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Deformation and flow of matter: Interrogating the physics of materials using rheological methodsa)
a)This work is based on the Bingham Medal address “Interrogating the physics of amorphous solids: Rheological and mechanical measurements,” given by the author at the 81st Annual Meeting of the Society of Rheology, October 20, 2009, Madison, WI.
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10.1122/1.3671401
/content/sor/journal/jor2/56/1/10.1122/1.3671401
http://aip.metastore.ingenta.com/content/sor/journal/jor2/56/1/10.1122/1.3671401

Figures

Image of FIG. 1.
FIG. 1.

Schematic of torsion of a cylinder held at constant length.

Image of FIG. 2.
FIG. 2.

Torque and normal force responses [normalized by geometry as suggested by Eqs. (15) and (16)] for a cylinder of dicumyl peroxide crosslinked natural rubber. [After McKenna and Zapas, Polymer, 24, 1495–1501 (1983).]

Image of FIG. 3.
FIG. 3.

Strain energy function derivatives with respect to the invariants of the deformation tensor for a dicumyl peroxide crosslinked natural rubber. [Data from Penn and Kearsley, Transactions of the Society of Rheology, 20, 227–238 (1976).]

Image of FIG. 4.
FIG. 4.

The VL function derivative vs stretch for natural rubber samples cured with 1, 5, and 15 parts per hundred (PHR) dicumyl peroxide. [After McKenna et al., Polymer, 31, 1937–1945 (1990).]

Image of FIG. 5.
FIG. 5.

Dependence of the Flory–Huggins interaction parameter for natural rubber and different solvents as a function of the degree of crosslinking. [After McKenna et al., Polymer, 31, 1937–1945 (1990).]

Image of FIG. 6.
FIG. 6.

Scaled difference between Flory–Huggins interaction parameters for crosslinked and uncrosslinked natural rubber showing “universal-like” dependence of for dicumyl peroxide crosslinked natural rubber. [After McKenna et al., Polymer, 31, 1937–1945 (1990).]

Image of FIG. 7.
FIG. 7.

as a function of the degree of crosslinking for poly(vinyl alcohol) gels prepared at different degrees of dilution (% in figure legend refers to concentration at crosslinking). [After McKenna and Horkay, Polymer, 35, 5737–5742 (1994).]

Image of FIG. 8.
FIG. 8.

Reduced stress vs swelling stretch for dicumyl peroxide crosslinked natural rubber. Different degrees of swelling result from equilibrium swelling in different solvents. APHRxx refers to the parts per hundred grams of rubber of dicumyl peroxide used in the crosslinking procedure. [After McKenna et al., Macromolecules, 22, 4507–4512 (1989).]

Image of FIG. 9.
FIG. 9.

Isochronal shear and normal stress results from torsional measurements on tubes of PMMA at ambient temperatures. (a) Shear stress in torsion of tubes in poly(methacrylate) as a function of the strain in the tube wall. (b) Normal stress as a function of strain squared. [After McKenna and Zapas, Journal of Rheology, 23, 151–166 (1979).]

Image of FIG. 10.
FIG. 10.

Comparison of the torque and normal force relaxation responses for PMMA and for poly(carbonate) at 30 °C and a torsional strain of 4% showing that the torsional (shear) responses are very similar, while the normal force responses are dramatically different. [Data from Flory and McKenna, Polymer, 45, 5211–5217 (2005) Copyright Elsevier, Amsterdam, and Flory and McKenna, Macromolecules, 38, 1760–1766 (2005). Copyright American Chemical Society, Washington, D.C.]

Image of FIG. 11.
FIG. 11.

Comparison of the torque and normal force relaxation responses for the series of materials PMMA, PEMA, PC, and PSF at their β-relaxation maxima. For PMMA, Tβ = Tg − 85 °C; for PEMA Tβ = Tg − 35 °C; for PC Tβ = Tg − 85 °C; for PSF Tβ = Tg − 130 °C. [Data from Flory and McKenna, Polymer, 45, 5211–5217 (2005) Copyright Elsevier, Amsterdam, and Macromolecules, 38, 1760–1766 (2005). Copyright, American Chemical Society, Washington, D.C.]

Image of FIG. 12.
FIG. 12.

Comparison of the relaxation behavior of the ratio of normal force modulus to torsional modulus for PMMA at Tβ = Tg − 85 °C; for PEMA at Tβ = Tg − 35 °C; for PC at Tβ = Tg − 85 °C; for PSF at Tβ = Tg − 130 °C. [Data from Flory and McKenna, Polymer, 45, 5211–5217 (2005). Copyright Elsevier, Amsterdam, and Flory and McKenna, Macromolecules, 38, 1760–1766 (2005). Copyright, American Chemical Society, Washington, D.C.]

Image of FIG. 13.
FIG. 13.

Representation of for the four polymers at isochrones of 1 s at the β-relaxation temperature. For PMMA, Tβ = Tg − 85 °C; for PEMA Tβ = Tg − 35 °C; for PC Tβ = Tg − 85 °C; for PSF Tβ = Tg − 130 °C. [After Flory and McKenna, Polymer, 45, 5211–5217 (2005). Copyright Elsevier, Amsterdam, and Flory and McKenna, Macromolecules, 38, 1760–1766 (2005). Copyright, American Chemical Society, Washington, D.C.]

Image of FIG. 14.
FIG. 14.

Volume of a cylinder of epoxy vs temperature. Dilatometry experiments performed at low rate compared to what would be anticipated for the higher rates typical of a DSC measurement. The approximately 13 °C difference in T g is typical of polymers where T g decreases approximately 3 °C for each logarithmic decade decrease in cooling rate. [Figure from Duran and McKenna, Journal of Rheology, 34, 813–839 (1990).]

Image of FIG. 15.
FIG. 15.

Volume recovery vs time after the temperature quench from 40 °C for a glass-forming material showing the intrinsic isotherm result catalogued by Kovacs. [Data from Kovacs, Fortschritte der Hochpolymeren-Forschung, 3, 394–507 (1963); figure from Zheng and McKenna, Macromolecules, 36, 2387–2396 (2003). Copyright, American Chemical Society, Washington, D.C.]

Image of FIG. 16.
FIG. 16.

Torque relaxation for a PC quenched from 142 °C to 70 °C and aged for different times as shown in legend. Time-aging time master curve offset for clarity. [After O’Connell and McKenna, Polymer Engineering and Science, 37, 1485–1495 (1997).]

Image of FIG. 17.
FIG. 17.

Semiquantitative schematic of the shift factor versus ageing or elapsed time for a material in a down-jump experiment showing the sigmoidal shape that the curve must have due to physical limitations at the short times and the fact that the material reaches equilibrium at long times. [After McKenna, Journal of Physics: Condensed Matter, 15, S737–S763 (2003). Copyright, IOPScience, Bristol.]

Image of FIG. 18.
FIG. 18.

Variation of the aging time shift factor with aging time for temperatures between 119 °C and 135 °C. Note that at 135 °C, the sample has equilibrated within the first 1800 s after the quench and that equilibration takes longer and longer as temperature is decreased. The lowest temperature for which equilibrium is achieved was 124.1 °C. [After O’Connell and McKenna, Polymer Engineering and Science, 37, 1485–1495 (1997).]

Image of FIG. 19.
FIG. 19.

Aging time shift factors vs aging time (double logarithmic representation) for a poly(vinyl chloride) glass at T = 40 °C after a quench from above the T g . The longest aging time is 1000 days and the plot results from performing time-aging time superposition on Struik’s (1976) data.

Image of FIG. 20.
FIG. 20.

Schematic that compares the aging response of a glass-forming system subjected to down-jump histories and the aging response “probed” by different magnitude stresses. As seen the shift factor for aging for small stresses is larger than for large stresses.

Image of FIG. 21.
FIG. 21.

Schematic that shows the “rejuvenation” hypothesis expectation of the impact of stress on the structure of the deformed glass (McKenna, 2003; Ricco and Smith, 1985).

Image of FIG. 22.
FIG. 22.

Schematic of the torsional dilatometer used for tests of rejuvenation in polymer glasses subjected to large deformations subsequent to a temperature jump from above to below the T g . [After Duran and McKenna, Journal of Rheology, 34, 813–839 (1990).]

Image of FIG. 23.
FIG. 23.

Relative volume change in structural recovery experiment on an epoxy glass. Black points are for sample strained to γ = 0.05 and red points are for sample subjected to “dither” strain of 0.0025. The fact that the curves all return to the same baseline structural recovery indicates that the mechanical rejuvenation does not occur. [Composite figure created from Santore et al., Polymer, 32, 2377–2381 (1991); figure from McKenna, Pacific Rim Conference on Rheology-Sapporo, Japan. (2010). Copyright, Japanese Society of Rheology.]

Image of FIG. 24.
FIG. 24.

Angell plot of the segmental relaxation shift factors for several polymer glass-forming liquids. The inset shows the heat capacity jumps at T g . [After Huang and McKenna, Journal of Chemical Physics 114, 5621–5630 (2001). Copyright American Institute of Physics, 2001.]

Image of FIG. 25.
FIG. 25.

Logarithm of segmental shift factor vs temperature (scaled relaxation times) for a PC aged into apparent equilibrium. (a) As a function of temperature and (b) as a function of reciprocal temperature. [After O’Connell and McKenna, Journal of Chemical Physics, 110, 11054–11060 (1999).]

Image of FIG. 26.
FIG. 26.

Influence of molecular weight and film thickness on the glass transition temperature of PS freely standing films. (After Forrest and Dalnoki-Veress, Advances in Colloid and Interface Science, 94, 167–196. Copyright © 2001, Elsevier, with permission.)

Image of FIG. 27.
FIG. 27.

(a) Schematic of a template with through channel and membrane deposited over the channel so that the membrane can be inflated and the inflated bubble measured in the AFM. (b) Image of inflated bubbles of a PVAc film [After O’Connell and McKenna, Science, 307, 1760–1763 (2005). Copyright American Association for the Advancement of Science, Washington, DC.]

Image of FIG. 28.
FIG. 28.

Bubble profiles for a 5 μ diameter bubble of PS having a film thickness of 22.5 nm at 55 °C and a pressure of 124 kPa (18 psi). Lines represent fits of Eq. (26c) to the shape. Creep times indicated in legend. [After O’Connell and McKenna, Review of Scientific Instruments, 78, 013901 (2007). Copyright American Institute of Physics.]

Image of FIG. 29.
FIG. 29.

Time-temperature master curves for PS films of different thicknesses as indicated. The reference temperatures are for the relevant glass transition temperature. [After O’Connell et al., Journal of Polymer Science, Polymer Physics Edition, 46, 1952–1965 (2008). Copyright Wiley Periodicals.]

Image of FIG. 30.
FIG. 30.

Log of the biaxial compliance in the plateau regime for (PVAc) and PS vs film thickness (log scale) showing dramatic stiffening of the polymer films as measured by the nanobubble inflation method [Composite of data published by O’Connell and McKenna (2005, 2006, 2009) and O’Connell et al. (2008).]

Image of FIG. 31.
FIG. 31.

Time-temperature master curves for PS films of different thicknesses as indicated. These curves are shifted to overlap, as appropriate, in the segmental regime. [After O’Connell et al., Journal of Polymer Science, Polymer Physics Edition, 46, 1952–1965 (2008). Copyright, Wiley Periodicals.]

Image of FIG. 32.
FIG. 32.

Temperature shift factors for PS films of different thicknesses vs temperature. Points are data and lines are WLF curves shifted relative to the macroscopic glass transition by the amounts indicated. [Adapted from O’Connell et al., Journal of Polymer Science, Polymer Physics Edition, 46, 1952–1965 (2008). Copyright Wiley Periodicals.]

Image of FIG. 33.
FIG. 33.

Change in T g as a function of film thickness for PS, PVAc, and PC from bubble inflation measurements. [From O’Connell and McKenna, ANTEC 2010—Proceedings of the 68th Annual Technical Conference and Exhibition, Orlando, FL, June 16–20 (2010). Copyright Society of Plastics Engineers.]

Tables

Generic image for table
TABLE I.

Designation of rubber samples, crosslinking quantities and network characteristics assuming dicumyl peroxide gives one crosslink per molecule. Mc is molecular weight between crosslinks and ν is the crosslink density. [After McKenna et al., Polymer Communications, 29, 272–275(1988); Macromolecules, 22, 4507–4512 (1989).]

Generic image for table
TABLE II.

Volume fraction of rubber, mixing contribution, and elastic contribution to the chemical potential for dicumyl peroxide crosslinked natural rubber swollen in various solvents. [After McKenna et al., Polymer, 32, 2129–2135 (1991).]

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2011-12-21
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Deformation and flow of matter: Interrogating the physics of materials using rheological methodsa)
http://aip.metastore.ingenta.com/content/sor/journal/jor2/56/1/10.1122/1.3671401
10.1122/1.3671401
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