The volume fractions of each component in the dilute phase (υ′
1, υ′
2, υ′
3) and concentrated phase (υ
1″, υ
2″, υ
3″) were calculated according to Flory's and Scott's theoretical equations, in the ternary system, solvent, nonsolvent, and polymers, for the polymerization degree of 1000, 5320, and ∞.
In these treatments it was assumed that
P1=
P2=1,
P3>>1 for the polymerization degree
Pi; and
A=
X13/
P1=
X31/
P3=
O,
B=
X12/
P1=
X21/
P2=
O,
C=
X32/
P3=
X23/
P2≠
O for the interaction parameters.
For further calculation, two cases were considered; in one, volume of the solution is kept constant by overflow of the excess solution such as in turbidimetric titration, and in the other, the whole solution is kept in a large vessel, such as in the case of the fractionation of a polymer. For these two cases, the volume fraction of the condensed phase Φ, the quantity of the precipitated polymer Φ
v3″, the ratio of the quantity of the precipitated polymer to the total quantity of the polymers in the system Φυ
3″/υ
3 were calculated as functions of the relative volume of the nonsolvents added to the system (
V/
V0). These treatments were made under the conditions where the interaction parameter
C was 2.27 and the initial concentration υ
30 was 0.0125, 0.0100, 0.0075, 0.0050, and 0.0025.
For each polymerization degree and each initial concentration, the volume of the nonsolvent, to be added to the system (
V/
V0)
p before the precipitation starts, was also calculated.
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