(LATF) Crystals from Induction Period and Atomic Force Micr

Jun 22, 2010 - †School of Science, University of Jinan, Jinan 250022, China, and ‡State ... Materials, Institute of Crystal Materials, Shandong Un...
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DOI: 10.1021/cg100147c

An Examination of the Growth Kinetics of L-Arginine Trifluoroacetate (LATF) Crystals from Induction Period and Atomic Force Microscopy Investigations

2010, Vol. 10 3442–3447

X. J. Liu,*,† D. Xu,‡ M. J. Ren,† G. H. Zhang,‡ X. Q. Wei,† and J. Wang† †

School of Science, University of Jinan, Jinan 250022, China, and ‡State Key Laboratory of Crystal Materials, Institute of Crystal Materials, Shandong University, Jinan 250100, China Received January 30, 2010; Revised Manuscript Received May 25, 2010

ABSTRACT: In this study, the induction period (tind) of L-arginine trifluoroacetate (LATF) at different levels of supersaturation have been examined at 298.15 K for both spontaneous and seeded growth systems. From the dependence of tind on supersaturation, it was possible to distinguish between the mechanisms of homogeneous and heterogeneous nucleation. On the basis of the experimental data pertaining to the homogeneous nucleation, the solid-liquid interfacial energy can be evaluated. Additionally, in the process of ascertaining the growth mechanism of LATF as two-dimensional (2D) nucleation-mediated growth using by theoretical expressions, a combined analysis of results in both experiments provides information about the growth and nucleation rate constants. Eventually, analysis of atomic force microscopy investigations on the facets of LATF crystals corroborates the 2D nucleation-mediated growth mechanism.

1. Introduction -

Since they have proton donor carboxyl acid groups (COO ) and proton acceptor amino groups (NH2-), amino acids with organic and inorganic complexes have been widely described by many research papers as one of the best potential candidates for nonlinear optical (NLO) applications.1 Salts of L-arginine have attracted much attention after L-arginine phosphate (LAP) was discovered as an alternate to potassium dihydrogen phosphate (KDP).2 Besides properties comprising having high NLO coefficients and short-wavelength cut-off of ultraviolet light and being less hygroscopic, the most outstanding feature of LAP crystal is its high damage threshold. A series of studies relating to L-arginine in reactions with various acids discovered as interesting NLO crystals have been reported.3-6 L-Arginine trifluoroacetate (LATF) is such a promising semiorganic NLO material, which possesses excellent optical, thermal, mechanical properties; in particular, it has high optical nonlinearity and large optical damage threshold.7 Crystal structure of LATF and growth of bulk single crystals have been investigated for the first time by us.7,8 Later, nucleation kinetics, surface morphologies, and detailed characterization of its properties were described in our research works.9-13 Nevertheless, little attention has been paid to the crystallization processes which are regulated by both thermodynamic properties and crystallization kinetics. In general, the dynamic event of crystallization is composed of three evolving stages of supersaturation, nucleation, and crystal growth. The induction period (tind) is frequently used as a measure of nucleation and growth kinetics. Experimental observation of tind contains valuable information about the kinetics and mechanism of the formation of crystalline phase and growth process, from critical nuclei to detectable crystals. The value of tind is also a measure of the ability of a supersaturated system to remain in the state of metastable equilibrium *Corresponding author. Tel.: þ86-531-8836-4233. E-mail: [email protected]. edu.cn. pubs.acs.org/crystal

Published on Web 06/22/2010

and has the physical significance of the system’s lifetime in this state. Therefore, analysis of the values of tind can help comprehension of the mechanisms of new phase formation and growth from critical nuclei into crystals. Until now, many researchers have tried to seek a general theoretical expression which can be used for finding the dependence of tind on the supersaturation for different nucleation and crystal growth mechanisms, and thus unravel the experimental results obtained from the process of nucleation.14-16 In addition, as is well-known, atomic force microscopy (AFM) allows not only visualization of growth mechanisms at the molecular level but also affords fundamental physics and chemistry information underlying the crystallization process. The aim of the present paper is to show that by combining the method presented by van der Leeden et al.15,16 and AFM investigations, detailed knowledge of the crystallization process, proper insight, and a quantitative description in LATF crystal can be obtained. 2. Experimental Section 2.1. Induction Period (tind) Measurements. The values of tind in both spontaneous (unseeded) and seeded crystallization experiments were examined by visual observation. Supersaturated solutions were prepared by mixing dissolving equimolar aqueous solutions of L-arginine and trifluoroacetic acid up to a total volume V = 50 mL. Prior to use, all solutions were filtered through a series of 0.45 μm membrane filters. The investigations were performed in a constant temperature bath controlled with a programmable controller, and a thermocouple placed into the bath was used to read the temperature of the solution. Initially, the crystallizer was filled with a saturated solution of LATF and heated 5 K above the saturation temperature for 8 h. The supersaturation level, explored in this study and defined as the ratio between the initial concentration and the concentration at the thermodynamic equilibrium at 25 °C, ranges between 2.00 and 1.35. Measurement of tind requires noting the time at which the initial supersaturation is established homogeneously throughout the solution and the time at which the cooled solution exhibits the first crystal. In the case of seeded crystallization experiments, the seed mass M and radius rs (estimated by SEM) was 3 mg and 0.5 μm, respectively, which corresponds to the seed number density N = 1.25  1015 m-3, calculated from N = 3M/4πrs3FV r 2010 American Chemical Society

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Table 1. Expression f(S ) for Different Growth Mechanisms growth mechanisms

f(S)16

rearrangement expression for eq 5

normal growth and diffusion-controlled growth spiral growth 2D nucleation-mediated growth

S-1 (S - 1)2 (S - 1)2/3S1/3 exp(-B2D/3 ln S)a

Fu(S) = ln[tu(S - 1)n-1/nS1/n] = ln Au þ B/n ln2 S Fu(S) = ln[tu(S - 1)2(n-1)/nS1/n] = ln Au þ B/n ln2 S Fu(S) = ln[tu(S - 1)2(n-1)/3nSnþ2/3n] = ln Au þ (n - 1)B2D/3n ln S þ B/n ln2 S

a The constant B2D = β2Dκ2a/(kBT )2, where β2D is a numerical 2D shape factor (π for circles), κ is the effective edge free energy of the nucleus, a is the molecular area, kB is Boltzmann constant.

(F = 1.524 g/cm3 is the LATF density). Every experiment was repeated at least three times to ensure reproducibility, and the average value for the tind was used in the analysis of the final results. 2.2. Atomic Force Microscopy (AFM) Investigations. To preserve the nascent surface structure, the samples which were grown into acceptable sizes were drawn from solution by passage slowly through a layer of an immiscible nonsolvent (n-hexane) and then dried with paper tissue immediately. Then transparent, smooth, and well-developed as-grown crystals were selected and fixed on the AFM sample holder using double-sided tape. The morphology of LATF crystals only shows {101} facets, thus keeping these facets parallel to the holder. AFM images were all collected under ambient atmosphere at room temperature employing a Nanoscope, IIIa MultiMode AFM instrument of Digital Instruments Incorporation, with a DI square pyramidal Si3N4 tips on V-shaped cantilevers 100 μm in length with 0.06 or 0.12 N/m spring constants. In order to minimize surface damage due to the AFM scanning, when a crystal face was chosen, the area was zoomed in on immediately to obtain images before the area had been scanned over too many times. Here, surface morphologies of LATF crystals were studied by ex situ AFM. According to our previous observations,10,11 as-grown surface morphologies after the cessation of growth and after removal of the crystals from the solutions can represent the final stage of crystal growth. No significant differences exist between in solution and in air. Thus, the disadvantages including image of the crystals in the absence of the mother liquor and after growth of crystals can be overcome and excluded.

3. Theoretical Basis According to the classical nucleation theory,17-20 the primary nucleation rate, J, can be expressed as !   3 2 ΔG βγ Ω crit ¼ A exp - f 3 J ¼ A exp - f kT kB T 3 ln2 S   B ð1Þ ¼ A exp - f 2 ln S where A* is pre-exponential factor; ΔGcrit, an activation free energy for nucleation; f, a factor for the energy barrier ( f = 1 for homogeneous and f < 1 heterogeneous nucleation); β, a geometric factor (e.g., 16π/3 for sphere and 32 for a cube); γ, interfacial energy between crystal and aqueous solution; Ω, molecular volume of the crystal; kB, Boltzmann constant (1.38  10-23 J/K); T, absolute temperature; S, supersaturation ratio; B, a constant = βγ3Ω2/kB3T3. For three-dimensional (3D) nucleation, the above formula for the steady-state nucleation rate is rearranged into   B ð2Þ J ¼ KJ S exp - 2 ln S where KJ is the S-independent nucleation rate factor. The value of tind, defined as the time elapsing between the attainment of supersaturation and the first detectable changes in some related properties of system (owing to the formation of solid phases) and is the experimentally accessible quantity. Several theoretical correlations between tind and supersaturation in which nucleation and growth mechanisms are taken

Figure 1. The homogeneous-heterogeneous nucleation transition by plotting ln tind vs ln-2 S for LATF crystallization in unseeded experiments.

into account have been brought forward. These theories relate this tind with both the time to form stable critical nuclei or embryos, tn, and the time for their subsequent growth to observable size, tg. It is worth pointing out that tn refers to the real induction period which includes the time needed to achieve a quasi-steady-state distribution of the molecular clusters (already present in solution) and the time for newly formed stable nuclei. Since tg can be derived theoretically from kinetics expression based on a particular growth mechanism and tn can be calculated experimentally, the tind thus investigated allows for an association of both nucleation models and experimental results for LATF crystals. In terms of the general expression reported by Kashchiev et al.,21 the induction period in unseeded crystallization experiments (tu) that accounts for mononuclear (MN) and polynuclear (PN) mechanisms is tu ¼ tMN þ tPN ¼ 1=JV þ ðR=an JGn - 1 Þ1=n

ð3Þ

where J is the nucleation rate; V, the volume of the solution; R = Vm/V, the smallest experimentally detectable volume fraction of the newly formed phase; an = cm/n, a shape factor (e.g., a4 = π/3 for sphere and 2 for a cube); G, the crystal growth rate and n = mv þ 1 [m is the dimensionality of growth and n denotes the power for parabolic (v = 1/2) and linear growth (v = 1)]. Generally, the relationship between G and S is of the form15 GðSÞ ¼ KG f ðSÞ ð4Þ where KG is an S-independent growth rate factor and f(S) is a given function of S relating to the growth mechanism of crystallites (see Table 1).22-25 The first term in eq 3 is often negligible in comparison to the second term. After substitution

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Figure 2. Different plots of Fu(S) vs ln-2 S or ln-1 S for unseeded LATF crystallization experiment. Data fit to (a) normal growth and diffusion-controlled growth; (b) spiral growth; (c) 2D nucleation-mediated growth, respectively.

of eqs 2 and 4 into eq 3, the following general expression is found: tu ½Sf ðSÞn - 1 1=n ¼ Au expðB=n ln2 SÞ

ð5Þ

n-1 1/n where Au = (R/anKJK G ) . For different expressions of f(S),

various expressions for eq 5 can be rearranged as tabulated in Table 1. The best fit of Fu(S) vs ln-2 S (for normal, diffusioncontrolled, and spiral growth) or Fu(S) vs ln-1 S [for twodimensional (2D) nucleation-mediated growth], characterized by the square coefficient, can extrude information about the different possible growth mechanisms. Then, some important parameters such as the crystal-solution interfacial energy, the number of molecules in the 2D nucleus, and the nucleation rate can be calculated. Similarly, in the case of seeded crystallization experiments, the induction period ts corresponding to different growth

mechanisms are given by16 ts ¼ As =f ðSÞ

ð6Þ

where As = (R/mcmrsm-1NKG) (cmrsmN g R). By plotting ln ts vs ln(S - 1), the information about the operative growth mechanism can be identified. For normal (diffusion-controlled) growth and spiral growth, the slope of a straight line obtained from ln ts vs ln(S - 1) is -1 and -2, respectively. For 2D nucleation-mediated growth, from eq 6 and f(S) in Table 1 we get Fs ðSÞ ¼ ln½ts ðS - 1Þ2=3 S 1=3  ¼ ln As þ ðB2D =3Þ=ln S ð7Þ Thus, calculation of effective edge free energy of the nucleus and growth rate can be afforded from the slope (B2D/3) and intercept (ln As), respectively.

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Figure 3. Dependence of ln ts (a) and Fs(S) (b) as a function of the supersaturation degree.

4. Results and Discussion 4.1. Nucleation and Induction Period Measurements. From eq 1, we see that the value of tind is diminished and nucleation is promoted by reducing the interfacial energy or increasing the supersaturation. If it is assumed that the nucleation time (tn) is much greater than the time required for growth of crystal nuclei to a detectable size (tg),26 then the statistical concept of nucleation is denoted as 1 ð8Þ tind ¼ J A correlation relating the induction period with the saturation level S is obtained by combining eqs 1 and 8: K 1 ln tind ¼ þ ln  ð9Þ A ðln SÞ2 where K= fβγ3Ω2/(kBT )3. The effect of increasing the supersaturation on reducing the induction period was recorded experimentally in Figure 1. The straight lines with different slopes (K ) suggest that two nucleation mechanisms may exist. The behavior of low supersaturation crystallization is more consistent with a heterogeneous nucleation mechanism (line B) in contrast to higher supersaturation where homogeneous nucleation (line A) is more likely. In the literature, a similar characteristic change in the slope of the induction period plot has been used to distinguish between nucleation mechanisms as well as for other compounds, both organic (e.g., abecarnil) and inorganic (e.g., calcium carbonate).27,28 As far as we know, the crystal-solution interfacial energy is a crucial parameter involved in the theories of crystal nucleation and growth. Generally, inorganic salts of low solubility generally give quite high interfacial energy values (30150 mJ/m2),29,30 soluble inorganics give lower values (48 mJ/m2),14 whereas organic materials show even lower values of interfacial energy (1.4-3.5 mJ/m2).31,32 In our case, from the slope of the plot in the homogeneous region, assuming spherical nucleus ( β = 16π/3) and Ω = 3.14  10-28 m3 for LATF, the interfacial energy can be estimated to be 3.32 mJ/m2, which is similar both to our previous results (1.252.73 mJ/m2)9 and to those values reported for other amino acids crystal system (e.g., 1.32-2.93 mJ/m2 for LAA; 2.5-5.0 mJ/m2 for LAP; 2.98-4.75 mJ/m2 for LLTF).33-35

4.2. Growth Mechanism and Nucleation Rate. As exhibited in section 3, the growth mechanism of LATF crystal can be specified by adopting these theoretical expressions for S dependence of tind in both unseeded and seeded experiments. Regarding the growth model in the unseeded crystallization experiments, different relationships between Fu(S) and ln-2 S or ln-1 S (as proposed in Table 1) were tested. In the case considered of linear three-dimensional (3D) spherical growth for LATF crystal, using m = 3, v = 1, n = 4, a4 = π/3, the final plots for the data fit to different growth models can be obtained. As exemplified in Figure 2, the best correlation coefficient for 2D nucleation-mediated growth with a parabolic equation is acquired. Data results failed to obtain excellent straight lines for Fu(S) vs ln-2 S, thus eliminating normal, diffusion-controlled, and spiral growth. From the intercept (ln Au) of Figure 2c and in view of the expression Au = 3 1/4 (R/a4KJK G ) , we can only calculate the nucleation and growth rate factors KJ and KG coupled. Therefore, complete determination of KJ for LATF requires the knowledge of KG which can be obtained from the seeded crystallization experiments. The induction period in the seeded crystallization experiments (ts) were shorter than those in the unseeded crystallization experiments (tu). A reasonable explanation for this is that ts only controlled by growth of the added seeds, implying that the effect of extra primary nucleation on ts is negligible.16 According to the eq 7, the corresponding ln ts data along with the best-fit straight lines are plotted in ln ts vs ln(S - 1) as illustrated in Figure 3a. The slope value of the best-fit line indicates the operative growth mechanism for LATF does not belong to normal, diffusion-controlled, or spiral growth. In order to validate that the slope value is an indication for 2D nucleation-mediated growth, a systematic regression analysis about Fs(S) vs ln-1 S plot (Figure 3b) is necessary as exhibited in Table 2. From the straight line with a good correlation coefficient, it can be deduced that 2D nucleation-mediated growth describes very well our results obtained in seeded LATF crystallization experiments. Furthermore, the value of B2D/3 and of the constant ln As can be estimated from the slope and intercept of the straight line, respectively. Then, the value of κ and KG can be summarized by taking β2D = π, a = Ω2/3= 4.62  10-19 m2,

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R = 1.5  10-6, and N = 1.25  1015 m-3 into the classical equation. Consequently, the value of KJ can be calculated to be 1.61  1024 m-3/s since the value of Au was already determined from the unseeded experiments. 4.3. AFM Images of Surface Morphologies. In order to corroborate the growth mechanism identified by the above kinetic analyses from induction period, it is essential to study the surface morphologies of the grown crystals using AFM. To our knowledge, AFM can yield images of uncommon clarity of intricate surfaces and specimens, providing valuable information in the delineation of growth mechanisms and kinetics of growth process. As seen in Figure 4, advancement of growth steps proceeding exclusively by 2D nucleation are observed under the supersaturation conditions here (∼2.00-1.35). No screw dislocation was observed. For the perfectly smooth surface of LATF crystals, the birth and spread model is used to depict the formation and distribution of 2D nuclei which are supposed to progress in an isotropic manner. In Figure 4a, some 2D nuclei kept forming on top of the other nuclei and ultimately led to the formation of the steep hills. In contrast, some districts fall behind and seemed to like valleys. The appearance of 2D nuclei provides step sources for further growth, and the step terraces can also become the nucleation sites. During the growth process, the Table 2. Results of Regression Analysis of Fs(S ) vs ln-1 S for the Seeded Experiments slope

B2D

intercept

As (min)

κ (J/m)

KG (m/s)

1.31

3.93

-0.67

0.51

6.77  10-12

1.25  10-11

frontal edges of the steps often advance with various velocities, and thus bring on the terraces with different widths. As seen in Figure 4b,c, numerous regular and irregular 2D nuclei settled at the slope or on the top of the terraces. As a conclusion from these images, it can be said that in the tested supersaturation range, the crystallization of LATF occurs exclusively through a 2D nucleation mechanism, which is coincident with the foregoing growth mechanism derived from the induction period data. 5. Conclusions In summary, the combined analyses of induction period data in both spontaneous and seeded LATF crystallization experiments have been presented. The abrupt slope change in the plot of ln tind versus ln-2 S indicates a change in nucleation mechanism from heterogeneous to homogeneous. By fitting the homogeneous nucleation rate measurements according to classical nucleation equation, the interfacial energy between crystal and aqueous solution was calculated. The induction periods are sufficiently shorter in the seeded crystallization experiments compared with those in the spontaneous crystallization experiments and reveal a remarkable inverse dependence on the solution supersaturation values. In addition, for both experimental cases, the relationship corresponding to 2D nucleation-mediated growth mechanism described our results best. Separate determination of the rate constants for growth and nucleation was drawn from these results. AFM images validate that in the investigated systems the 2D nucleation

Figure 4. AFM images acquired from the {101} facets of LATF crystals using contact mode, revealing the birth and subsequent spread of 2D nucleation. Scanning areas are 6  6, 5  5, and 3  3 μm2 for images (a-c), respectively.

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growth mechanism dominates on the crystal facets of LATF crystals. Acknowledgment. This work was supported by the Doctoral Foundation of University of Jinan (XBS0920) and the National Natural Science Foundation of China (60608010).

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