## Viscoelastic Properties of PolymersViscoelastic behavior reflects the combined viscous and elastic responses, under mechanical stress, of materials which are intermediate between liquids and solids in character. Polymers—the basic materials of the rubber and plastic industries and important to the textile, petroleum, automobile, paper, and pharmaceutical industries as well—exhibit viscoelasticity to a pronounced degree. Their viscoelastic properties determine the mechanical performance of the final products of these industries, and also the success of processing methods at intermediate stages of production. Viscoelastic Properties of Polymers examines, in detail, the effects of the many variables on which the basic viscoelastic properties depend. These include temperature, pressure, and time; polymer chemical composition, molecular weight and weight distribution, branching and crystallinity; dilution with solvents or plasticizers; and mixture with other materials to form composite systems. With guidance by molecular theory, the dependence of viscoelastic properties on these variables can be simplified by introducing certain ancillary concepts such as the fractional free volume, the monomeric friction coefficient, and the spacing between entanglement loci, to provide a qualitative understanding and in many cases a quantitative prediction of how to achieve desired results. The phenomenological theory of viscoelasticity—which permits interrelation of the results of different types of experiments—is presented first, with many useful approximation procedures for calculations given. A wide variety of experimental methods is then described, with critical evaluation of their applicability to polymeric materials of different consistencies and in different regions of the time scale (or, for oscillating deformations, the frequency scale). A review of the present state of molecular theory follows, so that viscoelasticity can be related to the motions of flexible polymer molecules and their entanglements and network junctions. The dependence of viscoelastic properties on temperature and pressure, and its descriptions using reduced variables, are discussed in detail. Several chapters are then devoted to the dependence of viscoelastic properties on chemical composition, molecular weight, presence of diluents, and other features, for several characteristic classes of polymer materials. Finally, a few examples are given to illustrate the many potential applications of these principles to practical problems in the processing and use of rubbers, plastics, and fibers, and in the control of vibration and noise. The third edition has been brought up to date to reflect the important developments, in a decade of exceptionally active research, which have led to a wider use of polymers, and a wider recognition of the importance and range of application of viscoelastic properties. Additional data have been incorporated, and the book’s chapters on dilute solutions, theory of undiluted polymers, plateau and terminal zones, cross-linked polymers, and concentrated solutions have been extensively rewritten to take into account new theories and new experimental results. Technical managers and research workers in the wide range of industries in which polymers play an important role will find that the book provides basic information for practical applications, and graduate students in chemistry and engineering will find, in its illustrations with real data and real numbers, an accessible introduction to the principles of viscoelasticity. |

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### Contents

The Nature | 1 |

Description of Linear TimeDependent Experiments in Shear | 8 |

Mechanical Model Analogies of Linear Viscoelastic Behavior | 15 |

Illustrations | 33 |

B Linear Viscoelastic Behavior in Bulk Voluminal Deformation | 48 |

Conclusions | 54 |

B The Relaxation and Retardation Spectra | 60 |

Calculation of Viscoelastic Functions and Constants from | 64 |

Interrelation of Effects of Temperature and Pressure | 294 |

E Reduced Variables and FreeVolume Parameters from Other Than | 301 |

Changes in Internal Structure due to Crystallinity | 312 |

NonNewtonian Viscosity | 315 |

The Transition Zone | 321 |

B The Monomeric Friction Coefficient | 328 |

Relation of fo to the Onset of the Transition Zone | 342 |

Behavior of Copolymers and Polymer Mixtures | 348 |

Evaluation of Viscoelastic Constants | 70 |

H Relations from Nonlinear Constitutive Equations | 76 |

B Interrelations between the Spectra | 87 |

F Table of Correction Factors | 94 |

Normal Stress Measurements | 105 |

E Dynamic Oscillatory Measurements of Characteristic | 116 |

G Dynamic Measurements on Liquids in Solid Matrices | 124 |

Experimental Methods | 130 |

Wave Propagation | 144 |

Experimental Methods | 154 |

Compound Resonance Vibration Devices | 160 |

Experimental Methods | 168 |

Partially Flexible Elongated Molecules | 204 |

E Behavior at High Frequencies and in HighViscosity | 214 |

Molecular Theory | 224 |

B CrossLinked Networks | 233 |

UncrossLihked Polymers of High Molecular Weight | 241 |

Concentrated Solutions | 248 |

E Nonlinear Behavior in UncrossLinked Polymers of High Molecular | 257 |

Dependence | 264 |

A Origin of the Method of Reduced Variables | 266 |

B Procedure and Criteria for Applicability of the Method of Reduced | 273 |

The WLF Equation and the Relation of Temperature Dependence | 280 |

The WLF Equation | 287 |

Behavior of Filled Systems | 356 |

The Plateau | 366 |

B Estimations of Entanglement Spacings | 372 |

Behavior in the Terminal Zone | 379 |

Behavior in the Plateau Zone | 391 |

CrossLinked Polymers | 404 |

The Classy State | 437 |

Crystalline Polymers | 457 |

Polymers with Low Degree of Crystallinity | 469 |

and Gels | 486 |

B The Plateau Zone | 501 |

Linear Viscoelastic Behavior in the Terminal Zone | 509 |

E Gels CrossLinked in Solution | 529 |

F Gels Swollen after CrossLinking | 539 |

Viscoelastic Behavior | 545 |

Dynamic Properties in Bulk Compression | 558 |

Applications | 570 |

Rupture below the Glass Transition Temperature | 587 |

Appendix B Applicability of Various Dynamic Methods | 599 |

Appendix E Theoretical Viscoelastic Functions Reduced | 610 |

Author Index | 617 |

633 | |

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### Common terms and phrases

A. V. Tobolsky Appl bulk calculated chain Chain unit Chapter Chem Colloid Colloid Sci components concentration configurational constant copolymer corresponding cross-linked crystal crystalline curves D. J. Plazek decrease deformation described dynamic effect elastic equilibrium experimental extension frequency scale friction coefficient glass transition temperature high molecular weight illustrated in Fig increasing J. D. Ferry linear viscoelastic Logarithmic plots loss tangent low molecular weight Macromolecules magnitude maximum measurements mechanical molecular weight distribution molecule motions non-Newtonian nonlinear normal stress obtained parameters Phys plateau zone polyisobutylene polymeric polystyrene predicted pressure proportional range ratio reduced variables relaxation modulus relaxation spectrum Rheol Rheology Rouse theory rubber sample Section shear modulus shear rate shown in Fig simple shear slope solutions spectra stress relaxation styrene-butadiene temperature dependence tensile terminal zone torsion Trans transition zone uncross-linked polymers undiluted polymer values viscoelastic behavior viscoelastic functions viscoelastic liquid viscoelastic properties viscosity Young's modulus