CRYSTAL GROWTH & DESIGN
Active Dissociated Species of Citric Acid for Growth Suppression of a Sodium Chloride Crystal
2008 VOL. 8, NO. 8 2770–2774
Shigeko Sasaki,* Norihito Doki, and Noriaki Kubota Department of Chemical Engineering, Iwate UniVersity, 4-3-5 Ueda Morioka, 020-8551 Japan ReceiVed October 12, 2007; ReVised Manuscript ReceiVed February 7, 2008
ABSTRACT: The equilibrium growth-starting supercooling ∆TGeq for the (100) and (111) faces of a sodium chloride crystal was measured at different pHs in the presence of citric acid. The equilibrium growth-starting supercooling ∆TGeq is defined for a given crystallographic face as the degree of supercooling at which the crystal face starts to grow when the solution is cooled continuously after the equilibrium impurity adsorption has been reached. It is a measure of the effectiveness of an impurity for adsorption and growth suppression. Different values of ∆TGeq were obtained at different pHs. Through the analysis of the data, the first, second, and third dissociated species of citric acid were determined to be simultaneously active for both adsorption and growth suppression. Magnitude of the activity of each dissociate was on the order of the third, second, and first dissociates. Introduction Crystal morphology has a large effect on powder characteristics of crystalline particles, such as flowability, bulk density, and caking tendency during storage. Therefore, it should be altered if not suitable for a given purpose. Morphology is determined by the relative growth rates of individual faces of a crystal. Crystal is bounded by the slowest growing faces, and fast growing faces disappear.1 Morphology thus developed is called growth form. Impurities or additives are used to change crystal morphology via an adsorption driven mechanism that alters the growth kinetics of crystallographic faces. Sodium chloride crystal is essential food-stuff in our daily lives, and is used widely as a raw material for chemical and pharmaceutical industries. However, crystalline particles of sodium chloride have a serious problem of caking during storage, which causes difficulties in handling and makes it lose its value as a powder. Caking (adhesion of crystals) begins with the adsorption of moisture from the air on the surface of particles.2,3 When the moist air is cooled to a temperature below the dew point, water vapor turns to liquid on the crystal surface and the liquid dissolves the crystals slightly, thus forming intercrystalline bridges due to temperature fluctuations. Sodium chloride crystals have a large surface area of contacts due to cubic shape and are prone to caking upon prolonged storage. In the case of spherical or near-spherical crystalline particles, the intercrystalline surface area of contacts decreases, and caking is unlikely to occur. Therefore, the alteration in shape (morphology) is needed for sodium chloride crystals to avoid caking. In addition, the altered morphology (noncubic) may improve solid flow characteristic, that is, these crystals are expected to flow more smoothly than cubic ones. For morphology control, the impurity (or additive) effect on crystal growth is effective and promising. In a previous study,4 the equilibrium growth-starting supercooling ∆TGeq was measured, respectively, for the (100) and (111) faces of a sodium chloride crystal in the presence of citric acid at pH ) 4.5. From the value of ∆TGeq, which increased with an increase in the concentration of citric acid, the Langmuir constants for adsorption of citric acid onto the (100) and (111) faces were determined. However, we could not determine what * Corresponding author. Tel/fax: +81-19-621-6343. E-mail: shigeko@ iwate-u.ac.jp.
kind of dissociated species of citric acid are active for changing the value of ∆TGeq. The growth-starting supercooling ∆TGeq is defined as a degree at which a crystal starts to grow when the solution is cooled continuously, after an impurity has adsorbed onto a crystal surface and reached an equilibrium.5,6 It is a measure of the effectiveness of an impurity for growth suppression and adsorption. In this study, ∆TGeq values were measured for the (100) and (111) faces of a sodium chloride crystal over a range of pH of the solution in the presence of citric acid. The Langmuir constants at different pHs were determined, and active dissociated species of citric acid for adsorption and the growthsuppression were estimated. The results of this study will be able to be applicable to morphology control of sodium chloride crystals. Theory The equilibrium growth-starting supercooling ∆TGeq can be related to the adsorption behavior of impurity as follows. The face growth rate G of a crystal is reduced by the presence of impurity, and it is given by the following equation if the equilibrium adsorption of impurities is assumed.7
G ) 1 - Rθeq (for Rθeq e 1) G0
(1)
and, for Rθeq > 1, G/G0 ) 0, where G0 is a face growth rate in the corresponding pure system, and θeq is the equilibrium coverage of active sites for impurity adsorption. The parameter R, the impurity effectiveness factor, is related to the critical radius of a two-dimensional circular nucleus of the crystal and defined6 as
R)
γa kTσL
(2)
where γ is the edge free energy per unit length of a step on the surface of a crystal, a is the surface area of crystal per growth unit, k is the Boltzmann constant, T and σ are the temperature and the relative supersaturation of a solution, respectively, and L is the average spacing between active sites, where impurities are to be adsorbed. In the case that the supersaturation is changed by altering the temperature T of a given solution as in this study, the supersaturation can be related to the supercooling ∆T() Ts T) as
10.1021/cg700995e CCC: $40.75 2008 American Chemical Society Published on Web 06/19/2008
Growth Suppression of a NaCl Crystal
σ)
Crystal Growth & Design, Vol. 8, No. 8, 2008 2771
∆T T + To
(3)
if the solubility C is approximated in the range of interest by a linear relation C ) β(T + To), where β and To are constants. By introducing the parameter r, defined by r ) (T + To)/T, the supersaturation can be converted to the supercooling by the following equation, if r is approximated to be constant in the temperature range of interest.6
σ)
∆T r
(4)
The sodium chloride-water system dealt with in this study is the case, where T ) 303-308 K and To ) 9 × 102 K and r ≈ 4. Therefore, the impurity effectiveness factor becomes, by inserting eq 4 to eq 2,
R)r
γa 1 γa r ) k∆TL ∆T kL
( )
(5)
From eqs 1 and 5, the face growth rate G can be written as a function of supercooling ∆T as
G ) G0(∆T)-1(∆T - ∆TGeq) (for ∆T g ∆TGeq)
Figure 1. Experimental setup: (1) sodium chloride seed crystal; (2) glass growth cell (50 mL beaker); (3) thermo-regulator; (4) cooler; (5) microscope; (6) CCD camera; (7) monitor screen; (8) video recorder; (9) magnetic stirring bar; (10) mercury in glass thermometer.
(6)
where ∆TGeq is the equilibrium growth-starting supercooling, which corresponds to (1 - Rθeq) ) 0 and below which G ) 0. The equilibrium growth-starting supercooling is written by
∆TGeq ) r
γa θ kL eq
(7)
Equation 7 can be related to an impurity concentration c, if the Langmuir adsorption isotherm θeq ) Kc/(1 + Kc) is assumed to apply, as
∆TGeq ) r
γa Kc kL 1 + Kc
(8)
where K is the Langmuir constant. Thus, the equilibrium growthstarting supercooling can be said to be a measure of the effectiveness of an impurity for adsorption and growth suppression. It is noted that, when an equilibrium adsorption is not reached, the supercooling at which the crystal starts to grow is called simply as the growth-starting supercooling and denoted by ∆TG.5 Experimental Section Measurements of the growth-starting supercooling ∆TG were performed as same as in a previous paper.4 The experimental setup is shown in Figure 1. Typically, the saturated 35 °C () Ts) sodium chloride aqueous solution doped with citric acid was introduced into the growth cell and the pH was adjusted to a given level by adding an appropriate quantity of solid sodium hydroxide. The solution was agitated with a magnetic stirrer and kept at 34.3 °C () TA), a temperature of 0.7 °C lower than the saturated temperature 35 °C, for a period of adsorption time tA, during which the crystal did not grow due to the presence of citric acid and the low supersaturation, and citric acid was made to adsorb on the crystal surface. Then, the solution was cooled continuously at a constant rate of 0.3 °C/min until the seed crystal surface started to grow. The start of the crystallization was detected visually on a monitor screen through a CCD microscope. The growth-starting supercooling ∆TG was calculated as the difference between the saturation temperature Ts and the growth-starting temperature TG. The experiments consist of two parts. In the first part, the adsorption time tA needed for an equilibrium adsorption to be established was determined, and, in the second part, the equilibrium growth-starting supercooling ∆TGeg was measured, under the condition of equilibrium adsorption, at different pHs over a wide range of impurity citric acid concentration.
Figure 2. Effect of adsorption time tA on the growth-starting supercooling. Adsorption temperature, TA ) 34.3 °C, adsorption supercooling, ∆TA ) 0.7 °C. The sodium chloride crystals used for the measurements were prepared as follows: The cubic crystals, which have only {100} faces, were crystallized from a pure aqueous solution by natural cooling, while the octahedral crystals having {111} faces were crystallized by natural cooling from a solution doped with citric acid, of which pH was adjusted to 4.5. The crystal having the {111} faces were cured, prior to the ∆TG measurement, by growing it at a supercooling of 2 °C in a pure sodium chloride solution for 6 h in order to remove citric acid which may remain on the crystal surface. Determination of Equilibrium Adsorption Time. The growthstarting supercooling for the (111) face was measured for an impurity concentration of 0.4 mol/L at pH ) 4.5, over a range of adsorption time tA from 1 to 23 h, to identify the adsorption time tA needed for an equilibrium adsorption to be established. The measured ∆TG values for the (111) face are shown in Figure 2 (square symbols) as a function of adsorption time tA, in which the corresponding ∆TG values for the (100) face, obtained in the previous study,4 are also plotted (triangles). Either of these values increases with an increase in adsorption time and reaches a constant level after about 20 h. According to these results, we concluded that equilibrium adsorption of citric acid was established at tA > 20 h. Measurements of the Equilibrium Growth-Starting Supercooling ∆TGeq. The equilibrium growth-starting supercooling ∆TGeq was measured under controlled pH conditions (pH ) 3.0, 3.8, and 5.4) over
2772 Crystal Growth & Design, Vol. 8, No. 8, 2008
Sasaki et al. Table 1. Values of the Langmuir Constant K and r(aγ/kL) for the (100) and (111) Faces Determined by Fitting the Data to Equation 8
with a Nonlinear Least Square Method surface
pH
r(aγ/kL)
K (mol/L)-1
(100) face
3.0 3.8 4.5 5.4 3.0 3.8 4.5 5.4
4.24
5.4 ( 0.3 5.1 ( 0.4 10.0 ( 0.8 12.3 ( 0.9 4.7 ( 0.4 7.2 ( 0.3 12.5 ( 0.8 16.3 ( 1.5
(111) face
Figure 3. Equilibrium growth-starting supercooling ∆TGeq for the (100) face as a function of citric acid concentration at different pHs. The solid lines are the best fits of eq 8.
4.79
starting supercooling ∆TGeq with a nonlinear least-squares method by assuming a constant value of the first parameter r(γa/ kL) for each crystallographic face. The assumption of a constant value of r(γa/kL) was considered to be reasonable, because r is constant (∼4) in the temperature range considered as mentioned above, γ and a are constant for a given crystallographic face and L, average spacing between adsorption-active sites, is also constant for a given combination of crystallographic face and impurity.8 The parameter values determined are listed in Table 1. The Langmuir constant obtained by fitting changed depending on the solution pH. It is because the concentration of dissociated species of citric acid depends on pH, as discussed below in detail. Therefore, the experimental Langmuir constants obtained above are considered to be apparent ones. Molar Concentrations of Dissociated Species of Citric Acid as a Function of pH. The dissociation behavior of citric acid in a supersaturated sodium chloride aqueous solution should be known to analyze the effect of pH on ∆TGeq. Generally, citric acid dissociates in aqueous solution as follows.
[HOOCCH2C(OH)(COOH)CH2COOH] ) [HOOCCH2C(OH)(COOH)CH2COO-] + H+ [HOOCCH2C(OH)(COOH)CH2COO-] ) [-OOCCH2C(OH)(COOH)CH2COO-] + H+ [-OOCCH2C(OH)(COOH)CH2COO-] ) [-OOCCH2C(OH)(COO-)CH2COO-] + H+ If the molar concentrations of the nondissociated species A, the first, second, and third dissociated species A1*, A2*, and A3* are denoted as c0, c1, c2, and c3, respectively, the total concentration of citric acid c can be written by the following equation. Figure 4. Equilibrium growth-starting supercooling ∆TGeq for the (111) face as a function of citric acid concentration at different pHs. The solid lines are the best fits of eq 8. a range of citric acid concentration from 0.05 to 0.5 mol/L under the condition of adsorption time tA ) 22 h.
c ) c0 + c1 + c2 + c3
The molar concentrations c0, c1, c2, and c3 can be expressed, respectively, as a function of pH() -log [H+]) as,
Results and Discussion Equilibrium Growth-Starting Supercooling as a Function of Impurity Concentration. Figures 3 and 4 show the results of ∆TGeq obtained for the (100) and (111) faces, respectively. In these figures, the data obtained at pH4.5 in a previous study4 are also plotted. The solid lines are the best fits of eq 8. Fitting procedure will be explained in the next section. The value of ∆TGeq increases as the impurity concentration is increased and depends on the value of pH of the solution. The highest value of ∆TGeq was obtained at pH ) 5.4 both for the (100) and the (111) faces. Determination of Langmuir Constant K and the Value of r(γa/kL). Equation 8, which includes two adjusting parameters of r(γa/kL) and K, was fitted to the experimental growth-
(9)
c0 ) f0(pH)c
(10a)
c1 ) f1(pH)c
(10b)
c2 ) f2(pH)c
(10c)
c3 ) f3(pH)c
(10d)
where f0(pH), f1(pH), f2(pH), and f3(pH) are molar fractional concentrations of A, A1*, A2*, and A3*, respectively. The molar fractional concentrations are given as follows:
f0(pH) )
{
}
1 1 + K1/10-pH + K1K2/10-2pH + K1K2K3/10-3pH (11) f1(pH) ) f0(pH)
K1 10-pH
(12a)
Growth Suppression of a NaCl Crystal
f2(pH) ) f0(pH) f3(pH) ) f0(pH)
Crystal Growth & Design, Vol. 8, No. 8, 2008 2773
K1K2 -2pH
10
K1K2K3 10-3pH
(12b) (12c)
where K1, K2, and K3 are molar dissociation constants defined by actual molar concentrations, of which numerical values were determined in this study for the saturated sodium chloride solution by the titration method.9
K1 )
c1[H+] ) 1.2 × 10-2 c0
(13a)
+
c2[H ] ) 3.1 × 10-4 c1
(13b)
c3[H+] ) 2.7 × 10-5 K3 ) c2
(13c)
K2 )
The calculated molar fractions f0(pH), f1(pH), f2(pH), and f3(pH) are shown in Figure 5 with dotted lines as a function of pH. Active Dissociated Species for Adsorption and Growth Suppression. The Langmuir constants K determined by fitting of eq 8 to the experimental ∆TGeq are shown in Figure 5, together with the molar fractional concentration distributions of citric acid and its dissociated species, which are designated with dotted lines (see y-axis on the right-hand side). The solid circles represent K values for the (100) faces and the open squares the (111) faces, whose error bars indicate the standard errors. The experimental K values change depending on the pH. This suggests that the experimental K values are not real ones but apparent ones that are affected by the concentration of active dissociated species of citric acid. As can be seen in Figures 3 and 4, citric acid is effective for the suppression of crystal growth (increasing ∆TGeq) at pH values above 3.0 and, as shown in Table 1, the K value increases with an increase in pH. From these experimental results and the distributions of f0(pH), f1(pH), f2(pH), and f3(pH), all of the dissociated species are considered to be responsible simultaneously for adsorption and increasing ∆TGeq, as will be shown later.
The apparent Langmuir constants K can be theoretically described as follows. Each of dissociated species A1*, A2*, and A*3 is assumed to adsorb on active sites at random, respectively, according to the Langmuir mechanism, and nondissociated citric acid is assumed not to adsorb. The adsorption rate of the ith dissociated species kaici(1 - θ) is equal to the corresponding desorption rate kdiθi if an equilibrium is reached, and the desorption rate constant kdi is assumed to have a same value (kd) for all the dissociated species, and the surface coverage by 3 the ith species, θi is assumed to satisfy ∑i)1 θi ) θ. Finally, the following adsorption isotherm can be obtained.
θ)
K1rc1 + K2rc2 + K3rc3 1 + K1rc1 + K2rc2 + K3rc3
(14)
where Kir() kai/kd) is the real Langmuir constant for the ith dissociated species, which does not depend on the concentration ci. Comparing eq 14 with the ordinary Langmuir isotherm θeq ) Kc/(1 + Kc), which was used for the derivation of eq 8, gives the following equation.
Kc ) K1rc1 + K2rc2 + K3rc3
(15)
Inserting eqs 10b, 10c, and 10d into eq 15 gives
Kc ) K1r f1(pH)c + K2r f2(pH)c + K3r f3(pH)c
(16)
Dividing both sides of eq 16 by the total concentration c gives
K ) K1r f1(pH) + K2r f2(pH) + K3r f3(pH)
(17)
The pH dependency of the apparent Langmuir constant K can be explained by eq 17. Equation 17 was fitted by using a nonlinear least-squares method to the experimental Langmuir constants K. The results of fitting are shown in Figure 5 as solid lines, which are seen to reasonably trace the experimental data. The values of K1r, K2r, and K3r obtained by the fitting were K1r ) 3.40 (mol/ L)-1, K2r ) 6.41 (mol/L)-1, K3r ) 13.44 (mol/L)-1 for the (100) face and K1r ) 3.77(mol/L)-1, K2r ) 7.93(mol/L)-1, K3r ) 17.78(mol/L)-1 for the (111) face. The order of magnitude is K1r < K2r < K3r both for the (100) and (111) faces, which are the same order of the magnitude in the valence of the dissociated species. This suggests that the dissociated species adsorb on the crystal surface with electrostatic force. Conclusions (1) The equilibrium growth-starting supercooling ∆TGeq was measured for the (100) and (111) faces of a sodium chloride crystal in the presence of citric acid as an impurity over a range of pH from 3.0 to 5.4. The experimental data were analyzed with a model presented in this study. (2) The apparent Langmuir constants K were determined from the measured data of ∆TGeq. The value of K increased with an increase in pH, for the both crystallographic faces. (3) The first, second, and third dissociated species of citric acid were estimated to be active for the adsorption and the growth suppression. Magnitude of the activity was on the order of those of the third, second, and first dissociates. (4) The dependency of the apparent Langmuir constant K on pH was explained theoretically by considering the adsorption activities of the dissociated species and their fractional concentration distributions (eq 17) as shown in Figure 5.
Figure 5. The relationship between the Langmuir constant K determined by the fitting and the fractional distribution of dissociated citric acid species as a function of pH. The solid lines are the theoretical Langmuir constant K for the (100) and (111) faces or best fit lines of eq 17.
References (1) Meenam, P. A.; Anderson, S. R.; Klug, D. L. In Handbook of Industrial Crystallization; Myerson, A. S., Ed.; Butterworth-Heinemann: Boston, 2002; pp 67-100.
2774 Crystal Growth & Design, Vol. 8, No. 8, 2008 (2) Lowry, T. M.; Hemmings, F. C. J. Soc. Chem. Ind.: London 1920, 39, 101T–110T. (3) Moss, H. V.; Schilb, T. W.; Warning, W. G. Ind. Eng. Chem. 1933, 25, 142–147. (4) Sasaki, S.; Kubota, N.; Doki, N. Chem. Eng. Technol. 2006, 29, 247–250. (5) Kubota, N.; Sasaki, S.; Doki, N.; Minamikawa, N.; Yokota, M. Cryst. Growth Des. 2004, 4, 533–537. (6) Kubota, N.; Sasaki, S.; Doki, N.; Yokota, M. Cryst. Growth Des. 2005, 4, 509–512.
Sasaki et al. (7) Kubota, N.; Yokota, M.; Mullin, J. W. J. Cryst. Growth 2000, 212, 480–488. (8) Kubota, N.; Mullin, J. W. J. Cryst. Growth 1995, 84, 509–514. (9) Yoshimura, N.; Okazaki, M.; Nakagawa, N. Anal. Sci. 2000, 16, 1331–1335.
CG700995E
