Abstract
The first part of this paper deals with the justification of B\assler's phenomenological random-walk model for viscous liquids [Phys. Rev. Lett. 58, 767 (1987)], which considers the random walk of a ``particle'' representing the liquid state on a d-dimensional infinite cubic lattice with site energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model---the energy master equation (EME)---is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures at long times in high dimensions. However, computer simulations show that the EME works well already in two dimensions and at only moderately low temperatures. The EME has no randomness and no fitting parameters. The EME is completely specified from the density of states and the attempt frequency of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent with statistical mechanics. The final part of the paper gives a comprehensive discussion, comparing the EME to related work and listing the EME's qualitatively correct predictions, its new predictions, and some ``wrong'' predictions, most of which go against the common picture of viscous liquids and the glass transition without violating experiments.
Highlights
— — a number of simplifying assumptions
The energy master equation (EME) is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures
The approximate EME description of the random-walk model is expected to be valid at low temperatures at long times in high dimensions
Summary
Energy master equation: A low-temperature approximation to Bassler s random-walk mode(. The first part of this paper deals with the justification of Sassier s phenomenological random-walk model for viscous liquids [Phys. 58, 767 (1987)], which considers the random walk of a "particle representing the liquid state on a d-dimensional infinite cubic lattice with site energies chosen randomly according to a Gaussian. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model the energy master equation (EME) is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures at long times in high dimensions. The final part of the paper gives a comprehensive discussion, comparing the EME to related work and listing the EME's qualitatively correct predictions, its new predictions, and some "wrong" predictions, most of which go against the common picture of viscous liquids and the glass transition without violating experiments
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
