APPENDIX 1. Binodal Curve calculations

Transcription

1 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, 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

2 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

3 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 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

4 Table A2.1 Refractive indices at different PEG 6000 and sodium citrate concentrations SALT, (% w/w) PEG 6000, (% w/w) Refractive Index, n D Table A2.2 LINEST Command Output from Microsoft Excel 2010 a 2 a 1 a

5 Table A2.3 Refractive Index Calibration Constants Component a o a 1 a 2 *AARD % Water Sodium Citrate PEG PEG PEG PEG PEG * Average arithmetic relative deviation (AARD) = ( ` 129

6 n D % Sodium Citrate 2% Sodium Citrate 4% Sodium Citrate 6% Sodium Citrate 8% Sodium Citrate PEG 6000, %w/w Figure A2.1: Refractive index calibration curves for PEG Sodium Citrate + water 130

7 Table A2.4 Sample calculation of AARD for PEG Sodium citrate +Water W P W SC Experimental n D Calculated n D Abs (Experimental n D Calculated n D ) / (Experimental n D ) E E E E E E E E E E E E % AARD =

8 APPENDIX 3 Table A3.1: Calculation of EEV values for PEG 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 E E E E E E E E E E E E E E E E E E E E E E-06 AVG EEV =

9 Table A3.2: Calculation of EEV values for PEG 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 E E E E E E E E E E E E E E E E E E E E E E E E E E-06 AVG EEV =

10 Table A3.3: Calculation of EEV values for PEG 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 E E E E E E E E E E E E E E E E E E E E E E E-08 AVG EEV =

11 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

12 StdOrder RunOrder CenterPt Blocks PEG SC ph NaCl Temp Y FFD Estimated Effects and Coefficients for Y FFD (coded units) Term Effect Coef Constant PEG SC ph NaCl Temp PEG*SC PEG*pH PEG*NaCl PEG*Temp SC*pH SC*NaCl SC*Temp ph*nacl ph*temp NaCl*Temp S = * PRESS = * 136

13 Analysis of Variance for Y FFD (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects * * PEG * * SC * * ph * * NaCl * * Temp * * 2-Way Inter * * PEG*SC * * PEG*pH * * PEG*NaCl * * PEG*Temp * * SC*pH * * SC*NaCl * * SC*Temp * * ph*nacl * * ph*temp * * NaCl*Temp * * Residual Error 0 * * * Total Estimated Coefficients for Y FFD using data in uncoded units Term Coef Constant PEG SC ph NaCl Temp PEG*SC PEG*pH PEG*NaCl PEG*Temp SC*pH SC*NaCl SC*Temp ph*nacl ph*temp NaCl*Temp

14 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 Effect Lenth's PSE = 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 =

15 Percent Half Normal Plot of the Effects (response is Y FFD, Alpha = 0.05) 98 Effect Type Not Significant Significant E AE D C F actor A B C D E Name PEG SC ph NaC l Temp Absolute Effect Lenth's PSE = 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 ph NaCl Temp PEG*Temp Error Total S = R-Sq = 95.82% R-Sq(adj) = 93.73% 139

16 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: Design Table Run Blk ph NaCl Temp

17 Response Surface Regression: Y RSM versus ph, NaCl, Temperature StdOrder RunOrder PtType Blocks ph NaCl Temperature Y RSM The analysis was done using coded units. Estimated Regression Coefficients for Y RSM Term Coef SE Coef T P Constant ph NaCl Temperature ph*ph NaCl*NaCl Temperature*Temperature ph*nacl ph*temperature NaCl*Temperature S = PRESS = R-Sq = 84.86% R-Sq(pred) = 0.00% R-Sq(adj) = 71.22% 141

18 Analysis of Variance for Y RSM Source DF Seq SS Adj SS Adj MS F P Regression Linear ph NaCl Temperature Square ph*ph NaCl*NaCl Temp*Temp Interaction ph*nacl ph*temperature NaCl*Temperature Residual Error Lack-of-Fit Pure Error Total Obs StdOrder Y RSM Fit SE Fit Residual St Resid R R R denotes an observation with a large standardized residual. 142

19 Estimated Regression Coefficients for Y RSM using data in uncoded units Term Coef Constant ph NaCl Temperature ph*ph NaCl*NaCl Temp*Temp ph*nacl ph*temperature NaCl*Temperature 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 ph NaCl Temperature ph*ph NaCl*NaCl Temp*Temp ph*nacl ph*temperature NaCl*Temperature S = PRESS = R-Sq = 97.27% R-Sq(pred) = 71.16% R-Sq(adj) = 94.54% 143

20 Analysis of Variance for Y RSM Source DF Seq SS Adj SS Adj MS F P Regression Linear ph NaCl Temperature Square ph*ph NaCl*NaCl Temp*Temp Interaction ph*nacl ph*temperature NaCl*Temperature Residual Error Lack-of-Fit Pure Error Total Obs StdOrder Y RSM Fit SE Fit Residual St Resid R R R denotes an observation with a large standardized residual. 144

21 Estimated Regression Coefficients for Y RSM using data in uncoded units Term Coef Constant ph NaCl Temperature ph*ph NaCl*NaCl Temp*Temp ph*nacl ph*temperature NaCl*Temperature Response Optimization Parameters Goal Lower Target Upper Weight Import Y RSM Maximum Global Solution ph = NaCl = 0.1 Temperature = Predicted Responses Y RSM = , desirability = Composite Desirability =

22 Optimization Plot Optimal D High Cur Low ph NaCl Temperat [7.4545] [0.10] [ ] Composite Desirability Y RSM Maximum y = d =

23 Residual Percent Checking Model Assumption for ffd: (Residual Plots) Normal Probability Plot (response is Y FFD) Residual Versus Fits (response is Y FFD) Fitted Value

24 Residual Versus Order (response is Y FFD) Observation Order

25 Percent Checking Model Assumption for RSM: (Residual Plots) Normal Probability Plot (response is Y RSM) Residual

26 Residual Residual Versus Fits (response is Y RSM) Fitted Value Versus Order (response is Y RSM) Observation Order