Viscoelastic Properties of Dilute Solutions of Unperturbed Chain Polymer and Poly-L-, Copoly-DL-Amino Acids

Abstract

In view of the theories of viscoelastic properties of dilute polymer solution dealing with the state at infinite dilution, we have introduced the following intrinsic quantities corresponding to infinite dilution, the complex intrinsic rigidity, [G^*]=lim_c→0(G^*-iωη_s)/c; the dynamic intrinsic viscosity, [η^*]= lim_c→0(η^*-η_s)/η_sc; and the limiting relaxation time, (τ_p)₀=lim_c→0τ_p(c)=lim_c→0K_p(η_sp/c)M/RT. Here K_p is the relaxation time factor determined by the theories.
The dimensionless functions of the intrinsic rigidity and viscosity are derived for random coil polymers from the Rouse-Zimm theories as follows,
[G']M/RT=Σ_pω_s²K_p²/(1+ω_s²K_p²), [G"]M/RT=Σ_pω^sK^p/(1+ω_s²K_p²),
[η']/[η]=Σ_pK_p/(1+ω_s²K_p²), [η"]/[η]=Σ_pω_sK_p²/(1+ω_s²K_s²),
ω_s=ω(τ_p)₀/K_p=ωη_s[η]M/RT,
where K₁=0.608 for the Rouse theory and K₁=0.422 for the Zimm theory. The same functions are derived for rod-like polymers from the Kirkwood-Auer and dumbbell model theories as follows,
[G']M/RT=Bω_s²K²/(1+ω_s²K²), [G"]M/RT=Aω_sK+Bω_sK/(1+ω_s²K²),
[η']/[η]=AK+BK/(1+ω_s²K²), [η"]/[η]=Bω_sK²/(1+ω_s²K²),
where A=1/5, B=3/5 and K=5/4 for the K-A theory, and A=1/3, B=1/2 and K=6/5 for the dumbbell model theory.
The intrinsic rigidity and the dynamic intrinsic viscosity are both obtained by means of torsional crystal method at frequencies of 19.6kc, 39.2kc and 117.7kc, and all the measurements are confined within concentration range 0.1 to 0.7%.
The results for polyisobutylene (PIB) in benzene at the temperature of 24.0°C agree with the Zimm theory (nondraining case). In the previous study it was shown that PIB in cyclohexane (good solvent) is partially-free-draining. It appears that the draining effects have correlation with excluded volume effects.
The results for poly-γ-methyl-D-glutamate (PMDG) and poly-γ-benzyl-L-glutamate (PBLG) in helix solvents show that the K-A theory gives qualitatively a good first approximation to viscoelastic behavious of α-helix molecules in dilute solution. The internal freedom of α-helix molecules is under strong restrictions and it is considered as consisting of rigid rod-like molecules.