Effect of Impurity on the Lateral Crystal Growth of l-Alanine: A

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Effect of Impurity on the Lateral Crystal Growth of L‑Alanine: A Combined Simulation and Experimental Study Xiangyu Yang, Gang Qian, Xuezhi Duan, and Xinggui Zhou* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237, China ABSTRACT: The effects of L-valine on the lateral growth of (011) and (120) surfaces of L-alanine are studied by combining molecular simulation and experimental studies. The growth of the (120) surface is significantly inhibited by L-valine, while the growth of the (011) surface is less affected. An intrinsic impurity effectiveness parameter is proposed by taking into consideration the selectivity of impurities to adsorb on both step and terrace, which explains the different inhibition effects of an impurity on different surfaces.

1. INTRODUCTION Impurities in solution may have profound effects on the rate of crystal growth, and the effects may differ according to the surface, impurity type, and impurity concentration.1−7 The most widely used theory for estimating the inhibition effects of impurities is the Cabrera−Vermilyea (C−V) theory,8−12 which assumes the impediment of step growth is due to the occupation of the active growth sites on crystal surface by impurity molecules. Based on this theory, Kubota and Mullin further developed the growth mechanism using different assumptions of the average step velocity and the different adsorption isotherms of impurity (R/R0 = 1 − αθ, α is the impurity effectiveness factor and θ is the surface coverage of impurity).9 From the definition, the impurity effectiveness (α = γa/kTσL) is treated as a criterion of the inhibition effects, and the larger the impurity effectiveness, the stronger the inhibition effect. However, the factor is determined by fitting the mathematical model to the experimental results.9−12 As an example, the relative growth rates of the L-asparagine monohydrate (012) and (101) surfaces in the presence of Lglutamic acid were measured, and then the experimental data were fitted to obtain the impurity effectiveness.7,9 Despite a large number of experimental studies of the different inhibition effects of impurities on crystal growth, a generally accepted molecular level description of the impurity effectiveness based on the solute−impurity interactions has not been provided. The impurity effects are usually explained by build-in and surface-docking models, where the mobility of impurity molecules, that is, the migration of adsorbed impurity molecules during crystal growth, is not taken into consideration. In fact, the inhibition effects of impurity molecules are largely determined by their mobility.13,14 For example, Martins et al. studied the effects of supersaturation variation on the growth rates of a model protein crystal and indicated that the delayed migration of the impurity molecules makes the poisoning crystallization possible.15 The impurities will not unidirectionally migrate from terraces to steps, and they may also diffuse away from steps. However, the classical predicting models do not consider the intrinsic mobility of impurity molecules, leading to poor predictions of different impurity effects. © 2012 American Chemical Society

In this work, the effects of L-valine impurity on the lateral growth of (011) and (120) surfaces of L-alanine are first studied. Molecular dynamics simulation is performed to calculate the competitive adsorption of impurity at either step or terrace and the competitive adsorption between step and terrace. An impurity effectiveness is then obtained to include the selectivity of impurity adsorption on step and terrace. The results provide a rational explanation of the experimental observations of the different inhibition effects of L-valine on the (011) and (120) surfaces of L-alanine crystal.

2. METHODS The growth of L-alanine single crystal and the L-alanine crystal structure have been extensively studied.16−21 The naturally zwitterionic molecules of L-alanine expose different functional groups on different crystal surfaces, resulting in different surface growth rates in the absence or presence of impurities. In this study, L-valine, which closely resembles the structure of Lalanine crystal, is chosen as the impurity. 2.1. Experiments. The Guaranteed Reagent L-alanine and L-valine (Adamas, >99%) are used in this study, and ultrapure water (ELGA PURELAB Classic, 18.2 MΩ·cm) is used to prepare the crystallizing solution. Slow evaporation method is employed to prepare the single L-alanine crystal. The crystallizing solution is prepared by dissolving L-alanine into H2O at a higher temperature of 35 °C. The warm solution is then filtered and slowly cooled to the saturated temperature of 25 °C. The glass tubes containing prepared saturated crystallizing solution are covered by filter papers to retard solvent evaporation. The evaporation rate is not measured but is slow enough for growing a single crystal. The Miller indices of the crystal surfaces are determined by measuring the interfacial angles. Crystal growth experiments are carried out to measure the surface growth rate of L-alanine at different impurity concentrations of L-valine. L-Alanine and L-valine are dissolved Received: Revised: Accepted: Published: 14845

June 18, 2012 September 14, 2012 October 11, 2012 October 11, 2012 dx.doi.org/10.1021/ie301600n | Ind. Eng. Chem. Res. 2012, 51, 14845−14849

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Figure 1. Images of L-alanine habits before (left) and after (right) growth of 7 days at a constant supersaturation (σ = 0.01) in the presence of Lvaline impurity (0.02%).

in H2O at 35 °C and the solution is stirred for 2 h to prepare impure crystallizing solutions (σ(25 °C) = (c − ceq)/ceq = 0.01) with different impurity concentrations (0−0.1 wt %), which are filtered through a 0.22 μm membrane and then slowly cooled to 25 °C. The as-prepared single crystals of L-alanine are immersed in the solutions and allowed to grow for 7 days at 25 °C, during which the vials are sealed to prevent solvent evaporation. The growth rate of (011) and (120) surfaces are obtained by measuring the crystal dimensions before and after the growth. The amount of solution is large enough to ensure that the supersaturation hardly changes after the crystal growth. 2.2. Simulation. L-Alanine crystallizes in an orthorhombic lattice with space group P212121,20 and there are four molecules in the unit cell linked by a three-dimensional network of hydrogen bonds. To understand the L-valine effects on (011) and (120) surfaces of L-alanine crystal, molecular dynamics simulation with NVT ensemble is carried out using Material Studio 5.0 (Accelrys Software Inc.: San Diego, 2009). The Ewald summation is used for the calculation of long-range interactions. First, CVFF, PCFF, COMPASS, and UNIVERSAL with the force field assigned charges and the equilibration and Gasteiger charge rules are used to optimize the unit cell of L-alanine adopted from Cambridge Structural Database (CSD). With CVFF and the force field assigned charges, the crystal structures before and after optimization have close similarity, and the calculated lattice energy (−70 kcal·mol−1) is also close to the experimental value (−66 kcal·mol−1).22 Therefore, the CVFF and the force field assigned charges are used in all the following simulations. On the basis of the optimized crystal structure, the (011) and (120) surfaces of L-alanine are cleaved to a depth of more than 30 Å and then extended and rebuilt into three-dimensional periodical boxes. The surface dimensions are set larger than 30 Å and the thickness of vacuum is set to 50 Å to make sure the nonbond interactions can reach their asymptotic values. Each crystal surface is optimized with a relaxed top layer. Then the impurity effects are studied by molecular dynamics simulations as follows: (1) The likelihood of L-valine incorporation into L-alanine crystal is assessed by dynamics simulations where one impurity molecule is buried into the rigid and partially relaxed boxes. The incorporation energy of pure L-alanine molecule in the crystal is calculated for comparison. (2) For the flat surface, both build-in and surface-docking models are employed to estimate the impurity effects on Lalanine crystal surfaces. In the build-in model, each orientation of L-alanine molecule is substituted by L-valine molecule once, and in the surface-docking model, L-valine molecule is docked on the middle of a given surface randomly. Minimization is first performed for a proper initial position. Then molecular

dynamics is carried out. During the simulations, the bulk crystal except for the top layer is constrained. (3) The stepped interfaces are built according to the strength of the hydrogen bonds. The linkage of molecules in crystal is stabilized by the strong hydrogen bonds and hence the step is built along the weak hydrogen bonds. The adsorption of the solute and impurity molecule on the stepped interface is dynamically optimized for at least 200 ps to reach equilibrium. Then the average interaction energies are obtained within the subsequent 200 ps.

3. RESULTS AND DISCUSSION 3.1. Growth of L-Alanine in the Presence of L-Valine. Figure 1 shows that the crystal is much more elongated along the c-axis in the presence of L-valine in solution, and Figure 2

Figure 2. L-Valine effects on the relative growth rates of (011) and (120) surfaces of L-alanine.

shows that the impurity has different effects on the two surfaces. The growth of L-alanine (011) surface is retarded by Lvaline, while the growth of (120) surface is almost completely inhibited even with a lower impurity concentration. 3.2. Impurity Incorporation. The molecular compatibility of L-valine is assessed by incorporating one L-valine molecule into the bulk L-alanine crystal. When the molecules in the crystal are rigid, the energy enhancement is 98 kcal·mol−1, whereas when the molecules in the crystal close to the L-valine are relaxed, the energy enhancement is as high as 149 kcal·mol−1. Because of the structural similarity, L-valine can form a similar configuration with the molecules in the crystal.23,24 However, the dissimilar part of L-valine makes the molecules in the crystal around L-valine severely deformed and results in a large energy increase. Therefore, it is not easy for the L-valine to incorporate into the bulk crystal of L-alanine. In contrast, the L-valine molecules prefer to interact with the interface molecules through the similar part, and thus hinder the movement of crystal steps. 14846

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Figure 3. (011) surfaces of L-alanine substituted by L-valine on four specific symmetry positions (a, b, c, d) in the build-in model. (Colorful: Lalanine. Turquoise: L-valine).

⎛ Δbhkl ⎞ pure ⎜ mod ⎟⎟ = − Eatt, E 1 hkl att, hkl ⎜ E b,alanine ⎝ hkl ⎠

3.3. Inhibition Mechanism of L-Valine Impurity. The different impurity effects of L-valine on (011) and (120) surfaces of L-alanine crystal may be attributed to the different host−guest interactions.25 The classical build-in and surfacedocking models,26,27 which are widely used for estimating the impurity effects, are employed to study the L-valine effects on the flat L-alanine interfaces. 3.3.1. Impurity Effects Predicted by Classical Models. The build-in model is first used to predict the impurity effect, which is done by calculating the surface energies (Esurface) when one Lalanine molecule on the surfaces is substituted by one L-valine molecule. Because of the four different orientations of L-alanine molecules on (011) and (120) interfaces, the substitution calculations on each surface are repeated four times. As shown in Figure 3, the regular arrangements of the molecules in the crystal on the (011) surface are disrupted by the presence of Lvaline and the molecules are forced to adjust the positions and conformations to lower the repulsive energy. The same consequence occurs on the (120) surface. As a result, the total surface energies with the presence of L-valine molecules are raised (Table 1), indicating that the growth of both surfaces

Table 2 shows the calculated results. The negative value of the energy difference (Δbhkl) indicates that L-valine molecules Table 2. Adsorption Energies and Attachment Energies Induced by L-Valine

(011) pure substitute substitute substitute substitute

1 2 3 4

(120) ΔEsurface

Esurface

ΔEsurface

−10007 −9965 −9964 −9995 −9972

42 43 12 35

−7031 −6967 −6980 −6965 −6991

64 51 66 40

surface

Ealanine b,hkl

Evaline b,hkl

Δbhkl

Epure att,hkl

Emod att,hkl

(011) (120)

−59 −17

−61 −21

−2 −4

−82 −64

−79 −49

are easier to adsorb on crystal surfaces than the L-alanine molecules. The absolute value of the energy difference and the modified attachment energy of the (120) surface are both higher than that of the (011) surface; therefore, on the (120) surface, the growth rate is lower and the inhibition effect of Lvaline is stronger. These results show that the surface-docking model provides the overall performance of the impurity effect based on the changes of attachment energy when an impurity molecule is docked on the surface and is more reliable than the build-in model to predict the impurity effect. However, the inhibition effectiveness of the adsorbed impurity is not considered, and the different growth rate dependencies of crystal surfaces on impurity are not resolved. For a better understanding of the impurity effectiveness, the competitive adsorption between the solute and impurity at different sites on different surfaces needs to be addressed. 3.3.2. Inhibition Effectiveness Based on Dynamic Simulation. Crystal growth involves sequential steps of surface diffusion and adsorption of solute molecules onto crystal steps. In impure crystallizing solutions, the mobility of the impurity molecules adsorbed at steps determines the crystal growth rates. Yani et al. measured the mean square displacements of different impurities on the model crystal surface by molecular simulation, and suggested that the mobility is a key parameter to understand the impurity effect.30 By dynamics simulation, the impurity mobility on the stepped interfaces of L-alanine crystal is evaluated. Figure 4 shows the adsorption of L-valine at steps and terraces on both surfaces. It can be seen that the L-valine molecule is weakly bound at the step on the (011) surface. However, the L-valine molecule on the (120) surface is strongly adsorbed at the step and it disturbs the regular arrangement of the crystal by squeezing out L-alanine molecule from the step. Consequently, on the (011) surface, L-valine has a large mobility, while on the (120) surface, it has a limited mobility.

Table 1. Energies of L-Valine Substituted Surfaces in the Build-In Model Esurface

(1)

is retarded, which coincides with the findings of Anuar et al.28 Moreover, the resulted energy differences (ΔEsurface) in Table 1 are lower on the (011) surface and therefore the impurity molecules are easier to incorporate into the surface, leading to a higher inhibition effect. However, the results are opposite to the experimental observations. Then the surface-docking model is employed to predict the impurity effects using the same method proposed by Ulrich et al.27 and Myerson et al.29 The binding energies for both Lvaline alanine (Ealanine b,hkl ) and L-valine (Eb,hkl ) on the (011) and (120) surfaces are calculated. The energy difference (Δbhkl = Evaline b,hkl − Ealaline b,hkl ) provides an indication of the degree of inhibition by Lvaline on crystal surfaces. With the attachment energy of the pure surfaces (Epure att,hkl), the modified attachment energy is estimated by 14847

dx.doi.org/10.1021/ie301600n | Ind. Eng. Chem. Res. 2012, 51, 14845−14849

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Figure 4. Adsorption of L-valine at terrace and step on (011) and (120) surfaces. (Thumb blue stick: bulk L-alanine crystal. Colorful stick: relaxed steps. Turquoise ball and stick: L-valine.).

unambiguously intrinsic description of the impurity effectiveness from a molecular level. The impurity effectiveness on (011) and (120) surfaces of Lalanine are 0.41 and 1.06, respectively. It suggests that the growth of crystal steps of (011) surface is slowed down but not completely inhibited, while that of the (120) surface is strongly inhibited.

Table 3 presents the adsorption energies of L-alanine and Lvaline at step and terrace. Similarly, the difference of the Table 3. Adsorption Energies and Mobility Factors in the Modified Surface-Docking Model (011) step terrace mobility index αrel hkl effectiveness factor eimp hkl

(120)

Ealanine hkl

Δbhkl

μhkl

Ealanine hkl

Δbhkl

μrel,s hkl

−114 −114

44 41 0.94 0.41

0.44 0.47

−66 −43

41 39 4.6 1.06

0.23 0.05

4. CONCLUSIONS The molecular mechanisms of the different impurity effects of L-valine on the crystal growth of L-alanine (011) and (120) surfaces are presented. The experimental results show that the inhibition effect of L-valine is significant on the (120) surface and is relatively small on the (011) surface. On the basis of dynamics simulation, an impurity effectiveness is proposed to consider the competitive adsorption, at either step or terrace, between the solute and the impurity, and the competitive adsorption of the impurity between steps and terraces. A rational interpretation of the experimental results is provided that can be used to estimate different impurity effects.

adsorption energies is defined as Δbhkl. The relative adsorption strength of L-valine at step and terrace can be estimated by μhkl =

valine Ehkl alanine Ehkl − Δbhkl

(2)

■

Thus, the relative adsorption strength (μhkl) will be larger if the adsorption of L-valine is stronger than that of L-alanine, at either step or terrace. To indicate the competitive adsorption of Lvaline between step and terrace, we define rel αhkl

=

*Tel.: +86-21-64253509. Fax: +86-21-64253528. E-mail: [email protected].

step μhkl terrace μhkl

Notes

(3)

The authors declare no competing financial interest.

■

which is the mobility index of impurity at step. When the impurity mobility at step is less than that at terrace, the effective surface migration of L-valine is from terrace to step, and the step will be poisoned, leading to a dramatic inhibition effect. Otherwise, the effective surface migration of L-valine is from step to terrace, i.e., the adsorbed impurities will leave the step sites. Because the steps are the active growth sites of crystal, the running away of impurity recovers the crystal growth, that is, continuous generation of steps and terraces. The larger the mobility of impurity, the easier the growth recovery. Therefore, the impurity effectiveness can be obtained by taking both the selectivity of impurity adsorption on step and terrace into consideration, imp rel step ehkl = αhkl ·μhkl

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REFERENCES

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A larger impurity effectiveness leads to a greater inhibition effect. This definition can reasonably be used to evaluate different inhibition effects of impurity, and it gives an 14848

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