Aqueous Solutions of Polyelectrolytes: Vapor–Liquid Equilibrium and Some Related Properties - Polymer Thermodynamics - page 90

where c s is the mass density of solute s and A s;s and A s;s;s are the second and third

osmotic virial coefficients, respectively, of solute s in the solvent. In nearly all light
scattering experiments of aqueous solutions of a polyelectrolyte, the solvent was
not only pure water but an aqueous solution of a salt, and the experimental results
were interpreted using (10). Then, the evaluated data for the osmotic virial coeffi-
cients depend on the nature and the concentration of that salt. Table 6 gives a survey
of literature sources for the second osmotic virial coefficients of a single polyelec-
trolyte in an aqueous solution from light scattering experiments. The second
osmotic virial coefficient is determined by extrapolating experimental results to
infinite dilution. Light scattering is particularly suited for the investigation of such
highly diluted mixtures.
However, even when the polymer contains no ionic groups the extrapolation
might be rather difficult (e.g., Hasse et al. [ 70 ], Kany et al. [ 71 , 72 ]). Figure 7 shows
a typical example of the influences of the molecular mass and the concentration of a
salt on the second osmotic virial coefficient of a polyelectrolyte in water. The
second osmotic virial coefficient increases considerably with decreasing salt con-
centration. The influence of the molecular mass is less distinct and often hidden by
the scattering of the experimental data, particularly if that data is from different
literature sources. In an aqueous solution of a strong electrolyte, the second osmotic
virial coefficient of polyelectrolytes with different backbone monomers can vary by
about one order of magnitude.

~

Table 6 Survey of literature data for the second osmotic virial coefficients of a single electrolyte
in an aqueous solution from light scattering investigations
Polymer

Polymer
concentration ~

Salt Salt

concentration c s

References

c p

(g/dm 3 ) (mol/dm 3 )

NaPSS 0.5 3 NaCl 0.005 4.2 [ 57 ]

Na/HPSS < 0.8 Na/H/NO 3 0.005 3.7 [ 47 ]

NaPSS; Pb/
HPSS

0.4 3 NaNO 3 , HNO 3 ,

Pb(NO 3 ) 2

0.005 2 [ 58 ]

KPSS KCl 0.1 [ 59 ]

NaPA 0.1 2 NaCl 0.01 1 [ 59 ]

HPAA 0.1 3 NaCl 0.01 1 [ 60 , 61 ]

NaBr 1.5

CaCl 0.1

NaCMC 0.1 4 NaCl 0.001 0.5 [ 62 ]

NaCMC 0.2 0.8 NaCl 0.005 0.5 [ 63 ]

NaPAMS NaCl 0.01 5 [ 64 ]

NaPAMA NaCl 1 [ 65 ]

PDADMAC NaCl 0.5 [ 66 ]

PDADMAC NaCl 1 [ 67 ]

PAAm 1.87 NaCl 0.05 3 [ 68 ]

PTMAC NaCl 1 [ 65 ]

PTMAC NaCl 0.1 4 [ 69 ]