When a polymeric material is subjected to deformation, it experiences the so-called “frictional” or “viscous heating” phenomenon. In a typical engineering analysis of a flowing polymer melt, one has to solve a system of partial differential equations, which includes the energy balance equation. For simplicity reasons, the internal energy of a fluid particle is taken as a unique function of temperature (i.e., not a function of deformation rate). This constitutes the formulation of the so called Theory of Purely Entropic Elasticity (PEE) [1-4] as applied to polymer melts. In other words, the internal energy of a polymer melt does not change when subjected to isothermal deformation, and elastic energy is accumulated exclusively through a decrease in conformational entropy. The objective of this work is to examine the nature of the elastic energy stored by polymer melts subjected to deformation.
We tested the validity of PEE using two complementary strategies. First, we made precise measurements of the constant volume heat capacity of polymeric melts subjected to either shear or uniaxial elongational flow. Next, we performed atomistic simulations of polydisperse n-alkane systems with an applied “uniaxial orienting field”[5, 6]. The average chain lengths in the simulations ranged from 24 to 78 CH2 units. The chains were modeled using the united-atom approach of Siepmann et al. . The free energy of the melts was evaluated either directly via thermodynamic integration, or by using viscoelastic models.
First, our experimental measurements seem to suggest that the polymeric materials under investigation deviate significantly from PEE at moderate to high deformation rates. This comes to complement the original experiments performed when PEE was formulated, where the spectrum of deformation rates investigated was very low [3, 4]. Next, our simulation results indicate that the changes in free energy and internal energy as the “orienting field” is applied are comparable in magnitude. Moreover, we have also found that the “conformational” part of the heat capacity [8, 9] is non-negligible, and has a strong dependence on temperature and molecular weight. We have found an excellent qualitative agreement between our own experimental measurements and simulation results. For example, the energetic contribution to the elastic response of a polymer melt is increasing as the temperature is lowered, or the deformation rate is increased. All of these effects will be presented and discussed in detail, as well as their implications to the Theory of Purely Entropic Elasticity.
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