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Cover
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
1. PROBLEMS
2. GENERAL REFERENCE TEXTS
3. REFERENCES
Chapter 2: Phenomenological Treatment of Viscoelasticity
1. A. ELASTIC MODULUS
2. 1. LINEAR‐MOTION GEOMETRIES
3. REFERENCES
Chapter 3: Viscoelastic Models
1. A. MECHANICAL ELEMENTS
2. B. DISTRIBUTIONS OF RELAXATION AND RETARDATION TIMES
3. C. MOLECULAR THEORIES—THE ROUSE MODEL
4. D. APPLICATIONS OF FLEXIBLE‐CHAIN MODELS TO SOLUTIONS
5. E. THE ZIMM MODIFICATION
6. F. EXTENSION TO BULK POLYMER
7. G. REPTATION
8. APPENDIX 3‐1: MANIPULATION OF THE ROUSE MATRIX
9. PROBLEMS
10. REFERENCES
Chapter 4: Time–Temperature Correspondence
1. A. FOUR REGIONS OF VISCOELASTIC BEHAVIOR
2. B. TIME–TEMPERATURE SUPERPOSITION
3. C. MASTER CURVES
4. D. THE WLF EQUATION
5. E. MOLECULAR INTERPRETATION OF VISCOELASTIC RESPONSE
6. PROBLEMS
7. REFERENCES
Chapter 5: Transitions and Relaxation in Amorphous Polymers
1. A. PHENOMENOLOGY OF THE GLASS TRANSITION
2. B. THEORIES OF THE GLASS TRANSITION
3. C. STRUCTURAL PARAMETERS AFFECTING THE GLASS TRANSITION
4. D. RELAXATIONS IN THE GLASSY STATE
5. E. RELAXATION PROCESSES IN NETWORKS
6. F. BIOPOLYMER VISCOELASTICITY
7. PROBLEMS
8. REFERENCES
Chapter 6: Elasticity of Rubbery Networks
1. 1. DERIVATION
2. 2. ENERGY CONTRIBUTION
3. 1. EFFECT OF DEGREE OF CROSSLINKing
4. 2. EFFECT OF SWELLING
5. 3. EFFECT OF FILLERs
6. 4. EFFECT OF STRAIN‐INDUCED CRYSTALLIZATION
7. PROBLEMS
8. REFERENCES
Chapter 7: Dielectric and NMR Methods
1. A. DIELECTRIC METHODS
2. B. NUCLEAR MAGNETIC RESONANCE METHODS
3. PROBLEMS
4. REFERENCES
Answers to Selected Problems
1. CHAPTER 2
2. CHAPTER 3
3. CHAPTER 4
4. CHAPTER 5
5. CHAPTER 6
6. CHAPTER 7
List of Major Symbols
List of Files on the Website
1. INTRODUCTION
2. LIST OF FILES
Author Index
Subject Index
End User License Agreement

List of Tables

Chapter 2
1. Table 2-1 Test Geometries for Instruments that Generate Axial (Linear) Motion
2. Table 2-2 Geometries for Instruments that Generate Rotational Motion
Chapter 3
1. Table 3-1 Behavior in Extension of Simple Viscoelastic Models in Various Experiments.^a
2. Table 3-2 Behavior of Generalized Maxwell and Voigt–Kelvin Models in Various Experiments
3. Table 3-3 Transition Region Slope for Several Polymers ¹⁶
Chapter 4
1. Table 4-1 WLF Parameters ^a
Chapter 5
1. Table 5–1 Pressure Dependence of T_g
2. Table 5–2 Glass Transition Temperatures of Selected Polymers
Chapter 6
1. Table 6-1 Thermoelastic Data of Selected Elastomers at 30 °C
Chapter 7
1. Table 7-1 Methods for Dielectric Measurements

List of Illustrations

Chapter 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.
2. Figure 1-2 Schematics of the modulus vs. temperature behavior for a rubber and a plastic over a broad temperature range.
3. Figure 1-3 Schematic modulus–time curve for a polymer at constant temperature.
4. Figure 1-4 Specific volume data for poly(vinyl acetate) used to determine its T_g. [Kovacs (1958).¹ Copyright 1958, John Wiley & Sons.]
Chapter 2
1. Figure 2-1 Tension (a) and shear (b) of a three‐dimensional sample subjected to very small deformations.
2. Figure 2-2 Forcing a sample to shear by fastening it to a solid surface and pulling on a plate adhered to its top surface.
3. Figure 2-3 Forces applied to the sample to cause shear will also lead to rotation unless the sample is constrained.
4. Figure 2-4 Rotation of the sample can be stopped by applying another pair of forces.
5. Figure 2-5 To keep the volume of the sample constant during stretching, the sample must become thinner.
6. Figure 2-6 Free‐body force diagram for the clamp used to stretch a sample. The clamp (dotted vertical line) is fastened to the end of the sample, which extends to the left.
7. Figure 2-7 Free‐body diagram of a virtual clamp pasted to the side of the sample.
8. Figure 2-8 This gasket material exhibits a negative Poisson ratio. On pulling, the rectangle marked on the sample increased in width from 7.1 to 7.6 mm, or about 7%. The thickness direction (not shown) expanded even more. The length of the rectangle increased ˜10%. Thus, Poisson's ratio is about −0.07/0.1 = −0.7.
9. Figure 2-9 A simple apparatus to measure shear creep.
10. Figure 2-10 A simple apparatus to measure tensile stress relaxation. The spring must be strong enough to stretch the sample very quickly.
11. Figure 2-11 Schematic of a dynamic experiment in shear. The electromechanical driver provides a sinusoidal motion of fixed frequency and amplitude.
12. Figure 2-12 Dynamic experiment in shear wherein the disk‐shaped sample is twisted sinusoidally. The dotted line in the shaded sample depicts a line of material points, showing the shearing of the sample from right to left. In some designs, one plate is connected to a servomotor that produces the sinusoidal motion while the other plate is connected to the load cell. Other manufacturers use one plate for both functions, with the other solidly fastened to the frame of the machine. This design, while simple, introduces error at high frequencies due to inertia.
13. Figure 2-13 The response of a sample to a sinusoidal shear strain γ(t) is a sinusoidal shear stress σ(t) (dashed line) that leads the strain by a phase angle δ. Arrows show the physical meaning of the stresses σ ′ and σ ″ corresponding to the elastic or in‐phase component G ′ of the dynamic shear modulus and the viscous, out‐of‐phase or loss component G″, that is, G ′ = σ ′/γ₀ and G″ = σ ″/γ₀.
14. Figure 2-14 Strain sweep using a silicone polymer melt (left) and a polyurethane foam (right). For the latter, the response is very linear at low strains (see derivative curve), but G′ starts to drop at a strain of 0.01 (barely visible) and rapidly around 5% (−1.3 on log scale). The PDMS melt response seems quite linear throughout the strain range, but analysis shows a slight but significant trend for both G′ (down) and G″ (up). At higher frequencies, some of the changes might well be due to viscous heating. (PDMS data courtesy of Dr. Si‐Wan Li.)
15. Figure 2-15 Simulated LAOS result. The curve labeled LAOS has a small portion of a third harmonic added to the linear stress signal. This harmonic will have a phase and amplitude.
16. Figure 2-16 Lissajous–Bowditch patterns generated by assuming the presence of a third harmonic, contrasted with what would happen if an even harmonic were present. Generally, even harmonics are not present.
17. Figure 2-17 Example of a Pipkin diagram. These data were generated using the frequency and phase characteristics of a Maxwell model for the fundamental and a proportional response for the third harmonic. Note the progression with strain to more extreme nonlinearity. Log De varies from 0 to 2 along the abscissa, whereas log Wi varies from −1 to 2 along the diagonal.
18. Figure 2-18 Schematic of setup for finding diffusivity of scattering objects (particles). The random‐walk path of the light under the condition of diffuse scattering involves many scattering events, so only a very small fraction of the light gets to the detector, which must be very sensitive and fast. Often a photomultiplier tube (PMT) is used for detection.
19. Figure 2-19 Schematic of the linear addition of strains resulting from sequentially applied stresses.
20. Figure 2-20 Stress history used in calculations.
21. Figure 2-21 An example of the relationship between creep compliance and a stress relaxation modulus. On the log–log plot shown, the two would be mirror images if reciprocally related.
Chapter 3
1. Figure 3-1 Spring, dashpot, and Maxwell model. In subsequent depictions of the dashpot, the “fluid” hatching will be removed for simplicity.
2. Figure 3-2 Creep response of a Maxwell body displayed using linear (left) and log–log (right) scales.
3. Figure 3-3 Maxwell body behavior using stress relaxation conditions: (a) linear plot, (b) linear–log plot, and (c) log–log plot.
4. Figure 3-4 Log–log plots of E ′(ω)/E and E ″(ω)/E versus ωτ for a Maxwell model.
5. Figure 3-5 Voigt model.
6. Figure 3-6 Frequency dependence of the complex dynamic compliance for the Voigt model.
7. Figure 3-7 Generalized Maxwell model.
8. Figure 3-8 Behavior of a two‐component generalized Maxwell model in stress relaxation.
9. Figure 3-9 Voigt−Kelvin model.
10. Figure 3-10 Discrete distribution of relaxation times and associated partial modulus values. The continuous line represents the stress relaxation modulus based on this distribution.
11. Figure 3-11 Continuous distribution of relaxation times expressed as H(τ) and the corresponding tensile stress relaxation modulus E(t).
12. Figure 3-12 Stress relaxation master curve for NBS polyisobutylene at 25 °C (dotted line) and corresponding box‐and‐wedge distribution (solid lines). [Tobolsky (1960).⁶ Copyright 1960, John Wiley & Sons.]
13. Figure 3-13 Bead‐and‐spring representation of a real polymer molecule in dilute solution.
14. Figure 3-14 Motions of submolecules with varying orientations in a medium subjected to a uniform extensional deformation. A polymer chain will contain many submolecules.
15. Figure 3-15 Experimental observation (PS in toluene at 30.3 °C) and prediction of the Rouse theory. The molecular weights (kDa) and concentrations (kg /m³) from left to right are: 6200, 1.44; 520, 8.9; and 253, 14.6. [Rouse and Sittel (1953.)¹¹ Copyright 1943, AIP Publishing.]
16. Figure 3-16 Predictions of the Rouse and Zimm theories. The subscript R indicates that the modulus is divided by NkT. [De Mallie et al., (1962).¹² Copyright 1962, American Chemical Society.]
17. Figure 3-17 Experimental results for 1% polystyrene in Arochlor^® compared with predictions according to the Zimm theory. [De Mallie et al., (1962).¹² Copyright 1962, American Chemical Society.]
18. Figure 3-18 Rouse theory in the rubbery plateau and flow regions. Varying numbers of segments are considered. Note increasing region of power‐law behavior (slope = −½) as the number of segments is increased.
19. Figure 3-19 Calculations of the viscosity from the stress relaxation master curve for NBS PIB at 25°C (see Figure 3‐12) via equation (3‐90), showing the important contribution to the integral from the long‐time data and the negligible contribution from the short‐time modes in the glassy region.
20. Figure 3-20 Two transitions predicted using the Ferry, Landel, and Williams⁸ modification of the Rouse theory. The parameters required to get this result are quite extreme; see text.
21. Figure 3-21 Comparison between master curve of polystyrene and predictions of the modified Rouse theory in the primary transition region.
22. Figure 3-22 Relaxation in the primary transition region considering varying numbers of relaxing elements. The number of elements in the transition region in each case is z – p_c.
23. Figure 3-23 Comparison of the relaxation behavior of the empirical KWW expression of equation (3‐106) with data for PIB in the rubbery flow region. Data: NBS PIB; see Ferry ³ for a table of these data. Copies of the data are also on the website (PIB‐Rel‐1.TXT and PIB‐Rel‐2.TXT).
24. Figure 3-24 Reptation model view of a polymer chain: (a) with obstacles (dots); (b) in a tube.
25. Figure 3-25 Tube model with definitions of important length scales. [Larson et al. (2003).²⁸ Copyright 2003, The Society of Rheology.]
26. Figure 3-26 The molecular‐weight dependence of the viscosities of a series of polyethylene melts. It can be seen that the slope of 3.0 predicted by equation (3‐115) falls short, while a slope of 3.4 is virtually perfect. (Data from various sources.)
Chapter 4
1. Figure 4-1 Schematic modulus–temperature curve showing various regions of viscoelastic behavior.
2. Figure 4-2 Shear modulus ^†vs. temperature for two polycarbonate samples of different molecular weights, along with the response of a partially crystallized sample. (See Chapter 5 for additional discussion.) [Mercier, et al. (1965).¹²
3. Figure 4-3 Comparison of 10‐s modulus vs. temperature curves for three common thermoplastics: polyvinyl chloride (PVC), polystyrene (PS), and polyethylene (PE).
4. Figure 4-4 Panel (a) shows the influence of plasticizer content on the modulus–temperature response of PVC through the glass transition region. Note that increasing plasticizer content tends to broaden the transition markedly at first and then the effect decreases at even higher concentrations. [Schmieder and Wolf (1952).² Copyright 1952, Springer.] The data in panel (b) suggest that the broadening effect is highly dependent on the chemical nature of the plasticizer as well..
5. Figure 4-5 Construction of a master curve using tensile stress relaxation data gathered at five temperatures. In this case, the reference temperature T₀ is T₄.
6. Figure 4-6 The WLF equation using the constants for polystyrene listed in Table 4‐1.
7. Figure 4-7 (a) Plot of the relaxation master curve for each of the temperatures indicated. The line through each of the data sets indicates the relaxation behavior over the entire time range expected for that temperature. The curves are moved only in the horizontal direction to fit the data. The empirical description for the curves follows an equation suggested by Smith,¹¹ i.e., E=(E_g−E_r) /[1+(τ/τ₁)^a]+E_r /[1+(τ/τ₂)^b], where τ is shifted time. The constants were obtained by a fit as shown in (b), to the original superposed data (open circles) listed in Ferry⁵ while the line is from the equation of Smith.
8. Figure 4-8 Simulations of master curves and modulus vs. temperature curves for a glassy polymer. (a) The master curves, shown at increments of 5 °C, tend to be spaced more widely as the temperature is lowered because of the nature of the WLF relationship used for the temperature dependence (see Figure 4‐6). (b) Demonstration of the influence of measurement time on the shape of the modulus–temperature curve. As the measurement time increases (by 1‐decade increments), the apparent T_g decreases but the sharpness of the transition increases. (Simulation uses Smith empiricism2 for glass transition and the KWW function for the rubbery flow region.)
Chapter 5
1. Figure 5–1 Specific volume versus temperature for a poly(vinyl acetate) sample quick‐quenched from well above T_g to the experimental temperatures. Volumes measured 0.02 and 100 h after quenching, as indicated. Filled points represent equilibrium behavior. [Kovacs (1958). [2] Copyright 1958, John Wiley and Sons.]
2. Figure 5–2 Thermal scans of polystyrene at 5.4 K /min (0.09 K/s) after cooling from well above T_g at the rates indicated. Curves have been shifted vertically for clarity. [Wunderlich et al. (1964). [3] Copyright 1964, AIP Publishing.]
3. Figure 5–3 Temperature dependencies of G ′, G ″ and tan δ for styrene butadiene copolymer. [Adapted from Nielsen (1962). [4] ]
4. Figure 5–4 Temperature dependencies of E′ and tan δ for polyvinyl chloride at various frequencies. [Becker (1955). [5] Copyright 1955, Springer.]
5. Figure 5–5 Temperature dependence of viscosity for a cyclic polystyrene sample of molecular weight 106,000 g /mol. The line is a fit with the WLF relationship, equation (4–6). [McKenna et al. (1987). [7] Copyright 1987, American Chemical Society.]
6. Figure 5–6 (a) Dependence of T_g on ϕ_p for mixtures of poly(methyl methacrylate) with diethyl phthalate. Comparison of experimental results with equation (5–8). Parameters found were: α _d /α _p = 2.32, T_g,d = −57 °C, ^† T_g,p = 104 °C. [Kelley and Bueche (1961). [8] Copyright 1961, John Wiley & Sons.]; (b) Variation of T_g for a miscible polymer blend of polycaprolactone (PCL) and poly(styrene‐co‐acrylonitrile) (SAN), with a description of the data using the Gordon–Taylor relationship, equation (5–27). The two points at low SAN content have a higher‐than‐expected T_g because of crystallization of the PCL. [Chiu and Smith (1984). [9] Copyright 1984, John Wiley & Sons.]
7. Figure 5–7 Schematic representation of conformational entropy vs. temperature for a glass‐forming substance. The temperature at which the entropy attains a value of zero is the T₂ of Gibbs and DiMarzio. The dotted line is the extrapolation of Kauzmann designed to illustrate the infeasibility of a glassy equilibrium state, and the proposal of Gibbs and DiMarzio. [Gibbs (1960). [13] Copyright 1960, Elsevier]
8. Figure 5–8 The influence of molecular weight on the glass transition temperatures of cyclic and linear oligomers of poly(dimethyl siloxane), and the comparison of these data with the prediction of the Gibbs–DiMarzio theory. [DiMarzio and Guttman (1987). [16] Copyright 1987, American Chemical Society.]
9. Figure 5–9 Contraction isotherms for glucose, a low‐molecular‐weight glass‐forming substance. Samples were quenched from equilibrium at 40 °C to the temperatures indicated. Solid line through the points at 24.9 °C was calculated using equations (5–23) and (5–25) with T_g = 35°C, f_g = 0.025, α _f = 3.6 × 10⁻⁴ K⁻¹, and τ( T_g, δ = 0) = 0.015 h. Fits to the other temperatures are possible using the same equations, but require small changes in the parameters. [Kovacs (1964). [17] Copyright 1964, Springer.]
10. Figure 5–10 Composition dependence of T_g for a series of random styrene–butadiene copolymers compared to the predicted curve calculated on the basis of equation (5–27) with k = 0.34. [Gordon and Taylor (1952).²¹ Copyright 1952, John Wiley & Sons.]
11. Figure 5–11 T_g versus reciprocal molecular weight for polystyrene fractions. The solid line is a plot of equation (5–28) with c = 1.7 × 10⁵ K Da. [Fox and Flory (1950). [23] Copyright 1950, AIP Publishing]
12. Figure 5–12 Glass transition change in the system poly(styrene‐co‐divinylbenzene) as a function of the crosslink density. N₀ is the number density (e.g., mmol /cm³) of crosslinks, whereas ρ is the mass density (e.g., g /cm³). The dotted line is the fit of equation (5–29) with the result that kρ is 130 ± 10 g /mol. [Fox and Loshaek (1955). [24] Copyright 1955, John Wiley & Sons.]
13. Figure 5–13 Temperature dependence of damping for polymethyl methacrylate showing the α and β relaxations. [Adapted from Nielsen, (1962). [28] ]^§
14. Figure 5–14 The crankshaft mechanism according to Schatzki.²⁹
15. Figure 5–15 Temperature dependence of tan δ for copolymers of methyl methacrylate and cyclohexyl methacrylate. Open circles are pure polymethyl methacrylate. [Heijboer, (1960).³⁰ Copyright 1960, Springer.]
16. Figure 5–16 Physical stress relaxation at 25 °C in a crosslinked network made by a zinc oxide cure of a halobutyl rubber. The elastomer has been soaked in oil to speed the relaxation. The line is the fit to the data using the Chasset–Thirion equation ³¹ with E_∞ = 0.018 MPa, τ = 1.04 s, and m = 0.31. The nature of the polymer and the cure makes for a chemically stable structure; otherwise, the plot would begin to curve downward at long time.
17. Figure 5–17 Chemical stress relaxation of natural rubber cured with dicumyl peroxide. [Adapted from Takahashi and Tobolsky (1970). [33] ]
18. Figure 5–18 Dynamic mechanical behavior during the chemical cure of a phenolic resole resin at 125 ^°C. The noise at the beginning of the experiment results from the rapid evolution of moisture, which causes some bubbles to form. [From Rose (2001). [36] ]
19. Figure 5–19 Schematic of device for controlling humidity in a small test chamber. The gas sources and meters are not shown. Also water must be supplied from a constant‐level source. ^§§Supplying vaporization heat to the water might be as simple as having a tall, narrow container, at least for low gas flow. In operation, the water‐saturated gas is mixed with a controlled amount of dry gas to give the desired humidity. Roughly, if the two gas streams have the same flow rate, the humidity will be 50%.
20. Figure 5–20 Diffusivity measured during the drying of thin slices of wood analyzed assuming molecular diffusion obeying Fick's second law. The higher diffusivity at higher water concentrations is very typical of water‐sensitive polymers.
21. Figure 5–21 Creep of European beech wood, along with time‐dependent Poisson's ratio. Left figure is the test sample. (a) With the grain as shown, tension or compression will be applied in the radial direction. The narrow straight areas in the center are sprayed with speckle patterns to serve as the strain‐measuring method. The positions of all speckles are recorded by cameras as functions of load and time. (b) Creep of specimen loaded in compression in the radial (R) direction, with strain measurements in radial and tangential directions. The Poisson's ratio ν_TR was calculated from these. [Ozyhar et al. (2013). [37] Copyright 2013, The Society of Rheology.]
22. Figure 5–22 Example of creep for wood with a constant tensile stress of 3.4 MPa. The presentation is quite unusual (although common for Civil Engineering applications) in that the values shown depict a normalized extra creep beyond the instantaneous and presumably recoverable elastic deformation. The curve is an attempt to fit the Voigt model to the data; a 3‐element fluid model would give a slightly better fit. [Data from Green, et al. (1999). [38] ]
23. Figure 5–23 Viscoelastic response of sodium alginate solution on exchanging calcium ions for sodium. At high calcium concentrations, the exchange is extremely rapid. [Data courtesy of Dr. C. Subramanian, 2010.]
24. Figure 5–24 (a) G ′(ω) at several temperatures that bring the sample from a nearly perfect solid to a typical polymer solution. Note that the curve at 37.5 °C is nearly power‐law, i.e., neither liquid nor solid. The dotted rectangle outlines the area where data were taken for Figure 5‐24b. (b) Response of tan δ with frequency plotted as a vertical set of points at a fixed temperature. The pinch point of the lines of fixed frequency defines the critical gel temperature very precisely; at this temperature, tan δ is invariant with frequency. [From Liu et al. (2016).⁴⁰ Copyright 2016, The Society of Rheology.]
Chapter 6
1. Figure 6-1 Stress–temperature curves of natural rubber. Extension ratios λ are indicated on the right of the figure. [Shen et al. (1967).† Copyright 1967, AIP Publishing.]
2. Figure 6-2 Schematic diagram of an ensemble of linear polymer chains being crosslinked into an infinite network. Note that the entanglement can become an extra crosslink.
3. Figure 6-3 A unit cube of elastomer: (a) in the unstrained state; (b) in the homogeneous strained state; (c) under uniaxial extension, assuming a homogeneous, incompressible material.
4. Figure 6-4 Stress–strain curve for natural rubber. The theoretical curve was calculated from equation (6‐60) with G = 0.4 MPa. [Treloar (1944).6 Copyright 1944, Royal Society of Chemistry.]
5. Figure 6-5 Determination of shear moduli for natural rubber at 10 °C and 60 °C by plotting nominal tensile stressσ_E₀ against λ − 1/λ² as suggested by equation (6‐66). [Shen and Blatz (1968).7 Copyright 1968, AIP Publishing.]
6. Figure 6-6 Simulated Mooney−Rivlin plot, equation (6‐82), for C₂ /C₁=2. Solid line is the undistorted response of the material; “data” are the results with a 1% (standard deviation) random error incorporated into both the force and length “measurements.”
7. Figure 6-7 Variation of shear moduli of natural rubber with reciprocal initial molecular weight for various degrees of crosslinking. See equation (6‐81) for explanation of C₁. [Mullins (1959).14 Copyright 1959, John Wiley & Sons.]
8. Figure 6‐8 Effect of swelling on the Mooney−Rivlin plot of natural rubber where Vr is the volume fraction of elastomer in the swollen sample, (swelling liquid, n‐decane). [Mullins (1959).14 Copyright 1959, John Wiley & Sons.]
9. Figure 6-9 Effect of filler concentration on the moduli of natural rubber samples (filler: MT carbon black). The curve was calculated from equation (6‐94). [Mullins and Tobin (1965).19 Copyright 1965, John Wiley & Sons.]
10. Figure 6-10 Mooney−Rivlin plots of natural rubber filled with MT carbon black: Top set: actual data without using the strain amplification factor. Bottom curves: after reduction using the strain amplification factor, equation (6‐97). [Mullins and Tobin (1965).19 Copyright 1965, John Wiley & Sons.]
11. Figure 6-11 Stress softening of natural rubber filled with MPC carbon black (Mullins effect). Numerals indicate the stress−strain cycles. [Bueche (1960).21 Copyright 1960, John Wiley & Sons.]
12. Figure 6-12 Schematic diagram of polymer chains attached to filler particles in an elastomer. The short chain will likely be the first to break on stretching the elastomer. [Bueche (1960).21 Copyright 1960, John Wiley & Sons.]
13. Figure 6-13 Stress−strain curves of natural rubber at 0 °C and 60 °C. The increase in stress at 0 °C at λ > 3 is attributed to strain‐induced crystallization. [Smith et al. (1964).22 Copyright 1964, Springer.]
14. Figure 6-14 Conformation of a polymer chain with one end fixed at the origin of a Cartesian coordinate system.
15. Figure 6-15 Radial distribution function of a chain of 10⁴ freely orienting segments each of length 0.25 nm.
16. Figure 6-16 Polymethylene backbone in the fully extended conformation.
Chapter 7
1. Figure 7-1 Schematic representation of an RC circuit comprising a resistor R in series with a capacitor C.
2. Figure 7-2 Debye plots for dielectric relaxation.
3. Figure 7-3 Alignment of dipoles in a field.
4. Figure 7-4 Polarization at the interface between a polymer and a polar inclusion. The interfacial charges are illustrated as effective dipoles, showing that distinguishing interfacial from dipolar polarization will depend critically on the characteristic time of the former.
5. Figure 7-5 Cole−Cole plot for a single relaxation time, ε_R = 8, ε_u_{= 3.}
6. Figure 7-6 Cole−Cole plot for the α relaxation in poly(2‐chlorostyrene). [From Alexandrovich et al., (1980). ¹⁵ Copyright 1980, Elsevier.]
7. Figure 7-7 Schematic of transformer ratio arm bridge.
8. Figure 7-8 (a) Impedance spectroscopy result for an ionically conductive epoxy composite [Courtesy of S. B. Boob (2003) ¹⁸ ]; (b) the equivalent circuit (inset) for the circular part of the response; and (c) same as (b), but plotted on a frequency scale.
9. Figure 7-9 TSC results for polycarbonate compared with NMR line width and dynamic mechanical (DMTA) measurements. [TSC data from Aoki and Brittain (1977). ²⁰ Copyright 1977, John Wiley & Sons; NMR data from Matsuoka and Ishida (1966). ²¹ Copyright 1966, John Wiley & Sons; DMTA data from Illers and Breuer (1961). ²² Copyright 1966, Springer.]
10. Figure 7-10 Comparison between tan δ_ε and tan δ for PMMA. [Dielectric and mechanical data from McCrum et al. (1967)⁵ by permission of copyright owner, N. G. McCrum. Original dielectric data were from Mikhailov and Borisova (1961). ²³ Copyright 1961, Elsevier. Original mechanical data from Heijboer (1965). ²⁴ Copyright 1965, North Holland.]
11. Figure 7-11 Correlation map for PMMA. Solid symbols, mechanical; open symbols, dielectric; and crosses, NMR. [McCrum et al. (1967). ⁵ Copyright 1967, John Wiley & Sons.]
12. Figure 7-12 Broadline NMR investigation of plasticized PVC. [Boo and Shaw (1982). ²⁹ Copyright 1982, John Wiley & Sons.]
13. Figure 7-13 Crossplot of broadline ¹H and CP‐MAS (narrow line) ¹³C spectra for a 43% mixture of erucamide with i‐PP. Erucamide is a fatty acid amide used with PP film to reduce adhesion of adjacent layers of film. The contours indicated by arrows are due to polypropylene –CH₃, >CH– and –CH₂– groups, respectively. This shows that the >CH– group at ˜ 26 ppm on the ¹³C resonance axis has the lowest mobility, as its proton resonance is the broadest. [Quijada‐Garrido et al. (1998). ³⁰ Copyright 1998, John Wiley & Sons.]
14. Figure 7-14 Changes in NMR spin–spin and spin–lattice relaxation times with temperature for a low‐T_g polymer PVME and a high‐T_g polymer PS. [Kwei et al. (1974). [32] Copyright 1974, American Chemical Society.]