The mechanical properties of a polymer network reflect the collective behavior of all of the constituent strands within the network. These strands comprise a distribution of states, and a central question is how the deformation and tension experienced by a strand is influenced by strand length. Here, we address this question through the use of mechanophore force probes with discrete molecular weights. Probe strands, each bearing a mechanochromic spiropyran (SP), were prepared through an iterative synthetic strategy, providing uniform PDMS-functionalized SP force probes with molecular weights of 578, 1170, and 2356 g/mol. The probes were each doped (9 mM) into the same silicone elastomer matrix. Upon stretching, the materials change color, consistent with the expected conversion of SP to merocyanine (MC). The critical strain at which measurable mechanochromism is observed is correlated with the strain hardening of the matrix, but it is independent of the molecular length of the probe strand. When a network with activated strands is relaxed, the color dissipates, and the rate of decoloration varies as a function of the relaxing strain ((ε_r ) ̅); faster decoloration occurs at lower (ε_r ) ̅. The dependence of decoloration rate on (ε_r ) ̅ is taken to reflect the effect of residual tension in the once-activated strands on the reversion reaction of MC to SP, and the effect of that residual tension is indistinguishable across the three molecular lengths examined. The combination of discrete strand synthesis and mechanochromism provides a foundation to further test and develop molecular-based theories of elasticity and fracture in polymer networks.
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Finite size effects in critical fiber networks
Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.
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- NSF-PAR ID:
- 10175214
- Date Published:
- Journal Name:
- Soft Matter
- ISSN:
- 1744-683X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/d0sm00764a
