Citation: Yong-jin Ruan, Yu-yuan Lu, Li-jia An. Tube Model[J]. Acta Polymerica Sinica, ;2018, 0(12): 1493-1506. doi: 10.11777/j.issn1000-3304.2018.18172 shu

Tube Model

1.
State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022
2.
University of Chinese Academy of Sciences, Beijing 100049

Corresponding author: Yu-yuan Lu, yylu@ciac.ac.cn
Received Date: 29 July 2018
Revised Date: 25 September 2018
Available Online: 16 October 2018

Nonlinear rheology for polymers is the foundational science underlying high efficiency and energy-saving processing of polymeric materials. For chainlike polymers, complicated interchain interactions affect their dynamics and determine the structure-processing-property relationship. This interaction is often called the entanglement, and becomes the key issue in polymer rheology. To our knowledge, the rheological behavior of entangled polymers is based on the de Gennes-Doi-Edwards tube model (DE theory), which reduces the many-chain interaction into a smooth confining tube and assumes the test chain undergoes the Rouse dynamics inside the tube. Some predictions based on the DE theory are in agreement with rheological results, for instance, the time-strain separated form of the reduced relaxation modulus. To overcome some obvious disadvantages and provide reasonable results, many improvements and refinements have also been made to the DE theory. However, the tube model is only an essential single-chain mean-field theory since its intuitive molecular picture is too simple the theory cannot be derived from first principles and lacks self-consistency. In brief, the tube model does not describe how entanglement arises and cannot address the problem of when, how, and why disentanglement occurs after the external deformation. The model is inadequate in describing the chain conformation under fast and large deformations, and fails to explain a number of experimental observations in recent studies, such as the shear banding and the nonquiescent relaxation which show remarkable strain localization phenomena. Therefore, it is necessary to reexamine the single-chain mean-field assumptions and to consider the many-chain interactions explicitly. In other words, the chain entanglement may involve active localized intermolecular interactions that should be preceived as network junctions, and the critical picture of barrier-free Rouse retraction is questionable. In this article, we provide a general introduction to the original tube model and its subsequent improvements, with an emphasis on the development, basic assumptions, and key concepts. We provide derivation of some key results and explain the physical meaning of the parameters. The article ends with an outlook of the challenges and opportunities in the theory for polymer rheology, hoping to motivate researchers to working on this field.
- Non-linear rheology,
- Tube model,
- Entangled polymers,
- GLaMM theory,
- Single-chain mean-field theory
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