Europhys. Lett.
Volume 61, Number 2, January 2003
Page(s) 207 - 213
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 January 2003
DOI: 10.1209/epl/i2003-00214-6
Europhys. Lett., 61 (2) , pp. 207-213 (2003)

Microscopic theory for the glass transition in a system without static correlations

R. Schilling1 and G. Szamel1, 2

1  Institut für Physik, Johannes Gutenberg-Universität Mainz D-55099 Mainz, Staudinger Weg 7, Germany
2  Department of Chemistry, Colorado State University Ft. Collins, CO 80523, USA

(Received 25 July 2002; accepted in final form 25 October 2002)

We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a. We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l), l=L/a. We get $D(l) \propto [1-\upsilon(l)]$, where $\upsilon(l)$ is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at $l_\ab{c}$, if $\upsilon(l_\ab{c})=1$. We present a variational and a numerically exact evaluation of $\upsilon(l)$. Close to $l_\ab{c}$ the diffusion constant decreases as $D(l) \propto (l_\ab{c}-l)^\gamma$, with $\gamma=1$. Our approach predicts a glass transition in the absence of any static correlations, in contrast to the present form of mode-coupling theory.

61.20.Lc - Time-dependent properties; relaxation.
61.43.Fs - Glasses.
64.70.Pf - Glass transitions.

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