Disorder-assisted melting and the glass transition in amorphous solids

Sharp symmetry-change marks the mechanical failure transition of glasses

Glasses acquire their solid-like properties by cooling from the supercooled liquid via a continuous transition known as the glass transition. Recent research on soft glasses indicates that besides temperature, another route to liquify glasses is by application of stress that drives relaxation and flow. Here, we show that unlike the continuous glass transition, the failure of glasses to applied stress occurs by a sharp symmetry change that reminds of first-order equilibrium transitions. Using simultaneous x-ray scattering during the oscillatory rheology of a colloidal glass, we identify a sharp symmetry change from anisotropic solid to isotropic liquid structure at the crossing of the storage and loss moduli. Concomitantly, intensity fluctuations sharply acquire Gaussian distributions characteristic of liquids. Our observations and theoretical framework identify mechanical failure as a sharp atomic affine-to-nonaffine transition, providing a new conceptual paradigm of the oscillatory yielding of this technologically important class of materials, and offering new perspectives on the glass transition.

Shear-stress relaxation and ensemble transformation of shear-stress autocorrelation functions

We revisit the relation between the shear-stress relaxation modulus G(t), computed at finite shear strain 0<γ≪1, and the shear-stress autocorrelation functions C(t)|(γ) and C(t)|(τ) computed, respectively, at imposed strain γ and mean stress τ. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general G(t)=C(t)|(τ)=C(t)|(γ)+G(eq) for t>0 with G(eq) being the static equilibrium shear modulus. G(t) and C(t)|(γ) thus must become different for solids and it is impossible to obtain G(eq) alone from C(t)|(γ) as often assumed. We comment briefly on self-assembled transient networks where G(eq)(f) must vanish for a finite scission-recombination frequency f. We argue that G(t)=C(t)|(τ)=C(t)|(γ) should reveal an intermediate plateau set by the shear modulus G(eq)(f=0) of the quenched network.

Shear banding of colloidal glasses: observation of a dynamic first-order transition

We demonstrate that application of an increasing shear field on a glass leads to an intriguing dynamic first-order transition in analogy with equilibrium transitions. By following the particle dynamics as a function of the driving field in a colloidal glass, we identify a critical shear rate upon which the diffusion time scale of the glass exhibits a sudden discontinuity. Using a new dynamic order parameter, we show that this discontinuity is analogous to a first-order transition, in which the applied stress acts as the conjugate field on the system's dynamic evolution. These results offer new perspectives to comprehend the generic shear-banding instability of a wide range of amorphous materials.

Rheology of cohesive granular materials across multiple dense-flow regimes

We investigate the dense-flow rheology of cohesive granular materials through discrete element simulations of homogeneous, simple shear flows of frictional, cohesive, spherical particles. Dense shear flows of noncohesive granular materials exhibit three regimes: quasistatic, inertial, and intermediate, which persist for cohesive materials as well. It is found that cohesion results in bifurcation of the inertial regime into two regimes: (a) a new rate-independent regime and (b) an inertial regime. Transition from rate-independent cohesive regime to inertial regime occurs when the kinetic energy supplied by shearing is sufficient to overcome the cohesive energy. Simulations reveal that inhomogeneous shear band forms in the vicinity of this transition, which is more pronounced at lower particle volume fractions. We propose a rheological model for cohesive systems that captures the simulation results across all four regimes.

Shear shocks in fragile networks

A minimal model for studying the mechanical properties of amorphous solids is a disordered network of point masses connected by unbreakable springs. At a critical value of its mean connectivity, such a network becomes fragile: it undergoes a rigidity transition signaled by a vanishing shear modulus and transverse sound speed. We investigate analytically and numerically the linear and nonlinear visco-elastic response of these fragile solids by probing how shear fronts propagate through them. Our approach, which we tentatively label shear front rheology, provides an alternative route to standard oscillatory rheology. In the linear regime, we observe at late times a diffusive broadening of the fronts controlled by an effective shear viscosity that diverges at the critical point. No matter how small the microscopic coefficient of dissipation, strongly disordered networks behave as if they were overdamped because energy is irreversibly leaked into diverging nonaffine fluctuations. Close to the transition, the regime of linear response becomes vanishingly small: the tiniest shear strains generate strongly nonlinear shear shock waves qualitatively different from their compressional counterparts in granular media. The inherent nonlinearities trigger an energy cascade from low to high frequency components that keep the network away from attaining the quasi-static limit. This mechanism, reminiscent of acoustic turbulence, causes a superdiffusive broadening of the shock width.

Compressibility and pressure correlations in isotropic solids and fluids

Presenting simple coarse-grained models of isotropic solids and fluids in d = 1 , 2 and 3 dimensions we investigate the correlations of the instantaneous pressure and its ideal and excess contributions at either imposed pressure (NPT-ensemble, λ = 0 or volume (NVT-ensemble, λ = 1 and for more general values of the dimensionless parameter λ characterizing the constant-volume constraint. The stress fluctuation representation F(Row)|λ=1 of the compression modulus K in the NVT-ensemble is derived directly (without a microscopic displacement field) using the well-known thermodynamic transformation rules between conjugated ensembles. The transform is made manifest by computing the Rowlinson functional F(Row)| also in the NPT-ensemble where F(Row)|λ=1 = K f 0(x) with x = P id/K being a scaling variable, P id the ideal pressure and f 0(x) = x(2-x) a universal function. By gradually increasing λ by means of an external spring potential, the crossover between both classical ensemble limits is monitored. This demonstrates, e.g., the lever rule F(Row)|λ= K[λ = (1 - λ)f 0(x)].

Thermomechanical properties and deformation of coarse-grained models of hard-soft block copolymers

In this paper, we investigate the enhancement mechanism of the mechanical properties for hard-soft block copolymers by using molecular dynamics simulations at various temperatures. A coarse-grained approach is adopted to study sufficiently generic models. Our numerical experiments demonstrate that the nonbond potential plays a more significant role in mechanical properties compared to the bond potential. This finding serves as a cornerstone to understand the hard-soft materials. To explore the effect of hard segments, four copolymers with different concentrations and energy factors that describe the interaction between hard beads are conducted. Simulation results show that the mechanical performances of the system with large attractive force and small concentration of hard segments could be improved dramatically in conjunction with a moderate increment of the glass transition temperature. In particular, the energy factor shows a substantial influence in determining the microphase separation as well as the morphology of hard domains. These observations are believed to provide design guidelines for polymeric materials in engineering practice.