1972 年 21 巻 224 号 p. 453-458
The steady-state compliance Je as a function of the molecular weight M and the concentration c for polymer solution can be expressed as:
Je=αM/cRT for smaller values of c or M
=βM0/c2∼3 for larger values of c and M
Here α and β are constants and RT is used in its usual meaning. The second behavior of Je is characteristic of highly entangled system. In the concentration range where the transition from the first to the second behavior occurs, the Je displays the maximum.
Either of the two relaxation spectra, A and B, are found to be compatible with these observed behaviors of Je. These are:
(A) HW(τ)=1/2cRT/Me(τc/τ)1/2 0<τ<τc
τc=τ1E-2, τm=τcE3.5, τl=τmeh(1/E-1)
(B) HW(τ)=1.75/3cRT/Me(τc/τ)2/3 0<τ<τc
τc=τ1E-1.5, τm=τcE3.5, τl=τme1.75h(1/E-1)/2
The former corresponds to the Rouse theory, while the latter to the Zimm theory. Here, τ1 represents the maximum relaxation time of the original Rouse or Zimm theory, Me is entanglement spacing, E is the number of entanglement point in a molecule, hence E=M/Me, and gN and h are parameters representing the intensities of HI and HB, respectively.
The viscosity η, storage modulus G' and loss modulus G" are also calculated on the basis of these spectra. These results are qualitatively in agreement with the observed one, particularly in the case of high value of h and low value of gN.