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Viscosity predictions for model miscible polymer blends: Including self-concentration, double reptation, and tube dilation
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10.1122/1.2039847
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Affiliations:
1 Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
2 Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 and Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
a) Author to whom correspondence should be addressed; electronic mail: lodge@chem.umn.edu
J. Rheol. 49, 1277 (2005)
/content/sor/journal/jor2/49/6/10.1122/1.2039847
http://aip.metastore.ingenta.com/content/sor/journal/jor2/49/6/10.1122/1.2039847

## Figures

FIG. 1.

Viscosity as a function of composition for (a) PI-78/PVE-10 and (b) PI-78/PVE-120 at selected temperatures. The symbols denote experimental measurements; error bars indicate estimated experimental uncertainty of . The predictions of the basic viscosity model of Sec. II (solid lines) and the viscosity predictions with the tube dilation model (broken lines) are plotted.

FIG. 2.

Viscosity as a function of composition for PS-30/PVME-105 at selected temperatures. The symbols denote experimental measurements; error bars indicate estimated experimental uncertainty of . The predictions of the basic viscosity model of Sec. II (solid lines) are plotted.

FIG. 3.

Viscosity as a function of composition for (a) PEP-35/hhPP-52, (b) PEP-88/hhPP-181, (c) PEP-135/hhPP-52, and (d) PEP-135/hhPP-95 at selected temperatures; the data are taken from Gell (1996). The predictions of the basic viscosity model of Sec. II (solid lines) are plotted.

FIG. 4.

Viscosity as a function of composition for (a) PB-410/PB-44, (b) PB-410/PB-12, (c) PB-410/PB-8.9, and (d) PB-410/PB-5.8 at selected temperatures; the data are taken from Wang et al. (2003). The predictions of the basic viscosity model of Sec. II (solid lines) and of the viscosity predictions with the tube dilation model (broken lines) are plotted.

FIG. 5.

(a) Test chain confined to a tube made up of two types of constraints. At short times, segments near the center of the test chain follow the unconstrained Rouse motion scaling relation of Eq. (9). On times scales greater than , the test chain is constrained by the tube wall, and segments follow the scaling relation of Eq. (10). (b) At some later time scale, all of the mobile constraints (gray) are removed. This process results in an immediate increase in the tube diameter. (c) The test chain explores the new tube. Over a certain time scale, segmental displacement follows the scaling relation of Eq. (9). At a later time, the segments will once again be confined by the tube wall, and will follow the scaling relation of Eq. (10).

FIG. 6.

Plot of for pure reptation (broken line) and reptation of a chain through a field of fixed and mobile constraints (solid line).

FIG. 7.

Illustration of possible mechanisms of tube exploration on time scales greater than . Mechanism (a), free uncorrelated Rouse motion, follows the scaling relation of Eq. (9). Mechanism (b), center of mass motion of the primitive path, is severely restricted by the remaining constraints that form the dilated tube.

FIG. 8.

Predicted normalized by the square of the initial tube diameter. Also plotted is the mean-squared displacement for a chain in a tube of fixed diameter (, dotted line) and (dashed line).

FIG. 9.

(a) Terminal relaxation times of PB in blends with lower molecular weight PB partners as a function of composition; data (symbols) from Wang et al. (2003). (b) Terminal relaxation times of PS in blends with lower molecular weight PS partners as a function of composition; data (symbols) from Watanabe and Kotaka (1984). Solid lines indicate the predictions of the tube dilation model.

FIG. 10.

(a) Diffusion coefficients of several PS tracers in PS matrices of molecular weight . Data (symbols) from Green et al. (1984), solid lines are predictions of tube dilation model. (b) Normalized PS diffusion coefficients plotted as a function of a dimensionless parameter intended to characterize the onset of constraint release; lines are drawn as guides to the eye.

## Tables

TABLE I.

Molecular characteristics of polymer samples.

TABLE II.

Cloud point temperatures of PS-30/PVME-105 blends.

/content/sor/journal/jor2/49/6/10.1122/1.2039847
2005-11-01
2014-04-25

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