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Crossover time in relative fluctuations characterizes the longest relaxation time of entangled polymers
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10.1063/1.4752768
/content/aip/journal/jcp/137/11/10.1063/1.4752768
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/11/10.1063/1.4752768
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Ensemble-averaged MSDs of CMs in the slip-spring model for N = 10, 20, 40, 80, and 160. Dashed lines represent curves which are proportional to Δ1 and Δ1/2. b and τ0 are the size and characteristic time of a segment, respectively.

Image of FIG. 2.
FIG. 2.

Relative fluctuations of TAMSDs of CMs in the slip-spring model for Δ/τ0 = 10 and N = 10, 20, 40, 80, and 160, where τ0 is the characteristic time of a segment. (a) N = 10 and 20, and (b) N = 40, 80, and 160. Dashed line represents a curve proportional to t −1/2. The power law exponents for the short time regions are α = 0.31, 0.24, and 0.19 for N = 40, 80, and 160, respectively.

Image of FIG. 3.
FIG. 3.

The longest relaxation time τ d and the crossover time τ c in the slip-spring model. τ d is determined from the shear relaxation modulus data22 whereas τ c is determined from the RF data of TAMSDs for Δ/τ0 = 10. Dashed lines represent fitting curves for large N d N 3.48 and τ c N 3.51).

Image of FIG. 4.
FIG. 4.

Ensemble-averaged MSDs of CMs in the discrete reptation model for Z = 10, 20, 40, 80, and 160. a is the step size of a tube segment and τ l is the characteristic time of the longitudinal motion of a segment along the tube.

Image of FIG. 5.
FIG. 5.

Relative fluctuations of TAMSDs of CMs in the discrete reptation model for Δ/τ l = 10 (see Appendix A) and Z = 10, 20, 40, 80, and 160. The dashed line represents a curve proportional to t −1/2. τ l is the characteristic time of the longitudinal motion of a segment along the tube.

Image of FIG. 6.
FIG. 6.

The longest relaxation time τ d and crossover time τ c in the discrete reptation model. τ d is determined from the shear relaxation modulus and τ c is determined from the RF data of TAMSDs in the same way as Fig. 3. The dashed line represents the reptation time τrep l = Z 32.

Image of FIG. 7.
FIG. 7.

Rescaled RFs of TAMSDs of CMs in the discrete reptation model for different values of Z. The data are the same as Figure 5 but the observation time t is rescaled by the reptation time τrep = Z 3τ l 2. All the data points collapse into one master curve except the short time region or the small Z data (Z = 10, in this case).

Image of FIG. 8.
FIG. 8.

Relative fluctuations of TAMSDs of CMs in the slip-spring model for N = 80. The dashed line represents a curve proportional to t −1/2.

Image of FIG. 9.
FIG. 9.

Relative fluctuations of TAMSDs of CMs in the discrete reptation model for Z = 40. The dashed line represents a curve proportional to t −1/2.

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/content/aip/journal/jcp/137/11/10.1063/1.4752768
2012-09-20
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Crossover time in relative fluctuations characterizes the longest relaxation time of entangled polymers
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/11/10.1063/1.4752768
10.1063/1.4752768
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