APPENDIX 1. Binodal Curve calculations

APPENDIX 1 Binodal Curve calculations The weight of salt solution necessary for the mixture to cloud and the final concentrations of the phase components were calculated based on the method given by Hatti-Kaul, 2000. A model spread sheet is given in the Table A.1. (Numerical values in italics are the experimental points and the remaining are calculated values) Table A1: Binodal Curve calculations 125

APPENDIX 2 A2.1 Determination of phase compositions The individual concentrations of phase components i.e. PEG and Sodium citrate were determined by refractive index method and flame photometry respectively. A2.1.1 Flame Photometry method to determine salt concentration The concentrations of sodium citrate in each phase were determined by flame photometry (Systronics128 flame photometer). Initially standard calibrations with sodium citrate solutions were done in the range of 10 to 100 ppm of then corresponding sodium citrate concentrations of unknown samples were calculated. A2.1.2 Calibration standards for sodium citrate concentrations using Flame photometry measurements Solution A: 5 g of sodium citrate salt was dissolved in 1000mL of water and this corresponds to 5000 ppm Solution B: 200 ml of solution A was made up to 1000mL with water which corresponds to 1000ppm (1:5 dilution) Solution C: 10 ml of solution B was made up to 1000mL with water which corresponds to 10 ppm (1:100 dilution) Same procedure was repeated with different dilutions to get different concentrations ranging from 10 ppm to 100 ppm The samples from the top and bottom phases were diluted in such a way that they would fall within this linear range and actual concentration of salt was calculated. 126

A2.1.3 Refractive index method to determine PEG concentration The equilibrium concentration of PEG in both phases was determined by refractive index measurements performed using an Abbe-type refractometer (Advance Research Instruments Co., New Delhi, Model R-4). Since the refractive index depends on both PEG and sodium citrate concentration calibration charts were drawn between refractive index versus different MW of PEG (10 50%) for the different concentration of sodium citrate (1 10%). One such calibration data and chart was shown in Table A2.1 and Figure A2.1 for refractive index and PEG 6000 (%w/w) with different concentration of sodium citrate. For all PEG fractions the curves are linear and have similar slopes for the salt concentrations investigated. The relation between the refractive index, n D, and the weight fraction of PEG, W P, and salt, W SC, is given by The values of the coefficients a 0, a 1 and a 2 for the PEG + Sodium citrate + Water system were determined by regression analysis using LINEST command (Table A2.2) in Microsoft Excel 2010. Table A2.3 summarizes the coefficient values along with the corresponding average arithmetic relative deviation (AARD). A sample calculation for AARD is shown in the Table A2.4. By knowing the WSC value from the previous part, the concentration of PEG can be calculated by using the above equation with known n D value. 127

Table A2.1 Refractive indices at different PEG 6000 and sodium citrate concentrations SALT, (% w/w) 0 2 4 6 8 1.0 PEG 6000, (% w/w) Refractive Index, n D 0 1.3322 1.3351 1.338 1.3409 1.3439 1.3468 1.0 1.3461 1.3495 1.3521 1.3550 1.3582 1.3603 2.0 1.3606 1.3636 1.3665 1.3697 1.3721 1.375 3.0 1.3741 1.3777 1.3801 1.3831 1.3860 1.3895 4.0 1.3882 1.3911 1.3948 1.3979 1.4001 1.4037 5.0 1.4021 1.4052 1.4082 1.4112 1.4149 1.4176 Table A2.2 LINEST Command Output from Microsoft Excel 2010 a 2 a 1 a 0 0.1466 0.1409 1.3322 0.001542 0.000308 0.000121 0.999849 0.000316 108995.4 33 128

Table A2.3 Refractive Index Calibration Constants Component a o a 1 a 2 *AARD % Water 1.3322 Sodium Citrate 0.1466 PEG 600 0.1357 0.02830 PEG 1000 0.1374 0.01803 PEG 2000 0.1387 0.04316 PEG 4000 0.1396 0.05395 PEG 6000 0.1409 0.01854 * Average arithmetic relative deviation (AARD) = ( ` 129

1.42 1.41 1.4 1.39 n D 1.38 1.37 1.36 1.35 1.34 0% Sodium Citrate 2% Sodium Citrate 4% Sodium Citrate 6% Sodium Citrate 8% Sodium Citrate 1.33 1.32 0 10 20 30 40 50 PEG 6000, %w/w Figure A2.1: Refractive index calibration curves for PEG 6000 + Sodium Citrate + water 130

Table A2.4 Sample calculation of AARD for PEG 6000 + Sodium citrate +Water W P W SC Experimental n D Calculated n D Abs (Experimental n D Calculated n D ) / (Experimental n D ) 0 0 1.3322 1.332100 7.50638E-05 0 0.02 1.3351 1.335038 4.64385E-05 0 0.04 1.338 1.337976 1.79372E-05 0 0.06 1.3409 1.340914 1.04407E-05 0 0.08 1.3439 1.343852 3.57169E-05 0 0.1 1.3468 1.346790 7.42501E-06 0.1 0 1.3461 1.346200 7.42887E-05 0.1 0.02 1.3495 1.349138 0.000268247 0.1 0.04 1.3521 1.352076 1.77502E-05 0.1 0.06 1.355 1.355014 1.03321E-05 0.1 0.08 1.3582 1.357952 0.000182595 0.1 0.1 1.3603 1.360890 0.000433728 0.2 0 1.3606 1.360300 0.000220491 0.2 0.02 1.3636 1.363238 0.000265474 0.2 0.04 1.3665 1.366176 0.000237102 0.2 0.06 1.3697 1.369114 0.000427831 0.2 0.08 1.3721 1.372052 3.49829E-05 0.2 0.1 1.375 1.3749900 7.27273E-06 0.3 0 1.3741 1.374400 0.000218325 0.3 0.02 1.3777 1.377338 0.000262757 0.3 0.04 1.3801 1.380276 0.000127527 0.3 0.06 1.3831 1.383214 8.24235E-05 0.3 0.08 1.386 1.386152 0.000109668 0.3 0.1 1.3895 1.389090 0.00029507 0.4 0 1.3882 1.388500 0.000216107 0.4 0.02 1.3911 1.391438 0.000242973 0.4 0.04 1.3948 1.394376 0.000303986 0.4 0.06 1.3979 1.397314 0.0004192 0.4 0.08 1.4001 1.400252 0.000108564 0.4 0.1 1.4037 1.403190 0.000363325 0.5 0 1.4021 1.402600 0.000356608 0.5 0.02 1.4052 1.405538 0.000240535 0.5 0.04 1.4082 1.408476 0.000195995 0.5 0.06 1.4112 1.411414 0.000151644 0.5 0.08 1.4149 1.414352 0.000387307 0.5 0.1 1.4176 1.417290 0.000218679 % AARD = 0.018538363 131

APPENDIX 3 Table A3.1: Calculation of EEV values for PEG 10000 + SC + Water System from Equation 6.2 PEG 10000, 100W P SC, 100W S Wp / PEG MW Ws/SC MW EEV Minimization of Equation 6.2 by Solver tool 38.93 1.41 36.41 1.49 34.56 1.69 31.22 1.99 26.72 2.56 24.15 3.09 22.39 3.43 20.69 3.57 18.11 4.04 16.48 4.36 14.81 5.11 12.65 5.92 7.67 8.52 6.15 9.84 5.12 10.74 4.29 11.52 3.79 12.83 2.68 13.77 2.18 14.75 1.52 16.79 1.43 17.53 1.11 18.51 0.003893 0.005465 127.7749 1.07E-07 0.003641 0.005775 129.7912-2.4E-07 0.003456 0.00655 126.4154-4.5E-07 0.003122 0.007713 123.5292-5.4E-07 0.002672 0.009922 117.0987-7.9E-07 0.002415 0.011977 110.3864 1.79E-07 0.002239 0.013295 107.2818-1E-06 0.002069 0.013837 108.1793-8E-07 0.001811 0.015659 105.6253-6.4E-07 0.001648 0.016899 104.237-5.3E-07 0.001481 0.019806 97.63582 1.53E-06 0.001265 0.022946 93.18194-8.4E-07 0.000767 0.033023 83.29419 4.71E-07 0.000615 0.03814 79.22485 5.42E-07 0.000512 0.041628 77.5136-3.5E-06 0.000429 0.044651 76.51639-3E-06 0.000379 0.049729 72.32773-3.8E-06 0.000268 0.053372 73.56551-2.1E-06 0.000218 0.057171 72.53612-1.8E-06 0.000152 0.065078 69.84513-1.5E-06 0.000143 0.067946 68.15546-1.6E-06 0.000111 0.071744 68.09101-1.2E-06 AVG EEV = 96.426 132

Table A3.2: Calculation of EEV values for PEG 10000 + KC + Water System from Equation 6.2 PEG 10000, 100W P KC, 100W S Wp / PEG MW Ws/KC MW EEV Minimization of Equation 6.2 by Solver tool 42.09 1.97 0.004209 0.006073 116.8541-2.2E-07 40.21 2.21 0.004021 0.006812 114.2193-2.7E-07 38.24 2.38 0.003824 0.007336 113.6223-2.4E-07 36.08 2.36 0.003608 0.007275 117.7143 6.75E-07 34.41 2.82 0.003441 0.008693 110.863 9.03E-07 31.79 3.13 0.003179 0.009648 109.4349 6.67E-07 29.96 3.35 0.002996 0.010326 108.6694 5.01E-07 27.88 3.68 0.002788 0.011344 106.7984-1.1E-06 25.86 4.12 0.002586 0.0127 103.6621 8.41E-07 23.84 4.37 0.002384 0.013471 103.7248 8.99E-07 21.17 5.13 0.002117 0.015813 98.88873-6.4E-07 18.96 5.91 0.001896 0.018218 94.42489-1E-06 17.24 6.35 0.001724 0.019574 93.33411-1E-06 15.65 6.79 0.001565 0.02093 92.39312-9.2E-07 13.35 7.71 0.001335 0.023766 89.42867-8.9E-07 12.13 8.19 0.001213 0.025246 88.42884-8.2E-07 10.82 8.69 0.001082 0.026787 87.85175-6.9E-07 9.33 9.55 0.000933 0.029438 85.78308 3.48E-06 8.64 10.12 0.000864 0.031195 84.06351 3.58E-06 7.18 11.04 0.000718 0.034031 82.90516 2.87E-06 5.72 12.03 0.000572 0.037083 82.38321 2.07E-06 4.53 13.32 0.000453 0.041059 80.6141 1.65E-06 3.03 14.35 0.000303 0.044234 83.20445 7.83E-07 2.17 15.27 0.000217 0.04707 84.86409-3.6E-06 1.79 16.52 0.000179 0.050923 82.72463-3.5E-06 0.87 17.43 0.000087 0.053728 90.21973-1.1E-06 AVG EEV = 94.615 133

Table A3.3: Calculation of EEV values for PEG 10000 + AC + Water System from Equation 6.2 PEG 10000, 100W P AC, 100W S Wp / PEG MW Ws/AC MW EEV Minimization of Equation 6.2 by Solver tool 43.23 2.91 0.004323 0.011964 84.33437 3.02E-07 41.08 2.97 0.004108 0.012211 85.59406 3.15E-07 38.14 3.31 0.003814 0.013609 83.80796 2.95E-07 35.41 3.81 0.003541 0.015665 80.28902 5.57E-07 31.89 4.18 0.003189 0.017186 79.7016 2.85E-07 29.22 4.69 0.002922 0.019283 77.21377 3.93E-07 26.83 5.01 0.002683 0.020599 76.72983 7.32E-07 24.55 5.62 0.002455 0.023107 73.88184 3.73E-07 22.72 6.11 0.002272 0.025121 72.04348 2.2E-07 20.77 6.85 0.002077 0.028164 68.98645 2.06E-07 18.73 7.48 0.001873 0.030754 67.32864 1.11E-07 16.61 8.21 0.001661 0.033755 65.64903 1.84E-08 15.05 9.03 0.001505 0.037127 63.31787 3.27E-08 12.74 10.12 0.001274 0.041608 61.28649 2.93E-10 11.03 10.73 0.001103 0.044116 61.12803 3.26E-09 9.53 11.82 0.000953 0.048598 59.16906 5.71E-08 7.57 12.74 0.000757 0.052381 59.26203 1.2E-07 6.04 13.66 0.000604 0.056163 59.28429 1.19E-07 4.73 14.83 0.000473 0.060974 58.76186 3.21E-07 4.04 15.88 0.000404 0.065291 57.59794-4.5E-08 2.82 16.64 0.000282 0.068415 59.69849 6.77E-07 1.79 17.83 0.000179 0.073308 61.50713 1.93E-07 1.13 18.69 0.000113 0.076844 64.12139 6.64E-08 AVG EEV = 68.7259 134

APPENDIX 4 Fractional Factorial Design Number of Factors: 5 Fraction: 1/2 Base Designs: 5, 16 Resolution: V Runs: 16 Replicates: 1 Blocks: 1 Center points (total): 0 Design Generators: E = ABCD Defining Relation: I = ABCDE Alias Structure I + ABCDE A + BCDE B + ACDE C + ABDE D + ABCE E + ABCD AB + CDE AC + BDE AD + BCE AE + BCD BC + ADE BD + ACE BE + ACD CD + ABE CE + ABD DE + ABC Design Table (randomized) Run A B C D E 1 - + + + - 2 + - + - + 3 - - - - + 4 + + + + + 5 - + - + + 6 - + + - + 7 + + + - - 8 - + - - - 9 + - - - - 10 + - + + - 11 + + - + - 135

12 + - - + + 13 - - + + + 14 - - + - - 15 + + - - + 16 - - - + - StdOrder RunOrder CenterPt Blocks PEG SC ph NaCl Temp Y FFD 15 1 1 1 20 23 8 0.3 20 67.24 6 2 1 1 30 15 8 0.1 40 68.24 1 3 1 1 20 15 6 0.1 40 33.95 16 4 1 1 30 23 8 0.3 40 83.42 11 5 1 1 20 23 6 0.3 40 52.71 7 6 1 1 20 23 8 0.1 40 50.49 8 7 1 1 30 23 8 0.1 20 52.21 3 8 1 1 20 23 6 0.1 20 37.29 2 9 1 1 30 15 6 0.1 20 29.89 14 10 1 1 30 15 8 0.3 20 71.77 12 11 1 1 30 23 6 0.3 20 54.59 10 12 1 1 30 15 6 0.3 40 64.49 13 13 1 1 20 15 8 0.3 40 75.33 5 14 1 1 20 15 8 0.1 20 61.46 4 15 1 1 30 23 6 0.1 40 48.93 9 16 1 1 20 15 6 0.3 20 58.49 Estimated Effects and Coefficients for Y FFD (coded units) Term Effect Coef Constant 56.906 PEG 4.572 2.286 SC -2.092-1.046 ph 18.728 9.364 NaCl 18.197 9.099 Temp 5.577 2.789 PEG*SC 3.283 1.641 PEG*pH 0.708 0.354 PEG*NaCl 0.553 0.276 PEG*Temp 8.577 4.289 SC*pH -3.767-1.884 SC*NaCl -0.938-0.469 SC*Temp 0.478 0.239 ph*nacl -1.858-0.929 ph*temp 0.623 0.311 NaCl*Temp 0.387 0.194 S = * PRESS = * 136

Analysis of Variance for Y FFD (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 5 2953.05 2953.05 590.61 * * PEG 1 83.63 83.63 83.63 * * SC 1 17.51 17.51 17.51 * * ph 1 1402.88 1402.88 1402.88 * * NaCl 1 1324.60 1324.60 1324.60 * * Temp 1 124.43 124.43 124.43 * * 2-Way Inter. 10 417.77 417.77 41.78 * * PEG*SC 1 43.10 43.10 43.10 * * PEG*pH 1 2.00 2.00 2.00 * * PEG*NaCl 1 1.22 1.22 1.22 * * PEG*Temp 1 294.29 294.29 294.29 * * SC*pH 1 56.78 56.78 56.78 * * SC*NaCl 1 3.52 3.52 3.52 * * SC*Temp 1 0.91 0.91 0.91 * * ph*nacl 1 13.80 13.80 13.80 * * ph*temp 1 1.55 1.55 1.55 * * NaCl*Temp 1 0.60 0.60 0.60 * * Residual Error 0 * * * Total 15 3370.82 Estimated Coefficients for Y FFD using data in uncoded units Term Coef Constant 7.80000 PEG -4.28094 SC 1.03875 ph 17.4666 NaCl 158.641 Temp -2.23553 PEG*SC 0.0820625 PEG*pH 0.0707500 PEG*NaCl 0.552500 PEG*Temp 0.0857750 SC*pH -0.470937 SC*NaCl -1.17187 SC*Temp 0.00596875 ph*nacl -9.28750 ph*temp 0.0311250 NaCl*Temp 0.193750 137

Term Effects Pareto for Y FFD Pareto Chart of the Effects (response is Y FFD, Alpha = 0.05) 5.39 C D AE E A BC AB B CD BD AC CE AD BE DE F actor A B C D E Name PEG SC ph NaC l Temp 0 5 10 Effect 15 20 Lenth's PSE = 2.09625 Half Normal Effects Plot for Y FFD Alias Structure I + PEG*SC*pH*NaCl*Temp PEG + SC*pH*NaCl*Temp SC + PEG*pH*NaCl*Temp ph + PEG*SC*NaCl*Temp NaCl + PEG*SC*pH*Temp Temp + PEG*SC*pH*NaCl PEG*SC + ph*nacl*temp PEG*pH + SC*NaCl*Temp PEG*NaCl + SC*pH*Temp PEG*Temp + SC*pH*NaCl SC*pH + PEG*NaCl*Temp SC*NaCl + PEG*pH*Temp SC*Temp + PEG*pH*NaCl ph*nacl + PEG*SC*Temp ph*temp + PEG*SC*NaCl NaCl*Temp + PEG*SC*pH * NOTE * Could not graph the specified residual type because MSE = 0 or the degrees of freedom for error = 0. 138

Percent Half Normal Plot of the Effects (response is Y FFD, Alpha = 0.05) 98 Effect Type Not Significant Significant 95 90 85 80 70 E AE D C F actor A B C D E Name PEG SC ph NaC l Temp 60 50 40 30 20 10 0 0 5 10 Absolute Effect 15 20 Lenth's PSE = 2.09625 ANOVA: Y FFD versus PEG, ph, NaCl, Temp Factor Type Levels Values PEG fixed 2 20, 30 ph fixed 2 6, 8 NaCl fixed 2 0.1, 0.3 Temp fixed 2 20, 40 Analysis of Variance for Y FFD Source DF SS MS F P PEG 1 83.63 83.63 5.93 0.053 ph 1 1402.88 1402.88 99.50 0.000 NaCl 1 1324.60 1324.60 93.95 0.000 Temp 1 124.43 124.43 8.83 0.014 PEG*Temp 1 294.29 294.29 20.87 0.001 Error 10 140.99 14.10 Total 15 3370.82 S = 3.75490 R-Sq = 95.82% R-Sq(adj) = 93.73% 139

Central Composite Design Factors: 3 Replicates: 1 Base runs: 20 Total runs: 20 Base blocks: 1 Total blocks: 1 Two-level factorial: Full factorial Cube points: 8 Center points in cube: 6 Axial points: 6 Center points in axial: 0 Alpha: 1.68179 Design Table Run Blk ph NaCl Temp 1 1-1.00000-1.00000-1.00000 2 1 1.00000-1.00000-1.00000 3 1-1.00000 1.00000-1.00000 4 1 1.00000 1.00000-1.00000 5 1-1.00000-1.00000 1.00000 6 1 1.00000-1.00000 1.00000 7 1-1.00000 1.00000 1.00000 8 1 1.00000 1.00000 1.00000 9 1-1.68179 0.00000 0.00000 10 1 1.68179 0.00000 0.00000 11 1 0.00000-1.68179 0.00000 12 1 0.00000 1.68179 0.00000 13 1 0.00000 0.00000-1.68179 14 1 0.00000 0.00000 1.68179 15 1 0.00000 0.00000 0.00000 16 1 0.00000 0.00000 0.00000 17 1 0.00000 0.00000 0.00000 18 1 0.00000 0.00000 0.00000 19 1 0.00000 0.00000 0.00000 20 1 0.00000 0.00000 0.00000 140

Response Surface Regression: Y RSM versus ph, NaCl, Temperature StdOrder RunOrder PtType Blocks ph NaCl Temperature Y RSM 1 1 1 1 6.405396 0.14054 24.05396 76.78 2 2 1 1 7.594604 0.14054 24.05396 87.69 3 3 1 1 6.405396 0.25946 24.05396 79.68 4 4 1 1 7.594604 0.25946 24.05396 84.34 5 5 1 1 6.405396 0.14054 35.94604 88.90 6 6 1 1 7.594604 0.14054 35.94604 89.56 7 7 1 1 6.405396 0.25946 35.94604 76.85 8 8 1 1 7.594604 0.25946 35.94604 79.21 9 9-1 1 6 0.2 30 83.22 10 10-1 1 8 0.2 30 88.15 11 11-1 1 7 0.1 30 92.46 12 12-1 1 7 0.3 30 81.51 13 13-1 1 7 0.2 20 88.62 14 14-1 1 7 0.2 40 78.55 15 15 0 1 7 0.2 30 89.56 16 16 0 1 7 0.2 30 88.62 17 17 0 1 7 0.2 30 89.85 18 18 0 1 7 0.2 30 90.66 19 19 0 1 7 0.2 30 90.50 20 20 0 1 7 0.2 30 89.65 The analysis was done using coded units. Estimated Regression Coefficients for Y RSM Term Coef SE Coef T P Constant 89.8802 1.1292 79.597 0.000 ph 1.9683 0.7492 2.627 0.025 NaCl -3.0216 0.7492-4.033 0.002 Temperature -0.7985 0.7492-1.066 0.312 ph*ph -1.9375 0.7293-2.657 0.024 NaCl*NaCl -1.4779 0.7293-2.026 0.070 Temperature*Temperature -2.6800 0.7293-3.675 0.004 ph*nacl -0.5688 0.9789-0.581 0.574 ph*temperature -1.5687 0.9789-1.603 0.140 NaCl*Temperature -2.7438 0.9789-2.803 0.019 S = 2.76864 PRESS = 577.272 R-Sq = 84.86% R-Sq(pred) = 0.00% R-Sq(adj) = 71.22% 141

Analysis of Variance for Y RSM Source DF Seq SS Adj SS Adj MS F P Regression 9 429.487 429.487 47.721 6.23 0.004 Linear 3 186.308 186.308 62.103 8.10 0.005 ph 1 52.911 52.911 52.911 6.90 0.025 NaCl 1 124.688 124.688 124.688 16.27 0.002 Temperature 1 8.709 8.709 8.709 1.14 0.312 Square 3 160.677 160.677 53.559 6.99 0.008 ph*ph 1 35.801 54.098 54.098 7.06 0.024 NaCl*NaCl 1 21.372 31.476 31.476 4.11 0.070 Temp*Temp 1 103.504 103.504 103.504 13.50 0.004 Interaction 3 82.501 82.501 27.500 3.59 0.054 ph*nacl 1 2.588 2.588 2.588 0.34 0.574 ph*temperature 1 19.688 19.688 19.688 2.57 0.140 NaCl*Temperature 1 60.225 60.225 60.225 7.86 0.019 Residual Error 10 76.654 76.654 7.665 Lack-of-Fit 5 73.949 73.949 14.790 27.34 0.001 Pure Error 5 2.704 2.704 0.541 Total 19 506.140 Obs StdOrder Y RSM Fit SE Fit Residual St Resid 1 1 76.780 80.755 2.266-3.975-2.50 R 2 2 87.690 88.967 2.266-1.277-0.80 3 3 79.680 81.337 2.266-1.657-1.04 4 4 84.340 87.274 2.266-2.934-1.84 5 5 88.900 87.783 2.266 1.117 0.70 6 6 89.560 89.720 2.266-0.160-0.10 7 7 76.850 77.390 2.266-0.540-0.34 8 8 79.210 77.052 2.266 2.158 1.36 9 9 83.220 81.090 2.158 2.130 1.23 10 10 88.150 87.710 2.158 0.440 0.25 11 11 92.460 90.782 2.158 1.678 0.97 12 12 81.510 80.618 2.158 0.892 0.51 13 13 88.620 83.643 2.158 4.977 2.87 R 14 14 78.550 80.957 2.158-2.407-1.39 15 15 89.560 89.880 1.129-0.320-0.13 16 16 88.620 89.880 1.129-1.260-0.50 17 17 89.850 89.880 1.129-0.030-0.01 18 18 90.660 89.880 1.129 0.780 0.31 19 19 90.500 89.880 1.129 0.620 0.25 20 20 89.650 89.880 1.129-0.230-0.09 R denotes an observation with a large standardized residual. 142

Estimated Regression Coefficients for Y RSM using data in uncoded units Term Coef Constant -434.827 ph 96.5599 NaCl 461.807 Temperature 9.07181 ph*ph -5.48007 NaCl*NaCl -418.007 Temp*Temp -0.0758007 ph*nacl -16.0867 ph*temperature -0.443710 NaCl*Temperature -7.76050 Response Surface Regression: Y RSM versus ph, NaCl, Temperature The analysis was done using coded units. Estimated Regression Coefficients for Y RSM (without outlier) Term Coef SE Coef T P Constant 89.8078 0.5011 179.231 0.000 ph 1.9683 0.3324 5.922 0.000 NaCl -3.0216 0.3324-9.091 0.000 Temperature 0.7622 0.4108 1.855 0.097 ph*ph -1.4647 0.3317-4.416 0.002 NaCl*NaCl -1.0051 0.3317-3.030 0.014 Temp*Temp -4.4476 0.4236-10.500 0.000 ph*nacl -0.5688 0.4343-1.310 0.223 ph*temperature -1.5687 0.4343-3.612 0.006 NaCl*Temperature -2.7438 0.4343-6.318 0.000 S = 1.22827 PRESS = 143.421 R-Sq = 97.27% R-Sq(pred) = 71.16% R-Sq(adj) = 94.54% 143

Analysis of Variance for Y RSM Source DF Seq SS Adj SS Adj MS F P Regression 9 483.698 483.698 53.744 35.62 0.000 Linear 3 180.715 182.794 60.931 40.39 0.000 ph 1 52.911 52.911 52.911 35.07 0.000 NaCl 1 124.688 124.688 124.688 82.65 0.000 Temperature 1 3.116 5.194 5.194 3.44 0.097 Square 3 220.481 220.481 73.494 48.71 0.000 ph*ph 1 32.870 29.416 29.416 19.50 0.002 NaCl*NaCl 1 21.281 13.851 13.851 9.18 0.014 Temp*Temp 1 166.331 166.331 166.331 110.25 0.000 Interaction 3 82.501 82.501 27.500 18.23 0.000 ph*nacl 1 2.588 2.588 2.588 1.72 0.223 ph*temperature 1 19.688 19.688 19.688 13.05 0.006 NaCl*Temperature 1 60.225 60.225 60.225 39.92 0.000 Residual Error 9 13.578 13.578 1.509 Lack-of-Fit 4 10.874 10.874 2.718 5.03 0.053 Pure Error 5 2.704 2.704 0.541 Total 18 497.275 Obs StdOrder Y RSM Fit SE Fit Residual St Resid 1 1 76.780 78.300 1.075-1.520-2.56 R 2 2 87.690 86.512 1.075 1.178 1.98 3 3 79.680 78.882 1.075 0.798 1.34 4 4 84.340 84.819 1.075-0.479-0.80 5 5 88.900 88.450 1.010 0.450 0.65 6 6 89.560 90.386 1.010-0.826-1.18 7 7 76.850 78.056 1.010-1.206-1.73 8 8 79.210 77.718 1.010 1.492 2.14 R 9 9 83.220 82.355 0.977 0.865 1.16 10 10 88.150 88.975 0.977-0.825-1.11 11 11 92.460 92.047 0.977 0.413 0.56 12 12 81.510 81.883 0.977-0.373-0.50 14 14 78.550 78.510 1.029 0.040 0.06 15 15 89.560 89.808 0.501-0.248-0.22 16 16 88.620 89.808 0.501-1.188-1.06 17 17 89.850 89.808 0.501 0.042 0.04 18 18 90.660 89.808 0.501 0.852 0.76 19 19 90.500 89.808 0.501 0.692 0.62 20 20 89.650 89.808 0.501-0.158-0.14 R denotes an observation with a large standardized residual. 144

Estimated Regression Coefficients for Y RSM using data in uncoded units Term Coef Constant -416.897 ph 77.8387 NaCl 408.318 Temperature 12.3341 ph*ph -4.14284 NaCl*NaCl -284.284 Temp*Temp -0.125797 ph*nacl -16.0867 ph*temperature -0.443710 NaCl*Temperature -7.76050 Response Optimization Parameters Goal Lower Target Upper Weight Import Y RSM Maximum 77 100 100 1 1 Global Solution ph = 7.45455 NaCl = 0.1 Temperature = 32.7273 Predicted Responses Y RSM = 94.4070, desirability = 0.756826 Composite Desirability = 0.756826 145

Optimization Plot Optimal D High Cur 0.75683 Low ph NaCl Temperat 8.0 0.30 40.0 [7.4545] [0.10] [32.7273] 6.0000 0.10 20.0 Composite Desirability 0.75683 Y RSM Maximum y = 94.4070 d = 0.75683 146

Residual Percent Checking Model Assumption for ffd: (Residual Plots) Normal Probability Plot (response is Y FFD) 99 95 90 80 70 60 50 40 30 20 10 5 1-8 -6-4 -2 0 Residual 2 4 6 8 Versus Fits (response is Y FFD) 5.0 2.5 0.0-2.5-5.0-7.5 30 40 50 60 Fitted Value 70 80 90 147

Residual Versus Order (response is Y FFD) 5.0 2.5 0.0-2.5-5.0-7.5 1 2 3 4 5 6 7 8 9 10 Observation Order 11 12 13 14 15 16 148

Percent Checking Model Assumption for RSM: (Residual Plots) Normal Probability Plot (response is Y RSM) 99 95 90 80 70 60 50 40 30 20 10 5 1-2 -1 0 Residual 1 2 149

Residual Residual Versus Fits (response is Y RSM) 1.5 1.0 0.5 0.0-0.5-1.0-1.5 76 78 80 82 84 86 Fitted Value 88 90 92 Versus Order (response is Y RSM) 1.5 1.0 0.5 0.0-0.5-1.0-1.5 2 4 6 8 10 12 Observation Order 14 16 18 20 150