Introduction to Polymer Viscoelasticity

Montgomery T. Shaw, William J. MacKnight

• Publisher: Wiley
• Year: 2018
• ISBN:
  9781119181828
• Edition: 4
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

Completely revised and updated, the fourth edition of this classic text continues to offer the reader a thorough understanding of viscoelastic behavior, essential for the proper utilization of polymers.

• Explains principles, corresponding equations, and experimental methods with supporting real-life applications
• Adds coverage of measurement techniques (nano-indentation, atomic force microscopy (AFM), and diffusing wave spectroscopy (DWS)), biopolymer viscoelasticity, and the relationship between mechanical polymer properties and viscoelastic functions
• Has two new ections to address modern areas of viscoelastic measurement: large amplitude oscillatory shear (LAOS) and microrheology
• Includes problems in the text and an Instructor's Manual (including solutions) available for adopting professors
• Prior edition reviews: "The book is clear written and…[is] appropriate for students in introductory undergraduate courses and for others wanting introduction to the fundamentals of the subject." (CHOICE, December 2005); "This book is invariably well written, logically organized and easy to follow...I highly recommend this book to anyone studying polymer viscoelasticity." (Polymer News, December 2005)

Chapter 1
Introduction

The subject matter of this book is the response that polymers exhibit when they are subjected to external forces of various kinds. Almost without exception, polymers belong to a class of substances known as “viscoelastic bodies.” As the name implies, these materials respond to external forces in a manner intermediate between the behavior of an elastic solid and a viscous liquid. To set the stage for what follows, it is necessary to describe in very general terms the types of forces to which the viscoelastic bodies might be subjected for characterization purposes.

Consider first the motion of a rigid body in space. This motion can be thought of as consisting of translational and rotational components. If no forces act on the body, it will maintain its original state of motion indefinitely in accordance with Newton’s first law of motion. However, if a single force or a set of forces whose vector sum is nonzero act on the body, it will experience acceleration or a change in its state of motion. Consider, however, the case where the vector sum of forces acting on the body is zero and the body experiences no change in either its translational or rotational component of motion. In such a condition, the body is said to be stressed. If the requirement of rigidity is removed, the body will in general undergo a deformation as a result of the application of these balanced forces. If this occurs, the body is said to be strained. It is the relationship between stress and strain that is our main concern. Depending on the types of stress and strain applied to a body, we can use these quantities to define new quantities—material properties—that ultimately relate to the chemical and physical structure of the body. These material properties are referred to using the terms “modulus” and “compliance.” To understand in rough terms the physical meaning of the modulus of a solid, consider the following simple experiment.

Suppose we have a piece of rubber (e.g., natural rubber), ½ cm × ½ cm × 4 cm, and a piece of plastic (e.g., polystyrene) of the same dimensions. The experiment to be performed consists of suspending a weight (applying a force) of, say 1 kg, from each sample as shown in Figure 1‐1.

Figure 1-1 Deformation of samples made from plastic vs. rubber. As a reference, the undeformed shape for both samples is shown on the left side. A₀ refers to the cross‐sectional area of the undeformed sample.

As is obvious, the deformation of the rubber will be much greater than that of the plastic. Using this experiment, we might define a spring constant k as the applied force f divided by the change in length ΔL

(1-1)

and use this number to compare the samples. However, to obtain a measure that is independent of the sample size, that is, a material property, as opposed to a sample property, we must divide the applied force by the initial cross‐sectional area A₀ and divide the ΔL by the initial sample length L₀. Then, the modulus M is

(1-2)

Because ΔL is much larger for the rubber than for the plastic, from equation (1‐2) it is clear that the modulus of the rubber is much lower than the modulus of the plastic. Thus, the particular modulus defined in equation (1‐2) specifies the resistance of a material to elongation at small deformations and is called the Young’s modulus. It is normally given the symbol E. (See www.rheology.org for suggestions on standard nomenclature for viscoelastic quantities.)

Further experimentation, however, reveals that the situation is more complicated than is initially apparent. If, for example, one were to carry out the test on the rubber at liquid nitrogen temperature, one would find that this “rubber” undergoes a much smaller elongation than with the same force at room temperature. In fact, the extension would be so small as to be comparable to the extension exhibited by the plastic at room temperature. A more dramatic demonstration of this effect is obtained by immersing a rubber ball in liquid nitrogen for several minutes. The cold ball, when bounced, no longer has the characteristic properties of a rubbery object but, instead, is indistinguishable from a hard sphere made of plastic.

On the other hand, if the piece of plastic is heated in an oven to 130 °C and then subjected to the modulus measurement, it is found that a much larger elongation, comparable to the elongation of the rubber at room temperature, results.

These simple experiments indicate that the modulus of a polymeric material is not invariant, but is a function of temperature T, that is, M=M(T).

An investigation of the temperature dependence of the modulus of our two samples is now possible. At temperature T₁, we measure the modulus as before, and then increase the temperature to T₂, and so on. Schematic data from such an experiment are plotted in Figure 1‐2. The temperature dependence of the modulus is so great that it must be plotted using a logarithmic scale. (This large variation in modulus presents experimental problems that will be treated subsequently.) The region between the vertical dashed lines represents normal‐use temperatures and, consistent with the openi...

Table of contents

• Cover
• Table of Contents
• Dedication
• Preface to the Fourth Edition
• Preface to the Third Edition
• Preface to the Second Edition
• Preface to the First Edition
• About the Companion Website
• Chapter 1: Introduction
• Chapter 2: Phenomenological Treatment of Viscoelasticity
• Chapter 3: Viscoelastic Models
• Chapter 4: Time–Temperature Correspondence
• Chapter 5: Transitions and Relaxation in Amorphous Polymers
• Chapter 6: Elasticity of Rubbery Networks
• Chapter 7: Dielectric and NMR Methods
• Answers to Selected Problems
• List of Major Symbols
• List of Files on the Website
• Author Index
• Subject Index
• End User License Agreement