Developing a global approach for determining the molar heat capacity of deep eutectic solvents

Table of Contents


Deep eutectic solvents (DES) are a new class of green solvents. Reliable characterization of DESs is a prerequisite for their successful applications. The molar heat capacity (Cp) is likely an essential thermal property often measured through expensive and time-consuming experimentations. Hence, it is necessary to derive an accurate model for Cp calculation from readily available features. 

This study introduces a universal computational approach for calculating the Cp of 26 different DESs as a function of temperature, acentric factor, and critical properties. Ranking investigations over four accuracy indices approve that the least-squares support vector regression with the Gaussian kernel function (LSSVR-G) is more reliable than thirteen intelligent and two regression-based models. The LSSVR-G estimates 503 experimental data points of DES molar heat capacity with an absolute average relative deviation (AARD%) of 0.27%. The results show that the LSSVR accuracy is better than the existing empirical correlations in the literature.

Graphical abstract


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).

Section snippets

Materials and methods

The section focuses on reviewing the experimental data and presenting the mathematical formula of the available empirical correlations for the molar heat capacity of the deep eutectic solvents. Furthermore, fundamentals of the computational estimators employed to simulate the molar heat capacity of the deep eutectic solvents have also been introduced. Indeed, four types of artificial neural networks, four adaptive neuro-fuzzy inference systems, and three least-squares support vector regressions 

Results and discussion

This section describes the developments and selection stages of the artificial intelligence (AI) models, uses different algebraic and graphic analyses to investigate their accuracy, and compares their predictions with the empirical correlations. Then, outlier and valid measurements are identified using the leverage methodology. Finally, the effect of temperature on the molar heat capacity of the deep eutectic solvent has been investigated.


This study approved that the least-squares support vector regression equipped with the Gaussian kernel function (LSSVR-G) is the most reliable/generalized model for estimating the molar heat capacity of the deep eutectic solvents. Combining the statistical and ranking investigations selects the LSSVR-G among huge intelligent models from fourteen different computational categories. A comparative analysis between LSSVR-G and five empirical correlations in the literature approved that the earlier

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


The authors would like to thank Dr. Amith Khandakar (Qatar University, Qatar) and Dr. Menad Nait Amar (Sonatrach, Algeria) for their valuable help in developing the decision tree (DT) and gene expression programming (GEP) models requested by reviewers during the revision stage.

Keywords: pretreatment and conversion, deep eutectic solvents dess, thermal conductivities, conductivity of deep eutectic solvents, thermal conductivity of deep eutectic, temperature range from to, natural deep eutectic