Characterization of the Dense Liquid Precursor in Homogeneous

Characterization of the Dense Liquid Precursor in Homogeneous Crystal Nucleation Using Solution State Nuclear Magnetic Resonance Spectroscopy Masaharu Kimura*

CRYSTAL GROWTH & DESIGN 2006 VOL. 6, NO. 4 854-860

Organic Synthesis Research Laboratory, Sumitomo Chemical Co., Ltd., 1-98, Kasugade-naka 3-chome, Konohana-Ku, Osaka, 554-8558, Japan ReceiVed March 13, 2005; ReVised Manuscript ReceiVed January 18, 2006

ABSTRACT: Crystallization is very complicated, and therefore the control of crystal nucleation has been basically performed by trial and error, so far. This paper provides a novel, basic idea to cope with this problem theoretically on the basis of the experimental data on crystal nucleation. Here, detailed analysis of the homogeneous crystal nucleation of a novel acaricide, amidoflumet, using solution state nuclear magnetic resonance spectroscopy is reported. The dominant interaction between solute molecules was identified by the complexation-induced changes in chemical shift, corrected by the external double reference method. Also, the concentration dependence of the structure of the dense liquid precursor was well characterized by the apparent averaged structure of the solute cluster. Besides the importance of the supersaturation ratio as a relevant parameter to both the energy difference and the transition probability between the solution state and the solid state, the significance of the absolute solution concentration, which is revealed to be highly relevant to the formation of clusters as a preparatory step in the crystal nucleation, is also pointed out. Introduction The brilliant sparkle of crystals is fascinating from many perspectives, and elucidation of crystal structures and the crystallization process has been one of the most challenging endeavors for many years. Crystallization is attractive scientifically and technologically because, for example, crystal formation is a kind of self-organization process that has recently been recognized as one of the key technologies in the mass production of nanostructures.1 From the industrial point of view, most organic and inorganic materials are produced in the crystalline phase, and controlling the crystalline morphology or polymorphism is very important because these relate so closely to their physical and chemical properties. The importance of the crystallographic characteristics of pharmaceuticals and agricultural chemicals is also emphasized, as they affect many properties of the technical product: ease of handling in industrial manufacturing processes, stability and shelf life, solubility, bioavailability, efficacy, and so on.2 In this context, much effort has been expended in recent decades on the study of crystals and crystallization processes. For the characterization and structural determination of solid crystals, various methodologies such as X-ray crystallography, X-ray diffraction (XRD), microscopy, thermal analysis, solubility testing, particle size analysis, infrared spectrophotometry, and solid-state nuclear magnetic resonance spectroscopy (solidstate NMR) are applied,3 and these methods have revealed many phenomena and principles successfully. Many studies have also been conducted to reveal what is happening in the course of crystallization processes, from thermal fluctuations in supersaturated solutions to crystal nucleation and growth.4-7 Here, a detailed investigation of the very early stage of crystal nucleation is focused on. Whereas it is recognized that the early stage of nucleation as a general step for the nucleation from the solution is important for understanding the total crystallization process, what happens prior to the formation of a critical nucleus has been popularly considered to be chaotic. Although * To whom correspondence should be addressed. E-mail: kimuram5@ sc.sumitomo-chem.co.jp.

crystallization is very complicated, it proceeds, of course, in accordance with causal processes. Therefore, it should be useful to study the solution state in detail as an earlier stage of crystallization to investigate and eventually to control the properties of solid crystals. The rearrangement of the structure of the dense liquid precursor is considered to occur depending on parameters such as temperature, pressure, and concentration of the solution, and the rearrangement process should be continuous as long as the system is in a solution phase even if it passes through the saturation point because the energy change of the solution phase is continuous as long as equilibrium is maintained. Moreover, because the chemical potential of the solid state is equal to that of the solution state at the saturation point, it is reasonable to consider that there should be some relationship between the solution structure and the crystal structure, even if the structures might not be exactly the same. Therefore, discrimination of the major molecular interaction in solution, which can be considered relevant to what is called “supramolecular synthons” in the crystal engineering field,8 is worthy of remark. This concept leads us to novel technological development. Hopefully, detection of the dominant interaction between solute molecules that aggregate in the dense liquid precursor and gaining an understanding of the events that take place at the initiation of the crystallization will enable us to find means to control the crystal nucleation. Some recent studies reported relationships between the existing condition of the solute molecules in solution and the crystal structure.9-11 From the structural determination of small molecules and biopolymers to the detailed analysis of molecular interactions between solute-solute and solute-solvent molecules, solution state NMR is a very powerful tool to study various properties of a solution phase. As for the analysis of molecular interactions, solution state NMR is successfully used to study the aggregation of dye molecules in aqueous solutions,12,13 the self-association of pharmaceuticals,14 and the clustering of steroid compounds,15 for example. In particular, Spitaleri et al. reported the possibility of the study of crystal nucleation process using 1H NMR spectroscopy in solution.11 Here, an accurate chemical shift measurement technique was introduced, which is applicable even

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Dense Liquid Precursor in Homogeneous Crystal Nucleation

Crystal Growth & Design, Vol. 6, No. 4, 2006 855

if the concentration range is so large as to pass the saturation point, and detailed analysis of the homogeneous crystal nucleation for the determination of the dominant interaction between solute molecules in solution and the method for characterizing and monitoring the structural change of the dense liquid precursor with solution state NMR are reported. Experimental Section The analytical standard of amidoflumet used for this study was manufactured and purified by Sumitomo Chemical Co., Ltd. The purity was determined by high performance liquid chromatography and differential thermal analysis to be 100%. Acetonitrile-d3 (CD3CN, 99.96 at. % D) and chloroform-d (CDCl3, 99.96 at. % D) used for the preparation of NMR sample solutions were purchased from Merck. Crystallization was performed by gradual cooling of the supersaturated solutions at room temperature after mild heating to dissolve the solute completely. Crystallization under a strong magnetic field was performed using the supersaturated solutions in 5 mm NMR sample tubes inserted into the superconducting magnet of the NMR spectrometer by the same procedure as described above, for the case without a magnetic field. The most stable conformation of amidoflumet in the gas phase was obtained by implementing the B3LYP hybrid density functional method16,17 with the 6-31G(d) basis set (B3LYP/6-31G(d)) in the Gaussian98 program.18 All NMR data were collected with a Varian UNITY 400 plus NMR spectrometer, using the standard pulse sequence and parameters. The temperature control was precalibrated with reference to the sample temperature dependence of methanol signals. When the temperature dependence experiments were performed, the sample temperature was varied from the high temperature, at which the solubility of solute molecules in the solvent was high, to the low. For the external double reference method (EDRM),19 the shape factor of a capillary tube with bulb, which was used for the external reference, was determined to be 4.7464 using hexamethyldisiloxane (HMDSO) as the reference substance, and chloroform-d, cyclohexane-d12, deuterated water, and dimethyl sulfoxide-d6 as solvents with known volume magnetic susceptibility. NMR spectra were obtained at the observation temperature after keeping the sample condition constant for at least 1 h to achieve equilibrium. All chemical shift data were corrected using EDRM. The effect of the temperature dependence of the HMDSO signal was neglected because it was not significant compared with the chemical shift change coming from the solute concentration. The apparent averaged structure of the cluster was determined as described in Results and Discussion using a custom-made software program coded in Microsoft Visual Basic. The radius of a loop where electrons are circulating was assumed to be 1.39 Å, based on the original paper of Johnson and Bovey model.20 Less than 0.01 Å difference between the calculated and the geometrically determined distances between two protons was allowed, and less than 0.001 ppm difference between the observed and the calculated complexation-induced changes in chemical shift (CIS) values were allowed. Determination of the crystal structure was performed by X-ray crystallography with a Rigaku R-AXIS RAPID controlled with RAPID AUTO software version 1.06. The diffraction data were collected with an imaging plate and processed with Crystal Structure, version 3.5.1/ Rigaku. The crystallinity of amidoflumet crystal was not so good, perhaps because the interaction between unit cell planes was not strong. Representative crystal data and detailed experimental conditions are reported elsewhere.21

Results and Discussion Characterization of the Dense Liquid Precursor. The crystal nucleation process is considered to start from the thermal fluctuation of solute molecular aggregation in solution. Therefore, solution state NMR was employed as a main tool to characterize the dense liquid precursor; however, the ultimate goal of this study was to understand the properties of solid crystals and the crystallization process.

Figure 1. (a) Structure of amidoflumet: methyl 5-chloro-2-{[(trifluoromethyl)sulfonyl]amino}benzoate: a structure of amidoflumet with numbering of nuclei used for the peak assignment in NMR spectra. Aromatic protons are not indicated, for simplicity. (b) Most stable conformation of amidoflumet in the gas phase. A presumed intramolecular hydrogen bond is indicated with a dotted line in a and b.

The chemical shift of a nucleus is very sensitive to its electrical environment, and molecular interactions in solution, which change the environment around the solute molecule, can be well characterized by detecting CIS values with solution state NMR. CIS can be estimated by comparing the chemical shift of a certain peak of the solute molecule existing in the solution as a monomer with the counterpart of the aggregation. To compare the chemical shifts derived from different solutions, a unified scale using a chemical shift reference independent of interactions with objective solute molecules is required. Moreover, when the concentration difference is so large that the solute molecules exist as monomers at the dilution limit and supersaturation is achieved at the concentration limit, it is necessary to correct the effect of volume magnetic susceptibility of sample solutions. Here, to cope with these difficulties, EDRM was introduced using HMDSO as a reference substance. This newly introduced external reference method of NMR plays a key role in the detailed analysis of chemical shift deviation throughout the wide concentration range. Amidoflumet is a novel acaricide developed by Sumitomo Chemical Co., Ltd. (Figure 1). This compound dissolves well in several organic solvents: N,N-dimethylformamide, chloroform, acetonitrile, methanol, ethanol, and so on, but it is hardly soluble in water. Polymorphism of amidoflumet has so far not been observed. The acetonitrile solution of amidoflumet was selected as a model system to study the aggregation and homogeneous crystal nucleation of biologically active small organic compounds because of its high solubility and rather simple structure; these factors were considered to be advantageous for the study of the behavior in solution and the molecular arrangement in the crystal. The fact that acetonitrile is not a hydrogen-bonding solvent and does not form a stable selfaggregation at room temperature was also important, to simplify the model system. 1H NMR spectra derived from diluted and concentrated solutions of amidoflumet in CD3CN are shown in Figure 2. These spectra were obtained at 293 K after keeping the sample conditions constant for at least 1 h to achieve equilibrium. Chemical shifts observed in comparison with the unified scale using EDRM and CIS values of corresponding peaks are summarized in Table 1. The concentrated solution listed was the saturated solution at 293 K. These results show the apparent tendency of all aromatic proton peaks to shift toward the higher magnetic field direction with different degrees of deviation. CIS values of methyl protons and the sulfonamide proton are rather small. Amidoflumet molecules are likely to exist as mutually

856 Crystal Growth & Design, Vol. 6, No. 4, 2006

Kimura

Figure 2. 1H NMR spectra of amidoflumet in CD3CN solution at 293 K: The numbers correspond to the positions of aromatic protons indicated in Figure 1a. Chemical shifts of observed peaks are corrected by EDRM. (a) Concentrated solution (mole fraction: 0.039): The spectral distortions for the peaks of position 3 and 4 arise from strong coupling. (b) Diluted solution (mole fraction: 0.002). Table 1. Chemical Shifts (in ppm) Corrected with EDRM and CIS Values of 1H NMR Peaks of Amidoflumeta sample solution mole fraction position of 1H 3 4 6 8 9

concentrated solution 0.039 7.677 (0.086) 7.660 (0.103) 8.050 (0.115) 3.990 (0.060) 10.997 (-0.006)

diluted solution

further diluted 10-fold

0.002

0.0002

7.763 7.763 8.165 4.050 10.991

7.765 7.765 8.164 4.053 10.989

a CIS values calculated by subtracting the chemical shifts of concentrated solution from those of diluted solution are indicated in parentheses. Positive CIS values correspond to the upper field shift of 1H NMR peaks. The observation was performed at 293 K.

noninteractive monomers in the diluted solution because there are not significant differences between chemical shifts derived from the diluted solution and the solution further diluted 10fold. Moreover, the occupied volume ratio of amidoflumet against CD3CN in the concentrated solution, as estimated from the density and mole fraction, was approximately 0.2; this means that amidoflumet molecules can be separated from each other by CD3CN molecules still in the concentrated solution. Therefore, these chemical shift deviations are considered to come from the change of the interaction between solute molecules, and this suggests the existence of the cluster in the concentrated solution as an averaged structure detected by solution state NMR. It is also suggested that the dominant interaction between solute

molecules resulting in cluster formation is the stacking of aromatic rings based on the so-called π-π interactions. Intermolecular hydrogen bonding is hardly possible, since the calculated most-stable conformation, shown in Figure 1, suggests the existence of an intramolecular hydrogen bond. The fact that the intramolecular hydrogen bond remains intact in the crystal structure is also supportive of this consideration. In reality, many kinds of clusters of various sizes may exist, and they are likely to be in equilibrium in the concentrated solution. However, it is difficult to analyze the multiple aggregation equilibrium in the dense solution. Therefore, in this study the NMR data were analyzed from the standpoint of taking the averaged structure observed as the apparent structure. This approach is sufficient and useful to characterize the solution structure as the dense liquid precursor. All NMR peaks of the aromatic protons show the upper field shift, but there are no newly appearing peaks on the spectra. This means that a symmetric property can be set for the apparent averaged structure of the cluster, which is observable by NMR, and it is reasonable to presume the dimeric molecular arrangement as the representative averaged structure of the cluster, because two molecules are the minimum unit of a cluster and the number of molecules included in the embryo estimated on the basis of the solubility data22 is also around two. In addition, the symmetric property of the averaged structure suggests that two amidoflumet molecules have their aromatic rings aligned in parallel with each other. To determine intra- and intermolecular interactions or a structure in solution, the nuclear Overhauser effect (NOE) is frequently used; however, the ring current effect was employed for the analysis of the molecular aggregation here because only the averaged structure of the cluster was observed by NMR, and the cluster was not stable enough to observe the NOE in this case. This kind of approach to the molecular aggregation is often successfully used for chemical compounds that have aromatic rings.23 In many cases, the ring current effect is used to estimate chemical shifts of nuclei under certain environmental conditions.24 Here, this effect was used for the estimation of the arrangement and the distance between interacting solute molecules on the basis of the precise chemical shifts corrected against the unified scale. The formulation of the local magnetic field induced by the current on an aromatic ring in the static magnetic field is necessary to calculate the position of a certain nucleus on the basis of its CIS value. It was theoretically obtained by Johnson and Bovey,20 for example, and their model with the equation shown below was used for the calculation of the averaged structure of the cluster.

∆δ (ppm) ) ne2 1 1 - F 2 - z2 K+ E (1) 2 2 2 1/2 6πmc a [(1 + F) + z ] (1 - F)2 + z2

[

]

where, ∆δ is the observed CIS value, n is the number of electrons, e is the charge of an electron, m is the mass of an electron, c is light speed, and a is the radius of a loop where electrons are circulating. F and z are cylindrical coordinates expressed in units of a. The modulus k of the complete elliptic integrals K and E is expressed by

k2 )

4F (1 + F)2 + z2

(2)

CIS values of the three aromatic protons were used for the calculation of the arrangement and the distance between aromatic rings of the two molecules constituting an apparent


dimeric cluster. Usually, the effects of the local electric field and the anisotropy of the local magnetic field should be taken into account when this kind of treatment is performed precisely;25 however, these two effects were neglected here based on the assumption that they did not have significant effects on the chemical shift deviation of the three aromatic protons, as judged from the structure of amidoflumet. The effects of substituted side chains of the aromatic ring were unlikely to reach the aromatic protons to a significant degree. The molecular arrangement of two molecules in this apparent dimeric cluster had to satisfy the following two conditions: (1) All three observed chemical shift deviations of aromatic protons were in good agreement with the calculated values based on the presumed molecular arrangement; (2) The distances between any two out of three aromatic protons were consistent with the geometry of amidoflumet. On the basis of the discussion above, the apparent averaged structure of the cluster has a symmetric character, and two aromatic rings of the constituting amidoflumet molecules are in parallel. In addition, eq 1 shows that ∆δ can be determined from F and z alone, and conversely, that the coordinates F and z of the position can be determined from ∆δ. When there is only one proton to consider, there are many positional possibilities where a certain ∆δ is observable. However, an amidoflumet molecule has three aromatic protons forming a right angled triangle, and the position of this right angled triangle can be determined as only one set of possible symmetric two positions. Therefore, by determining the arrangement of the two right triangles, the arrangement of two amidoflumet molecules in an apparent dimeric cluster is determined. A brief custom software program was coded for modeling positions of three aromatic protons of one amidoflumet molecule in the vicinity of the local magnetic field induced by the ring current on the aromatic ring of another amidoflumet molecule, set at the zero point on the x-y plane (Figure 3). The distance between two aromatic rings and the arrangement of two molecules in the apparent cluster were determined based on the results obtained by this program. The apparent averaged structure of the cluster is shown in Figure 4. The located directions of the substituted side chains were presumed as indicated in Figure 4 based on the calculated most stable conformation in the gas phase because the bulky side chains were considered to be obstacles to the approach of two molecules. This is just the averaged structure of the cluster, which is detectable with solution state NMR; however, it surely reflects the structure of the solution, and as the arrangement of the solute molecules as part of the solution structure in the stage prior to crystallization it can be called the “embryo.” Also, the dominant interaction between solute molecules is identified as the stacking of aromatic rings. The CIS value of methyl protons was larger than the estimated value based on the determined structure with the ring current effect. Also, the CIS value of the sulfonamide proton was very small. These anomalies were considered to come from the effects of the substituted side chain, neglected here. Although it is not essential for the determination of the molecular arrangement in this case, the effects of the local electric field and the anisotropy of the local magnetic field should be taken into account to evaluate the respective CIS values precisely. Comparison with Molecular Arrangement in the Crystal. Here, the dimeric structure was presumed as the apparent averaged structure of the cluster in the concentrated solution. On the other hand, the number of molecules included in the embryo estimated on the basis of the solubility data22 is also


Figure 3. Schematic representation of the determination of molecular arrangement in an apparent cluster: One aromatic ring is set at the zero point on the x-y plane, and there is a local magnetic field induced by the ring current on the aromatic ring in this three-dimensional space. F and z are the cylindrical coordinates, indicated in green, expressed in units of a as defined in the formula of Johnson and Bovey. Three points in this space designated as A, B, and C, which satisfy two conditions described in the text, were found with a custom-made software program, and then the arrangement of two amidoflumet molecules in an apparent cluster was determined based on the symmetrical property of the cluster.

Figure 4. Schematic presentation of the apparent averaged structure of the cluster in the amidoflumet solution in CD3CN (mole fraction 0.039) at 293 K: The length of the unit square side is one angstrom. The distance between two aromatic ring planes is 7.20 Å. (a) Top view of a cluster. Red and blue right triangles indicated are the direct results of the calculation. (b) Side view of a cluster. (c) Another side view of a cluster.

around two. Therefore, the apparent averaged structure of the cluster, which reflects the structure of the solution as a species of the highest frequency, is likely to be similar to the dimeric structure of the embryo, especially in the concentrated solution.


Kimura

Figure 5. Comparison of the structure of the apparent cluster with the molecular arrangement in the crystal: (a) Arrangement of two amidoflumet molecules in a unit cell. (b) Space-filling model view shows the close contact of two amidoflumet molecules in a unit cell. (c) Top view of the molecular arrangement in a unit cell. (d) Side view of the molecular arrangement in a unit cell. (e) Top view of the apparent cluster. (f) Side view of the apparent cluster.

It is now possible to investigate and deduce the process of the crystal nucleation by minutely comparing the structure of the apparent cluster and the crystal. So far, amidoflumet is not considered to have polymorphism. The crystals, obtained with and without the existence of a strong magnetic field at 9.4 T, were investigated with X-ray crystallography, and it was confirmed that they have the same crystal structure. Therefore, the crystal nucleation process under the strong magnetic field was considered to be the same as that without the magnetic field. The molecular arrangement in the crystal determined by X-ray crystallography is shown in Figure 5, and it is compared with the structure of the apparent cluster in solution. The dimeric structure of the apparent cluster has an antiparallel motif of two molecules, the same as in the crystal structure. However, the distance between two aromatic rings of amidoflumet is different between the apparent cluster and the crystal. Whereas two molecules approach the limit of the van der Waals contact in the crystal, the distance in the cluster is longer than that of the crystal structure. The relative position of two molecules along with the direction, parallel to the plane of aromatic rings, is also different between the cluster and the crystal. In the apparent cluster, one molecule lies on top of the other with less deviation than in the crystal. This observation suggests that other step(s) may exist between the embryo and the critical nucleus. Thus, comparison of the structure between the embryo and the crystal can provide insight into the process of the crystal nucleation. Concentration Dependence of the Dense Liquid Precursor Structure. To investigate the early stage of nucleation, the apparent averaged structures of the clusters under various

Figure 6. Supersaturation ratio dependence and mole fraction dependence of CIS values: The difference in degree of chemical shift deviation between positions 4, 6 and 3 is considered to come from the change of the relative molecular arrangement in an embryo. ∆µ is the difference of chemical potential between the solid crystal and the solution state. When ∆µ > 0, solution state is more stable than solid crystal. The higher the CIS value is, the more the solution is well structured. The shown lines are only guide. (a) Supersaturation ratio dependence. (b) Mole fraction dependence.

conditions were determined using the methodology described above. The solution concentrations and observation temperatures were varied. The observed CIS values of the three aromatic protons are summarized with supersaturation ratio (S) dependence and mole fraction dependence in Figure 6. Here, the definition of S is the actual concentration divided by the equilibrium saturation concentration at a certain temperature (S ) C/C*). The influence of the temperature on CIS values was rather small compared with the concentration dependence in this case. Judging from comparison of Figure 6, panels a and b, to analyze the concentration dependencies it is appropriate to plot CIS values against mole fractions, since the expression of S dependence of CIS values does not show a coherent trend. The reason for this inconvenience is likely attributable to S, because S is the normalized value at the equilibrium saturation concentration, which depends on the temperature of the sample solution. On the other hand, mole fraction of amidoflumet does not have temperature dependence. That is to say, this result shows that CIS values depend not on S but on mole fraction. This is reasonable because the aggregation can occur without the existence of solid crystals.



Figure 7. Mole fraction dependence of the distance between two amidoflumet molecules in an apparent dimeric cluster: D is the distance between planes of two amidoflumet molecules, in units of Å. M is the mole fraction of solute molecule in the sample solution. R2 is the coefficient of determination.

Figure 8. Comparison of the mole fraction dependence of the distance between two amidoflumet molecules in an apparent cluster in the case of chloroform solution and the acetonitrile solution at 293 K: The definitions of D and M are the same as described in Figure 7. R2 is the coefficient of determination.

Observed CIS values of the three aromatic protons can be directly translated into the arrangement of two molecules in the apparent averaged structure of the cluster. The distance between two molecules in an apparent cluster becomes nearer to that of a crystal as the concentration becomes higher. It means that the solution has a more ordered structure at high concentration. On the basis of this mole fraction dependence of the solution structure, Figure 6a gives us a very important insight: there is not a strong relationship between S and the structuralization of the solution. It indicates even when the CIS values are large such as 0.25 ppm for positions 4 and 6 at 323 K, and the solution is well-structured, crystallization will never occur because S < 1 in this concentration range at this temperature. However, when the CIS values are rather small such as 0.17 ppm for positions 4 and 6 at 293 K, and the solution is not well-structured, crystallization can occur because S > 1 in this concentration range at this temperature. This is understandable because the parameter S is relevant to the probability of transition between the solution state and the solid crystal, as it relates to the chemical potential difference between them. It is presumable that monomers will aggregate to form the critical nucleus in the diluted solution when S > 1, and clusters are likely to aggregate to form the critical nucleus in a well-structured, concentrated solution when S > 1. The refrigeration of the diluted solution exemplifies the former case, and the condensation of a solution, such as the evaporation of solvent, is an example of the latter case. This discussion suggests that the events occurring in the course of refrigeration and condensation are microscopically different crystallization processes. The distance between two molecules constituting the dimeric cluster can characterize the change of the apparent averaged structure of the cluster depending on the solution concentration. The mole fraction of amidoflumet and the distance between two molecules could be connected according to the following linear relation as indicated in Figure 7, based on the experimental data:

of these coefficients was not so significant in this case. The regression line passed almost through the origin, as is reasonable since 1/D3 will be zero when M goes to zero. Thus, the equation can be rewritten as follows on the assumption that coefficient B is zero, and it indicates that the product of the mole fraction of amidoflumet and the cube of the distance between two molecules in the apparent averaged structure is constant, at least within the concentration range examined in this study.

1 )A×M+B D3

(3)

where, D is the distance between the centers of two aromatic rings in units of angstroms (Å), M is the mole fraction of solute molecules, and A and B are the regression coefficients. In the case of amidoflumet solution in acetonitrile, coefficients A and B at 293 K were determined as 0.0721 ( 0.0004 and -0.00015 ( 0.00003, respectively. The temperature dependence

M × D3 ) C

(4)

where C is a constant and is equal to 1/A. To examine this prospect, additional experiments using amidoflumet solution in chloroform were performed. Chloroform is also not considered to form a stable self-aggregation at room temperature. It was confirmed that the structure of the crystal obtained from chloroform solution was the same as that from acetonitrile. The results of the analysis performed with the amidoflumet-chloroform system are shown in Figure 8. Coefficients A and B in the chloroform case were determined as 0.0095 + 0.0004 and 0.00000 + 0.00007, respectively. These data support the assumption described above. Coefficient C has units of volume, and it is considered to be specific to the combination of solute and solvent molecules. Therefore, eq 4 can be interpreted to mean that a certain volume determined by the combination of solute and solvent is constant, and the increment of the mole fraction of solute molecule is likely to correspond to constraining the solute molecules to within a certain limited volume, although the partial molar volume of amidoflumet, estimated by the density of the solution and the mole fractions of solute and solvent molecules, is constant within the concentration range tested here. Even though it is not clear which property of the solvent, i.e., size and/or the affinity for the solute molecule, affects the constant C, it is interesting that the product of the mole fraction of solute and the cube of the distance between two molecules in an apparent cluster is constant, at least within the rather diluted range. Once this constant C is characterized, it might be applicable to the solvent selection for crystallization. Conclusion The apparent averaged structure of the cluster determined by solution state NMR was used for the characterization of the homogeneous crystal nucleation process, and the dominant


interaction between amidoflumet molecules in the apparent cluster was identified as the stacking of aromatic rings. It was also revealed that the structural change of the apparent cluster depends not on the supersaturation ratio but on the mole fraction. This result suggests the idea that the supersaturation ratio plays a role only as one parameter relevant to the probability aspects of nucleation, while the absolute concentration of solute molecules plays a more important role in the preparative structurization of the solution, which is detectable as the apparent averaged structure of the cluster. The product of the mole fraction of amidoflumet and the cube of the distance between two molecules in an apparent cluster is a constant. This constant, which is expressed in units of volume, is considered to be specific to the combination of solute and solvent molecules, although the definitive meaning of this constant as a physical property is not identified. The similarity between the apparent structure of the cluster and the crystal structure is revealed in the case in which the molecular interaction in solution is considered to be very simple, as amidoflumet in acetonitrile. The possibility of the existence of the other step(s) between the dense liquid precursor and the crystal nucleus is also suggested. Verification of this concept in other systems, especially where there are more complicated molecular interactions, and applications to other cases will be investigated in the future. Application of the analysis described here to a system that has polymorphism would be very interesting. Crystal nucleation is one of the most exciting boundary fields of science and technology, and the approach to the solid crystal properties by way of the analytical methods for the solution state is considered to be promising, as reported here. A closer collaboration of crystal engineering26 and solution science is now demanded. Acknowledgment. I thank Dr. Shogo Sudo and Dr. Ritsuko Furuta for scientific discussions, Dr. Katsuhiro Suenobu for the calculation of the most stable conformation in the gas phase, Ms. Masami Kida for technical assistance, and greatly appreciate very kind and inspiring suggestions of Professor Hiroshi Ooshima of Osaka City University.

Kimura

References (1) Colfen, H.; Mann, S. Angew. Chem., Int. Ed. 2003, 42, 2350-2365. (2) Bernstein, J. Polymorphism in Molecular Crystals; Oxford University Press: Oxford, 2002. (3) Byrn, S. R.; Pfeiffer, R. R.; Stowell, J. G. Solid-State Chemistry of Drugs, 2nd ed.; SSCI Inc.: West Lafayette, IN, 1999. (4) Mullin, J. W.; Leci, C. L. Philos. Mag. 1969, 19, 1075-1077. (5) Larson, M. A.; Garside, J. Chem. Eng. Sci. 1986, 41, 1285-1289. (6) Kashchiev, D.; van Rosmalen, G. M. Cryst. Res. Technol. 2003, 38, 555-574. (7) Vekilov, P. G. Cryst. Growth Des. 2004, 4, 671-685. (8) Desiraju, G. R. Angew. Chem., Int. Ed. Engl. 1995, 34, 2311-2327. (9) Saito, A.; Igarashi, K.; Azuma, M.; Ooshima, H. J. Chem. Eng., Jpn. 2002, 35, 1133-1139. (10) Maruyama, S.; Ooshima, H. J. Cryst. Growth 2000, 212, 239-245. (11) Spitaleri, A.; Hunter, C. A.; McCabe, J. F.; Packer, M. J.; Cockroft, S. L. CrystEngComm 2004, 6, 489-493. (12) Hamada, K.; Take, S.; Iijima, T.; Amiya, S. J. Chem. Soc., Faraday Trans. 1 1986, 82, 3141-3148. (13) Asakura, T.; Ishida, M. J. Colloid Interface Sci. 1989, 130, 184189. (14) Ding, X.; Stringfellow, T. C.; Robinson, J. R. J. Pharm. Sci. 2004, 93, 1351-1358. (15) Shikii, K.; Sakamoto, S.; Seki, H.; Utsumi, H.; Yamaguchi, K. Tetrahedron 2004, 60, 3487-3492. (16) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (17) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785-789. (18) Frish, M. J. et al. Gaussian98, Revision A.11; Gaussian Inc.: Pittsburgh, PA, 2001. (19) Mizuno, K.; Tamiya, Y.; Mekata, M. Pure Appl. Chem. 2004, 76, 105-114. (20) Johnson, C. E., Jr.; Bovey, F. A. J. Chem. Phys. 1958, 29, 10121014. (21) Kimura, M.; Hourai, S. Acta Crystallogr. Sec. E 2005, 61, 39443945. (22) Nakai, T. Bull. Chem. Soc. Jpn. 1969, 42, 2143-2148. (23) Abraham, R. J.; Smith, K. M. J. Am. Chem. Soc. 1983, 105, 57345741. (24) Williamson, M. P.; Asakura, T. J. Magn. Reson. B 1993, 101, 6371. (25) Hunter, C. A.; Packer, M. J. Chem. Eur. J. 1995, 5, 1891-1897. (26) Desiraju, G. R. Crystal Engineering: The Design of Organic Solids; Elsevier: Amsterdam, 1989.

CG050090P

Characterization of the Dense Liquid Precursor in Homogeneous

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