On the Effective Lifetime of Reversible Bonds in Transient Networks

The renormalized bond lifetime model (RBLM) is a popular scaling theory for the effective lifetime of reversible bonds in transient networks. It recognizes that stickers connected by a reversible bond undergo many (J) cycles of dissociation and reassociation. After finally separating, one of these stickers finds a new open partner in time τ_open via a subdiffusive process whose mean-squared displacement is proportional to t^α, where t is the time elapsed, and α is the subdiffusion exponent. The RBLM makes convenient mathematical approximations to obtain analytical expressions for J and τ_open. The consequences of relaxing these approximations is investigated by performing fractional Brownian motion (FBM) simulations. It is found that the scaling relations developed in the RBLM hold surprisingly well. However, RBLM overestimates both τ_open and J, especially at lower values of α. For α = 0.5, corresponding to the Rouse limit, it is found that τ_open is overestimated by a factor of approximately 4x, while the approximation for J is nearly exact. The degree of overestimation worsens as α decreases, and increases to 1–2 orders of magnitude at α = 0.25, corresponding to the reptation limit. This has important ramifications for experimental studies that use RBLM to interpret rheology and dielectric spectroscopy observations.