Fixed point of second virial coefficients in the glass transition

TL;DR

This paper demonstrates that the fixed point of the reduced second Virial coefficient at 3/8 plays a crucial role in the glass transition, balancing kinetic energy and chemical potentials in self-similar clusters.

Contribution

It establishes a fixed point for second Virial coefficients in percolation clusters and links it to the thermodynamics of the glass transition through scaling theory.

Findings

Fixed point of B2* at 3/8 proven by scaling theory.

Balance of kinetic energy and potentials at the fixed point.

Glass transition associated with zero chemical potentials in subsystems.

Abstract

Classical thermodynamic theory still holds true in subsystem that is a percolation connected by 8 orders of self-similar 2-body-3-body coupling clusters. The fixed point, $B_2^* \equiv 3/8$, for the clusters of different size, existing in reduced second Virial coefficients has been proved by scaling theory in percolation field. It is shown that, if $B_2^* \equiv 3/8$ is combined with $B_3^* \equiv 5/8$, the potentials of 2-body-3-body coupling clusters, in critical local cluster growth phase transition, balance the kinetic energy in the glass transition. It is also proved that the glass transition corresponds to the regime in which the chemical potentials in all subsystems hold zero.