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Concentration dependence of shear and extensional rheology of polymer solutions: Brownian dynamics simulations
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10.1122/1.2167468
/content/sor/journal/jor2/50/2/10.1122/1.2167468
http://aip.metastore.ingenta.com/content/sor/journal/jor2/50/2/10.1122/1.2167468

Figures

Image of FIG. 1.
FIG. 1.

Reduced viscosity, , as a function of Weissenberg number, , for systems subjected to planar elongational flow. Comparison of results for systems at when different numbers of chains per simulation cell are considered. With little difference in the results for systems of and chains, we use chains for all other results presented in this work.

Image of FIG. 2.
FIG. 2.

Mean-square radius of gyration, , plotted as a function of normalized concentration, , for various chain lengths.

Image of FIG. 3.
FIG. 3.

Excluded volume energy contribution to the net system energy for DNA at various concentrations.

Image of FIG. 4.
FIG. 4.

Scaling of the static chain size as a function of normalized concentration. Solid lines indicate fits following the scaling law in the dilute regime and in the semidilute regime .

Image of FIG. 5.
FIG. 5.

Scaling of the static chain size as a function of molecular weight at and . Solid line indicates predicted dilute regime scaling while dashed line gives the expected semidilute scaling .

Image of FIG. 6.
FIG. 6.

(a) Short-time and (b) long-time time diffusivity normalized against that of the infinitely dilute case for -phage DNA systems as a function of normalized concentration both with and without hydrodynamic interactions. At infinite dilution, the short-time and long-time diffusivities match for each hydrodynamic case and are and .

Image of FIG. 7.
FIG. 7.

Ratio of long-time to short-time diffusivity of DNA systems as a function of normalized concentration both with and without hydrodynamic interactions.

Image of FIG. 8.
FIG. 8.

Average number of chain crossings per chain during a given time step for systems subjected to (a) simple shear flow and (b) planar elongational flow.

Image of FIG. 9.
FIG. 9.

Flow direction fractional extension as a function of shear rate for systems subjected to simple shear flow both with and without hydrodynamic interactions.

Image of FIG. 10.
FIG. 10.

Flow direction fractional extension as a function of Weissenberg number for systems subjected to simple shear flow both with and without hydrodynamic interactions.

Image of FIG. 11.
FIG. 11.

Reduced viscosity as a function of shear rate for systems subjected to simple shear flow both with and without hydrodynamic interactions.

Image of FIG. 12.
FIG. 12.

Reduced viscosity as a function of Weissenberg number for systems subjected to simple shear flow both with and without hydrodynamic interactions.

Image of FIG. 13.
FIG. 13.

Comparison of polymer contribution to the viscosity in simple shear flow as calculated from simulations including hydrodynamic interactions with experimental values of Hur et al. (2001). The concentration is . Simulation results have been rescaled to account for differences in solvent viscosity.

Image of FIG. 14.
FIG. 14.

Flow directional extension as a function of extension rate for systems subjected to planar elongational flow both with and without hydrodynamic interactions. Panels (a) and (b) give the fractional chain stretch, while panels (c) and (d) give the stretch normalized against that of the infinitely dilute case in order to facilitate the description of the concentration effects.

Image of FIG. 15.
FIG. 15.

Flow directional extension as a function of Weissenberg number for systems subjected to planar elongational flow both with and without hydrodynamic interactions. Panels (a) and (b) give the fractional chain stretch, while panels (c) and (d) give the stretch normalized against that of the infinitely dilute case in order to facilitate the description of the concentration effects.

Image of FIG. 16.
FIG. 16.

Reduced elongational viscosity as a function of extension rate for systems subjected to planar elongational flow both with and without hydrodynamic interactions. Panels (a) and (b) give the calculated reduced viscosity, while panels (c) and (d) give the viscosity normalized against that of the infinitely dilute case in order to facilitate the description of the concentration effects.

Image of FIG. 17.
FIG. 17.

Reduced elongational viscosity as a function of Weissenberg number for systems subjected to planar elongational flow both with and without hydrodynamic interactions. Panels (a) and (b) give the calculated reduced viscosity, while panels (c) and (d) give the viscosity normalized against that of the infinitely dilute case in order to facilitate the description of the concentration effects.

Tables

Generic image for table
TABLE I.

Radius of gyration and overlap concentration, , for chains of varying molecular weight.

Generic image for table
TABLE II.

Minimum number of chains, , required to guarantee as a function of concentration and molecular weight.

Generic image for table
TABLE III.

Calculated longest relaxation times for DNA as a function of concentration both with and without hydrodynamic interactions. Experimental values are those of Hur et al. (2001), where the solvent viscosity has been normalized to match that of our simulated system.

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/content/sor/journal/jor2/50/2/10.1122/1.2167468
2006-03-01
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Concentration dependence of shear and extensional rheology of polymer solutions: Brownian dynamics simulations
http://aip.metastore.ingenta.com/content/sor/journal/jor2/50/2/10.1122/1.2167468
10.1122/1.2167468
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