Thermal conductivity calculation of nano-suspensions using Green-Kubo relations with reduced artificial correlations

The presence of artificial correlations associated with Green-Kubo (GK) thermal conductivity calculations is investigated. The thermal conductivity of nano-suspensions is calculated by equilibrium molecular dynamics (EMD) simulations using GK relations. Calculations are first performed for a single alumina (Al₂O₃) nanoparticle dispersed in a water medium. For a particle size of 1 nm and volume fraction of 9%, results show enhancements as high as 235%, which is much higher than the Maxwell model predictions. When calculations are done with multiple suspended particles, no such anomalous enhancement is observed. This is because the vibrations in alumina crystal can act as low frequency perturbations, which can travel long distances through the surrounding water medium, characterized by higher vibration frequencies. As a result of the periodic boundaries, they re-enter the system resulting in a circular resonance of thermal fluctuations between the alumina particle and its own image, eventually leading to artificial correlations in the heat current autocorrelation function (HCACF), which when integrated yields abnormally high thermal conductivities. Adding more particles presents 'obstacles' with which the fluctuations interact and get dissipated, before they get fed back to the periodic image. A systematic study of the temporal evolution of HCACF indicates that the magnitude and oscillations of artificial correlations decrease substantially with increase in the number of suspended nanoparticles.