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Quantifying the impact of molecular defects on polymer network elasticity

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Science  16 Sep 2016:
Vol. 353, Issue 6305, pp. 1264-1268
DOI: 10.1126/science.aag0184
  • Fig. 1 Cyclic defects in end-linked polymer networks.

    (A) Synthetic schemes for the preparation of A2 + B3 and A2 + B4 gels labeled for loop counting analysis. (B to D) Topological structure of primary loops (the average number of primary loops per f-functional network junction is n1,f) (B), secondary loops (the average number of secondary loops per f-functional junction is n2,f) (C), and ternary loops (the average number of ternary loops per f-functional junction is n3,f) (D) formed in A2 + B3 (f = 3; top) and A2 + B4 (f = 4; bottom) gels, respectively.

  • Fig. 2 Shear rheology and loop measurements in PEG gels.

    (A to C) Trifunctional (A2 + B3) gels: (A) Representative rheological curves demonstrating reproducibility of this gelation system (A2 concentration for all samples, 14 mM). (B) G′ and the average number of primary loops per junction in these f = 3 networks (n1,3) versus A2 concentration. Error bars of G′ represent SD of three measurements; error bars of n1,3 represent SD of nine measurements. (C) Experimentally estimated coefficient C with and without first-order affine correction. (D to F) Tetrafunctional (A2 + B4) gels: (D) Representative rheological curves demonstrating reproducibility of this gelation system (A2 concentration for all samples, 14 mM). (E) G′ and the average number of primary loops per junction in these f = 4 networks (n1,4) versus A2 concentration. Error bars of G′ represent SD of three measurements; error bars of n1,4 represent SD of nine measurements. (F) Experimentally estimated coefficient C with and without first-order affine correction.

  • Fig. 3 Real elastic network theory (RENT).

    (A) Schematic depiction of the conversion of independent loops to a mixture of phantom strands with different effective length. (B) Schematic that illustrates the calculation of effective phantom length of strands in lth-order loops at a distance m from the loop. (C) Elastic effectiveness of polymer strands as a function of topological distance m from a primary (l = 1) and secondary (l = 2) loops in f = 3 or f = 4 networks. (D) Elastic effectiveness of polymer strands in loops of different order l for f = 3 and f = 4 networks. (E) Fraction of secondary and ternary loops (n2,f and n3,f) as a function of the number of primary loops per junction (n1,f) in f = 3 and f = 4 networks.

  • Fig. 4 Elastic moduli predicted by RENT.

    Comparison of experimentally determined G′/kTν0 (black circles) to that predicted by affine theory (green dashed line), phantom theory (green dashed line), RENT with only a correction for primary loops (blue line), and RENT accounting for primary, secondary, and tertiary loops (black line). (A) f = 3 networks. (B) f = 4 networks. Error bars represent SD of nine measurements.

Supplementary Materials

  • Quantifying the impact of molecular defects on polymer network elasticity

    Mingjiang Zhong, Rui Wang, Ken Kawamoto, Bradley D. Olsen, Jeremiah A. Johnson

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S32
    • References

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