Introduction

Separation is an inevitable stage in relatively all industrial processes ranging from the nanoscale [1] to large-scale wastewater treatment plants [2]. Although there are broad ranges of separation processes, solvent-based processes like liquid–liquid extraction [3], absorption [4], and leaching [5] are more common in industrial applications. Anastas and Kirchhoff stated that about eighty volumetric percent of chemicals used in a process are solvent media [6]. Since solvents may undesirably affect environmental and human health [7], serious attention needs to be given to their proper selection. Furthermore, the solvents are better to fulfill the requirements of the green technology, pose low toxicity, and have low volatility [6].

Deep eutectic solvents (DES) have been approved as a new category of sustainable solvents that fully satisfy the green chemistry principles [8]. Furthermore, they have very low toxicity, are easy to synthesize at relatively low expense, and are biodegradable [8]. They can be synthesized by mixing two compounds so that their blend shows a significantly lower melting temperature than its pure constituents [9]. The hydrogen bond donors (HBD) and hydrogen bond acceptors (HBA) constitute the chemical structure of the deep eutectic solvents [10].

Deep eutectic solvents have various applications, such as metal electropolishing [11], gas absorption and separation [12], polymer fabrication [13], biomass processing [14], water absorption [15], drug solubilization [8], biocatalyst synthesis [16], nanotechnology [17], food industry [18], natural gas sweetening [19], biomass pretreatment and conversion [20], and biomaterials extraction [21]. They also considered as media for manufacturing nanosized and functional materials [22].

The precise value of transport [23], thermal [24], and physicochemical [25] properties of deep eutectic solvents are necessary for the appropriate design and operation of these processes. Moreover, it is mandatory to characterize thermophysical features of new solvents to investigate their potential for commercial applications [26]. Therefore researchers experimentally measured thermal conductivity [23], molar heat capacity [24], [26], [27], [28], [29], [30], [31], [32], density [33], refractive index [33], surface tension [34], and diffusion and kinetics coefficients [35] of deep eutectic solvents.

Furthermore, computer-based technologies such as process optimization prefer to handle mathematical models instead of working with scatter experimental data [36]. Machine learning methods are efficient tools to analyze historical data of fluidized beds [38], [39], wearable biomedical systems [40], sulfur solubility in hydrogen [41], early disease detection [44], ionic liquid thermodynamic properties [45], [46], nanofluid thermal features [48], hydrate formation [49], and carbon dioxide capture. Moreover, different computational approaches have been developed for estimating molar heat capacity [10], thermal conductivity [50], surface tension [51], density [52], viscosity [53], CO₂ capture ability [54], and refractive index [55] of deep eutectic solvents.

Thermal features like molar heat capacity (Cp) help set operation conditions in processes that utilize deep eutectic solvents [26]. This property is also required to evaluate the DES suitability in energy-based applications [56]. However, there are only eight experimental studies [24], [26], [27], [28], [29], [30], [31], [32] and one modeling investigation [10] about the molar Cp of DESs. As mentioned earlier, the experimental measurements are often complicated and time-consuming [10], have economic cost [10], and contain different levels of noise [57] and uncertainties [58]. Furthermore, the available empirical correlations provide a prediction with a relatively high uncertainty [10]. The suggested empirical correlations in the literature even present an absolute average relative deviation (AARD%) of more than 50%. Hence, it seems that heat capacity has not received the attention it deserves.

Thus, the current work proposes a universal model based on least-squares support vector regression with the Gaussian kernel function (LSSVR-G) to estimate the molar heat capacity of deep eutectic solvents. This LSSVR-G has been chosen among fourteen intelligent and two regression-based methodologies. The performance of the constructed LSSVR-G has been checked by the 503 experimental molar heat capacities of twenty-six deep eutectic solvents and five empirical correlations in the literature (one model for DES and four models for ionic liquids).