In Situ Probing Calcium Carbonate Formation by Combining Fast

Feb 25, 2014 - The initial stage of calcium carbonate nucleation and growth, found usually in “natural” precipitation conditions, is still not wel...
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In Situ Probing Calcium Carbonate Formation by Combining Fast Controlled Precipitation Method and Small-Angle X‑ray Scattering Yanjia Chao,†,‡,§ Olivier Horner,†,∇ Philippe Vallée,∥ Florian Meneau,⊥ Olga Alos-Ramos,† Franck Hui,‡,§ Mireille Turmine,‡,§ Hubert Perrot,*,‡,§ and Jean Lédion@ †

EDF R&D, Laboratoire National d’Hydraulique et Environnement, 6 Quai Watier, 78401 Chatou, Cedex, France CNRS, Laboratoire Interfaces et Systèmes Electrochimiques, 4, place Jussieu, 75252 Paris, Cedex 05, France § Université P. et M. Curie, LISE, 4, place Jussieu, 75252 Paris Cedex 05, France ∥ Biophys-Solutions, 24, rue Alphand, 75013 Paris, France ⊥ Synchrotron Soleil, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex, France @ ARTS, 151, boulevard de l’Hôpital, 75013 Paris, France ‡

S Supporting Information *

ABSTRACT: The initial stage of calcium carbonate nucleation and growth, found usually in “natural” precipitation conditions, is still not well understood. The calcium carbonate formation for moderate supersaturation level could be achieved by an original method called the fast controlled precipitation (FCP) method. FCP was coupled with SAXS (small-angle X-ray scattering) measurements to get insight into the nucleation and growth mechanisms of calcium carbonate particles in Ca(HCO3)2 aqueous solutions. Two size distributions of particles were observed. The particle size evolutions of these two distributions were obtained by analyzing the SAXS data. A nice agreement was obtained between the total volume fractions of CaCO3 obtained by SAXS analysis and by pH-resistivity curve modeling (from FCP tests).

1. INTRODUCTION The formation of calcium carbonate (CaCO3) in water has an important implication in biology and geoscience research, ocean chemistry studies, and CO2 emission issues1,2 It is also a major concern in some industrial processes (i.e., energy production),3−5 where the scaling phenomenon can cause problems such as reduction of heat transfer efficiency in cooling systems and obstruction of pipes. A lot of studies have been carried out to understand the different polymorphs of CaCO3,6,7 their nucleation and crystallization processes,8,9 as well as the control of CaCO3 particles formation (size and phase).10,11 However, the initial stage of CaCO3 nucleation is not well understood, due to the difficulties of in situ observation at the nanometer scale. A variety of experimental methods have been applied to study the formation and growth of CaCO3 particles. The widely used SEM technique allows the observation of particles at the micrometer scale. However, SEM investigations potentially suffer from drying artifacts, which may leave some ambiguities.12,13 Gebauer et al.14 have provided evidence for the existence of prenucleation clusters, even in undersaturated solutions, by using analytical ultracentrifugation (AUC). Highresolution Cryo-TEM was also used to detect CaCO 3 nanoparticles of less than 10 nm and CaCO3 clusters with dimensions from 0.6 to 1.1 nm.12,13,15,16 With these techniques, © 2014 American Chemical Society

a nucleation process was demonstrated, involving prenucleation CaCO3 clusters as early precursors. These precursors aggregate to form amorphous calcium carbonate (ACC), which will further evolve to crystallize. However, due to some technical limitations, these works were not always able to make in situ quantitative analysis (i.e., size distribution and number density) for the nucleation process. The synchrotron small-angle X-ray scattering (SAXS) has been proven to be a useful tool to study in situ nucleation and growth stages of CaCO3.17 CaCO3 particle size distribution and number density could be obtained from the scattering curves, Bolze et al. have carried out a series of works using the SAXS measurements for the CaCO3 study.17−19 They provided captivating scattering curves with clear-cut evidence for spherically shaped particles at the point of nucleation.20 Particle size, number density, and mass density were also successfully extracted. Nevertheless, in these studies and many others,8,21 the CaCO3 formation was triggered by direct mixing of a Ca2+ solution with a CO32− solution of high concentrations for high pH values. In this case, the reaction starts at the interface of two liquids in conditions of supersaturation which are not Received: June 17, 2013 Revised: February 21, 2014 Published: February 25, 2014 3303

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homogeneous. In addition, the timescale of CaCO3 nucleation is similar to that of the mixing process and is not very wellknown. It is therefore difficult to achieve, through this direct mixing method, homogeneous nucleation conditions.22−24 Moreover, the test solution rapidly reaches a very high supersaturation level, which is not the case in natural conditions. A few studies have been carried out to achieve homogeneous CaCO3 nucleation at moderate supersaturation level. Faatz et al. described a method in which the homogeneous release of CO2 was obtained by the hydrolysis of dialkyl carbonate to give a slow precipitation of CaCO3.22 Wolf et al. used an approach where the nucleation of CaCO3 was triggered by gradual evaporation and CO2 degassing.23 Nevertheless, the SEM, TEM, and WAXS measurements used in these studies were not powerful enough to characterize the nucleation stage. In this work, a new experimental setup which combines the SAXS measurement and the fast controlled precipitation or FCP method25,26 is presented. In these conditions, it is possible to study the in situ formation of CaCO3 under conditions of moderate supersaturation levels. The principle of the FCP method is indeed based on the degassing of CO2 by a moderate stirring.26 The process of nucleation−growth of CaCO3 is therefore similar to that of a real scaling phenomenon. The goal of this work is to characterize the calcium carbonate particles, with respect to their geometry and their distributions, which appear during a FCP test.

Figure 1. Experimental setup for FCP test coupled with time-resolved SAXS measurements.

were changed for new ones. The reaction cell and the circulation system was cleaned with 0.1 M HCl and rinsed with pure water.

3. DATA ANALYSIS 3.1. Model for the SAXS Data Analysis. The scattering patterns of the reaction cell filled with pure water was measured separately and subtracted from the scattering patterns of the sample. The resulting isotropic patterns were azimuthally averaged to give out the 1D scattering profile I(q) as a function of the scattering vector q:27

2. EXPERIMENTAL SECTION 2.1. Materials. Ca(HCO3)2 test solutions were prepared by dissolving solid calcium carbonate (VWR AnalaR NORMAPUR, 99.7% purity) in pure water (Milli -Q water, resistivity of 18.2 MΩ cm, TOC < 5 μgL−1) by CO2 gas bubbling. After the dissolution of the solid, the pH of the solution was in the range of 5.2−5.5. In these conditions, no spontaneous precipitation of CaCO3 happened because the supersaturation of the solution was very low. The solution was then filtered by using Millipore filters of 0.45 μm to eliminate dusts or undissolved solids. 2.2. FCP Experiment. In a typical FCP experiment,26,27 400 mL of Ca(HCO3)2 solution was stirred at 850 r min−1 to accelerate the CO2 degassing. This gradually increased the pH value of the solution and thus gave rise to the CaCO3 precipitation. By this method, precipitation for a moderate supersaturation level was ensured. During the FCP experiment, the pH and the resistivity of the solution were measured and registered every five seconds by lab-made software, with a pH electrode (radiometer pHG301) associated to its reference electrode (Radiometer REF421) and a conductivity electrode (radiometer CDC741T). The temperature of the experiment was controlled with a water bath at 30 °C and measured with a lab-made sensor. The reaction cell was made of a Teflon beaker with a covering lid. An open hole located at the center of the lid ensured that the CO2 would vent. The covering lid also helped to hold the electrodes. 2.3. SAXS Experiment. Synchrotron small-angle X-ray scattering experiments were conducted at the SWING beamline (Synchrotron SOLEIL, Saint-Aubin, France). The wavelength λ of radiation was set to λ = 1.033Å. The sample-to-detector distance was set to 1.385 m. The acquisition time for one frame was in the range of 0.8−3 s. 2.4. FCP-SAXS Coupling. The FCP experiment was coupled with SAXS measurements, as shown in Figure 1. A peristaltic pump was used to pump the test solution from the FCP reaction beaker to the scanning cell and then back to the FCP reaction beaker. The scanning cell was made of a thin-walled quartz capillary (inner diameter = 1.5 mm, wall thickness = 0.01 mm). PTFE thin hoses were used to connect the different parts of the experimental setup. For each experiment, the quartz capillary and the PTFE hoses

q = 4π sin(θ /2)/λ

(1)

where θ is the scattering angle. Absolute scattering intensities were obtained by calibration with pure water (Milli-Q water, I(q)absolute = 0.0162 cm−1). For a single particle with a spherical symmetry, the SAXS amplitude is given by A(q) = 4π

∫0

R

Δρ

sin(qr ) 2 r dr qr

(2)

where r refers to particles radius that ranges from 0 to R and Δρ the scattering density difference between the solvent and the solute. In order to calculate the scattering density of the formed CaCO3 particles, their mass densities needed to be determined. At the initial stage of precipitation, the formation of CaCO3 is often referred to as ACC.15,18,23,28 As proposed by Raiteri et al.,29 the nucleation clusters observed before the point of precipitation are also supposed to be ACC. Therefore, all size distributions of particles before and after the precipitation were supposed to have the structure of ACC. The mass density of ACC is determined as DACC = 1.48 g cm−3,15,16 and its scattering density (ρAC) is 12.685 × 1010 cm−2. For an ensemble of noninteracting spherical particles with a given size distribution, the scattering intensity I(q) was calculated from A(q) by I(q) =

2 ∑ NA i i (q)

(3)

where the index i refers to the fraction of particles with a radius ri and a particle number density Ni. In the case of homogeneous spheres, I (q) could be calculated by combining eqs 2 and 3 which gave 3304

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Figure 2. (a) pH and resistivity of the tested solutions during the FCP experiments at 30 °C. (b) Evolution of SAXS scattering intensity I(q) as a function of time during a FCP test with [Ca2+] = 100 mg L−1.

I(q) =

∑ NiΔρ

2

⎡

sin(qri) Vi2*⎢3* ⎣

− qri cos(qri) ⎤ ⎥ (qri)3 ⎦

2

(4)

where Vi represents the volume per particle. This relation will be used in the following fitting procedure. 3.2. SAXS Data Fitting. The fitting of I(q) from SAXS was carried out using SANS_Analysis provided by the National Institute of Standards and Technology.30 In the fitting procedure, a spherical form factor with a LogNormal particle size distribution model was used. The LogNormal distribution is a continuous distribution in which the logarithm of a variable has a normal distribution, as follows: fR (r , μ , σ ) =

2 2 1 e−(ln r − μ) /2σ rσ 2π

(5) Figure 3. Fitting of the experimental SAXS scattering curve at t = 15 min for a FCP test ([Ca2+] = 200 mg L−1).

where f R is the particle distribution, μ is the logarithm of the median radius, and σ is the standard deviation of the logarithm of r. Equation 5 could be combined with eq 4 to obtain the I(q) values as the function of q in the SAXS curve fitting process. Thus, for a given size distribution, four key parameters were involved in the fitting process: the volume fraction Φ, the median radius r, the standard deviation σ and the background b.29 To launch the fitting process, the initial values for Φ, r, and σ needed to be determined for each considered distribution of particles. For each I(q) vs q curve, the calculation of the number density related to each particles distribution could be achieved after the fitting process thanks to the function ‘NumberDensity_LogN’ in SANS_Analysis.30

Ca(HCO3)2 solution, where a significant drop in pH was observed when precipitation occurred. The start of precipitation is also indicated by a sharp change in the slope of the resistivity versus time curve. The solution was pumped to the quartz capillary continuously, where in situ SAXS measurements were carried out. An example of SAXS scattering curves related to a FCP test, with [Ca2+] = 100 mg L−1, is presented in Figure 2b. As shown in Figure 2b, a slight increase of the scattering intensity occurs in domain 1. Afterward, as the massive precipitation begins (domain 2), a sharp increase of the scattering intensity can be observed. 4.2. Estimation of the Initial Values of the Fitting Parameters for the SAXS Data Analysis. Preliminary fittings were carried out using a single component system (i.e., by considering a single size distribution of spherical particles). However, a significant improvement of the fitting could be obtained by considering a bimodal system with two size distributions of spherical particles, as shown in Figure 3. In fact, the mean square deviation decreased from 458 to 364 with the bimodal system, compared to a single component system.30 To launch the I(q) curves fitting process, the initial values of some fitting parameters (see SAXS Data Fitting) were estimated for each distribution in domain 1 and domain 2. The first distribution (distribution I) is likely to be related to smaller nanoparticles. In accordance with recent studies, this distribution could correspond to nucleation clusters of CaCO3

4. RESULTS AND DISCUSSION 4.1. SAXS and FCP Coupled Measurements. Figure 2a shows the pH and the resistivity changes during FCP tests of two different Ca(HCO3)2 solutions with [Ca2+] = 100 mg L−1 and [Ca2+] = 200 mg L−1. The FCP experiment highlights the frontier between two domains (Figure 2a). The first domain, called domain 1, is a metastable one already observed previously,26 which could correspond to a prenucleation stage.14 The second domain, called domain 2 (Figure 2a) is dominated by a rapid precipitation process. The maximum of the pH versus time curve corresponds to the threshold of CaCO3 precipitation (P point in Figure 3a). A similar pH curve was also obtained by Pouget et al.16 during CO2 outgassing from a supersaturated 3305

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Figure 4. The median radius evolution of particles and the number density evolution of particles in distribution I and distribution II obtained by SAXS data fitting, for FCP tests with [Ca2+] = 100 mg L−1 (red curves) and [Ca2+] = 200 mg L−1 (green curves).

in the range of a few nanometers (0.7−4 nm).14,16,29 In the fitting procedure, these values were set as the starting point for the median radius of the particles in distribution I. The second distribution (distribution II) corresponds to larger nanoparticles. In the fitting procedure, the starting point of the median size for distribution II was set to 8−20 nm. This was based on the study of Donnet et al.15 who observed CaCO3 seeds of this size range in filtered Ca(HCO3)2 solution. It must be noticed that the fitting results were sensitive to the choice of initial size values for both distributions of particles. Only satisfactory results were obtained with the above starting points. 4.3. SAXS Fitting Results. The fitting of the experimental I(q) curves was carried out taking into consideration the initial parameter values (see Estimation of the Initial Values of the Fitting Parameters for the SAXS Data Analysis). Results of the size evolution of the two particle distributions are shown in Figure 4: In domain 1 (before precipitation), distribution I corresponds to particles with median radii of 0.8−1 nm (standard deviation of σ = 0.45−0.5) and distribution II corresponds to particles with median radius of 9.5−10 nm (standard deviation σ = 0.73−0.76). Both distributions of particle sizes undergo a slight growth (Figure 4). At the beginning of the test, the number density for distribution I is about 0.7 E14 cm−3 ([Ca2+] = 100 mg L−1) or 2.7 E14 cm−3 ([Ca2+] = 200 mg L−1). It increases gradually to 3.5 E14 cm−3 ([Ca2+] = 100 mg L−1) or 4.6 E14 cm−3 ([Ca2+] = 200 mg L−1) just before the point P of precipitation. This suggests that particles in distribution I follow essentially a prenucleation process. By contrast, the number density related to distribution II is much lower (1.2 E10 cm−3 for ([Ca2+] = 100 mg L−1 or 1.5 E10 cm−3 for [Ca2+] = 200 mg L−1) and remains almost constant all over domain 1. In fact, the

increasing number of nanoparticles in distribution I is the main contribution to the increase of total volume fraction. Recently, Demichelis et al. show,31 using computer simulations combined with the analysis of experimental data,14 that the initial stages of CaCO3 formation involve a dynamic polymer that was referred to as DOLLOP and which has an exponential size distribution. In light of this very interesting work, distribution I before precipitation might correspond to these species. It must be noted that all SAXS data have been analyzed here with a unique model involving spherically shaped particles (see the I(q)q4 vs q4 curve obtained at t = 25 min in Figure 4). Then, DOLLOP might convert to phase-separated particles, which corresponds to well-defined spherical clusters, as discussed by Faatz et al.22 In domain 2 (after precipitation), particles in distribution II undergo a sharp size increase. The number density for distribution II remains almost constant, whereas the number density for distribution I decreases gradually. This indicates a “monomer” addition growing mechanism, where smaller particles disappear in favor of larger particles.21,32 Indeed, particles in distribution II are likely to be growing centers that grow by consuming CaCO3 species of the distribution I. These particles (distribution II) could be CaCO3 seeds coming from the CaCO3 dissolution. Finally, the increase of the total volume fraction after precipitation is mainly due to the sharp increase of particle sizes in distribution II. 4.4. Calculation of the pH vs Resistivity Curve. Before the point of precipitation (domain 1), the pH-resistivity curve modeling in a FCP test was carried out by considering that the solution is under equilibrium. In fact, the solution is undergoing a continuous evolution during the FCP test. Before the point of precipitation, this evolution is very slow and corresponds to a succession of pseudoequilibrium states. Thus, it will be possible 3306

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For a totally dissociated Ca(HCO3)2 solution at 25 °C, eq 7 reduced to:

to calculate, over the time, the volume fraction of CaCO3. The related equations and constants of equilibrium at 30 °C are given in Table S1 of the Supporting Information. The calcium mass balance and the charge balance (refer to the Supporting Information) were used to calculate the [Ca2+]free concentration: ⎧ ⎪[Ca 2 +]free ⎪ [CO 2 −](2 + [H+]/K ) + [OH−] − [H+] − [Ca 2 +] 3 2 total ⎪= ⎪ 1 − K CaCO3[CO32 −] ⎪ ⎪ where ⎪ ⎪ − b + b2 − 4ac 2− ⎪[CO3 ] = 2a ⎨ ⎪ a = (2 + [H+]/K )(K [H+]/K 2) 2 CaCO3 + K CaHCO+ 3 ⎪ ⎪ 2+ + ⎪b = 2 + [H ]/K 2 + [Ca ]total K CaCO3 ⎪ ⎪+ (K CaCO3 + K CaHCO+3 [H+]/K 2)([OH−] − [H+] ⎪ 2+ ⎪ − [Ca ]total ) ⎪ 2+ − + ⎩ c = [OH ] − [H ] − 2[Ca ]total 2+

Λ = 104.0 − (136.28 I )/(1.0 + 1.728 I )

(8)

The conductivity σ could be calculated according to the following equation:

σ = Λ[Ca 2 +]Free

(9)

After the point of precipitation (domain 2), the evolution of the solution is very fast. Ion concentrations can no longer be estimated by using association constants of solution equilibrium. Thus, it is difficult to estimate the resistivity values from the measured pH values. However, an estimation of the amount of [Ca2+]free based on the pH and conductivity measurements could be done. The test solution is still considered as a totally dissociated Ca(HCO3)2 solution, in which [Ca2+]free decreases rapidly to form solid calcium carbonate. Equations 8 and 9 were used to calculate the [Ca2+]free concentration. The contribution of CO32− ions to ionic force F was not taken into consideration because its concentration is negligible compared to that of [Ca2+]free and [HCO3−]. The [HCO3−] concentration was estimated by using the following equation:

(6) +

The [Ca ]total value is well-known, and the value of [H ] can be determined by pH measurements. The solution conductivity/resistivity could be then deduced from all the determined ions concentrations. The limiting values of molar conductivity for the different ions used in this study are given in Table S2 of the Supporting Information. It must be noticed that these molar conductivity values are given for a temperature of 25 °C. Therefore, the experimental resistivity values measured at 30 °C had to be corrected at 25 °C. In order to carry out this adaptation, measurements were carried out at different temperatures in standard buffer solutions. The coefficients of resistivity values between these two different temperatures could be then estimated. The Debye−Hückel−Onsager equation was developed to calculate the conductivity at finite concentrations for a symmetric electrolyte, taking into consideration the ionic interactions as retarding electrophoresis and retarding relaxation forces. However, the Debye−Hückel−Onsager equation is only suitable for the symmetric electrolyte, and the Ca(HCO3)2 solution is a 1:2 electrolyte. Thus, a modified equation developed by Jacobson and Langmuir33 was used here for the Ca(HCO3)2 aqueous solution (eq 7):

[HCO3−] = 2[Ca 2 +]Free

(10)

On the basis of the evolution of resistivity versus pH calculated for the FCP test ([Ca2+] = 100 mg L−1 and [Ca2+] = 200 mg L−1) by using the previous procedure, a comparison was made between the calculated and experimental resistivity versus pH curves. A satisfactory agreement (difference