Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.4 Measurement of solvent activity 149
In summary, investigations on vapor-liquid equilibrium of polymer solutions are the
most important source for obtaining solvent activities in polymer solutions. Therefore, emphasis
is laid in this subchapter on the experimental methods, which use this equilibrium.
Reviews on experimental methods, sometimes including tables with thermodynamic
data were prepared more or less continuously during the last three decades. Especially
methods and results of the application of IGC to polymers and polymer solutions are carefully
reviewed. 13-25 Special reviews on determining solvent activities from various scattering
techniques could not be found. However, there is a large number of reviews and books
on scattering methods and their applications. Some references may give a starting point for
the interested reader. 26-32 Experimental techniques for vapor-pressure measurements were
reviewed in the paper by Bonner. 10 Ebulliometry, cryoscopy and vapor-pressure osmometry
were reviewed by Cooper, 33 Glover, 34 Mays and Hadjichristidis, 40 and a recent summary can
be found in a new book edited by Pethrick and Dawkins. 26 Reviews that account for the
measurement of thermodynamic data from sedimentation equilibria using the ultracentrifuge
are given by Fujita, 35 Harding et al. 36 or Munk. 37 An overview on membrane
osmometry was given by Adams, 38 Tombs and Peacock 39 or Mays and Hadjichristidis, 40 and
a recent summary can again be found in the book edited by Pethrick and Dawkins. 26 Reviews
on liquid-liquid demixing of polymer solutions will not be summarized in detail here,
some references should be enough for a well-based information. 41-45 A short summary on
equipment and thermodynamic equations of most techniques was given in Danner’s handbook.
2 Finally, the classical books on polymer solutions written by Flory, 46 by Huggins, 47
and by Tompa 48 must not be forgotten for the historical point of view on the topic of this
subchapter.
4.4.2 NECESSARY THERMODYNAMIC EQUATIONS
Here, the thermodynamic relations are summarized which are necessary to understand the
following text. No derivations will be made. Details can be found in good textbooks, e.g.,
Prausnitz et al. 49
The activity of a component i at a given temperature, pressure, and composition can be
defined as the ratio of the fugacity of the solvent at these conditions to the solvent fugacity
in the standard state; that is, a state at the same temperature as that of the mixture and at
specified conditions of pressure and composition:
0 0
( , , ) ≡ ( , , ) / ( , , )
a TPx f TPx f TP x
i i i
[4.4.1a]
where:
ai activity of component i
T absolute temperature
P pressure
x mole fraction
fi fugacity of component i
In terms of chemical potential, the activity of component i can also be defined by:
0 0
( TPx , , ) − ( TP , , x )
⎧
⎪μ
i μ i
ai( T, P, x)
≡exp⎨
RT
⎩⎪
⎫
⎪
⎬
⎭⎪
[4.4.1b]