## 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 \(\cdots\) 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 \(\Delta\)T = 58 degrees by the relation \(\Delta\)T = \(\Delta\)Q/ (m C\({}_{p}\)) within an initial solute mass of 0.004 g. Therefore, the rise in temperature in supersaturation 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.