Solvent Blend Formulation (Chapter 2)

CHAPTER II EXPERIMENTAL Godfrey’s solvent list was used as the QSPR taining set, but the list contained many out-dated common names (like amyl alcohol). The National Institute of Standards and Technology Chemistry WebBook (NIST) database number 69 and The PubChem Project were utilized to find current International Union of Pure and Applied Chemistry (IUPAC) names and Chemical Abstract Service Registry (CAS) numbers. The CAS number was searched in the Hansen Solubility Parameters in Practice (HSPiP) software 12 to determine the δD, δP, δH, and Vm values. The solvent list in Godfrey’s ChemTech article was used because the list from Perry’s Chemical Engineer’s Handbook had at least one error. An example of an incorrect entry is 1,1,2-trichloro-2,2,2-trifluoroethane, where Godfrey’s article listed 1,1,1- trichloro-2,2,2-trifluoroethane. The solvent 1,1,2-trichloro2,2,2-trifluoroethane listed in Perry’s is a mistake because the name implied one carbon was bonded to five atoms. Godfrey’s list was correlated to NIST and HSPiP twice to help find any possible transcription errors. An effective method for obtaining the CAS number was to search for the Godfrey solvent name in the NIST WebBook. Sometimes PubChem was needed to find a match, then structures were compared to NIST. The CAS number was entered in HSPiP to obtain the δD, δP, δH, and Vm values. Of the 31 standards Godfrey utilized, 30 were retrieved through NIST/HSPiP. The HSPs for Godfrey’s 31st standard, petrolatum, were given by Dr. Steven Abbott of the HSPiP Team in a personal correspondence. 20 Of the 407 Godfrey solvents, 344 were matched with the appropriate δD, δP, δH, and Vm values, and this formed the training set for the QSPR. The δD, δP, δH, and Vm were entered into MicroSoft Excel and formulas were used to determine the energy of vaporization, Hildebrand parameter, dipole moment, and index of refraction for each solvent (eqs 4-7). Once these results were calculated, several trial QSPRs were computed to model Godfrey’s M-numbers. In the cases where a solvent had a dual M-number, the average of the dual numbers was used. There was no justification to use anything other than the average Mnumber for the dual M-number solvents to constrain the outer miscibility limits without changing the ΔM value. So for nitromethane, an M-number of 14.5 was assigned as explained in Figure 2. This would give the dual M-number solvents a larger miscibility range than Godfrey intended, but for ease of calculation it was a reasonable option. In Excel, the relationship to the Hildebrand parameter was tested with δT as the XInput and M as the Y-Input in Excel’s regression tool. M calc = a + bδ T (11) In Excel, the relationship to the Hansen solubility parameters (δD, δP, and δH) was tested as the X-Input and M as the Y-Input. M calc = a + bδ D + cδ P + dδ H (12) The values were then imported into Minitab 16 and a multitude of regressions were performed to decide on an equation that can be used to quickly determine if two solvents were miscible. The best subsets regression tool in Minitab16 was used to search through all the possible combinations of x-input factors given in Eq 12. M calc = a + bδ T + cδ D + dδ P + eδ H + fVm + gµ + h(∆H vap ) (13) CHAPTER III RESULTS A performance chart compares the QSPR output to the training set values. In a perfect model the QSPR output would match the training set values yielding a performance plot where the data lies on a line with a slope of one and the intercept zero with no scatter (R2 = 1). The performance plot of several trial QSPRs are given for comparison and discussion. They range from simple one-factor designs to the most complicated seven-factor design. The one-factor Hildebrand solubility parameter regression compares Godfrey’s M-numbers to the Hildebrand solubility parameter. The performance plot of this model showing the calculated M-number against the literature M-number is Figure 3. 35 30 25 20 Mcalc 15 10 y = 0.7503x + 4.5439 R² = 0.7503 5 0 0 -5 5 10 15 20 25 30 35 Mlit Figure 3. Performance plot of the one-factor Hildebrand regression Mcal=47.2-1.41δT. A linear regression was performed comparing the three factor Hansen solubility parameters to Godfrey’s M-numbers. The performance plot is shown in Figure 4. 35 30 25 20 Mcalc 15 10 y = 0.8631x + 2.4908 R² = 0.8631 5 0 0 5 10 15 -5 20 25 30 35 Mlit Figure 4. Performance plot of M-number to Hansen solubility parameters Mcal=37.80.600δD-0.536δP-0.776δH. The figures of merit for the Hansen solubility parameters to M-number regression performed in Minitab is shown in Table 2. Table 2 Figures of Merit for Hansen Solubility Parameters Regression Predictor Coefficient p-value VIF Constant 37.8 0.000 δD -0.600 0.000 1.050 δP -0.536 0.000 1.388 δH -0.776 0.000 1.380 A best subsets was performed in Minitab to help determine the most reasonable QSPR. The regression analysis forced the elimination of refractive index as a factor because it was correlated too directly with δD. Table 3 shows the results from the best subset performed. Table 3 Best Subset Equations in Increasing Number of Factors Vars R2 adj R2 Cp σ δT δD δP δH 1 75.0 75.0 398.0 3.39 X 1 73.3 73.2 450.7 3.51 1 52.5 52.3 1065.4 4.67 X 2 84.9 84.8 107.7 2.64 X 2 83.5 83.4 150.3 2.76 2 81.0 80.9 222.9 2.96 3 87.3 87.2 38.9 2.42 3 86.3 86.2 68.6 2.52 3 86.1 86.0 73.5 2.53 4 88.3 88.2 11.4 2.33 4 88.2 88.1 14.7 2.34 4 87.5 87.3 36.9 2.41 X X 5 88.5 88.3 8.7 2.32 X X X 5 88.4 88.2 11.0 2.32 X X X 5 88.4 88.2 12.0 2.33 X X X X X 6 88.6 88.4 6.3 2.30 X X X X X 6 88.6 88.4 7.6 2.31 X X X X X 6 88.5 88.3 9.4 2.31 X X X X X X 7 88.6 88.4 8.0 2.31 X X X X X X Vm µ ΔHvap X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Further regressions were carried out on the most promising models from Table 3 to determine the corresponding p-values and VIF. A regression using all seven factors was performed as shown in Table 4. Table 4 The Seven Factor Model of Best Subset Predictor Coefficient p-value VIF Constant 32.1 0.000 δT 0.644 0.008 65.17 δD -0.992 0.000 3.678 δP -0.459 0.065 85.43 δH -0.996 0.000 13.53 Vm 0.0229 0.011 20.04 µ -0.979 0.202 54.64 ΔHvap -0.0000184 0.567 35.99 The regression for the top six factor equation was performed as shown in Table 5. Table 5 Second Regression of Best Subset with Six Factors Predictor Coefficient p-value VIF Constant 33.5 0.000 δT 0.538 0.001 27.25 δD -0.973 0.000 3.55 δP -0.355 0.036 39.730 δH -0.987 0.000 12.96 Vm 0.0181 0.000 2.672 µ -1.32 0.006 21.25 CHAPTER IV DISCUSSION Multiple QSPRs were evaluated to determine which had the most rational support. The first regression performed was the simplest model which only had one factor, the Hildebrand solubility parameter. This regression was first performed because Godfrey had issues with the miscibility rule of thumb that utilized the Hildebrand solubility parameter and a miscibility limit of 3.4 MPa1/2 between two solvents. The regression showed an R2 value of 75.0%, which is not bad for a rule of thumb. The example used by Godfrey where the rule of thumb failed was shown in Table 1. Godfrey’s M-numbers for hexadecane (15, 19) and benzonitrile (30) have a ΔM of 15, which he later stated that sometimes there are near misses with miscibility. Since the Hildebrand parameter was separated into three parts to account for dispersion, polarity, and hydrogen bonding ability, the next regression performed was Mlit versus the Hansen solubility parameters. This regression was performed in MS Excel. The R2 of the HSP regression model was 86.3%. The increase in R2 is expected because more factors were introduced into the model. This is a better R2 than the single parameter Hildebrand model, but a more thorough search for relevant factors was performed in Minitab (Table 2). The p-values for the coefficients in the HSP were 0.000 for each factor, showing that random noise was not a significant part of any coefficient. Since the HSP regression had more than one factor, the VIF was analyzed. The highest value was 1.380 showing minimal multicollinearity in the model. Overall the Hansen solubility parameters model was a better choice than the Hildebrand model. Dr. Steven Abbott, of the Hansen Team, hinted that molar volume plays a significant role in miscibility but could not expand further because of proprietary concerns with his HSPiP software. So, a regression was performed on Mlit versus the Hansen solubility parameters and molar volume (eq 14). With the addition of molar volume the model increased the R2 to 87.3% (Figure 5). M calc = 35.1 − 0.557δ D − 0.495δ P − 0.750δ H + 0.0117Vm (14) 35.0 30.0 25.0 20.0 Mcalc 15.0 10.0 5.0 y = 0.8727x + 2.3178 R² = 0.8727 0.0 0 -5.0 5 10 15 20 25 30 35 Mlit Figure 5. Performance plot of the QSPR of Hansen solubility parameters and molar volume Mcal=35.1-0.557δD-0.495δP-0.750δH+0.0117Vm. The addition of Vm improved R2 by 1%, this model is shown in Table 6. The pvalues are all 0.000, and the highest VIF is 1.470, this is within the desired limits. Table 6 Regression of Hansen Solubility Parameters in Addition to Molar Volume Predictor Coefficient p-value VIF Constant 35.1 0.000 δD -0.557 0.000 1.058 δP -0.495 0.000 1.470 δH -0.750 0.000 1.433 Vm 0.0117 0.000 1.211 To further explore different models, the best subsets tool in Minitab was used. Table 3 shows the results of the best subsets tool. A best subsets analysis uses all of the factors in every possible combination. The table is ranked in order based on the number of factors used then highest R2 for each set, starting with lowest number of factors and increasing to using all factors. For this experiment, Minitab showed the best set of three for each number of increasing factors. The best subset function does not provide the pvalue or the VIF, so separate regressions must be performed to determine the values that assist in selecting a model. When sorting through the multitude of equations given by the best subset table the goal is to find the simplest model with the best performance, significant p-values (<0.05), low VIF, and appropriate Mallows Cp. Starting with the model utilizing all of the factors (Table 4) the R2 is 88.6 and the adjusted R2 is 88.4, which is better than both the Hildebrand and Hansen regression models. As with the Hansen model, there is more than one factor, so further figures of merit needed to be checked. The Mallows’ Cp of the seven factor model is 8.0, which is acceptably close to the number of factors. The highest p-value in the model is 0.567, which is above the 0.05 significance level. The VIF for the seven factor model is very high for each factor except δD showing that there is multicollinearity in the model. Based on these results, the seven factor model is not a good model. The next model in the best subsets is the first model with six factors. The R2 and adjusted R2 of the model is the same as the seven factor model, 88.6% and 88.4% respectively. The Mallows’ Cp of the model is 6.3 where there are six factors, so the value of the Mallows’ Cp is great. The p-values of the coefficients are all below the 0.05 limit. The VIF values are lower than the seven factor model but only two factors, δD and Vm, are below 10. This model had the best Mallows’ Cp value to number of factors, good p-values but the VIF was above the limit of 10 and showing that there was multicollinearity in the model. From the results of the six factor model, this model’s VIF does not meet the requirements. Based on the Mallows’ Cp and using the last model as a starting point, attempting to remove the multicollinearity components from the model one at a time was the next step. By knowing that δP and µ are correlated (eq 6), determining which needed to be removed was resolved by the highest VIF values, in this case δP. The results of the new regression (Table 7) reduced the VIF to where four of the five factors in the model were within acceptable limits of multicollinearity.