Continuous deformations in random networks

Thorpe, M. F.

doi:10.1016/0022-3093(83)90424-6

Cited by 1,387 publications

(992 citation statements)

References 26 publications

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“…For the homogeneous case, the bulk modulus depended mainly on the mean atomic coordination, with a Spearman's rank correlation coefficient [35] ρ = 0.98 -supporting previous studies also pointing out this trend [12,[16][17][18]. For heterogeneous networks, the dependence on the mean correlation diminished a little, with ρ = 0.9.…”

Section: Resultssupporting

confidence: 76%

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Modeling of amorphous carbon structures with arbitrary structural constraints

Jornada¹,

Gava²,

Martinotto³

et al. 2010

J. Phys.: Condens. Matter

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In this paper we describe a method to generate amorphous structures with arbitrary structural constraints. This method employs the Simulated Annealing algorithm to minimize a simple yet carefully tailored Cost Function (CF). The Cost Function is composed of two parts: a simple harmonic approximation for the energy-related terms and a cost that penalizes configurations that do not have atoms in the desired coordinations. Using this approach, we generated a set of amorphous carbon structures spawning nearly all the possible combinations of sp, sp 2 and sp 3 hybridizations. The bulk moduli of this set of amorphous carbons structures was calculated using Brenner's potential. The bulk modulus strongly depends on the mean coordination, following a power law behavior with an exponent ν = 1.51 ± 0.17. A modified Cost Function that segregates carbon with different hybridizations is also presented, and another set of structures was generated.With this new set of amorphous materials, the correlation between the bulk modulus and the mean coordination weakens. This method proposed can be easily modified to explore the effects on physical properties of the presence hydrogen, dangling bonds, and structural features such as carbon rings.

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Section: Resultssupporting

confidence: 76%

“…We found the phase transition from rigid to floppy states [17] to occur at mean coordination z f = 2.10 ± 0.11, with B 0 = 140 ± 26 GPa and ν = 1.51 ± 0.17. These results, particularly the exponent, are close to those reported by [12,14,18], as compared in Table III.…”

Section: Resultsmentioning

confidence: 81%

Modeling of amorphous carbon structures with arbitrary structural constraints

Jornada¹,

Gava²,

Martinotto³

et al. 2010

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

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“…These therefore correspond to M zero-energy deformation modes in which particles slide past one another. These modes, which are in general global modes, have been called floppy modes [12,23].…”

Section: Isostaticity and Marginally Connected Solidsmentioning

confidence: 99%

The jamming scenario—an introduction and outlook

Liu

Nagel

Saarloos

et al. 2011

Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

119

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Abstract. The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored in in a variety of systems. This chapter contains an introductory review of these recent developments and provides an outlook on their applicability to different physical systems and on future directions. The first part of the paper is devoted to an overview of the findings for model systems of frictionless spheres, focussing on the excess of low-frequency modes as the jamming point is approached. Particular attention is paid to a discussion of the cross-over frequency and length scales that govern this approach. We then discuss the effects of particle asphericity and static friction, the applicability to bubble models for wet foams in which the friction is dynamic, the dynamical arrest in colloids, and the implications for molecular glasses.

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“…For example, Gupta and Mauro [92] derived an analytical expression showing that liquid fragility depends on the change in configurational entropy. This was later applied in topological constraint theory [96][97][98][99][100][101][102], from which the composition dependence of liquid fragility can be predicted with the temperature derivative of configurational entropy as the scaling parameter [39,[103][104][105].…”

Section: Test Of the Shoving Modelmentioning

confidence: 99%

Elastic interpretation of the glass transition in aluminosilicate liquids

et al. 2012

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One of the remaining puzzles of the glass transition is the origin of a glass-forming liquid's "fragility," which quantifies the departure of its relaxation time from Arrhenius activated kinetics. According to the shoving model proposed by Dyre, fragility is controlled by the instantaneous shear modulus of the liquid, since any flow event requires a local volume increase and the related activation energy is equal to the work done in shoving aside the surrounding atoms. Here, we present an in situ high-temperature Brillouin spectroscopy test of the shoving model near the glass transition of eight aluminosilicate glass-forming systems. We find that the measured viscosity data agree qualitatively with the measured temperature dependence of shear moduli, as predicted by the shoving model. However, the model systematically underpredicts the values of fragility for our aluminosilicate liquids. This suggests that the dynamics of the glass transition are governed by additional factors beyond the evolution of the shear modulus, such as configurational entropy. We have also compared the glass transition temperature T g,vis obtained from viscosity (temperature at 10 12 Pa s) with the onset temperatures of the decrease in elastic moduli (T g,elas ) and increase in the thermal expansion coefficient (T g,CTE ) during heating. While we find an approximate one-toone correlation between T g,vis and T g,CTE , it is clear that the elastic moduli probe a different frequency response of the glass structure since T g,elas is systematically lower than T g,vis .2

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Continuous deformations in random networks

Cited by 1,387 publications

References 26 publications

Modeling of amorphous carbon structures with arbitrary structural constraints

Modeling of amorphous carbon structures with arbitrary structural constraints

The jamming scenario—an introduction and outlook

Elastic interpretation of the glass transition in aluminosilicate liquids

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