Influence of Organic Phosphonates on Hydroxyapatite Crystal Growth


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Langmuir 1996, 12, 2853-2858

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Influence of Organic Phosphonates on Hydroxyapatite Crystal Growth Kinetics A. Zieba, G. Sethuraman, F. Perez, G. H. Nancollas,* and D. Cameron Department of Chemistry, State University of New York at Buffalo, Amherst, New York, 14260-3000 Received October 6, 1995. In Final Form: February 9, 1996X Phosphonate additives have important applications both in biomineralization processes and in industrial mineral scale formation. The kinetics of crystal growth of hydroxyapatite (HAP) has been investigated in the presence of seven phosphonate additives: HEDP (hydroxyethylenediphosphonic acid), DETPMP (diethylenetriaminepenta(methylenephosphonic acid)), DHTPMP (dihexyltriaminepenta (methylenephosphonic acid)), AMP (aminotris(methylenephosphonic acid)), HDTMP (hexyldiaminetetra(methylenephosphonic acid)), EDTMP (ethylenediaminetetra(methylenephosphonic acid)), and DETMP (diaminoethoxytetra(methylenephosphonic acid)). The constant composition (CC) method, used in this study, enabled reliable crystal growth rate data to be obtained even when the reactions were appreciably inhibited. The experiments were performed at pH 7.40, ionic strength 0.15 mol L-1 (maintained with NaCl), and an HAP relative supersaturation, σ, of 5.5. The results indicate that traces of some phosphonates (e10-6 mol L-1) are extremely effective in inhibiting crystal growth. Assuming that the adsorbed additives block discrete growth sites on the crystal surfaces, the kinetic results may be interpreted in terms of a Langmuir adsorption model yielding kinetic affinity constants. The order of inhibitory effectiveness, DETMP > EDTMP > DETPMP > HEDP g DHTPMP > HDTMP g AMP, reflects the ability of the phosphonates to bind to the apatite surfaces. ζ potential measurments of HAP surfaces in the presence of additives provide important corroboratory data for the interpretation of the crystal growth results.

Introduction The precipitation of calcium phosphates is of fundamental importance because of the involvement of phases such as hydroxyapatite (HAP), the most stable calcium phosphate phase, in diverse areas including pathological biomineral deposits resulting in problems such as dental calculus, arthritis, arteriosclerosis, and urinary calculi.1-4 In addition, undesirable calcium phosphate precipitation is involved in some industrial scaling situations such as oil and gas production, water purification and energy production technology.5 The inhibition or even prevention of calcium phosphate formation by the addition of trace amounts of inhibitors is therefore of considerable interest. Organic phosphonates are among the most effective inhibitors of calcium phosphate growth,5,6 probably through adsorption at active crystal growth sites on the microcrystallite surfaces. Since most are nontoxic, they are useful in medicine for a number of important bone/calcium related diseases1,2,7,8 as well as in the water treatment industry. The usefulness of the phosphonates is enhanced by their stability over wide ranges of pH and temperature. In the present work, the effectiveness of seven different organic phosphonates (Table 1) on hydroxyapatite (HAP) mineralization was studied by the use of the constant * Correspondence should be addressed to Professor G. H. Nancollas, Department of Chemistry, 756 Natural Sciences and Mathematics Complex, State University of New York at Buffalo, Amherst, NY 14260-3000. Telephone: (716) 645 6800 ext 2210. Fax: (716) 645 6947. X Abstract published in Advance ACS Abstracts, May 1, 1996. (1) Golomb, G.; Schlossman, A.; Saadeh, H.; Levi, M.; van Gelder, J. M.; Breuer, E. Pharm. Res. 1992, 9, 143. (2) Golomb, G.; Schlossman, A.; Eitan, Y.; Saadeh, H.; van Gelder, J. M.; Breuer, E. J. Pharm. Sci. 1992, 81, 1004. (3) Koutsoukos, P. G.; Amjad, Z.; Nancollas, G. H. J. Colloid Interface Sci. 1981, 83, 599. (4) Breuer, E.; Golomb, G.; Hoffman, A.; Schlossman, A.; van Gelder, J. M.; Saadeh, H.; Levi, M.; Eitan, Y. Phosphorus, Sulphur Silicon 1993, 76, 167. (5) Amjad, Z. Langmuir 1987, 3, 1063. (6) van Rosmalen, G. M.; van der Leeden, M. C.; Gouman, J. Kris. Tech. 1980, 15, 1269. (7) Tomson, M. B.; Kan, A. T.; Oddo, J. E. Langmuir 1994, 10, 1442. (8) Kan, A. T.; Oddo, J. E.; Tomson, M. B. Langmuir 1994, 10, 1450.

S0743-7463(95)00842-0 CCC: $12.00

composition (CC) method.9,10 In this procedure, supersaturation was maintained constant by the automated addition of calcium, phosphate, phosphonate, and hydroxide ions, controlled by ion selective electrodes, following the addition of seed material to stable supersaturated calcium phosphate solutions. Using this method, mineralization reactions could be investigated over a range of constant thermodynamic driving forces, and by choosing appropriately low supersaturation levels, the exclusive mineralization of HAP could be ensured without interference from other, more acidic, calcium phosphate phases.11 Moreover, by employing the constant composition method, the rates of mineralization of HAP in the absence and presence of the phosphonate inhibitors could be measured with an accuracy and reproducibility unachievable by conventional free drift crystal growth methods. Data so obtained enable comparisons to be made of the phosphonates in terms of their effectiveness in inhibiting HAP crystal growth. The marked differences in the ability of various phosphonates to influence HAP crystallization may be related to their potential for forming complexes with calcium ions. Additional information about the interactions between HAP surfaces and phosphonates was obtained from extensive ζ potential measurements as well as some selected equilibrium adsorption determinations. Experimental Section Stock solutions (calcium chloride, potassium dihydrogen phosphate, and sodium chloride), prepared using triply distilled water and Reagent grade chemicals dried under vacuum, were filtered twice (0.22 µm Millipore filters) before use. Calcium chloride solutions were standardized by EDTA titration. Phosphonate solutions were prepared from samples obtained from the Synthetic Organic Chemical Manufacturers Association. They (9) Tomson, M. B.; Nancollas, G. H. Science 1978, 200, 1059. (10) Koutsoukos, P.; Amjad, Z.; Tomson, M. B.; Nancollas, G. H. J. Am. Chem. Soc. 1980, 102, 1553. (11) Nancollas, G. H. In In vitro Studies of Calcium Phosphate Crystallization in Biomineralization. Chemical and Biochemical Perspectives; Mann, S., Webb, J., Williams, R. J. P., Eds.; VCH Verlagsgesellschaft: Weinheim, 1989; pp 157-187.

© 1996 American Chemical Society

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Zieba et al. Table 1. Phosphonates Studied

name

structure

abbr.

Diaminoethoxytetra(methylenephosphonic acid) Ethylenediaminetetrta(methylenephosphonic acid) Diethylenetriaminepenta(methylenephosphonic acid) Dihexyldiaminepenta(methylenephosphonic acid) Hydroxyethylenediphosphonic acid Aminotris(methylenephosphonic acid) Hexyldiaminetetra(methylenephosphonic acid)

(H2O3PCH2)2NCH2CH2OCH2CH2N(CH2PO3H2)2 (H2O3PCH2)2N(CH2)2N(CH2PO3H2)2 [(H2O3PCH2)2N(CH2)2]2NCH2PO3H2 [(H2O3PCH2)2N(CH2)6]2NCH2PO3H2 CH3C(OH)(PO3H2)2 N(CH2PO3H2)3 (H2O3PCH2)2N(CH2)6N(CH2PO3H2)2

DETMP EDTMP DETPMP DHTPMP HEDP AMP HDTMP

were used as their sodium salts, after neutralization, where necessary, with sodium hydroxide solution. Carbon dioxide-free potassium and sodium hydroxide solutions were prepared in a nitrogen atmosphere from washed pellets and standardized against potassium hydrogen phthalate. HAP seed crystals were prepared from calcium nitrate and potassium dihydrogen phosphate, as detailed elsewhere.12 The specific surface area, 26.6 m2 g-1, was determined by BET nitrogen adsorption using a 20.1%/79.7% N2/He mixture (Quantasorb II, Quantachrome Corp.). CC crystal growth kinetic measurments9,10 were made in double-walled Pyrex glass vessels maintained at 25.0 ( 0.1 °C by the circulation of the thermostated water. Supersaturated reaction solutions were prepared by the slow mixing of calcium chloride, phosphonate, and potassium dihydrogen phosphate solutions with the ionic strength maintained at 0.15 mol L-1 by the addition of sodium chloride. The possible removal of free calcium ion by complexation with phosphonate ions, monitored by means of a calcium electrode, could be compensated for by the addition of calcium but was found to be negligible. Potassium hydroxide solution was added to the reaction solution to bring the pH to 7.40 ( 0.005. Nitrogen gas, presaturated with water vapor, was continuously bubbled through the reaction solution during pH adjustment and crystallization experiments. The total calcium concentration in all experiments was 7.00 × 10-4 mol L-1 with a calcium/phosphate molar ratio of 1.67, so as to achieve a supersaturation with respect to HAP of σ ) 5.5 (defined in eq 1), as computed from mass balance, proton dissociation, electroneutrality, and equilibrium expressions involving calcium and phosphate species.13-15

σ ) (IP1/ν - KSO1/ν)/KSO1/ν ) S - 1

(1)

In eq 1, ν is the number of ions per formula unit of precipitating phase and IP and KSO are the ionic product and solubility product of HAP, respectively. The addition of the phosphonates at micromolar levels to the reaction solutions did not affect the established supersaturation. It should be noted that the reaction solutions were undersaturated with respect to other calcium phosphate phases such as octacalcium phosphate, OCP, and dicalcium phosphate dihydrate, DCPD. HAP crystal growth was initiated by the introduction of HAP seed slurry. The composition of the working solution was maintained constant by the simultaneous addition of two titrant solutions from coupled burets, one containing calcium and sodium chlorides and the other potassium dihydrogen phosphate, the phosphonate additive, and potassium hydroxide. The concentrations of the titrant solutions were calculated using eqs 2-6 to compensate for dilution effects caused by the use of multiple titrant burets as well as the consumption of ions accompanying crystal growth.

[phosphonate]t ) 2[phosphonate]rs

(6)

In eqs 2-6, the subscripts t and rs represent titrant and reaction supersaturated solutions, respectively. Ceff, the effective HAP concentration, is the number of moles of growing phase per liter of added titrant solutions. The rate of titrant addition, controlled by means of a glass electrode, was used to calculate the rate of crystal growth, normalized to initial seed surface area by eq 7

R ) (dV/dt)(Ceff/A)

(7)

where A is the total surface area of the added seed crystals.16 During the experiments, the constancy of concentrations was verified by analysis of filtered aliquots (0.22 µm Millipore filters) for calcium by atomic absorption spectroscopy (Perkin Elmer Atomic Absorption Spectrometer 3100) and for phosphate spectrophotometrically as the vanadomolybdate complex (Varian 210 Cary Spectrophotometer).17 In all cases, the concentrations remained constant throughout the precipitation reactions to within (3%. In order to investigate the uptake of phosphonate ions by HAP surfaces, an equilibrium adsorption experiment was performed in which 0.050 g of HAP in its saturated solution was equilibrated with a 2.0 × 10-6 mol L-1 solution of DETPMP. Phosphonate analysis of the solution performed using the Hach procedure18 indicated that, in the presence of the relatively high concentrations of phosphate ions (approximately 5.0 × 10-5 mol L-1), it was not possible to quantify phosphonate ion uptake. However, since the ζ potential of HAP surfaces was markedly influenced by the presence of phosphonates, this parameter was used as an indication of the extent of adsorption. The ζ potential of the HAP surfaces in the presence of phosphonate additives was measured using a Malvern Zetasizer IIc. HAP suspensions were prepared by introducing 30 mg of HAP crystals to 150 mL of 0.15 mol L-1 solution of sodium chloride. The pH of the suspension was adjusted in a nitrogen atmosphere to 7.40 ( 0.01 by the addition of hydrochloric acid solution (0.1 mol L-1). Following equilibration, the crystals were filtered, air dried, and resuspended in 150 mL of 0.15 mol L-1 sodium chloride. Prior to the measurements, the suspension was doped with the phosphonate additive and ultrasonicated. Kinetic studies and ζ potential measurements were performed for phosphonate concentrations ranging from 5.0 × 10-8 mol L-1 to 5.0 × 10-6 mol L-1 (Table 2).

Results

[CaCl2]t ) 2[CaCl2]rs + 5Ceff

(2)

[NaCl]t ) 2[NaCl]rs - 10Ceff

(3)

[KH2PO4]t ) 2[KH2PO4]rs + 3Ceff

(4)

[KOH]t ) 2[KOH]rs + 7Ceff

(5)

Constant composition growth experiments were first performed in pure supersaturated solutions of HAP and then in the presence of the phosphonates as a function of additive concentration. The results are presented in Table 2 and are plotted in Figures 1and 2. The former shows typical plots of titrant volume required to maintain the supersaturation, as functions of time and of phosphonate concentration. For comparison, a curve of titrant consumption for the growth of HAP in pure supersaturated solutions of the salt is included (“std” curve). All the rate curves showed a rapid titrants addition immediately

(12) Ebrahimpour, A. E. Ph.D. Thesis, SUNY Buffalo, 1990. (13) I, T.-P.; Nancollas, G. H.; Anal. Chem. 1972, 44, 1940. (14) Dalpi, M.; Karayianni, E.; Koutsoukos, P. G. J. Chem. Soc., Faraday Trans. 1993, 89, 965. (15) Amjad, Z.; Koutsoukos, P. G.; Nancollas, G. H. J. Colloid Interface Sci. 1984, 101, 250.

(16) Zhang, J.-W.; Nancollas, G. H.; In Mineral-Water Interface Geochemistry; Hochella, M. F., Jr., White, A. F., Eds.; Reviews in Mineralogy; Mineralogical Society of America: Washington, DC, 1990; Vol. 23, pp 365. (17) Tomson, M. B.; Barone, J. P.; Nancollas, G. H. At. Absorp. Newsl. 1977, 16, 117. (18) Hach, Cat. No. 21133-00, 21133-02.

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Table 2. Inhibition (%) of HAP Crystal Growth in the Presence of Phosphonates percent growth inhibition at the following phosphonate concentrations/10-6 mol L-1 phosphonate

0.05

AMP HEDP DHTPMP DETPMP EDTMP DETMP HDTMP

15

0.10 17 5

7 3a

[DETMP] ) 0.08 × mol L-1. a

65 4 24 10-6

0.25

30 48 47 mol

0.50

1.00

2.00

5.00

42 56 47 66 81 87 55

65 69 67 83

70 80 77 91 86 90 69b

82

L-1. b

[HDTMP] ) 1.50 × 10-6

linearity of the rate plots of HAP crystal growth (reflected by the constant slopes of volume versus time curves) was usually achieved 20-50 min after seed introduction to the supersaturated solution in experiments performed with or without phosphonate. It should be noted that at high concentrations of inhibitors HAP crystals appeared to grow only during the initial stage of the reaction. Additional studies were made of seed pretreatment. It is shown in Figure 2 that the use of pregrown seed, harvested at the end of a crystal growth experiment, to initiate a new crystal growth reaction resulted in a markedly reduced initial surge, suggesting that changes in surface properties may be important. As may be seen in Figure 2, similar decreases in the initial surges were observed both in the presence and absence of additives. However, the use of pregrown seed crystals did not influence the steady HAP growth rate (compare slopes of curves: A with B and A′ with B′ in Figure 2). The growth rate reduction in the presence of phosphonate additives can be expressed as a percent of inhibition, I, using eq 8.

I ) 100[(R0 - R)/R0]

Figure 1. HAP CC crystal growth in the presence of the phosphonates: pH, 7.40; IS, 0.15 mol L-1; 25 °C. Plots of volume of titrant added as a function of time (HEDP, DETPMP, and DHTPMP, 1 × 10-6 mol L-1; DETMP, 5 × 10-7 mol L-1).

(8)

where R and Ro are the growth rates in the presence and absence (“std”) of inhibitors, respectively. Values of I, given in Table 2, may be used to compare the inhibition effectiveness of the phosphonate additives. They illustrate the strong growth inhibition by DETPMP, DETMP, and EDTMP. It is quite well established that strong inhibitors of crystal growth, such as the phosphonates, act by blocking, through adsorption, active growth sites at the crystal surfaces.16,20 Commonly, inhibition kinetics data are interpreted in terms of a simple Langmuir adsorption isotherm model. Assuming that the adsorbed phosphonate ions occupy a fraction, θ, of the active growth sites, thereby preventing them from participating in the crystal growth reactions, the rates of crystal growth in their presence, R, can be written in terms of the unihibited rate R0, as in eq 9.

R ) R0(1 - θ)

(9)

Application of a simple Langmuir model leads to eq 10.

R0/R ) 1 + K[phosphonate]

Figure 2. HAP CC crystal growth curves using normal and pregrown seed crystals in pure HAP supersaturated solutions (curves A and B, respectively) and in the presence of 10-6 mol L-1 AMP (curves A′, B′, respectively): pH, 7.40; IS, 0.15 mol L-1; 25 °C. Plots of volume of titrant added as a function of time.

following the introduction of seed crystals. This frequently observed phenomenon, usually attributed to conditioning of the surface of the seed crystals in the supersaturated solution, may reflect ion exchange involving solution and surface cations and protons, or the removal of active growth sites on the seed crystals due to the rapid mineralization of high-energy sites.16,19 Significant reductions of the initial surges observed in the presence of the phosphonates suggest their adsorption at the higher energy sites on the HAP seed crystals, thus competing with other initial surface processes. It can also be seen in Figure 1 that the (19) Zieba, A.; Nancollas, G. H. J. Cryst. Growth 1994, 144, 311.

(10)

in which K is the adsorption affinity constant with units of liters per mole. Linear plots of R0/R as a function of phosphonate concentration are shown in Figure 3, for the different phosphonate additives. The slopes of the resulting linear plots (correlation coefficients, r, ranging from 0.95 to 0.99) yielding the values of K (L mol-1) are shown in Table 3. The K values calculated from that simple model reflect both the affinity of phosphonate molecules for the HAP surfaces and their ability to cover active growth sites. In Table 3, it can be seen that the K values are appreciable, ranging from 1 × 106 to 1 × 107 L mol-1. On the basis of these data, the order of inhibition in terms of decreasing effectiveness is DETMP > EDTMP > DETPMP > HEDP g DHTPMP > HDTMP g AMP. In the proposed inhibition model it is assumed that the phosphonates adsorb at growth sites on the HAP crystals. As may be seen in Figure 4, the HAP ζ potentials in the presence of all the phosphonates studied were markedly more negative than those in a pure saturated solution of HAP at the same pH. This clearly indicates an appreciable (20) Richardson, C. F. Ph.D. Thesis SUNY Buffalo, 1991.

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Zieba et al.

Figure 3. Langmuir adsorption isotherms. Plots of R0/R against phosphonate concentration: (3) EDTMP; (2) AMP; (]) HEDP; (b) DETPMP, (9) DETMP; ([) DHTPMP; (×) HDTMP. Table 3. HAP Adsorption Affinity Constants (K) of the Phosphonates (Eq 9) at pH ) 7.4 and T ) 25 °C phosphonate DHTPMP DETMP HEDP AMP EDTMP DETMP HDTMP a

affinity constant/ correlation literaturea values/ coefficient, R 106 L mol-1 106 L mol-1 1.7 5.9 1.9 1.2 8.5 11.2 1.3

0.99 0.99 0.99 0.95 0.96 0.98 0.98

1.335 0.625 1.805 1.405

pH ) 7.4; T ) 37 °C.

Figure 4. Changes in ζ potential of HAP crystal surfaces in the presence of phosphonates: (3) EDTMP; (2) AMP; (]) HEDP; (b) DETPMP; (9) DETMP; ([) DHTPMP; (×) HDTMP; pH, 7.4; IS, 0.15 mol L-1, 25 °C.

uptake of phosphonate anions at the positively charged HAP surfaces. It should be noted that although HEDP was not as effective an inhibitor as, for example, DETPMP or DETMP, it exhibited a stronger effect on the ζ potential of HAP surfaces than other phosphonates. As can be seen in Table 1, all the phosphonates, with the exception of HEDP, contained nitrogen atoms which would be positively charged at pH ) 7.4, and this might influence the net charge of the adsorbing phosphonate on the HAP crystal surfaces. Discussion It is generally accepted that the inhibition of scale formation is influenced by both the location of the adsorbed inhibitor at the crystal surface and the extent of chemical

bonding with the surface.6,16,20,21 Three types of crystal surface sites, having different binding energies, are available for the adsorbing inhibitor molecules. In order of decreasing bond strength they are kinks, steps, and terraces.16 In related studies22-24 calculation of the effective area of coverage for the adsorption of phosphonates on gypsum and barite suggested that the maximum crystallization inhibition may be achieved when less than 5% of the crystal surface is covered by adsorbate molecules. This suggests that the relatively small inhibitor molecules such as the phosphonates of the present work are preferentially adsorbed at the most active (kink) growth sites. The results of an attempted adsorption experiment, in which the phosphonate DETPMP was equilibrated with the HAP crystals, seemed to support this hypothesis, since it indicated that a very small amount of the additive was adsorbed. The marked differences in the initial CC surges (Vtit ) f(t)) obtained in HAP growth studies in the presence and absence of the phosphonate inhibitors also suggested that adsorption occurred at active kink sites. The adsorption of phosphonates at HAP crystal surfaces probably results from the binding of phosphonate anions to surface calcium ions. The initial bonding would be favored if longer range electrostatic forces between the crystal surface and the approaching phosphonate molecule were possible. However, the interaction may be enhanced if hydrogen bonding involving partially protonated phosphonate groups also participates in the surface binding.6,21,24,25 It has been recognized, for polycarboxylic inhibitors, that highly deprotonated, relatively acidic molecules, are less effective inhibitors of crystal growth than those which retain some degree of protonation. It has been suggested that the less acidic carboxylic acid groups form stronger complexes with alkaline earth cations typical of those at the crystal surface.21 Studies of various phosphonic acids, over a wide pH range, have shown that the presence of both deprotonated and protonated phosphonate groups leads to stronger interactions between adsorbing inhibitor molecules and crystal surfaces. Additionally, potentially electrodonating groups or atoms, such as hydroxyl, amino nitrogen, and oxygen atoms, in the inhibitor molecule, can also participate in the coordination to surface cations, enhancing both adsorption and, subsequently, crystal growth inhibition.1,2,6,21,25-27 If these electrodonating species are not already involved in calcium coordination, they may form hydrogen bonds with surface anions, thus shielding negatively charged growth sites.6,21 In contrast, increasing the number of hydrophobic groups in the inhibitor molecule, even to the extent of a single methylene group, may result in a decrease in the inhibitor effectiveness, as has been shown for both polyelectrolytes and phosphonate inhibitors.5,21 Such groups may also sterically hinder the interaction of active phosphonic and other functional electrodonating groups. It follows that several factors, such as the number of functional groups available for complexation with surface calcium ions, the degree of protonation of the phosphonic acid groups, hydrogen bond formation between phosphonate and the HAP surface, and the presence of hydrophobic groups in the inhibitor molecules, should be taken into (21) Weijnen, M. P. C.; Rosmalen, G. M. Desalination 1985, 54, 239. (22) Gill, J. S.; Nancollas, G. H. Corrosion 1981, 37, 120. (23) Leung, W. H.; Nancollas, G. H. J. Cryst. Growth 1978, 44, 163. (24) Leung, W. H.; Nancollas, G. H. J. Inorg. Nucl. Chem. 1978, 40, 1871. (25) Weijnen, M. P. C.; van Rosmalen, G. M. J. Cryst. Growth 1986, 79, 157. (26) van der Leeden, M. C.; van Rosmalen, G. M. Spec. Publ.sR. Soc. Chem. 1988, 67, 68-86. (27) Bryson, A.; Nancollas, G. H. Chem. Ind. 1965, 654.

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Table 4. Protonation Constants of EDTMP, HDTMP, and DETPMP phosphonate protonation constant

EDTMP31

EDTMP29

HDTMP29

DETPMP31

DETPMP7

log K1 log K2 log K3 log K4 log K5 log K6 log K7 log K8 log K9 log K10

10.6 9.22 7.43 6.63 6.18 5.05 2.72 1.46

10.6 10.48 9.27 7.39 5.63 3.8 not determined not determined

11.82 7.71 6.23 5.68 5.12 3.25 not determined not determined

12.04 10.1 8.15 7.17 6.38 5.5 4.45 2.8 not determined not determined

12.58 11.18 8.3 7.23 6.23 5.19 4.15 3.11 2.08 1.04

Figure 5. Complexation of calcium ion by EDTMP, as postulated in ref 28.

account in attempting to formulate a unifying model for HAP crystallization inhibition by phosphonates. Under the experimental conditions of the present work (phosphonate concentrations range from 5 × 10-8 mol L-1 to 5 × 10-6 mol L-1, temperature 25 °C, and pH 7.40), all the phosphonates dramatically reduced the rate of HAP crystal growth in the order DETMP > EDTMP > DETPMP > HEDP g DHTPMP > HDTMP g AMP. As was expected, potential octadentate and hexadentate molecules (DETMP, EDTMP, DETPMP) are more effective than the tetradentate (AMP) and tridentate (HEDP) ligands. The results clearly indicate the importance of the number of active groups available for surface complexations. It has been sugested that the coordination of free calcium ions by the phosphonate EDTMP in solution results in complexes (Figure 5) involving both phosphonic acid groups and amino nitrogen atoms.28 It is therefore likely that the nitrogen atoms participating in surface calcium coordination although alkaline earth metals do not readily bind to nitrogen donor atoms.29 On the other hand, DETMP, containing an ether oxygen atom, exhibits extremely high affinity for the HAP surfaces. The participation of ether oxygen atoms in calcium ion complexation has been established in a NMR study.27 It is likely that this will also markedly enhance DETMP adsorption. Moreover, this ether oxygen atom may be involved in hydrogen bonding to protonated surface groups, providing additional interactions with the crystal. The influence of different phosphonates containing ether oxygen atoms on the growth and morphology of barium sulphate crystals has also recently been documented.30 A comparison of the protonation constants for HDTMP and EDTMP28,29,31 (Table 4) may be used to discuss the observed differences between the affinity constants, KHDTMP and KEDTMP. Only the first protonation constant of EDTMP is lower than that of HDTMP; the remaining constants indicate the increased basicity of the functional (28) Westerback, S.; Rajan, K. S.; Martell, A. E. J. Am. Chem. Soc. 1965, 87, 2567. (29) Zaki, M. T. M.; Rizkalla, E. N. Talanta 1980, 27, 709. (30) Bromley, L. A.; Cottier, D.; Davey, R. J.; Dobbs, B.; Smith, S. Langmuir 1993, 9, 3594. (31) Stability Constants of MetalsIon Complexes, Section I: Organic Ligands; compiled by A. E. Martell; The Chemical Society: Burlington House, London, 1964.

groups of EDTMP as compared to those of HDTMP. Thus, the kinetic data, showing a greater effectiveness of EDTMP as compared with HDTMP, are in agreement with the results of the polycarboxylic inhibitor studies, in which the groups of higher basicity form stronger complexes with surface calcium ions. It should be noted that, in most of the phosphonates studied, the charge localized on the nitrogen (resulting from the deprotonation of the phosphonic acid groups) can be reduced by the formation of hydrogen bonds between two phosphonate groups and the imino group.29 The removal of one of these protons in the phosphonate HDTMP (which occurs relatively easily, as indicated by the second protonation constant, K2, in Table 4) probably leads to the formation of a stable cyclic structure.29 This will decrease the availability of the phosphonate sites for complexation with surface calcium ions. The lower inhibitory influence of the phosphonate HDTMP as compared to EDTMP can also be explained in terms of the steric difficulties in localizing the phosphonate groups of HDTMP around individual HAP surface calcium sites.5 Additional methylene groups create a higher hydrophobicity in the compound and, simultaneously, lower anionic charge density in the phosphonate HDTMP in comparison to EDTMP. This may also account for the observed differences in the KHDTMP and KEDTMP values. The difference in the number of methylene groups separating the nitrogen atoms of EDTMP and HDTMP is the same as that for DETPMP and DHTPMP. Thus, the arguments presented above may be used to explain the observed difference in the KDETPMP and KDHTPMP affinity constant values although the protonation constants for phosphonate DHTPMP have not been determined. The relation between the mineralization inhibition exhibited by DETPMP and EDTMP (KDETPMP < KEDTMP) is rather surprising. The protonation constants for DETPMP7,31 can not be used to explain its lower effectiveness as compared with EDTMP. The data in Table 4 show that the protonation of DETPMP is slightly higher than that of EDTMP. Moreover, the number of phosphonate groups, an approximate measure of the molecular activity, is greater for DETPMP than for EDTMP. This suggests that DETPMP might be more strongly bonded to the HAP crystal surfaces. However, when a complex, similar to that shown in Figure 5, is formed between surface calcium ions and DETPMP, the three remaining phosphonate groups (probably nonbonded) carry a relatively high negative charge which may impede the approach of other negatively charged DETPMP molecules. These repulsive forces can reduce the interaction between crystal surfaces and phosphonate DETPMP and, subsequently, lower the phosphonate inhibiting activity. Comparison between the affinities of AMP and HEDP phosphonate additives for the HAP surfaces indicates that the potentially tetradentate AMP ligand is less effective than the tridentate HEDP ligand. It has been previously

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reported6 that a very efficient inhibition is achieved in cases where the substituent at a carbon atom can easily form a strong hydrogen bond with lattice anions. Thus, the formation of hydrogen bonds involving HEDP hydroxyl groups and HAP surface anions may account for the relatively high activity of the phosphonate HEDP in reducing the crystallization rates. Data for the sensitivity of HAP crystallization to the presence of the phosphonates EDTMP, AMP, and HEDP reported by Amjad5 correlate well with the present results. Since the HAP surface affinity constants of these phosphonates were determined at 37 °C with pH ) 7.40 and ionic strength 0.1 mol L-1 (Table 3), it is possible to estimate the enthalpy change using the limited affinity constant data at the two temperatures. Such estimation yielded ∆H values of -10, -17, and -41 kJ mol-1 for HEDP, AMP, and EDTMP, respectively, and indicated that the adsorption of these phosphonates to HAP crystal surfaces is exothermic. It is interesting to note that kinetic studies of the growth of DCPD,32 calcium carbonate,33 and calcium oxalate34 in the presence of EDTMP, HEDP, and AMP gave quite different results. For example, the orders of phosphonate effectiveness were HEDP > HDTMP > EDTMP > AMP, EDTMP > HDTMP > AMP > HEDP, and EDTMP > (32) Amjad, Z. Can. J. Chem. 1988, 69, 2181.

Zieba et al.

HDTMP > HEDP for calcium carbonate, DCPD, and calcium oxalate monohydrate growth inhibition, respectively. These data support the suggestion, discussed above, that the degree of protonation of the inhibitors is important in determining their influence on crystal growth. Thus, HEDP, with proton ionization constants pK2 ) 2.54, pK3 ) 6.97, and pK4)11.41,35 shows the greatest inhibitor effectiveness with CaCO3 at pH = 8. Under these conditions, the additive molecule is negatively charged yet still retains a protonated site to optimize hydrogen bonding to carbonate oxygens at the crystal surface. In contrast, the surfaces of DCPD and COM, at lower pH, will be exposed to more extensively protonated HEDP molecules with resulting decreases in crystal growth inhibition. Acknowledgment. We thank SOCMA and NIDR (DE03223) for grants in support of this work. LA950842P (33) Nancollas, G. H.; Reddy, M. M. In Aqueous Environmental Chemistry of Metals; Rubin, A. J., Ed.; Ann Arbor Science: Ann Arbor, MI, 1974. (34) Rizkalla, E. N.; Mqawad, M. N. J. Chem Soc., Faraday Trans. 1 1984, 80, 1617. (35) Caroll, R. L.; Irani, R. R. Inorg. Chem. 1967, 6, 1994.