We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we extrapolate the low-density expansion outside the dilute regime, obtaining the osmotic pressure for any concentration in the semidilute region. Comparison with field-theoretical predictions and experimental data shows that the obtained expression is quite accurate. The error is approximately 1%–2% below the overlap concentration and rises at most to 5%–10% in the limit of very large polymer concentrations.
REFERENCES
In experimental works the virial coefficients are usually defined from the expansion of in terms of the weight concentration , , where is the molar mass of the polymer. The coefficients are related to those we have defined by , where is the Avogadro number.
In Sec. 17.3.2 of Ref. 4 field theory is used to obtain a prediction for the virial expansion in the exponential ensemble. In terms of the variable , . This implies . Note that also for this polydisperse case field theory predicts a negative fourth virial coefficient.
