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Analytical rheology of branched polymer melts: Identifying and resolving degenerate structures
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10.1122/1.3523627
/content/sor/journal/jor2/55/1/10.1122/1.3523627
http://aip.metastore.ingenta.com/content/sor/journal/jor2/55/1/10.1122/1.3523627

Figures

Image of FIG. 1.
FIG. 1.

The experimental data for the star-linear blend SL75-25 (black squares). The dynamic moduli of the corresponding monodisperse star (green circles) and linear (blue triangles) components are also shown. The response of the blend is similar to the response of the monodisperse star, and is responsible for degeneracy encountered.

Image of FIG. 2.
FIG. 2.

For SL75-25, the MCMC algorithm suggests a star-linear blend with 64% probability, a linear-linear blend with 11% probability, and a star-star blend with 25% probability. The best solutions for these three types of blends, namely linear-linear, star-linear, and star-star are shown together with the experimental data, and indicate that they indeed constitute degenerate solutions.

Image of FIG. 3.
FIG. 3.

The error or distance between the star-star (blue squares) and linear- linear (black circles) best-of-class samples from the star-linear best-of-class sample computed via Eq. (6). The additive used is (solid lines) and 50 KDa (broken lines), over a range of . For , it appears that a concentration of is able to isolate the linear-linear blend, and is able to isolate the star-star blend. These concentrations are denoted by red vertical lines. On the other hand, for , it seems hard to isolate the linear-linear blend over the entire range of .

Image of FIG. 4.
FIG. 4.

Given the magnitude of the errors , , and (represented by the axes), the individual can be assigned a unique position in three-dimensional space (represented by the circles). The criteria imposed by specifying a define a parallelepiped whose size is dependent on . The points within the parallelepiped define the set , which have the lowest overall errors.

Image of FIG. 5.
FIG. 5.

The relative fraction of the different blend types retained in the set , as a function of . For a certain value of , the set only contains those structures for which the errors , and , all lie in the top fraction of structures. When , we start from the original probabilities of 64%, 11%, and 25% for star-linear (solid line), linear-linear (dotted line), and star-star (dashed line) blends, respectively. As is decreased, the probability of the star-linear blend increases to 100%.

Image of FIG. 6.
FIG. 6.

Histogram of the configurations that consist of structures that are simultaneously consistent with all the three available data- sets , , and . The peak at 25 KDa corresponds to the star and at 50 KDa to the linear polymer, in the top panel. Only the weight fraction of the star is depicted in the lower panel.

Image of FIG. 7.
FIG. 7.

The original data set (black line with circles), and the additional data sets (red line with triangles) obtained by blending with and , and (blue line with squares) obtained by blending with and . Predictions using all the are superimposed using the green symbols.

Image of FIG. 8.
FIG. 8.

The relative fraction of the different blend types retained in the set , as a function of . For a certain value of , the set only contains those structures for which the errors , and , all lie in the top fraction of structures. When , we start from the original probabilities of 64%, 11%, and 25% for star-linear (solid line), linear-linear (dotted line), and star-star (dashed line) blends, respectively. As is decreased, the probability of the star-linear blend increases to 100%.

Image of FIG. 9.
FIG. 9.

Histogram of the configurations that consist of structures that are simultaneously consistent with all the three available data- sets , , and . The peak at 25 KDa corresponds to the star and at 50 KDa to the linear polymer, in the top panel. Only the weight fraction of the star is depicted in the lower panel.

Tables

Generic image for table
TABLE I.

The composition of the best-of-class solutions identified by the algorithm for the data set . The composition used to determine is presented as the last data set, for reference. The comparison with the experimental data is presented in Fig. 2. Molecular weights are in KDa. For species type, and denote star and linear polymers, respectively.

Generic image for table
TABLE II.

The three sets of synthesized experimental data. Molecular weights are in KDa.

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/content/sor/journal/jor2/55/1/10.1122/1.3523627
2010-12-22
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analytical rheology of branched polymer melts: Identifying and resolving degenerate structures
http://aip.metastore.ingenta.com/content/sor/journal/jor2/55/1/10.1122/1.3523627
10.1122/1.3523627
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