| Abstract: | A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude. |
