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Microstructure and Mechanical Enhancement in Randomly End-linked Bimodal Networks

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Microstructure and Mechanical Enhancement in Randomly End-linked Bimodal Networks. Bimodal Elastomer Networks. Short Chains. Long Chains. Cross-links. s m. Bimodal. Unimodal Short Chains. Unimodal Long Chains. a m.

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Bimodal Elastomer Networks

Short Chains

Long Chains




Unimodal Short Chains

Unimodal Long Chains


Bimodal Networks: formed by end-linking two sets of chemically identical linear chains with different molar mass

Mechanical Enhancement: When sizes differ by a factor greater than 10, enhanced mechanical properties can result.

  • Large ultimate stress and strain
  • Stress upturn
  • Increased toughness

Mechanical Enhancement in Bimodal Networks

The two main hypotheses for the mechanical enhancement are:

Slightly heterogeneous, quasi-homogeneous

  • Limited extensibility of short chains at large deformation1

Short chains

  • Heterogeneous domains of short chains can act as reinforcing agents2

Highly heterogeneous

Limited extensibility of short chains seems to be the correct interpretation3

Slightly heterogeneous

Relationship between toughening mechanism and microstructure: not well understood

Highly heterogeneous

  • Polym. Sci., Polym. Phys., 22, 1849–1855 (1984).
  • Macromolecules, 23, 351–353 (1990).
  • Macromolecules, 41, 8231-8241 (2008).

Mechanical Enhancement and Topology

A percolation transition occurs for short chains1,2

90 mol%: Slightly heterogeneous, rather extensible and high modulus. Optimum! ~ Elastic coupling of short chains

60 mol%: Highly heterogeneous, very extensible, but with poor modulus

Short chains

95 mol%: quasi-homogeneous, high modulus, but brittle

95 mol%

60 mol%

90 mol%

90 mol%

60 mol%

95 mol%

95 mol%

95 mol%

SANS Measurements2

90 mol%

90 mol%

60 mol%


60 mol%

  • Macromolecules, 41, 8231 (2008).
  • Macromolecules, in preparation.

Pshort chain= fraction of short chains in largest cluster


Summary (Bimodal Networks)

  • Optimal tensile properties occurs when most of short chains are elastically coupled with the greatest amount of long chains
  • Short-chain elastic coupling ocurrs near the percolation transition for the short chains
  • Percolated short chains form a hard skeleton with flexibility due to softer regions of long chains that join different parts of the skeleton

Ongoing work

  • A more quantitative analysis of elastic coupling of short chains through network connectivity order parameters