600
Langmuir 1991, 7, 600-603
Constant Composition Study of Crystal Growth of Calcium Fluoride. Influence of Poly(carboxylic acids), Polyphoshates, Phosphonates, and Phytate Zahid Amjad The BFGoodrich Company, Specialty Polymers and Chemicals Division, Brecksville Research Center, Brecksville, Ohio 44141 Received March 6, 1990. I n Final Form: July 13, 1990 The constant composition technique has been used to study the crystal growth of calcium fluoride on calcium fluoride seed crystals at sustained supersaturation, 37 O C , in the presence of inhibitors of varying functional groups. The inhibitors investigated include (1)poly(carboxy1icacids) (benzenehexacarboxylic acid, mellitic acid, MA; benzene-1,3,5-tricarboxylic acid, trimesic acid, TMA; poly(acry1icacid), PAA mol wt 5100; citric acid, CA), (2)polyphosphates (pyrophosphate, PYP, hexametaphosphate, HMP; phytic acid, PA), and (3) phosphonocarboxylic acid (2-phosphono-1,2,4-butanetricarboxylic acid, PCA). The effect of these inhibitors on the growth kinetics has been studied at several inhibitor concentrations. The retarding effect of these inhibitors is interpreted in terms of adsorption, following the Langmuir isotherm, of inhibitor ions at the active crystal growth sites. The order, in terms of decreasing effectiveness on the rate of CaFl crystal growth, of various inhibitors studied is as follows: PAA >> PCA > MA > HMP > PYP > PA > CA > TMA. Introduction Several studies have been reported on the precipitation of alkaline earth metal The crystallization of calcium fluoride has recently received considerable attention due to its participation in many areas including fluoridation of water, electronics, spectroscopy, etc. Biologically, crystallization of calcium fluoride is of considerable importance in evaluating the influence of topical application of fluoride solution to tooth enamel. Gray and co-workers5 suggested that following treatment with sodium fluoride, the enamel surface coated with a layer of calcium fluoride protected the tooth from dissolution. McCann6 reported that the mechanism of caries inhibition by fluoride was related to the reduced solubility of fluorapatite. Liang and Higuchi' proposed a model based upon the simulataneous diffusion and chemical equilibrium of the fluoride and phosphate ions at the calcium fluoride/ hydroxyapatite interface. The influence of phosphate on the crystal growth of calcium fluoride has been studied under highly reproducible conditions by the constant composition method.8 At a phosphate concentration of 1.92 X lo+ M, calcium fluoride growth was shown to be completely inhibited for at least 24 h. A t lower concentrations ((1-9) X lo-' M) induction periods of 10-50 min were observed. Furthermore, at higher phosphate concentrations, calcium phosphate phase was seen in scanning electron micrographs of the growing solids. The inhibitory effect of diphosphonate on calcium fluoride crystallization has also been investigated. On the basis of the kinetic data, the decrease in the observed rate of crystallization with increasing diphosphonate concentration follows the Langmuir ad(1) Yoshikawa, Y.; Nancollas, G. H.; Barone, J. P. J. Crystal Growth 1984, 69, 357. (2) Bochner, R. A.; Rehman, A. A.; Nancollas, G. H. J . Chem. SOC., Faraday Trans. 1984, BO, 217. (3) Shyu, L. S.; Rehman, A. A.; Nancollas, G. H. J. Cryst. Growth 1985, 73, 245. (4) Barone, J. P.; Svrjcek, D.; Nancollas, G. H. J . Cryst. Growth 1983, 62. . ~27. -, (5) Gray, J. A.; Schweizer, H. C.; Rosevear, F. B.;Broge, R. W. J . Dent. Res. 1958, 37, 638. (6) McCann, H. G. Arch. Oral B i d 1968, 13, 987. (7) Liang, Z. S.; Higuchi, W. I. J. Phys. Chem. 1973, 77, 1704. (8) Shyu, L. S.; Nancollas, G. H. Croat. Chem. Acta 1980, 53, 281.
sorption isotherm.8 Recently Hamza and Nancollasg have shown that dissolution of magnesium fluoride appears to be controlled by a surface polynucleation process which, in contrast to a bulk diffusion reaction, is markedly inhibited by the presence of inhibitors. A surface adsorption mechanism involving a simple Langmuir type isotherm model has been proposed to account for the inhibition of magnesium fluoride and strontium fluoride dissolution in the presence of polyphosph~nates.~J~ Previous papersl1-l4 report the effects of a variety of inhibitors on the rate of seeded growth of several sparingly soluble salts. The experimental results indicated that the poly(carboxy1ic acids) such as poly(acry1ic acids) and benzenehexacarboxylic acids, phytic acid phosphonates, and polyphosphates are effective crystal growth inhibitors for calcium phosphates, calcium carbonates, and calcium sulfate dihydrate. The present work deals with the effect of inhibitors on the crystallization of calcium fluoride on well-characterized calcium fluoride seed crystals at low sustained supersaturation using the constant composition te~hnique.'~ The inhibitors investigated were: phytic acid (PA), sodium pyrophophosphate (PYP), sodium hexametaphosphate (HMP), 2-phosphono-1,2,4-butane tricarboxylic acid (PCA), citric acid (CA), benzenehexacarboxylic acid (mellitic acid, MA), 1,3,5-benzenetricarboxylic acid (trimesic acid, TMA), and poly(acry1ic acid) (PAA, molecular weight 5100). The structures of inhibitors tested in the present investigation are summarized in Table I. Experimental Section Reagent grade chemicals and grade A glassware were used. Calcium stock solutions were prepared from calcium chloride and were standardized as described previously.ll Fluoride solutions were prepared in polyethylene bottles and concentrations were determined by use of a fluoride combination electrode (Orion Model 960900). (9) Hamza, S. M.; Nancolas, G. H. Langmuir 1985, 1, 573. (10) Hamza, S. M.; El-Hamouly, S. H. J . Chem. Soc., Faraday Trans. 1 . 1989.85. 3725. . _ , -. -, _ - -(11) Amjad, Z. J . Colloid Interface Sci. 1987, 117, 98. (12) Amjad, Z. Langmuir 1987, 3, 224. (13) Amjad, Z.; Hooley, J. J. Colloid Interface Sci. 1986, 111, 496. (14)Amjad, Z. Can. J. Chem. 1988,66, 2188. (15) Tomson, M. B.; Nancollas, G. H. Science 1978,200, 1059.
0743-7463191/2~07-0600$02.50/00 1991 American Chemical Society
Crystal Growth of Calcium Fluoride
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Table I. List of Inhibitors inhibitor acronym structure mol wt 342 benzenehexacarboxylic acid (mellitic acid) MA Cs(COOH)6 1,3,5-benzenetricarboxylicacid (trimesic acid) TMA C&,(COOH)3 210 citric acid CA HOC(CH~CO~H)ZCO~H 192 poly(acry1ic acid) 5100 PAA (CHFCHCO~H)R sodium pyrophosphate PYP N~P20~10H20 446 sodium hexametaphosphate HMP (NaP03)6 612 phytic acid 660 PA CsHs(OP03Hzh 2-phosphono-1,2,4-butanetricarboxylic acid PCA HOOCCHzC(COOH)(P03H2)CH2CH2COOH 270 Table 11. Crystallization of CaFz on CaFz Seed Crystals in the Presence of Inhibitors. expt inhibitor concn X lo6, M rate X 106, mol min-1 m-2 20 60.5 21 64.2 25 62.3b 23 59.8C MA 0.010 28 61.6 MA 26 47.1 0.100 29 MA 0.150 43.2 MA 30 37.6 0.200 MA 31 35.5c 0.200 34 MA 31.1 0.250 MA 35 33.2 0.250 MA 0.400 38 22.3 36 MA 10.8 0.500 MA 33 1.000 2.83d 40 TMA 0.250 58.5 TMA 0.500 44 49.0 TMA 1.000 36.8 41 TMA 42 2.000 13.2 0.250 46 CA 46.8 PAA 0.025 23.3 48 PAA 0.250 2.2d 49 0.250 PYP 42.5 52 51 PYP 0.500 29.2 1.000 55 PYP 16.9 56 0.160 45.3 HMP 0.250 57 HMP 38.2 25.5 0.500 58 HMP 49.8 0.150 60 PA 45.5 0.250 62 PA 61 PA 29.1 0.500 63 16.9 PA 1.000 PCA 66 43.1 0.100 22.5 67 PCA 0.250 PCA 13.1 68 0.500 Initial conditions: Tc.= 0.500 X 10-3 M, TF= 1.000 X M, 37 "C, NaCl = 14.4 X 10-3 M, CaF2 seed crystals = 30 mg. * 22 mg of CaF2 seed crystals. 16 mg of CaF2 seed crystals. d Initial rate. Polyphosphates, phytic acid, and poly(carboxy1ic acids) stock solutionswere made from reagent grade materials and commercial poly(acry1ic acid) (Good-Rite K-732, The BFGoodrich Co.). The phosphonate solutions used in this study were prepared from commercial phosphonic acids. The calcium fluoride seed crystals, prepared and characterized as described previously: were aged for a t least 6 months before use. The specific surface area of the seed crystals as determined by a BET method was found to be 3.3 m2 g-l. Crystal growth experiments were made in a double-walled Pyrex cell of 250-mL capacity fitted with Teflon lid and polyethylene liner. The cell was maintained at 37 f 0.1 "C by circulating the thermostated water through the outer jacket. The metastable supersaturated solutions of calcium fluoride were carefully prepared by the slow addition of calcium chloride solution to the sodium fluoride solution such that the final CaF2 solution concentration would be 0.500 X M. Inhibitors were added after the addition of NaF, but before the addition of CaC12, as dilute solutions in water. All calcium fluoride supersaturated solutions were made up to a total ionic strength of 15.90 X M using sodium chloride. The calcium fluoride supersaturated solution were continuously stirred (-350 rpm) while nitrogen gas, presaturated with water a t 37 "C, was bubbled through the solution to exclude carbon dioxide. Following the addition of CaF2 seed crystals to the supersaturated solutions, the super-
source Aldrich Chemical Co. Sigma Chemical Co. Fisher Scientific Co. BFGoodrich Co. Fisher Scientific Co. Pfaltz & Bauer, Inc. Pfaltz & Bauer, Inc. Mobay Chemical Co.
Figure 1. Crystal growth of CaF2 on CaF2 seed crystals. Plots of mol m-2 crystallized as a function of time in the presence of mellitic acid (lo+ M): expt 20,O.O; expt 26,O.lO; expt 29,0.15; expt 30, 0.20; expt 35, 0.25; expt 38, 0.40; expt 36, 0.50. saturation was maintained constant by the addition of titrant solutions from mechanically coupled automatic burets mounted on a modified pH stat (Model 600 series, Brinkman Instruments, Westbury, NY). The rate of titrant addition was controlled by the emf of a specific fluoride electrode. The titrant solutions in burets consisted of calcium chloride and sodium fluoride. In the investigation of the crystal growth in the presence of inhibitor, in order to avoid dilution, the appropriate amount of inhibitor was added in one of the two burets. The molar concentration ratio of the titrants corresponded to the stoichiometry of CaFz. By addition of sodium chloride to the calcium fluoride supersaturated solution, the ionic strength was maintained constant to within 1Yo. This was necessary since changes in activity coefficients could also trigger the addition of titrant solutions. During the experiments, aliquots were withdrawn from time to time, filtered (0.22-pm filter, Millipore Corp., Bedford, MA), and analyzed for calcium ion by atomic absorption spectroscopy. The data confirmed the constancy of the lattice-ion concentrations The rates of crystallization were determined to within &l%. from rates of addition of titrants and corrected for surface area changes.8
Results and Discussions The experimental conditions used in this study are summarized in Table 11. Typical plots of moles of calcium fluoride grown on CaFz seed crystals as a function of time, after correction of the raw data for the observed changes in specific surface area, are shown in Figure 1. The slopes of the lines are used to calculate the growth rates expressed as moles of CaFz grown per square meter of surface in Table 11. Experiments performed both in the presence and in the absence of inhibitors (experiments 21, 23,25, 30, 31) at different seed concentrations showed that crystallization took place on the seed crystals exclusively. Crystallization experiments made in the presence of poly(carboxy1ic acids) (i.e., MA, TMA, CA, PAA) are summarized in Table 11. Plots of the moles of CaF2 grown per unit surface area of CaFz seed crystals as a function of time in the presence of MA are shown in Figure 1. It can be seen that MA a t a concentration of 1.00 X M
602 Langmuir, Vol. 7, No. 3, 1991
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Figure 2. Comparative effect of inhibitors on crystal growth of CaF2 at constant supersaturation. Plots of mol m-2 of CaF2 crystallized as a function of time in the presence of 2.50 X M poly(carboxy1ic acids): expt 20, 0.0; expt 40, TMA; expt 46, CA; expt 34, MA; expt 49, PAA.
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Figure 3. Crystal growth of CaF2 at constant supersaturation. Plots of mol m-2 of CaFz crystallized as a function of time in the presence of pyrophosphate (10" M): expt 20,O.O; expt 52,0.25; expt 51, 0.50; expt 55, 1.00. (experiment 28, Table 11) shows no significant inhibitory effect on the crystal growth of CaF2. However, increasing the MA concentration to 1.0 X lo4 M resulted in -95% reduction in the rate of crystallization (experiment 33, Table 11). Figure 2 illustrates the plots of newly grown CaFz on CaFz seed crystals as a function of time in the presence M concentration of each poly(carboxy1ic of 2.50 X acids) present in the supersaturated solution. It is interesting to note that poly(acry1ic acid) at 2.50 X lo-' M concentration shows excellent inhibitory activity. Under similar conditions, however, mellitic acid has a relatively more marked inhibitory effect compared to citric acid and trimesic acid but significantly less than observed for poly(acry1ic acid). For example, rates of CaF2 crystal growth in the presence of 2.50 X M mellitic acid, citric acid, and trimesic acid are 33.2 X lo+, 46.8 and 58.5 X lo+ mol min-1 m-2, respectively, compared to 2.2 x lo4 mol min-l m-2 obtained for poly(acry1ic acid). The influences of polyphosphates such as PYP and HMP as CaF2 crystal growth inhibitors are summarized in Table 11. Figure 3 shows plots of moles of newly grown CaF2 as a function of time for crystal growth experiments in the presence of varying concentrations of PYP. As shown in Figure 3, the crystallization in the presence of 2.50 X M PYP results in -30% reduction of the growth rate. Table I1 shows that HMP at a concentration of 2.50 x 10-7 M (experiment 57) retarded crystal growth of CaFz to a greater degree than PYP under similar conditions (ex-
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Figure 4. Crystal growth of CaF2. Plots of mol m-2 of CaF2 crystallized as a function of time in the presence of polyphosphate, phytic acid, and phosphonocarboxylic acid (2.50 x M): expt 20,O.O; expt 62, Pa; expt 52, PYP; expt 57, HMP;expt 67. PCA. periments 52 and 57, Table 11). Results of kinetic data (Table 11)for polyphosphates suggest that the inhibition by polyphosphate decreases as the chain length decreases. It is interesting to note that a similar inhibiting effect of these polyphosphates has been reported for the crystallization of dicalcium phosphate dihydrate14and hydroxyapatite.l6 The effects of phytic acid (PA)and phosphonocarboxylic acid (PCA) on the crystallization of CaFz were also studied by a series of experiments summarized in Table 11. Figure 4 shows the plots of moles of newly grown CaF2 on CaF2 seed crystals as a function of time in the presence of 2.50 X M PYP, HMP, PA, and PCA present initially in the supersaturated solutions (experiments 52, 57, 62, 67, and 73, Table 11). On the basis of the rate data (Table 11) the order of effectiveness for polyphosphates and phosphonocarboxylic acid as crystal growth inhibitors is as follows: PCA > HMP > PYP > PA. There are several possible mechanisms by which an additive can inhibit the crystal growth reaction. An additive may form stable complexes with one of the precipitating ions and decrease solution supersaturation. Polyphosphates, phosphonates, and poly(carboxy1ic acids) used in the present study form moderatly stable complexes with calcium ions. Relevant to the systems the results of species calculations obtained by using literature constant values show that in supersaturated solutions with 1.0 X lo4 M inhibitor, less than -3% of the total dissolved calcium is bound as calcium inhibitor containing complex. Thus, the effect of ion-pair formation on kinetics is virtually negligible. The assumption that the inhibitory effect of the additives is mainly due to adsorption and subsequent blocking of the active growth sites was tested by using the Langmuir adsorption model. According to the Langmuir adsorption model, the decrease in crystallization rate can be related to the crystal surface area covered by the adsorbed inhibitor molecules. If Ro and Ri are the rates of crystallization in the absence and presence of inhibitors, respectively, the Langmuir isotherm requires a linear relationship between the relative reduction in rate, Rol(R0 - Ri), and the reciprocal of the inhibitor concentration (C) according to the relationship
Ro/(R,-Ri) = 1 + (kZ/ki)(l/C)
(1)
where k1 and k2 are the specific rate constant for adsorption and desorption, respectively, for the inhibiting ions. Plots (16) Amjad, 2. Langmuir 1987,3, 1063.
Crystal Growth of Calcium Fluoride GO
Langmuir, Vol. 7, No. 3, 1991 603
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Figure 5. Langmuir adsorption isotherms. Plots of Ro/(Ro-Ri) against [Cl-l: (0) T M A ; (A) PA; ( 0 )HMP, (v)MA; (0) PCA. Table 111. Affinity Constants for Various Inhibitors of HAP, DCPD, and CaFz Crystal Growth a t 37 "C inhibitor PYP HMP PA PCA MA TMA HEDP
HAP
1.90 11.5" 0.84b
DCPD 21.4d 210d 410d
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CA
CaFz 14.g 20.u 13.8, 37.lf 27.lf 5.u 23.28 9.7
PKML 3.2 7.6 3.2 5.4 3.5 1.1 7.1 4.7
a Amjad, Z. Langmuir 1987,3,1063. Koutsoukos, P . G.; Amjad, Z.; Nancollas, G. H. J . Colloid Interface Sci. 1981,83,599. Amjad, Z. In Adsorption on andsurface Cemistry ofHydroxapatite; Misra, D. W . , Ed.; Plenum: New York, 1984. dAmjad, Z. Can. J . Chem. 1988, 66, 2181. e Amjad, Z. J . Colloid Interface Sci. 1987, 117, 98. f This work. 8 Shyu, L. Ph.D. Thesis, State University of New York
at Buffalo, New York, 1982.
according to eq 1 are shown in Figure 5 for CaFz crystal growth in the presence of PYP, PCA, and MA. Figure 5 confirms that the inhibitory effect of these inhibitors is due to adsorption a t active growth sites. The values of the "affinity constant" ( k l l l z z ) , as calculated from data shown in Table 11, are summarized in Table 111. A list of other affinity constant values for a variety of inhibitors for the crystal growth of hydroxyapatite (HAP) and dicalcium phosphate dihydrate (DCPA) is also shown in Table 111. The value of the "affinity constant" for MA as calculated from Figure 5 is 27.1 X lo5, which can be compared with 5.0 X lO5obtained for TMA. These differences may reflect stronger equilibrium absorption of mellitate ion than of trimesicate ion at the interface, probably due to a reduction in the desorption rate constant, k ~ .It is interesting to note that the high affinity constant value or marked reduction in growth rate by MA as observed in the presence study is consistent with the results reported in the study on the adsorption of benzene poly(carboxy1ic acids) onto
hydroxyapatite. According to Voegel and Frank17 the adsorption of benzenepoly(carboxy1icacids) on hydroxyapatite followed a Langmuir-type adsorption model and the amounts of MA adsorbed were 7-10 times greater than those of TMA. The difference in the ability of the various inhibitors, i.e., benzene poly(carboxy1ic acids), phosphonate and phosphonocarboxylic acid, and polyphosphates, etc., to retard or inhibit crystallization of calcium fluoride could be rationalized in terms of their abilities to form a complex with the calcium ion. Table I11 summerizes the comparative data on calcium-inhibitor complexation constant (KML)and "affinity constants" for a variety of inhibitors. It can be seen that on the basis of affinity constant values the order of effectiveness of benzene poly(carboxy1icacids) is: MA >> TMA, which can be compared with the order in terms of decreasing KMLvalues (Table 111). Unfortunately there are insufficient data available in the literature on TMA; however, a close comparison may be obtained with calcium phthalate, PKML= 1.07.18 The poor inhibitory activity shown by crystallization experiments summarized in Table I1 is thus consistent with the chelating ability of benzene poly(carboxy1ic acids). It is interesting to note that whereas the value of PKMLfor citric acid is approximately 1.3 times as large as that for MA (Table 111), the inhibitory effect on the other hand as shown by kl/kz values (Table 111) is surprisingly -3 times larger for MA. The relatively good inhibitory activity shown by MA compared to CA may be attributed t o the relatively highly charged mellitate ion. The kl/kz values presented in Table I11 for organophosphonates show that PCA is more effective as calcium fluoride growth inhibitor than HEDP. This is in contrast to the K M Lvalues. The differences observed in the order of PCA and HEDP effectiveness may be due to several factors including different rates of adsorption and desorption of two different adsorbates on CaFz seed crystals and the presence of carboxyl groups in PCA.
Summary The constant composition technique used in this work provides a simple and convenient means for measuring the CaFz growth rate and studying the effect of inhibitors. The results of the present study indicate that the presence of inhibitors, namely poly(carboxy1ic acids), polyphosphates and phytate, and phosphonocarboxylic acids a t low concentrations, can markedly inhibit the crystal growth of CaFz. The inhibitory effect of the inhibitors may be explained by adsorption of inhibitor molecules a t growth sites. On the basis of the kinetic data, effectiveness of the inhibitors follows the order: poly(carboxy1ic acids) PAA >> MA > CA > TMA; phosphonocarboxylic acid, polyphosphates, and phytate PCA > HMP > PYP > PA; overall PAA >> PCA > MA > HMP > PYP > CA > TMA. (17) Voegel, J. C.; Frank, R. M. J . Colloid Interface Sci. 1981,83,26. (18) Joseph, N. R.J . Biol. Chem. 1946, 164, 529.
