Abstract
The non-Newtonian viscosity derived from the previously proposed constitutive equation7) was expressed as follows,
η(γ)=∫∞0H(λ)1/2α2[1/A(α)]dλ, A(α)=∫∞0e-x-α2x2dx, α2=1/2βλγ
where H(λ) was the relaxation spectrum and λ, γ, and β were the relaxation time, shear rate and a nondimensional parameter of order 1, respectively. When polymers are approximated in their narrow-distribution H(λ) by
H(λ)={H1/1-δ00, λ0≤λ≤λ1, δ0=λ0/λ1 Otherwise
the non-Newtonian viscosity calculated from these equations can be superposed as shown in Fig. 1. If λ1 is replaced by the natural time λN defined by λN=η(0)J(0), which is more directly related to measurable quantities, the reduced shear rate in Fig. 1 becomes
βδs/1+δ0λNγ
where J(0) is steady-state compliance and δs=1+1.8δ00.86.
Prest's data8) of J(0) are expressed in terms of entanglement density E as follows
J(0)/JRc=1.22E/1+0.22E, E=M/Mc or CM/(CM)c
where JRc is the Rouse steady-state compliance at the critical molecular weight Mc. If this experimental equation is used with assumptions that β is independent of M and δ0-1=E, the relation between the characteristic time λch and M is to be expressed as
λch∝η(0)E/1+0.34E.
This is in the same relation as Graessley's, and is applied to the narrow distribution of polydimethyl siloxane melts9) with fairly good agreement as shown in Fig. 2. The solid line in this figure shows the viscosity curve at δ0=1 in Fig. 1.
