초록
Some methods have been evaluated to predict the stress relaxation behavior of concentrated polymer solutions from their linear viscoelastic functions. The linear viscoelastic properties and the linear relaxation modulus of concentrated aqueous poly(ethylene oxide) (PEO) solutions were measured with a Rheometrics Fluids Spectrometer (RFS II) and an Advanced Rheometric Expansion System (ARES-200 FRTN1). The discrete relaxation spectrum (DRS) was determined using three methods, namely, a linear regression, without and with regularization, and a nonlinear regression of the dynamic storage and loss moduli. The effects of several factors on the fitting procedure to determine the DRS and of the molecular weight and solution concentration on the relaxation behavior were discussed. Further, the experimentally measured retaxation modulus G(t) was compared with the results obtained from the two kinds of calculation methods. The first kind is to calculate C(t) from the DRS using the generalized Maxwell model, and the second one is a direct conversion of the dynamic moduli using the Fourier transform. Finally, the reliability of the DRS determination and G(t) calculation methods was examined by comparing the experimental storage and loss moduli with those back-calculated from the DRS and calculated from the measured G(t). Main results obtained from this study can be summarized as follows : (1) All three methods for the determination of DRS from dynamic data give similar values of the relaxation strength of modulus for a given value of each relaxation time, even though the number of relaxation times becomes different to avoid a mathematically ill-posed problem. (2) For highly concentrated polymer solutions, both linear and nonlinear regression methods have a restriction on the number of relaxation times. On the other hand, a linear regression method with regularization has a larger number of relaxation times, and consequently, shows a more distinct shape of the relaxation spectrum than the other regression methods. (3) The G(t) calculated from the DRS and by a direct conversion of the dynamic moduli is in good agreement with the experimentally measured G(t). Therefore, the C(t) calculated from the linear viscoelastic functions using the two kinds of methods provides a sufficient information to predict the actual stress relaxation behavior. (4) The storage and loss moduli back-calculated from the DRS and calculated from the measured G(t) coincide well with the experimentally measured data. It can, therefore, be concluded that the DRS determination as well as G(t) calculation methods adopted in this study have a considerably high reliability.
