Abstract
To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we have extended the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, τα(T, V). We also employ the thermodynamic scaling idea reflected in the density scaling power law, τα = f(T−1V−γ), recently acknowledged as a valid unifying concept in the glass transition physics, to differentiate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time τα and the configurational entropy SC, giving evidence that also SC(T, V) = g(T−1V−γ) with the exponent γ that enables to scale τα(T, V). This important findings have meaningful implications for the connection between thermodynamics and molecular dynamics near the glass transition, because it implies that τα can be scaled with SC.
Highlights
SC(T) is defined as the configurational entropy, and estimated as the difference between the entropy of the melt and the vibrational contribution to the entropy[2], SC(T) = Smelt − Svib
Assuming that a short range effective intermolecular potential can be approximated by a combination of dominating repulsive inverse power law and small attractive background, the validity of the thermodynamic scaling was demonstrated on the basis of molecular dynamics (MD) simulations[7,16,29,30,31,32,33,34]
Can be plotted onto a single master curve as a function of the configurational entropy. This meaningful result clearly shows that the structural relaxation time can be a single variable function of the configurational entropy, τα = h(SC), the more complex formula (Eq (16)) is required to meet the power law density scaling criterion in terms of the AG model originally based on Eq (1)
Summary
A lot of interest has been directed toward the analysis of molecular dynamics of supercooled liquids in terms of thermodynamic scaling[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] This alternative approach is very appealing due to the possibility of universal description of relaxation phenomena for all supercooled liquids based on the generalized Lennard-Jones potential[18]. At the first stage of development of the thermodynamic scaling approach, it was postulated[19] that the value of scaling exponent should be equal to 4 in accordance with the initial finding for OTP19,20 It has been subsequently demonstrated by a number of research groups that the value of γ can significantly differ from 4 for other glass formers. The generalization of the AG(T) model to T-V variables might be essential for testing its validity in general
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