Stability and anomalous entropic elasticity of subisostatic random-bond networks

Abstract

We study the elasticity of thermalized spring networks under an applied bulk strain. The networks considered are sub-isostatic random-bond networks that, in the athermal limit, are known to have vanishing bulk and linear shear moduli at zero bulk strain. Above a bulk strain threshold, however, these networks become rigid, although surprisingly the shear modulus remains zero until a second, higher, strain threshold. We find that thermal fluctuations stabilize all networks below the rigidity transition, resulting in systems with both finite bulk and shear moduli. Our results show a T 0.66 temperature dependence of the moduli in the region below the bulk strain threshold, resulting in networks with anomalously high rigidity as compared to ordinary entropic elasticity. Furthermore we find a second regime of anomalous temperature scaling for the shear modulus at its zero-temperature rigidity point, where it scales as T 0.5 , behavior that is absent for the bulk modulus since its athermal rigidity transition is discontinuous.

Viscoelastic properties of marginal networks in a solvent

“…Critical exponents in elastic networks such as those studied here are usually universal for a given network topology. That is, while they can change for different network topologies (e.g., square lattice networks [53], triangular networks [9], and random-bond networks [54] all show different critical exponents when stabilized with temperature), exponents that evolve in a continuous manner such as these have, to our knowledge, not been reported (although we note that the critical exponent of a quantum phase transition has been shown to vary with the properties of the sub-Ohmic reservoir to which the system is coupled [55]). This, therefore, represents an additional control parameter for the behavior of marginal networks.…”

Thermalized connectivity networks of jammed packings

“…Numerous consequences can be derived from this peculiar vibrational spectrum, with regards to, for instance, elastic or transport properties [4][5][6]. Some of these features are shared with lattices close to isostaticity [7][8][9][10][11][12], which may be exploited to develop meta-materials with novel mechanical properties [13,14].While most studies have focused on the zerotemperature consequences of the vibrational spectrum, we here study the impact of thermal fluctuations. Specifically, we consider the harmonic connectivity network obtained from a jammed packing of repulsive, frictionless spheres close to isostaticity, and study its mechanical properties as we heat up the system to a low but finite temperature.Elastic properties of ordered and disordered networks of springs at finite temperatures have been studied previously [15][16][17].…”

“…Specifically, we consider the harmonic connectivity network obtained from a jammed packing of repulsive, frictionless spheres close to isostaticity, and study its mechanical properties as we heat up the system to a low but finite temperature.Elastic properties of ordered and disordered networks of springs at finite temperatures have been studied previously [15][16][17]. Most recently, motivated by the attractive properties of highly responsive marginal solids for material science and biophysics, spring networks have been studied near the isostatic threshold [10][11][12]18]. These studies revealed, amongst others, interesting anomalies in the entropic elasticity.…”

“…Numerous consequences can be derived from this peculiar vibrational spectrum, with regards to, for instance, elastic or transport properties [4][5][6]. Some of these features are shared with lattices close to isostaticity [7][8][9][10][11][12], which may be exploited to develop meta-materials with novel mechanical properties [13,14].…”

“…Elastic properties of ordered and disordered networks of springs at finite temperatures have been studied previously [15][16][17]. Most recently, motivated by the attractive properties of highly responsive marginal solids for material science and biophysics, spring networks have been studied near the isostatic threshold [10][11][12]18]. These studies revealed, amongst others, interesting anomalies in the entropic elasticity.…”