Architecture effects on the bulk and shear rheology and PVT behavior of polymers
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The viscoelastic bulk modulus [K(t)] plays an important role in residual stress development during polymer and composite processing and application, and in developing relationships among the four fundamental material functions, bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio. In addition, the origins of viscoelastic bulk and shear moduli are still unresolved. However, while the viscoelastic shear modulus has been widely studied, only a handful of investigations can be found in the literature concerning the viscoelastic bulk response. In order to investigate the viscoelastic bulk modulus, pressure relaxation responses were measured in a custom-built pressurizable dilatometer capable of making K(t) and pressure-volume-temperature (PVT) behavior measurements. The architectural effects on the bulk and shear relaxation responses of two polycyanurate networks have been studied and suggest that the shift factors used to construct the reduced curves are identical in the liquid states. Furthermore, comparisons of retardation time spectra indicates that bulk and shear responses have similar underlying molecular mechanisms at short times since the slopes are similar for the spectra; however, long-time mechanisms that are available to the shear are not available to the bulk. In addition, the architectures are found to have negligible effects on the bulk response; on the other hand, the relaxation/retardation time distributions for the shear are observed to increase with decreasing the crosslink density. The architecture effects were also studied on the bulk and shear responses for linear and star shape polystyrenes. The shift factors are also found to be identical for the bulk and shear responses of the two polymers in the liquid state; moreover, by comparing the bulk and shear retardation time spectra, shear deformations are found to have long-time mechanisms that are not available for the bulk. The pressure-volume-temperature (PVT) behavior of the thermosetting networks is studied to investigate the pressure-dependent glass transition temperature (Tg) and the architecture effects on the PVT behavior. The results show that although the Tg values are different, the two networks have similar values of dTg/dP. By comparing the PVT data calculated from Tait equation with best fits to the experimental data for the two networks, the most important variable governing the PVT behavior of the thermosetting materials is found to be the glass transition temperature, which strongly depends on crosslink density. Finally, the temperature- and pressure-dependent shift factors which are related to the relaxation times are reduced using a thermodynamic scaling, where Tau= ƒ(T^-1V^-gamma), and compared the results to the T – Tg scaling, where Tau = ƒ(T – Tg). The thermodynamic scaling law successfully reduces the data for all of the samples; however, polymers with similar structures, but with different Tg and PVT behavior, i.e., the two polycyanurates, cannot be superposed unless the scaling law is normalized by TgVg^gamma. On the other hand, the T – Tg scaling successfully reduced the polymers having similar microstructures.