TimeTemperature

Time-temperature, sometimes written time–temperature, is a concept describing how temperature and time jointly influence the rate and extent of processes in physical, chemical, and biological systems. Temperature changes alter kinetic barriers and mobilities, so higher temperatures typically accelerate reactions, diffusion, phase transitions, and aging. This coupling is central to predicting material performance, product shelf life, and failure times.

In materials science, a principal framework is the time-temperature superposition principle (TTSP). For many polymers and some other viscoelastic materials, the entire temperature-dependent relaxation spectrum at a given temperature can be shifted along the logarithm of time to superpose onto a single master curve obtained at a reference temperature. The shift factor a_T increases with temperature, so that higher temperatures correspond to shorter effective times. TTSP assumes thermorheological simplicity; when multiple relaxation mechanisms couple differently to temperature, the principle may fail.

Shift factors are commonly described by the Williams-Landel-Ferry equation near the glass transition: log10(a_T) = -C1 (T - T_ref) / (C2 + (T - T_ref)). At higher temperatures or for simple liquids, an Arrhenius form log10(a_T) = (Ea/2.303R)(1/T_ref - 1/T) is used.

Applications of timetemperature include predicting long-term polymer creep and relaxation, documenting shelf life and microbial or chemical reactions in foods, and assessing diffusion, aging, and reliability in electronic materials. Limitations include departures from thermorheological simplicity and notable changes in microstructure with temperature.