Aqueous biphasic systems based on ethyl lactate: Molecular interactions and modelling

Figures & data

Table 1. Chemicals used in this study.

Chemical	Molecular formula	Manufacturers’ stated purity (mass %)	CAS no.	Source
Ethyl lactate	C5H10O3	98	687-47-8	Sigma-Aldrich
Potassium triphosphate	K3PO4	≥ 99	7778-53-2	Sigma-Aldrich
Potassium diphosphate	K2HPO4	≥ 99	7758-11-4	Sigma-Aldrich
Potassium carbonate	K2CO3	≥ 99	584-08-7	Sigma-Aldrich
Trisodium citrate	Na3C6H5O7	≥ 99	6132-04-3	Sigma-Aldrich
Disodium tartrate dihydrate	Na2C4H4O6·2H2O	≥ 99	6106-24-7	Sigma-Aldrich
Disodium succinate	Na2C4H4O4	≥ 98	150-90-3	Sigma-Aldrich
Potassium thiosulfate	K2S2O3	> 95	10294-66-3	Sigma-Aldrich
Sodium thiosulfate	Na2S2O3	99	10102-17-7	Sigma-Aldrich
Ammonium thiosulfate	(NH4)2S2O3	96	7783-18-8	Fisher Scientific

Figure 1. The architecture of an artificial neural network with three layers: input, hidden and output. Letters w and b stand for adjustable weights and bias, respectively.

Table 2. Exponents D and E that gave the best fitting and corresponding root mean square deviations, RMSD (Equation 4(4) $$\mathit{RMSD}=\sqrt{\frac{\sum _i{\left(w_{EL}^{\mathit{calc}}-w_{EL}^{\exp }\right)}^2}{N}}$$(4) ) and r² (Equation 5(5) $$r^2=1-\frac{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{calc}}\right)}^2}{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{mean}}\right)}^2}$$(5) ), obtained by fitting Equation (1)(1) $$w_{\mathit{sol}}=A·\exp \left(B·w_{\mathrm{salt}}^D-C·w_{\mathit{salt}}^E\right)$$(1) to binodal data of systems containing ethyl lactate, water and salt.

Salt	D	E	r^2	RMSD
K3PO4	0.20	2.5	0.9987	0.0084
K2HPO4	0.20	2.0	0.9984	0.0102
K2CO3	0.20	2.5	0.9992	0.0074
Na3citrate	0.50	2.0	0.9994	0.0055
Na2tartrate	0.01−0.9	1.0	0.9984	0.0073
Na2succinate	0.01−0.02	1.0	0.9993	0.0058
K2S2O3	0.50	1.5	0.9983	0.0089
Na2S2O3	0.05	1.5	0.9983	0.0107
(NH4)2S2O3	0.05−0.20	1.5	0.9945	0.0166

Figure 2. Average coefficient of determination (r²) obtained using different exponents of Merchuk’s equation (Equation 1(1) $$w_{\mathit{sol}}=A·\exp \left(B·w_{\mathrm{salt}}^D-C·w_{\mathit{salt}}^E\right)$$(1) ), fitted to binodal data given in Table S1 for the systems containing ethyl lactate, water and various salts at 298 K.

Figure 3. Comparison of coefficient of determination (r²) obtained by fitting Merchuk’s equation (Equation 1(1) $$w_{\mathit{sol}}=A·\exp \left(B·w_{\mathrm{salt}}^D-C·w_{\mathit{salt}}^E\right)$$(1) ) for the systems containing ethyl lactate, water and various salts system at 298 K, using two different sets of exponents: D = 0.05 and E = 1.5 (black bars) and D = 0.5 and E = 3 (white bars).

Table 3. Summary of root mean square deviations (RMSD from Equation 4(4) $$\mathit{RMSD}=\sqrt{\frac{\sum _i{\left(w_{EL}^{\mathit{calc}}-w_{EL}^{\exp }\right)}^2}{N}}$$(4) ) and coefficient of determination (r² from Equation 5(5) $$r^2=1-\frac{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{calc}}\right)}^2}{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{mean}}\right)}^2}$$(5) ) obtained using Equation (2)(2) $$w_{\mathit{sol}}=A·\exp \left(B·w_{\mathit{salt}}\right)$$(2) .

	NP*	A	B	RMSD	r^2
K3PO4	22	0.8046	−10.17	0.0289	0.9849
K2HPO4	13	0.7852	−10.89	0.0238	0.9915
K2CO3	13	0.7877	−7.876	0.0343	0.9835
Na3citrate	11	0.7423	−9.790	0.0141	0.9960
Na2tartrate	11	0.7534	−9.317	0.0074	0.9984
Na2succinate	10	0.8641	−10.36	0.0077	0.9989
K2S2O3	13	0.8352	−7.703	0.0101	0.9978
Na2S2O3	13	0.8616	−11.64	0.0197	0.9944
(NH4)2S2O3	12	0.8777	−8.005	0.0180	0.9952
Average				0.0182	0.9932

*NP – Number of data points

Table 4. Summary of root mean square deviations (RMSD from Equation 4(4) $$\mathit{RMSD}=\sqrt{\frac{\sum _i{\left(w_{EL}^{\mathit{calc}}-w_{EL}^{\exp }\right)}^2}{N}}$$(4) ) and coefficient of determination (r² from Equation (5)(5) $$r^2=1-\frac{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{calc}}\right)}^2}{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{mean}}\right)}^2}$$(5) ) obtained using Equation (3)(3) $$\ln \left(V_{213}^{\mathrm{*}}\frac{w_{\mathit{salt}}}{M_{\mathit{salt}}}+f_{213}\right)+V_{213}^{\mathrm{*}}\frac{w_{\mathit{sol}}}{M_{\mathit{sol}}}=0$$(3) .

	NP*	${\mathit{V}}_{213}^{\mathit{*}}$/ g mol^−1	f213	RMSD	r^2
K3PO4	22	533	0.010	0.0262	0.9876
K2HPO4	13	506	0.017	0.0244	0.9910
K2CO3	13	347	0.096	0.0321	0.9844
Na3citrate	11	606	0.010	0.0343	0.9763
Na2tartrate	11	512	0.018	0.0235	0.9837
Na2succinate	10	459	0.018	0.0264	0.9866
K2S2O3	13	441	0.016	0.0194	0.9919
Na2S2O3	13	474	0.014	0.0288	0.9880
(NH4)2S2O3	12	362	0.057	0.0222	0.9927
Average				0.0264	0.9869

*NP – Number of data points

Table 5. Summary of root mean square deviations (RMSD from Equation 4(4) $$\mathit{RMSD}=\sqrt{\frac{\sum _i{\left(w_{EL}^{\mathit{calc}}-w_{EL}^{\exp }\right)}^2}{N}}$$(4) ) and coefficient of determination (r² from Equation 5(5) $$r^2=1-\frac{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{calc}}\right)}^2}{\sum _i{\left(w_{EL}^{\exp }-w_{EL}^{\mathit{mean}}\right)}^2}$$(5) ) obtained using Equation (3)(3) $$\ln \left(V_{213}^{\mathrm{*}}\frac{w_{\mathit{salt}}}{M_{\mathit{salt}}}+f_{213}\right)+V_{213}^{\mathrm{*}}\frac{w_{\mathit{sol}}}{M_{\mathit{sol}}}=0$$(3) , assuming that f₂₁₃ = 0.

	NP*	${\mathit{V}}_{213}^{\mathit{*}}$/ g mol^−1	f213	RMSD	r^2
K3PO4	22	559	0	0.0330	0.9804
K2HPO4	13	547	0	0.0359	0.9805
K2CO3	13	513	0	0.1334	0.7300
Na3citrate	11	642	0	0.0425	0.9636
Na2tartrate	11	539	0	0.0295	0.9742
Na2succinate	10	491	0	0.0397	0.9696
K2S2O3	13	459	0	0.0228	0.9888
Na2S2O3	13	502	0	0.0363	0.9810
(NH4)2S2O3	12	443	0	0.0801	0.9052
Average				0.0503	0.9415

*NP – Number of data points

Figure 4. Binodal lines for the nine ABS containing ethyl lactate, water and salt (Na₃citrate—black, K₃PO₄—grey, Na₂tartrate—bark blue, K₂HPO₄—red, Na₂S₂O₃—yellow, Na₂succinate—green, K₂S₂O₃—brown, (NH₄)₂S₂O₃—pink and K₂CO₃—light blue) obtained by fitting Equation (3)(3) $$\ln \left(V_{213}^{\mathrm{*}}\frac{w_{\mathit{salt}}}{M_{\mathit{salt}}}+f_{213}\right)+V_{213}^{\mathrm{*}}\frac{w_{\mathit{sol}}}{M_{\mathit{sol}}}=0$$(3) using constants given in Table 4, expressed in molalities (m). The insert shows the obtained values for $V_{213}^{*}$ for each system (the same color code applies).

Figure 5. Effective excluded volume, $V_{213}^{*}$ (Table 4), as a function of molecular masse of salt.

Figure 6. Relationship of average RMSD and transfer functions in the hidden layer.

Figure 7. Relationship of average RMSD and the number of neurons in the hidden layer.

Figure 8. (a) Regression of training, validation and test steps for the optimum artificial neural network architecture. (b) Error histogram diagram.

Table 6. Summary of the statistics of the ANN model.

Number of iterations	Root mean square deviation (RMSD)				r^2
	Training	Validation	Test	Overall	Training	Validation	Test	Overall
143	0.0127	0.0299	0.0347	0.0205	0.9834	0.9340	0.9797	0.9627

Figure 9. Predicted binodal lines using the ANN model for (a) water-ethyl lactate-K₂S₂O₃ system; (b) water-ethyl lactate-Na₂ succinate system. The training dataset included 95 experimental data points for seven ternary systems containing different salts, K₃PO₄, K₂HPO₄, K₂CO₃, Na₃-citrate—Na₃C₆H₅O₇, Na₃-tartrate—Na₂C₄H₄O₆, Na₂S₂O₃ and (NH₄)₂S₂O₃).

Figure 10. FTIR–ATR spectra of the salt-rich ternary solutions (Na₃ citrate—black, Na₂ tartrate—dark blue, Na₂ succinate—green, K₃PO₄—grey, K₂HPO₄—red, K₂CO₃—light blue, K₂S₂O₃—brown, Na₂S₂O₃—yellow and (NH₄)₂S₂O₃—pink) between 2400–3800 cm⁻¹.

Figure 11. Full-width half maxima (FWHM) of the peak versus peak position for the O–H band in the FTIR–ATR spectra of the salt-rich ternary solutions (Na₃ citrate—black, Na₂ tartrate—dark blue, Na₂ succinate—green, K₃PO₄—grey, K₂HPO₄—red, K₂CO₃—light blue, K₂S₂O₃—brown, Na₂S₂O₃—yellow and (NH₄)₂S₂O₃—pink).