Viscoelasticity of Moderately Concentrated Polymer Solution

Abstract

Investigation has been made on viscoelastic properties of moderately concentrated high-polymer solutions of the order of small percentage. Tschoegl, Ferry et al. have developed a general theory on the viscoelasticity of random coiled chain polymers, adopting into it the so-called hydrodynamic interaction effect and the excluded volume effect between the segments from the well-known Rouse-Zimm theory, Making a comparison between their theoretical complex modulus and experimental ones, they have pointed out that the hydrodynamic interaction seems to decrease with increasing concentration of solutions and increasing molecular weight of polymers. With increase of interpolymer interactions the polymers will behave with increased free-draining coils.
This is rather a strange thing from the theoretical view-point. It even betrays some discrepancy between the theory and the experimental results in some cases. Though the Tschoegl's calculation shows the relation G"-ωη_s>G' excepting very high frequency region corresponding to the minimum relaxation time, there are some systems that give the inverse relation G"-ωη_s<G' at moderately high frequency region.
In the case of concentrated solutions or melts of polymers, there exists the flat, so-called“box” region of relaxation spectrum due to the entanglement of polymer chains in the longer relaxation time region than the“wedge”region corresponding to the mechanism described by the Rouse-Zimm-Tschoegl's theory. Even in our moderately concentrated solution, the relaxation spectrum may have the box region to some extent, though the entanglement is not so remarkable. This effect may decrease the average gradient of spectrum as a whole as the reduction of the hydrodynamical interaction.
In this paper, we assume the relaxation spectrum
H(lnτ)={τ^-α τ_α<τ<τ_c=1
1 1=τ_c<τ<τ_M
0 otherwise
α=0.63 for non-draining (Zimm's) case
α=0.50 for free-draining (Rouse's) case
and calculate the complex modulus G' and G" for some values of maximum relaxation time τ_M. Our complex modulus is qualitatively in good agreements with the experimental results carried out by Ferry et al. It is also pointed out that the value of τ_M in this case, ≈20, is well explained by Hayashi's theory of weakly coupled rubber-like network structure.