Topological Control on the Structural Relaxation of Atomic Networks under Stress

Mathieu Bauchy (1) , Mengyi Wang , Yingtian Yu , Bu Wang , N. m. Anoop Krishnan , Enrico Masoero (2) , Franz-Joseph Ulm (3) , Roland J. M. Pellenq (4)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 Civil Engineering and Geosciences, Newcastle University
3 CEE - Department of Civil and Environmental Engineering [Cambridge]
4 CINaM - Centre Interdisciplinaire de Nanoscience de Marseille

Upon loading, atomic networks can feature delayed irreversible relaxation. However, the effect of composition and structure on relaxation remains poorly understood. Herein, relying on accelerated molecular dynamics simulations and topological constraint theory, we investigate the relationship between atomic topology and stress-induced structural relaxation, by taking the example of creep deformations in calcium silicate hydrates (C─S─H), the binding phase of concrete. Under constant shear stress, C─S─H is found to feature delayed logarithmic shear deformations. We demonstrate that the propensity for relaxation is minimum for isostatic atomic networks, which are characterized by the simultaneous absence of floppy internal modes of relaxation and eigenstress. This suggests that topological nanoengineering could lead to the discovery of nonaging materials. Out-of-equilibrium systems—e.g., quenched glasses or jammed granular materials—tend to spontaneously relax over time towards more stable equilibrium states. In terms of energy landscape, such relaxation can be described as a succession of " jumps " between energy basins (local energy minima) through pathways (modes of relaxation) [1], wherein the temperature and height of the energy barriers define the relaxation kinetics [2]. On the other hand, starting from a stable equilibrium state, external stress can deform the energy landscape, place the system in an out-of-equilibrium state, and, thereby, induce relaxation [3,4]. Relaxation can result in delayed variations of volume or shape. This behavior is exemplified by creep, i.e., the delayed time-dependent strain shown by a material under constant load. Although creep can affect, among others, metals, ceramics, or minerals [5], it is especially pronounced in concrete, even at ambient temperature, and can lead to the failure of structures [6]. In addition, glasses, archetypical out-of-equilibrium systems, can feature long-term volume relaxation after being quenched, a behavior known as the " thermometer effect " [7,8]. Although the role of the composition and structure of atomic networks in controlling the propensity for relaxation remains poorly understood, specific glass compositions have been reported to feature little, if any, relaxation over time after quenching. This has been explained within the framework of topological constraint theory (TCT) [9–12]. Following Maxwell's study on the stability of mechanical trusses [13], TCT describes the rigidity of atomic networks, which can feature three distinct states: (1) flexible, having internal degrees of freedom called floppy modes [14] that allow for local deformations, (2) stressed rigid, being locked by their high connectivity, and (3) isostatic, the optimal intermediate state [see Fig. 3(a)]. The isostatic state is achieved when the number of constraints per atom, n c , comprising radial bond stretching and angular bond bending , equals 3, the number of degrees of freedom per atom. Compositions characterized by an isostatic network have been found to exist inside a window [15], located between the flexible (n c < 3) and the stressed-rigid (n c > 3) compositions , known as the Boolchand intermediate phase, and show some remarkable properties such as a stress-free character [16,17], space-filling tendency [18], anomalous dynamical and structural signatures [19,20], and maximum resistance to fracture [21]. Interestingly, isostatic networks have been shown to feature limited relaxation phenomena [22]. Herein, relying on accelerated molecular dynamics (MD) simulations and TCT, we investigate the creep deformations under constant shear stress of calcium silicate hydrates (CaO─SiO 2 ─H 2 O, or C─S─H), the phase that binds and controls the properties of concrete [23]. We show that, in analogy with glass relaxation, isostatic C─S─H compositions feature a low propensity for relaxation. In contrast, flexible and stressed-rigid networks show significant creep deformations, on account of the presence of low

Domaines: Physique [physics]

Mathieu Bauchy, Mengyi Wang, Yingtian Yu, Bu Wang, N. m. Anoop Krishnan, et al.. Topological Control on the Structural Relaxation of Atomic Networks under Stress. Physical Review Letters, 2017, 119 (3), ⟨10.1103/PhysRevLett.119.035502⟩. ⟨hal-01782950⟩