Do Solids Flow?

Abstract

Are solids intrinsically different from liquids? Must a finite stress be applied in order to induce flow? Or, instead, do all solids only look rigid on some finite timescales and eventually flow if an infinitesimal shear stress is applied? Surprisingly, these simple questions are a matter of debate and definite answers are still lacking. Here we show that solidity is only a time-scale dependent notion: equilibrium states of matter that break spontaneously translation invariance, e.g. crystals, flow if even an infinitesimal stress is applied. However, they do so in a way inherently different from ordinary liquids since their viscosity diverges for vanishing shear stress with an essential singularity. We find an ultra-slow decrease of the shear stress as a function of the shear rate, which explains the apparent yield stress identified in rheological flow curves. Furthermore, we suggest that an alternating shear of frequency ω and amplitude γ should lead to a dynamic phase transition line in the (ω,γ) plane, from a 'flowing' to a 'non-flowing' phase. Finally, we apply our results to crystals, show the corresponding microscopic process leading to flow and discuss possible experimental investigations.We clearly know how to make the difference between a solid and a liquid in everyday life. However, the question of whether solid and liquid are distinct states of matter is far from being conclusively answered in the literature. A difficulty in addressing this issue is that even ordinary liquids may look solid, as one learns when diving into the water from an height of, say, 10 meters without being a pro. Actually, supercooled liquids and soft matter, such as emulsions, foams, and pastes behave like bona-fide solids, if probed on timescales that range from microseconds to hours. This phenomenon, called visco-elasticity, is a property

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

“…Following Ref. [11] we have argued that G(t) = C(t)| τ = C(t)| γ = G F (t) should reveal an intermediate plateau G P and that this plateau is set by the finite shear modulus of the quenched network, G P = G eq (f = 0).…”

“…Since the network topology is by construction permanently fixed, the shear response G(t) must become finite for t → ∞ for all temperatures at variance to systems with plastic rearrangements as considered, e.g., in Ref. [11], or the transient networks mentioned in Sec. II D.…”

“…The static equilibrium shear modulus G eq [1][2][3][4][5][6][7] is an important order parameter [8][9][10] characterizing the transition from the liquid/sol (G eq = 0) to the solid/gel state (G eq > 0) where the particle permutation symmetry of the liquid state is lost for the time window probed [6,7]. Examples of current interest for the determination of G eq include crystalline solids [11], glass-forming liquids and amorphous solids [5,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], colloidal gels [28], permanent polymeric networks [2,[29][30][31], hyperbranched polymer chains with sticky end-groups [32] or networks of telechelic polymers [33]. As emphasized by the thin horizontal line in Fig.…”

Fluctuation-dissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited

“…5. Using an ensemble of 10 4 configurations sampled over a total time interval 10 6 with ζ = 5 we obtain first the dis- 20]. Note that the wavevector q must be commensurate to the square simulation box of linear length L, Eq.…”

“…Examples of current interest for the determination of G eq include crystalline solids [10], glass forming liquids and amorphous solids [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], colloidal gels [27], polymeric networks [1,[28][29][30], hyperbranched polymer chains with sticky end-groups [31] or bridged equilibrium networks of telechelic polymers [32]. * Electronic address: hongxu@univ-lorraine.fr temperature T (β = 1/k B T denoting the inverse temperature) [33].…”