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Article

Prediction of Solvatochromic Polarity Parameters for Aqueous Mixed-Solvent Systems

by
Alif Duereh
1,
Amata Anantpinijwatna
2 and
Panon Latcharote
3,*
1
Research Center of Supercritical Fluid Technology, Graduate School of Engineering, Tohoku University, Aramaki Aza Aoba 6-6-11, Aoba-ku, Sendai 980-8579, Japan
2
Department of Chemical Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
3
Department of Civil and Environmental Engineering, Faculty of Engineering, Mahidol University, Nakhon Pathom 73170, Thailand
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(23), 8480; https://doi.org/10.3390/app10238480
Submission received: 15 October 2020 / Revised: 23 November 2020 / Accepted: 24 November 2020 / Published: 27 November 2020
(This article belongs to the Section Chemical and Molecular Sciences)

Abstract

:
Solvent polarity is important data being used in solvent selections for preliminary engineering design of chemical processes. In this work, a predictive model is proposed for estimating the solvatochromic polarity of electronic transition energy (ET) of Reichardt indicator for aqueous mixtures. To validate the model, the ET values of eighteen aqueous mixtures collected from the literature were used. The predictive model provided a good estimation of ET values with an overall deviation of 2.1%, compared with an ideal model (5.1%) from the mole fraction average. The linear relationship of the contribution factor of hydrogen bond donor interactions (CFHBD) in the predictive model with Kamlet–Taft acidity was newly proposed in order to extend the model for other aqueous mixtures. The predictive model is applicable to many aqueous mixtures and simply requires three properties of pure components as: (i) ET values, (ii) gas-phase dipole moment and (iii) Kamlet–Taft acidity.

1. Introduction

The use of aqueous mixtures is preferable in many chemical processes (e.g., biomass conversion [1,2], separation and fractionation [3] and processing of active pharmaceutical ingredients [4,5,6]) because of the benefit of a safe solvent. Solvent polarity is an informative data being used in solvent selections [7,8,9,10] for preliminary engineering design and understanding the solvent effects on the chemical processes [11]. Polarity [12] is generally referred to as a solvent’s capability for solute dissolution and can be quantified with many physical properties of solvents (e.g., electronic transition energy, solubility parameters and dielectric constant). Among the physical properties of solvents, the electronic transition energy (ET) is commonly used to quantify an empirical solvent scale (also known as Reichardt’s polarity) because the parameter requires a simple measurement using a solvatochromic technique with an indicator [13,14].
The ET values of aqueous mixtures [15] generally tend to have a negative deviation from the ideality line (Figure 1b) due to preferential interactions of an indicator with cosolvents. There are the correlative models (preferential solvation model [16,17,18] and Jouyban–Acree model [19]) for representing a preferential trend in the aqueous mixtures, while there is no predictive model for estimating ET values of the mixture. It is supposed that an ideal model (Equation (1), Section 2.1) is most likely applied for estimations due to a simple calculation from a mole fraction average. However, the ideal model (dashed line, Figure 1b) caused a large deviation from experimental data (symbol, Figure 1b).
According to our previous works, the predictive models for estimating ET values [20] and Kamlet–Taft dipolarity/polarizability (KT-π*) [21,22] of nonpolar-polar mixtures have been proposed and the models provided a good predictive result as shown by the example for ET values in Figure 1a (blue solid line). Since both nonpolar-polar mixtures (Figure 1a) and aqueous mixtures (Figure 1b) show a similar negative deviation from ideality, the predictive model (Equation (2)) is expected to be applicable to the aqueous mixtures.
With preliminary assessment, the predictive model (Equation (2)) is applicable to the aqueous mixtures (blue solid line, Figure 1b). The objective of this work is to predict the polarity parameters (ET values) of aqueous systems using the predictive model (Equation (2)). The predictive model was validated by experimental ET data of Reichardt indicator for eighteen aqueous mixtures that were collected from the literature [15,23,24,25].

2. Models and Methods

2.1. Ideal Model

The ideal model is used to compare the deviation of experimental data from ideality and is defined by Equation (1):
E T ( ideal ) = x 1 E T , 1 0 + x 2 E T , 2 0
where E T , i 0 is the electronic transition energy of pure component i. Component 1 denotes water and component 2 denotes hydrogen bond acceptor (HBA) cosolvent or hydrogen bond donor (HBD) cosolvent.

2.2. Predictive Model

A predictive model was originally proposed for estimating Kamlet–Taft dipolarity/polarizability (KT-π*) [22] of binary nonpolar-polar mixtures with an assumption that the gas-phase dipole moment (µ) of the polar component can quantify a trend of mixture KT-π* values at a fixed mole composition. Due to a linear relationship between KT-π* and ET values (homomorphism line, Figure 2), the predictive model for KT-π* values can directly transform into a function form for estimating ET values for nonpolar-polar mixtures reported in our previous work [20], as shown by Equation (2). In this work, the model (Equation (2)) was used to predict the ET values of aqueous mixtures due to similar negative deviation trends in both aqueous mixtures and nonpolar-polar mixtures as mentioned in the introduction (Figure 1).
Δ E T , m i x N = μ 2 ( x 1 ln ( x 1 + 1.981 x 2 ) x 2 ln ( x 2 + 0.181 x 1 ) ) × C F HBD
where µ2 is the gas-phase dipole moment of component 2. The 1.981 and 0.181 values are the universal Wilson constant parameters (Λ12 and Λ21) for predictions and were evaluated by correlating experimental data with Wilson thermodynamic excess function [22]. The Δ E T , m i x N is relative normalized electronic transition energy and defined by Equations (3)–(5).
Δ E T , m i x N , = E T , m i x N ( x 1 E T , 1 N + x 2 E T , 2 N ) = E T , m i x N x 2
E T , m i x N = E T , m i x E T , 1 0 E T , 2 0 E T , 1 0
E T ( kcal mol 1 ) = 28591 / λ max ( nm )
where λmax (nm) is the maximum absorption of the wavelength of a solvatochromic indicator (Reichardt indicator) obtained from UV-Vis spectroscopy. The E T , m i x and E T , m i x N are the electronic transition energy and the normalized electronic transition energy of the binary mixtures. To apply the predictive model (Equation (2)) to aqueous systems studied in this work, component 1 refers to water and component 2 refers to cosolvent (HBA or HBD). According to normalization (Equation (4)), the E T , 1 N and E T , 2 N of pure components 1 and 2 in Equation (3) are set equal to zero and unity, respectively.
The CFHBD parameter in Equation (2) is the HBD contribution factor and the parameter is only applied to an aqueous mixture of HBD cosolvents due to specific interaction of HBD solvent with indicator [20] that causes a deviation in the pure E T , 2 0 value (HBD solvent) from the homomorphism line (Figure 2). The CFHBD values in Equation (6) can be estimated by a deviation of the actual ET value of pure HBD cosolvent ( E T , 2 0 ) from the homomorphism line in Figure 2 as shown in Equation (6).
C F HBD = E T 0 , Non E T , 2 0
where E T 0 , Non is a non-HBD bonding ET value of pure HBD cosolvents defined as a linear function of dipolarity/polarizability (KT-π*), that is the homomorphism linear line in Figure 2. The linear relationships of E T 0 , Non were given in detail in our previous work [20], and the CFHBD values of nine HBD cosolvents studied in this work are given in Table 1 along with their Kamlet–Taft acidity (α).
An average CFHBD value from three indicators (Table 1) was used in predictions (Equation (2)) for nine aqueous mixtures of HBD cosolvents. To extend to other HBD cosolvents, a linear relationship of CFHBD with Kamlet–Taft acidity (α) was proposed in Equation (7) and Figure 3, because the α values of HBD cosolvents are widely available in the literature [27,28].
C F HBD = 2.766 α 0.0115 ,   ( R 2   =   0.89 )
Figure 4 shows a flow chart developed in this work for predicting ET values of aqueous mixtures that is divided into five steps. In step 1, pure properties of electronic transition energy ( E T , i 0 ) and gas-phase dipole moment (µ2) of components 1 and 2 are compiled from the literature. In step 2, solvent characteristics of component 2 (cosolvent) are determined to check HBD ability by considering their molecular structures and KT-acidity. For example, HBD cosolvents are able to donate a proton so that their KT-acidity values are relatively high (Table 1). On the other hand, HBA cosolvents lack proton donor groups and, thus, the CFHBD value of HBA cosolvent is equal to unity. In step 3, CFHBD values of HBD cosolvent are calculated by either Figure 2 or Equation (7). In steps 4 and 5, the predictive model (Equation (2)) was used to estimate the ET values of aqueous mixtures and was validated, respectively. To validate the predictive model in step 5, nine aqueous mixtures of HBA cosolvents and nine aqueous mixtures of HBD cosolvents (Table 2) were used and discussed in Section 3. Table 2 tabulates the E T , i 0 , µ2 [29], Hunter basicity (βH) of component 2 [30,31] and CFHBD values of solvents used in the predictions.

2.3. Evaluation of the Frameworks

Average relative deviation (ARD) was used to evaluate a deviation between experimental ( E T Exp ) and calculated ( E T Cal ) data as shown in Equation (8):
ARD   ( % )   =   ( 1 / N ) | ( E T Cal E T Exp ) / E T Exp | × 100

3. Results and Discussion

3.1. Prediction for Aqueous Mixtures of HBA Cosolvents

Figure 5 shows the ET values of nine aqueous mixtures of water (1)—HBA cosolvent (2) as a function of component 2 (HBA cosolvent). The ET values of all aqueous mixtures (Figure 5) exhibited a negative deviation from the ideality (dashed lines, Figure 5), except for the aqueous mixtures of acetonitrile (ACN), tetrahydrofuran (THF) and gamma-butyrolactone (GBL) that showed a sigmoid function (Figure 5a–c). Blue solid lines (Figure 5) show predicted ET values of the aqueous mixture using Equation (2) without CFHBD value (CFHBD = 1) that generally tended toward the experimental data (symbols, Figure 5).
Table 2 shows a comparison of ARD values obtained between the ideal model (Equation (1)) and predictive model (Equation (2)) for the aqueous mixtures of HBA cosolvents (entries 1–9, Table 2) and HBD cosolvent (entries 10–18, Table 2). The predictive model (Equation (2)) generally provided a lower ARD value (2.7%, entries 1–9, Table 2) than that estimated from the ideal model (5.4%). However, the model gave a relatively high ARD value (entries 1–3, Table 2) for the aqueous mixtures that showed the sigmoid functions (Figure 5a–c). These results inferred a limitation of the predictive model and were discussed later in Section 3.4. The predictive results of aqueous mixtures of HBD cosolvents were discussed in the following section.

3.2. Prediction for Aqueous Mixtures of HBD Cosolvents

Figure 6 shows the ET values of nine aqueous mixtures of water (1)—HBD solvent (2) as a function of component 2 (HBD solvent) that also exhibited a negative deviation from the ideality. A comparison in predictive model (Equation (2)) with considering CFHBD value (Table 1) and without considering CFHBD value (CFHBD = 1). Red solid lines in Figure 6 show predictions with considering CFHBD value, while the blue ones are the predictions without considering CFHBD value.
The predictive model with the addition of CFHBD values (red solid lines, Figure 6) could provide a better result in the calculated ET value that followed the experimental data than the result without the CFHBD value (blue solid lines, Figure 6). The ARD values obtained from the predictive model (Equation (2)) with considering CFHBD value (1.6%, entries 10–18, Table 2) are lower than those estimated from the ideal model (4.8%). Figure 7 shows parity plots of calculated ET values that are estimated from the predictive model (Figure 7a) and the ideal model (Figure 7b). The estimated ET values from the predictive model (R2 = 0.91, Figure 7a) are less scattered than those obtained from the ideal model (R2 = 0.81, Figure 7b).

3.3. Evaluation of CFHBD Methods for Predictions

In Section 3.2, the predicted ET values of aqueous mixtures of HBD cosolvents were estimated based on the actual CFHBD values evaluated from Figure 2 and Table 1. In the section, a comparison in evaluated ET values between actual data (Table 1) and calculations with KT-acidity (Equation (7)) was made for predictions. Red solid lines (Figure 6) show predicted ET values of the mixtures with actual CFHBD values, while the green solid lines (Figure 6) show predictions using calculated CFHBD values from the correlation (Equation (7)). The predictive model with the calculated CFHBD values provided a similar trend in predictions with the actual CFHBD values (Figure 6), in which the ARD values from the calculated CFHBD (gray-shaded rows, Table 2) are comparable to those estimated from the actual ones (entries 10–18, Table 2).

3.4. Limitation of the Predictive Model

According to predictive results in Section 3.1, the model (Equation (2)) provided a high ARD value for aqueous mixtures having a sigmoid function (entries 1–3, Table 2). Marcus reported [33,34] that the sigmoid trends were found in aqueous mixtures when microheterogeneity occurred. It is expected that the microheterogeneity phenomenon caused a high error in predictions because this phenomenon was not considered in the development of the model as mentioned in Section 2.2. Hunter basicity of HBA solvents (βH, Table 2) can quantify the hydration shell strength in aqueous mixtures [35]. It was found that the sigmoid behaviors occurred in the aqueous mixtures that have low βH values (βH ≤ 5.3, entries 1–3, Table 2). Thus, the model (Equation (2)) is effective for predicting the aqueous mixtures having high βH values (βH ≥ 5.3).

4. Conclusions

In this work, a predictive model is proposed for estimating the solvatochromic polarity of electronic transition energy (ET) for aqueous mixtures. The function form for ET values for aqueous mixtures can be adopted from the previous model for nonpolar-polar mixtures due to similar interactions and trends in the mixture ET values in both systems. The predictive model was validated by eighteen aqueous mixtures and was found to give a reliable ET value with an overall deviation of 2.1%. Three properties of pure components are basically needed for predictions: (i) ET values, (ii) gas-phase dipole moment and (iii) Kamlet–Taft acidity.

Author Contributions

Conceptualization, A.D. and A.A.; methodology, A.D., A.A. and P.L.; software, A.D. and P.L.; validation, A.D., A.A. and P.L.; formal analysis, A.D. and A.A.; investigation, A.D. and A.A.; resources, A.D.; data curation, A.D.; writing—original draft preparation, A.D., A.A. and P.L.; writing—review and editing, A.D., A.A. and P.L.; visualization, A.D. and P.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding and The APC was funded by the Mahidol University.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

AcOHacetic acid
ACNacetonitrile
ARDaverage relative deviation, according to Equation (8)
BuOH1-butanol
DMFdimethylformamide
DMSOdimethyl sulfoxide
ETGethylene glycol
EtOHethanol
FAformamide
GBLgamma butyrolactone
GVLgamma valerolactone
HBAhydrogen bond acceptor
HBDhydrogen bond donor
iPrOH2-propanol
Indindicator
KTKamlet–Taft solvatochromic parameter
MeOHmethanol
Nile red9-diethylamino-5-benzo(a) phenoxazinone indicator
NMPN-Methyl-2-pyrrolidone
Phenol blue N, N-dimethylindoaniline indicator
PrOH1-propanol
PYR2-pyrrolidinone
Reichardt 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridinio) phenolate indicator
T-BuOHtert-butyl alcohol
THFtetrahydrofuran
Latin symbols
CFHBDHBD contribution factor, according to Equation (6)
xmole fraction of solvent i
Greek symbols
βHHunter basicity
αKamlet–Taft acidity
ETelectronic transition of solvent polarity
E T 0 , Non non-HBD bonding electronic transition, according to Equation (6)
Δ E T , m i x N relative normalized electronic transition energy, according to Equation (3)
E T , m i x N normalized electronic transition energy, according to Equation (4)
ET (ideal)ideal electronic transition energy, according to Equation (1)
E T Cal calculated electronic transition energy, according to Equation (8)
µgas-phase dipole moments
π*Kamlet–Taft dipolarity/polarizability
Superscript
0pure property
Nnormalized property
Subscript
1water, solvent type 1
2HBA or HBD, solvent type 2
mixmixture property

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Figure 1. Comparison in electronic transition (ET, kcal·mol−1) for (a) nonpolar-polar systems of carbon tetrachloride (1)—dimethylformamide (2) and (b) aqueous systems of water (1)—dimethylformamide (2) as a function of mole composition of component 2 (x2) at 25 °C. Black dashed lines show calculations from the ideal model (Equation (1)). Blue solid lines show predictions with the predictive model (Equation (2)) without considering hydrogen bond donor (HBD) contribution factor (CFHBD = 1). The ET values in part (a) were collected from the phenol blue indicator [26]. The ET values in part (b) were obtained from the Reichardt indicator [15].
Figure 1. Comparison in electronic transition (ET, kcal·mol−1) for (a) nonpolar-polar systems of carbon tetrachloride (1)—dimethylformamide (2) and (b) aqueous systems of water (1)—dimethylformamide (2) as a function of mole composition of component 2 (x2) at 25 °C. Black dashed lines show calculations from the ideal model (Equation (1)). Blue solid lines show predictions with the predictive model (Equation (2)) without considering hydrogen bond donor (HBD) contribution factor (CFHBD = 1). The ET values in part (a) were collected from the phenol blue indicator [26]. The ET values in part (b) were obtained from the Reichardt indicator [15].
Applsci 10 08480 g001
Figure 2. Plot of Kamlet–Taft dipolarity/polarizability (KT-π*) and electronic transition ( E T 0 , kcal·mol−1) of three indicators as (a) Reichardt indicator, (b) phenol blue indicator and (c) Nile red indicator in () pure nonpolar solvent, () pure hydrogen bond acceptor (HBA) solvent and pure polar hydrogen bond donor (HBD) solvent. Symbols of HBD solvents are given in Table 1. Solid line shows a linear relationship (reference homomorphism line) of KT-π* values and ET values of pure nonpolar solvents and pure HBA solvents. The deviation of ET values of pure HBD solvents from the linear line is due to HBD contribution. Data are given in detail in our previous work [20].
Figure 2. Plot of Kamlet–Taft dipolarity/polarizability (KT-π*) and electronic transition ( E T 0 , kcal·mol−1) of three indicators as (a) Reichardt indicator, (b) phenol blue indicator and (c) Nile red indicator in () pure nonpolar solvent, () pure hydrogen bond acceptor (HBA) solvent and pure polar hydrogen bond donor (HBD) solvent. Symbols of HBD solvents are given in Table 1. Solid line shows a linear relationship (reference homomorphism line) of KT-π* values and ET values of pure nonpolar solvents and pure HBA solvents. The deviation of ET values of pure HBD solvents from the linear line is due to HBD contribution. Data are given in detail in our previous work [20].
Applsci 10 08480 g002
Figure 3. Relationship of HBD contribution factor (CFHBD) with Kamlet–Taft acidity (KT-α) of hydrogen bond donor (HBD) cosolvents at 25 °C. The CFHBD and KT-α data are given in Table 1. Dashed line represents Equation (7). Symbols of HBD solvents are given in Table 1.
Figure 3. Relationship of HBD contribution factor (CFHBD) with Kamlet–Taft acidity (KT-α) of hydrogen bond donor (HBD) cosolvents at 25 °C. The CFHBD and KT-α data are given in Table 1. Dashed line represents Equation (7). Symbols of HBD solvents are given in Table 1.
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Figure 4. Flow chart for predicting electronic transition (ET) of aqueous mixture with five steps.
Figure 4. Flow chart for predicting electronic transition (ET) of aqueous mixture with five steps.
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Figure 5. Electronic transition of (ET (30), kcal·mol−1) of nine aqueous mixtures of water (1)—hydrogen bond acceptor (HBA, 2) as a function of mole composition of component 2 (x2) at 25 °C. Symbols (ai) and reference sources are given in Table 2 (entries 1–9). Black dashed lines show calculations from the ideal model (Equation (1)). Blue solid lines show predictions with the predictive model (Equation (2)) without considering HBD contribution factor (CFHBD = 1).
Figure 5. Electronic transition of (ET (30), kcal·mol−1) of nine aqueous mixtures of water (1)—hydrogen bond acceptor (HBA, 2) as a function of mole composition of component 2 (x2) at 25 °C. Symbols (ai) and reference sources are given in Table 2 (entries 1–9). Black dashed lines show calculations from the ideal model (Equation (1)). Blue solid lines show predictions with the predictive model (Equation (2)) without considering HBD contribution factor (CFHBD = 1).
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Figure 6. Electronic transition of (ET (30), kcal·mol−1) of nine aqueous mixtures of water (1)—hydrogen bond donor (HBD, 2) as a function of mole composition of component 2 (x2) at 25 °C. Symbols (ai) and reference sources are given in Table 2 (entries 10–18). Black dashed lines show calculations from the ideal model (Equation (1)). Blue solid lines show predictions with the predictive model (Equation (2)) without considering HBD contribution factor (CFHBD = 1). Red solid lines show prediction with the predictive model (Equation (2)) with considering actual CFHBD values in Table 1. Green solid lines show prediction with the predictive model (Equation (2)) with considering calculated CFHBD values using Equation (7).
Figure 6. Electronic transition of (ET (30), kcal·mol−1) of nine aqueous mixtures of water (1)—hydrogen bond donor (HBD, 2) as a function of mole composition of component 2 (x2) at 25 °C. Symbols (ai) and reference sources are given in Table 2 (entries 10–18). Black dashed lines show calculations from the ideal model (Equation (1)). Blue solid lines show predictions with the predictive model (Equation (2)) without considering HBD contribution factor (CFHBD = 1). Red solid lines show prediction with the predictive model (Equation (2)) with considering actual CFHBD values in Table 1. Green solid lines show prediction with the predictive model (Equation (2)) with considering calculated CFHBD values using Equation (7).
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Figure 7. Parity plots of electronic transition (ET) in eighteen aqueous mixtures obtained from (a) the predictive model (Equation (2), R2 = 0.91) and (b) the ideal model (Equation (1), R2 = 0.81). Symbols and conditions are defined in Table 2.
Figure 7. Parity plots of electronic transition (ET) in eighteen aqueous mixtures obtained from (a) the predictive model (Equation (2), R2 = 0.91) and (b) the ideal model (Equation (1), R2 = 0.81). Symbols and conditions are defined in Table 2.
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Table 1. Pure properties of hydrogen bond donor (HBD) at 25 °C showing Kamlet–Taft acidity (KT-α) [27,28] and HBD contribution factor (CFHBD) evaluated from three indicators (Ind.) a.
Table 1. Pure properties of hydrogen bond donor (HBD) at 25 °C showing Kamlet–Taft acidity (KT-α) [27,28] and HBD contribution factor (CFHBD) evaluated from three indicators (Ind.) a.
EntryHBD SolventsKT-αActual CFHBD (-) bCalculated CFHBD (-) c
(Symbol)(Abbreviation)(-)Ind. 1Ind. 2Ind. 3Avg(Equation (7))
1 ( Applsci 10 08480 i001)Methanol (MeOH)1.003.652.322.342.772.75
2 ( Applsci 10 08480 i002)Ethanol (EtOH)0.893.052.212.212.492.45
3 ( Applsci 10 08480 i003)1-Propanol (PrOH)0.842.791.962.512.422.31
4 ( Applsci 10 08480 i004)2-Propanol (iPrOH)0.762.441.722.172.112.09
5 ( Applsci 10 08480 i005)1-Butanol (BuOH)0.842.652.043.042.582.31
6 ( Applsci 10 08480 i006)Tert-Butanol (T-BuOH)-2.65--2.65-
7 ( Applsci 10 08480 i007)Ethylene glycol (ETG)0.903.01-1.592.302.48
8 ( Applsci 10 08480 i008)Acetic acid (AcOH)1.124.341.832.782.983.09
9 ( Applsci 10 08480 i009)Formamide (FA)0.632.091.271.321.561.73
a Indicators: Ind. 1 = 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridinio) phenolate indicator; Ind. 2 = phenol blue and Ind. 3 = Nile red. b Actual CFHBD values are evaluated from Figure 2. c Calculated CFHBD values are obtained from Equation (7).
Table 2. Comparison between electronic transition (ET, kcal·mol−1) values calculated with the predictive model (Equation (2)) and ideal model (Equation (1)) for nine aqueous mixtures of hydrogen bond acceptor (HBA) cosolvents and nine aqueous mixtures of hydrogen bond donor (HBD) cosolvents at 25 °C that were obtained with Reichardt indicator. Average relative deviations (ARD) were calculated with Equation (8) along with dipole moment of component 2 (µ2), HBD contribution factor (CFHBD), Hunter basicity (βH) of component 2, pure properties of electronic transition energy ( E T , i 0 ) and the number of data used (N). Gray-shaded rows indicate the ARD results estimated from the calculated CFHBD (Equation (7)).
Table 2. Comparison between electronic transition (ET, kcal·mol−1) values calculated with the predictive model (Equation (2)) and ideal model (Equation (1)) for nine aqueous mixtures of hydrogen bond acceptor (HBA) cosolvents and nine aqueous mixtures of hydrogen bond donor (HBD) cosolvents at 25 °C that were obtained with Reichardt indicator. Average relative deviations (ARD) were calculated with Equation (8) along with dipole moment of component 2 (µ2), HBD contribution factor (CFHBD), Hunter basicity (βH) of component 2, pure properties of electronic transition energy ( E T , i 0 ) and the number of data used (N). Gray-shaded rows indicate the ARD results estimated from the calculated CFHBD (Equation (7)).
EntryComponent 2µ2CFHBDβH E T 0 ARD (%)NRef.
(Symbol) D(-)(-)(1)(2)PredictIdeal
Water (1)—HBA cosolvent (2)
1 ()ACN3.921.004.763.1046.006.643.3611[15]
2 ()THF1.631.005.363.1037.504.364.9711[15]
3 ()GBL3.821.005.363.0044.623.454.4212[23]
4 ()GVL5.301.005.363.0047.852.616.2712[23]
5 ()PYR3.101.008.363.0047.901.495.2411[24]
6 ()NMP4.091.008.363.0042.201.859.8510[24]
7 ()DMF3.861.008.363.1043.801.374.7711[15]
8 ()DMSO3.961.008.963.1045.000.755.2911[15]
9 ()Pyridine2.191.007.063.1040.301.294.7711[15]
Overall (aqueous HBA mixtures)2.655.44
Water (1)—HBD cosolvent (2)
10 ( Applsci 10 08480 i001)MeOH1.702.775.863.1055.700.232.4011[15]
2.75 0.23
11 ( Applsci 10 08480 i002)EtOH1.692.495.863.1051.700.343.9211[15]
2.45 0.38
12 ( Applsci 10 08480 i003)PrOH1.662.425.863.1050.601.425.1411[15]
2.31 1.53
13 ( Applsci 10 08480 i004)iPrOH1.662.115.863.1048.702.646.7311[15]
2.09 2.67
14 ( Applsci 10 08480 i005)BuOH1.662.585.863.1043.902.584.2810[15]
2.31 2.19
15 ( Applsci 10 08480 i006)T-BuOH1.672.655.863.1043.304.6712.5411[25]
16 ( Applsci 10 08480 i007)ETG2.312.30-63.1056.240.502.4410[15]
2.48 0.69
17 ( Applsci 10 08480 i008)AcOH1.742.985.363.1055.001.032.1011[15]
3.09 1.12
18 ( Applsci 10 08480 i009)FA3.731.565.863.1053.740.973.2211[15]
1.73 1.32
Overall (aqueous HBD mixtures)1.604.75
Overall (both HBA and HBD mixtures)2.125.10197
The µ2 values for all solvents are taken from handbook [29], except for GVL [32]. The overall average relative deviation (ARD) values are calculated without considering the values in the gray-shaded rows. Solvent abbreviations for HBD cosolvent are given in Table 1. Solvent abbreviations for HBA cosolvent: ACN = acetonitrile; THF = tetrahydrofuran; GBL = gamma butyrolactone; GVL = gamma valerolactone; PYR = 2-pyrrolidinone; NMP = N-methyl-2-pyrrolidone; DMF = dimethylformamide and DMSO = dimethyl sulfoxide.
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Duereh, A.; Anantpinijwatna, A.; Latcharote, P. Prediction of Solvatochromic Polarity Parameters for Aqueous Mixed-Solvent Systems. Appl. Sci. 2020, 10, 8480. https://doi.org/10.3390/app10238480

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Duereh A, Anantpinijwatna A, Latcharote P. Prediction of Solvatochromic Polarity Parameters for Aqueous Mixed-Solvent Systems. Applied Sciences. 2020; 10(23):8480. https://doi.org/10.3390/app10238480

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Duereh, Alif, Amata Anantpinijwatna, and Panon Latcharote. 2020. "Prediction of Solvatochromic Polarity Parameters for Aqueous Mixed-Solvent Systems" Applied Sciences 10, no. 23: 8480. https://doi.org/10.3390/app10238480

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