125

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

126

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.

127

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, nD, and the weight fraction of PEG, WP, and salt,

WSC, is given by

The values of the coefficients a0, a1 and a2 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 nD value.

128

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, nD

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

a2 a1 a0

0.1466 0.1409 1.3322

0.001542 0.000308 0.000121

0.999849 0.000316

108995.4 33

129

Table A2.3 Refractive Index Calibration Constants

Component ao a1 a2 *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) = ( ∑ ‖

‖

`

130

Figure A2.1: Refractive index calibration curves for PEG 6000 + Sodium Citrate + water

1.32

1.33

1.34

1.35

1.36

1.37

1.38

1.39

1.4

1.41

1.42

0 10 20 30 40 50

nD

PEG 6000, %w/w

0% Sodium Citrate

2% Sodium Citrate

4% Sodium Citrate

6% Sodium Citrate

8% Sodium Citrate

131

Table A2.4 Sample calculation of AARD for PEG 6000 + Sodium citrate +Water

WP

WSC

Experimental

nD

Calculated

nD

Abs (Experimental nD – Calculated nD) /

(Experimental nD)

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

132

APPENDIX 3

Table A3.1: Calculation of EEV values for PEG 10000 + SC + Water System from Equation 6.2

PEG

10000,

100WP

SC,

100WS Wp / PEG MW Ws/SC MW EEV

Minimization of

Equation 6.2 by

Solver tool

38.93 1.41 0.003893 0.005465 127.7749 1.07E-07

36.41 1.49 0.003641 0.005775 129.7912 -2.4E-07

34.56 1.69 0.003456 0.00655 126.4154 -4.5E-07

31.22 1.99 0.003122 0.007713 123.5292 -5.4E-07

26.72 2.56 0.002672 0.009922 117.0987 -7.9E-07

24.15 3.09 0.002415 0.011977 110.3864 1.79E-07

22.39 3.43 0.002239 0.013295 107.2818 -1E-06

20.69 3.57 0.002069 0.013837 108.1793 -8E-07

18.11 4.04 0.001811 0.015659 105.6253 -6.4E-07

16.48 4.36 0.001648 0.016899 104.237 -5.3E-07

14.81 5.11 0.001481 0.019806 97.63582 1.53E-06

12.65 5.92 0.001265 0.022946 93.18194 -8.4E-07

7.67 8.52 0.000767 0.033023 83.29419 4.71E-07

6.15 9.84 0.000615 0.03814 79.22485 5.42E-07

5.12 10.74 0.000512 0.041628 77.5136 -3.5E-06

4.29 11.52 0.000429 0.044651 76.51639 -3E-06

3.79 12.83 0.000379 0.049729 72.32773 -3.8E-06

2.68 13.77 0.000268 0.053372 73.56551 -2.1E-06

2.18 14.75 0.000218 0.057171 72.53612 -1.8E-06

1.52 16.79 0.000152 0.065078 69.84513 -1.5E-06

1.43 17.53 0.000143 0.067946 68.15546 -1.6E-06

1.11 18.51 0.000111 0.071744 68.09101 -1.2E-06

AVG EEV =

96.426

133

Table A3.2: Calculation of EEV values for PEG 10000 + KC + Water System from Equation 6.2

PEG

10000,

100WP

KC,

100WS

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

134

Table A3.3: Calculation of EEV values for PEG 10000 + AC + Water System from Equation 6.2

PEG 10000,

100WP

AC,

100WS

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

135

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 + + - + -

136

12 + - - + +

13 - - + + +

14 - - + - -

15 + + - - +

16 - - - + -

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 = *

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

137

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

138

Effects Pareto for Y FFD

DE

BE

AD

CE

AC

BD

CD

B

AB

BC

A

E

AE

D

C

20151050

Te

rm

Effect

5.39

A PEG

B SC

C pH

D NaC l

E Temp

Factor Name

Pareto Chart of the Effects(response is Y FFD, Alpha = 0.05)

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.

139

20151050

98

95

90

85

80

70

60

50

40

30

20

100

Absolute Effect

Pe

rce

nt

A PEG

B SC

C pH

D NaC l

E Temp

Factor Name

Not Significant

Significant

Effect Type

AE

E

D

C

Half Normal Plot of the Effects(response is Y FFD, Alpha = 0.05)

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%

140

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

141

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%

142

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.

143

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%

144

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.

145

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

146

Optimization Plot

CurHigh

Low0.75683D

Optimal

d = 0.75683

Maximum

Y RSM

y = 94.4070

0.75683

Desirability

Composite

20.0

40.0

0.10

0.30

6.0000

8.0NaCl TemperatpH

[7.4545] [0.10] [32.7273]

147

Checking Model Assumption for fFD: (Residual Plots)

86420-2-4-6-8

99

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Residual

Pe

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nt

Normal Probability Plot(response is Y FFD)

90807060504030

5.0

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-7.5

Fitted Value

Re

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Versus Fits(response is Y FFD)

148

16151413121110987654321

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Observation Order

Re

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(response is Y FFD)

149

Checking Model Assumption for RSM: (Residual Plots)

210-1-2

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Normal Probability Plot(response is Y RSM)

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929088868482807876

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Fitted Value

Re

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lVersus Fits

(response is Y RSM)

2018161412108642

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Observation Order

Re

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Versus Order(response is Y RSM)