Abstract
Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials such as polymers and inorganic glasses,
both in production and during subsequent use. The Narayanaswamy theory from 1971 describes
physical aging—an inherently nonlinear phenomenon—in terms of a linear convolution integral over
the so-called material time ξ. The resulting “Tool–Narayanaswamy (TN) formalism” is generally
recognized to provide an excellent description of physical aging for small, but still highly nonlinear, temperature variations. The simplest version of the TN formalism is single-parameter aging
according to which the clock rate dξ/dt is an exponential function of the property monitored. For
temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation
for property monitored, involving a system-specific function. The present paper shows analytically
that the solution to this equation to first order in the temperature variation has a universal expression
in terms of the zeroth-order solution, R0(t). Numerical data for a binary Lennard–Jones glass former
probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging
correctly from R0(t) (which by the fluctuation–dissipation theorem is the normalized equilibrium
potential-energy time-autocorrelation function).
both in production and during subsequent use. The Narayanaswamy theory from 1971 describes
physical aging—an inherently nonlinear phenomenon—in terms of a linear convolution integral over
the so-called material time ξ. The resulting “Tool–Narayanaswamy (TN) formalism” is generally
recognized to provide an excellent description of physical aging for small, but still highly nonlinear, temperature variations. The simplest version of the TN formalism is single-parameter aging
according to which the clock rate dξ/dt is an exponential function of the property monitored. For
temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation
for property monitored, involving a system-specific function. The present paper shows analytically
that the solution to this equation to first order in the temperature variation has a universal expression
in terms of the zeroth-order solution, R0(t). Numerical data for a binary Lennard–Jones glass former
probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging
correctly from R0(t) (which by the fluctuation–dissipation theorem is the normalized equilibrium
potential-energy time-autocorrelation function).
Originalsprog | Engelsk |
---|---|
Artikelnummer | 2 |
Tidsskrift | Journal of Thermo |
Vol/bind | 2 |
Udgave nummer | 3 |
Sider (fra-til) | 160-170 |
Antal sider | 11 |
ISSN | 2673-7264 |
DOI | |
Status | Udgivet - 6 jul. 2022 |