Insights into solvent-dependent nucleation behavior of benzoic acid from metastable zone widths

Highlights

• Relationship between the interfacial tension and saturation temperature shows opposite behavior in methanol and chloroform.

• Relationship between the interfacial tension and Δμ shows different behavior in methanol and chloroform.

• The balance between the dimer and monomer moving towards the monomer at higher temperatures in chloroform is proved by FTIR.

• Different rate-determining step for nucleation of BA in methanol and chloroform are discussed.

Abstract

Currently, how the solvents and temperature affect the solution species and rate-determining step in the nucleation process, thus altering the nucleation behavior remains elusive. In this contribution, by employing metastable zone width (MSZW) experiments, the modified Sangwal’s theory and the molecular dynamic simulations, we explore nucleation behavior of benzoic acid (BA) in polar and non-polar solvents. We find that in methanol, the solid–liquid interfacial tension γ decreases with increasing the saturation temperature, in contrast, the value of γ increases with increasing the saturation temperature in chloroform. Furthermore, in the classical nucleation framework, we conclude that the critical nuclei size and critical Gibbs free energy monotonous decline as the driving force increases in methanol, which implies that the interfacial tension is independent of the driving force. On the contrary, the relationship between critical nucleation parameters and driving force indicates that the interfacial tension changes with the driving force in chloroform. By employing FTIR, we find that dimerization of BA is restricted in methanol, and BA always exists as the monomer even near the nucleation point, which implies that desolvation is the rate-determining step in the nucleation process. While in chloroform, we demonstrate that the form of monomers and dimers coexist in solution. As the saturation temperature increases, the equilibrium is broken and moves toward the monomer. It implies that the rate-determining step of the nucleation process of BA may change from molecular rearrangement to desolvation with increasing the saturation temperature in chloroform.

Introduction

As the first step of the crystallization process, nucleation has always been a hot topic in the academic and industrial community because of its mystery and concealment. When it comes to the nucleation process, we urgently want to know what the mechanical mechanism of nucleation is and how to precisely control the process. Research on nucleation theory can be traced back to the basic thermodynamic research of Gibbs in 1878 [1]. After nearly 150 years of development, the most popular and the oldest theory is still classical nucleation theory (CNT), which describes that the nucleation process is governed by the competition between the volume free energy and surface free energy [2]. Following the thermodynamic concept of CNT, the kinetic part of CNT is developed by Becker and Döring [3] and further polished by Kashchiev and other scholars [4], [5], [6]. However, as the crystallization field continues to evolve, the basic assumptions of CNT are constantly being challenged. As early as in 1997, Ten Wolde et al. [7] found that near the critical point, large density fluctuation precedes structral fluctuation. After nearly 8 years of development, such similar phenomenon had been discovered by more and more scholars [8], [9], [10], [11], [12], [13], [14] and was named the two-step nucleation theory by Vekilov, P.G. [15] in 2004. In 2008, Gebauer et al. [16] pointed out that the dissolved calcium carbonate has stable pre-nucleation clusters even in an unsaturated solution. The discovery of these aggregates contradicts the hypothesis in CNT that monomers associate to form unstable clusters. In the ensuing decade, the mechanism of pre-nucleation theory was widely recognized [17], [18], [19], [20]. However, non-classical nucleation theory has not formed a mature theoretical model like CNT to describe the fluctuations of density and structure in the nucleation process. Although it enriches the nucleation theory in content, the CNT still plays a guiding role in understanding nucleation process. The development of nucleation theory has been thoroughly reviewed in our previous work [21].

As the window for nucleation, MSZW can help us to reveal the nucleation path in metastable zone and may provide new ideas for understanding the nucleation process. It is well known that MSZW is dependent on temperature, cooling rate, level of agitation and impurities and different detection technique [22], [23], [24], [25], [26]. As early as in 1985 and 2008, the relationship between cooling rate (R) and MSZWs was established by Nývlt [26] and Kubota [27] respectively. The nucleation constant k₁ is uncertain because the fixed number density of accumulated crystals N_det/V cannot be obtained in the measurement of MSZWs. Hereafter, Sangwal [28] proposed a self-consistent Nývlt-like model and a novel approach [29] to describe the effect of temperature and cooling rate on MSZWs. Although the nucleation order m* and nucleation constant K are redefined and related to solute–solvent interaction, it is difficult to identify the physical signification of both parameters. Besides, the effect of impurities can not be reflected in this model [30]. Then, Sangwal’s novel approach has been rephrased by Xu S. et al. [31] to make its main parameters be temperature independent, which allows scientists and engineers obtaining solid–liquid interfacial tension and pre-exponential factor from MSZWs rather than from an induction time experiment. Thus, one can control the crystallization process through the MSZWs, and then provide practical guidance for scale-up production. Although the questions of how mechanical disturbances [32], [33], [34], [35] and impurities [36], [37], [38], [39], [40], [41], [42] affect the MSZWs was discussed in numerous literatures, there are few studies about the effects of solvents on MSZWs and its effects on nucleation kinetics. Furthermore, it is still unclear how desolvation and solution species affect the MSZWs and the nucleation kinetics.

Benzoic acid, as a typical small molecule with carboxylic acid group, has been widely concerned. The solubility of BA in various solvents has been reported [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], and it shows different nucleation behavior in different solvents. As Pauling discovered, “Benzoic acid and other carboxylic acids have been shown to associate to double molecules in solution in certain solvents such as benzene, chloroform, carbon tetrachloride, and carbon disulfide. It exists in monomeric form in solution in acetone, acetic acid, ethyl ether, ethyl acetate, and phenol; in these solutions, single molecules are stabilized by hydrogen bond formation with the solvent” [53].

Additionally, predecessors tried to reveal the nucleation behavior of BA. Davey et al. [54] studied the molecular self-assembly process of three carboxylic acids, including benzoic acid, in concentrated solutions by infrared spectroscopy in 2006. It was found that in the cases of benzoic acid and tetrolic acid, a link between the growth synthon and the structural synthon is apparent, which suggests that the solution species of BA plays a significant role in the nucleation outcome. Later, by employing EPSR (empirical potential structure refinement) combined with small-angle neutron diffraction, the researchers [55] pointed out the desolvation of the carboxylic acid groups of BA and the creation of H-bonded dimers is the key steps in the nucleation process in supersaturation BA-methano system. Further, Davey et al. [56] compared the kinetic and thermodynamic parameters of benzoic acid and terephthalic acid based on CNT, emphasizing the important role of aromatic stacking self-assembly weak interaction in the nucleation process. In a word, BA shows significant different nucleation behaviors in different solvents. It seems like that in the nonpolar solvents, BA is mainly present as a dimer that is ready to be assembled into macroscopic crystals. Tang W. et al. [57] also reported such views. In the polar solvents, BA is strongly solvated even in supersaturated solutions, which means that desolvation and rearrangement are on the way of self-assembly. Thus, the nucleation pathway of BA is dependent on the solvent.

However, how the solvents affect the self-assembly process of BA in the perspective of MSZWs is still unclear. Therefore, the main purpose of this article is to explore the effect of solvent and temperature on the nucleation behavior of benzoic acid from the perspective of the metastable region. In addition, we use molecular dynamics simulations to supplement the solvent–solute interaction strength of BA in chloroform and methanol, respectively. In this way, we aim to gain more insights into how the solvent and temperature affect the solution species of BA and the rate-determining steps in nucleation process.