Preface
Nonlinear Polymer Rheology explores the rich phenomenology of the mechanical behavior of polymer melts and concentrated polymer solutions. My main purpose is to expose the reader to the latest knowledge and understanding of the subject, developed in the past decade. This book explores and establishes a microscopic foundation that provides a coherent molecular-level interpretation for various nonlinear rheological behaviors. In absence of such a foundation, the book would not and could not have been written.
Covering nearly every aspect of the nonlinear rheological responses of entangled polymers, this book may be used as a textbook to introduce essential phenomenological information. The reader does not need to be an experienced researcher in the field of rheology. The book presents the subject in a self-contained manner, although familiarity with the literature on nonlinear polymer rheology would allow the reader to contrast different standpoints.
My approach to nonlinear polymer rheology places a great emphasis on understanding transient viscoelastic responses. While steady-flow behavior is also of interest, Nonlinear Polymer Rheology differs from other works in that it treats nonlinear responses as primary and linear responses as secondary. We aim to collect sufficient first-hand phenomenology before proposing theoretical concepts, although key concepts including yielding and disentanglement are utilized in as early as Chapter 6 and 7 without elaborative discussion. Since fresh viewpoints are required, the reader will recognize sharp contrasts with conventional knowledge and methodology.
Many excellent books have treated the subject of polymer rheology in a traditional way. The most classical literature is cited and discussed in books including those by Ferry,[1] Doi and Edwards,[2] Bird et al.,[3] Dealy and Larson,[4] Graessley,[5] and Phillies.[6] In general, these books do not have a sufficient discussion of nonlinear rheology that is based on a coherent gathering of key phenomenology. Limited by the available space, the present book omits discussion of the older literature before 2000 and only includes a few pertinent references since 2000.
Scientific inquiries develop in three stages: A. "Empirical," where we find out what happens; B. "Phenomenological," where we learn how it happens; C. "Theoretical," where we explain why it happens. For a complicated subject such as polymer rheology, it is not feasible to formulate a theory without first having sufficient and coherent phenomenological knowledge. Nonlinear Polymer Rheology acknowledges this logical sequence and strives to collect and establish the phenomenology before developing any theoretical treatment and formulation. However, these three types of research can and do often proceed interactively and interchangeably. For example, a particular theoretical idea or picture can prompt one to organize phenomenological information in a more coherent manner and to design additional experiments using hypothetical and unproven concepts.
The responses of polymeric liquids to large and rapid external deformations are challenging to depict and understand in molecular terms. The task is difficult because molecular behavior on nanometer scales dictates rheological properties characterized on macroscopic (millimeter) scales: There exists a gap of six orders of magnitude in length scales. Thus, we should begin by "listening to" what the experiments tell us, and first build a sound phenomenological base. Until we have a sense of the full picture, which could stem from an adequate analysis of the available phenomenology, it is challenging and risky to make theoretical simplifications, for example, in modeling such complex behavior as the response of polymer entanglement to sudden, fast, large external deformations.
Our goal is to arrive at a realistic physical picture for nonlinear polymer rheology. Having collected the essential phenomenology, the process of rational thinking must take us beyond empirical knowledge. To illustrate the merit of reason-guided thinking, let us consider, for example, the phenomenon of viscoelasticity. By definition, all viscoelastic materials are mechanically solid-like (elastic) when probed on short time scales. Viscoelastic liquids become completely viscous only on long time (relative to the material relaxation time) scales. Where does the "elasticity" come from in such a liquid? What is the structure of the material that produces the elasticity? How should we think about the microscopic origin of viscoelasticity?
Upon external deformation, it is clear from the established phenomenology that an initial elastic response must end, and a transition to flow must begin. In other words, all viscoelastic liquids undergo yielding when subjected to fast deformation. The transition to flow suggests that there exists some kind of a potential barrier on short time scales. The next question is what creates such a potential barrier. As soon as we ask questions like this, we can make progress toward an instructive understanding of viscoelasticity, instead of stopping at the level of phenomenological models including the Maxwell model and the Oldroyd[7] model.
This idea to associate the "elasticity" with a potential barrier for any viscoelastic materials is useful even for an external deformation rate R that is lower than the reciprocal of the dominant relaxation time t, that is, when the Weissenberg number Wi < 1. In other words, a transition from elastic deformation to flow must occur even when the product Wi = R t is below unity. For Wi » 1, the initial elastic deformation can be rather remarkable, persisting up to many strain units in the case of entangled polymers. The termination of the elastic-dominant response apparently stems from a breakdown of some microscopic structure. It is an essential task of polymer rheology to identify and delineate the nature of potential barriers, in terms of intermolecular interactions, and show how the structural breakdown takes place.
Figuring out the nature of intermolecular interactions in entangled polymeric liquids under large deformation is a daunting task. Historically, the task has challenged the brightest minds in polymer science. An entangled polymer can be regarded as a physical network of Gaussian chains. Its stress response to startup shear reveals a finite cohesive strength of the network junctions. Maxwell was right[8]: Entangled polymer melts yield, just like ductile polymeric solids (e.g., glasses) do, under continuous external deformation. The rate dependence of the yielding response indicates that chain entanglements are dynamic and have finite lifetimes.
In 1979, Maxwell and Nguyen[9] described the stress overshoot of polystyrene melts upon startup shear by stating "the yielding behavior indicates that, as straining progresses, the structure of the melt is broken down, thereby permitting flow." In the same year, Doi and Edwards published Paper 4, completing their treatment of nonlinear response aspects in the tube model,[10-13] building on the appealing idea of reptation from de Gennes.[14] The tube model had a very different molecular interpretation of shear stress overshoot. Perhaps the tube model made the Maxwell and Nguyen's idea of yielding unnecessary and obsolete. Ever since 1979, theory, experiment, and interpretation of polymer rheology have developed on the presumption that the Doi-Edwards tube model encompasses the right physical picture and tells us how to understand the nonlinear rheological behavior of entangled polymers. The tube model paradigm provides a huge backdrop, against which this book discusses the same subject, polymer rheology, especially nonlinear rheology of entangled polymers.
It seems that modern scientific inquiries rarely follow the preaching of Karl Popper (1902-1994) concerning the objective of doing science, that is, (i) to develop falsifiable theories and (ii) to falsify existing theories with experiment. On the contrary, we prefer to work within an existing paradigm as described by Kuhn (1922-1996).[15] There is a tendency for one to do anything and everything to validate and defend a given theory instead of performing experiments aimed at falsifying it. The notion of scientific truth is often not established by objective criteria and logical rationalization in the Popperian sense but instead by the consensus of a scientific community. Consequently, for two reasons it may be difficult to carry out unconventional research: (i) We are predisposed to accept textbooks and literature results. (ii) Unconventional ideas can be inharmonious. Transformative knowledge find it hard to gain acceptance by the community, especially by people who are accustomed to the standard knowledge and approach. Fortunately, science is ultimately not an affair of democracy, dictated by popular vote. The state of our knowledge is not defined by the status quo.
Doing science often amounts to sorting out relationships between causes and effects. Depending on the level of description, causality can be confused or even reversed. Something taken as the cause at a coarser level may actually be an effect at a finer, deeper, or higher level. For polymer rheology, it is unnecessary to go to the quantum-mechanical level; but it is unacceptable to stay at the continuum mechanical level as the Maxwell model does when it is feasible to probe molecular origins. A short presentation has been posted at www.youtube.com/watch?v=2HDD51Mxu8U to discuss this matter of causality in nonlinear polymer rheology.
Our objective as well...
