Divergence of the third harmonic stress response to oscillatory strain approaching the glass transition

Abstract

The leading nonlinear stress response in a periodically strained concentrated colloidal dispersion is studied experimentally and by theory. A thermosensitive microgel dispersion serves as well-characterized glass-forming model, where the stress response at the first higher harmonic frequency (3ω for strain at frequency ω) is investigated in the limit of small amplitude. The intrinsic nonlinearity at the third harmonic exhibits a scaling behavior which has a maximum in an intermediate frequency window and diverges when approaching the glass transition. It captures the (in-) stability of the transient elastic structure. Elastic stresses in-phase with the third power of the strain dominate the scaling. Our results qualitatively differ from previously derived scaling behavior in dielectric spectroscopy of supercooled molecular liquids. This might indicate a dependence of the nonlinear response on the symmetry of the external driving under time reversal.

Unifying different interpretations of the nonlinear response in glass-forming liquids

“…In fact, the growth of the peak of χ 5 as the temperature is reduced is stronger than that of χ 3 , and provides strong qualitative and quantitative evidence for the existence of an underlying critical point that drives the physics of supercooled liquids [18]. We also note that the non-linear mechanical response has also been studied in colloids [19,20], extending the BB results [11,21] to that case as well.…”

Third and fifth harmonic responses in viscous liquids

“…This is illustrated in Fig. 1 displaying the third harmonic cubic susceptibility χ (3) 3 -defined in Section 2.1-for four very different kinds of glasses [1,2,3,4,5,6]. In the case of spin glasses [1,7] -see Fig.…”

“…(D): Strain-stress experiment in the colloidal system studied in Refs. [5,6]. When increasing the volumic density φ the increasing peak of Q 0 = |χ (3) 3 /χ 1 | reveals that any shear strain connects the system to a non equilibrium steady state -see [5,6]-.…”

“…[5,6]. When increasing the volumic density φ the increasing peak of Q 0 = |χ (3) 3 /χ 1 | reveals that any shear strain connects the system to a non equilibrium steady state -see [5,6]-. In all these four examples χ (3) 3 unveils informations about the nature of the glassy state that cannot be obtained by studying the linear susceptibility χ lin .…”

“…Because these domains are independent from each other, one can use Eq. (1), provided that we change the elementary volume a d by that of a domain - [1,2,3,6]. Third-harmonic susceptibilities of very different types of glasses approaching their glass transition.…”