Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation.

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C1000H2002 polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory.

A theory for the coexistence of coiled and stretched configurational phases in the extensional flow of entangled polymer melts.

It has recently been demonstrated via nonequilibrium molecular dynamics (NEMD) simulation [M. H. Nafar Sefiddashti, B. J. Edwards, and B. Khomami, J. Chem. Phys. 148, 141103 (2018); Phys. Rev. Lett. 121, 247802 (2018)] that the extensional flow of entangled polymer melts can engender, within a definite strain-rate regime [expressed in terms of the Deborah number (De) based on the Rouse time], the coexistence of separate domains consisting primarily of either coiled or stretched chain-like macromolecules. This flow-induced phase separation results in bimodal configurational distributions, where transitions of individual molecules between the coiled and stretched states occur very slowly by hopping over an apparent energy activation barrier. We demonstrate that the qualitative aspects of this phenomenon can be described via the single-mode Rolie-Poly model including Convective Constraint Release (CCR) and finite extensibility of the chain-like macromolecules. This analysis reveals the physical mechanism for the configurational coexistence, namely, the nonlinear rate of change of the average entropic restoring force of a given entangled chain with extension. Under conditions of significant flow-induced disentanglement, the rate of change of the effective restoring force initially decreases with extension (effective spring softening) and then increases (hardens) as the maximum chain length is approached. When balanced by flow-induced chain stretching, we find that there can be two configuration states within the same De regime, as covered by the NEMD simulations; therefore, a region of conformational coexistence can indeed exist. However, we demonstrate that this coexistence of configurational microstates is only possible when the magnitude of the CCR parameters is consistent with the rate of flow-induced disentanglement, as observed in the NEMD simulations.

Atomistic Simulation of Flow-Induced Microphase Separation and Crystallization of an Entangled Polyethylene Melt Undergoing Uniaxial Elongational Flow and the Role of Kuhn Segment Extension.

Atomistic simulations of the linear, entangled polyethylene C1000H2002 melt undergoing steady-state and startup conditions of uniaxial elongational flow (UEF) over a wide range of flow strength were performed using a united-atom model for the atomic interactions between the methylene groups constituting the polymer macromolecules. Rheological, topological, and microstructural properties of these nonequilibrium viscoelastic materials were computed as functions of strain rate, focusing on regions of flow strength where flow-induced phase separation and flow-induced crystallization were evident. Results of the UEF simulations were compared with those of prior simulations of planar elongational flow, which revealed that uniaxial and planar flows exhibited essentially a universal behavior, although over strain rate ranges that were not completely equivalent. At intermediate flow strength, a purely configurational microphase separation was evident that manifested as a bicontinuous phase composed of regions of highly stretched molecules that enmeshed spheroidal domains of relatively coiled chains. At high flow strength, a flow-induced crystallization (FIC) occurred, producing a semicrystalline material possessing a high degree of crystallinity and primarily a monoclinic lattice structure. This FIC phase formed at a temperature (450 K) high above the quiescent melting point (≈400 K) and remained stable after cessation of flow for temperature at or below 435 K. Careful examination of the Kuhn segments constituting the polymer chains revealed that the FIC phase only formed once the Kuhn segments had become essentially fully extended under the UEF flow field. Thermodynamic properties such as the heat of fusion and heat capacity were estimated from the simulations and found to compare favorably with experimental values.

Individual Molecular Dynamics of an Entangled Polyethylene Melt Undergoing Steady Shear Flow: Steady-State and Transient Dynamics.

The startup and steady shear flow properties of an entangled, monodisperse polyethylene liquid (C1000H2002) were investigated via virtual experimentation using nonequilibrium molecular dynamics. The simulations revealed a multifaceted dynamical response of the liquid to the imposed flow field in which entanglement loss leading to individual molecular rotation plays a dominant role in dictating the bulk rheological response at intermediate and high shear rates. Under steady shear conditions, four regimes of flow behavior were evident. In the linear viscoelastic regime ( γ ˙ < τ d - 1 ), orientation of the reptation tube network dictates the rheological response. Within the second regime ( τ d - 1 < γ ˙ < τ R - 1 ), the tube segments begin to stretch mildly and the molecular entanglement network begins to relax as flow strength increases; however, the dominant relaxation mechanism in this region remains the orientation of the tube segments. In the third regime ( τ R - 1 < γ ˙ < τ e - 1 ), molecular disentangling accelerates and tube stretching dominates the response. Additionally, the rotation of molecules become a significant source of the overall dynamic response. In the fourth regime ( γ ˙ > τ e - 1 ), the entanglement network deteriorates such that some molecules become almost completely unraveled, and molecular tumbling becomes the dominant relaxation mechanism. The comparison of transient shear viscosity, η + , with the dynamic responses of key variables of the tube model, including the tube segmental orientation, S , and tube stretch, λ , revealed that the stress overshoot and undershoot in steady shear flow of entangled liquids are essentially originated and dynamically controlled by the S x y component of the tube orientation tensor, rather than the tube stretch, over a wide range of flow strengths.