Universal scaling description of the strain-softening behavior in the semidilute uncross-linked polyacrylamide-water solution

The strain-dependent linear viscoelastic properties of several semidilute polyacrylamide-water solutions have been investigated by using our modified forced-oscillating torsion resonator. It is shown that these simple, semidilute uncross-linked flexible polymer aqueous solutions exhibit a strain softening behavior, as observed in the monodisperse compressed emulsions. More surprisingly, for all polyacrylamide-water samples, the strain-dependent linear elastic moduli can be scaled onto a universal master curve. We propose a physical model, based on P.G. de Gennes' notion of blobs and the spring-network model previously for compressed emulsions, to accurately and quantitatively account for these data, that the semidilute polyacrylamide-water solutions can be suggested to have the disordered structure of random and close packing of the polymer-blobs; their elasticity is universal, dependent on the packing geometry of the blobs and arising from the energy storage at the deformed interfaces of the blobs; and the scaling strain-softening behavior originates from the rearrangement of the densely packed blobs under the sufficiently small perturbing strain or stress. Furthermore, a similar scaling behavior is also observed in previous results for compressed emulsions and glassy colloidal suspensions when the externally perturbing strain is sufficiently small, further confirming the universality of this scaling behavior existing in glassy soft materials. We report a universal strain-softening scaling behavior in semidilute polyacrylamide-water solutions, suggesting a disordered structure of randomly packed-blobs. Similar behavior is also found in compressed emulsions and glassy colloidal suspensions.