- Email: [email protected]
The crystallization of vaterite on fibrin
Journal of Crystal Growth 219 (2000) 277}282
The crystallization of vaterite on "brin J. Kanakis, E. Dalas* Department of Chemistry, Section Physical, Inorganic and Nuclear Chemistry, University of Patras, GR-26500 Patras, Greece Received 1 July 2000; accepted 11 July 2000 Communicated by M. Schieber
Abstract Fibrin, a protein endoproduct of blood coagulation was found to be a substrate favoring the deposition of vaterite crystals from stable supersaturated solutions at pH 8.5 and at 253C. The apparent order for the vaterite crystallization reaction was found to be 1.0$0.1, suggesting a surface di!usion-controlled mechanism. The crystallization was studied by the constant solution composition technique thus making it possible for relatively large amounts of the overgrowth phase to be formed and identi"ed exclusively as vaterite. Fibrin stabilizes this calcium carbonate polymorph, preventing the transformation to the thermodynamically more stable calcite. Analysis of the initial rates of the reaction as a function of the solution supersaturation, according to the classical nucleation theory, yielded a value of 21$1 mJ m\ for the surface energy of the growing phase and a three-ion cluster forming the critical nucleus. 2000 Elsevier Science B.V. All rights reserved. PACS: 81.10.Dn; 87.15.!v Keywords: Biomineralization; Vaterite; Crystallization; Fibrin
1. Introduction Calcium carbonate is the most abundant mineral formed by organisms followed by silica, calcium phosphate and others [1]. The formation of calcium carbonate polymorphs (calcite, aragonite, vaterite and calcium carbonate monohydrate) has been reported in a number of cases such as gallstones [2], pancreatic stones in both human and cattle [3,4] animal phyla, algae, in mollusc shells [5] and in human atherosclerotic aorta (9% calcium carbonate) [6]. It has been found that supersaturation as well as the organic matrix are critical
* Corresponding author. Tel.: #30-61-997-145; fax: #3061-997-118. E-mail address: [email protected] (E. Dalas).
in determining the calcium carbonate polymorph precipitating [7}10]. Thus, at high degrees of supersaturation, where spontaneous precipitation occurs, vaterite forms predominantly even at 253C. Since vaterite transforms easily to the more thermodynamically stable calcite when in contact with water [11,12], there are only a few data about it in the literature. Despite numerous and diverse studies, our knowledge of the molecular mechanism of biological calci"cation and the role of the organic matrix is still nuclear. Fibrin is the protein endoproduct of blood coagulation. It is generally formed from the plasma protein "brinogen by thrombin in the presence of Ca(II) ions. Fibrinogen is the only coagulable protein in the blood plasma of vertebrates and some arthropods. Its concentration in human plasma is 200}300 mg/100 ml. Fibrin is a very important
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 6 2 3 - 0
278
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
factor in the blood-clotting system. Structurally, the material is periodic and repeats every 230 As [13,14]. The aim of the present work is to investigate the possibility of calcium carbonate formation on "brin substrate by the constant composition technique [15,16], and attempting to answer the following questions: (a) does "brin substrate induce calcium carbonate formation? (b) do they a!ect the nature, the rate or the particle size of the calcium carbonate phase forming? The methodology of the constant solution composition was applied, because of the advantages the method presents in accurately assessing the rates of crystallization and the nature of the precipitating crystalline polymorph [17,18].
2. Experimental procedure All experiments were done at 25$0.13C, in a thermostated double-walled Pyrex vessel. Calcium carbonate supersaturated solutions of 0.2 dm total volume were prepared from calcium nitrate, sodium bicarbonate and potassium nitrate (Merck, pro analysi) stock solutions as described in detail elsewhere [19]. The conditions of the experiments selected in the present work were such that the supersaturated solutions employed were stable for periods up to 2 days, their stability veri"ed by the constancy of pH and calcium concentration. The arrangement was such that the air volume over the aqueous phase was kept at a minimum, so that the partial pressure of the carbon dioxide may be considered to be constant [16]. The pH in all experiments herein was adjusted at 8.5 by the addition of standard potassium hydroxide (Merck, titrisol) solution. The solution pH was measured by a glass/saturated calomel pair of electrodes (Metrom) standardized before and after each experiments by NBS bu!er solutions (pH 6.86 and 7.4 at 373C) [20]. Following veri"cation of the stability of the supersaturated solutions 40 mg of "brin (Sigma; washed, from borine blood) was added to the supersaturated solution. The "brin used was X-ray amorphous, and had a BET speci"c surface area (Perkin}Elmer Sorptometer, Model 212D) of 4.8 m g\. The powder was thoroughly dispersed
in the magnetically stirred supersaturated solutions with a Te#on-coated stirring bar at ca. 350 rpm. Following the addition of "brin the precipitation of the crystalline phase resulted in proton release which, when lowering solution pH by 0.003 pH units, triggered the addition of titrants, with the stoichiometry of calcium carbonate from two mechanically coupled burettes of an appropriately modi"ed pH stat (Metrohm, 614). The concentration of the titrant in the two burettes was calculated as described in detail elsewhere [18]. Random sampling during the course of reaction veri"ed that the solution supersaturation was kept constant [16]. Employing a constant solution composition has the advantage of determining the reaction rates very accurately, since the initial conditions are kept constant for a large part of the precipitation reaction, and also the possibility to follow the growth of the overgrowing phase, su$ciently large to be characterized by physicochemical methods. The samples withdrawn during the reaction were "ltered through membrane "lters (Gelman, 0.1 lm); the "ltrates were analyzed for calcium by atomic absorption spectroscopy (Varian 1200) and the solid residues by powder X-ray di!raction (Phillips PW 1830/1840 using Cu K a radiation Ni "lter), scanning electron microscopy (Jeol GSM 5200) and FT-IR spectroscopy (Perkin}Elmer 16-PC FT-IR using KBr pellets) and thermal analysis, DSC, (Du Pond 910). The rate of calcium carbonate formation was taken from the plots of titrant addition as a function of time, normalized for the total surface area of the "brin used as substrate.
3. Results and discussion The experimental conditions are summarized in Table 1. The solution speciation in all the experiments was calculated from the proton dissociation and ion-pair formation constants for calcium and carbonate, the mass balance and electroneutrality conditions by successive approximations for the ionic strength [21]. The driving force for the crystal growth of the calcium carbonate polymorphs is the change in Gibbs free energy, *G, for the transfer from the supersaturated solutions to
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
279
Table 1 Crystal growth of vaterite at sustained supersaturation, 253C, pH 8.5 total calcium (Ca )"total carbonate (C ) Exp. No
Ca (10\ mol dm\)
Ionic strength (10\ mol dm\)
*G (kJ mol\)
*G (kJ mol\)
*G (kJ mol\)
*G
(kJ mol\)
R (10\ mol min\ m\)
f3 f6 f7 f9 f14
3.0 2.75 2.5 2.25 2.0
7.2 6.6 6.0 5.4 4.8
!3.08 !2.90 !2.72 !2.51 !2.27
!2.34 !2.16 !1.97 !1.76 !1.53
!1.46 !1.30 !1.10 !0.89 !0.65
!1.40 !1.20 !1.04 !0.83 !0.60
5.7 4.1 3.2 2.4 2.1
Table 2 Thermodynamic solubility products of the calcium carbonate polymorphs Polymorph
K
Ref.
Calcite Aragonite Vaterite Calcium carbonate mono-hydrate
3.311;10\ 4.613;10\ 1.222;10\ 1.279;10\
[37] [37] [37] [38,39]
equilibrium R ¹ IP (1) *G "! ln V . V K 2 V In Eq. (1) IP is the activity product (Ca>)(CO\), V K the thermodynamic solubility product of the V polymorph x (see Table 2), R the gas constant and ¹ the absolute temperature. The supersaturation ratio with respect to each polymorph, X , is de"ned V as IP X " V (2) V K V and the relative solution supersaturation, S , is V de"ned by (IP ) !(K ) V S " V "X !1. (3) V V (K ) V The solid phases were found to be well-formed vaterite from: (a) the examination of the powder X-ray di!raction spectra (Fig. 1) [8,22,23], the spectrum (Fig. 1b) exhibit the characteristic re#ection for vaterite h k l: 1 1 0, 1 1 1, 1 1 2, 3 0 0, 3 0 2, 1 1 4, 2 2 2; (b) FT-IR spectroscopy as shown in Fig. 2 (exhibit the characteristic absorption for vaterite at
Fig. 1. Scanning electron micrographs: (a) "brin substrate; (b) vaterite crystals on "brin, Ca "3;10\ M, pH"8.5, 253C.
1480, 1070, 873, 848 and 745 cm\) [8] and (c) SEM photographs (Fig. 3). The absence of hydrated polymorphs was also ruled out by di!erential scanning calorimetry.
280
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
Fig. 2. Scanning electron microscopy of precipitated vaterite crystals, transformed to calcite during the precipitation reaction, Ca "4.75;10\ M, pH"8.5, 253C.
the curves of titrant addition (re#ecting the amount of solid precipitating) at time zero. This is justi"ed by the fact that the amount precipitated continuously increased, thus changing the total surface area. Changes in the stirring rate (between 60 and 350 rpm) had no e!ect on the measured crystallization rates. It may, therefore, be suggested that vaterite overgrowth was induced by the polymer matrix by heterogeneous nucleation [24,25]. Similar considerations were obtained for the mineralization of other polymer matrices [8}11,18,26}32]. Also, the "brin matrix stabilize the vaterite polymorph, preventing the transformation of vaterite to calcite (Fig. 3b). It was found that the thermodynamically unstable vaterite transforms into the stable calcite at pH 8.5, 253C even at low supersaturation. It was suggested that the transformation takes place through dissolution of vaterite, preferably of the small crystals followed by the crystallization of calcite [11,12]. This procedure is shown by SEM photograph in Fig. 4 at Ca " 4.75;10\ M, pH 8.5 and 253C. The transformation taking place during the precipitation reaction. The size of the critical nucleus may be estimated from the slope of plots of the logarithm of initial rates, R, as a function of the logarithm of the initial free calcium concentration [33]. d ln R "nH. d ln[Ca>]
(4)
Fig. 3. Powder X-ray di!raction spectra of: (a) "brin; (b) vaterite grown on "brin.
The reproducibility of the measured rates of crystallization was $2% (an average of "ve experiments). As can be seen from Table 1 the subsequent rates of crystallization were found to increase with supersaturation. Doubling or tripling the amounts of "brin introduced in the supersaturated solution had no e!ect on the initial rates normalized per unit surface area of the substrate. It should be noted that the rates we have used in the kinetic analysis of our experiments were obtained from the slopes of
Fig. 4. FT-IR spectra of: (a) "brin; (b) vaterite grown on "brin.
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
Fig. 5. Initial rate of vaterite formation on "brin substrate as a function of the initial calcium concentration in solution.
A typical plot is shown in Fig. 5, from which a value n*"3 was estimated. It should be noted that the estimate of ions forming the critical nucleus is not very vigorous as there is a lack of agreement on the nature, an composition of what is called `critical nucleusa. The number obtained herein for n* is given for sake of comparison with similar kinetic studies. Using nucleation rate equations derived from the classical homogeneous nucleation theory, the interfacial energy, p, for vaterite overgrowth on "brin was calculated,
b< p f (h)
R"X exp ! . (5) k¹(ln S ) In Eq. (5) < is the molecular volume (3.129;
10\ m) of the precipitated vaterite, p the interfacial emerge, S the supersaturation ratio with respect to vaterite, f (h) a factor expressing the compatibility between the salt formed and the substrate, (2#cos h)(1!cos h) f (h)" . 4 X is a constant and b is the shape factor (b"16.76, assuming spherical shape nuclei). From the slope of the line (ln R against 1/(ln S ) as shown in Fig. 6, a value of 21$1 mJ m\ was obtained for p f (h) of the growing vaterite. Similar values were obtained for the overgrowth of vaterite on foreign substrates as shown in Table 3. The theoretical
281
Fig. 6. Initial rate of the deposition of vaterite on "brin as a function of the solution supersaturation according to the classical nucleation theory (Eq. (5)).
Table 3 Surface energy, p, for vaterite formation Substrate
p/mJ m\
Ref.
Cholesterol Carboxylated copolymer Fibrin
11 24 21
8 39 This work
value for the surface energy computed for homogeneous nucleation for vaterite is p"90 mJ m\ [34,35]. The theoretical high value pertains to homogeneous conditions in contrast to our experiments, where the new phase is grown on a foreign substrate with a de"nite number of active growth sites [35,36]. Logarithmic plots of the rates of vaterite formation R on "brin substrate as a function of the relative solution supersaturation, S , according to Eq. (7) R"kSL
(7)
yielded a straight line from the slope of which the apparent order n of the reaction was calculated (n"1.0$0.1). Such a plot is shown in Fig. 7. The same value for the slope n was obtained for the overgrowth of vaterite on cholesterol [8], indicative of a surface di!usion control mechanism.
282
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
Fig. 7. Rate of crystallization of vaterite on "brin as a function of the relative solution supersaturation.
4. Conclusions In conclusion, it can be said that "brin is a substrate on which vaterite may nucleate and subsequently grow. Moreover, "brin stabilizes the vaterite phase preventing the transformation to the thermodynamically more stable calcite. The number of ions forming the critical nucleus was found to be n*"3 and a surface energy of 21$1 mJ m\ was estimated form kinetics data, a value that is rather low for sparingly soluble inorganic salts. The apparent growth order was found to be 1.0$0.1, typical for surface di!usion controlled growth process. References [1] C.S. Sikes, A.P. Wheeler, Chemtech (1988) 620. [2] H.S. Kanfman, T.H. Magnnson, H.A. Pitt, P. Frasca, K.D. Lillemoe, Hepatology 19 (1994) 1124. [3] H.J. Verine, Bull. Comp. Pathol. 3 (1973) 5. [4] E.W. Moore, H.J. Verine, J. Am. Phys. Soc. G707 (1987) 5. [5] M.A. Grenshaw, in: G.H. Nancollas (Ed.), Biological Mineralization and Demineralization, Springer, Berlin, 1982, pp. 243}257. [6] R.L. Levy, F.J. Schoen, J.T. Levy, A.C. Nelson, S.L. Howard, L.J. Oshry, Am. J. Pathol. 113 (1983) 142. [7] A.G. Xyla, J. Microyanidis, P.G. Koutsoukos, J. Colloid Int. Sci. 153 (1992) 537.
[8] E. Dalas, P.G. Koutsoukos, J. Colloid Int. Sci. 127 (1989) 273. [9] E. Dalas, J. Kallitsis, P.G. Koutsoukos, J. Crystal Growth 89 (1988) 287. [10] F. Manoli, E. Dalas, J. Crystal Growth 204 (1999) 369. [11] N. Spanos, P.G. Koutsoukos, J. Crystal Growth 191 (1998) 783. [12] N. Spanos, P.G. Koutsoukos, Phys. Chem. B 102 (1998) 6679. [13] D.E. Metzler, Biochemistry, Academic Press, London, 1977. [14] M. Brewer, T. Scott, Concise Encyclopedia of Biochemistry, de Gruyter, Berlin, 1983. [15] M.B. Tomson, G.H. Nancollas, Science 200 (1977) 1059. [16] T.F. Kazmierczak, M.B. Tomson, G.H. Nancollas, J. Phys. Chem. 86 (1982) 103. [17] P.G. Koutsoukos, Z. Amjad, M.B. Tomson, G.H. Nancollas, J. Am. Chem. Soc. 102 (1980) 1553. [18] F. Manoli, S. Koutsopoulos, E. Dalas, J. Crystal Growth 182 (1997) 116. [19] E. Giannimaras, P.G. Koutsoukos, J. Colloid Int. Sci. 116 (1987) 423. [20] R.G. Baters, Determination of pH, Wiley, New York, 1973. [21] G.H. Nancollas, Interactions in Electrolyte Solutions, Elsevier, Amsterdam, 1966. [22] ASTM card "le No 25-127. [23] JCPDS card "le No 13-0192. [24] N. Watable, Prog. Crystal Growth Characterization 4 (1981) 182. [25] J. Nyvlt, P. Sohnel, M. Matuchova, M. Broul, The Kinetics of Industrial Crystallization, Elsevier, Amsterdam, 1985, pp. 68, 284. [26] E. Dalas, P.G. Koutsoukos, Langmuir 4 (1988) 907. [27] P.G. Koutsoukos, G.H. Nancollas, Colloids Surf. 28 (1987) 95. [28] E. Dalas, J. Chem. Soc. Faraday Trans. 17 (1990) 86. [29] P.G. Koutsoukos, G.H. Nancollas, Colloids Surf. 17 (1986) 81. [30] S. Koutsopoulos, P.G. Paschalakis, E. Dalas, Langmuir 10 (1994) 2423. [31] E. Dalas, J. Mater. Chem 11 (1992) 473. [32] E. Dalas, J. Mater. Sci. Lett. 11 (1992) 1408. [33] A.E. Nielsen, Kinetics of Precipitation, Pergamon, Oxford, 1964, p. 18. [34] D. Kralz, L. Brecevic, A.E. Nielsen, J. Crystal Growth 104 (1990) 793. [35] A.E. Nielsen, J. Crystal Growth 67 (1984) 289. [36] A.E. Nielsen, Pure Appl. Chem . 53 (1981) 2025. [37] N.L. Plummer, T.M.L. Wigley, D.C. Parkhurst, Am. J. Sci. 278 (1978) 179. [38] H. Hull, A.G. Turnbull, Geochim. Cosmoch. in Acta 37 (1973) 685. [39] E. Dalas, P. Klepetsanis, P.G. Koutsoukos, Langmuir 15 (1999) 8322.
The crystallization of vaterite on "brin J. Kanakis, E. Dalas* Department of Chemistry, Section Physical, Inorganic and Nuclear Chemistry, University of Patras, GR-26500 Patras, Greece Received 1 July 2000; accepted 11 July 2000 Communicated by M. Schieber
Abstract Fibrin, a protein endoproduct of blood coagulation was found to be a substrate favoring the deposition of vaterite crystals from stable supersaturated solutions at pH 8.5 and at 253C. The apparent order for the vaterite crystallization reaction was found to be 1.0$0.1, suggesting a surface di!usion-controlled mechanism. The crystallization was studied by the constant solution composition technique thus making it possible for relatively large amounts of the overgrowth phase to be formed and identi"ed exclusively as vaterite. Fibrin stabilizes this calcium carbonate polymorph, preventing the transformation to the thermodynamically more stable calcite. Analysis of the initial rates of the reaction as a function of the solution supersaturation, according to the classical nucleation theory, yielded a value of 21$1 mJ m\ for the surface energy of the growing phase and a three-ion cluster forming the critical nucleus. 2000 Elsevier Science B.V. All rights reserved. PACS: 81.10.Dn; 87.15.!v Keywords: Biomineralization; Vaterite; Crystallization; Fibrin
1. Introduction Calcium carbonate is the most abundant mineral formed by organisms followed by silica, calcium phosphate and others [1]. The formation of calcium carbonate polymorphs (calcite, aragonite, vaterite and calcium carbonate monohydrate) has been reported in a number of cases such as gallstones [2], pancreatic stones in both human and cattle [3,4] animal phyla, algae, in mollusc shells [5] and in human atherosclerotic aorta (9% calcium carbonate) [6]. It has been found that supersaturation as well as the organic matrix are critical
* Corresponding author. Tel.: #30-61-997-145; fax: #3061-997-118. E-mail address: [email protected] (E. Dalas).
in determining the calcium carbonate polymorph precipitating [7}10]. Thus, at high degrees of supersaturation, where spontaneous precipitation occurs, vaterite forms predominantly even at 253C. Since vaterite transforms easily to the more thermodynamically stable calcite when in contact with water [11,12], there are only a few data about it in the literature. Despite numerous and diverse studies, our knowledge of the molecular mechanism of biological calci"cation and the role of the organic matrix is still nuclear. Fibrin is the protein endoproduct of blood coagulation. It is generally formed from the plasma protein "brinogen by thrombin in the presence of Ca(II) ions. Fibrinogen is the only coagulable protein in the blood plasma of vertebrates and some arthropods. Its concentration in human plasma is 200}300 mg/100 ml. Fibrin is a very important
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 6 2 3 - 0
278
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
factor in the blood-clotting system. Structurally, the material is periodic and repeats every 230 As [13,14]. The aim of the present work is to investigate the possibility of calcium carbonate formation on "brin substrate by the constant composition technique [15,16], and attempting to answer the following questions: (a) does "brin substrate induce calcium carbonate formation? (b) do they a!ect the nature, the rate or the particle size of the calcium carbonate phase forming? The methodology of the constant solution composition was applied, because of the advantages the method presents in accurately assessing the rates of crystallization and the nature of the precipitating crystalline polymorph [17,18].
2. Experimental procedure All experiments were done at 25$0.13C, in a thermostated double-walled Pyrex vessel. Calcium carbonate supersaturated solutions of 0.2 dm total volume were prepared from calcium nitrate, sodium bicarbonate and potassium nitrate (Merck, pro analysi) stock solutions as described in detail elsewhere [19]. The conditions of the experiments selected in the present work were such that the supersaturated solutions employed were stable for periods up to 2 days, their stability veri"ed by the constancy of pH and calcium concentration. The arrangement was such that the air volume over the aqueous phase was kept at a minimum, so that the partial pressure of the carbon dioxide may be considered to be constant [16]. The pH in all experiments herein was adjusted at 8.5 by the addition of standard potassium hydroxide (Merck, titrisol) solution. The solution pH was measured by a glass/saturated calomel pair of electrodes (Metrom) standardized before and after each experiments by NBS bu!er solutions (pH 6.86 and 7.4 at 373C) [20]. Following veri"cation of the stability of the supersaturated solutions 40 mg of "brin (Sigma; washed, from borine blood) was added to the supersaturated solution. The "brin used was X-ray amorphous, and had a BET speci"c surface area (Perkin}Elmer Sorptometer, Model 212D) of 4.8 m g\. The powder was thoroughly dispersed
in the magnetically stirred supersaturated solutions with a Te#on-coated stirring bar at ca. 350 rpm. Following the addition of "brin the precipitation of the crystalline phase resulted in proton release which, when lowering solution pH by 0.003 pH units, triggered the addition of titrants, with the stoichiometry of calcium carbonate from two mechanically coupled burettes of an appropriately modi"ed pH stat (Metrohm, 614). The concentration of the titrant in the two burettes was calculated as described in detail elsewhere [18]. Random sampling during the course of reaction veri"ed that the solution supersaturation was kept constant [16]. Employing a constant solution composition has the advantage of determining the reaction rates very accurately, since the initial conditions are kept constant for a large part of the precipitation reaction, and also the possibility to follow the growth of the overgrowing phase, su$ciently large to be characterized by physicochemical methods. The samples withdrawn during the reaction were "ltered through membrane "lters (Gelman, 0.1 lm); the "ltrates were analyzed for calcium by atomic absorption spectroscopy (Varian 1200) and the solid residues by powder X-ray di!raction (Phillips PW 1830/1840 using Cu K a radiation Ni "lter), scanning electron microscopy (Jeol GSM 5200) and FT-IR spectroscopy (Perkin}Elmer 16-PC FT-IR using KBr pellets) and thermal analysis, DSC, (Du Pond 910). The rate of calcium carbonate formation was taken from the plots of titrant addition as a function of time, normalized for the total surface area of the "brin used as substrate.
3. Results and discussion The experimental conditions are summarized in Table 1. The solution speciation in all the experiments was calculated from the proton dissociation and ion-pair formation constants for calcium and carbonate, the mass balance and electroneutrality conditions by successive approximations for the ionic strength [21]. The driving force for the crystal growth of the calcium carbonate polymorphs is the change in Gibbs free energy, *G, for the transfer from the supersaturated solutions to
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
279
Table 1 Crystal growth of vaterite at sustained supersaturation, 253C, pH 8.5 total calcium (Ca )"total carbonate (C ) Exp. No
Ca (10\ mol dm\)
Ionic strength (10\ mol dm\)
*G (kJ mol\)
*G (kJ mol\)
*G (kJ mol\)
*G
(kJ mol\)
R (10\ mol min\ m\)
f3 f6 f7 f9 f14
3.0 2.75 2.5 2.25 2.0
7.2 6.6 6.0 5.4 4.8
!3.08 !2.90 !2.72 !2.51 !2.27
!2.34 !2.16 !1.97 !1.76 !1.53
!1.46 !1.30 !1.10 !0.89 !0.65
!1.40 !1.20 !1.04 !0.83 !0.60
5.7 4.1 3.2 2.4 2.1
Table 2 Thermodynamic solubility products of the calcium carbonate polymorphs Polymorph
K
Ref.
Calcite Aragonite Vaterite Calcium carbonate mono-hydrate
3.311;10\ 4.613;10\ 1.222;10\ 1.279;10\
[37] [37] [37] [38,39]
equilibrium R ¹ IP (1) *G "! ln V . V K 2 V In Eq. (1) IP is the activity product (Ca>)(CO\), V K the thermodynamic solubility product of the V polymorph x (see Table 2), R the gas constant and ¹ the absolute temperature. The supersaturation ratio with respect to each polymorph, X , is de"ned V as IP X " V (2) V K V and the relative solution supersaturation, S , is V de"ned by (IP ) !(K ) V S " V "X !1. (3) V V (K ) V The solid phases were found to be well-formed vaterite from: (a) the examination of the powder X-ray di!raction spectra (Fig. 1) [8,22,23], the spectrum (Fig. 1b) exhibit the characteristic re#ection for vaterite h k l: 1 1 0, 1 1 1, 1 1 2, 3 0 0, 3 0 2, 1 1 4, 2 2 2; (b) FT-IR spectroscopy as shown in Fig. 2 (exhibit the characteristic absorption for vaterite at
Fig. 1. Scanning electron micrographs: (a) "brin substrate; (b) vaterite crystals on "brin, Ca "3;10\ M, pH"8.5, 253C.
1480, 1070, 873, 848 and 745 cm\) [8] and (c) SEM photographs (Fig. 3). The absence of hydrated polymorphs was also ruled out by di!erential scanning calorimetry.
280
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
Fig. 2. Scanning electron microscopy of precipitated vaterite crystals, transformed to calcite during the precipitation reaction, Ca "4.75;10\ M, pH"8.5, 253C.
the curves of titrant addition (re#ecting the amount of solid precipitating) at time zero. This is justi"ed by the fact that the amount precipitated continuously increased, thus changing the total surface area. Changes in the stirring rate (between 60 and 350 rpm) had no e!ect on the measured crystallization rates. It may, therefore, be suggested that vaterite overgrowth was induced by the polymer matrix by heterogeneous nucleation [24,25]. Similar considerations were obtained for the mineralization of other polymer matrices [8}11,18,26}32]. Also, the "brin matrix stabilize the vaterite polymorph, preventing the transformation of vaterite to calcite (Fig. 3b). It was found that the thermodynamically unstable vaterite transforms into the stable calcite at pH 8.5, 253C even at low supersaturation. It was suggested that the transformation takes place through dissolution of vaterite, preferably of the small crystals followed by the crystallization of calcite [11,12]. This procedure is shown by SEM photograph in Fig. 4 at Ca " 4.75;10\ M, pH 8.5 and 253C. The transformation taking place during the precipitation reaction. The size of the critical nucleus may be estimated from the slope of plots of the logarithm of initial rates, R, as a function of the logarithm of the initial free calcium concentration [33]. d ln R "nH. d ln[Ca>]
(4)
Fig. 3. Powder X-ray di!raction spectra of: (a) "brin; (b) vaterite grown on "brin.
The reproducibility of the measured rates of crystallization was $2% (an average of "ve experiments). As can be seen from Table 1 the subsequent rates of crystallization were found to increase with supersaturation. Doubling or tripling the amounts of "brin introduced in the supersaturated solution had no e!ect on the initial rates normalized per unit surface area of the substrate. It should be noted that the rates we have used in the kinetic analysis of our experiments were obtained from the slopes of
Fig. 4. FT-IR spectra of: (a) "brin; (b) vaterite grown on "brin.
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
Fig. 5. Initial rate of vaterite formation on "brin substrate as a function of the initial calcium concentration in solution.
A typical plot is shown in Fig. 5, from which a value n*"3 was estimated. It should be noted that the estimate of ions forming the critical nucleus is not very vigorous as there is a lack of agreement on the nature, an composition of what is called `critical nucleusa. The number obtained herein for n* is given for sake of comparison with similar kinetic studies. Using nucleation rate equations derived from the classical homogeneous nucleation theory, the interfacial energy, p, for vaterite overgrowth on "brin was calculated,
b< p f (h)
R"X exp ! . (5) k¹(ln S ) In Eq. (5) < is the molecular volume (3.129;
10\ m) of the precipitated vaterite, p the interfacial emerge, S the supersaturation ratio with respect to vaterite, f (h) a factor expressing the compatibility between the salt formed and the substrate, (2#cos h)(1!cos h) f (h)" . 4 X is a constant and b is the shape factor (b"16.76, assuming spherical shape nuclei). From the slope of the line (ln R against 1/(ln S ) as shown in Fig. 6, a value of 21$1 mJ m\ was obtained for p f (h) of the growing vaterite. Similar values were obtained for the overgrowth of vaterite on foreign substrates as shown in Table 3. The theoretical
281
Fig. 6. Initial rate of the deposition of vaterite on "brin as a function of the solution supersaturation according to the classical nucleation theory (Eq. (5)).
Table 3 Surface energy, p, for vaterite formation Substrate
p/mJ m\
Ref.
Cholesterol Carboxylated copolymer Fibrin
11 24 21
8 39 This work
value for the surface energy computed for homogeneous nucleation for vaterite is p"90 mJ m\ [34,35]. The theoretical high value pertains to homogeneous conditions in contrast to our experiments, where the new phase is grown on a foreign substrate with a de"nite number of active growth sites [35,36]. Logarithmic plots of the rates of vaterite formation R on "brin substrate as a function of the relative solution supersaturation, S , according to Eq. (7) R"kSL
(7)
yielded a straight line from the slope of which the apparent order n of the reaction was calculated (n"1.0$0.1). Such a plot is shown in Fig. 7. The same value for the slope n was obtained for the overgrowth of vaterite on cholesterol [8], indicative of a surface di!usion control mechanism.
282
J. Kanakis, E. Dalas / Journal of Crystal Growth 219 (2000) 277}282
Fig. 7. Rate of crystallization of vaterite on "brin as a function of the relative solution supersaturation.
4. Conclusions In conclusion, it can be said that "brin is a substrate on which vaterite may nucleate and subsequently grow. Moreover, "brin stabilizes the vaterite phase preventing the transformation to the thermodynamically more stable calcite. The number of ions forming the critical nucleus was found to be n*"3 and a surface energy of 21$1 mJ m\ was estimated form kinetics data, a value that is rather low for sparingly soluble inorganic salts. The apparent growth order was found to be 1.0$0.1, typical for surface di!usion controlled growth process. References [1] C.S. Sikes, A.P. Wheeler, Chemtech (1988) 620. [2] H.S. Kanfman, T.H. Magnnson, H.A. Pitt, P. Frasca, K.D. Lillemoe, Hepatology 19 (1994) 1124. [3] H.J. Verine, Bull. Comp. Pathol. 3 (1973) 5. [4] E.W. Moore, H.J. Verine, J. Am. Phys. Soc. G707 (1987) 5. [5] M.A. Grenshaw, in: G.H. Nancollas (Ed.), Biological Mineralization and Demineralization, Springer, Berlin, 1982, pp. 243}257. [6] R.L. Levy, F.J. Schoen, J.T. Levy, A.C. Nelson, S.L. Howard, L.J. Oshry, Am. J. Pathol. 113 (1983) 142. [7] A.G. Xyla, J. Microyanidis, P.G. Koutsoukos, J. Colloid Int. Sci. 153 (1992) 537.
[8] E. Dalas, P.G. Koutsoukos, J. Colloid Int. Sci. 127 (1989) 273. [9] E. Dalas, J. Kallitsis, P.G. Koutsoukos, J. Crystal Growth 89 (1988) 287. [10] F. Manoli, E. Dalas, J. Crystal Growth 204 (1999) 369. [11] N. Spanos, P.G. Koutsoukos, J. Crystal Growth 191 (1998) 783. [12] N. Spanos, P.G. Koutsoukos, Phys. Chem. B 102 (1998) 6679. [13] D.E. Metzler, Biochemistry, Academic Press, London, 1977. [14] M. Brewer, T. Scott, Concise Encyclopedia of Biochemistry, de Gruyter, Berlin, 1983. [15] M.B. Tomson, G.H. Nancollas, Science 200 (1977) 1059. [16] T.F. Kazmierczak, M.B. Tomson, G.H. Nancollas, J. Phys. Chem. 86 (1982) 103. [17] P.G. Koutsoukos, Z. Amjad, M.B. Tomson, G.H. Nancollas, J. Am. Chem. Soc. 102 (1980) 1553. [18] F. Manoli, S. Koutsopoulos, E. Dalas, J. Crystal Growth 182 (1997) 116. [19] E. Giannimaras, P.G. Koutsoukos, J. Colloid Int. Sci. 116 (1987) 423. [20] R.G. Baters, Determination of pH, Wiley, New York, 1973. [21] G.H. Nancollas, Interactions in Electrolyte Solutions, Elsevier, Amsterdam, 1966. [22] ASTM card "le No 25-127. [23] JCPDS card "le No 13-0192. [24] N. Watable, Prog. Crystal Growth Characterization 4 (1981) 182. [25] J. Nyvlt, P. Sohnel, M. Matuchova, M. Broul, The Kinetics of Industrial Crystallization, Elsevier, Amsterdam, 1985, pp. 68, 284. [26] E. Dalas, P.G. Koutsoukos, Langmuir 4 (1988) 907. [27] P.G. Koutsoukos, G.H. Nancollas, Colloids Surf. 28 (1987) 95. [28] E. Dalas, J. Chem. Soc. Faraday Trans. 17 (1990) 86. [29] P.G. Koutsoukos, G.H. Nancollas, Colloids Surf. 17 (1986) 81. [30] S. Koutsopoulos, P.G. Paschalakis, E. Dalas, Langmuir 10 (1994) 2423. [31] E. Dalas, J. Mater. Chem 11 (1992) 473. [32] E. Dalas, J. Mater. Sci. Lett. 11 (1992) 1408. [33] A.E. Nielsen, Kinetics of Precipitation, Pergamon, Oxford, 1964, p. 18. [34] D. Kralz, L. Brecevic, A.E. Nielsen, J. Crystal Growth 104 (1990) 793. [35] A.E. Nielsen, J. Crystal Growth 67 (1984) 289. [36] A.E. Nielsen, Pure Appl. Chem . 53 (1981) 2025. [37] N.L. Plummer, T.M.L. Wigley, D.C. Parkhurst, Am. J. Sci. 278 (1978) 179. [38] H. Hull, A.G. Turnbull, Geochim. Cosmoch. in Acta 37 (1973) 685. [39] E. Dalas, P. Klepetsanis, P.G. Koutsoukos, Langmuir 15 (1999) 8322.