kinetics of crystal nucleation in ionic solutions: electrostatics and … · 2017-02-19 ·...

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Geochimica et Cosmochimica Acta 74 (2010) 469–481

Kinetics of crystal nucleation in ionic solutions: Electrostaticsand hydration forces

Magdalena Kowacz a,*, Manuel Prieto b, Andrew Putnis a

a Institut fur Mineralogie, Universitat Munster, Correnstrasse 24, 48149 Munster, Germanyb Departamento de Geologıa, Universidad de Oviedo, C/Jesus Arias de Velasco, s/n, 33005 Oviedo, Spain

Received 29 May 2009; accepted in revised form 14 October 2009; available online 21 October 2009

Abstract

The heat of precipitation, the mean crystal size and the broadness of crystal size distribution of barium sulfate precipitatingin aqueous solutions of different background electrolytes (KCl, NaCl, LiCl, NaBr or NaF), was shown to vary at constantthermodynamic driving force (supersaturation) and constant ionic strength depending on the salt present in solution. The rel-ative inversion in the effect of respective background ions on the characteristics of barite precipitate was observed between twostudied supersaturation (X) and ionic strength (IS) conditions. The crystal size variance (b2) increased in the presence of back-ground electrolytes in the order LiCl < NaCl < KCl at X = 103.33 and IS = 0.03 M and KCl < NaCl < LiCl at X = 103.77 andIS = 0.09 M. At a given X and IS the respective size of barite crystals decreased with increasing b2 in chloride salts of differentcations and remained constant in sodium salts of different anions.

We suggest that ionic salts affect the kinetics of barite nucleation and growth due to their influence on water of solvationand bulk solvent structure. This idea is consistent with the hypothesis that the kinetic barrier for barium sulfate nucleationdepends on the frequency of water exchange around respective building units that can be modified by additives present insolution. In electrolyte solution the relative switchover between long range electrostatic interactions and short range hydrationforces, which influence the dynamics of solvent exchange between an ion solvation shell and bulk fluid, results in the observedinversion in the effect of differently hydrated salts on nucleation rates and the resulting precipitate characteristics.� 2009 Elsevier Ltd. All rights reserved.

1. INTRODUCTION

The specific chemistry of a solvent can affect crystalgrowth and nucleation kinetics, morphology, crystal size dis-tribution and purity of precipitates. In an aqueous solvent,step spreading velocity and rates of surface nucleation havebeen recognized to depend on ion and surface hydrationcharacteristics. Kinetics of attachment of molecules to agrowing phase during crystallization and other phase transi-tion processes have been shown to be limited by the activa-tion energy for diffusion that can result from the need toexpel waters attached to the incoming molecules and to thegrowth site (Petsev et al., 2003). The kinetics of new kink for-

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doi:10.1016/j.gca.2009.10.028

* Corresponding author. Tel.: +49 2518333487.E-mail address: [email protected] (M. Kowacz).

mation (surface nucleation) was hypothesized to depend onthe frequency of water exchange between a building unitand a bulk fluid (Kowacz and Putnis, 2008). It has beenshown that changing the properties of the aqueous solvationenvironment by organic additives as well as simple inorganicsalts can result in modification of the reaction rates as well asmodes of crystal dissolution and growth, surface features,bulk crystal morphology and impurity incorporation evenif the thermodynamic driving force is kept constant (De Yor-eo and Dove, 2004; Dove et al., 2005; Piana et al., 2006, 2007;Kowacz et al., 2007). The influence of the ionic strength onprecipitation kinetics was found to be in agreement withthe Bronsted–Bjerrum theory that relates reaction rates withpolar properties of the solvent (salt medium effect) and theconsequential hydration of ions (Zuddas and Mucci, 1998).The origin of salt-specific effects at constant ionic strengthwas explained by the fact that the phenomenon of ionic

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470 M. Kowacz et al. / Geochimica et Cosmochimica Acta 74 (2010) 469–481

strength itself is determined by the water affinity of particularions (Collins et al., 2007). Consistent with this idea is that theeffect of additives on surface processes was recently suggestedto result from their influence on solvent structure and dynam-ics in solvation shells and in the bulk, and not necessarilyfrom specific interactions between species present in solutionand the crystal face (Elhadj et al., 2006; Kowacz and Putnis,2008; Stephenson et al., 2008). Such a concept creates somecommon framework relating fluid properties and mineralprecipitation/dissolution behavior. Recognition of the rela-tion between solution composition, aqueous solvent proper-ties and mineral crystallization can add to our understandingof phase transition processes in multicomponent naturalsolutions such as seawater or body fluids. It is also of impor-tance for medical and industrial purposes such as inhibitionof pathological mineralization, preventing scale formationor designing a product with desirable characteristics suchas defined size, morphology and narrow size distribution.Crystal size and crystal size distribution affect dissolutionrates and eventual bioavailability, and thus, for example,determine formulation strategies of pharmaceuticalproducts.

This study is concerned with three-dimensional nucle-ation in multicomponent electrolyte solutions. For the nucle-ation event to take place in solution, the dissolved ions haveto come into contact to form pairs, clusters or aggregates.Association of ions is promoted by the tendency of an aque-ous solvent to preserve its hydrogen-bonded network (Hawl-icka and Swiatla-Wojcik, 2003). The more structured thesolvent the higher its tendency to exclude ions in order to pre-serve the integrity of the network. Structure (and mobility) ofthe aqueous solvent depends on solution composition(hydration of solutes and/or the effect of cosolvents) (Hawl-icka and Swiatla-Wojcik, 2003; Marcus, 2009). In order toassociate, ions have to lose some of their hydration water.Therefore the facility to exchange the water molecules be-tween a solvation shell and the bulk solution also assists asso-ciation. Dynamics of the solvation shells is affected by theelectric fields and hydration properties of the other solutespresent in solution (Rull and Ohtaki, 1997; Palka and Hawl-icka, 2005). Ion association in solution, the prerequisite fornucleation, depends then on the dynamic and structural char-acteristics of solvent–solvent and ion–solvent interactions,these being defined by solution composition.

The aim of this work is to investigate the effect of simpleionic salts on three-dimensional nucleation in solution fromthe perspective of the influence of the electrolytes on solventstructure and on flexibility of ion hydration shells. We pres-ent experimental results of barium sulfate precipitation inaqueous solutions of different background electrolytes andaddress kinetics of nucleation and the resulting characteris-tics of the precipitate. Electrolyte solution concentrationswere adjusted to obtain conditions for which the action ofbackground ions is determined either mainly by their elec-trostatic influence on ion–water interactions (low ionicstrength) or by the effect of their hydration on solvent–sol-vent interactions (high ionic strength). The composition ofbackground salts was selected to produce distinct electro-static and hydration characteristics. A calorimetric studyon the enthalpy of solution of barium chloride in selected

background electrolytes provided information on the ener-getical effects of modifying the composition of the aqueoussolvent on the solvation of Ba2+ ions.

2. METHODS AND MATERIALS

2.1. Experimental procedure

Precipitation experiments were performed in a solutioncalorimeter (PARR 6755) equipped with a PARR 6772high-precision thermometer. The experiments were carriedout at constant room temperature (25 ± 1 �C) using deion-ized (MilliQ) water. Each experiment was repeated at leastsix times. The Dewar flask was filled with 100 ml of 0.033 Mor 0.1 M electrolyte solution (KCl, NaCl, LiCl, NaBr orNaF) containing Na2SO4. Ten milliliter of solution contain-ing BaCl2 in deionized water was loaded into a glass cellsealed with a detachable Teflon dish. The cell was immersedinto the Dewar and rotated by an external electric motor.As soon as thermal equilibrium was achieved, the glass cellwas opened and the reactants were mixed. The measuredtemperature change (DTc) due to the exothermic crystalliza-tion was used to calculate the heat of barium sulfate precip-itation (QBaSO4) in respective background salts. DTc wasconverted to heat (QBaSO4) by multiplying DTc by the en-ergy equivalent (e) of the calorimeter and its contents:QBaSO4 = DTc�e (e was derived by a pre-experimental stan-dardization process). Immediately after the crystallizationreaction had taken place (as indicated by abrupt tempera-ture change followed by lag period) 15 ml of the resultingsolution was filtered through a filter with 0.45 lm porediameter. The filtrate was then analyzed with ICP-AES(inductively coupled plasma atomic emission spectroscopy)using an iCAP 6000 (Thermo) plasma spectrometer for[Ba2+] concentration. The precipitate remaining on the filterwas imaged by scanning electron microscopy (SEM) andanalyzed by X-ray diffraction. Heat of dilution of the BaCl2solution (from 10 to 110 ml) in the solution of backgroundelectrolyte was equal within an experimental error for all ofthe background salts and therefore the heat of dilution wasnot included in the calculation of QBaSO4. The calorimetricdata reported in this work are then used to compare the rel-ative effects of different background electrolytes and not toderive absolute values. The enthalpy of BaSO4 precipitation(DHppt) was calculated as: DHppt = (�QBaSO4)/N, where N

is the number of moles of BaSO4 determined by comparingthe final concentrations of barium in the aqueous solutionto their initial values (under assumption that all the[Ba2+] consumed during the crystallization process is takenup by the stoichiometric precipitation of BaSO4).

The solution composition, the supersaturation (X) with re-spect to barium sulfate, the experimentally determined QBa-

SO4, DHppt and the measured concentration of [Ba2+] left insolution after the crystallization process are presented in Ta-ble 1. The error in the final barium concentrations representsthe reproducibility involved in the whole precipitation proce-dure. The saturation state is expressed as X = IAP/Ksp (IAP—ion activity product; Ksp—solubility product). The computerprogram PHREEQC (Parkhurst and Appelo, 1999) was usedto calculate the saturation index SI = log(IAP/Ksp) and ionic

Tab

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al Table 2Enthalpy of solution of BaCl2 � 2H2O (DHBaCl2) in electrolytesolutions.

Electrolyte DHBaCl2

Type Conc. = (M) (kJ/mol)

LiCl 0.1 15.53NaCl 13.57KCl 14.08

LiCl 0.03 13.33NaCl 12.61KCl 14.44

Nucleation in solution: Electrostatics and hydration forces 471

strength (IS). The concentration of [Ba2+] and [SO42�], back-

ground salts and X express concentrations of species and thesaturation state of the system that would be achieved in caseof complete mixing of working solutions in the final 110 ml ofsolution. Nevertheless it is worth noting that supersaturationin fact develops during the time of the mixing process. More-over [Ba2+] in solution is initially concentrated in a volume tentimes smaller than the [SO4

2�]. As a result the actual X in areal reaction time can be different from the calculated “nom-inal supersaturation”.

The enthalpy of solution of barium chloride dihydrate(BaCl2 � 2H2O) in selected background electrolytes wasdetermined by loading a glass cell of the calorimeter witha 0.15 g sample of solid BaCl2 � 2H2O and dissolving thesolid in the Dewar flask containing 100 ml of 0.03 M or0.1 M KCl, NaCl or LiCl aqueous solution. The calculatedheat of solution (QBaCl2 = DTc�e) was converted to enthal-py of solution (DHBaCl2) according to the formula:DHBaCl2 = (�Q BaCl2)/N, where QBaCl2 is expressed in kJand N in moles of BaCl2 � 2H2O. DHBaCl2 provides infor-mation about the solvation of Ba2+ in aqueous solutions ofdifferent chloride salts. The results are presented in Table 2.

2.2. Average crystal size

The average size of the crystals obtained in the precipita-tion experiments was determined from two-dimensional X-ray diffraction patterns collected using a single-crystal dif-fractometer equipped with an X-ray area detector (CCD).X-ray area detectors were initially used for protein crystal-lography in the 1980s, but more recently their use has beenextended to a number of applications, including the studyof polycrystalline materials (He, 2005). Two-dimensionaldiffraction patterns of polycrystalline samples consist of con-centric (Debye–Scherrer) rings associated with differentBragg reflections. Each ring is produced by the superpositionof reflections of many crystals illuminated by the X-raybeam, all of them with a set of (h k l) crystallographic planesoriented to fulfil the Bragg condition. These 2D-diffractionpatterns can be converted into conventional diffractograms(2h-scans) by radial integration of pixel intensities. Theseconventional diffractograms can be processed as usual formineral phase identification, crystallinity and crystallite sizemeasurements, refinement of cell parameters, etc. However,the 2D-diffraction pattern contains additional informationabout the grain size, the existence of preferential orienta-tions, and other textural features.


For instance, depending on the specific characteristics ofthe sample, the rings can be continuous or spotty. When aring is spotty, the variation of intensity along a ring associ-ated with a given h k l reflection (w-scan) gives an intensityprofile (after azimuthal integration) with a series of peaks.In a w-scan, each peak corresponds to the reflection froman individual crystal with the corresponding (h k l) planesoriented to fulfil the Bragg condition. These w-scan peakintensities depend on the crystal size: as the average crystalsize increases, the peak intensities increase and the numberof peaks decreases. From the average intensity of thesepeaks and using a calibration curve obtained with standardsamples, the crystal size can be determined. It is worth not-ing that the crystal size determined in this way representsthe real average physical size, a parameter that may be com-

Fig. 1. (a) Two-dimensional diffraction pattern of a sample of the precipassociated with the 1 2 1 reflection of barite. (b) 2h-Scan and peaks of the(For interpretation of color mentioned in this figure the reader is referre

pletely different from the so-called crystallite size. The crys-tallite size is an XRD term that indicates the size of acoherently diffracting domain and thus does not necessarilycoincide with the crystal size. This latter parameter is usu-ally determined by considering the full width at half maxi-mum of a given reflection in a conventional 2h-scan.

Here, the two-dimensional X-ray diffraction patterns ofthe precipitates have been obtained using an Oxford Dif-fraction Xcalibur Nova single-crystal diffractometerequipped with a CCD area detector Onyx (165 mm) andCu-Ka radiation. The precipitate samples were glued to afibre (the type commonly used for mounting single crystals)and placed at a distance to the detector of 65 mm. The 2D-patterns (Fig. 1a) were then studied using the XRD2DScan

software (Rodrıguez-Navarro, 2006). The samples were first

itate obtained in experiment 331-Na. The blue line delimits a ring24–1035 card (Barite, Pbnm). (c) w-Scan of the ring masked in (a).

d to the web version of the article.)

R2 = 0.99

5

10

15

5 10 15 20 25 30average size (µm) - X-ray

mea

n si

ze (µ

m) -

imag

e pr

oces

sing

Fig. 3. Correlation between mean crystal size (X ) and averagecrystal size of barium sulfate precipitate derived by image process-ing and X-ray diffraction method, respectively.


indentified to be barite by analyzing the reflections in a con-ventional 2h-scan diffractogram (Fig. 1b). Then, in order toperform the crystal size study, the reflection 1 2 1(2h = 28.744�) was selected. This is one of the three mainreflections of barite and is usually very well defined in thediffractograms. Fig. 1c shows the variation of intensityalong the 1 2 1 ring as a function of the w-angle (from 0to 180�) in the case of the sample 331-Na. These w-scanswere calculated by integrating pixel intensities within a 2hrange from �28.4� to �29.3�. The XRD2DScan softwaredetermines the number of peaks and the average peakintensity. From this average value, and using a calibrationcurve, the average crystal size can be determined. Here, thiscalibration curve was obtained using barite grains of knownsize. Table 1 shows the crystal sizes determined in this way.

2.3. Crystal size distribution (CSD)

SEM images of the barium sulfate precipitate were pro-cessed with the UTHSCSA Image Tool computer software(developed at the University of Texas Health Science Cen-ter at San Antonio, Texas and available from the Internetby anonymous FTP from maxrad6.uthscsa.edu) to deter-mine the sizes of the individual barite crystals representativefor the size distribution of the crystals that precipitated indifferent electrolytes. In all experiments the resulting precip-itate has a plate-like morphology (Fig. 2) and therefore thearea of the best expressed crystal face was used in this workas an indication of the relative size of the crystal. Crystalsize was then described by the diameter of the square withthe same area as the measured area of the respective crystalface. The crystal diameters estimated in this way (approxi-mately 100 for each sample) were used to generate crystalsize distributions with the program CrystalCounter (Eberlet al., 2000). The program calculates CSD shape, the meancrystal size (X ¼

PXf ðX Þ, where f(X) is the frequency of

group size X), the mean of the natural logarithms of thesizes (a ¼

PlnðX Þf ðX Þ), and the variance of the natural

Fig. 2. SEM image showing barite crystals precipitated in thepresence of 0.09 M NaCl as background electrolyte.

logarithms of the sizes (b2 ¼Pðln X � aÞ2f ðX Þ). According

to the approach proposed by Eberl et al. (1998), CSDshapes can be related to the crystal growth mechanism.Three basic CSD shapes corresponding to different growthmodes are: (a) an asymptotic CSD produced in systemswith constant-rate nucleation followed by size-dependent(proportional) surface controlled growth; (b) universal,steady-state curve attributed to Ostwald ripening, and (c)lognormal (one of the most common CSD in natural sys-tems (Eberl et al., 2002)) generated by a crystal growthmechanism having decaying-rate nucleation accompaniedby size-dependent growth. Size-dependent growth meansthat crystal growth rate is proportional to the initial crystalsize, so that larger crystals grow faster than smaller crystalsleading to increasing crystal size variance (b2) with time.Calculated mean crystal sizes (X ), crystal size variance(b2) and CSD shapes are reported in Table 1.

Because of the complex morphology of the crystals, sizesdetermined by image processing (IP) are not a very accurateexpression of the actual dimensions of the crystalline mate-rial. Therefore for selected samples, calculated mean crystalsizes determined from SEM images were compared withaverage crystal sizes determined by the X-ray diffractionmethod. The X-ray method probably gives a better estima-tion of the actual mean crystal size, but it has the disadvan-tage that does not allow estimating the CSD. Thus, as weneed to determine the CSD we have used the IP methodand the X-ray method is used just to check if there is a goodcorrelation with the mean sizes obtained by the IP. Thetrends in the relative differences in sizes of the crystals thatprecipitated in respective background electrolytes at givenexperimental conditions are in good agreement betweenthe two methods (Fig. 3). The actual values are different,but sizes obtained by X-ray diffraction correlate with realcrystal volume, while those based on image processing cor-relate with the area of the imaged faces only.

3. RESULTS

In all our experiments barium sulfate crystals are log-normally distributed (Table 1 and Fig. 4) implying a com-mon nucleation and growth mechanism (Eberl et al.,1998). At the same time crystal size (X ) and broadness ofcrystal size distribution (b2) vary at constant ionic strength

0

0.1

0.2

1 5 9 13 17diameter (µm)

freq

uenc

y

Fig. 4. Example of the crystal size distribution (CSD) of bariumsulfate precipitated in 0.03 M NaCl as a background electrolyte.Lognormal distribution was verified by the K–S (Kolmogorov–Smirnov) statistical test that compares CSD generated by Crystal-Counter (Eberl et al., 2000) based on the introduced data (solidline) with theoretical lognormal CSD (dashed line).


(IS) and constant thermodynamic driving force (supersatu-ration) depending on the background electrolyte present insolution (Table 1). The specific correlations are outlined be-low and presented explicitly in Fig. 5.

Chloride electrolytes (with different cations: Li+, Na+

and K+):

1. At X = 103.33 and IS = 0.03 M, b2 increases in the orderLiCl < NaCl < KCl.

2. At X = 103.77 and IS = 0.09 M, b2 increases in the orderKCl < NaCl < LiCl, that is, the effect is the reverse.

3. With KCl as background electrolyte the mean crystalsize (X ) is considerably larger at X = 103.77 (andIS = 0.09 M) than at X = 103.33 (and IS = 0.03 M).

4. With NaCl as background electrolyte the mean crystalsize (X ) is only slightly larger at X = 103.77 (andIS = 0.09 M) than at X = 103.33 (and IS = 0.03 M). (Atconstant IS = 0.03 M changing X does not seem to affectX ).

5. With LiCl as background electrolyte the mean crystalsize (X ) is smaller at X = 103.77 (and IS = 0.09 M) thanat X = 103.33 (and IS = 0.03 M) (the effect is the reverseto that of KCl).

6. For a given supersaturation (X = 103.33 or X = 103.77)and IS the mean crystal size (X ) decreases with increas-ing b2.

7. For a given background electrolyte, b2 increases withincreasing X and IS. The effect is less marked with KCl.

0

4

8

12

16

0 0.05 0.1 0.15 0.2 0.25 0.3

ß2

mea

n si

ze (µ

M)

3.77

3.47

3.33

KCl

LiCl

KCl

LiCl

NaCl

NaClNaBr NaF NaCl

= 10 , IS = 0.09 M

= 10 , IS = 0.03 M

= 10 , IS = 0.03 M

Fig. 5. Mean crystal size (X ) of barium sulfate precipitate atdifferent supersaturation (X) and IS conditions as a function ofcrystal size variance (b2). The dashed lines show the tendencies fordifferent chlorides, whereas the short-dash ellipse shows thetendency for different sodium halides.

Sodium electrolytes (with different anions: Br�, Cl� andF�):

8. At X = 103.33 and IS = 0.03 M the mean crystal size (X )is virtually the same for all the three electrolytes.

9. b2 depends on the background salt type, increasing in theorder NaBr < NaCl < NaF.

The enthalpy of precipitation of barium sulfate depends onthe background electrolyte and is less negative at higher X andIS (Table 1). The enthalpy of precipitation is given by:DH ppt ¼ UðBaSO4Þ � DH hydðBa2þÞ � DH hydðSO2�

4 Þ, whereU(BaSO4) is the lattice energy, DHhyd(Ba2+) andDHhyd(SO4

2�) are the enthalpies of hydration of the ions. Be-cause lattice energy does not depend on solution composition,the less negative DHppt implies higher energy expended ondehydration of the ions (enhanced ion–water attraction) athigher IS.

Enthalpy of solution of BaCl2 � 2H2O (DHBaCl2) de-pends on the ionic strength and on the salt type (Table2). DHBaCl2 results from the energy expended on breakingsolute–solute bonds (here constant lattice energy) and sol-vent–solvent interactions and the energy gain on ion solva-tion. Therefore, as the energy involved in solute–solutebonds does not depend on the background electrolyte,DHBaCl2 in different chloride salts is expected to be an indi-cation of the relative changes of water–water vs. barium–water interactions in respective electrolytes. Consequentlyless positive DHBaCl2 at higher KCl concentration impliesmore energetically favorable hydration of Ba2+ while morepositive DHBaCl2 at higher NaCl and LiCl concentrationindicates less favorable hydration of Ba2+ at higher IS.The hydration in this context is defined by the relative dif-ference in the affinity of water to the ion and the affinity ofwater to other water molecules (Samoilov, 1965).

4. DISCUSSION

The observed dependence of the characteristics of thesolid (b2 and X ) precipitated at constant X (by a commonmechanism as indicated by CSD shape) on the solutioncomposition (Fig. 5) can be explained by considering differ-ences in the reaction kinetics. A lognormal distribution ofbarium sulfate crystals precipitated in our experiments indi-cates that crystals were generated in systems with a decay-ing nucleation rate accompanied by size-dependent crystalgrowth (Kile et al., 2000). Such a crystal size distributionsuggests that nucleation and growth is controlled by advec-tion rather than diffusion of the reactants (Kile and Eberl,2003). In the our experimental procedure supersaturation(X) buildup starts after mixing the working solutions. Thetheoretical supersaturation level that could be achieved inthe system is very high. However, because of a very shortinduction period the actual X cannot exceed the thresholdvalue over which the nucleation rate surpasses the mixingvelocity, so that X is limited by crystal precipitation (Sohneland Mullin, 1987; Philips et al., 1999; Kile et al., 2000; Vi-cum et al., 2003; Schwarzer and Peukert, 2004). As a resultthe first nucleating particles grow while further nuclei aresimultaneously generated. The longer the period of nucle-


ation the higher the resulting crystal size variance (b2) (Phi-lips et al., 1999). For a given nominal supersaturation andmixing velocity (as applied in this work), the period inwhich nucleation and growth coexist depends on the induc-tion time (s) for nucleation, because the shorter the induc-tion time the higher the number of nucleation events duringthe “mixing period”. As a consequence, b2 is proportionalto s�1. Moreover, as s is inversely proportional to thenucleation rate, b2 results to be an indication of the nucle-ation kinetics. The variance of the CSD yields informationabout nucleation and initial growth conditions because,during the first few nanometers of growth (as relevant forour experiments), the b2 changes in response to solutionchemistry (Eberl et al., 1998).

The observation that means crystal size decreases withincreasing b2 (for different chloride salts at constant X) isconsistent with conclusion that in the investigated systemb2 tracks nucleation rates. In our experiments the only var-iable (for a given X and IS) is the background electrolyte.Therefore differences in the kinetics of barium sulfate crys-tallization and consequent crystal size variance and meancrystal size result from the influence of background ions.

4.1. Frequency of water exchange as rate-limiting factor for

nucleation

According to the classical nucleation theory increasingthe supersaturation and/or reducing the solid–liquid inter-facial tension lowers the nucleation barrier. The height ofthe nucleation barrier, in the case of spherical nuclei, is ex-pressed by free energy of formation of critical nuclei:

DG� ¼ 16p3

c3

�qjDlj2; ð1Þ

where c is the solid–liquid interfacial tension, q is the num-ber density of a crystal phase, Dl = lðBaSO4ÞðsÞ�lðBa2þÞðaqÞ � lðSO2�

4 ÞðaqÞ (where l designates the chemicalpotential of respective species in the solid (s) and the liquidstate (aq)). The rate J at which nuclei are formed dependsexponentially on DG*:

J ¼ j expð�DG�=kBT Þ ð2Þ

where kB is Boltzmann’s constant and j is a kineticprefactor.

Our experimental observations suggest that nucleationrates of barite (as predicted by b2) vary in different back-ground electrolytes regardless of the same X (i.e. constantDl) (Table 1 and Fig. 5). Therefore, from Eq. (2), differ-ences in the nucleation rates of barite are determined by dif-ferences in the kinetic barrier for nucleation (j) and/orsurface tension (c). The kinetic prefactor (j) is proportionalto the diffusion coefficient of crystal building units (Walton,1969; Jones et al., 2005). Diffusion of ions in aqueous solu-tions is determined by the frequency of water exchange(fH2O) between an ion solvation shell and a bulk fluid(Lee and Rasaiah, 1994, 1996; Chong and Hirata, 1999;Rasaiah and Lynden-Bell, 2001; Du et al., 2007), which de-pends on the competition between the tendency of the ionto orient water molecules in its solvation shell and the ten-dency of the water to preserve its hydrogen-bonded net-

work (Hribar et al., 2002). Solid–liquid interfacial tensionis also defined by the competition between cohesive forcesof the liquid and adhesive forces between water moleculesand the solid surface. Therefore fH2O (hence j) and c arein fact correlated. A longer residence time of water in thevicinity of an ion (as a result of enhanced ion–water or re-duced water–water affinity) means a less favorable j butlower interfacial tension. This implies that the same changesin solution can cause opposite effects on nucleation rate.This is in agreement with AFM (Kowacz et al., 2007) andmolecular simulation studies (Piana et al., 2006; Joneset al., 2008) that have shown that addition of methanol toan aqueous solution increases kinetics of two-dimensional(2D) nucleation on a barite surface in spite of the increasein c. These findings were attributed to the reduced kineticbarrier of cation desolvation as a result of the strengtheningof H-bonds in the aqueous solvent. The frequency of waterexchange around crystal building units was then suggestedto be the rate-limiting factor for surface-controlled 2Dnucleation of barium sulfate (Kowacz and Putnis, 2008) be-cause it defines the probability of contact of the ion in its“dehydrated state” with the crystal surface. Such an effec-tive contact, the starting point for a nucleation event, canmean that an ion is moved to a position where it sharesits water of solvation with the surface (or with anotherion in solution) so that its position at the surface (or inthe vicinity of the ion) is stabilized with respect to its resi-dence in the bulk. The results presented here suggest thation dehydration rates also control three-dimensional nucle-ation of barite in solution.

4.2. Long range electrostatic interactions and short range

hydration forces as controls of water exchange frequency

The dependence of the nucleation rates of barite (as indi-cated by b2) on the background salt (at given X and IS) andthe relative switchover in the effect of respective electrolyteson nucleation kinetics between the two studied X (and IS)conditions (Fig. 5) can be explained by considering factorsaffecting dehydration rates of ions immersed in electrolytesolution. The dehydration and association of ions will beaffected by the facility to strip water molecules from theion solvation shell and by the tendency of the structuredfluid to exclude ions from its H-bonded network.

The frequency of water exchange (fH2O) around an ion isdefined by the ratio (si/s0) of the residence time of a watermolecule in the closest position to the ion (si), to the residencetime of water in the bulk (s0). In electrolyte solution the po-tential energy of a water molecule oriented in an ion solvationshell (here we consider Ba2+ and SO4

2�) is lowered by attrac-tive interaction between the partial charge of the water dipoleand the unlike electric field of counterions (components ofbackground salt) (Samoilov, 1967, 1971). As a result theposition of a water of solvation of an ion immersed in electro-lyte solution is stabilized and the residence time of this water(si–salt) increases in salt solution in comparison to pure water(si) (Kinoshita and Harano, 2005).

The mean time during which two solvent molecules stayin the immediate vicinity of each other in the electrolytesolution (s0–salt) depends on the effect of the electrolyte on

IS = 0.09 M

0.3

NaClLiCl


water structure dynamics. The higher the potential of back-ground ions to orient water in their solvation shells (hydra-tion) the more retarded is the mobility of water molecules insolution (s0–salt increases). When high charge density of theion retards water mobility in its vicinity compared to mobil-ity within the hydrogen-bonded network of bulk water(si > s0) the hydration of an ion is defined as “positive”.Examples are Na+, Li+ and F�. When the water mobilityis increased in its vicinity compared to in the bulk(si < s0) the hydration of an ion is “negative”, e.g. K+,Cl�, Br� (Samoilov, 1965).

At IS = 0.03 M (lower electrolyte concentration) thefH2O around Ba2+ and SO4

2� (hence diffusion of the ions)is controlled by the “electrostatic environment”, which isrelated to the nature of the background electrolyte, partic-ularly to the tendency to form ion pairs (KCl(aq), NaCl(aq),etc.). For simple 1:1 electrolytes this tendency is related tothe electrolyte solubility: the lower the solubility the higherthe tendency of the electrolyte cations and anions to pair(Collins, 1995, 1997), which decreases the effect of theircharges on the residence time of water of hydration (si–salt)and thus on the mobility of Ba2+ and SO4

2�. Therefore themobility of Ba2+ and SO4

2� is higher in less soluble saltsand the nucleation rate of barite increases with decreasingsolubility of background electrolyte (Fig. 6).

Ion distribution in solution (and solubility of simple io-nic salts) depends on hydration characteristics. Similarlyhydrated ions tend to associate while oppositely-hydratedions tend to stay apart in solution (Hawlicka and Swiatla-Wojcik, 2003; Collins et al., 2007). As a result the kineticsof barite nucleation is faster in background salts composedby ions of the same (positive–positive or negative–negative)hydration compared to salts composed of ions of opposite(positive–negative) hydration. This can be illustrated bythe noticeably higher b2 in KCl with respect to NaCl asbackground electrolyte regardless of a very small differencein the solubility of these salts (Fig. 6).

IS = 0.03 M

0.04

0.08

0.12

0.16

0 10 20 30 40 50 60

solubility

ß2

opposite hydration

like hydration

NaFKCl

NaCl

LiCl

NaBr

Fig. 6. Crystal size variance (b2) of barium sulfate precipitate as afunction of solubility of background salt at ionic strength(IS) = 0.03 M and supersaturation (X) = 103.33. Trend lines followb2 in salts composed of ions of the same (“like-hydration”—NaF,KCl) and unlike (“opposite-hydration”—NaBr, LiCl, NaCl)hydration characteristics. Solubility is expressed as a mass percentof solute (Lide, 2004).

At IS = 0.09 M (higher electrolyte concentration), whereelectrostatic interactions are suppressed and hydrationshells overlap, the differences in the fH2O around Ba2+

and SO42� in respective background electrolytes are no

longer controlled by the “electrostatic environment” (ioncharge distribution) but by the effect of the electrolyte ionson the bulk solvent structure dynamics (s0–salt). The higherthe affinity of water to other solvent molecules (otherwaters or ions) in electrolyte solution, the less mobile andless prone the water will be to hydrate solutes (Ba2+ andSO4

2�) immersed in the electrolyte solution. Therefore,nucleation rates of barite increase with increasing positivehydration of background cation (the anion is common forall background electrolytes) (Fig. 7). This can be under-stood from the perspective of the competition for hydrationwater between background ions and barite building units:the higher the competition the faster the frequency of waterexchange. Such a conclusion is consistent with Raman spec-tral studies showing the effect of hydration of counterion(Rb+, Cs+, K+, Na+, Li+) on frequency of water exchangearound SO4

2� (Rull and Ohtaki, 1997). The difference inthe effect of background ions on the nucleation rate of bar-ite is the most strongly expressed between solutions of chlo-ride salt of negatively hydrated K+ and solutions ofchloride salts of positively hydrated Na+ and Li+. The effectof positively hydrated ions is very similar in spite of the sig-nificant difference in their hydration energy. Neverthelessthe mobility of water in electrolyte solutions (thereforethe residence time of water in the vicinity of other watermolecules) depends not only on the energy of ion–water

0.1

0.2

-1.00 -0.50 0.00 0.50 1.00 1.50

cation hydration ( E i = [kcal/mol])

ß2

positive hydrationnegative hydrationKCl

Δ

Fig. 7. Crystal size variance (b2) of barium sulfate precipitate as afunction of hydration (DEi) of background cation (i = K+, Na+,Li+) of respective chloride salt at ionic strength (IS) = 0.09 M andsupersaturation (X) = 103.77. Hydration values are taken fromChong and Hirata (1997) and expressed as a difference (DEi) in theactivation energy of removing a water molecule from the ionsolvation shell (Ei) and the activation energy of transferring a watermolecule from the first to the next coordination shell of anotherwater molecule (E0), i.e. DEi = Ei � E0 (Samoilov, 1965). DEi < 0corresponds to “negative hydration” (enhanced translationalmotion of water molecules in the vicinity of the ion, si < s0) andDEi > 0 to “positive hydration” (retarded water mobility in theadjacent environment of the ion, si > s0).

99.83

99.89

99.95

0 10 20 30 40 50 60

solubility

Ba2+

= [%

]

opposite hydrationlike hydration

NaF

KCl

NaCl

LiCl NaBr

Fig. 8. Relative amounts of Ba2+ (as a percent of initial Ba2+

concentration in solution) consumed during crystallization processas a function of solubility of background salt at ionic strength(IS) = 0.03 M and supersaturation (X) = 103.33. Amount of Ba2+

represents an average value from the precipitation experiments inthe presence of the respective background salt, and the error barsrepresent one standard deviation about that mean.

95

96

97

98

99

Ba2+

= [%

]

IS = 0.09 M

KCl

NaCl

LiCl


interaction, but is defined by the structure of water modi-fied by the ion (Koneshan et al., 1998). Experimental resultsshow that the mobility of water is significantly different inKCl solution in comparison to the relatively small differ-ences in water mobility in NaCl and LiCl (Ionov and Maz-itov, 1968).

The inversion in the influence of different chloride saltson the reactivity of barite with increasing ionic strength isconsistent with our previous AFM observations (Kowaczand Putnis, 2008). Such an effect can be explained by con-sidering the fact that the frequency of water exchangearound solute ions (here Ba2+ and SO4

2�) is a result of acompetition between the tendency of the solute to orientwater in its solvation shell and the tendency of a solventto preserve its structure, both factors that are affected bydifferent properties of the electrolyte solution. The solute–water affinity is affected by propagation of electric fieldsof background ions, the property that is most expressedat low ionic strength conditions. The dynamics of the sol-vent structure is affected by the hydration characteristicsof the individual background ions, the property that be-comes most pronounced at higher ionic strength. The rela-tive switchover between long range electrostaticinteractions and short range hydration forces is in agree-ment with the fact that in the limit of dilute solutions, ther-modynamic properties of electrolytes can be approximatedby continuum electrostatics, but when the ionic strength isgreater than �1 � 10�2 M, charge propagation (Debyelength) is comparable or smaller than the size of water mol-ecules (Akiyama et al., 2007) and the thermodynamicbehavior of the electrolyte depends significantly on the ef-fect of ions on solvent structure and dynamics (Conwayand Ayranci, 1999; Petsev and Vekilov, 2000; Kunz et al.,2004; Collins et al., 2007).

94-1.00 -0.50 0.00 0.50 1.00 1.50

cation hydration ( Ei =[kcal/mol])Δ

Fig. 9. Relative amounts of Ba2+ (as a percent of initial Ba2+

concentration in solution) consumed during crystallization processas a function of hydration (DEi) of background cation (i = K+,Na+, Li+) of respective chloride salt at ionic strength (IS) = 0.09 Mand supersaturation (X) = 103.77. Amount of Ba2+ represents anaverage value from the precipitation experiments in the presence ofthe respective background salt, and the error bars represent onestandard deviation about that mean.

4.3. Activation energy of nucleation and growth

The information about the nucleation rate and theamount of barite precipitate that has been generated in solu-tions of different background electrolytes allows us to extractsome information about the relative input of the nucleationvs. growth process in solid formation in respective solutions.The calorimetric study then provides information about theenergetical response of the system to specific processes incrystal formation. This data is then correlated with the rela-tionship between the fundamental steps in the crystallizationprocess and the respective phenomena involving rearrange-ment of solvent molecules around solutes and around othersolvent molecules in the bulk.

The relative amounts of [Ba2+] that have been consumedduring the crystallization process (assumed to be propor-tional to the amount of precipitate) correlates with solubil-ity at lower ionic strength and hydration of the backgroundelectrolyte at higher ionic strength conditions and thereforewith predicted nucleation rates (Figs. 8 and 9).

However the correlation between the solubility of thebackground salt and the relative amount of barium sulfateprecipitate follows different trend lines for the crystalliza-tion process in salts composed of oppositely-hydrated (i.e.NaBr, LiCl and NaCl) and like-hydrated (i.e. KCl and

NaF) ions. Less precipitate is generated in like-hydrated(more associated) salts, in which nucleation rates of bariteare higher, which suggests that X in these solutions is re-duced more by nucleation and less by growth comparedto precipitation in oppositely-hydrated salts and precipitatemass is added mainly by growth. The heat of barium sulfateprecipitation (QBaSO4) results from the net effect of nucle-ation and growth and generally increases with increasingamount of precipitate (Fig. 10).

However at lower X and lower IS conditions the depen-dence of QBaSO4 on the amount of precipitated solid followsdifferent trends for like-hydrated and oppositely-hydratedbackground salts, with relative dominance of nucleationin the former and growth in the latter (Fig. 11).

5

7

9

11

2.538 2.548 2.558 2.568 2.578 2.588

Ba2+ = [mM]

QB

aSO

4 = [J

]

IS = 0.09 M

NaCl

KCl

LiCl

Fig. 10. Heat of barium sulfate precipitation (QBaSO4) as a functionof concentration of Ba2+ consumed during crystallization processat ionic strength (IS) = 0.09 M and supersaturation (X) = 103.77.QBaSO4 and [Ba2+] represent average values from the precipitationexperiments in the presence of the respective background salt, andthe error bars represent one standard deviation about that mean.


Barite crystallization seems to be more exothermic inlike-hydrated electrolytes (the trend line for QBaSO4 as afunction of precipitate concentration is shifted towardshigher values on the y-axis) which implies that nucleationgives a more positive heat signal than growth. Due to thesignificant experimental variability, the relationship basedon the average values of QBaSO4 and [Ba2+] can be ques-tioned. Nevertheless it was shown that the dependence ofthe rate of nucleation (this work) and growth (Kowaczand Putnis, 2008) of barite on properties of the electrolytesolution also follows different trends for like and oppo-sitely-hydrated salts. This observation together with thefact that kinetics of nucleation and growth of barite changedifferently in response to the same changes in solution com-position (Kowacz et al., 2007; Kowacz and Putnis, 2008)supports the suggestion that the energetical costs of these

1.5

2.5

3.5

4.5

329.4 329.5 329.6 329.7 329.8 329.9

Ba2+ = [µM]

QB

aSO

4 =

[J]

opposite hydrationlike hydration

KCl

NaF

LiClNaBr

NaCl

Fig. 11. Heat of barium sulfate precipitation (QBaSO4) as a functionof concentration of Ba2+ consumed during crystallization processat ionic strength (IS) = 0.03 M and supersaturation (X) = 103.33.QBaSO4 and [Ba2+] represent average values from the precipitationexperiments in the presence of the respective background salt, andthe error bars represent one standard deviation about that mean.

elementary steps can be different. This can result from theproposed differences in the kinetic barriers for nucleationand ion addition at kinks (Kowacz and Putnis, 2008).Growth of barite was assumed to be limited by the energyrequired to remove water molecules hydrating the ion andthe surface while nucleation is limited by the probabilityof contact of building units in a “dehydrated state” i.e. bythe frequency of water exchange that determines dehydra-tion rates and mobility of ions in solution. Therefore ifwe treat water exchange as a spontaneous thermal fluctua-tion (Zhang et al., 2007), the energetic costs of a nucleationevent can be lower than that of ion attachment on the crys-tal surface. However, ion incorporation at kinks is morefrequent because it is stabilized by strong electrostatic inter-actions with neighboring molecules within the crystal struc-ture. Yet Coulombic forces can be insufficient to overcomethe energy barrier of dehydration and stabilize the ion posi-tion on a flat terrace or next to another ion in solution.

4.4. Weakly hydrated ions and heterogeneous nucleation

The tendency of the structured solvent to exclude ionsfrom its H-bonded network affects not only barite buildingunits but also background ions present in solution. Thesolutions are undersaturated with respect to backgroundsalts, therefore those do not precipitate, but composing ionscan associate in solution (Hawlicka and Swiatla-Wojcik,2003) and separate from bulk water structure. Our findingssuggest that such phenomena can have implications for het-erogeneous nucleation of barite in solution.

In our experiments the size of barite crystals precipitatedin different background sodium salts seems to be unaffectedby changes in nucleation rates (as inferred from indepen-dence of size on b2 at constant X) and for NaCl as a back-ground electrolyte crystal size does not depend onsupersaturation (for X = 103.33 and X = 103.47) (Fig. 5).Constant nucleus size regardless of increasing solutionsupersaturation (X) was observed for BaSO4 precipitationin the presence of NaCl and interpreted as an indicationof the dominant influence of heterogeneous nucleation (Ku-cher et al., 2006). At constant X, increasing nucleationkinetics should also result in precipitation of a higheramount of smaller particles. Therefore the independenceof particle size on nucleation rates and on the saturationstate of the solution observed in our experiments, impliesthe predominance of heterogeneous nucleation in the pre-cipitation of the solid. This is consistent with the fact thatthe lower investigated supersaturation level (X = 103.33)represents the borderline conditions between homoge-neously and heterogeneously dominated nucleation of bar-ite (He et al., 1995).

The experimental observation that Na+ can be incorpo-rated into the barite structure when present in solution as asalt of strongly hydrated anions (Kowacz and Putnis, 2008)suggests a possible explanation for the role of Na+ in thenucleation process. Sodium incorporation was attributedto the fact that this weakly hydrated ion is preferentially ex-cluded from the aqueous solvent with increasing solvent–solvent affinity. The tendency of an ion to separate fromthe bulk water structure leads to ion segregation at the


air/water interface (Jungwirth and Tobias, 2001, 2002; Gar-ret, 2004; Ghosal et al., 2005; Manciu and Ruckenstein,2005) or other interfaces (Collins, 1995) that can potentiallyserve as charged nucleation centers. The less hydrated theion (the lower its charge to radius ratio) the higher the ten-dency to separate it from the structured aqueous solvent.Therefore the suggested mechanism for heterogeneousnucleation should be more strongly expressed with dimin-ishing hydration of ions. This is in agreement with theexperimental observation that barite nucleation rates inthe heterogeneous region increase with increasing radiusof monovalent ions (Na+ < K+ < Cs+ < (CH3)4N+) (Heet al., 1995).

4.5. Solvent structure dynamics, kinetics of nucleation and

crystal size

Control of the water structure dynamics on the kinetics ofbarite nucleation results in differences in the dependenceof nucleation rates on supersaturation between solutions ofbackground salts of distinct hydration characteristics (as in-ferred from changes of b2 with X). This is expressed by only aminor increase in barite nucleation rates with increasing X inthe chloride salt of negatively hydrated potassium, and a rel-atively sharp increase of nucleation kinetics in chloride saltsof positively hydrated sodium and lithium (Fig. 5). Nega-tively hydrated K+ ions reduce the affinity of water to othersolvent molecules (s0–KCl decreases with concentration)which results in a higher degree of ordering of water mole-cules around a solute molecule immersed in KCl solutionas the electrolyte concentration increases. On the contrary,positively hydrated Li+ and Na+ ions retard water mobilityand therefore increase the average time that a solvent mole-cule spends in the bulk electrolyte solution (s0–NaCl and s0–

LiCl increase with concentration) with respect to its residencetime in the solute solvation shell. As a consequence, the fre-quency of water exchange around respective building units(i.e. the suggested rate-limiting factor for barium sulfatenucleation) increases with increasing KCl concentrationand decreases with increasing LiCl and NaCl concentrationin solution. This is in agreement with the respective changesin solution enthalpy of BaCl2 (DHBaCl2) in solutions of differ-ent background electrolytes (Table 2). DHBaCl2 expresses therelative differences between barium–water and water–waterattractions, and therefore the enthalpy of solution data canindicate differences in the water exchange around Ba2+ in dif-ferent background salts. At the same time the kinetic barrierfor growth increases at higher IS in all background salts, dueto electrostatic stabilization of water hydrating barite build-ing units in solution and at crystal surface. This is expressed inthe less negative enthalpy of precipitation at IS = 0.09 M(Table 1).

At higher X more material is brought into the reacting sys-tem, increasing the flux of ions into the surface and the prob-ability of effective contact of building units in the bulk.Therefore growth and nucleation rates increase. Neverthelessbecause of the strong dependence of nucleation rate and crit-ical nucleus size on supersaturation, the particle size is ex-pected to diminish with increasing X. However in ourexperiments this is only the case with LiCl as a background

electrolyte, while in negatively hydrated KCl a significant in-crease in crystal size at higher supersaturation (and ionicstrength) can be actually observed. For colloidal systems anincrease in the crystallite size at larger supersaturations wasrecently attributed to the fact that the probability of forma-tion of critical nuclei goes through a maximum as the X is in-creased because of the increase of solid–liquid interfacialtension (Auer and Frenkel, 2001), in contrast to the interpre-tation explaining crystal size as the effect of heterogeneousnucleation. Our findings suggest that the increase of bariteparticle size with increasing X can result from a solution-dependent kinetic barrier for nucleation which suppressesthe dependence of nucleation rates on X. Furthermore,growth rates of barite (in the region where two-dimensionalnucleation is not rate limiting) were suggested to be deter-mined by the energetic costs of expelling waters of solvationand not by the frequency of water exchange (Kowacz andPutnis, 2008). It is worth noting that the residence time ofwater in an ion solvation shell can be relatively long, depend-ing on the solvent structure dynamics, regardless of the weakelectrostatic ion–water attractions (Koneshan et al., 1998).Because of the differences in kinetic barriers for nucleationand for ion attachment at kinks, growth can be more favoredthan nucleation at higher X, thus increasing crystal size. Thiscan be the case in solutions where the dynamics of the aque-ous solvent structure increases with X, for example as a resultof addition of negatively hydrated solutes. Our observationsare in agreement with other experimental results that haveshown that increasing the concentration of the chloride saltof the negatively hydrated potassium ion increases the lineargrowth rate of barite, while chloride salts of positively hy-drated sodium and calcium ions mainly increase nucleationrates (Matynia et al., 2004).

5. CONCLUSIONS

Our findings suggest that nucleation rates of barite andthe resulting precipitate characteristics such as mean crystalsize and crystal size variance can be modified by back-ground salts present in solution, due to the effects of theseelectrolytes on the dynamics of the bulk aqueous solventstructure and on the water of solvation. The results pre-sented here support the hypothesis that the frequency ofwater exchange, which determines the diffusion of ions insolution, is the kinetic barrier for the nucleation processof barium sulfate (Kowacz and Putnis, 2008). The resultingdependence of the nucleation kinetics on solvent structuredynamics allows the prediction of the effect of aqueous sol-vent properties on the crystallization process. Our resultsimply that weakening water–water interactions will sup-press nucleation kinetics while increasing water affinity toother water molecules will assist nucleation kinetics. Ourconclusions are consistent with experimental observationssuch as the enhanced nucleation rates of barite by additionof methanol (Tomson et al., 2005) which reduces waterstructure dynamics and consequently lowers the kinetic bar-rier of the cation desolvation (Piana et al., 2006). Identifica-tion of the kinetic barriers for crystal nucleation andgrowth and recognition of their dependence on solutioncomposition suggests that it is possible to selectively control


fundamental steps in the crystallization process by adjust-ing solution composition. Such knowledge can add to ourunderstanding of the influence of additives on crystal pre-cipitation and should be helpful in designing a solvent withdesirable impact on crystallization product characteristics.

ACKNOWLEDGMENTS

The experimental work was carried out at Department of Geol-ogy at University of Oviedo within the EU Early Stage TrainingNetwork MIR (Mineral–fluid Interface Reactivity) Contract No.MEST-CT-2005-021120.

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