PEI_Phys_Age_Model_Woo - A N onlinear Regression Approach...

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A Nonlinear Regression Approach to Model the Physical Aging of Poly(Ether Imide) E. M. WOO* and SEN-MAW KUO Department of Chemical Engineering National Cheng Kung University Tainan, Taiwan, 701 -01 Differential scanning calorimetry (DSC) was used to measure the relaxation enthalpy of glassy amorphous poly(ether imide) (PEI) at three high isothermal aging temperatures between 190 and 200°C. A three-parameter model based on the Williams-Watts relaxation function was utilized to describe the aging process of PEI, and nonlinear regression approach was used to estimate the model parame- ters. The prediction according to this model was found to be more accurate in comparison with the two-parameter model based on the same Williams-Watts relaxation function. Furthermore, the peculiar aging behavior at the highest aging temperature of 200°C was explained from the molecular view point of transition from sub-T, P-relaxation to a-relaxation near ‘I,. INTRODUCTION olymers are known to be not in an equilibrium P glassy state, but can gradually approach an equi- librium in a temperature range below T,. The time dependence of changes in the behavior is the subject of physical aging. Physical aging of glassy polymers has been extensively studied since it strongly affects the physical and mechanical performances of the ma- terials ( 1 ). The physical aging proceeds at different rates de- pending on the temperatures of the use environment as well as the processing conditions. A quantitative description of aging for polymeric materials is highly desirable in predicting or controlling the performance of the materials. In molecular level, the physical aging is associated with onset of restrained mobility of poly- mer chain segments. Long-term properties of poly- mers can be affected by the extent of physical aging. One of our concurrent studies (2) on the aging be- havior of poly(ether imide) (PEI) has demonstrated that sub-T, relaxations exist and that the p-relaxation (-50 to 200°C with the peak at 70°C) is associated with the aging treatment while the y-relaxation (-1 10°C) is not affected at all by the aging. The p-relaxation peak magnitude is significantly suppressed by the aging treatment, and this result turned out to be different from that reported by Hay et al. who observed no @relaxation in PEI (3. 4). It must be pointed out that different DMA equipment were used. We used Rheo- vibron DDV-I1 (tensile mode) and they used Polymer * To whom correspondence should be addressed. Laboratory DMA (flexural mode). Later, in 1995 Bren- nan and Feller (5) investigated the PEI aging behavior and molecular relaxation using dynamic mechanical analysis (Seiko DMS-200). They reported that the y-relaxation was totally suppressed in the aged PEI samples and attributed the disappearance of y-peak to adsorbed water in the aged PEI samples. However, the appropriateness of that interpretation may be doubtful since their experimental data for the y-relax- ation exhibited pronounced scattering in the temper-
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This note was uploaded on 07/20/2011 for the course EMA 6165 taught by Professor Brennan during the Spring '08 term at University of Florida.

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PEI_Phys_Age_Model_Woo - A N onlinear Regression Approach...

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