How accurately do mechanophores report on bond scission in soft polymer materials?

Mechanophores are molecules that are incorporated into a host material and react to the local mechanical condition—the state of stress or strain—of that host material. Among their many purposes is that of a reporter: Mechanophores whose optical activity changes in response to mechanical cues can reveal bulk material processes that are ordinarily hidden, such as fatigue and fracture. Moreover, they may do so well before a material is fully fractured. To extract quantitative information from the optical signals from embedded mechanophores it is important that the mechanophores, which are generally a minority component of the material, report proportionally and unambiguously on the mechanical condition of the bulk. This is particularly important for early reporting of damage and wear, for which the optical signal from the mechanophore should accurately reflect bulk bond scission. In this article, we develop and analyze a general theory for the quality of optical mechanoreporting by mechanophores in soft materials, based on the Bell-Evans theory of bond breaking. We find, that at the typical low fractions in which mechanophores are incorporated the overall change in strength is limited, but that the proportionality of the reporting can be off by significant amounts, particularly at short times after loading but, for non-scissile bonds, at long times as well.