Spherulitic Crystallization of L-Tryptophan: Characterization, Growth

Article pubs.acs.org/crystal

Spherulitic Crystallization of L‑Tryptophan: Characterization, Growth Kinetics, and Mechanism Jingxiang Yang,†,‡ Yongli Wang,*,†,‡ Hongxun Hao,*,†,‡ Chuang Xie,†,‡ Ying Bao,†,‡ Qiuxiang Yin,†,‡ Junbo Gong,†,‡ Chen Jiang,†,‡ Baohong Hou,†,‡ and Zhao Wang†,‡ †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China

‡

ABSTRACT: L-Tryptophan was successfully crystallized in the form of spherulites by introducing trace amounts of gelatin into the crystallization solution. The physicochemical properties of L-tryptophan products were significantly improved by using this polymer-induced spherulitic growth strategy. This newly developed polymer-induced spherulitic growth strategy provides another choice for controlling the size distribution of particles. Furthermore, the formation and growth of these spherulites under different conditions was monitored in situ by using particle vision measurement and microscopy. It was found that the morphologies of spherulites could be influenced by the additives, the crystallization temperature, and the initial concentration of L-tryptophan. The influence of temperature on the growth rate of spherulites was investigated. It was found that the growth rate is constant at given temperatures. A population-based empirical model was developed and used to explain the spherulitic growth of L-tryptophan spherulites. It was verified that the growth of L-tryptophan spherulites is interface kinetics controlled.

1. INTRODUCTION Crystals with small sizes, especially flake-like and needle-like microcrystals, always raise difficulties in their downstream processing, due to their low bulk density and poor flowability, compressibility, and compactibility. Clearly, formation of large and spherical particles is an effective way to solve this problem. Generally, the micronized crystals can be mixed with fillers and then be agglomerated to form large particles by using a granulation technique. It would be more efficient to transform the small crystals into large particles directly through the crystallization process. Spherical crystallization, pioneered by Kawashima and co-workers,1 is a typical technique to achieve this goal by an agglomeration process of microcrystals. The polymer-induced spherulitic growth strategy presented in this work is an addition to currently available approaches for preparation of large spherical particles. Spherulitic growth is radial polycrystalline growth, which will result in an outer spherical envelope.2 Spherulites can be widely observed in high viscosity crystallization systems, such as melt, mineral, and polymer.3 The spherulitic growth of smaller molecules, such as barium carbonate (BaCO3),4 calcium carbonate (CaCO3),5 L-glutamic acid, and an aromatic amine6 in solution crystallization, has been reported. Previously, spherulites are generally regarded as a source of trouble. This term is sometimes used pejoratively to describe a failed attempt to prepare well-defined single crystals. However, recently, the use of a spherulitic growth strategy for the fabrication of particles that exhibit unique physical or chemical properties has © XXXX American Chemical Society

been extensively demonstrated. For example, controlled fabrication of vaterite hierarchical structures,7 apatite spherulites,8 and spherulites of human interferon with improved pharmacokinetics has been demonstrated.9 The spherulitic growth strategy can also be used in the area of product design. For example, in Beck’s work, formation of spherulitic particles was used to increase the filterability of CaCO3 crystals.10 The model compound of this work, L-tryptophan (C11H12N2O2, CAS registry No. 73-22-3, Figure 1), is one kind of essential amino acid for many organisms. It has been widely used as food and feed additives, nutraceutical, and medicine.11 Moreover, L-tryptophan has antioxidation func-

Figure 1. Chemical structure of L-tryptophan. Received: July 30, 2015 Revised: September 14, 2015

A

DOI: 10.1021/acs.cgd.5b01089 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Figure 2. Schematic diagram for lab-scale cooling crystallization. circulating water of thermostat 1. On the basis of the solubility data of L-tryptophan,12 the saturated solution of L-tryptophan was prepared in the crystallizer by dissolving L-tryptophan and additive into distilled and deionized water. The ending point of the dissolution process was determined by the statistic data of focused beam reflectance measurement (FBRM) (Mettler Toledo, Redmond, WA). After the preparation of saturated solution, the valves 2 and 3 were opened, while valves 1, 4, and 5 were shut off. The system was quickly quenched down to a lower temperature in 1 min by thermostat 2. After 30 min, the crystallization process was stopped. The suspension was filtered. The obtained crystalline products were washed with ethanol and dried in a vacuum oven at room temperature. 2.3. Product Characterization. The particle size distribution (PSD) was determined by using a particle size analyzer (Mastersizer 3000, Malvern Instruments Ltd., U.K.). A saturated ethanol solution of L-tryptophan was employed as the dispersing medium for the measurement. Scanning electron microscopy (SEM, TM3000, Hitachi, Japan) was used to observe the morphology of particles. Both bulk density (ρb) and tapped density (ρt) of all products were determined using a measuring cylinder (25 mL). The Carr index was determined to evaluate the flowability of powder.13 The Carr index (IC) could be calculated as follows14

tions, and it can be used to prevent the decomposition of powdered milk. In the livestock farming industry, L-tryptophan is very effective for accelerating the growing up of livestock and enhancing the disease-resistant ability of livestock. However, Ltryptophan crystals obtained by the normal crystallization method generally exhibit a flake-like morphology and are pretty small in size, which will result in problems such as low bulk density, poor flowability, and poor compressibility. In this paper, a polymer-induced spherulitic crystallization method is presented to produce particles of L-tryptophan with a controlled size distribution. Detailed characterization of particle size, size distribution, and microstructure of the spherulites was reported. The bulk density, flow property, and purity of spherulitic particles were compared with those of flake-like crystalline products. Particle vision measurement (PVM) and time-lapse optical microscopy were used to observe the evolution process in both a lab-scale cooling crystallization system and evaporating droplet. Furthermore, in order to better understand this process, the effects of experimental parameters, such as additives, the crystallization temperatures, and the initial concentrations of solution, on the morphologies of spherulites were systematically investigated. The growth kinetics of spherulitic structures in evaporating drops was also investigated, and a population-based empirical power-law model was developed.

IC = (ρt − ρb )/ρt

(1)

The crystal structures of products were identified by powder X-ray diffraction (PXRD, D/MAX 2500 Japan) patterns. The diffraction patterns were collected with a Rigaku D/max 2500 powder X-ray diffractometer with Cu Kα (λ = 1.5418 Å) as the source. It was operated at 40 kV and 100 mA. The samples were scanned from 2° to 50° (2θ) with a step size of 0.02°. 2.4. Droplet Evaporation (Isothermal) Crystallization. As shown in Figure 3, the droplet evaporation (isothermal) crystallization experiments were carried out by using a water-evaporation method. Solutions used in these experiments were made by dissolving the Ltryptophan and additive in distilled and deionized water. Clean and dried glass slides were heated/cooled to the desired temperature on the hot stage of a hot stage polarized optical microscopy system (HSPOM, Olympus BX51, Olympus Corporation, Tokyo, Japan). This hot stage ensures a homogeneous temperature field across the glass slide with an accuracy of ±0.5 K. Time-lapse images were acquired using a sensitive Kodak digital camera at a fixed time interval. A polarizer was arranged in an orthogonal position for the cross-polarizer imaging.

2. EXPERIMENTAL SECTION 2.1. Materials. For the experiments, L-tryptophan (99% reagent grade, from Aladdin, USA) and gelatine (from Kewei, Tianjin, China) were used as received. Distilled, deionized water was used wherever applicable. 2.2. Lab-Scale Cooling Crystallization Experiments. The cooling crystallization experiments of L-tryptophan were performed in a stirred (three-bladed propeller) lab-scale glass crystallizer. The evolution process of L-tryptophan spherulites was investigated by using Particle vision measurement (PVM) (Mettler Toledo, Redmond, WA). The apparatuses for the cooling crystallization system are shown in Figure 2. First, valves 2 and 3 were shut off and valves 1, 4, and 5 were opened. The crystallizer was heated up to a higher temperature by B



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Figure 3. Experimental setup for droplet evaporation (isothermal) crystallization of L-tryptophan. (a) The hot stage polarized optical microscopy and (b) the detailed sketch of heating of L-tryptophan solutions.

3. RESULTS AND DISCUSSION 3.1. Characterization of Spherulitic Products. In the lab-scale cooling crystallization system, crystallization experiments under various conditions were conducted. L-Tryptophan products with different morphologies and particle size distributions were obtained by changing the crystallization temperatures, initial concentrations of L-tryptophan, and the amounts of of gelatine. The experimental conditions are summarized in Table 1. Table 1. Experimental Conditions in Lab-Scale Crystallization System

condition

concentration of gelatine (g/mL)

initial concentration of L-tryptophan (g/mL)

initial temperature (K)

final temperature (K)

1 2 3

0.0006 0.0006 0

0.04 0.04 0.04

363 363 363

274 293 293

Figure 4. SEM images of L-tryptophan crystals: (a, b) Spherulites obtained at 293 K which are composed of larger subindividuals. (c, d) Spherulites obtained at 274 K which are composed of smaller subindividuals. (e, f) Flake-like crystals obtained in the absence of gelatine. (g, h) Flake-like crystals from Aladdin. Panels (b), (d), (f), and (h) are SEM images with higher magnification showing the structural details of L-tryptophan crystals obtained under different conditions.

To compare physicochemical properties of different Ltryptophan products, L-tryptophan purchased from Aladdin was selected as representative of current products. The morphologies of all products were observed and recorded by SEM (Figure 4). Flake-like crystals of L-tryptophan were obtained in the absence of gelatine, and it looks similar to the product from Aladdin. Spherulitic particles of L-tryptophan were obtained in the presence of gelatine. The flake-like particles (Figure 4e,g) which are stacks of single crystalline sheets (Figure 4f,h) are apparently different from the spherulites (Figure 4a−d). Additives are often found to be responsible for spherulitic morphologies.15 Similar results have been observed in the crystallization of fluoroapatite in the presence of citrate16,17 and calcite spherulites in the presence of Mn2+ and Co2+.18 This considerable morphology difference indicates that gelatine is the key factor point for the formation and growth of Ltryptophan spherulites. By the close observation of SEM images at higher magnification (Figure 4b), the spherulitic particles prepared at 293 K were composed by subindividuals with sizes of 20−50 μm in width and about 1 μm in thickness. Although the morphologies of L-tryptophan spherulitic particles prepared at 274 K are similar to those of products from 293 K, the size of these porous microspheres is smaller (about 100 μm) and the width and thickness of their subindividuals are about 3−9 μm and 100−200 nm, respectively. Apparently, the lower

crystallization temperature results in not only smaller spherulites sizes but also lower values of width and thickness of subindividuals. Figure 5a shows the light-microscopy image of the microsphere of L-tryptophan prepared at 274 K. When viewed

Figure 5. Analysis of internal structure. (a) Polarized optical microscopy image of spherulites prepared at 274 K and (b) SEM image of the inner microtexture of a broken spherulite.

by polarized optical microscopy, the microspheres show a clear Maltese-cross extinction pattern between crossed polarizers, which suggests that spherulite lamellar are elongated along a radial orientation toward the surface of spherulite. The internal microstructure of a spherulitic particle prepared at 293 K was analyzed by SEM, which characterized the inner microtexture of C



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The curves of the particle size distribution for different products are provided in Figure 7. Apparently, the size

a broken spherulite (Figure 5b). The fractured ball clearly shows a radial organization of building blocks. These results suggest the radial morphology of particles produced in the presence of gelatine. The crystal structure of all products was examined with powder X-ray diffraction (PXRD), and the results are shown in Figure 6. Compared with the PXRD pattern of L-tryptophan

Figure 7. Particle size distributions of all obtained L-tryptophan products.

distributions of spherulitic particles (CV = 37.19 and 38.71 for products prepared at 293 and 274 K, respectively) are much narrower than the size distributions of flake-like crystals (CV = 81.20 and 115.41). It is worth noting here that the most striking difference between the two kinds of products is the complete absence of extremely small crystals in the size range of 0−30 μm for the spherulitic particles. Because the existence of fine crystals might result in the risk of dust explosion, elimination of small crystals will be helpful to ensure the process safety of the production. It is also worth noting that the crystallization temperature has considerable influence on the size of the spherulitic particles. From the size distribution of particles produced at 274 and 293 K in the presence of gelatine (Figure 7), the higher crystallization temperature resulted in larger spherulites. Hence, choosing the appropriate temperature would be a simple and convenient method for controlling particle size. On the basis of the previous studies,21,22 it is well-known that the physicochemical properties of powder products generally depend on the particle shape, particle size, and size distribution. From our work, it was found that the physicochemical properties of spherulitic particles are much better than the flake-like small crystals of L-tryptophan. The polymer-induced spherulitic growth strategy enables manufacturing of products with better physicochemical properties. Furthermore, the enantiopure amino acid microspheres that have an appropriate size and porosity are especially promising for chromatographic applications. Currently, the microspheres of L-glutamate, D-glutamate, L-histidine, and L-lysine·HCl have

Figure 6. XRD patterns of experimental products.

reported in previous studies,19,20 the PXRD results indicated that spherulites and flake-like crystals have the same crystal structure. When patterns of spherulites and flake-like crystals are compared with the calculated pattern from single crystal structure data reported by Görbitz et al.,19 an orientation effect can be observed. The intensities of the (002) peak in the microspheres and the (206) peak in the flake-like crystals are highly decreased. The physicochemical properties, such as particle size, size distribution, bulk density, tapped density, and flowability of spherulitic particles and flake-like crystals, were characterized, respectively. The results are listed in Table 2. The spherulitic particles prepared at 274 K in our experiments show a bulk density as high as 0.317 g/mL and even higher at 293 K (0.414 g/mL), whereas the flake-like crystals obtained from experiments without the additive and Aladdin show a significantly lower value of bulk density as 0.063 and 0.203g/mL, respectively. In addition, the Carr index compression ratio of spherulitic particles (0.083 for product prepared at 293 K, and 0.211 at 274 K) is much smaller than the corresponding values of the flake-like crystals obtained from Aladdin (0.477) and experiments in the absence of gelatine (0.406). A lower/smaller Carr index indicates that the spherulitic particles obtained in the presence of gelatine have much better flowability than the flake-like crystals.

Table 2. Characterization of Physicochemical Properties of All L-Tryptophan Products product

obtained from

morphology of products

mean particle size (μm)

CVa

bulk density (g/mL)

tapped density (g/mL)

Carr indexb

1 2 3 4

condition 1 (table1) condition 2 (table1) condition 3 (table1) Aladdin

spherulitic particles spherulitic particles flake-like crystals flake-like crystals

102.98 484.81 88.72 42.59

37.19 38.71 81.20 115.41

0.317 0.414 0.063 0.203

0.401 0.452 0.106 0.387

0.211 0.083 0.406 0.477

a

CV is calculated by the equation CV = 100(PD84 − PD16)/2PD50. bCarr index = (Tapped density − Bulk density)/Tapped density. D



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been synthesized by the so-called “polymer-induced liquidprecursor” (PILP) process.23,24 To the best of our knowledge, this is the first time that crystalline, porous L-tryptophan microspheres were prepared (Figure 4c). The crystallization strategy presented in this work could be used not only in the area of pharmaceutical industry but also in some other areas such as chromatographic applications. 3.2. Evolution of L-Tryptophan Spherulites. The formation of spherulitic particles in experiment condition 2 (Table 1) are monitored in situ by PVM, and the results are shown in Figure 8. To further illustrate and confirm the

representation of the possible formation mechanism of the Ltryptophan spherulites is proposed in Figure 9b. At the very early stage of growth, precursor crystals, which look like a sheaf of straw, are formed first. Then, a larger fantail grows at one side of the straw-sheaf and a “broccoli” is observed. This smallangle branching at the growth front of the “broccoli” will lead to the blooming of the crystal “flowers”, which finally result in spherulitic particles. 3.3. Effect of Temperature and Initial Concentration on Morphology of Spherulitic Particles. In order to better understand the formation and evolution of L-tryptophan spherulites, further investigations on the morphologies of crystals were conducted via droplet evaporation (isothermal) crystallization experiments. The crystallization conditions are shown in Table 3. Table 3. Experimental Conditions in Evaporating Droplet System condition

concentration of gelatin (g/mL)

Initial concentration of L-tryptophan (g/mL)

temperature (K)

1 2 3 4 5 6

0.0004 0.0004 0.0004 0.0004 0.0004 0.0004

0.020 0.020 0.020 0.020 0.015 0.025

293.15 313.15 323.15 333.15 293.15 293.15

Figure 10 shows optical microscopy images of L-tryptophan crystals obtained at T = 293, 313, 323, and 333 K in the

Figure 8. Process of spherulitic growth monitored by PVM.

morphology evolution process of L-tryptophan spherulites, the spherulitic growth inside an evaporating (isothermal) drop was also observed in situ by HS-POM. The images of spherulites at different formation stages in the presence of gelatine at 293 K and an initial concentration of c0 = 0.02 g/mL are shown in in Figure 9a. On the basis of the comparison of Figures 8 and 9a,

Figure 10. Polycrystalline particles of L-tryptophan obtained at c0 = 0.020 g/mL and (a) 293, (b) 313, (c) 323, and (d) 333.15 K.

Figure 9. (a) Sequence of optical microscopic images showing the morphology evolution process of L-tryptophan spherulites. (b) Schematic diagram for the formation process of L-tryptophan spherulites.

presence of the additive, respectively. It can be found that temperature difference could lead to different degrees of branching and significant change in the morphologies of the crystals. At relatively low temperatures, compact spherulitic particles with denser structures and smaller crystalline subindividuals were obtained, whereas coarse spherulites with rough interfaces and bigger subindividuals were obtained at higher temperature. Figure 11 shows the morphology of spherulitic particles obtained at initial concentrations of c0 = 0.015, 0.020, and 0.025 g/mL, respectively. It can be found that higher initial concentrations will result in more compact and fully developed spherulitic particles. The influence of initial concentration on

the process of spherulitic growth in lab-scale cooling crystallization was confirmed to be the same with that in an evaporating (isothermal) drop. From the literature, several mechanisms have been proposed to explain the development of spherulitic particles.25 For the first category, spherulites grow from the central precursor and branch multidirectionally to form a space-filling particle. For the second category, spherulites are formed by small-angle branching from both sides of the threadlike precursor fibers.16,25 It seems that the development of L-tryptophan spherulites is different from those two categories. A schematic E



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Figure 11. Polycrystalline particles of L-tryptophan obtained at 293 K and (a) c0 = 0.015 g/mL, (b) c0 = 0.020 g/mL, and (c) c0 = 0.025 g/ mL.

the growth and morphology of L-tryptophan spherulites in aqueous systems is pretty similar to L-glutamic and BaCO3, which were discussed by Beck et al.2 and Yu et al.26 This result can be explained by a higher rate of growth front nucleation (GFN)25 at higher initial concentration. 3.4. Crystal Growth Kinetics of Spherulitic Particles. The growth kinetics and mechanism for the formation of spherulites have been a standing issue over many decades. In our experiments, the growth mechanism of L-tryptophan spherulites was investigated by collecting and analyzing the kinetics data in an evaporating drop. As shown in Figure 12, optical microscopy was used to obtain the spherulitic growth rate. The growth curves for L-tryptophan crystals at different temperatures in the presence of a small amount of gelatine (e.g., 0.0004 g/mL) are presented in Figure 13. It was found that the change of position of the growth front with time is linear. Apparently, the spherulitic growth rate decreases dramatically with the decreasing of temperature. The growth rate decreased by about 27 times as the temperature was changed from 333 to 293 K. As shown in Figure 13, the growth rate seems to be independent of time for all temperatures (except the initial stage of the growth curves at 293 K, which will be discussed later). As is known to all, the concentration of solute and the additive could influence the crystal growth rate. The constant growth rate of L-tryptophan indicates the constant composition at the growth front throughout the growth process. Normally, the additive molecules gradually accumulate at the crystal surface with the growth of the crystals. However, in this work, this assumption is not consistent with the constant growth rate of L-tryptophan. It has been surmised that the adsorption of the additive within corresponding growth sectors would produce strain,27 and the relaxation of stress via formation and motion of dislocations can drive macroscopic noncrystallographic misorientations or branching.15 In the literature,28 macroscopic misorientation of apatite crystals nucleated in gelatine has been observed, and well-shaped apatite gelatine nanocomposite crystals (several μm in size) which contain ∼2 wt % gelatine were formed. It has also been reported that spherulites can be formed via noncrystallographic branching.15 It is reasonable to

Figure 13. Growth curves for L-tryptophan crystals at various temperatures.

believe that the molecules of the additive should exist in the crystalline domain instead of in the solution near the front of growth crystals. Considering that the crystal structure of Ltryptophan did not change in the presence of the additive, the molecules of gelatine should be adsorbed on the boundary of separate domains within the crystalline phase. This adsorption gives rise to dislocation of the L-tryptophan crystal lattice, which finally results in macroscopic branching. According to the existing literature, the constant growth rate could also be an argument for the assumption that spherulitic growth is controlled by the interface kinetics.29,30 It is worth noting that there is a nonlinear regime at the initial stage of the growth curves at 293 K (Figure 13). To determine whether the growth of L-tryptophan spherulites is interface kinetics controlled or diffusion controlled, more solid evidence is needed. By capturing optical microscopy images and measuring the radius of each spherulite as a function of time, the growth curves for six separate L-tryptophan spherulites (Figure 14) in the field of view at an initial concentration c0 = 0.025 g/mL and T = 288 K in the presence of 0.0004 g/mL gelatine are presented in Figure 15. The spherulite growth patterns of the six particles are similar to each other, and they are similar to the initial stage of the growth curves at 293 K (Figure 13). Apparently, they all share the same characteristics: an initial rapid growth, followed by a gradual decrease in growth rate. On the basis of previous research in the modeling of crystal growth,31,32 a simple empirical power-law relationship can be used to express the relationship between L-tryptophan spherulite growth rate and local supersaturation ratio for a population of spherulites in an evaporating drop:

Figure 12. Optical microscopy images of growing spherulitic crystals at 303 K and c0 = 0.010 g/mL. The red line is the edge of the evaporating droplet, and the white dotted line is perpendicular to the edge. The growth rate is obtained from the distance between the growth front and the edge as a function of time. F



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dR i = k[Si(t ) − 1]g dt

(2)

In this model, the growth of each spherulite, i, is modeled at an overall rate which is proportional to a temperaturedependent growth rate coefficient k. g is the growth rate order, and the value of g depends on the controlling mechanism of crystal growth. If the growth is diffusion controlled, then g is 1. If the incorporation of solute molecules into the growing crystal lattice is the slowest step, then g should be larger than 1.31 Ri is the diameter of the spherulite; Si(t) is the local supersaturation ratio of the supersaturated solution, which can be expressed as follows Si(t ) =

ci(t ) ceq

(3)

where ci(t) is the local concentration of the supersaturated solution and ceq is the equilibrium solubility of L-tryptophan in water at 293 K. It can be assumed that the underlying mechanism of different spherulites in the field of view is the same and the temperature throughout the field is relatively uniform. In order to compute the spherulite growth rate within a population, an exponential equation was used to fit the raw data that are shown in Figure 15.

Figure 14. Six spherulites in the field of view and the parameters for fitting the growth of spherulites.

R i = A + B exp(Ct )

(4)

where A, B, and C are the parameters of this equation. The coefficient of correlation, R2, is used to evaluate the applicability of this fitting model. According to the value of R2 listed in Table 4, the calculated data by eq 4 show good agreement with experimental values. For all the raw data of six separate L-tryptophan spherulites, the analysis on model residuals can provide confidence in the model’s ability of describing the spherulite growth rate accurately. To evaluate Si(t) of each spherulite, the following model was used to calculate the local concentration of Ltryptophan as a function of time ⎛ πR 3ερ ⎞ ⎛ t⎞ ci(t ) = ⎜⎜c0− i ⎟⎟ /⎜1 − ⎟ 12V0, i ⎠ ⎝ t0 ⎠ ⎝

(5)

In this model, the spherulites located on the glass slide are regarded as hemispheres and c0 is the initial concentration of Ltryptophan in the droplet. ε is the porosity of the spherulites. ρ is the solid density of L-tryptophan crystals. t0 is set to be equal to the time when the droplet stops shrinking, which is equal to the time when the spherulites stop developing; the shrinkage

Figure 15. Growth curves for six L-tryptophan spherulites in the field of view, and the data were fitted by eq 4.

Table 4. Summary of the Parameters for the Population-Based Empirical Power-Law Relationship eq 4

eq 8

spherulite

A

B

C

R2a

R0,i (μm)b

ln(k)c

gd

1 2 3 4 5 6 average value

180.67 154.85 167.81 153.53 183.3 170.15

−994.93 1044.02 −969.47 1072.04 1085.7 1283.78

0.006 0.0075 0.0078 0.0077 0.0071 0.0082

0.9922 0.9954 0.9853 0.9963 0.9948 0.9972

221.11 195.28 216.08 197.42 229.81 215.38

−1.247 −1.119 −1.141 −1.254 −1.058 −1.001

2.572 2.423 2.614 2.704 2.355 2.463 2.522

a 2 R is the coefficient of correlation. bR0,i is the diameter of fully developed spherulite, i. ck is the temperature-dependent growth rate coefficient. dg is the growth rate order of the overall crystal growth process for L-tryptophan spherulites.

G



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time of the droplet in this experiment is about 60 min. V0,i represents the volume of the initial solution, which is consumed by a fully developed spherulite, and it can be calculated by V0, i =

As shown in Table 4, the average value of the order of the overall crystal growth for L-tryptophan spherulites is 2.522. These results evidently indicate that the growth of Ltryptophan spherulites is interface kinetics controlled. Investigations on several types of spherulites by other researchers have also suggested that the growth of spherulites is normally limited by kinetics rather than by mass transportation.15,33,34 Putting all the evidence together, we could hypothesize that subindividuals probably accommodate the additive in interstices. The adsorption of gelatine on the growth sectors not only produces strains that result in macroscopic branching but also reduces the kinetic coefficient of the interface reaction that result in stronger interface control. The verification of this hypothesis is a subject of our future research.

πR 0,3 iερ 12c0

(6)

where R0,i is the diameter of fully developed spherulite, i. The values of R0,i for each spherulite are listed in Table 4. Assuming that the concentration of L-tryptophan around each spherulite is uniform in a relatively small space (less than V0,i), the local diffusion rate of the solute through this small space can be thought to be relatively faster. By inserting eq 6 into eq 5, the local concentration of Ltryptophan could be expressed as follows ⎛ R3 ⎞ ⎛ t⎞ ci(t ) = c0⎜⎜1 − 3i ⎟⎟ /⎜1 − ⎟ t0 ⎠ R 0, i ⎠ ⎝ ⎝

4. CONCLUSIONS In this work, spherulitic particles of L-tryptophan were successfully prepared via a polymer-induced spherulitic growth strategy. The obtained L-tryptophan spherulites have much better physicochemical properties than the flake-like crystals. By this method, the particle size distribution, the bulk density, and flow property of L-tryptophan could be manipulated to meet different kinds of application requirements. The application field of L-tryptophan might be extended because of this polymer-induced spherulitic growth strategy. It was found that spherulites of L-tryptophan are formed by nucleation of strawlike precursor crystals, which is followed by a radial small-angle branching at only one side of the precursor. This morphology evolution theory has never been reported before. Investigations on the crystallization conditions indicated that addition of gelatine, higher initial concentration, and lower temperature favor the formation of compact spherulites. A new population-based model was proposed to model the spherulitic growth of L-tryptophan. It was revealed that the spherulitic growth of L-tryptophan is interface kinetics controlled.

(7)

Since the initial concentration of L-tryptophan in the droplet c0, diameter of fully developed spherulite R0,i, and the experimental relationship between spherulite diameter and time are known, we can obtain ci(t) and hence Si(t). Moreover, by taking the derivative versus time of eq 4, the spherulite growth rate at a given time can be expressed as ⎛ dR ⎞ ln⎜ i ⎟ = g ln[Si(t ) − 1] + ln(k) ⎝ dt ⎠

(8)

The growth rate coefficient k and the growth rate order g could be obtained by eq 8. The results are presented in Figure 16. The values of ln(k) and g for each spherulite are listed in Table 4.

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AUTHOR INFORMATION

Corresponding Authors

*Tel: +86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected] (H.H.). *Tel: +86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected] (Y.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is financially supported by the National Natural Science Foundation of China (No. 21376165 and No. 21376164) and the Key Project of Tianjin Science and Technology Supporting Programme (No. 13ZCZDNC02000). The authors would also like to thank Mettler Toledo for providing the PAT tools and thank NERCICT for providing all necessary equipment.

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Figure 16. Relationship between ln(dRi/dt) and ln(Si(t) − 1) and the corresponding linear regression lines for six L-tryptophan spherulites in the field of view. H



Article

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Spherulitic Crystallization of L-Tryptophan: Characterization, Growth

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