Schematic of the sliplink creation process for the original NR scheme: (a) scanning for a partner subchain, with chain end and scanning sphere shown as a filled circle and a dashed circle, respectively; (b) creation of the new sliplink, with dashed and bold solid lines indicating the hooked subchain before and after the hooking process, respectively.
Schematic of the sliplink creation process for both the no-stretch and the fluctuating NR schemes.
Distribution of the sliplink number per chain, , for NR1, NR2, and NR3 schemes from top to bottom. Four values of are shown, namely 5, 10, 20, and 40. The corresponding Poisson distributions are indicated by dashed lines.
Distribution of the subchain monomer number, , for , 10, 20, and 40, from top to bottom. Dotted, dot-dashed, and solid lines refer to NR1, NR2, and NR3 schemes, respectively. In panel (d), the bold dot-dashed line is the single exponential of classical theory, while the bold solid line is Eq. (11) with and .
Comparison of the monomer distribution predicted by our simulation (with NR3) to data (symbols) from Refs 7, 10, and 11.
Distribution of the subchain length, , for , 10, 20, and 40, from top to bottom. Dotted, dot-dashed and solid lines refer to the NR1, NR2, and NR3 schemes, respectively. Bold line in panel (d) is Eq. (13) with .
Comparison to data of the subchain length distribution predicted by our simulation. Triangles are data for C1000 from Fig. 15 of Ref. 6; circles are data for PB1000 (Ref. 7); the histogram is for from Fig. 3 of Ref. 8.
Average values of subchain properties vs molecular weight. Empty circles and triangles, and filled circles refer to NR1, NR2, and NR3, respectively.
Scaling of several chain and network properties with molecular weight: (a) average subchain number per chain, (b) square end-to-end distance, (c) longest relaxation time, (d) diffusion coefficient. Solid lines indicate equality, while dotted lines show typical scaling exponents. Empty circles and triangles, and filled circles refer to NR1, NR2, and NR3, respectively.
Viscoelastic moduli (solid line) and (dotted line) from the NR1, NR2, and NR3 schemes, from top to bottom. Symbols are experimental data for monodisperse linear polyisoprene from Ref. 27. Simulation parameters are in Table I.
Simulation parameters used for Fig. 10.
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