高分子物質の応力緩和に及ぼす分子量分布の影響

抄録

It has been made very clear by recent works of many researchers that the distribution of mechanical relaxation time in the rubbery region of a linear amorphous polymer is related closely to the shape of the molecular weight distribution. Attempts have been made to express this relation quantitatively, from a phenomenological point of view.
These criteria have been considered helpful as indicators of the degree of polymer polydispersity. One is that the height of the relaxation spectrum increases with increasing sharpness of the molecular weight distribution, and this fact was previously discovered by Tobolsky and his co-workers and the indicator of the degree of polymer polydispersity in this case is here shown by E_m.
The other is that the relaxation spectrum approximates a“box”more closely with increasing sharpness of molecular weight distribution, and this fact was ascertained by Tobolsky and Murakami, and the indicator of the degree of polymer polydispersity in this case is here expressed by α, and α is satisfied by the equation α=τ_mE_m/η.
Some researchers have previouly studied the relation between the steady state compliance J_e and the structure of polymers. According to Leaderman, Ninomiya, and others, J_e appears to be dependent upon the molecular weight distribution rather than the molecular weight of polymers. The authors have succeeded in proving that J_e is dependent upon the molecular weight distribution by applying procedure X developed by Murakami and Tobolsky.
According to procedure X, relaxation modulus E_r (t) can be written by the following equation using the distribution of relaxation time in the rubbery region.
E_r(t)=E_me^-t/τm+E_m-1e^-t/τm-1+…… (1)
The steady state viscosity ηt is shown by
η_t=∫^∞₀E_r(t)dt (2)
Substituting equation (1) into equation (2), we obtain
η_t=E_mτ_m+E_m-1τ_m-1+…… (3)
The steady state compliance J_e is indicated by
J_e=1/η²t∫^∞₀∫^∞_t^*Er(t)dtdt^* (4)
Substituting equation (1) into equation (4), we obtain
J_e=1/η²_t(E_mτ²_m+E_m-1τ²_m-1+……) (5)
In the region of t>>τ_m, equation (3) is simplified into equation (6), and equation (5) is similarly modified into equation (7), neglecting the second and more terms.
η_t=E_mτ_m (6)
J_e=1/η²_tE_mτ²_m
=1/E_m (7)
In conclusion, equation (7) shows that the steady state compliance J_e is proportional to 1/E_m. Here E_m is just the indicator of the polydispersity of polymers as mentioned above.
To be more exact however, J_e becomes α²/E_m by using the other indicator α.
The data actually obtained and the logical conclusion is thus compared. It is discussed also whether the steady state compliance J_e can precisely be the parameter of the molecular weight distribution.