A full-chain tube-based constitutive model for living linear polymers

We present a new strategy for introducing population balances into full-chain constitutive models of living polymers with linear chain architectures. We provide equations to describe a range of stress relaxation processes covering both unentangled systems (Rouse-like motion) and well entangled systems (reptation, contour length fluctuations, chain retraction, and constraint release). Special attention is given to the solutions that emerge when the 'breaking time' of the chain becomes fast compared to various stress relaxation processes. In these 'fast breaking' limits, we reproduce previously known results (with some corrections) and also present new results for nonlinear stress relaxation dynamics. Our analysis culminates with a fully developed constitutive model for the fast breaking regime in which stress relaxation is dominated by contour length fluctuations. Linear and nonlinear rheology predictions of the model are presented and discussed.

[1]  S. Muller,et al.  Flow of viscoelastic fluids around a sharp microfluidic bend: Role of wormlike micellar structure , 2017 .

[2]  R. Pasquino,et al.  Adding salt to a surfactant solution: Linear rheological response of the resulting morphologies , 2015 .

[3]  R. Larson,et al.  A mesoscopic simulation method for predicting the rheology of semi-dilute wormlike micellar solutions , 2014 .

[4]  S. K. Sukumaran,et al.  A full-chain constitutive model for bidisperse blends of linear polymers , 2012 .

[5]  N. Wagner,et al.  Rheology and spatially resolved structure of cetyltrimethylammonium bromide wormlike micelles through the shear banding transition , 2009 .

[6]  Gareth H. McKinley,et al.  A network scission model for wormlike micellar solutions: I. Model formulation and viscometric flow predictions , 2007 .

[7]  M. Cates,et al.  Rheology of giant micelles , 2006, cond-mat/0702047.

[8]  Richard S. Graham,et al.  Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation , 2003 .

[9]  Richard S. Graham,et al.  Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release , 2003 .

[10]  S. Fielding,et al.  Kinetics of the shear banding instability in startup flows. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Tom C. B. McLeish,et al.  Quantitative Theory for Linear Dynamics of Linear Entangled Polymers , 2002 .

[12]  T. McLeish,et al.  Microscopic theory of convective constraint release , 2001 .

[13]  P. Olmsted,et al.  Shear banding in reaction-diffusion models , 1999 .

[14]  S. Milner,et al.  Packing Length Influence in Linear Polymer Melts on the Entanglement, Critical, and Reptation Molecular Weights , 1999 .

[15]  T. McLeish,et al.  REPTATION AND CONTOUR-LENGTH FLUCTUATIONS IN MELTS OF LINEAR POLYMERS , 1998 .

[16]  G. Porte,et al.  Inhomogeneous shear flows of wormlike micelles:mA master dynamic phase diagram , 1997 .

[17]  G. Porte,et al.  Linear rheology of entangled wormlike micelles , 1993 .

[18]  Cates,et al.  Nonlinear rheology of wormlike micelles. , 1993, Physical review letters.

[19]  M. Cates,et al.  Stress relaxation in living polymers: Results from a Poisson renewal model , 1992 .

[20]  R. Jerome,et al.  Telechelic polymers : synthesis, characterization and applications , 1991 .

[21]  Michael E. Cates,et al.  Linear viscoelasticity of living polymers: a quantitative probe of chemical relaxation times , 1991 .

[22]  F. Lequeux.  Linear response of self assembling systems: mean field solution , 1991 .

[23]  W. Howells,et al.  The structural properties of liquid sulphur , 1990 .

[24]  H. Rehage,et al.  Rheological properties of viscoelastic surfactant systems , 1988 .

[25]  Michael E. Cates,et al.  Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions , 1987 .

[26]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[27]  G. Faivre,et al.  Viscoelastic properties and molecular structure of amorphous selenium , 1986 .

[28]  Fixman.  Dynamics of semidilute polymer rods: An alternative to cages. , 1985, Physical review letters.

[29]  J. Peterson.  Shear Induced Demixing in Polymer Melts and Solutions , 2018 .

[30]  M. Cates.  Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers) , 1990 .

[31]  H. Giesekus.  A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility , 1982 .

[32]  S. Edwards,et al.  Dynamics of concentrated polymer systems. Part 3.—The constitutive equation , 1978 .