Sucrose crystal growth in the presence of dextran of different molecular weights

Journal of Crystal Growth 355 (2012) 17–25

Contents lists available at SciVerse ScienceDirect

Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro

Sucrose crystal growth in the presence of dextran of different molecular weights Issam Khaddour n, Anto´nio Ferreira, Luı´s Bento, Fernando Rocha n LEPAE, Departamento de Engenharia Quı´mica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

a r t i c l e i n f o

abstract

Article history: Received 23 November 2011 Received in revised form 25 May 2012 Accepted 29 May 2012 Communicated by S. Veesler Available online 7 June 2012

The effects of variable concentrations of different molecular weight fractions of dextran on the interfacial free energies and the kinetic coefficients of the overall linear growth rates of the sucrose crystal were evaluated at 40 and 50 1C. Dextrans-reducing effects on the interfacial free energy increased the overall linear growth rates of sucrose at 40 1C. Further, dextrans-reducing effects of the growth kinetic coefficients resulted in lower growth rates of the sucrose crystals at 50 1C. Impurity effectiveness factor, differential heat of adsorption and Langmuir isotherm constant were determined, for the used dextrans, at 50 1C and relative supersaturation of 0.161. The dextran of molecular fraction of 2000 kilo Daltons (kDa) showed considerably high effectiveness factor in comparison with the dextrans of molecular fractions of 70 and 250 kDa. Role of dextran in retarding the advancement of the growth steps in the vicinity of its incorporation on the face (100) of the sucrose crystal is pointed out using AFM technique. & 2012 Elsevier B.V. All rights reserved.

Keywords: A1. Impurities A1. Surface structure A2. Growth from solutions B1. Sucrose

1. Introduction Dextrans are a class of extracellular microbial polyglucose, where the glucose units are linked through a-(1–6) linkages with branching at a-(1–3), and less frequently at a-(1–4) and a-(1–2). Microbial infection of the damaged sugar beet and sugar cane crops by Leuconostoc mesenteroides forms dextrans [1]. Dextrans were found to cause elongation of the sucrose crystals along the c-axis [2]. In many cases, needle-like sucrose crystals were observed [2–4]. Number of attempts was carried out to research the effect of dextran on sucrose crystal growth from technical and synthesized sucrose solutions [5–12]. However, only few studies were performed to evaluate the effect of the different molecular fractions of dextran on the growth rate of the sucrose crystal [3,5,7,10]. Abdel Rahman et al. [3] applied only mass balance equations and did not show any estimation of the growth rate. Promraksa et al. [7] estimated the partition coefficient of different molecular fractions of dextran, and concluded that the increase of dextran concentration and/or the molecular weight do not strongly affect the partition coefficient. Impurity effectiveness factor aeff determines the strength of the impurity in retarding the growth rate, which can be estimated

n

Corresponding authors. Tel.: þ 351 225081678; fax: þ 351 225081632. E-mail addresses: [email protected] (I. Khaddour), [email protected] (F. Rocha). 0022-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jcrysgro.2012.05.039

from Kubota–Mullin model [13–16]   K L ci Ri =R ¼ 1aef f yeq ¼ 1aef f 1 þK L ci

ð1Þ

where R and Ri (m/s) are the overall linear growth rates from pure and impure solutions, respectively, yeq (dimensionless) is the fractional surface coverage by the adsorbed impurity at equilibrium, KL (dimensionless) is Langmuir constant and ci is the impurity concentration in mole fraction. The aim of this work is to estimate and compare the growth rate of sucrose crystals at two temperatures (40 and 50 1C) in the presence of variable concentrations of three dextrans of molecular fractions 70, 250 and 2000 kDa. Also, the effects of dextrans on the surface pattern of the sucrose crystals will be discussed. Finally, theoretical aspects regarding the effect of dextrans on the growth and the morphology of the sucrose crystal will be presented.

2. Experimental section 2.1. Growth rate experiments Supersaturated, pure and dextran-doped, aqueous sucrose solutions were prepared at two temperatures, i.e., 40 and 50 1C, to perform isothermal batch crystallization runs starting from initial relative supersaturations of 0.181 and 0.161, respectively. The relative supersaturation s is expressed as s ¼(a  a*)/a*, where a and a* are the activities of sucrose in the supersaturated

18

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

the sieves of 125 and 250 mm, however, this can be easily ascribed to the difference between the used sizing techniques, i.e., between the sieves and Coulter laser sizer. At the end of each run a dissolution experiment was carried to estimate the effect of dextran on the solubility of sucrose, where an amount of 100 ml of ultrapure water which contains dextran concentration equal the one in the solution was added into the crystallizer, and the found saturation 1Brix reading was reported and compared with the one of the pure system. Considering Charles’ solubility data [17] as reference for solubility of sucrose in pure aqueous solutions, negligible changes in the saturation Brix were found.

and the saturated solutions, respectively. Dextran fractions of average molecular weights of 70, 250, and 2000 kDa were purchased from ChemApplic, VWR and SIGMA, respectively, and the used concentrations of each dextran are shown in Table 2. The size distribution of the dextran of 2000 kDa ranges from 1500 to 2800 kDa; but the ranges of the size distribution profiles for the other dextrans are not available, and the suppliers showed only that 70 and 250 kDa are approximate and average molecular weight values. 4 L jacketed batch crystallizer made of stainless steel was used. Fig. 1 shows a cross section of the crystallizer and the impeller and the shape of the impeller blades. Dextran-doped solutions were prepared by adding, sequentially, the required quantities of dextran, ultrapure water (of resistivity of 18 mOcm), and refined sucrose crystals of purity of 99.95%. The dissolution was always carried out at 60 1C, and then a cooling was performed to the work temperature. An accurate amount of seed crystals (16 g) of characteristic size of 250710 mm was used for each run. Agitation speed was set on 250 rpm. Duration of each run was approximately 24 h. Crystals samples were drawn at different intervals of the growth (using vacuum filtration with filter pore size of 0.45 mm) to perform the AFM experiments. Further, the final crystals were also analyzed for their dextran content, their shape using image analysis and their specific surface area using BET method. The used seeds were prepared by sieving several batches of refined sucrose crystals to obtain the product between two sieves, i.e., 125 and 250 mm, and the sieving time was 30 min for each batch. The sieving products were gathered in one big sample and sieved again to obtain the product between the sieves of 125 and 250 mm. The amount of the final product was sufficient to supply all the performed runs, and its characteristic size was determined using Coulter laser sizer (Coulter LS 230) and found to be 250710 mm. One may question obtaining a characteristic size of 250710 mm as the seeds were obtained from sieving between

2.2. Surface pattern using AFM technique Surface pattern observations of the face (100) of sucrose crystals grown, at 50 1C, from dextran-doped solutions were carried out at different time intervals of the growth. The obtained crystals were washed 3 times, 5 min each time, using sucrosesaturated ethanol solution. AFM imaging of the examined crystals was conducted in the contact mode using Multimode NanoScope IVa (Veeco, Santa Barbara, USA). Standard silicon nitride AFM tips (Veeco, Santa Barbara, USA) were used. Cantilevers with nominal force constants of 0.12 N/m were typically utilized in order to minimize the force applied to the crystal surface during the scanning, and the set point voltage was continually adjusted to the lowest level for which tip-crystal contact was maintained. In AFM, the used silicon nitride tips had an apex angle of 351. Scanning frequency was typically 5 Hz with 512 lines per frame. 2.3. Determination of the incorporated dextran into the sucrose crystals Fast protein liquid chromatography (FPLC) system (Pharmacia LKB, Sweden) was connected to an evaporative light scattering detector (ELSD), and used to analyze the dextran content. A separation column, Superose 12 (Pharmacia LKB), with size exclusion limit of circa 2  106 g/mol as globular protein was used. One litre of the eluent was composed of 70% (volume to volume) ultrapure water, 30% (volume to volume) acetonitrile and 0.005 mol of ammonium acetate. The pH of the eluent was 7.070.1. The eluent was filtered through a 0.45 mm membrane, and then degassed for 15 min using ultra-sounds. Samples of dry sucrose crystals with or without dextran were diluted in ultrapure water to obtain 50% (mass to mass), and then adjusted to pH 7.0 70.1 using filtered sodium hydroxide solution 0.015 N. Calibration curve was prepared for each dextran fraction with concentrations range from 100 to 4800 mg/kg of solution

Table 1 Effectiveness factor, Langmuir constant, differential heat of adsorption and the fractional surface coverage of the dextrans (70, 250 and 2000 kDa) obtained from applying Kubota–Mullin model for sucrose growth runs performed at sin ¼ 0.161 and 50 1C. Parameter

aeff KL  10  6 Qdiff (kJ/mol)

yeq

Dextran fraction (kDa) 70

250

2000

0.77 3.9 40.8 0.53, 0.77, 0.87

0.58 2.0 39.0 0.14, 0.33, 0.49

3.00 20.0 45.2 0.17, 0.25

Table 2 Interfacial free energies g and the kinetic coefficients C4 of the growth of sucrose, at 40 and 50 1C, from pure solutions and in the presence of different concentrations of the three used molecular weight fractions of dextran. Run

Pure system Dextran fraction (kDa) 70

250

2000

At 40 1C

At 50 1C

Dextran (g/L of water)

g (10  3 J/m2)

C4 (10  7 m/s)

Dextran (g/L of water)

g (10  3 J/m2)

C4 (10  7 m/s)

0

5.17 0.2

3.7 7 0.2

0

3.67 0.1

4.5 7 0.1

1.28 3.85 7.71 1.28 3.85 7.71 1.28 3.85 7.71

4.3 4.2 4.1 4.0 4.1 3.9 4.0 4.1 4.1

2.5 2.5 2.5 2.2 2.3 2.3 2.5 2.6 2.6

1.28 3.85 7.71 1.28 3.85 7.71 1.28 2.10 3.85

3.9 4.0 3.6 3.6 3.4 3.6 4.0 3.2 –

5.1 2.1 1.8 4.2 3.8 4.0 2.3 1.7 –

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

19

Fig. 1. Left: a cross section profile of the used crystallizer and impeller; right: the shape of the impeller blades. A, agitator; R, refractometer; S, seed vessel; V, on–off valve. Dimensions in mm.

containing 50% mass of sucrose, and the peak height was used as reference to evaluate the concentration of the dextran. Working conditions of the ELSD were nitrogen flow rate of 5 L/min at temperature of 80 1C. The system was stabilized for at least 45 min before each run; during this period the eluent flow rate was adjusted as 0.3 ml/min. After the ELSD signal became stable, the column was connected to the ELSD and the flow rate was set on 0.6 ml/min. Run time was set on 80 min, and air-free sample was injected into the motor valve to start the run.

3. Results and discussion 3.1. Effects of dextran fractions on the solubility of sucrose and the metastable zone width The solubility experiments which were performed at the end of each run showed negligible effects of the used concentrations of the dextran fractions on the solubility of sucrose. Previous works did not show the effect of dextrans on the solubility of sucrose, and most of these works were carried out using technical sucrose solutions [3,5,6,10–12]. However, Promraksa et al. [7] assumed negligible influence of the different dextrans on sucrose solubility (at 40 1C) when the dextran concentration is less than 2000 ppm/1Brix. The used concentrations of dextran are 1.28, 3.85 and 7.7 g/1 L of water which correspond to 500, 1500 and 3000 ppm/1Brix. So and taking into account the solubility experiments performed in this work, one accepts negligible effects of the used dextrans on the solubility of sucrose. The metastable zone width at 40 1C was experimentally found to be s ¼[0  0.259] [18], so this work was carried out within the metastable zone range for this temperature. Size distribution analyses of the final crystals were performed for the runs containing concentrations of dextran equal to 3.85 g/L of water at 50 1C (see Fig. 2). No sharp nucleation peaks were detected, i.e., the work was done within the metastable zone width. However agglomeration can be claimed due to the broad spread of the main peaks towards the larger sizes. This noticed tendency of

Fig. 2. Size distribution functions (by volume percentage) for final sucrose crystals grown from pure system and for sucrose crystals grown from dextran-doped solutions at concentration of 3.85 g/L of water at 50 1C.

agglomeration can be ascribed to the increase in the viscosity of the sucrose solutions due to dextrans [19,20]. 3.2. Shape factor problem The specific surface areas of the sucrose crystals were estimated using the BET method, and then the shape factors of the crystals were evaluated using image analysis following similar approach to the one applied by Ferreira et al. [21]. The aim was to understand the effect of the different dextrans on the surface and the volume shape factors of sucrose crystal. However, only nitrogen gas was available to determine the surface area. In fact, krypton gas is recommended for estimating the specific surface area of sucrose, which renders the results to be not rigorous enough. Even so, the specific surface area for a sample of final sucrose crystals, resulted from growth from pure solution, was

20

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

detected when used at initial concentrations higher than 40 g/L of water (not shown in this work). These findings can be ascribed to the use of aqueous sucrose solutions, and not technical solutions. Promraksa et al. [7] used Roberts’ method to analyze the dextrans of 75 and 250 kDa, and found that only about 7% of the total dextran in the solution was transferred to the sucrose crystals. Overall linear growth rates R, Ri (m/s) were calculated using a1 ¼0.64 and b1 ¼4.52, and applying the same growth rate formula as shown in other work [18]. Growth rate curves were represented as R vs. s or Ri vs. s. 3.3. The effect of dextran fractions on sucrose crystals growth at constant supersaturation

Fig. 3. Shapes of normal and slightly elongated sucrose crystals along the c-axis resulted at 50 1C of the growth from doped solution with dextran of molecular weight of 2000 kDa and a concentration of 3.85 g/L of water. The circle shows needle-like crystal of size less than 200 mm.

found to be 0.057 m2/g, which is in the range of the reported surface areas of the sucrose crystals by Bubnik and Kadlec [22]. However, the use of the krypton gas is still advisable and more rigorous. Randolph and Larson [23] reported that b1 ¼6a1 is valid even for highly irregular particles, where a1 is the volume shape factor and b1 is the surface shape factor. Further, Barreiros et al. [24] found that the results of analyzing few hundreds of crystals did not differ much from those obtained by analyzing more than 1000 crystals. They also emphasized that the shape factor varies from one sample to another and depends on the technique used for their assessment. Furthermore, consideration should be given to the changes of the morphology of the sucrose crystal as a function of temperature or supersaturation [25,26]. Dextran is known to cause elongation of the sucrose crystals along the c-axis, especially for the growth from industrial syrups [17]. Performed image analysis experiments showed needle crystals, but only in the case of crystals of sizes less than 0.2 mm (see Fig. 3), but it was hard to distinguish the crystallographic directions and the faces for these crystals. Also only few slightly elongated crystals of sizes larger than 0.2 mm were found (see Fig. 3). The authors believe that the tiny seed crystals (say r50 mm) have higher chance to form needle crystals in comparison with the large seed crystals (say Z250 mm), as the tiny crystals require lower amounts of dextran to pin or stop the growth, so a change in the morphology will result. A comparison between the images of the simple sucrose crystals, as obtained in this work for the growth at 50 1C from dextran-doped solutions, and an image of a sucrose crystal grown by Mantovani [2] from pure solution, at the same temperature, indicates that the expected crystals to be elongated are merely normal crystals. Furthermore, Faria et al. [27] found, at 40 1C, negligible effects of the dextrans of molecular weights of range 5  106–40  106 Da on the shape of sucrose crystal at concentrations of 0.5% and 1% (on a weight basis). As a conclusion, the same values of the shape factors of the pure sucrose crystals [22,28] are considered, and applied to estimate the growth rate of the sucrose from dextran-doped solutions, as this procedure does not change the final conclusions of the work. One reasonable support for this assumption comes from the analysis of the dextran content in the final sucrose crystals, using FPLC system, where the incorporated concentrations of the used dextrans in the final crystals were not detectable. For example, only traces of the dextran 70 kDa were

The current study reports the growth rate of sucrose in presence of three different concentrations of each used dextran fraction with the decay of supersaturation, and starting from a constant initial supersaturation. So, one can use the growth rate values at the initial supersaturation of every run to apply Kubota–Mullin model [13–16]. At the initial supersaturation the conditions are equal for all runs and there is no growth history effect [29,30]. Fig. 4 shows the application of Kubota–Mullin model for the performed runs at 50 1C. Table 1 shows the estimated effectiveness factors of the impurities, the Langmuir constants, the differential heats of adsorption, and the surface coverage fractions. Table 1 and Fig. 4 indicate that the growth rate of sucrose never reaches zero at any concentration of the dextrans of molecular fractions of 70 and 250 kDa. Fig. 4 shows that the dextran fraction of 70 kDa has bigger negative effect on the growth rate than the fraction of 250 kDa. On the other hand, the negative effect of the dextran fraction of 2000 kDa on the growth rate of the sucrose crystal is remarkably stronger than of the other two impurities. Differential heat of adsorption Qdiff (J/mol) can be estimated after the knowledge of the value of the Langmuir constant using the given equation [31]: K L ¼ expðQ dif f =RG TÞ

ð2Þ

Where RG is the universal gas constant. In general, the value of Qdiff for a certain material decreases steadily with increasing of the adsorbed amount [32]. However, the development of the Kubota–Mullin model was carried out on the basis of the Langmuir adsorption isotherm, where the value of the differential heat of

Fig. 4. The results of application of Kubota–Mullin model to predict the growth kinetics of sucrose in the presence of variable concentrations of different molecular weights of dextran at 50 1C.

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

adsorption Qdiff does not depend on the surface coverage [31]. The differences in the found heats of adsorption (see Table 1) indicate differences in the strength of the adsorption, and/or differences in the sites of the dextrans adsorption on the surface, i.e., terraces, steps or kinks. Notice that the dextran of molecular fraction of 2000 kDa showed the highest differential heat of adsorption, i.e., it is adsorbed stronger than the other two fractions do. Fig. 4 indicates the importance of the impurity effectiveness factor as a decisive factor in determining the impurity strength rather than the fractional surface coverage. Kubota and Mullin [14] pointed out that the growth suppression characteristics of an impurity are expected to depend on the size, the shape or the structure of the impurity molecule. In fact, these parameters are implied in the effectiveness factor of the impurity. The molecular weight (size) criterion represents the main difference between the used dextrans. In other words, the relatively high molecular weight (size) of the dextran of 2000 kDa plays an important role in obtaining high effectiveness factor. On the other hand, the lower effectiveness factor of the dextran of 250 kDa in comparison with the dextran of 70 kDa can be ascribed to differences in the detailed structures of both dextrans, i.e., branching points and the degree of branching. So, it is not incorrect to assume that the dextran of molecular fraction of 70 kDa contains higher percentage of the a-(1–6) linkages than the dextran of the molecular fraction of 250 kDa [6,10]. Atkins and McCowge [33] reported that the dextran fraction of 2000 kDa, at concentration of 1% on solids, reduced the growth rate of sucrose crystals by 35%, while the dextran fraction of 40 kDa reduced the growth rate by only 18%. Fig. 4 shows a similar trend, as the effect of the dextran fraction of 70 kDa can be comparable, as first approximation, with the effect of the dextran fraction of 40 kDa. Sangwal [31] indicated that, irrespective of considering the geometric or the arithmetic time-averaged lateral growth velocity, the impurity adsorption on the terraces results in higher effectiveness factor values than to be adsorbed at the steps or the kinks. So, the dextran fraction of 2000 kDa may have higher probability in adsorbing on the terraces at the dextran-targeted faces, and due to its relatively high molecular size it may cause a pinning effect on the advancement of the steps. It is to be mentioned that, when using the dextran fraction of 2000 kDa at concentration 3.85 g/L of water, traces of solidified masses of dextran inside the crystallizer, at the walls and at the base, were found after the end of this run, i.e., the used dextran mass was not completely dissolved, which affects the validity of this run; for that it was neglected. Other run, for the same molecular fraction, was performed using dextran concentration of 7.71 g/L of water, and relatively big quantities of hard solid masses of dextran were also found at the heating surfaces and at the agitator of the crystallizer. In this course, it is worthy to remember this quoting of Henderson (C.S. Henderson (1972), Proc. Queensland. Soc. Sug. Cane Tech. 39, p. 267) as reported by Kelly [34] ‘‘perhaps the most frightening aspect of the dextran problem occurredywhen the massecuites solidified in the crystallizery. and between 3 and 4 h after dropping it was possible to walk the full length of the crystallizers on top of the massecuite’’. Further, the viscosity of the technical sugar juices increases considerably with the increase of the degree of dextran polymerization and its concentration; for example, the viscosity of technical sugar juices increases exponentially with the increase of the concentration of the dextran of 2000 kD [19]. Taking into account these facts and observations, one may assume that the dextran of molecular fraction 2000 kDa behaves in a way similar to the heat-solidified polymers, which may present an explanation to obtaining stiff massecuites during the industrial crystallization of sucrose.

21

3.4. Growth rate curves Growth rate curves of sucrose, at 40 and 50 1C, in the presence of different concentrations of dextrans are shown in Fig. 5 and in Fig. 6, respectively. At 40 1C, slight growth-enhancing effects due to the different dextrans were found. These general enhancing

Fig. 5. Overall linear growth rates of sucrose as function of the relative supersaturation reported at 40 1C and in the presence of the three used fractions of dextran at different concentrations; 70 (a), 250 (b) and 2000 kDa (c).

22

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

the estimation of g through 2

g¼

Fig. 6. Overall linear growth rates of sucrose as function of relative supersaturation reported at 50 1C and in the presence of the three used fractions of dextran at different concentrations; 70 (a), 250 (b) and 2000 kDa (c).

effects can be understood applying birth and spread model [28], which is applied in the form:  ln

R

s2=3 ½lnð1 þ sÞ1=6



¼ ln C 4 C 2

1 3T 2 lnð1 þ sÞ

ð3Þ

where T (K) is the temperature, C4 (m/s) is the kinetic coefficient and measures the lateral spreading velocity, which due to the use of the overall linear growth rate R is an averaged value of all the faces of the crystal, and the determination of the slope C2 allows

C 2 kB phvm

!1=2 ð4Þ

where g (J/m2) is the interfacial free energy of the growth (which is also a value averaged over all the crystal faces), kB (J/K) is the Boltzmann constant, vm is the volume of the sucrose molecule, and h is the height of monomolecular step on the growing face. At 40 1C, the application of birth and spread model (see Table 2) shows lower kinetic coefficients for all the runs of growth from dextran-doped solutions in comparison with the growth from the pure system; also lower interfacial free energies were obtained for the growth of sucrose from dextran-doped solutions in comparison with the growth from the pure system. So, the used dextrans lowered the interfacial free energy about 20% in comparison with the one of the pure system, causing a slight increase in the growth rate of sucrose from dextran-doped solutions. Glucose units form the backbone of the dextran molecules, so the asymmetry of the glucose molecule can be a key factor to understand better the mechanism in which the different dextrans reduce the interfacial free energy of sucrose growth from dextrandoped solution at 40 1C. In other words, it is required to characterize the orientation of the glucose moieties of the dextran molecule on the dextran-targeted faces. Hardy [35] and Harkins [36] introduced the concept of ‘‘force field’’ around the molecule, which depends on the polarity and the specific details of the structure of the molecule. The least abrupt change in the ‘‘force field’’ determines the orientation of the molecule at the interface. Later, Adamson and Gast [32] replaced the term ‘‘force field’’ by the interaction energy, i.e., the molecules will be oriented so that their mutual interaction energy will be a maximum. Further, Langmuir [37] proposed, qualitatively, that each part of the molecule possesses a local energy. So, in a similar manner to that of ethanol example, which is shown by Adamson and Gast [32], one may assume that the lower interfacial free energy in the case of sucrose crystals grown from dextran-doped solutions, at 40 1C, is due to the hydrocarbon parts of the glucose moieties, i.e., they project outwards from the dextran-targeted faces, reducing the value of the interfacial free energy. van Enckervort and van den Berg [38] reported that when the interaction between the immobile impurity and the growth units is exceeding the bond energy between adjacent growth units, the impurities will promote rather than decrease the growth rate. Dextrans are macromolecules; as a result they mostly act like immobile impurities. So, the hypothesis of van Enckervort and van den Berg can be other aspect of the case of sucrose growth in the presence of different dextrans at 40 1C. This assumption is also supported by the structural similarity between the dextran and the sucrose, i.e., both molecules contain glucose units in their structures. The kinetic coefficients of sucrose growth from dextran-doped solutions at 40 1C were between 60% and 70% of the one obtained for the growth from the pure system. The lowest C4 values were obtained for the runs with dextran fraction of 250 kDa. One may expect that the dextran fraction of 70 kDa will show the lowest C4 values, and not the dextran of 250 kDa; this also can be due to the effect of the structural differences (branching points and degrees) between these two dextrans. Growth of sucrose in the presence of the dextran fraction of 70 kDa, at temperature of 50 1C, showed a noticeable decrease with the increase of the dextran concentration (see Fig. 6). For the run with dextran concentration of 1.28 g/L of water, the kinetic coefficient was higher than the one of the pure system, but the interfacial free energy was higher than the one of the pure

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

23

system. So, one concludes that the interfacial free energy increase is responsible for the noticed decrease in the overall growth rate for this run in comparison with the pure system run. For the run performed at concentration of dextran of 3.85 g/L of water, a considerable decrease in the growth rate of sucrose occurred in comparison with the run of the pure system, and the run of dextran concentration of 1.28 g/L of water. Practically, the same interfacial free energy was found for the runs with dextran concentrations of 1.28 and 3.85 g/L of water, so what determines the growth rate for the later run is the kinetic coefficient, which represents less than half of the value of the kinetic coefficient for the pure system run, and equals about 40% of the kinetic coefficient for the run performed with dextran concentration of 1.28 g/L of water (see Table 2). Finally, a comparison between the run performed in the presence of 7.71 g of dextran/L of water and the pure system run will show that both runs have the same interfacial free energy, but the kinetic coefficient for the dextrandoped run is only 40% of the one for the pure system run. So, the low value of the kinetic coefficient, which means slow step advancement rate, is responsible for the noticed decrease of the overall growth of sucrose in the presence of this concentration of dextran in comparison with the pure system. A comparison between sucrose growth in the presence of the dextran fraction of 250 kDa at 50 1C and from the pure solution indicates that the growth of sucrose is controlled by the kinetic coefficient, rather than by the interfacial free energy effect. Similar conclusion can be reached for the growth runs of sucrose in the presence of the dextran fraction of 2000 kDa (see Table 2 and Fig. 6). Notice that Table 2 shows the confidence intervals for the pure system runs only, which were calculated at confidence level of 95%. 3.5. Surface structure Surface pattern of the face (100) for sucrose crystals grown from dextran-doped solutions was studied using AFM technique, and the results are presented in Figs. 7 and 8. The observed cavities (indicated by arrows in Fig. 7) in these figures are ascribed to defects which may occur during the preparation

Fig. 8. Face (100) of a sucrose crystal grown, at 50 1C, for 22 h from doped solution with dextran of molecular fraction of 250 kDa and concentration of 7.71 g/L of water. Two cavities and one domelike shape at the front of the advancing step are observed, where the cavities are indicated by dashed and dotted arrows and the domelike shape is indicated by solid arrow (top); cross sections of the domelike shape and the cavities (bottom); taking into account the possible differences in the orientation of the cross sections one may assume that these shapes (domelike and cavities) may belong to dextran molecules or (sub-)microcrystals.

Fig. 7. Cavities were detected on the face (100) of a sucrose crystal grown, at 50 1C, for 2 h from doped solution with dextran of molecular fraction of 2000 kDa and concentration of 2.1 g/L of water; the cavities are expected to represent the locations where the dextran molecules or the (sub-)microcrystals are incorporated. It is clearly seen that the step advancement is reduced at the places of the incorporation of the dextran molecules or the (sub-)microcrystals. Dimensions of the image are approximately 3 mm  3.5 mm.

(washing step) of the crystal surface for AFM imaging. In other words, the removal of some surface-incorporated impurities, which are mainly the dextran fractions in this work or the incorporated (sub-)microcrystals, will form cavities on the surface. It is clear that the advancement of the steps fronts is retarded in the neighborhood of these cavities. The chemical potential of the crystal surface at the incorporation points of the foreign particles is higher than in other locations on the surface, and this is due to the resulted stress energy which is induced by the incorporation of the foreign particles [39,40]. So, a lower step advancement rate in the neighborhood of the incorporation points of the (sub-)microcrystals or the dextran will result, that in comparison with other areas of the crystal surface. These cavities can also result from the surface-incorporation of dust particles which exist even in highly purified solutions [41]. The domelike shape observed at the front of the advancing step, as shown in Fig. 8, has approximately a circular periphery (isotropic base), but an anisotropic lateral spread is expected due to the inequality of the edge free energies at different spread directions [42]. So, this domelike shape may belong to a macromolecule like the dextran or a foreign particle or a (sub-) microcrystal. In fact, the relatively high agitation speed used can induce the breakage of the crystals at the impeller blades or at the walls of the crystallizer, and fragments of broken crystals were observed using image analysis (related figures are not

24

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

shown). As a result the formation of the (sub-)microcrystals during the growth is expected. So, one may believe that the incorporated dextran or the (sub-)microcrystal was overridden by several sucrose growth layers [39] (see Fig. 8). One may argue that the found cavities in these figures are hollow cores of dislocations. A dislocation with large Burgers (mh, where m is a whole number) vector, energetically, requires having free surface along its core to release the strain associated with it, thus forming a hollow core [43–47]; this can be the case as the effective supersaturation can vary from one location to other on the surface. However, the found stopping of the growth steps in the vicinity of these cores and the absence of the dislocations’ steps do not support this reasoning. 3.6. Theoretical aspects of sucrose crystal elongation It was proposed that dextrans block the growth of certain faces, i.e., (110), (1 10), (110) and (110), of the sucrose crystal causing an elongation along the c-axis [5]. However, if one considers the occurrence of the dextran adsorption on the face (100), then the lateral spread of the steps of the growth sources will be anisotropic, with higher spread rates along the c-axis than along the b-axis. So, thinner (elongated) crystals, than that could be predicted on the basis of the proportionality between the face growth rate and the attachment energy of a face slice, will result. Further, the degree of supersaturation is expected to be less at the surface points of the incorporation of the impurities [39,48], which decreases the incorporation of the solute molecules in directions normal to the alignment of the adsorbed dextran molecule on the surface. In other words, the maximum interaction energy of the orientation of the incorporating sucrose molecule is not achieved, which directs the growth to other directions to satisfy the higher interaction energy condition. So, when a linear molecule of dextran is adsorbed on the face (100), one can expect its alignment to be parallel to the c-axis, and accompanied with reduced supersaturation in the direction normal to the alignment of this molecule (see Fig. 9). So, the anisotropy of the growth islands increases creating an elongation in the crystal. Experimentally, the low degree of branching of the dextran molecule was responsible for higher elongation along the c-axis [10]. Regardless of its high molecular weight, the elongating effects of the dextran on the sucrose crystal represent effects of tailormade impurities. Tailor-made impurities are adsorbed mainly on the terraces, and so they affect the lateral growth velocities on the targeted faces in directions perpendicular to their favorable alignment on these faces [31]. However the size of the dextran

Fig. 9. Effect of dextran adsorption on the growth pattern of the face (100) of the sucrose crystal.

molecule does not easily fit into the structure of the sucrose crystal, so one may assume that a dextran molecule adsorbs by linking at several sites of its length with different sites of the crystal surface, but not fully integrating into the structure of the crystal. In other words, the dextran content in the sucrose crystal is quite negligible, and this point of view is in accordance with having no detection of the dextran content as analyzed using size exclusion chromatography technique in this work. Considering the problem of dextran adsorption in a three dimensional space, segments of the dextran molecule are projected away from the surface, so providing the conditions for limited growth normal to the dextran molecule alignment, and the growth normal to the dextran molecule alignment may stop later due to the pinning mechanism effect (see Fig. 9). Further, and considering that the growth is limited to the direct integration mechanism, the impingement rate at which the sucrose molecules impinge a square array of a certain face of the crystal can be given by the relation K þ ¼ f v expðDm=kB TÞ, where fv (s  1) is an overall frequency factor having the same unity of K þ and includes any retardation to the attachment, Dm (J) is the chemical potential difference between the actual value and the crystal–fluid equilibrium value, and T (K) is the temperature. On the other hand, the dissolution of the surface sucrose molecules depends on their coordination and occurs at rate of K  , where K  ¼ f v expðnf=kB TÞ [49], n is the number of the nearest neighbors of the molecule and f (J) is the bond energy between pair of such neighbors. The ratio K þ =K  ¼ expððnf þ DmÞ=kB TÞ can be used to evaluate the relative importance of the attachment and the detachment fluxes. So, if the solute molecule is attempting to be added in the vicinity of the alignment of the dextran molecule on a dextran-targeted face, say the face (100), and in direction perpendicular to the alignment of the dextran molecule, lower interaction energy f and less number of neighbors at reduced chemical potential will prevail. So, a reduction of the growth rate along this direction will result. This theoretical discussion applies for the case where the dextran shows a reducing effect on the growth rate, and/or when it modifies the morphology of the sucrose crystal (c-axis elongation) in comparison with a sucrose crystal grown from pure system.

4. Conclusions Three dextrans of different molecular fractions were used as impurities for the growth of the sucrose crystal. Results were interpreted using Kubota–Mullin model, and birth and spread model. Application of Kubota–Mullin model, at 50 1C, showed that the dextran of molecular fraction of 2000 kDa causes the highest retarding effect on the growth rate of the sucrose crystal, that in comparison with the other two dextrans, i.e., 250 and 70 kDa, having an impurity effectiveness factor equal to 3. At 40 1C, the different dextrans lowered the mean interfacial free energy of the sucrose crystal growth by about 20%, in comparison with sucrose growth from the pure system, which caused the increase of overall linear growth rates of the sucrose. Orientation of the glucose moieties of the dextran molecule, at the crystal surface, was assumed to be the key factor in lowering the interfacial free energy of the sucrose growth from dextran-doped solutions. On the other hand, at 50 1C, the different dextrans lowered the mean kinetic coefficient of the sucrose crystal growth, up to 60% in comparison with the growth from the pure system, which caused the decrease of overall linear growth rates of the sucrose. Further, indications which support the classification of the dextran of molecular fraction of 2000 kDa as heat solidified polymer were observed, but more future research is required to explain the

I. Khaddour et al. / Journal of Crystal Growth 355 (2012) 17–25

effect of this dextran, or other dextrans of molecular fractions higher than 2000 kDa, in producing highly viscous intermediate products or stiff massecuites in the sugar factories. Furthermore, the surface points of dextran incorporation were assumed to show higher chemical potential than other areas on the surface, which allowed interpretation of the observed retardations of the advancing steps in the vicinity of found cavities (resulted from dextran removal) on the surface. It is believed that the proposed effect of dextran and its orientation on the interfacial free energy of the sucrose crystal growth can be judged in better way by conducting face-by-face growth experiments, and then using sum frequency generation (SFG) technique to confirm the orientation of the dextran molecule on the studied faces. References [1] J.F. Kennedy, C.A. White, in: J.F. Kennedy (Ed.), Carbohydrate Chemistry, Oxford University Press, New York, 1988, pp. 220–262. [2] G. Mantovani, Morphology of industrial sugar crystals, in: W.A. VanHook, M. Mathlouthi, G. Mantovani (Eds.), Sucrose Crystallization: Science and Technology, Bartens, Berlin, 1997, pp. 152–171. [3] E.A. Abdel-Rahman, Q. Smejkal, R. Schick, S. El-Syiad, T. Kurz, Influence of dextran concentrations and molecular fractions on the rate of sucrose crystallization in pure sucrose solutions, Journal of Food Engineering 84 (2008) 501–508. [4] G. Vavrinecz, Atlas of Sugar Crystals, Verlag Dr. Albert Bartens, Berlin, 1965. [5] D.N. Sutherland, Dextran and crystal elongation, International Sugar Journal 70 (1968) 355–358. [6] M.T. Covacevich, G.N. Richards, G. Stockie, Studies on the effect of dextran elongation on cane sugar crystal elongation and methods of analysis in: ISSCT, 1977, pp. 2493–2507. [7] A. Promraksa, A.E. Flood, P.A. Schneider, Measurement and analysis of the dextran partition coefficient in sucrose crystallization, Journal of Crystal Growth 311 (2009) 3667–3673. [8] E.E. Coll, M.A. Clarke, E.J. Roberts, Dextran problems in sugar production, in: Proceedings of the Technical Session on Cane Sugar Refining Research, 1978, pp. 92–106. [9] R.A. Kitchen, Dextrans: their effects on refinery processes, in: Proceedings of the International Dextran Workshop, Sugar Processing Research Institute Inc., New Orleans, 1984, pp. 53–61. [10] D.N. Sutherland, N. Paton, Dextran and crystal elongation: further experiments, International Sugar Journal 71 (1969) 131–135. [11] M. Saska, J.A. Polack, Effects of dextran on sucrose crystal shapes, in: Proceedings of the Sugar Processing Research Conference, Georgia, 1982, pp. 134–139. [12] Z. Bubnik, G. Vaccari, G. Mantovani, G. Sgualdino, P. Kadlec, Effect of dextran, glucose and fructose on sucrose elongation and morphology, Zuckerindustrie 117 (1992) 557–561. [13] N. Kubota, Effect of impurities on the growth kinetics of crystals, Crystal Research and Technology 36 (2001) 749–769. [14] N. Kubota, J.W. Mullin, A kinetic model for crystal growth from aqueous solution in the presence of impurity, Journal of Crystal Growth 152 (1995) 203–208. [15] N. Kubota, M. Yokota, J.W. Mullin, Supersaturation dependence of crystal growth in solutions in the presence of impurity, Journal of Crystal Growth 182 (1997) 86–94. [16] N. Kubota, M. Yokota, J.W. Mullin, The combined influence of supersaturation and impurity concentration on crystal growth, Journal of Crystal Growth 212 (2000) 480–488. [17] J.C.P. Chen, C.C. Chou, Cane Sugar Handbook, 12th ed., John Wiley & Sons, New York, 1993. [18] I. Khaddour, F. Rocha, Metastable zone width for secondary nucleation and secondary nucleation inside the metastable zone, Crystal Research and Technology 46 (2011) 373–382. [19] P.F. Greenfield, G.L. Geronimos, Effect of dextran on the viscosity of sugar solutions and molasses, International Sugar Journal 84 (1982) 67–72. [20] H.E.C. Powers, Sucrose crystals: inclusions and structure, Sugar Technology Reviews 1 (1969–1970) 85–190.

25

[21] A. Ferreira, N. Faria, F. Rocha, S. Feyo De Azevedo, A. Lopes, Using image analysis to look into the effect of impurity concentration in NaCl crystallization, Chemical Engineering Research and Design 83 (2005) 331–338. [22] Z. Bubnik, P. Kadlec, Sucrose crystal shape factors, Zuckerindustrie 117 (1992) 345–350. [23] A.D. Randolph, M.A. Larson, Theory of Particulate Processes, Academic Press, New York, 1971. [24] F.M. Barreiros, P.J. Ferreira, M.M. Figueiredo, Calculating shape factors from particle sizing data, Particle & Particle Systems Characterization 13 (1996) 368–373. [25] D. Aquilano, M. Rubbo, G. Mantovani, G. Vaccari, G. Sgualdino, Sucrose crystal growth: theory, experiment, and industrial applications, in: A.S. Myerson, K. Toyokura (Eds.), Crystallization as a Separation Process, ACS, 1990, pp. 72–84. [26] G. Mantovani, Growth and morphology of sucrose crystal, International Sugar Journal 93 (1991) 23–32. [27] N. Faria, M.N. Pons, S. Feyo de Azevedo, F.A. Rocha, H. Vivier, Quantification of the morphology of sucrose crystals by image analysis, Powder Technology 133 (2003) 54–67. [28] I.A. Khaddour, L.S.M. Bento, A.M.A. Ferreira, F.A.N. Rocha, Kinetics and thermodynamics of sucrose crystallization from pure solution at different initial supersaturations, Surface Science 604 (2010) 1208–1214. [29] P. Pantaraks, A.E. Flood, Effect of growth rate history on current crystal growth: a second look at surface effects on crystal growth rates, Crystal Growth & Design 5 (2004) 365–371. [30] P. Pantaraks, M. Matsuoka, A.E. Flood, Effect of growth rate history on current crystal growth. 2. Crystal growth of sucrose , Al(SO4)2  12H2O, KH2PO4, and K2SO4, Crystal Growth & Design 7 (2007) 2635–2642. [31] K. Sangwal, Additives and Crystallization Processes, John Wiley & Sons, Chichester, 2007. [32] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, 6th ed., Wiley Interscience, New York, 1997. [33] P.C. Atkins, R.J. McCowage, Dextran—an overview of the Australian experience, in: Proceedings of the International Dextran Workshop, Sugar Processing Research Inc., New Orleans, Louisiana, USA, 1984, pp. 108–140. [34] F.H.C. Kelly, The morphology of sucrose crystals, Sugar Technology Review 9 (1982) 271–323. [35] W.B. Hardy, The influence of chemical constitution upon interfacial tension, Proceedings of the Royal Society (London) 88 (1913) 303–313. [36] W.D. Harkins, The Physical Chemistry of Surface Films, Reinhold, New York, 1952. [37] I. Langmuir, Colloid Symposium Monograph, The Chemical Catalog Company, New York, 1925. (p. 48). [38] W.J.P. van Enckevort, A.C.J.F. van den Berg, Impurity blocking of crystal growth: a Monte Carlo study, Journal of Crystal Growth 183 (1998) 441–455. [39] A.J. Malkin, Y.G. Kuznetsov, A. McPherson, Defect structure of macromolecular crystals, Journal of Structural Biology 117 (1996) 124–137. [40] N. Cabrera, D. Vermilyea, The growth of crystals from solution, in: R. Doremus, B. Roberts, D. Turnbull (Eds.), Growth and Perfection of Crystals, Wiley & Sons, New York, 1958. [41] J.W. Mullin, Crystallization, 4th ed., Butterworth-Heinemann, Oxford, 2001. [42] W.J. Dunning, N. Albon, The kinetics of the crystal growth of sucrose from aqueous solution, in: R. Doremus, B. Roberts, D. Turnbull (Eds.), Growth and Perfection of Crystals, John Wiley & Sons, Inc, New York, 1958, pp. 446–457. [43] M. Kawasaki, K. Onuma, I. Sunagawa, Morphological instabilities during growth of a rough interface: AFM observations of cobbles on the (0 0 0 1) face of synthetic quartz crystals, Journal of Crystal Growth 258 (2003) 188–196. [44] K. Maiwa, M. Plomp, W.J.P. van Enckevort, P. Bennema, AFM observation of barium nitrate {1 1 1} and {1 0 0} faces:spiral growth and two-dimensional nucleation growth, Journal of Crystal Growth 186 (1998) 214–223. [45] F. Frank, Capillary equilibria of dislocated crystals, Acta Crystallographica 4 (1951) 497–501. [46] I. Sunagawa, Crystals: Growth, Morphology and Perfection, Cambridge University Press, Cambridge, 2005. [47] L. Guang-Zhao, J.P. Van Der Eerden, P. Bennema, The opening and closing of a hollow dislocation core: a Monte Carlo simulation, Journal of Crystal Growth 58 (1982) 152–162. [48] P.J.C.M. van Hoof, R.F.P. Grimbergen, H. Meekes, W.J.P. van Enckevort, P. Bennema, Morphology of orthorhombic n-paraffin crystals: a comparison between theory and experiments, Journal of Crystal Growth 191 (1998) 861–872. [49] G.H. Gilmer, Simulation of 2D nucleation and crystal growth, Faraday Symposia of the Chemical Society 12 (1977) 59–69.