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Uniaxial extensional rheology of well-characterized comb polymers
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10.1122/1.4789443
/content/sor/journal/jor2/57/2/10.1122/1.4789443
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/2/10.1122/1.4789443

Figures

Image of FIG. 1.
FIG. 1.

Analysis of PS comb polymers from Table I . GPC (a) and TGIC (b) analysis. The curves appear in sequence with C712 being the curve to the right and C742 the curve to the left in part (a). The opposite sequence holds for part (b).

Image of FIG. 2.
FIG. 2.

(a) Linear rheology data of the PS combs (Δ) C622, (▶) C642, (●) C712, (X) C722, (○) C732, (right triangle) C742 at a reference temperature Tref = 170 °C. The tangent of the phase angle is plotted against the shifted angular frequency aTω. (b) Respective data of the PI combs (hexagon) PI211, (○) PI254, (+) PI472 at Tref = 0 °C.

Image of FIG. 3.
FIG. 3.

Variation of the normalized specimen width, −2ln(W/W0) (to its unstretched value W0) with t. The linear dependence indicates uniaxial extension and determines the true stretch rate, here 0.097 s−1 (squares), which compares well to the experimentally imposed (circles) 0.1 s−1.

Image of FIG. 4.
FIG. 4.

Transient tensile stress growth coefficients obtained at Tref = 170 °C for comb PS samples of different molecular characteristics at different Hencky strain rates (from 0.003 s−1 up to 10 s−1). The samples from (a) to (d) have the same backbone molar mass Mb = 860 kg/mol and varying branch (arm) molar mass (a) C742 with Ma = 47 kg/mol, (b) C732 with Ma = 25.7 kg/mol, (c) C722 with Ma = 11.7 kg/mol, and (d) C712 with Ma = 6.5 kg/mol. Samples (e) and (f) have the same Mb = 275 kg/mol but varying Ma: (e) C642 with 47 kg/mol and (f) C622 with 11.7 kg/mol. The rates from right to left are 0.003, 0.01, 0.03, 0.05, 0.07, 0.1, 0.3, 1, 3, and 10 s−1. Also, plotted as a solid line are the linear viscoelastic data.

Image of FIG. 5.
FIG. 5.

Transient tensile stress growth coefficients obtained at Tref = 0 °C of comb PI samples of different molecular characteristics: (a) PI472, (b) PI254, and (c) PI211 at different Hencky strain rates (from 0.003 up to 10 s−1). The rates from right to left are 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, and 10 s−1. Also, plotted as a solid line is the linear viscoelastic envelope from the linear viscoelastic data.

Image of FIG. 6.
FIG. 6.

Transient tensile stress growth functions plotted against Hencky strain ε obtained at (a) Tref = 0 °C for PI472 and (b) Tref = 170 °C for PS C732, and different Hencky strain rates (shown in the plots).

Image of FIG. 7.
FIG. 7.

(a) Tensile stress growth functions σE + plotted against Hencky strain ε obtained at Tref = 170 °C for PS comb C7 series samples of equal backbone Mb = 860 kg/mol and varying branch (arm) molar mass Ma = 47 kg/mol (filled hexagon), Ma = 25.7 kg/mol (open diamond), Ma = 11.7 kg/mol (filled square), and Ma = 6.5 kg/mol (filled star), at high Hencky strain rate of 10 s−1; (b) respective data at intermediate Hencky strain rate of 0.3 s−1; (c) respective data at low Hencky strain rate of 0.01 s−1. Also plotted in (a) as a solid line is the neo-Hookean prediction. (d) Tensile stress growth functions σE + plotted against Hencky strain ε obtained at Tref = 0 °C for samples PI211 (×), PI254 (filled circle), and PI472 (open hexagon) at high Hencky strain rate of 3 s−1; (e) same as (d) but at intermediate Hencky strain rate of 0.3 s−1; (f) same as (d) but at low Hencky strain rate of 0.03 s−1.

Image of FIG. 8.
FIG. 8.

Transient tensile stress growth functions plotted against Hencky strain obtained at Tref = 170 °C for comb PS samples of equal Ma = 47 kg/mol but of different backbone molar mass: C742 with Mb = 860 kg/mol (filled circle) and C642 with Mb = 275 kg/mol (open pentagon). Data are shown at (a) high Hencky strain rate of 3 s−1, (b) intermediate Hencky strain rate of 0.3 s−1, and (c) low Hencky strain rate of 0.03 s−1.

Image of FIG. 9.
FIG. 9.

Top: Indicative master curves of frequency-dependent G′ and G″ for entangled linear (left) and comb (right) polymers whose diluted backbone has the same number of entanglements Z as the linear chains. Bottom: Cartoon representation of the tube of the linear chain (left) and the comb (right). In the latter case, once the branches have escaped their tubes, the backbone tube diameter increases (and becomes equal to that of the linear chain for the present considerations) and bears extra friction due to the branches (indicated by the arrow).

Tables

Generic image for table
TABLE I.

Molecular characteristics of model comb polymers used in this work.

Generic image for table
TABLE II.

Results from the GPC/TGIC analysis of the high-Mb PS combs.

Generic image for table
TABLE III.

Experimental and predicted time scales for assessing the onset of extension hardening. For PI, we used Tref = 0 °C and for PS Tref = 170 °C.

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/content/sor/journal/jor2/57/2/10.1122/1.4789443
2013-02-04
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Uniaxial extensional rheology of well-characterized comb polymers
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/2/10.1122/1.4789443
10.1122/1.4789443
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