Influence of Additives on Nucleation of Vanillin: Experiments and

Influence of Additives on Nucleation of Vanillin: Experiments and Introductory Molecular Simulations Osvaldo Pino-Garcıá and A° ke C. Rasmuson* Department of Chemical Engineering and Technology, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 5 1025-1037

ABSTRACT: Nucleation of vanillin (VAN) in 2-propanol/water in the presence of additives, viz., acetovanillone (AVA), ethyl vanillin (EVA), guaiacol (GUA), guaethol (GUE), 4-hydroxyacetophenone (HAP), 4-hydroxybenzaldehyde (HBA), and vanillic acid (VAC) is investigated experimentally and by molecular simulations. In the experimental work, the induction time for nucleation is measured at different temperatures and levels of supersaturation using a multicell apparatus. A large variation in the experimental data is observed, and this variation is analyzed by statistical methods. By classical nucleation theory, the induction time data are used to estimate the solid-liquid interfacial energy of vanillin for each VAN-additive system. At 1 mol %, the interfacial energy becomes lower in the presence of AVA, EVA, HAP, and VAC, while it becomes higher in the presence of the other additives. As the additive concentration increases from 1 to 10 mol %, the interfacial energy also increases. The interfacial energy ranges from 6.9 to 10.1 mJ m-2. Molecular modeling, implemented in the program Cerius2, is used to simulate and examine the surface chemistry of the likely crystal growth faces of VAN (i.e., {0 0 1} and {1 0 0}). To evaluate the additivecrystal face interaction energy, two approaches are used: the surface adsorption method and the lattice integration method. Both experimental and molecular simulation results indicate that the additives studied are potential modifiers of the nucleation of VAN. However, a simple and clear relationship between the experimental values of interfacial energy and the calculated interaction energies for the most important crystal faces of VAN cannot be identified. The modeling does not concern the actual nucleation but rather the conditions of a growing surface and are based on several severe simplifications. Obviously, this simplistic approach does not sufficiently capture the influence of additives on the nucleation of vanillin. Introduction Industrial crystallization is used in production of inorganic and organic compounds and is of great importance in the production of pharmaceuticals. Nucleation is the most important mechanism by which new crystals are formed, but unfortunately, the understanding of crystal nucleation processes is still quite unsatisfactory. While the influence of additives and impurities on crystal growth has been studied to a certain extent, much less work has been done on the influence on nucleation. The action of additives and impurities in crystallization can be related to different mechanisms (e.g., alteration of the solution structure or the structural properties of the solid-liquid interface by chemical reaction, complexation or ion paring in solution, or adsorption at the interface or on the nuclei surface).1 Adsorption has two effects. Adsorption of additives at the interface generally provides active sites for the nucleation.2 This effect reduces the interfacial energy, γSL, thus reducing the required free energy for the formation of nuclei and resulting in greater surface nucleation.3 On the other hand, additive adsorption can either increase the interfacial energy and inhibit nucleation or inhibit nucleus growth by blocking the growth attachment sites on the nucleus surface.2 Additives, which have a molecular structure similar to the crystallizing compound like byproducts and nonreacted reactants, have the tendency to block the movement of surface steps, kinks, or terraces, and may be incorporated into the growing crystals, especially at unfavor* Corresponding author. Phone: +46 8 7908227. Fax: +46 8 105228. E-mail: [email protected].

able processing conditions.4 Additives and impurities that have a marked effect on nucleation and on the overall crystal growth rate are usually associated with a change in the crystal habit already at very low concentrations. This effect results from the distinct effect the impurities and additives have on the different crystallographic faces. Davey3,5 observed that face growth rates may be increased, decreased, or remain the same in the presence of additives. While often the presence of impurities is disadvantageous to the desired purposes of a crystallization process, many times their presence is indispensable. Crystallization of gypsum from wet phosphoric acid is an example where some of the impurities present in the raw material are of vital importance to obtain the wanted crystal size and shape. A wider theoretical and experimental description of the influence of additives on crystallization has been published elsewhere.1,4,6 The effect of additives on nucleation can be explained by different mechanisms in which the strength of intermolecular bonds that form during the adsorption process plays an essential role.7 Structurally related substances or so-called tailor-made additives,6 as those studied in this work, can be easily incorporated into the host nucleus,8,9 and the succeeding ease of a further host molecule to be deposited onto or next to the guest molecule depends on its similarity in size, shape, and intermolecular interactions. In the literature,10 it has been reported that both metastable zone width and induction time for nucleation of succinic acid increase with increasing binding (interaction) energy of additives. In other cases,3 additives can either promote or inhibit the effective nucleation and hence reduce or increase the width of the metastable zone and the induction time.

10.1021/cg049955+ CCC: $27.50 © 2004 American Chemical Society Published on Web 08/17/2004

1026 Crystal Growth & Design, Vol. 4, No. 5, 2004

Molecular modeling is a powerful tool for analysis of effects in crystallization processes that are related to structure and surface chemistry. For this purpose, the program Cerius211 has recently been successfully applied to organic crystals, in work of Myerson and Jang12 on the comparison of binding energy and metastable zone width for adipic acid in the presence of additives, Givand and co-workers,13 on the prediction of L-isoleucine crystal morphology, and by others.10,14,15 Vanillin [CAS 121-33-5], 4-hydroxy-3-methoxybenzaldehyde, C8H8O3, is a savory organic compound with a wide spectrum of applications, not only in the food and liqueur industries, but also in chemical, pharmaceutical, agrochemical, and galvanometallic industries.16,17 Single crystals of vanillin are useful for their nonlinear optical properties.18-20 Vanillin is produced industrially by different methods (e.g., by chemical synthesis from guaiacol, from lignin as a byproduct of the pulp and paper industry,16,17 or by biosynthesis from eugenol or vanillic acid).21,22 The synthesis of VAN from guaiacol (GUA) comprises its condensation with glyoxylic acid followed by processes of oxidation and decarboxylation. If guaethol (GUE, pyrocatechol monoethyl ether) is used instead of GUA, then ethylvanillin (EVA, 4-hydroxy-3-ethoxy benzaldehyde) can be obtained. When VAN is produced from the lignin-containing waste, the VAN formed is separated from the byproducts, particularly acetovanillone (AVA, 4-hydroxy-3methoxy-acetophenone), vanillic acid (VAC, 4-hydroxy3-methoxy-benzoic acid), 4-hydroxy-benzaldehyde (HBA), and 4-hydroxy-acetophenone (HAP), and by extraction, vacuum distillation, and crystallization. In the literature on crystallization of vanillin, most work has been devoted to the influence of solvents on the crystallization in general, and little work has been done specifically on nucleation. Lier23 studied the effect of pure organic solvents on the solubility and on the width of the metastable zone of vanillin. Hussain24 measured the solubility and metastability of vanillin using aqueous alcohols as solvents. Sorensen et al.25 investigated the cluster formation in precrystalline solutions of vanillin by means of static light scattering (SLS), photon correlation spectroscopy (PCS), and small angle neutron scattering (SANS). In our previous work,26 the induction time for nucleation of vanillin in water/2-propanol solutions was determined at different levels of supersaturation and temperature, and the solid-liquid interfacial energy was estimated. The influence of additives on nucleation of vanillin has not been explored, and so far, molecular modeling has not been applied to improve the process of crystallization of vanillin. The overall purpose of the present work is to study the effect of additives on the crystallization behavior of organic substances. In this particular study, vanillin is used as the crystallizing substance, and seven different additives of structural similarity are included. The influence of additives on the induction time for nucleation of vanillin is determined experimentally, and molecular simulation is used to estimate the interaction energy between dominant crystal faces and additive molecules. Theoretical Basis The formation of new crystals is largely due to different mechanisms that are collectively termed nucle-

Pino-Garcıá and Rasmuson

ation. Primary nucleation occurs by mechanisms that do not require the presence of crystals in the suspension, while secondary nucleation requires the presence of suspended solute crystals.27 At high levels of supersaturation, the formation of nuclei takes place spontaneously at random sites in the pure bulk solution (homogeneous primary nucleation) or at solid surfaces acting as templates (heterogeneous primary nucleation). Induction Time and Interfacial Energy. According to the classical theory of homogeneous nucleation1,7,28 the nucleation rate is expressed as

[

J ) J0exp -F

γ 3SLϑ 2m k3T 3(ln S)2

]

(1)

where J0 is the kinetic preexponential coefficient; F is the geometrical shape factor of the nuclei, which is equal to 16π/3 for spheres; ϑm ) MW/FcNA is the molecular volume; k ) R/NA is the Boltzmann constant; R is the universal gas constant; NA is Avogadro’s number; MW is the molecular weight; Fc is the crystal density; γSL is the interfacial energy of the solid nucleus in the supersaturated solution; and S is the supersaturation ratio defined as

S ) x/xeq

(2)

and relates the mole fraction of the solute in actual supersaturated solution to the mole fraction of the solute in a solution that is in thermodynamic equilibrium with the crystalline solid state at the given absolute temperature, T. The nucleation rate assumes ideal stationary conditions and predicts immediate nucleation upon the creation of supersaturation in solution (e.g., by assessing a fast cooling). However, in practice, some characteristic period of time must elapse from the attainment of supersaturation state up to the appearance of the first stable nuclei of detectable size. This macroscopic measure of the nucleation event is referred to in the literature1,28-30 as the induction time of nucleation, tind. According to the classical nucleation theory, the induction time is related to the nucleation rate in logarithm form as1,30

ln tind ∝ ln J-1 ) ln J -1 0 +

F ϑ 2m γ 3SL k3T 3(ln S)2

(3)

Eq 3 predicts a linear dependence between ln tind and T -3(ln S)-2 when the value of the interfacial energy and the preexponential factor are constant and independent of supersaturation and temperature. If eq 3 is fitted to the experimental data (over a wide range of supersaturations and temperatures), then from the slope

β ) d(ln tind)/d(T-3(ln S)-2) ) F ϑ 2m γ 3SL / k3

(4)

of such a linear plot, the interfacial energy γSL can be determined. If additives are present in the solution, primarily two parameters in the nucleation equation may be influenced: the supersaturation and the interfacial energy. The supersaturation may be affected directly by changes in equilibrium solubility, xeq, and by an influence on the

Influence of Additives on Nucleation of Vanillin

Crystal Growth & Design, Vol. 4, No. 5, 2004 1027

Figure 1. Chemical structures of vanillin and additives. Functional groups: acetyl (-Ac ) -COCH3), aldehyde (-CHO), carboxy (-CO2H), ethoxy (-OEt ) -OC2H5), hydroxy (-OH), and methoxy (-OMe ) -OCH3).

chemical potential of the solute in the solution. However, the strongest effect on primary nucleation is likely to be on the mechanisms of clustering and on the conditions at the interface. Ny´vlt and Ulrich31 suggest that the similarity between the curve of the nucleation rate versus additives concentration and adsorption isotherms of surface-active substances indicates a direct link between the nucleation rate and the adsorption of the additives on the surface. From the Gibbs adsorption isotherm for a single component, it is expected that adsorption of additives at the interface reduces the interfacial energy, γSL, thus causing a reduction in the required free energy of formation of nuclei3 by which nucleation is facilitated. However, additives can increase or decrease the interfacial energy.2 Blockage of the attachment sites on the nucleus surface by the additives has been suggested as a mechanism in the case of nucleation inhibition. The interfacial energy accounts for the free energy per unit of surface area required to form a new interface between two phases (e.g., solid and liquid), and its determination is still a difficult problem.32,33 Values of the interfacial energy, γSL, are normally obtained experimentally from determination of contact angles or from the dependence of the nucleation rate, J, on the temperature, T, and supersaturation ratio, S, as defined previously. Experimental Procedures The induction time has been determined for nucleation of vanillin in the presence of the seven different additives shown in Figure 1. Two different concentration levels of the additives have been investigated. Chemicals. Vanillin (VAN, 4-hydroxy-3-methoxy-benzaldehyde, 99.9 mass % of USP, BP, and Eur. Ph. grade white crystalline solid) and the additives: acetovanillone (AVA, 4-hydroxy-3-methoxyacetophenone, 98 mass %), ethyl vanillin (EVA, 3-ethoxy-4-hydroxy-benzaldehyde, 98 mass %), guaiacol (GUA, 2-methoxyphenol, 98 mass %), guaethol (GUE, 2-ethoxyphenol, 98 mass %), 4-hydroxy-acetophenone (HAP, 4-acetylphenol, 98 mass %), 4-hydroxybenzaldehyde (HBA, 4-formylphenol, 98 mass %), and vanillic acid (VAC, 4-hydroxy-3methoxybenzoic acid, 97 mass %) all supplied by Borregaard

Figure 2. Multicell nucleation block (MCNB). Synthesis (Norway) were used without further purification. 2-Propanol (99.5 mass %) supplied by Merck EuroLab (Sweden) and water (distilled, ion-exchanged, and filtered) were used to prepare a 20 mass % (solute free basis) 2-propanol/ water mixture. Apparatus. A newly developed apparatus was used for determination of the induction time simultaneously in different nucleation cells. A simplified diagram of this so-called multicell nucleation block (MCNB) is shown in Figure 2, and details are given by Pino-Garcıá and Rasmuson.26 The MCNB consists of a set of 15 identical cylindrical chambers (nucleation cells) with volume of about 6 mL each. The wall of an individual cell is made of stainless steel with a polished surface from the solution side. The cover and the base of the cells are made of chemically resistant and optically transparent plastic plates. Silicon gaskets with Teflon washer and O-rings are used to seal the cells hermetically. Two thin draining tubes connected to the cell cover are used for flushing the solution in and out during the charging and discharging of the cells, respectively. The cells are immersed and hermetically fixed in a chamber through the channels of which a temperature-controlled fluid (either cooling or heating) circulates continuously. The MCNB is placed on a multiple magnetic position stirrer, having 15 agitation units, by which the same stirring speed is given to all the solutions. The use of optically transparent covers and bases allows the contents in the cells to be backlighted and the changes in solution turbidity due to the formation of a new phase to be continuously recorded by a video camera. Procedure. Mother solutions are prepared by weighing predefined amounts of solid vanillin and the solvent mixture (2-propanol + water, 20 mass % of 2-propanol) in a glass flask of volume 250 cm3. When applied, the additive is added to the solution at either 1 or 10 mol % level. The additive concentration is given as number of moles of additive per total number of moles of solute (i.e., on solvent-free basis). The flasks are closed with screw caps and sealed up with Parafilm to prevent evaporation losses. The crystalline vanillin



Table 1. Slopes and Intercepts Calculated from Induction Time Data by Least-Square Minimization 1 mol % additive in solution AVA EVA GUA GUE HAP HBA VAC pure VANa a Ref 26.

no. of data points n

slope (β ( SEβ) × 10-7 (K3)

100 103 99 102 102 98 94 n: 414

7.7 ( 1.1 7.4 ( 1.1 11.6 ( 1.1 12.5 ( 1.1 8.5 ( 1.3 9.6 ( 1.2 8.0 ( 1.3 slope: (8.6 ( 0.6) × 107 (K3)

10 mol % intercept R ( SER

no. of data points n

1.43 ( 0.20 1.48 ( 0.20 0.66 ( 0.21 29 0.57 ( 0.22 20 0.95 ( 0.24 0.96 ( 0.23 1.08 ( 0.26 100 intercept: 1.38 ( 0.13

is allowed to dissolve completely by immersing the flask in a thermostated water bath under gentle warming and mixing for at least 12 h. Just about 60 min before the start of each experiment, the fluid from the thermostat is allowed to circulate through the flow channels of the MCNB. The temperature is set and stabilized at a value (TH) that is approximately 5 K above the corresponding saturation temperature (TS) of the solution. This is done to ensure that no nuclei are formed during filling of the solution into the cells and that no nuclei are present from the start of the experiments. A preheated syringe, provided with a 0.45 µm membrane filter in its tip, is used to transfer the mother solution into the temperature-controlled nucleation cells of the MCNB. The clear solution in the nucleation cells is stirred with Teflon-coated magnetic spinbars at 500 rpm. By lowering the temperature of the circulating water from the thermostat, the saturation temperature, TS, is slowly approached. Induction time experiments then start by noting he starting temperature and quickly switching over to the circulating fluid of a cryostat instead, which has been steadily kept at the desired experimental temperature (TC). The supercooling temperature (TC) is held constant during the process for as long as is necessary for crystals to form in all the nucleation cells. The cells are continuously monitored, and the time is recorded by the video recorder. The onset of nucleation is easily observed as a very rapid change in solution turbidity, and the event finishes with complete obscuration of the light through the solution. The aim is to establish the temperature TC within the cells as rapidly as possible and to make the transient period of time to do so negligible as compared to the induction time. In a previous work,26 it has been determined that within 2 min of transient cooling time, about 95% of the desired temperature change in the cells is established. Since the rate of nucleation has a very strong dependence on supercooling, it is reasonable to start the induction time measurement not until we are close to the final temperature. Thus, for each individual cell, a safety limit of 3 min in total is taken to exclude outliers from the data, and only experiments where the resulting tind ) (t - 2 min) g 1 min are included in the evaluations. Here, t is defined as the time lapse from the moment when quickly switching over to the circulating fluid of a cryostat. In this work, three different supercooling temperatures have been used alternatively (283.15, 288.15, and 293.15 ( 0.05 K) to generate mole fraction supersaturation ratios in the range S ) 2.6-9.3. The solute (vanillin + additive) concentration is in the range of 1.4-3.8 mol %. The influence of additives on solubility is neglected since concentration levels are low, and changes in solubility up to 10% lead to only small changes in the supersaturation term [T-3 (ln S)-2] as compared to the spread in induction time data. When the nucleation in all the cells is completed and recorded, the temperature is raised again to dissolve the crystals in solution and to repeat the experiment or to start the cleaning. Each solution is only used twice and only during the same day because of the limited stability of vanillin.34,35 When cleaning, the cells are drained, flushed thoroughly with alcohol, rinsed with distilled water, and dried with oil-free compressed air. Results. The induction time data for nucleation of vanillin from solutions without additives have been reported previ-

slope (β ( SEβ) × 10-7 (K3)

intercept R ( SER

22.7 ( 4.7 20.0 ( 2.2

-0.29 ( 1.08 -1.72 ( 0.76

9.8 ( 1.5

2.97 ( 0.29

ously.26 The data collection of induction time for nucleation of vanillin containing additives are plotted and given in Figure 3. In all cases with 1 mol % additive, the number of data points, n, are in the order of 100, and this is also the true for the case of 10 mol % of VAC. For the cases of 10 mol % of GUA and GUE, the number of data points are about 20-30 (Table 1). An extensive statistical analysis performed in the previous work26 revealed that (i) the induction time does not depend on the particular cell in the MCNB, (ii) a straight line (eq 3) does describe the data, and (iii) the value of the slope of the straight line is statistically significant. In the present work, eq 3 is fitted to the data of induction times for nucleation of vanillin as a function of [T-3 (ln S)-2]. For each case, the slope of the linear regression β (eq 4) and the intercept R ) ln J0-1 are calculated by the method of least squares using directly the entire set of data, and the result is presented in Table 1. As shown in Figure 3 and Table 1, the slope and intercept depend on the additive and additive concentration. There is a significant spread in the data, but because of the large number of data points, there is statistical significance that justifies further evaluation. For each case, the slope and intercept values of the linear regression are used to compare induction times at different driving forces as given in Figure 4. At 1 mol % concentration of additives and at low value of the driving force (e.g., [T-3 (ln S)-2] ) 0.1216 × 10-7), the induction time for all the additives is lower than that for pure vanillin. As the driving force level increases, the behavior is almost the same except for additives GUA, GUE, and HBA for which an increase in induction time as compared to pure vanillin is observed. At 10 mol % concentration, only three additives were evaluated: GUA, GUE, and VAC. In this case, additives GUA and GUE, as at 1 mol % level, decrease the induction time at low driving force values, but as the driving force value increases, there is a tendency to increase the induction time as compared to pure vanillin. Additive VAC tends to increase the induction time for all the values of the driving force. From the slope of the linear plots, the solid-liquid interfacial energy γSL is calculated and reported in Table 2. SE is the standard error of the estimation. The results at 1 mol % level show that the interfacial energy slightly decreases in the presence of AVA, EVA, HAP, and VAC, while it slightly increases in the presence of GUA, GUE, and HBA. The highest interfacial energy (10.05 mJ m-2) is obtained in the presence of the additive GUA at 10 mol %, an increase of 40% of the interfacial energy of pure VAN. In this work, all interfacial energies determined in the presence of additives at 10 mol % level are higher than that obtained for pure VAN. The values of interfacial energy obtained in this work are in the same order of magnitude as those found for organic compounds in general , for example, for urea36 and paracetamol,8,37 interfacial energy values are found in the range of 3.88.9 and 1.4-3.5 mJ m-2, respectively. Statistical Analysis of Interfacial Energy Values. Interfacial energy values reported in Table 2 that were obtained from nucleation of vanillin in the presence of additives are only in a few cases strongly deviating from the value obtained for pure vanillin. Even though smaller changes in interfacial energy do have a fairly strong effect on nucleation, as shown by eq 1, we need to ascertain the statistical



Figure 3. Induction time data (dots) for nucleation of vanillin in 2-propanol/water in the presence of additives and regressions (solid lines) based on the method of least squares. confidence of the influence of the additives. If the difference between two values (i.e., with and without the presence of the additive) is significant at the 5% level (e.g., R ) 0.05), the probability of such a difference occurring solely as a random variation is less than 1 in 20, which suggest that the difference is the result of the presence of the additive. The format of the significance test (t-test) depends on whether the standard errors are equal or not, and this is evaluated by the F-test. The F-test38 considers the ratio of the two sample variances

F)

S 2M S 2m

(5)

where S 2M and S 2m in eq 5 are chosen such that F > 1. If the calculated value of F exceeds a certain critical value F(R/2, dfM, dfm)39, then the standard errors are significantly different, and this is found to be true in all cases of the present work. When the population standard errors are significantly different, an approximated t-test method is used38

t)

- γVAN (γADM SL SL ) )2/nADM + (SE VAN )2/nVAN x(SE ADM γ γ

(6)

where SE ADM and SE VAN are the two individual standard γ γ errors, and nADM and nVAN are the respective sample sizes.



Figure 5. 3-D view of the monoclinic crystal structure (unit cell) of vanillin (form I). Carbon, hydrogen, and oxygen atoms are represented with gray, white, and red sticks, respectively. Hydrogen bonding is represented with black dotted lines. than the critical value and the influence on the interfacial energy is not statistically significant.

Molecular Simulation

Figure 4. Relative induction times as a function of the driving force. Table 2. Interfacial Energy Values and Standard Errors Calculated from Induction Time Data additive in solution AVA EVA GUA GUE HAP HBA VAC pure VANa a Ref 26.

γ ( SEγ (mJ m-2) 1 mol %

10 mol %

7.00 ( 0.33 6.92 ( 0.33 8.03 ( 0.25 10.05 ( 0.70 8.24 ( 0.25 9.63 ( 0.34 7.24 ( 0.36 7.54 ( 0.32 7.09 ( 0.39 7.59 ( 0.38 (7.27 ( 0.17) mJ m-2

The number of degrees of freedom is

df ) )2/nADM + (SE VAN )2/nVAN]2 [(SE ADM γ γ [(SE ADM )2/nADM]2/(nADM + 1) + [(SE VAN )2/nVAN]2/(nVAN + 1) γ γ - 2 (7) In the t-test, the calculated t-value from eq 6 is compared with a critical value, tcrit(R/2, df)40, which depends on the number of degrees of freedom (eq 7) and the level of confidence requested. In the present work, df is in the range of 101-126, except for the cases of 10 mol % of GUA and GUE where it becomes 28 and 19, respectively. This leads to that tcrit is always in the range of 1.9-2.1, on the 95% confidence level (R ) 0, 05).40 The calculated t-value ranges from about 4 to about 38. This means that the influence of the additive is clearly statistically significant and that there is a difference between the experimental values of interfacial energy for vanillin in a pure solution and in a solution containing the additive. The only exception is for 1 mol % of HAP, where the t-value is lower

The modeling and simulation software environment, Cerius2,11 is used to evaluate the influence of additives on nucleation on the molecular level. The interaction energy of additive molecules with the crystal surfaces of vanillin is estimated. The calculations begin with the generation of a crystal structure, then the crystal lattice energy is minimized, and the macroscopic morphology is derived. From the selected crystal face, a section of surface is cleaved, and each individual additive molecule in its most stable conformation is allowed to move and interact with the molecules of the crystal surface resulting in estimates of the interaction energy. Crystal Structure of Vanillin I. The crystal structure (unit cell) of the stable polymorphic form of VAN (form I) (Figure 5) is generated from the crystallographic data41 presented in Table 3. Yuan and co-workers20 have reported very similar parameters. Using the data of atom positions, space group, and lattice parameters, the unit cell and the three-dimensional periodic superlattice is created. Then, the lattice parameters are held fixed, and molecular mechanics (MM), using the conjugate gradient 200 algorithm42 is applied to minimize the crystal lattice enthalpy by improving atom positions leading to a stable crystalline structure. The generic force field Dreiding243 along with a charge equilibration method44 are used in the calculations. The calculated crystal lattice enthalpy calc TOT ∆H Lattice ) H Lattice /Z - HM ) -95.83 kJ mol-1 (8)

is the difference in conformational energy between the molecules in the solid state and in the gas phase. This value is in good agreement with the experimental value that is based on the sublimation enthalpy exp ) -∆HSublimation - 2RT ) -94.07 kJ mol-1 ∆H Lattice (9) TOT The difference is 1.9%. H Lattice is the total potential energy per unit cell taking into account all valence contributions as well as all intra- and intermolecular interactions in the solid state; HM is the potential energy



Table 3. Crystallographic Data of VAN (Stable Polymorphic Form I)a

a

molecular formula molecular weight crystal shape and color crystal system space group

C8H8O3 152.15 needles, grow along b axis, colorless monoclinic P21, point group 2

lattice parameters (Å, deg, respectively)

a ) 14.049 R ) 90

unit cell volume molecules in unit cell crystal density

Vcell ) 1500 Å3 Z)8 Dx ) 1.347 g cm-3

structure factors, fractional atom coordinates, and isotropic displacement parameters

International Union of Crystallography (Ref. No. LI1126)

b ) 7.874 β ) 115.45

c ) 15.017 γ ) 90

Ref 41. Table 4. Attachment Energy and Slice Thickness for Each Crystal Face of Vanillin slice thickness dhkl

face {h k l}

attachment energy hkl Eatt [kJ mol-1]

calculated

Velavan et al.41

relative difference (%)

001 100 1 0 -1 011 1 1 -1 110

-21.19 -27.32 -28.43 -49.29 -53.18 -53.97

13.5598 12.6857 12.2569 6.8092 6.6248 6.6900

13.5562 12.6874 12.2603 6.8099 6.6222 6.6920

0.027 0.013 0.028 0.010 0.039 0.030

of a free molecule in gas phase; ∆HSublimation ) 88.7 kJ mol-1 is the sublimation enthalpy determined by Serpinskii et al.45 in the temperature interval (293-353 K); and the term 2RT is a correction for the difference between the gas-phase enthalpy pV + 3RT and the estimated vibrational contribution to the crystal enthalpy ∼6RT.46 The simulated crystal structure shows a good match with the experimental structure reported by Yuan and co-workers.20 Theoretical Morphology and Crystal Faces. The theoretical morphology of VAN can be calculated either by the Bravais-Friedel-Donnay-Harker (BFDH) method47 or by the attachment energy (AE) approach.48,49 In the BFDH method, the growth rate of each face is related to the corresponding interplanar distance of the crystal lattice, dhkl, but neglects specific energetic interactions between atoms influencing the crystal morphology. The AE method does take the energetics into account. The relative face growth rates are estimated via the calculation of the attachment energy, Eatt, defined as the energy released when a new growth slice of thickness dhkl is added to the (h k l) crystal face. The larger the face’s interplanar spacing, dhkl, the lower the attachment energy and the lower the growth rate

1/dhkl ∝ |E hkl att | ∝ RG

(10)

The AE method is expected to predict the shape of the crystal more accurately than the BFDH method. The number of possible faces, especially for the symmetry of VAN, is very high, and in Figure 6, only the likely growth faces in the crystal are visualized. The BFDH morphology is quite close to AE morphology shown in Figure 6. In Table 4, the faces are ranked in order of decreasing slice thickness or increasing attachment energy. Thus, those at the top of the list are more likely to be important faces since slow-growing faces will dominate the morphology. The predicted values of dhkl are in good agreement with those determined experimentally by Velavan et al.41

Figure 6. Theoretical morphology of vanillin crystals as predicted by the AE method.

Analysis of Surface Chemistry. The molecular arrangement of the six most important crystal faces of vanillin, according to the predictions stated previously, is shown in Figure 7. The dotted line marks the {h k l} surface plane, and each face cuts orthogonal into the plane of the paper sheet. For each case, only four molecules are represented, and the depth of the surface slab is proportional to the corresponding crystallographic slice thickness (dhkl) obtained from morphology calculations (Table 4). The surfaces with larger dhkl are those with {0 0 1}, {1 0 0}, and {1 0-1} indices (Figure 7a-c). The other three families of surfaces {0 1 1}, {1 1-1}, and {1 1 0} (Figure 7d-f) show a more compact molecular arrangement in the surface slab. The largest {0 0 1} face (Figure 7a) has a unique molecular arrangement where the hydrogens of the methoxy groups (-O-C-H3) and of the aromatic ring



Figure 8. Optimal position and orientation of an additive molecule (vanillic acid, VAC) on the {0 0 1} crystal surface of vanillin (view along Y-axis), when using the surface adsorption approach. A Connolly surface, equivalent to van der Waals surface of molecules, is represented by dots.

Figure 7. Molecular arrangement in crystal surfaces of vanillin: (a) {0 0 1}, (b) {1 0 0}, (c) {1 0-1}, (d) {0 1 1}, (e) {1 1-1}, and (f) {1 1 0}.

(tCsH) are sticking out of the surface. Second in importance are the {1 0 0} and {1 0-1} faces, where there are both hydrophobic sites (tCsH) and hydrophilic sites (dCdO and -O-H). The smallest faces {0 1 1}, {1 1-1}, and {1 1 0} differ significantly from the others showing a zigzag pattern, and the presence of H-bond donors and H-bond acceptors can lead to strong molecular interactions with the environment. Interaction Energy Calculation. The calculation of interaction energy is so far only done for the two most dominating faces (i.e., {0 0 1} and {1 0 0}). Two different methods have been used: surface adsorption (similar to the binding energy calculation method of Myerson and Jang10,12) and lattice integration (a new approach described next), to evaluate the interaction of each additive molecule (Figure 1), viz., acetovanillone (AVA), ethylvanillin (EVA), guaiacol (GUA), guaethol (GUE), 4-hydroxy-acetophenone (HAP), 4-hydroxy-benzaldehyde (HBA), vanillic acid (VAC), including the solvent molecules, and the molecule of vanillin (VAN) itself, with the crystal surface of vanillin. In the surface adsorption approach (Figure 8), a surface slab is defined as a flat surface with dimensions 7 × 7 unit cells, having the same structure as the corresponding crystal surface and a thickness corresponding to the crystallographic slice thickness (dhkl) obtained from morphology calculations (Table 4). The additive molecule is initially located on a central point of the crystal surface (position 0 in Figure 9). The crystalline surface is fixed (i.e., the surface itself does not change its structure), and Molecular Mechanics minimization (MM) is applied to relax the strain of the additive molecule and to find the optimum interaction. At that particular location, several orientations of the additive with respect to the surface are tried by rotating

Figure 9. Locations of the additive molecule on the surface during calculation of interaction energy by the surface adsorption method. Perspective view from above.

the molecule about the X-, Y-, and Z-axes with a step of 45° at a time. The same procedure is applied for eight new locations at the surface around the central point (Figure 9). The local minimum of the surface interaction energy at each location and orientation is registered, and from these data the global minimum is identified. This energy value, ESM, is used to calculate the interaction energy, ES, of the adsorbed additive molecule by subtracting the energy of the additive alone, EM.

ES ) ESM - EM

(11)

If the additive has significant interaction with the crystal surface, the interaction energy must be negative. The larger the absolute value of the energy is, the stronger the affinity of the additive to the surface. In the lattice integration approach, one of the substrate molecules present in the crystal lattice at the surface is replaced by an additive molecule (Figure 10). The additive molecule is located in such a way that common functional groups match those of the substrate molecule. As in the adsorption method, the crystal surface is fixed, and MM is applied to the additive molecule. The number of calculations using this approach to determine the interaction energy (ESL) is reduced to the finite number of symmetry positions (i.e. two symmetry positions for the surface {0 0 1} and four for the surface {1 0 0}). The interaction energy EL is obtained by


Crystal Growth & Design, Vol. 4, No. 5, 2004 1033 Table 5. Maximum Interaction Energies (ES) of Additives on the Surfaces {0 0 1} and {1 0 0} of Vanillin Using the Surface Adsorption Method interaction energy ES (kJ mol-1) additive

{0 0 1}

{1 0 0}

VAN AVA EVA GUA GUE HAP HBA VAC water 2-propanol

-658.5 -699.6 -688.3 -625.4 -655.4 -636.9 -584.5 -1018.4 -397.5 -498.9

-664.6 -900.0 -774.6 -710.5 -761.9 -729.0 -676.3 -1036.7 -492.4 -547.4

Table 6. Calculated Interaction Energies (EL) of Additives on the Surfaces {0 0 1} and {1 0 0} of Vanillin Using the Lattice Integration Method additive VAN

Figure 10. View along the face {0 0 1} of vanillin showing an additive (guaiacol, GUA) in the positions a and b selected in the crystal lattice as substitution centers when using the lattice integration approach.

AVA

EVA

subtracting the energy of the additive alone, EM, from the energy value calculated when the additive is integrated into the crystal lattice, ESL.

EL ) ESL-EM

GUA

(12)

An advantage of the lattice integration method is that the additive molecule interacts with the substrate molecules also sideways, while in the surface adsorption method, the additive molecule interacts only with the molecules beneath the surface. A drawback of both methodologies is the limitation of only using a fixed, nonperiodic surface. However, the lack of periodicity has been overcome by using a sufficiently large slab of surface in comparison to the size of the additive molecule. The energy of each individual additive molecule, EM, is estimated using the charge equilibrium method mentioned previously and an appropriate force field. From an initial arbitrary conformation obtained from the literature,50 an isothermal constant volume (NVT) equilibrium molecular dynamics (MD), followed by molecular mechanics (MM) minimization is done to arrive to the optimal structure. This conformation can change when the molecule is docked onto the crystal surface. In these simulations, the solvation of the surface and of the additive molecule is ignored. Accounting for solvation would make the calculations significantly much more complex, and as a first approximation, we assume that the difference in solvation depending on the additive molecule can be neglected. Interaction Energy Results. The resulting interaction energies are reported in Table 5 for the surface adsorption method (ES) and in Table 6 for the lattice integration approach (EL). The resulting interaction energy values are extremely high if compared, for instance, with the crystal lattice enthalpy (eq 8). However, in these calculations, the reference for the

GUE

HAP

HBA

VAC

lattice position a b c d a b c d a b c d a b c d a b c d a b c d a b c d a b c d

interaction energy EL (kJ mol-1) {0 0 1}

{1 0 0}

-544.9 -849.4

-835.8 -1320.9 -771.3 -742.3 -1061.7 -1379.8 -832.2 -901.4 -846.0 -839.9 -922.1 -556.5 -653.7 -1188.7 -890.9 -902.8 -731.5 -1065.2 -642.9 -747.5 -895.8 -785.9 -302.6 -657.2 -630.6 -853.4 -493.9 -441.7 -1194.2 -1514.4 -938.5 -1066.8

-352.9 -570.9 -386.6 -818.9 -292.3 -785.7 -360.2 -762.4 -495.5 -553.0 -475.2 -610.8 -884.6 -1147.8

obtained energy values is automatically set by the program. The surface adsorption energies of AVA, EVA, and VAC on (0 0 1) are higher than that of VAN itself. Hence, these additives are expected to influence more strongly the crystallization of vanillin. On the surface {1 0 0}, all the additives show a surface adsorption energy that is higher than the value obtained for VAN. In general, all the additives give interaction energies that are higher than the values obtained for typical solvent molecules such as water and 2-propanol. The values presented in Table 5 are interpreted as global minima. However, we have found that the interaction value exhibits a strong variation with the exact location and the orientation of the molecule at the surface. This is illustrated in Figure 11. The figure shows the frequency distribution for the interaction energy of the simulations for AVA on the {0 0 1} face.



Figure 11. Frequency distribution for surface adsorption energy (ES) showing the influence of location and orientation of an additive (AVA) on the surface {0 0 1}. First interval -∞-0, second 1-50, third 51-100, and so on.

The deepest minimum found for AVA is ES ) -699.6 kJ mol-1 (Table 5). However, in trying to find the global minimum, there are actually six coordinates that are to be adjusted, and the capability of the program itself is quite limited. Thus, very much of manual work is required; hence, we cannot ensure that the actual global interaction energy minimum has been found. In the literature,10,12 interaction energy calculations have been presented. In the present work, the situation is difficult because all molecules involved exhibit polar and nonpolar functional groups, and molecular sizes are fairly comparable. The lattice interaction energy (Table 6) depends significantly on the lattice position. On the {0 0 1} face, the lattice position b leads to a much stronger interaction, and for {1 0 0}, the position b is usually the most favorable. With the exception of VAC, the energy value of VAN for each respective location on {0 0 1} is higher than the values obtained for the additive molecules. However, for the face {1 0 0}, we can find higher (AVA and VAC) and lower (EVA, GUA, GUE, HAP, HBA) values than the value obtained for pure VAN. When comparing the results presented in Tables 5 and 6 (e.g., for the crystal surface {0 0 1}), we can see that all the additives show absolute values for the surface adsorption energy that are higher than those calculated for the position a when using the lattice integration approach (|ESadd| > |ELadd|) (see dots below the diagonal line in Figure 12). For the crystal surface {0 0 1}, the lattice integration energy of the additives in position b is larger than the lattice integration in position a. For almost all the additives, the lattice integration energy in position b is larger than the surface adsorption energy (dots above the diagonal line in Figure 12), except for AVA and HAP. For the surface {1 0 0}, all the additives show higher absolute values for the lattice integration mechanism (|ELadd| > |ESadd|). Evaluation and Discussion The relation between experimental interfacial energy (γ) and by simulation determined interaction energy (ES and EL) is presented in Figure 13. No simple and clear correlation is found for all the additives regardless of face or method of estimation of interaction energy.

Figure 12. Correlation between values of lattice integration and surface adsorption energy for the crystal face {0 0 1}.

However, some correlation is found when additive molecules are analyzed when separated into two groups (i.e., group 1 including AVA, EVA, and VAC and group 2 including GUA, GUE, HAP, and HBA). In group 1, all molecules have three functional groups attached to the aromatic ring and in the same configuration as VAN itself. Like VAN, all three have a hydroxyl group, a methoxy, or an ethoxy group in meta position to that and a group containing a carbonyl oxygen in para position. Common for additives in group 2 is that they all have only two functional groups attached to the aromatic ring and that one of these is always a hydroxyl group. For both groups of additives, the interfacial energy tends to increase with increasing interaction energy, but for the first group (AVA, EVA, and VAC), a very steep slope is observed. In addition, all additives of group 1, at the 1 mol % level, lead to a reduced interfacial energy for vanillin. The VAC molecule by virtue of its -OH and -COOH groups is capable of extensive hydrogen bonding and always has a high interaction energy. In group 2, we can identify that GUA and GUE increase the interfacial energy and do not adsorb more strongly than VAN itself (Figure 13). The incompatibility of the additives GUA and GUE can also affect the growth patterns within the structure during the formation of nuclei. The structural feature that singles them out is that they lack the carbonyl oxygen. The lack of the methoxy group in the remaining two compounds of the second group, HAP and HBA, seems to be less critical. Additives HAP and HBA (Figure 13) exhibit no strong influence on the interfacial energy and from an adsorption point of view are about equal to VAN. However, with respect to surface integration, they interact less strongly than VAN. In the present work, we do not find a clear overall relation between interfacial energy and calculated ener-



Figure 13. Relation between interaction energies and interfacial energies for faces {0 0 1} (a and b) and {1 0 0} (c and d). Interaction energies calculated by the surface adsorption method (a and c) and by the lattice integration method (b and d).

gies of interaction. We believe that there are several reasons for this. To start with, there is so far no clear theoretical basis for the action of additives on the nucleation. It is fairly well-established how an additive may disturb the growth of a crystalline face, and the same mechanism may also be active on the nucleus length scale. In addition, however, the additive may influence the clustering process ahead of the nucleation as well as the thermodynamic stability of the nucleus. Hence, we do not know to what extent interaction energies are relevant for the description of the influence of additives on nucleation. Furthermore, we know that the estimation of the interaction energy by the molecular modeling is strongly simplified because (i) the role of the solvent (i.e., the solvation of the surfaces and molecules joining them) is not accounted for by the model; (ii) in modeling the surface adsorption, it is difficult to identify the energetically most favorable arrangements for adsorption of the additives, and the adsorption is only studied on flat faces not at steps and kinks; (iii) in the surface integration, we do not account for the influence on the adherence of the next layer of vanillin molecules to the surface; and (iv) the assumption that the nucleus shape is identical to that of a large crystal can be ill-founded since the nucleus is formed under quite different conditions. Using the nucleation theorem,51 the nucleus size is estimated to be quite small and contains only a small number of molecules. A very small nucleus can either have rough surfaces, or if partially faceted, may have many of the faces conceivable for the crystal symmetry. In addition, the experimental determination of the influence of additives on the nucleation is a challenge. The induction time is fairly easy to determine, but its relation to the fundamental parameters of the rate of nucleation is based on several assumptions, some of which are not easily verified. The induction time consists of three components: (i) the transient period (i.e., a relaxation time needed to achieve a quasi-steady-

state distribution of molecular clusters as response to the imposed supersaturation); (ii) the period for the formation of stable nuclei: the nucleation time; and (iii) the period required for the critical nuclei to grow to detectable dimensions: the growth time. At moderate supersaturation level and low viscosity, the time of the transient period is negligible.1,7,30 Without information of the growth kinetics, the time of growth is not known. However, since the induction times of the present work are fairly long (2 min cooling + 1 min minimum time), the nucleation time is likely to at least be dominating. The stochastic nature of nucleation (discussed in our previous paper26), which shows up as a significant variation in induction time, reduces the confidence in the determination of the influence of the additives. An outcome of the present work is that we have found that a very simplistic approach to predict the influence of additives on nucleation is not successful. The analysis has to be much more detailed, and we probably need a new generation of simulation tools. Conclusions The induction time for nucleation of vanillin has been determined in the presence of additives at two different levels of additive concentration. The experimental results reveal that the additives do have an influence on the induction time for nucleation of vanillin. At low additive concentration and low supersaturation, the induction time is reduced by the additive, while increased additive concentration and increased supersaturation tends to increase the induction time above that of pure vanillin. Despite the large spread in induction time data, the solid-liquid interfacial energy can be estimated with statistical confidence. The main reason for this is that a very large number of measurements have been performed, which has been made possible by using a novel multicell device. Except for the case of HAP at 1 mol %, there is an effect that is


statistically significant of the additive on the interfacial energy. The interfacial energy of pure vanillin is 7.3 ( 0.2 mJ m-2. The lowest interfacial energy, 6.9 ( 0.3 mJ m-2, was obtained in the presence of 1 mol % of EVA, while the highest value, 10.1 ( 0.7 mJ m-2, was obtained in the presence of GUA at 10 mol %. The presence of additives at low concentrations (1 mol %) increases the interfacial energy in the following order: EVA < AVA < VAC < HAP < VAN < HBA < GUA < GUE. By increasing the additive concentration from 1 to 10 mol %, the interfacial energy is enhanced by up to 40% and increases in the following order: VAN < VAC < GUE < GUA. The molecular modeling software Cerius2 was employed to simulate the crystal lattice structure and morphology of vanillin and to calculate the interaction energy of different additive molecules with the two morphologically most important faces of vanillin: {0 0 1} and {1 0 0}. The simulation of the crystal structure was validated by comparing the calculated crystal lattice enthalpy with the experimental sublimation enthalpy. Two different methods were adopted for estimation of the interaction energy: surface adsorption and lattice integration. On both faces, the strongest adsorption is found for VAC, AVA, and EVA, in decreasing order of interaction energy, and all three adsorb more strongly than vanillin. However, the simulations are not efficient in finding the globally most favorable adsorption configurations. A great deal of manual work is required, and we cannot ascertain that the true minimum interaction energy has been found. When using the lattice integration method, VAC always has the highest interaction energy and always was above that of vanillin itself. This suggests that VAC, when present in a solution from which vanillin crystallizes, may be incorporated into the lattice. On the {1 0 0} face, AVA has an interaction energy above that of vanillin. No simple and clear correlation is found between molecular modeling interaction energies for the two most morphologically important faces of VAN and the influence of additives on the experimental interfacial energy. However, the data can to some extent be correlated to the molecular structure of the additives when the additives are divided into two groups having AVA, EVA, and VAC, containing three functional groups attached to the aromatic ring in one group, and GUA, GUE, HAP, and HBA, containing two functional groups attached to the aromatic ring in the other. However, it is recognized that the modeling does not concern the actual nucleation but rather the conditions of a growing surface and is based on several severe simplifications. Obviously, this simplistic approach does not sufficiently capture the influence of additives on the nucleation of vanillin. However, still the modeling and the visualization of the molecular scale is a valuable tool in the analysis of the problem. Acknowledgment. The authors gratefully acknowledge the Swedish Research Council (TFR/VR) and financial support of the Industrial Association for Crystallization Research and Technology (IKF) for financial support and especially to Borregaard Synthesis (Norway) for kindly supplying pure vanillin and the additives.


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