Abstract
We develop a single segment differential tube model including interchain tube pressure effect (ITPE) [G. Marrucci, G. Ianniruberto, Interchain pressure effect in extensional flows of entangled polymers, Macromolecules 36 (2004) 3934–3942], able to describe the non-linear behaviour of entangled linear polymers. The model accounts for the effect of flow on the tube length and diameter. It is presented in two versions, depending on which tube dimension is assumed to deform affinely. The classical relaxation mechanisms, i.e., reptation, stretch dynamics, convective constraint release (CCR), as well as finite extensibility, are incorporated in a simple manner; hence the model allows an explicit comparison of the relative importance of various effects. A striking result is the insignificance of finite extensibility and the detrimental influence of CCR for moderately entangled systems when ITPE is taken into account. For highly entangled systems, CCR regains importance to avoid the well-known shear stress instability. The proposed model is able to make quantitative predictions of steady elongational and shear data for monodisperse melts, while transient values are less accurate but within experimental errors.
Highlights
Doi and Edwards [2], following the concept of reptation by de Gennes [3], first proposed a tube model to describe the rheology of linear entangled polymers in the linear viscoelastic regime
In order to see the effect of finite extensibility on interchain tube pressure effect (ITPE), we use the values p/ d = 10, r → ∞, and = 0 in order to make convective constraint release (CCR) inactive
Finite extensibility plays some role at high elongational rates, though the difference becomes less significant while moving from affine squeezing to affine stretching and with the inclusion of stretch dynamics
Summary
Doi and Edwards [2], following the concept of reptation by de Gennes [3], first proposed a tube model to describe the rheology of linear entangled polymers in the linear viscoelastic regime. Steady progress over two decades has made quantitative predictions possible for linear properties [4,5,6]. The development of theories for the non-linear response of entangled polymers is much more limited and even in the case of monodisperse linear chains, additional relaxation-mechanisms are still proposed today to improve the description of the flow properties [1]. The Doi and Edwards (DE) model [2] was a first attempt to build a tube-based constitutive equation for linear polymers. The DE model predicts a constitutive instability in steady shear
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