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Stress relaxation of narrow molar mass distribution polystyrene following uniaxial extension
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10.1122/1.2930872
/content/sor/journal/jor2/52/4/10.1122/1.2930872
http://aip.metastore.ingenta.com/content/sor/journal/jor2/52/4/10.1122/1.2930872

Figures

Image of FIG. 1.
FIG. 1.

Measured loss, (open circles; ) and storage moduli, (bullets; ) both as a function of the angular frequency, . The data are obtained from small angle oscillatory shear rheometry. The experiments have been performed at 120, 130, and , and shifted to a reference temperature of . The solid lines (—–) are the least-squares fitting to the BSW model in Eq. (2).

Image of FIG. 2.
FIG. 2.

Evolution of filament diameter, , and plate separation, , for an elongational rate of at , stretched for and then relaxed. During the relaxation, the diameter is kept constant by the closed loop controller in the experiment in the left figure, and the distance between the end plates is kept constant in the experiment in the figure to the right. The initial filament diameter and the initial plate separation for both the controlled and uncontrolled experiments are: and .

Image of FIG. 3.
FIG. 3.

Quenched polystyrene filaments after cessation of flow. The elongational rate at startup is , the strain at relaxation is , and the temperature in all performed experiments. The samples are relaxed, respectively ( ), before the quenching. The ruler to the right shows the length in millimeters.

Image of FIG. 4.
FIG. 4.

Measured stress (at ) as a function of time at startup and relaxation of elongational flow, as in Fig. 2. The diameter is kept constant by the closed loop controller in one of the experiments . In the two other curves is the plate separation, , stopped at . The boxes are the calculation of the true stress , where the open circles curve are calculated with the assumption of a constant midfilament diameter during the relaxation as .

Image of FIG. 5.
FIG. 5.

Figure (a) shows the measured startup and relaxation viscosity performed at an elongational rate of . In one experiment the filament is stretched for and then relaxed (pluses, ), and in the other experiment the filament is stretched for and then relaxed, (boxes, ). The two dotted lines (- - -) are the linear viscoelastic prediction for startup and relaxation after . Figure (b) is the evolution of filament diameter, , and plate separation, , for the experiment with elongational rate of at , stretched for and then relaxed. The diameter is kept constant by the closed loop controller in this experiment.

Image of FIG. 6.
FIG. 6.

The measured corrected startup and relaxation viscosity performed at rates of at . In all cases the flow is stopped at an extension of and allowed to relax for , . The solid lines (——) are the Doi–Edwards predictions of the transient elongational viscosity, Eq. (8) with . The dashed lines (- - - -) are the MSF model prediction from Eq. (10) with a tube diameter relaxation time of .

Image of FIG. 7.
FIG. 7.

The steady stress divided with the plateau modulus against the Marrucci-Deborah number for , , , and at . The value of is at . is the zero-shear viscosity.

Image of FIG. 8.
FIG. 8.

The stretch, , calculated using the measured relaxation viscosity at in Fig. 6, as a function of the time, from the start of the stress relaxation. The stretch is found using Eq. (11) based on the independent alignment approximation, Eq. (8). The solid lines are the stretch calculated using Eq. (13), with a tube diameter relaxation time and stretch of the fully extended molecule of .

Tables

Generic image for table
TABLE I.

Linear viscoelastic and molecular weight properties of the NMMD polystyrene melts at . The and constants in the BSW model are obtained from Jackson and Winter (1995) and from Bach et al. (2003a). The two parameters and are the time constants for specific models for the nonlinear relaxation of stretch.

Generic image for table
TABLE II.

At Prestretch values.

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/content/sor/journal/jor2/52/4/10.1122/1.2930872
2008-07-01
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Stress relaxation of narrow molar mass distribution polystyrene following uniaxial extension
http://aip.metastore.ingenta.com/content/sor/journal/jor2/52/4/10.1122/1.2930872
10.1122/1.2930872
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