Nature identification and morphology characterization of anion-exchange membrane fouling during conventional electrodialysis

The aim of this work was to study the effect on the fouling of anion-exchange membranes (AEM) of (1) the pH value of the concentrate solution and (2) the composition in calcium, carbonate, and protein of the diluate solution to be treated by conventional electrodialysis. It appeared that after demineralization of solutions containing CaCl(2) using a concentrate solution maintained at a pH value of 7 or 12, mineral fouling appeared on the AEM surface in contact with the concentrate. The mineral deposits presented a cylindrical filament shape for conditions with a concentrate solution pH value of 7, while, for a pH value of 12, the mineral deposit had a crumbly and spongy texture formed by irregular aggregates. The nature of the fouling was identified as a calcium phosphate with or without calcium hydroxide. In addition, gel-like protein fouling was detected on the AEM surface in contact with the diluate after demineralization procedures using a concentrate pH value of 2 or 7, regardless of the mineral composition of the diluate.     

Effect of concentrate solution pH and mineral composition of a whey protein diluate solution on membrane fouling formation during conventional electrodialysis

The aim of this work was to study the effect of the concentrate solution pH and the composition in calcium, carbonate and protein of the diluate solution to be treated by conventional electrodialysis on the fouling of ion-exchange membranes. Conductivity, system resistance, pH of the diluate and cation migration were monitored to follow the evolution of the demineralization. Total cation migration was similar for all conditions although different forms of fouling were identified after three consecutive 100 min electrodialysis treatments. The nature of fouling and the membrane surface fouled depended on the concentrate pH value, the diluate mineral composition and the intrinsic composition of the whey isolate. Once conditions leading to membrane fouling were identified, an alternative configuration for our electrodialysis stack is proposed to prevent fouling onset.     

Multistep mineral fouling growth on a cation-exchange membrane ruled by gradual sieving effects of magnesium and carbonate ions and its delay by pulsed modes of electrodialysis

The aim of this study was to reveal the mechanisms ruling a fouling growth on both sides of a CMX-SB cation-exchange membrane (CEM), run after run during three consecutive electrodialysis (ED) treatments. A model solution containing a high magnesium/calcium ratio (2/5) was demineralized under two different pulsed electric field (PEF) on-duty ratios and dc current. The results showed a series of mechanisms ruling a multilayer mineral fouling growth and its delay by PEFs. The nature of the fouling layer, during a first run, depended on the diluate pH-value evolutions and the ion migration rates through the membrane. A subsequent multilayer fouling growth during consecutive treatments was ruled by the already formed mineral layers, where gradual sieving effects inverted the migration rates and led to a multistep crystal growth. Calcium carbonate grew on the diluate side of CEM, starting from its amorphous phase to then crystallize in a coexisting presence of aragonite and calcite. Amorphous magnesium hydroxide appeared on CEM apparently through fouling dehydration ruled by the mineral layers themselves and by overlimiting current regimes. A delayed fouling growth was observed for PEF ratio 0.3. A long pause lapse during pulse modes was demonstrated as an important parameter for fouling mitigation.     

Electrodialysis of calcium and carbonate high concentration solutions and impact on composition in cations of membrane fouling

Fouling, which is the accumulation of undesired solid materials at the phase interfaces of permselective membranes, is one of the major problems in electrodialysis. The objectives of the present work were to investigate the effect of the composition in calcium and carbonate of a model solution to be treated by conventional electrodialysis on their migration kinetics and the composition in cations of the membrane fouling. In the absence of sodium carbonate in the solution, no fouling was visually observed on anion-exchange membranes (AEM) and fouling was observed only at 1600 mg/L CaCl2 on cation-exchange membrane (CEM), while at only 800 mg/L CaCl2 with sodium carbonate, a deposit was observed on both membranes. This difference could be explained by the fact that carbonate has a high buffer capacity, and the time to reach pH 4.0 was then longer than the one without carbonate. Consequently, the migration of the ionic species was carried out over a longer period of time during ED treatment with sodium carbonate addition and in extent the demineralization rates were higher: 43 vs 86%. For treatment with sodium carbonate and 1600 mg/L CaCl2, the higher migration during ED treatment, increased the concentration of calcium, from 14.24 to 93.38 mg/g dry membrane and from 0.74 to 10.27 mg/g dry membrane for CEM and AEM, respectively. Due to the basic pH on the side of the membrane in contact with the NaCl solution, the calcium would precipitate to form calcium hydroxide on CEM while the calcium migrated through the CEM was blocked by the AEM where it formed another fouling.     

Impact of electrodialytic parameters on cation migration kinetics and fouling nature of ion-exchange membranes during treatment of solutions with different magnesium/calcium ratios

During electrodialysis (ED) treatment of solutions with different Mg/Ca ratios (R = 0, 1/20, 1/10, 1/5 and 2/5) and in different pH conditions (acid, neutral and basic), foulings on ion-exchange membranes were previously characterized and identified, by the way of X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses. A mineral fouling was observed in neutral and basic conditions (for R = 1/5 and 2/5) on the anion-exchange membrane (AEM) concentrate side and in basic conditions on the cation-exchange membrane (CEM) concentrate side as well as on the diluate side for R = 1/5 and 2/5. The objectives of this present work were to link the morphological characterization and identification of membrane fouling to electrodialytic parameters and cation migration kinetics. It appeared that the CEM permselectivity was severely affected in basic conditions for R ≥ 1/5. The consequence of this alteration was the migration of OH⁻ through the CEM, a pH increase in the diluate compartment and different treatment durations. The calcite observed on AEM concentrate side for Mg/Ca ≥ 1/5 would be due first to the particular operating conditions such as the recirculation of the concentrate solution, and also to the supersaturated conditions reached or not at the AEM interface and favourable pH conditions.     

Effect of calcium and carbonate concentrations on anionic membrane fouling during electrodialysis

A previous study on electrodialysis of calcium and carbonate high concentration solutions demonstrated that calcium migrated through the cation-exchange membrane (CEM) was blocked by the anion-exchange membrane (AEM) where it formed another fouling. The aim of the present work was to complete the identification of the deposit formed on AEM during electrodialysis and to characterize its physical structure at the interface of the membrane. No fouling was found on the anionic membranes treated without calcium chloride in presence of sodium carbonate, while membranes used during ED process of solutions containing calcium chloride and sodium carbonate were slightly fouled. A thin layer of precipitates was observed on the anionic membrane surface. The appearance of precipitates was typical of a crystalline substance. The size and form of crystal increased in proportion to the concentration of calcium chloride in solution. Large and cubic crystals were the best defined on the membrane treated at 1600 mg/L of CaCl2. The precipitate was identified as calcium hydroxide. However, this fouling was not found to affect significantly the electrical conductivity and the thickness of the membranes. Furthermore, the fouling formed was reversible.     

无添加剂条件下文石型碳酸钙晶须制备及影响因素研究

在不加任何结晶控制剂或模板条件下,以CaCl2和Na2CO3为原料,利用复分解反应法制备了具有较好形貌和高长径比,且分布均一的文石型碳酸钙晶须,并利用扫描电镜(SEM)、X-射线粉末衍射(PXRD)和傅里叶转换红外光谱图(FT-IR)等手段对其进行了表征。研究了浓度、滴加速度、反应温度、搅拌速度以及滴加方式等因素对碳酸钙晶须的影响。结果表明最佳制备工艺为:CaC12溶液与Na2CO3溶液的浓度为0.05 mol.L-1,溶液滴加速度为1 mL.min-1,反应体系温度为80℃,搅拌速度为250 r.min-1。     

Impact of pulsed electric field on electrodialysis process performance and membrane fouling during consecutive demineralization of a model salt solution containing a high magnesium/calcium ratio

Pulsed electric fields (PEFs), hashed modes of current consisting in the application of a constant current density during a fixed time (Ton) followed by a pause lapse (Toff), were recently demonstrated as an effective alternative for mineral fouling mitigation and process intensification during electrodialysis (ED) treatments. Recent ED studies have continuously reported a considerable mineral fouling formation on ion-exchange membranes, especially during the demineralization of solutions containing a high Mg/Ca ratio and a basified concentrate solution. The aim of this study was to evaluate the process performance under two different PEF conditions on a mineral solution containing a mineral mixture giving a high Mg(2+)/Ca(2+) ratio of 2/5. Two different pause-lapse durations (PEF ratio 1 (Ton/Toff 10s/10s); PEF ratio 0.3 (Ton/Toff 10s/33.3 s)) during consecutive ED treatments and their comparison with dc current were evaluated at a current density of 40 mA/cm(2). Our results showed that PEFs resulted in an intensification of ED process, enhancing the demineralization rates (DRs), reducing the system resistance (SR), and reducing the fouling and energy consumption (EC). PEF ratio 1 was the most optimal condition among the current regimes applied, leading to faster and higher demineralization rates due to a lower fouling and with low energy consumption during all consecutive runs.     

Divisive effect of alcohol-water mixed solvents on growth morphology of calcium carbonate crystals

Controlling the process of crystal growth is of importance to the biomineralization and materials science. In this work, some novel morphology of calcium carbonate (CaCO3) was precipitated in an ethanol-water binary solvent (EWBS) with a CaCl2/Na2CO3 reaction system. For the solutions of CaCl2/Na2CO3 in EWBS, the alcoholization and hydration of Ca2+ and CO3(2-) were discussed from the radial distribution functions by molecular dynamics simulations, and the number density profiles of water molecules around and approximately 15 A away from CO3(2-) were employed to reveal the distribution of water molecules. It is found that EWBS has a divisive effect on Ca2+ and CO3(2-), and the local inhomogeneity of EWBS would be enhanced by adding some Na2CO3 into it. This inhomogeneity results in an aqueous two-phase system as x E goes up to 0.7. In addition, the novel morphology of CaCO3 under different molar ratios of Ca2+/CO3(2-) and in different mixed solvents were confirmed by XRD and SEM, and the relationships between the morphology of CaCO 3 and the structural properties of mixed solvents were further explored.     

Effect of calcium and carbonate concentrations on cationic membrane fouling during electrodialysis

Fouling, which is the accumulation of undesired solid materials at the phase interfaces of permselective membranes, is one of the major problems in electrodialysis. The aim of the present work was to investigate the effect on the fouling of cation-exchange membranes of the composition in calcium and carbonate of a model solution to be treated by electrodialysis. No fouling was observed at 400 and 800 mg/L of CaCl(2) in the absence of carbonate, while at only 400 mg/L CaCl(2) with carbonate, a deposit was observed. This difference could be explained by the buffering capacity of the carbonate, which affects the treatment duration with and without sodium carbonate. Since the duration was longer with carbonate, more calcium ions were able to migrate across the CMX-S membrane, which explained the higher deposit on its surface. Furthermore, whether there was carbonate in the solution treated by electrodialysis or not, the deposit on the surface of the cationic membrane was calcium hydroxide. However, this fouling formed during conventional ED was easily cleaned by an acid procedure.     

Crystallization and Transformation Mechanism of Calcium Carbonate Polymorphs and the Effect of Magnesium Ion

The crystallization of calcium carbonate was carried out by mixing CaCl(2) and Na(2)CO(3) solutions. The morphology of precursor formed prior to the nucleation of the polymorphous crystals (calcite and vaterite) varies depending on the feed concentration. The faster nucleation rate of polymorphous crystals in 0.2 mol/L than in 0.05 mol/L solution results in the prompt disappearance of the precursor at 0.2 mol/L. In 0.05 mol/L solutions the lifetime of the precursor is relatively long. The crystallization fraction of vaterite increases with the feed concentration and decreases with the addition rate of Na(2)CO(2) solution. Vaterite takes on the various morphologies of the aggregates of the primary flocculation body (spherulite) depending on the crystallization conditions. Vaterite transforms to calcite by a direct solution-mediated mechanism. During crystallization the concentration attains a stationary value, which increases with the feed concentration and decreases with the addition rate of Na(2)CO(2) solution. This may be due to the crystal size decrease expected from the Gibbs-Kelvin equation. Magnesium ion suppresses the transformation of vaterite by inhibiting the growth of the calcite. Magnesium ion is selectively included in calcite and causes the increase of the attained concentration and the remarkable change in the morphology of calcite especially in 0.05 mol/L solution. Copyright 2001 Academic Press.     

Influence of sodium dodecyl sulfate and static magnetic field on the properties of freshly precipitated calcium carbonate

Properties of calcium carbonate precipitated from aqueous solutions of CaCl(2) and Na(2)CO(3) in the presence of sodium dodecyl sulfate (SDS) and S-S 0.1 T magnetic field (MF) were studied. The nucleation and precipitation processes of CaCO(3) were investigated by pH and zeta potential measurements at 20 +/- 1 degrees C up to 2 h after mixing the solutions. Also the amounts of calcium carbonate deposited on the glass surfaces and its structure were examined. It was found that SDS influences the kinetics of precipitation, crystallographic forms, and crystal size of CaCO(3). The SDS effects are more pronounced in MF presence. A small amount of SDS accelerates transformation of vaterite into calcite, whereas increasing surfactant concentration moderates such a transformation. On the other hand, in all the systems, MF in the presence of SDS causes a slower transformation of vaterite into calcite. These effects are reflected in pH and zeta potential changes, although there is no clear dependence between the SDS amount present during the precipitation and changes of the parameters investigated. It seems that MF effect is most significant at a defined optimal SDS concentration. The results, however, do not allow suggestion of any detailed mechanism of the field interaction.     

Electrospray ionization tandem mass spectrometric study of salt cluster ions: part 2--salts of polyatomic acid groups and of multivalent metals

Salt cluster ions formed from 0.05 M solutions of CaCl(2), CuCl(2) and Na(A)B (where A = 1 or 2 and B = CO(3)(2-), HCO(3)(-), H(2)PO(4)(-) and HPO(4)(2-)) were studied by electrospray ionization tandem mass spectrometry. The effects on salt cluster ions of droplet pH and of redox reactions induced by electrospray provide information on the electrospray process. CaCl(2) solution yielded salt cluster ions of the form (CaCl(2))(n)(CaCl)(x)(x+) and (CaCl(2))(n)(Cl)(y)(y-), where x, y = 1-3, in positive- and negative-ion modes, respectively. Upon collision induced dissociation (CID), singly charged CaCl(2) cluster ions fragmented, doubly charged cluster ions generated either singly or both singly and doubly charged fragment ions, depending on the cluster mass, and triply charged clusters fragmented predominantly by the loss of charged species. CuCl(2) solution yielded nine series of cluster ions of the form (CuCl(2))(n)(CuCl)(m) plus Cu(+), CuCl(+), or Cl(-). CuCl, the reductive product of CuCl(2), was observed as a neutral component of positively and negatively charged cluster ions. Free electrons were formed in a visible discharge that bridged the gap between the electrospray capillary and the sampling cone brought about the reduction of Cu(2+) to Cu(+). Upon CID, these cluster ions fragmented to lose CuCl(2), CuCl, Cl, and Cl(2). Na(2)CO(3) and NaHCO(3) solutions yielded cluster ions of the form (Na(2)CO(3))(n) plus Na(+) or NaCO(3)(-). Small numbers of NaHCO(3) molecules were found in some cluster ions obtained with the NaHCO(3) solution. For both Na(2)HPO(4) and NaH(2)PO(4) solutions, ions of the form (Na(2)HPO(4))(h), (NaH(2)PO(4))(i), (Na(3)PO(4))(j), (NaPO(3))(k) plus Na(+), PO(3)(-) or H(2)PO(4)(-) were observed. In addition, ions having one or two phosphoric acid (H(3)PO(4)) molecules were observed from the NaH(2)PO(4) solution while ions containing one sodium hydroxide (NaOH) molecule were observed from the Na(2)HPO(4) solution. The cluster ions observed from these four salts of polyatomic acid groups indicate that changes in pH occur in both directions during the electrospray process principally by solvent evaporation; the pH value of the acidic solution became lower and that of the basic solution higher.     

Effect of magnesium/calcium ratio in solutions subjected to electrodialysis: characterization of cation-exchange membrane fouling

Electrodialysis is based on the migration of charged species through perm-selective membranes under an electric field. Fouling, which is the accumulation of undesired solid materials at the interfaces of these membranes, is one of the major problems of this process. The aim of the present work was to investigate the nature and the morphology of fouling observed at different Mg/Ca ratios (R=0, 1/20, 1/10, 1/5, 2/5) on cation-exchange membranes (CEM) during conventional electrodialysis treatments. It appeared that for R=0, the fouling observed on the surface in contact with the basified concentrate was formed of only Ca(OH)2. As soon as magnesium was introduced into the solution treated, CaCO3 was observed. Furthermore, the X-ray diffraction results also identified the CaCO3 observed as calcite. To our knowledge, this is the first time that the presence of magnesium has been demonstrated to induce a CaCO3 fouling on CEM during electrodialysis.     

A quasi-time-resolved CryoTEM study of the nucleation of CaCO3 under langmuir monolayers

Calcium carbonate biomineralization uses complex assemblies of macromolecules that control the nucleation, growth, and positioning of the mineral with great detail. To investigate the mechanisms involved in these processes, for many years Langmuir monolayers have been used as model systems. Here, we descibe the use of cryogenic transmission electron microscopy in combination with selected area electron diffraction as a quasi-time-resolved technique to study the very early stages of this process. In this way, we assess the evolution of morphology, polymorphic type, and crystallographic orientation of the calcium carbonate formed. For this, we used a self-assembled Langmuir monolayer of a valine-based bisureido surfactant (1) spread on a CaCl2-containing subphase and deposited on a holey carbon TEM grid. In a controlled environment, the grid is exposed to an atmosphere containing NH3 and CO2 (the (NH4)2CO3 diffusion method) for precisely determined periods of time (reaction times 30-1800 s) before it was plunged into melting ethane. This procedure allows us to observe amorphous calcium carbonate (ACC) particles growing from a few tens of nanometers to hundreds of nanometers and then crystallizing to form [00.1] oriented vaterite. The vaterite in turn transforms to yield [10.0] oriented calcite. We also performed the reaction in the absence of monolayer or in the presence of a nondirective monolayer of surfactant containing an oligo(ethylene oxide) 2 head group. Both experiments also showed the formation of a transient amorphous phase followed by a direct conversion into randomly oriented calcite crystals. These results imply the specific though temporary stabilization of the (00.1) vaterite by the monolayer. However, experiments performed at higher CaCl2 concentrations show the direct conversion of ACC into [10.0] oriented calcite. Moreover, prolonged exposure to the electron beam shows that this transformation can take place as a topotactic process. The formation of the (100) calcite as final product under different conditions shows that the surfactant is very effective in directing the formation of this crystal plane. In addition, we present evidence that more than one type of ACC is involved in the processes described.     

Carbonate adsorption on goethite in competition with phosphate

Competitive interaction of carbonate and phosphate on goethite has been studied quantitatively. Both anions are omnipresent in soils, sediments, and other natural systems. The PO4-CO3 interaction has been studied in binary goethite systems containing 0-0.5 M (bi)carbonate, showing the change in the phosphate concentration as a function of pH, goethite concentration, and carbonate loading. In addition, single ion systems have been used to study carbonate adsorption as a function of pH and initial (H)CO3 concentration. The experimental data have been described with the charge distribution (CD) model. The charge distributions of the inner-sphere surface complexes of phosphate and carbonate have been calculated separately using the equilibrium geometries of the surface complexes, which have been optimized with molecular orbital calculations applying density functional theory (MO/DFT). In the CD modeling, we rely for phosphate on recent parameters from the literature. For carbonate, the surface speciation and affinity constants have been found by modeling the competitive effect of CO3 on the phosphate concentration in CO3-PO4 systems. The CO3 constants obtained can also predict the carbonate adsorption in the absence of phosphate very well. A combination of inner- and outer-sphere CO3 complexation is found. The carbonate adsorption is dominated by a bidentate inner-sphere complex, (FeO)2CO. This binuclear bidentate complex can be present in two different geometries that may have a different IR behavior. At a high PO(4) and CO3 loading and a high Na+ concentration, the inner-sphere carbonate complex interacts with a Na+ ion, probably in an outer-sphere fashion. The Na+ binding constant obtained is representative of Na-carbonate complexation in solution. Outer-sphere complex formation is found to be unimportant. The binding constant is comparable with the outer-sphere complexation constants of, e.g., SO(2-)4 and SeO(2-)4.     

Analysis of the nucleation and growth of amorphous CaCO3 by means of time-resolved static light scattering

The formation of amorphous calcium carbonate particles from supersaturated aqueous solution is relevant to many processes in nature and industry. The present work introduces time-resolved static light scattering as a new tool to investigate the initial stage of this process. The process is initiated by mixing a solution of Na(2)CO(3) with a CaCl(2) solution or, alternatively, by mixing solutions of the dimethyl ester of carbonic acid and CaCl(2) with solutions of NaOH. Particle formation was analyzed by recording scattering curves as a function of time. Scattering data indicate the formation of compact spheres with diameters close to 360 nm. In the case of particle formation induced by ester hydrolysis, nucleation sets in after a certain lag time. Particle size is homogeneous, and the growth mechanism corresponds to an addition of ions or small constituent particles to a constant number of growing spheres. An increase of the NaOH concentration, which triggers ester hydrolysis, decreases the lag period prior to the onset of particle formation. An increase of the solution temperature also decreases this lag period. The temperature and NaOH dependent duration of the lag time could successfully be interpreted in terms of the kinetics of the ester hydrolysis. The work establishes time-resolved static light scattering as an efficient tool to investigate the particle formation process of amorphous calcium carbonate.     

Interaction between biopolyelectrolytes and sparingly soluble mineral particles

We investigate the complex physicochemical behavior of dispersions containing calcium carbonate (CaCO(3)) particles, a sparingly soluble mineral salt; and carrageenans, negatively charged biopolyelectrolytes containing sulfate groups. We reveal that the carrageenans suspend and stabilize CaCO(3) particles in neutral systems by absorbing on the particle surface which provides electrosteric stabilization. In addition, carrageenans provide a weak apparent yield stress which keeps the particles suspended for several months. The absorption measurements of carrageenan on the CaCO(3) particle indicate that more carrageenan is removed from the solution than expected from the case of a simple monolayer adsorption. Confocal laser scanning microscopy observations confirm that polyelectrolyte-containing precipitate is formed in both CaCO(3)-carrageenan and CaCl(2)-carrageenan mixtures. On the basis of these results, we confirm that in the presence of carrageenan some CaCO(3) dissolves and the Ca(2+) ions interact with the sulfate groups leading to aggregation and formation of particle-like structures. These new insights are important for fundamental understanding of other mineral-polyelectrolyte systems and have important implications for various industrial applications where calcium carbonate is used.     

CO2矿化反应基础研究 II．有机胺介质中碳酸化反应热力学研究

对有机胺介质中CaCl₂与二氧化碳的碳酸化反应进行了研究,在二氧化碳压力为2MPa~5MPa、CaCl₂浓度为1.31mol/L~2.44mol/L下考察了压力和浓度对该多相反应体系碳酸钙收率和有机胺萃取效率的影响。结果表明,碳酸化反应过程中碳酸钙收率和有机胺萃取效率随二氧化碳压力和CaCl₂初始浓度的增大而增加。结合Pitzer电解质溶液模型、二氧化碳溶解模型对该多相反应进行热力学平衡分析。有机胺的萃取平衡决定了HCl在有机相和水相的分配平衡,水相中H⁺浓度限制H₂CO₃解离,制约碳酸钙沉淀反应。CaCl₂浓度大小影响了HCO₃^-和CO₃²-的活度系数,对沉淀/溶解平衡也有一定影响。热力学平衡转化率与实验结果接近,表明该反应受化学反应平衡控制。     

Effects of Carboxylic Acids on the Crystallization of Calcium Carbonate

The effects of seven carboxylic acids, i.e., acrylic acid, maleic acid, tartaric acid, malic acid, succinic acid, and citric acid, on CaCO(3) crystallization were studied using the unseeded pH-drift method along with a light-scattering technique. Experiments were started by mixing solutions of CaCl(2) and NaHCO(3) in the presence or absence of additives. The crystallization was studied by recording the decrease in pH resulting from the reaction Ca(2+)+HCO(3)(-)-->CaCO(3)+H(+). A given amount of carboxylic acid was added to the solution of CaCl(2) or NaHCO(3) before mixing the reactants. The pH profiles obtained in the case of the CaCl(2) solution containing an additive were similar to those for the NaHCO(3) solution containing one, and when an additive was added after the onset of crystallization, the growth of CaCO(3) immediately stopped. The light-scattering observations, in all cases, indicated that CaCO(3) nucleation occurred at 10-20 s after mixing of the reactants. The results indicated that the nucleation of CaCO(3) was not influenced by the presence of carboxylic acids, but CaCO(3) crystal growth was reduced by their adsorption to the surface of the CaCO(3) crystals. These phenomena were explained by assuming a stronger affinity of the carboxylic acids for CaCO(3) particles than for the free Ca(2+) ions in solution. The crystallization of CaCO(3) in the presence of additives was divided into three stages: nucleation, growth incubation, and growth periods. Copyright 2001 Academic Press.