Infrared Thermography Investigation of Crystallization in Acoustically Levitated Supersaturated Aqueous Solution

Abstract

In this study, crystallization in highly supersaturated aqueous urea solutions was investigated using in situ infrared thermography facilitated by an acoustic levitation apparatus. A notable contribution of this thermographic approach is the identification of a transient heat release signature, particularly pronounced beyond the solubility limit, indicating the enhanced formation of bonds between urea molecules in the supersaturated states. Surprisingly, the temporal evolution of the heat release measurements on an acoustically levitated droplet strongly suggests a two-stage process for urea crystallization. A comprehensive statistical analysis based on classical nucleation theory is used to further investigate the exceptionally high degree of supersaturation and the emergence of prominent heat signatures observed toward the onset of crystallization.

1. Introduction

The nucleation of crystals from solution is a ubiquitous phenomenon that spans a broad spectrum of scientific disciplines. Gaining a profound insight into the process holds crucial implications for practical areas, including the production of pharmaceutical compounds [1,2,3], food and fertilizer manufacturing [4,5], and the fabrication of high-quality optoelectrical devices [6,7]. Of particular interest are the initial stages of crystallization in metastable states because of their potential uses for synthesizing materials with diverse structures and functionalities. However, achieving precise control over the crystallization requires an accurate understanding of the mechanism by which atoms and molecules aggregate during the pre-nucleation stage, ultimately culminating in crystal formation. In a stable undersaturated regime in an aqueous solution, the solute molecules are fully solvated, thereby minimizing the system’s free energy and preventing the process of crystallization. As the solution becomes supersaturated, the possibility of crystal nucleation emerges because of a drastic increase in the thermodynamic driving force. During this process, the excess solute molecules aggregate and align, forming clusters or nuclei of the solute phase that disrupt the initial hydration shell structure [8,9,10,11]. In practice, classical nucleation theory (CNT) is widely used to study such phase transitions in various metastable states because of its analytical simplicity [12,13,14]. It provides a theoretical framework to describe the initial steps of nucleation, where a small nucleus of the new phase forms in a metastable parent phase. In this model, nuclei must surpass a critical size to proceed with stable phase formation. While CNT has proven useful in metallic systems composed of alloys [15,16], its applicability to complex systems or non-equilibrium conditions has been brought into question [17,18,19,20,21,22]. In particular, the classical theory assumes that clusters evolve in size by adding individual molecules at a time, during which fluctuation between the distributions of embryo clusters is neglected. Since the theory only accounts for growth units of monomers, it fails to provide insights into the nature of pre-nucleation clusters formed in solutions [23,24,25]. Therefore, more sophisticated theories and experimental validations of pre-nucleating dynamics are highly desirable.

Despite the extensive historical use and widespread application of crystallization, comprehending the intricate relationship between the degree of supersaturation and the kinetics and thermodynamics of crystallization remains a challenging task. This complexity is due to the underlying mechanisms operating at microscopic time and length scales and the difficulty in maintaining extreme levels of metastability. However, investigating a highly supersaturated aqueous solution in a contact-based experiment proves extremely difficult because of the interface between the aqueous solution and the container, which acts as an efficient heterogeneous nucleation site. Additionally, the characterization of sample properties can be contaminated by interactions between the sample and the container or by the addition of foreign substances that are used to control crystallization [1]. Such shortcomings have prompted the development of space-platform experiments to exploit microgravity conditions.

The use of acoustic levitation in crystallization studies offers a notable advantage by providing a non-contact environment. This eliminates the influence of vessel walls, which can act as unwanted heterogeneous nucleation sites and prohibit manifesting highly supersaturated states, as well as affect crystal shape and purity. The absence of a container also minimizes the risk of impurities or foreign particles being introduced to interfere with the crystallization process. In addition, the controlled drop-evaporation process allows precise monitoring of the solution concentration, enabling systematic studies and the integration of in situ diagnostic tools, such as X-ray diffraction and thermography. Overall, acoustic levitation offers improved control, accuracy, and detail for the study of crystallization in aqueous solutions in comparison to traditional methods.

This work demonstrates measuring the transient thermal effect and spontaneous nucleation within a highly concentrated aqueous urea solution in a contact-free environment. The drop-evaporation method [22,26] is enabled by using an acoustic levitation apparatus [27,28] to achieve unprecedented levels of supersaturation. The progression of temperature variations on the droplet surface is monitored by using in situ infrared (IR) thermography. The infrared thermography approach has the potential to offer valuable insights into the thermodynamic aspects of various phenomena while also offering hints about bond formation or chemical reactions. Consequently, it can exhibit a highly effective capability to complement optical microscopy measurements. By comparing the rate of heat release as a function of supersaturation, the nature of the pre-nucleation process within the solution is elucidated. Our result reveals two distinctive stages of heat signatures leading up to final crystallization, which implies two possible stages of crystal nucleation. When the concentration of the solution increases to a level equivalent to supersaturation of S = 0.5, a gradual rise in the droplet temperature is measured. This behavior persists throughout the entire width of the metastable zone [14,22,29]. However, as supersaturation reaches a critical limit (approximately S = 2), a brief stagnation in the temperature is observed, which is followed by an instantaneous heat release and rapid growth of polycrystalline urea crystals. The implications of these findings are discussed through comparative analysis with the CNT perspective.

2. Materials and Methods

A schematic of our experimental setup is shown in Figure 1a. An acoustic levitator comprising two parallel transducer arrays in a vertical orientation was utilized to suspend a liquid droplet measuring 2 to 3 mm in diameter [27]. This was achieved by generating a 40 kHz sinusoidal electrical signal using a PC scope, which was then amplified and directed to the transducers, thereby generating a stable standing acoustic field. Within the acoustic levitator, the solution droplet was inserted into the node of the sound wave, an area characterized by lower air density. For the levitation experiment, urea solutes with a purity of 99.8% (provided by Aldrich) were dissolved in deionized water with a resistivity of 18.2 MΩ·cm. The samples underwent filtration through a syringe filter with 220 nm pore size (BIOFIL) to ensure the removal of any unwanted impurities. The meticulously prepared solution was then introduced to the injection needle positioned close to the designated sound node. Through precise adjustments of the flow rate facilitated by a motorized syringe pump, the solution was shaped into a droplet at the tip of the needle. The high-precision motorized syringe pump (KDS 100), capable of delivering a flow rate with a precision of 0.1 $\mathsf{\mu }$L/h, and the optical magnifying lens setup allowed us to levitate droplets of the same diameter with a precision of 20 $\mathsf{\mu }$m so that our result was self-consistent. Once the droplet achieved stable suspension between the acoustic nodes, the needle was gently detached from the sample. Subsequently, time-varying sizes of the evaporating droplet were monitored and recorded using a high-resolution CCD camera (Lumenera Lt365) equipped with a microscopic zoom lens, allowing 5 times magnification at a frame rate of 100 Hz. Concurrently, a thermographic camera (FLIR) was used to measure the evolution of the surface temperature of the solution droplet during evaporation as well as crystallization. To ensure accurate temperature measurement, the temperature of the suspended water droplets was compared using both contact-based thermal coupling and IR thermography. It should be noted that infrared thermography may introduce a potential source of error due to the altered emissivity of the highly supersaturated aqueous solution.

3. Results

Figure 1b shows the evaporation of both pure water and an aqueous urea solution at an ambient temperature of 24 ± 0.2 ${}^{\circ }$C and a relative humidity of 42 ± 2%. The interplay between the sound pressure acting on the sample surface and its surface tension resulted in a continuous alteration of the vertical-to-lateral dimensions ratio throughout the entire evaporation process. To measure volume changes over time, sequential snapshots of backlight-illuminated droplet images were captured. An edge detection algorithm was employed to extract the droplet’s shape profile from these images. Subsequently, a 6th-order Legendre polynomial fitting was used to obtain volumes of the droplet as a function of time [26]. Assuming a spherical shape of the drop, this procedure enabled the calculation of the temporal evolution of its diameter, represented as $D\left(t\right)$. As depicted in Figure 1a, the drying kinetics of the pure water drop followed the $D^2$ law [26,30], indicating that the square of the droplet diameter decreased linearly over time according to the following relationship:

$$\frac{D{\left(t\right)}^2}{D_o^2}=1-\beta \frac{t}{D_o^2},$$

(1)

where $D_o$ is the diameter of the droplet at t = 0. The evaporation rate $\beta$ = 2.88 × 10${}^{-3}$ mm${}^2$/s was obtained by fitting Equation (1) to the water data. Assuming the evaporation of water is solely during levitation, the evaporation kinetics of the urea solution were considered. This assumption is grounded in the non-volatile nature of urea, which resulted in a minimal initial-to-final mass difference of less than 1%. Thus, the evaporation of the solution led to a progressive rise in solute concentration. As shown in Figure 1b, within the relatively dilute concentration range, its evaporation kinetic was close to that of the water. However, this rate continuously decreased with increasing solute concentration, eventually falling below 20% of the water’s rate beyond its solubility limit. Figure 1c illustrates the water activity–corrected supersaturation curve [31,32] for the urea solution across relevant time scales. When the supersaturation reached approximately S = 2, a rapid solidification occurred within 0.2 s (see Figure 2 (top)).

The surface temperature of the supersaturating solution droplet was monitored by using an IR thermographic camera with an emissivity value of 0.9. The measurement was performed at a constant interval of 0.2 s throughout the entire evaporation and solidification processes. Overall, a progressive increase in droplet temperature was measured with increasing solute concentration, and this trend continued until the culmination of final crystallization. Furthermore, our data showed a concurrent temperature increase with slowing evaporation rates. As shown in Figure 2 (bottom), the temperature increase within the initial 1000 s after levitation was minimal, suggesting the presence of a stable hydration structure in the solution. However, near the supersaturation of S = 0.5, a gradual increase in temperature is observed. The gradual release of heat from the solution droplet implies that solute molecules were aggregating to form larger clusters. During this process, it was expected that the hydrogen bonding between water and urea molecules was broken while the bonding between urea molecules formed. The latter likely yielded the structural adjustment of lower energy states. The exothermic reaction became considerably more notable near the solubility limit (S = 1). Assuming that the heat release from the drying droplet was proportional to the number of urea molecules forming bonds, it was reasonable to expect that urea molecules were being added to an unidentified embryonic pre-nuclei, whose sizes were still small enough to be held soluble in the solution form. Approximately 100 s prior to the final crystallization, the temperature stagnated. This behavior indicates that the urea–urea bond-making process had ceased and the cluster size was no longer increasing. Soon after the urea solution reached a critical level of supersaturation (S = 2), an instantaneous release of heat occurred, followed by rapid crystallization.

As depicted in Figure 2 (top), the initial crystallization site is indicated by the yellow arrow at Δt = 0.00 s, which coincides with the abrupt temperature rise shown in Figure 2 (bottom). This temperature increase ($\mathsf{\Delta }T\sim 25$ K) observed in the urea sample closely parallels the substantial temperature rise previously recorded in an experiment conducted on a high-temperature (∼350 K) hydrophobic coated surface [33]. The transparent droplet turned into a visibly opaque white polycrystalline solid, as shown in Figure 2 (top). Afterward, a relatively slow radiative cooling of the solidified sample took place. Based on the evolution of temperature, the release of energy in the supersaturating urea solution occurred in two distinctive stages. Initially, the urea molecules existed in the solution form of mostly fully hydrated molecules. Commencing around S = 0.5, evidence emerges indicating the formation of microscopic pre-nucleation clusters, wherein approximately 10% of the entire heat energy was involved (assuming constant specific heat). Lacking any visible crystallization, the sample was still in a solution form. At S = 2, a very rapid solidification occurred, during which about 90% of the heat of crystallization was released. This was likely due to the large surface energy of the pre-nucleation clusters dispersion in the solution.

Figure 3 presents the probability distribution of the crystallization events derived from 100 experimental trials. Notably, the frequency of the crystallization event increases with supersaturation because of the rapid increase in thermodynamic driving force (namely, the chemical potential difference between solution and crystal phases) until S = 2. A statistical methodology formulated by Skripov [34,35], previously applied in the study of nucleation phenomena in metal alloys [36], is used to verify the experimental result. As nucleation is inherently stochastic, characterized by independent occurrences, the Poisson distribution is employed to describe the discrete probability of nucleation as a function of supersaturation. Assuming that a singular nucleation event is sufficient to trigger solidification, the probability of such an event transpiring within the sample volume $V\left(t\right)$ between S and $S+dS$ can be expressed as follows:

$$P(1,S+dS)=\frac{J_{ss}V\left(t\right)}{dS/dt}exp\left(-\underset{S_o}{\overset{S}{\int }}\frac{J_{ss}V\left(t\right)}{dS/dt}dS\right).$$

(2)

The steady-state nucleation rate $J_{ss}$ per unit volume is given by

$$J_{ss}=\frac{k_{B}T{N}_A}{3a^3{V}_m\eta \left(C\left(t\right)\right)}exp\left(-\frac{\mathsf{\Delta }{G}^{*}}{k_{B}T}\right),$$

(3)

where $N_A$ and $k_B$ represent Avogadro’s number and Boltzmann’s constant, respectively. The concentration-dependent viscosity $\eta \left(S\right)$ of the bulk urea solution is obtained by extrapolating experimental data [32,37]. The analysis employs the molar volume of $V_m=7.56\times {10}^{-29}$ m${}^3$ and the atomic jump distance of $a=5.5\times {10}^{-10}$ m. Finally, the nucleation barrier is given by

$$\mathsf{\Delta }{G}^{*}=\left(\frac{4\pi }{3}\right)\sigma {\left(r^{*}\right)}^2.$$

(4)

where $r^{*}=2\sigma /k_{B}TlnS$ represents the critical nucleus size with $\sigma$ denoting the crystal-liquid interfacial free energy that is determined through fitting with the data.

Fitting Equation (2) to the volume and supersaturation data yields a mean interfacial free energy of $\sigma$ = 11 mJ/m² with a critical radius of r* = 1.5 nm. The estimated interfacial free energy is significantly greater than previously reported values that were obtained through contact-based methods [38]. In the context of liquid metals, the crystal–liquid interfacial free energy originates from the configurational entropy difference between the crystalline and liquid states. This suggests that a more pronounced distinction in local structure between the liquid and solid phases leads to a greater disparity in free energy, subsequently resulting in a heightened nucleation barrier. From a classical perspective, the remarkable degree of supersaturation observed in our experiments indicates a notable structural difference between the local configuration of the urea solution and the eventual crystalline state. Thus, the persistent increase in supersaturation levels, even with the elevated urea solute concentration, can be attributed to the aggregation of urea molecules onto embryonic nuclei that may possess distinctive local structures compared to the final crystal phase. Consequently, the nucleation process is hampered, driving the system toward higher supersaturation levels until the critical nucleus size is achieved.

Table 1. Reported values of maximum supersaturation and crystal–liquid interfacial free energy.

Methods	Temperature (K)	$\mathit{\sigma }$ (mJ/m2)	Maximum Supersaturation	Reference
Containerless	297	11	2	This work
Container	303	5.1	1.47	[39]
Container	298	1.3	1.35	[38]
Container	308	5.3	1.33	[40]

compares the results of our study with previous experimental attempts using a contact-based method. A significantly higher degree of supersaturation was achieved in our current investigation using an acoustic levitation apparatus. In addition, the value of the crystal–solution interfacial free energy estimated using CNT in this work significantly exceeded previously reported values.

4. Discussion

The interaction between urea and water in aqueous solutions remains a subject of active research, providing essential insights into a range of interesting functional properties. These include the heightened solubility of hydrocarbons in water, the denaturation of proteins dependent on solute concentration, and the inhibition of micelle formation within the solution. Of particular interest is the self-aggregation of urea molecules, which plays a pivotal role in crystal nucleation within aqueous solutions. Comprehending the self-aggregation behaviors of urea in solutions and the interplay between urea and water molecules is pivotal for gaining insights into the regulation of crystallization processes and enhancing the precision of crystal size, shape, and purity. This knowledge holds immense value in advancing the development of novel materials, such as organic semiconductors, pharmaceuticals, and functional polymers.

While structural aspects of the relevant processes have been explored in several experimental [41,42] and simulation studies [8,9,11,43], there remains a notable absence of thorough thermophysical investigations. Classically, a free-energy barrier needs to be overcome to create a solid-to-liquid interface between the newly forming phase (the nucleus) and the parent phase. A critical cluster size must be surpassed, at which point the nucleus becomes energetically favorable to sustain continuous growth by incorporating smaller sub-critical clusters (such as monomer and dimer additions). However, more recent studies have proposed a non-classical nucleation pathway, in which a highly concentrated solution is predominantly populated with large pre-nucleation clusters (e.g., oligomeric species) [17].

With increasing solute concentration, the number of hydration water molecules around the solute molecule decreases, resulting in a disruption of the initial hydration structure. This facilitates urea molecules to aggregate and form intermolecular bonds, resulting in the release of energy. Thus, the temperature increase of the droplet during supersaturation is attributed to the hydrogen bonding of urea molecules in water. In a concentrated aqueous solution, urea molecules draw closer and organize themselves through the formation of hydrogen bonds. Urea molecules, which possess two amino (NH2) groups and one carbonyl (C=O) group, establish bonds with other urea molecules. The creation of these hydrogen bonds results in the release of energy in the form of heat. As the aqueous solution approaches a very anhydrous state, the frequency of C=O $···$ H-N-C hydrogen bond formation between urea molecules increases. This study shows an increase in heat release that corresponds to the higher solute concentration, indicating the heightened bond formation between urea molecules. Such an interpretation is consistent with the results of previous simulations [11] and in situ Raman and IR spectroscopy studies [44]. One simulation study showed that the hydrogen bond energy between urea molecules is estimated to be about 18 kJ/mol [11]. This is very close to the enthalpy of the solution of urea in water at room temperature, which is typically about 15 kJ/mol [45]. Using the parameters near the solubility limit (a density of 1.145 g/mol; specific heat of C${}_p$ = 0.722 cal/K/g [46]), the upper limit of the temperature rise is estimated to be about $\mathsf{\Delta }$T = 58 degrees by the relation $\mathsf{\Delta }$T = $\mathsf{\Delta }$Q/(m C${}_p$) within an initial solute mass of 0.004 g. Therefore, the rise in temperature in supersaturating urea solution serves as an indicator of the extent of urea–urea bond formation. As demonstrated in our in situ temperature measurements, such behavior commences at S = 0.5 (a molarity of near 5 M). Here, the observed trends are also consistent with previous experimental and simulation studies. In particular, a temperature-dependent dynamic light scattering study reported the aggregation of urea monomers into relatively larger clusters, 400 nm in size, occurs at a concentration of 6 M [47]. An IR spectroscopy–based study reported a rapid structural adjustment occurs at relevant solute concentrations, in which broken hydrogen bonds between the water and urea and the formation of urea–urea hydrogen bonds promote the generation of crystalline nuclei [44,48]. These results imply that the highly concentrated aqueous urea solution is likely populated with building units of large solute clusters rather than monomers.

In classical nucleation theory, the energetically favorable critical nucleus is directly formed from the solution, which continuously grows by incorporating sub-critical clusters, such as monomers and dimer additions. On the other hand, more recent studies have proposed a non-classical nucleation pathway, in which a highly concentrated solution is predominantly populated with large pre-nucleation clusters of oligomer species [17,21,49]. In this regard, our thermography measurement presents a compelling case of crystallization unfolding in two distinct thermal stages, distinctly different from the continuous growth envisioned in classical nucleation theory. This observation lends strong support to the non-classical pathway, suggesting the potential dominance of pre-nucleation clusters populated with oligomer species in this system.

5. Conclusions

This study demonstrates the measurement of transient thermal effects and spontaneous nucleation in a highly concentrated aqueous urea solution using a non-contact approach. The drop-evaporation method, facilitated by acoustic levitation, achieves unprecedented supersaturation levels. In situ infrared thermography monitors temperature variations on the drop surface. A comparison of heat release rates with supersaturation levels reveals two distinct stages leading to final crystallization. A gradual temperature rise occurs with increasing solution concentration and continues throughout the metastable zone. At a critical supersaturation limit (approximately S = 2), a brief temperature stagnation is observed, followed by an instantaneous temperature rise and rapid growth of polycrystalline urea crystals within 0.2 s. Here, our in situ heat release measurements on an acoustically levitated droplet strongly suggest that urea crystallization unfolds as a two-step process. It is also noteworthy that the extracted critical radius from the CNT analysis is orders of magnitude smaller than the average cluster size measured by previous dynamic light scattering studies [47]. This discrepancy suggests that analysis based on CNTs alone may not provide a complete picture of the initial nucleation processes in an aqueous urea solution. Our result also suggests that a two-step crystallization process may be a more plausible scenario. That is, pre-nucleation clusters form first, serving as an intermediate step before progressing to full crystallization rather than direct nucleation from the solution itself.