TY - JOUR
T1 - A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit
AU - Schweizer, Kenneth S.
AU - Sussman, Daniel M.
N1 - Funding Information:
K.S.S. thanks Shi-Qing Wang for many stimulating, informative, and motivating discussions (and arguments) over the years. We thank Rob Hoy for a careful reading of the manuscript and valuable comments and suggestions. The later stages of this work were supported by DOE-BES via the Frederick Seitz Materials Research Laboratory Grant No. DE-FG02-07ER46471 (K.S.S.) and by the Advanced Materials Fellowship of the American Philosophical Society (D.M.S.).
Publisher Copyright:
© 2016 Author(s).
PY - 2016/12/7
Y1 - 2016/12/7
N2 - We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a “microscopic absolute yielding” event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
AB - We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a “microscopic absolute yielding” event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
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U2 - 10.1063/1.4968516
DO - 10.1063/1.4968516
M3 - Article
C2 - 28799380
AN - SCOPUS:85000956361
SN - 0021-9606
VL - 145
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 21
M1 - 214903
ER -