## Determination of the Binodal

By convention, the component predominantly in the bottom phase is plotted as the abscissa and the component predominantly in the top phase is plotted as the ordinate. The three methods are illustrated graphically in Fig. 2 (see Note 4).

### 3.1.1. Turbidometric Titration

1. In test tubes, using the appropriate stock solutions, prepare systems with different compositions of known weight. Account for the additional volume owing to titration, e.g., if 5 g systems are prepared, 10 mL test tubes should be used (see Note 5). As an example Table 1 shows systems that can be used for various PEG-phosphate and PEG-dextran systems, and the necessary calculations. This table may be reproduced in a spreadsheet program to allow ease of calculation.

2. Note the weight of the test tube and titrate, drop-wise, with the appropriate diluent (see Note 7) until the system just turns clear, i.e., one phase is formed. This can be carried out while the system is continually being mixed or by adding a drop, mixing, adding a second drop, and so on. To ensure that a one-phase system has formed, systems should be centrifuged (e.g., 1000-2000g, 5 min) (see Note 8).

3. Note the final weight of the test tube and calculate the weight of diluent added just prior to one-phase formation.

4. Because the number of systems titrated is proportional to the number of points on the binodal, greater accuracy is achieved with a greater number of systems (see Note 9).

3.1.2. Cloud Point Method

1. Weigh 5 g of a stock solution of component X into a 25-mL conical flask.

2. Weigh the flask and add, drop-wise, a stock solution of component Y until the first sign of turbidity, i.e., the cloud point. Mix as previously noted.

3. Note the weight of component Y necessary for the mixture to cloud. This provides the first point on the binodal. Refer to Table 2 for calculations.

4. Add a known weight of diluent (see Note 7) to below the cloud point and repeat as noted.

Fig. 2. Graphical representation of three methods used to determine the binodal. 1. illustrates the cloud point method, where a concentrated stock of component 1, i.e., polymer/salt X is added to a concentrated stock of component 2, i.e., polymer Y. The solution is repeatedly taken above and below the cloud point; the binodal lies between these two points (shown by the "zig zag" line). 2. illustrates turbidometric titration where a series of systems (•) are prepared and titrated until a one-phase system is formed—the binodal lies just above this point (A). 3. illustrates the determination of nodes (■) for systems, which is accomplished by preparing a series of systems lying on different tie-lines (------•------) and analyzing the concentration of components in the top and bottom phase.

Fig. 2. Graphical representation of three methods used to determine the binodal. 1. illustrates the cloud point method, where a concentrated stock of component 1, i.e., polymer/salt X is added to a concentrated stock of component 2, i.e., polymer Y. The solution is repeatedly taken above and below the cloud point; the binodal lies between these two points (shown by the "zig zag" line). 2. illustrates turbidometric titration where a series of systems (•) are prepared and titrated until a one-phase system is formed—the binodal lies just above this point (A). 3. illustrates the determination of nodes (■) for systems, which is accomplished by preparing a series of systems lying on different tie-lines (------•------) and analyzing the concentration of components in the top and bottom phase.

3.1.3. Node Determination

1. Prepare a series of systems and analyze the phase composition of the top and bottom phase. (See Subheading 3.2.).

2. To aid in the selection of systems, start with, e.g., 5% (w/w) of component X and 5% (w/w) of component Y. If the resultant mixture forms one phase, then prepare additional systems in, e.g., 2% (w/w) increments until two phases form. Continue to prepare additional systems in this way for phase concentration analysis.

System Composition for Various PEG-Phosphate (bold) and PEG-Dextran (unbold) Systems (see Note 6) and the Necessary Calculations for Binodal Determination Using Turbidometric Titration

Component X Component Y Salt eg NaCI__

Final weight of system (g)

50 100

"'., IH »)

(» «)

7.0 / 1.0

27.5 / 7.0

7

27.5

7.5 / 2.0

25.0 / 6.0

8.0/3.0

22.5 / 5.5

8.5 / 4.0

20.0/5.0

11.0/4.5

17.5/4.5

12.5/6.0

15.0/4.0

13.5/7.0

12.5/3.5

15.0/9.0

10.0 / 3.0

17.5 / 10.0

7.5 ; 2.5

20.0 / 11.0

5.0 / 2.0

22.5/' 13.0

Vmmmt ol* stock

Dilimiil

Final composition

Y final

=(A19*BI0)/B3 =(B19*BI0)/B5 =(CI9»BI0)/B7 =BI0-(D19+E19+F19)

=( A ] 9* B1 ())/( B10+H ! 9 ) =(B19*Bi0)/(BI0+II19)

X, concentration of polymer/salt X; Y, concentration of polymer Y; X, Y final, composition on the binodal; d, amount of diluent required just to pne-phase formation. Example shown has the necessary calculations below the values.

Table 2

Calculations for Binodal Determination Using the Cloud Point Method

Table 2

Calculations for Binodal Determination Using the Cloud Point Method

 A 1 B C 1 D E 1 F G 1 5 Component X Component Y 50 6 7 8 9 X stock Amount oi slock I' inul composition !i 10 11 Y stock K 1 olul \ slock Xiiiul "■;, (« «) ^ llnul 1 Dial ivi'i^hl 12 13 5 y =(B3*A13)/(A13+B13) =(B5*B13)/(A13+B13) d 14 y i =B13+B14 =(B3*A13)/(A13+F13+C14) =(B5*B 13)/(A 13+F13+C14) d / =F13+F14 15 y-' =C14+B15 =(B3*A13)/(A13+G14+C15) =(B5*B13)/(A13+F14+C15) d2 =G14+F15 16 y-i =C15+B16 =(B3*A13)/(A13+G15+C16) =(B5*B 13)/( A! 3+F 15+C16} di =G15+F16 17 y 4 =C16+B17 =(B3*A13)/(A13+G16+C17) =(B5*B13)/(A13+F16+C17) cW =G16+F17

Example shown starts with 5 g of the stock solution of component X. A known amount of the stock solution of component Y is required to cloud the solution. X, Y final: concentration of component X and Y at the point of clouding, y: amount of stock Y required just prior to clouding and d: diluent necessary to reach below the cloud point.

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