Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.4 Measurement of solvent activity 181
( 2)
AM = AM / [4.4.37]
3 n 2 n
⎛ π ⎞
⎜
⎟
⎝c
⎟
2 ⎠
05 . 05 .
RT
=
Mn
⎛ ⎞
⎜
⎟
⎝ ⎠
2
⎡ AM 2 n
⎢1+
c
⎣ 2
2
⎤
⎥
⎦
[4.4.38]
Examples for experimentally determined virial coefficients can be found in the above
mentioned papers 139-145 and in the tables prepared by Lechner et al. 9 Solvent activities can be
calculated via Equations [4.4.35 to 38] from osmotic second virial coefficients with some
care regarding the necessary accuracy of all numerical values included. The partial molar
volume of the solvent can be approximated in most cases by the molar volume of the pure
solvent. Noda et al. 139 published a combined investigation of the thermodynamic behavior
of poly(α-methylstyrene)s having sharp molar mass distributions and covering a wide range
of molar masses in toluene. They applied osmotic pressure, light scattering and vapor pressure
measurements and demonstrated the capabilities of these methods in comprehensive
and detailed form. Gaube et al. 126,127 could show that in the case of aqueous dextran solutions,
water activity data and virial coefficients measured by VPO and by membrane
osmometry are in good agreement.
4.4.3.2.2 Light scattering
Light scattering is one of the most widespread characterization techniques for polymers.
Therefore, technical and methodical details will not be explained here - please see Refs. 26-32
for such information. The general set-up of
a scattering principle is illustrated by Figure
4.4.18. The scattering vector q is the difference
between the wave vectors ki and ks of
the incident and the scattered plane waves,
the scattering angle θ is the angle between
both vectors. Both are related by |q| =(4
π/ λ0
)sin(θ /2), where λ0 is the wavelength
of light in vacuum. Laser light is used today
for the light source.
Light scattering in homogeneous flu-
Figure 4.4.18. General set-up of a scattering experiment: ids is caused by fluctuations in the dielectric
ki, ks - wave vectors of the incident and the scattered constant. In pure liquids these are due to
plane waves, q - scattering (or wave) vector, D- detector,
density fluctuations, in homogeneous solu-
S - sample, θ - scattering angle from the transmitted
beam, I tions mainly to concentration fluctuations
0 - incident intensity of unpolarized light, r-the
distance between sample and detector.
which generally lead to much larger fluctuations
in dielectric constant than density
variations. The difference between solution and pure solvent is called excess scattering.
This excess scattering is of interest here, since it is related to the second derivative of Gibbs
free energy of mixing with respect to concentration (and via this way to solvent activities):
I
excess
() θ
TP
∝
2
∂ ΔmixG
∂ϕ ∂ϕ
i j
[4.4.39]