202e

**Introduction**

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.

** **

**Approach**

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 CH_{2} units. The
chains were modeled using the united-atom approach of Siepmann et al. [7]. The free
energy of the melts was evaluated either directly via thermodynamic
integration, or by using viscoelastic models.

**Results**

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*.

**References:**

1. Astarita, G., *Thermodynamics of Dissipative Materials with Entropic
Elasticity.* Polymer Engineering and Science, 1974. 14(10): p. 730-733.

2. Astarita,
G. and G.S. Sarti, *Approach to Thermodynamics of Polymer Flow Based on
Internal State Variables.* Polymer Engineering and Science, 1976. 16(7): p.
490-495.

3. Astarita,
G. and G.C. Sarti, *Dissipative Mechanism in Flowing Polymers - Theory and
Experiments.* Journal of Non-Newtonian Fluid Mechanics, 1976. 1(1): p.
39-50.

4. Sarti,
G.C. and N. Esposito, *Testing Thermodynamic Constitutive Equations for
Polymers by Adiabatic Deformation Experiments.* Journal of Non-Newtonian
Fluid Mechanics, 1977. 3(1): p. 65-76.

5. Mavrantzas,
V.G. and D.N. Theodorou, *Atomistic simulation of polymer melt elasticity:
Calculation of the free energy of an oriented polymer melt.* Macromolecules,
1998. 31(18): p. 6310-6332.

6. Mavrantzas,
V.G. and H.C. Ottinger, *Atomistic Monte Carlo simulations of polymer melt
elasticity: Their nonequilibrium thermodynamics GENERIC formulation in a
generalized canonical ensemble.* Macromolecules, 2002. 35(3): p. 960-975.

7. Siepmann,
J.I., S. Karaborni, and B. Smit, *Simulating the Critical-Behavior of Complex
Fluids.* Nature, 1993. 365(6444): p. 330-332.

8. Dressler,
M., B.J. Edwards, and H.C. Ottinger, *Macroscopic thermodynamics of flowing
polymeric liquids.* Rheologica Acta, 1999. 38(2): p. 117-136.

9. Dressler,
M., *The Dynamical Theory of Non-Isothermal Polymeric Materials*. 2000,
ETH: Zurich.

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