Abstract
In the present work, we have successfully predicted the refractive indices of binary mixtures containing ionic liquids (ILs) and water as a component following the approach of Gladstone–Dale and Newton. These approaches were proposed as adequate to predict the refractive indices of mixtures containing imidazolium-based ILs with water or ethanol. It requires just the knowledge of the density and refractive index of pure components to obtain the value of refractive index of binary mixtures at any composition. We have selected 30 binary systems that contain ILs from imidazolium, ammonium, pyrrolidinium, and pyridinium families for validation. The tested data comprise of more than 400 mixture points. The results are presented in terms of average percentage deviations (APDs) from the experimental values. The Gladstone–Dale method gives better results compared to the Newton approach. The reasons why these approaches give large APDs for some mixtures are discussed in the manuscript.
1. Introduction
Ionic liquids (ILs) are compounds that are entirely composed of ions [1]. The mismatch of cation and anion sizes and insufficient crystal packing are the reasons that many of these salts exist in liquid form at or around room temperature [2, 3]. Due to their peculiar properties such as low melting point compared to conventional salts, large liquid range, wide electrochemical window, solvent properties, and designer nature, their use is widespread across many disciplines [4–8].
ILs are being used in many applications where due to their high viscosity, they are most often mixed with other molecular solvents [9–11]. These mixtures differ from the mixtures of molecular solvents where only neutral molecular entities are present [12]. For many biological applications, ILs are dissolved in water to form aqueous solutions [13]. Prior to their use in a given application, the physicochemical properties (e.g., density, viscosity, surface tension, and refractive index) of such mixtures and solutions are often required.
Refractive index is an important property that is often used to characterize materials, which indicates the ratio of the velocity of light in vacuum to the velocity of light in the material [14]. It is a thermodynamic property, which depends on temperature, pressure, and wavelength [15]. Compared to other bulk properties, the measurement of refractive index is relatively fast and convenient; therefore, it is often used to gain molecular insights between the component molecules.
A survey of the literature indicates that several workers have proposed the strategies to predict the refractive indices of pure ILs. Deetlefs et al. [16] presented a simple strategy to calculate refractive indices of pure ILs using parachor and molar refraction data obtained through group contribution method. Wang et al. [17] collected a large amount of data to construct a database which was used to propose a group contribution method to predict the refractive indices of ILs. Sattari et al. [18] developed a linear quantity structure property relation (QSPR) model using genetic function approximation (GFA) to predict the refractive indices of ILs. More recently, extreme learning machine (ELM) intelligence algorithm was also used to predict the refractive indices of ILs [19].
As far as refractive indices of binary liquid mixtures containing ILs + water/molecular solvents are concerned, only a handful studies are available. Iglesias-Otero et al. [20] proposed correlations between the volumetric properties and refractive indices of binary mixtures of ILs with organic solvents. Similarly, Rilo et al. [21] presented an easy method for the prediction of refractive indices of mixtures of ILs with water/ethanol based on the approach of Gladstone–Dale and Newton. Soriano et al. [22] presented a model based on artificial neural network (ANN) to predict the refractive indices of binary solutions of ILs + alcohols. Goodarzi et al. [23] presented a predictive tool based on the least square support vector machine optimization to determine the refractive indices of mixture of IL + alcohols.
Tremendous progress has been made, in recent years, on the front of predicting refractive indices of ILs and binary mixture containing ILs; however, simple models are still unavailable. Some of the proposed sophisticated predictive models require special skills for their usage. Therefore, in this work, following the suggestions proposed by Rilo et al. [21], we have chosen the Gladstone–Dale and Newton method to determine the refractive indices of aqueous mixtures containing ILs as one of the component. Both these approaches are extremely user friendly and require just information about the refractive indices and density of pure components.
In order to validate these approaches, we have collected data for 30 IL + H2O mixtures from the literature containing ILs from different families at 298.15 K [24–34]. One of the objectives of this work is to see whether the models work for functionalized imidazolium ILs and can it be applied successfully to other families as well?
2. Results and Discussion
2.1. Collection of Refractive Index Data for IL + H2O Mixtures
Table 1 presents the density and refractive index data of neat ILs that were used in this work for the prediction of refractive indices of their binary mixtures with water at 298.15 K [24–34]. The data were used to calculate the molar volume and molar refraction of respective ILs. It must be stressed that the data for the common component (water) were slightly differing in magnitude from one source to another; therefore, an average value of its density and refractive index is reported in Table 1. However, in the calculations, the respective ρ and nD data were used.
The data are presented in a chronological order of the year of its publication, and each mixture has been assigned a number denoted with Mn, where n = 1–30. The density and refractive index data for IL, 1-allyl-3-methylimidazolium chloride were not reported; therefore, the refractive index values for the binary system M4 cannot be calculated.
The density and refractive index variations for all the collected systems as a function of mixtures composition are plotted in Figure 1. It is clear from Figure 1 that the density-composition profile of IL + H2O mixtures is system specific. In some cases, when the IL is mixed in water, the density increases up to a certain composition and afterwards reaches a plateau whereas, in some cases, the density increases linearly towards the density of IL. In a few cases, where the density of IL is lower than water, the density decreases almost linearly towards the density of ILs. In case of refractive indices, except for a few systems, on mixing the IL in water, the refractive index value increases rapidly up to a certain extent and then reaches almost linearly towards the IL refractive index.
2.2. Calculation of Refractive Index of Binary Mixtures
To calculate the refractive indices of mixtures, the following relation from Gladstone–Dale was used [35]:where nD, nIL, and are the refractive index of binary mixture, IL, and water, respectively, whereas ϕIL and represent the volume fraction of IL and water.
The volume fractions can be defined as follows:where i represents one of the component (water or IL) of binary mixtures. The density ρ at any given composition of the mixtures can be calculated from the values of the density of pure components using the following expression:
Therefore, the volume fraction of IL can be calculated as follows:
Since, for a binary mixture, , the volume fraction of water for a given system can simply be calculated as follows:
Similarly, the Newton relation to obtain the refractive indices of binary liquid mixtures using the values of pure components is indicated as follows [36]:
The results of the prediction of both approaches for some selected systems are presented in Figure 2 whereas the same for all systems in the chronological order (according to Table 1) are given in the various subsections of Figure S1 of supplementary material. It is evident that both the methods are predicting the refractive index behavior of liquid mixtures quite accurately. There does not seem any effect of the family of IL (imidazolium, pyrrolidinium, pyridinium, and ammonium) on the predictive efficiency of both the approaches.
The results are also presented in terms of average percentage deviations (APDs), which were calculated as follows:where nexp is the experimentally measured refractive index, ncal is the calculated ones, and N is the number of data points. Table 2 lists the APDs obtained for both the approaches for each system.
It must be clarified that to understand the efficiency of the G-D and Newton approach, in Table 2, the systems are divided according to the families of ILs. Afterwards, the systems are listed according to the lowest APD obtained to highest APD obtained in case of each family.
One can see that the obtained APD values are very small for both G-D and Newton methods. In general, the G-D approach is presenting lower APD values compared to the Newton. It shows the applicability of these approaches to obtain the refractive indices of IL + H2O binary systems irrespective of the family of ILs. There are systems in each family that are showing APD values that are several orders of magnitude higher compared to the APDs of other systems in the same group.. Four such systems, from each imidazolium, pyrrolidinium, pyridinium, and ammonium families, show that the highest APDs are presented in Figure 3. These results can be explained considering the applicability of these approaches to systems that show nearly ideal behavior [37].
For instance, in imidazolium family, the system containing IL 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate + H2O (M5) shows the highest APD within the family as well as among the systems undertook in this work (Table 2). It is clear from Figure 3 that both the approaches are giving completely different trend compared to the experimentally obtained linear trends of refractive index versus composition. It is interesting to note that this IL is very similar to other ILs studied in the imidazolium family except it is slightly functionalized with an additional -OH group attached to the cation. The excess volume for the system shows large negative values which indicate strong molecular interactions between the component molecules [28]. Since the system is not quasi-ideal, both the approaches were not able to consider the large change in volumes and failed to predict the correct trends for this binary system.
The other systems that show relatively high APD values among pyrrolidinium family are pyrrolidinium octanoate + H2O (M3) and pyrrolidinium nitrate + H2O (M2). It must be stressed that both of these ILs are protic ILs, and the excess volumes for these systems were large positive [25, 26]. The protic ILs influence the structure of water immensely like polar solvents [38].
In case of pyridinium family, both the approaches were able to satisfactorily predict the refractive index trends for the system M14, 1-butyl-3-methylpyridinium trifluoromethanesulfonate + H2O, but the APD value was highest among the family. The excess volumes for the system show asymmetrical curves due to large difference in the molar masses of the component molecules [30].
The case for ammonium family is very different, as all the systems are showing highest APD values among the families considered in this work. One of the reason for this behavior is due to the fact that all these systems involve protic ILs that many a times show irregular volumetric trends [31, 32]. The thermophysical properties of protic IL systems behave in a peculiar manner and are therefore difficult to predict [9].
For all ionic liquids discussed in this manuscript, experimental refractive index values (circular symbols) as a function of ionic liquid (IL) mole fraction (xIL) for the IL + H2O systems used in this work along with the predicted values using Gladstone–Dale (green line) and Newton (red line) approach at 298.15 K are plotted in Figure S1.
3. Conclusions
The refractive indices of 30 binary mixtures containing ionic liquid and water as a common component were predicted using two simple approaches, namely, Gladstone–Dale and Newton. These approaches just require the knowledge of density and refractive indices of pure components. The results were presented in terms of average percentage deviations (APDs), and satisfactory outcomes from both the approaches were obtained. Systems that were not ideal in terms of large or asymmetrical excess volume trends give high APD values. Both these approaches can be applied to any family of ILs and to the systems that show quasi-ideal behavior. However, care must be taken to use it to predict the refractive index–composition trends for systems involving protic ILs.
Data Availability
All data were included in the manuscript.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Authors’ Contributions
Mohd Sajid Ali investigated the study, proposed the methodology, wrote the original draft, and reviewed and edited the paper; Mohammad Tariq conceptualized the study, investigated the study, and reviewed and edited the paper.
Acknowledgments
The authors acknowledge the financial support through the Researchers Supporting Project number (RSPD2023R724), King Saud University, Riyadh, Saudi Arabia.
Supplementary Materials
Figure S1: experimental refractive index values (circular symbols) as a function of ionic liquid (IL) mole fraction (xIL) for the IL + H2O systems used in this work along with the predicted values using Gladstone–Dale (green line) and Newton (red line) approach at 298.15 K. The systems are presented in chronological order and marked as M1–M30 as per Table 1 of the main text. (Supplementary Materials)