Universal scaling characteristics of stress overshoot in startup shear of entangled polymer solutions

Abstract

We have carried out conventional rheological measurements to explore the well-known stress overshoot behavior in startup shear of eight entangled polybutadiene solutions. In the elastic deformation regime with γ̇τR>1, we have identified universal scaling features associated with the stress maximum σmax for samples of different levels of entanglements per chain ranging from 27, 40 to 64. Specifically, at the moment tmax of the peak stress σmax where the applied strain is γmax=γ̇tmax: (a) σmax varies linearly with γmax, (b) σmax scales with tmax as σmax∼(tmax)−1∕2. The combination of (a) and (b) yields a striking “prediction” that γmax∼γ̇1∕3. Remarkably, these scaling laws form master curves when the peak stress, strain rate, and peak time are all normalized with the crossover modulus Gc, reciprocal Rouse time, and Rouse time τR, respectively. The dependence of σmax on tmax and γ on γ̇ is weaker in the crossover regime with γ̇τR<1. Equally noteworthy is the emergence of a super-master curve for the normalized stress σ(t)∕σmax as a function of the normalized strain γ̇t∕γmax at various applied rates in these solutions. The solution with only 13 entanglements per chain exhibits behavior deviating appreciably from the well entangled systems. Strain recovery experiments revealed irreversible deformation (i.e., flow) when the sample is sheared beyond the stress maximum (for γ̇τR>1) or when sheared with γ̇τR<1 for a period longer than the Rouse relaxation time τR.