphonate on the magnesium fluoride surfaces, adsorption equilibrium experiments were made for HEDP on magnesium fluoride crystals at u = 0 and pH 5.6 f 0.2. The time allowed for adsorption varied between 2 min and 24 h but it was confirmed that adsorption was effectively completed within 5 min. A typical adsorption isotherm is plotted in Figure 5. It has been shown that the rate of crystallization18J9may be reduced virtually to zero when only 5-7% of the crystal surface was covered by adsorbed inhibitor molecules. In the present dissolution work, assuming that the area occupied by an HEDP molecule is 50 X m2, the fraction of the solid surface covered by adsorbed molecules is only 9% a t the plateau in Figure 5. At this HEDP concentration, the dissolution rate is reduced by more than 80%. This again points to a surface-controlled dissolution process. Dissolution will be inhibited when the average distance between the inhibitor molecules is less than the critical size of a dissolution etch pit.
Acknowledgment. We thank the National Science Foundation for Grant CPE8313383 in support of this work. Registry No. ENTMP, 1429-50-1; HEDP, 2809-21-4; MgF,, 7783-40-6.
(21) Cabrera. N.: Vermilvea. D. A. 'Growth and Perfection of C ~ s & s " ;Doremus,'R. H.; Roberta, B. W., Turnbull, D., Eds.; Wiley: 1958, p 393.
(22) van Rosmalen, G. M.; Weijnen, M. P. C.; Meiser, J. A. M. 36th International Conference CEBEDEAU-Liege, 1983.
Microemulsions of Methyl Methacrylate in Aqueous Sodium Lauryl Sulfate: Structure and Interaction Energetics by SAXS, NMR Spectroscopy, and GC Headspace Analysis Joseph 0. Carnali* and Frederick M. Fowkes Department of Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015 Received April 19, 1985 A study was conducted to elucidate the structure of oil in water microemulsions in the three- (or four-) component system water, sodium lauryl sulfate (SLS),and methyl methacrylate (MMA) (and hexanol). These systems were studied by three complementary techniques, and all resulta were interpreted in terms of a core/shell model for the oil phase dispersed as droplets within the aqueous phase. The partitioning of MMA and hexanol between the droplet core and ita shell was determined by headspace analysis combined with a NMR chemical shielding study. The data indicate that the stability of the three-component system may be due to mixing of the MMA within the core with the alkane chains of the SLS, resulting in a lowered free energy for the system. In the four-component systems, hexanol partitioning into the core further dilutes the MMA and promotes additional MMA solubilization, while hexanol partitioning into the droplet shell provides excess surface area for the growing droplet. The core/shell model was tested by fitting small-angle X-ray scattering data from selected systems to the theoretical scattering expected from such a model. The comparison supported the model and provided estimates for the droplet radii ranging from 2 to 5 nm depending on their MMA content.
Introduction Microemulsions are an example of the nonrandom systems which have recently been termed 'organized solutions" by Shinoda.' The organization in micro0743-7463/85/2401-0576$01.50/0
emulsions appears to vary with the time scale of the inV@tkati0nu and with the Particular S y s t e m being studied. (1) Shinoda, K. J. Phys. Chem. 1985,89, 2429.
0 1985 American Chemical Society
