Rigidity percolation and the spatial heterogeneity of soft modes in disordered materials

Abstract

We show how the spatial character of unconstrained motion in a network of bonds can be directly inferred from the topological arrangement of constraints. Relaxation time scales of these soft modes are determined, and from this information we generate spatial maps of the heterogeneous distribution of relaxation times in the disordered network. We show that the nature of the dynamic heterogeneity and its sensitivity to changes in bond configuration depends dramatically on the proximity of the system to the rigidity percolation point.dynamic heterogeneity ͉ glass transition ͉ inherent structure ͉ local mode ͉ supercooled liquid T he kinetic behavior of supercooled liquids is dominated by those configurations, known as inherent structures (1), which correspond to the local minima of the potential energy. This perspective, articulated by Goldstein (2) in 1969, is now generally accepted (3-6). The inherent structures can be regarded as zero-temperature disordered solids. The continuous transition from fluidity to rigidity that characterizes the glass transition is accomplished by the supercooled liquid sampling these disordered solids at nonzero temperatures for durations that increase as the temperature drops. Eventually, a low enough temperature is reached such that 1 local minimum persists indefinitely. To understand the kinetic and structural features of the transitions between different inherent structures we must understand the types of motion available to disordered solids. In this article we start from the proposal that constraint networks provide a general description of such solids and then develop a method for identifying the spatial distribution of the motions that remain unconstrained in such materials (i.e., the soft modes) and the spectrum of relaxation times associated with these modes.In the absence of explicit structural correlates for dynamics, the descriptive approach of dynamic heterogeneities has proved a powerful way forward in developing microscopic accounts of glassy relaxation and in articulating questions about determining dynamics from structure (7). Recently, it was shown that the spatial distribution of low-frequency quasi-localized normal modes is strongly correlated with the spatial distribution of irreversible reorganization (8). This study and related work (9-13) underline the importance of understanding the relation between local soft modes and structure in disordered solids. Understanding how features of an inherent structure determine the spatial pattern of motions is of central importance in developing a useful microscopic treatment of glass transitions and is the goal of this article.Faced with the daunting variety of particle arrangements that typically comprise a disordered solid, geometrical characterizations of such solids are difficult to both perform and interpret. An alternative treatment of amorphous rigidity is based on networks of constraints. The constraint approach to rigidity focuses on topology, instead of geometry, and the global balance between constraints and deg...

Structural Evolution of Supercritical CO2across the Frenkel Line

“…Jj,5.70.Fh, 05.70.+a Unlike the long-range order of ideal crystalline structures, local order is an intrinsic characteristic of soft matter materials and often serves as the key to the tuning of their properties and their possible applications [1][2][3][4][5][6][7][8]. Liquid materials often exhibit medium and/or short range order, such as nanoscale structural motifs, clustering, or local ordering at the level of the atomic coordination spheres.…”

Length scales of dynamic heterogeneities in a network of fluctuating mechanical constraints

“…The details concerning the constraint network model and the analysis of the spatial distribution of the unconstrained motions have been described elsewhere [12,13]. The technical innovation of this paper is the inclusion of fluctuations in the bonds and the analysis of their consequences.…”

“…Further details of the methods for identifying and characterizing these motions are given in Refs. [12] and [13]. Each unconstrained motion has a characteristic thermal velocity and hence, a relaxation time (τ ), dependent on inertia ( , given by the mass or moment of inertia as appropriate).…”

“…We shall define our basic unit of time τ o to be the relaxation time due to translation of a isolated particle so that the relaxation time associated with any cluster of particles with inertia will be τ ( ) = √ τ o . Relaxation functions for an individual structure are constructed using the fastest relaxation time for each particle τ i chosen from all the unconstrained motions to which the particle belongs [12,13]. The fastest motion is chosen because it is this velocity that limits the relaxation time of the individual particles and provides the best representation of the range of time scales available within the system.…”

Liquids: Condensed, disordered, and sometimes complex

“…This special issue of PNAS features 18 articles (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) to illustrate research in this area (liquid interfaces, structural glass formers and dense packing, polymer networks, chemical dynamics) exhibiting current tools of experiment and theory. The field is too big to capture it all with such a small collection, but the examples give a feeling for its scope and possibilities.…”