The Effect of Finite Temperature on the Jamming Transition

The Effect of Finite Temperature on the Jamming Transition

Clemens Buß

Doctoral thesis

Date of Examination: 2015-06-19

Date of issue: 2016-05-30

Advisor: Hallatschek, Oskar Prof. Dr.

Referee: Hallatschek, Oskar Prof. Dr.

Referee: Wörgötter, Florentin Prof. Dr.

Persistent Address: http://hdl.handle.net/11858/00-1735-0000-0028-8764-1

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Abstract

English

We study the effect of finite temperatures on spring networks obtained from amorphous, jammed packings of repulsive spheres. By means of a Monte Carlo Metropolis scheme, we analyse this two-dimensional model of an amorphous solid with fixed connectivity. Those spring networks act as a general model system for the thermal behaviour of amorphous solid materials. A particularly interesting feature of the model system is that it contracts with increasing temperature and starts to collapse when crossing a certain threshold temperature. Our observables include thermal expansion, bulk and shear modulus and the localisation length of particles in response to changes in temperature, pressure and distance from the isostatic point. We find scaling relations which strongly support theoretical considerations of the model system based on the analysis of its soft modes and their non-affine contributions. Using these results we are able to construct the phase diagram for the system so that we can understand the parameters which lead to collapse. In order to complement the research on spring networks, we investigate the processes in jammed packings. One would expect that these packings expand with increasing temperature. Counterintuitively, the packings contract similarly to the spring networks in a regime of low temperatures and far away from isostaticity. Based on this evidence we conjecture that spring networks might be seen as a higher level of abstraction with regard to the corresponding sphere packings.

Keywords: Jamming; Amorphous Matter; Soft Matter; Glass; Computational Physics