Page 120 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 83

FIGURE 3.24 Common solution viscometers.
Nr 23/ 2
()
η
[] = (3.29)
M
The actual average end-to-end distance, r, is related to the nonsolvent expanded average end-to-
end distance r using the Flory expansion factor, α, as follows:
o
r = α r o (3.30)
Substitution of Equation 3.30 into Equation 3.29 and rearrangement gives

[η]M = N (r ) α 2 (3.31)
2 3/2
o
Values for α vary for Flory theta solvents from 0.5 to about 3 for polymers in good solvents.
In Equation 3.26, “a” values for random coils range from 0.5 for theta solvents to 0.8 for good
solvents, 0 for hard spheres, about 1 for semicoils, and 2 for rigid rods.
The theta temperature corresponds to the Boyle point in an imperfect gas and is the range in
which the virial coeffi cient B in the expanded gas law becomes zero. This same concept applies to
the modification of the gas law (PV = nRT) used to determine the osmotic pressure of a polymer

solution and is simply the van’t Hoff equation that reduces to Equation 3.32 when B = 0.
RTC
π = (3.32)
M n

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