Some animated charts are shown to help to understand used principle presented on our theory papers.

### Model for Relaxation Modulus

Real polymer relaxation occurs in two phases: first, Rouse (1953) relaxation and later
in second phase with reptation, collisions,

and entangling in longitudinal modes, all of which we refer to here as entanglement relaxation. Molecular entanglements will open

and relax after deformation at times t >0.001 s,

where most G(t) observations are made.

Fig. 1. Schematic models of the relaxation modulus.a. The standard normal rheologically effective distribution (RED), w(t), plotted on a logarithmic scale with t_{c} = 1 s.

Its characteristic relaxation according to Eq. (5) is very close to the classical Maxwellian single-element relaxation, with t = 100 s (dashed line).
b. Relaxation by Eq. (7) using the log-normal distributions w(log t) and w(log t/R), with constants t_{c} = 10^{-6} s, P' and P'' set to 0.1,

and R = 10^{4}. Both normalized relaxation moduli G(t)/G_{0} and logarithmic log G(t) with illustrated G_{0}=10Pa are shown.

Typical similar real polymer has average molecular weight M in range 100,000, and the polydispersity index, M/Mn below 1.2.
### Melt calibration

We need to convert distribution scales between molecular weight scale M and rheologically effective scale as a function of time t

by introducing the melt calibration, which is the relation between rheological properties and the molecular weight.

Fig. 2. Relation model for melts, and conversions from the RED to the MWD.

a. In a relaxed polymer, a test point in the melt after a small shear deformation at t_{0}
is equivalent to a statistical nonrelaxed sphere of volume V_{0},

which shrinks as a function of radius r(t) as the farthest molecules or the ends of individual molecules relax first, resulting in less deformation relative to the test point.
b. Melt calibration curve M(t) for PS, and the respective typical universal calibration curves for different SEC columns marked by dashed lines.
c. RED w(log t) from the time scale converted to inverse molecular weight scale w (top) and MWD w(log M) using Eq. (9).
### Model for Viscosity and Dynamic Moduli

We have developed a principle for using complex viscosity data obtained from a dynamic rheometer measured in the frequency-sweep mode.

Fig. 3. Schematic model of the viscosity and dynamic moduli.

### General Model for Viscosity and dynamic moduli

Fig. 4. General Model for Viscosity and dynamic moduli

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and entangling in longitudinal modes, all of which we refer to here as entanglement relaxation. Molecular entanglements will open

and relax after deformation at times t >0.001 s,

where most G(t) observations are made.

Fig. 1. Schematic models of the relaxation modulus.

Its characteristic relaxation according to Eq. (5) is very close to the classical Maxwellian single-element relaxation, with t = 100 s (dashed line).

and R = 10

Typical similar real polymer has average molecular weight M in range 100,000, and the polydispersity index, M/Mn below 1.2.

by introducing the melt calibration, which is the relation between rheological properties and the molecular weight.

Fig. 2. Relation model for melts, and conversions from the RED to the MWD.

which shrinks as a function of radius r(t) as the farthest molecules or the ends of individual molecules relax first, resulting in less deformation relative to the test point.

Fig. 3. Schematic model of the viscosity and dynamic moduli.

Fig. 4. General Model for Viscosity and dynamic moduli